Collected Experimental Papers of P. W. Bridgman, Volume VI: Papers 122-168

Table of contents :
Contents
122. Rough compressibilities of fourteen substances to 45,000 kg/cm2
123. Polymorphic transitions up to 50,000 kg/cm2 of several organic substances
124. The nature of metals as shown by their properties under pressure
125. Reflections on rupture
126. Shearing experiments on some selected minerals and mineral combinations (with Esper S. Larsen)
127. The high pressure behavior of miscellaneous minerals
128. Considerations on rupture under triaxial stress
129. Absolute measurements in the pressure range up to 30,000 kg/cm2
130. Compressions to 50,000 kg/cm2
131. New high pressures reached with multiple apparatus
132. The measurement of hydrostatic pressure to 30,000 kg/cm2
133. The linear compression of iron to 30,000 kg/cm2
134. The compression of 46 substances to 50,000 kg/cm2
135. Explorations toward the limit of utilizable pressures
136. Compressions and polymorphic transitions of seventeen elements to 100,000 kg/cm2
137. Freezings and compressions to 50,000 kg/cm2
138. Freezing parameters and compressions of twenty-one substances to 50,000 kg/cm2
139. Pressure-volume relations for seventeen elements to 100,000 kg/cm2
140. Recent work in the field of high pressures
141. On torsion combined with compression
142. Some irreversible effects of high mechanical stress
143. The stress distribution at the neck of a tension specimen
144. Flow and fracture
145. Discussion of “Flow and fracture”
146. Discussion of Boyd and Robinson, “The friction properties of various lubricants at high pressures”
147. The compression of twenty-one halogen compounds and eleven other simple substances to 100,000 kg/cm2
148. The compression of sixty-one solid substances to 25,000 kg/cm2, determined by a new rapid method
149. Polymorphic transitions and geological phenomena
150. Effects of high hydrostatic pressure on the plastic properties of metals
151. Recent work in the field of high pressures
152. The tensile properties of several special steels and certain other materials under pressure
153. Studies of plastic flow of steel, especially in two-dimensional compression
154. The effect of hydrostatic pressure on plastic flow under shearing stress
155. On higher order transitions
156. An experimental contribution to the problem of diamond synthesis
157. The rheological properties of matter under high pressure
158. The effect of hydrostatic pressure on the fracture of brittle substances
159. The effect of high mechanical stress on certain solid explosives
160. The compression of 39 substances to 100,000 kg/cm2
161. Rough compressions of 177 substances to 40,000 kg/cm2
162. Large plastic flow and the collapse of hollow cylinders
163. Fracture and hydrostatic pressure
164. General survey of certain results in the field of high pressure physics
165. The linear compression of various single crystals to 30,000 kg/cm2
166. Viscosities to 30,000 kg/cm2
167. Further rough compressions to 40,000 kg/cm2, especially certain liquids
168. Linear compressions to 30,000 kg/cm2, includng relatively incompressible substances

Citation preview

Collected Experimental Papers of P. W. Bridgman

Volume VI

P. W. BRIDGMAN

Collected Experimental Papers

Volume VI Papers 122-168

Harvard University Press Cambridge, Massachusetts 1964

® Copyright 1964 by the President and Fellows of Harvard College AU rights reserved

Distributed in Great Britain by Oxford University Press, London

Library of Congress Catalog Card Number 6J+-16060 Printed in the United States of America

CONTENTS Volume VI 122-3253.

"Rough compressibilities of fourteen substances to 45,000 kg/cm 2 ," Proc. Am. Acad. Arts Sei. 72, 207-225 (1938).

123-3273.

"Polymorphic transitions up to 50,000 kg/cm 2 of several organic substances," Proc. Am. Acad. Arts Sei. 72, 227-268 (1938).

124-3315.

The nature of metals as shown by their properties under pressure, Am. Inst. Mining Met. Engrs. Technical Publication No. 922 (1938).

125-3337.

"Reflections on rupture," J. Appl. Phys. 9, 517-528 (1938).

126-3349.

"Shearing experiments on some selected minerals and mineral combinations" (with Esper S. Larsen), Am. J. Sei. 36, 81-94 (1938).

127-3363.

"The high pressure behavior of miscellaneous minerals," Am. J. Sei. 287, 7-18 (1939).

128-3375.

"Considerations on rupture under triaxial stress," Mech. Eng., February 1939, pp. 107-111 [1-6].

129-3381.

"Absolute measurements in the pressure range up to 30,000 kg/cm 2 ," Phys. Rev. 57, 235-237 (1940).

130-3385.

"Compressions to 50,000 kg/cm 2 ," Phys. Rev. 57, 237-239 (1940).

131-3388.

"New high pressures reached with multiple apparatus," Phys. Rev. 57, 342-343 (1940).

132-3391.

"The measurement of hydrostatic pressure to 30,000 kg/cm 2 ," Proc. Am. Acad. Arts Sei. 74, 1-10 (1940).

133-3401.

"The linear compression of iron to 30,000 kg/cm 2 ," Proc. Am. Acad. Arts Sei. 74, 11-20 (1940).

134-3411.

"The compression of 46 substances to 50,000 kg/cm 2 ," Proc. Am. Acad. Arts Sei. 74, 21-51 (1940)

vi

CONTENTS

135-3443.

"Explorations toward the limit of utilizable pressures," J. Appl. Phys. 12, 461-469 (1941).

136-3453.

"Compressions and polymorphic transitions of seventeen elements to 100,000 kg/cm2," Phys. Rev. 60, 351-354 (1941).

137-3458.

"Freezings and compressions to 50,000 kg/cm2," J. Chem. Phys. 9, 794-797 (1941).

138-3463.

"Freezing parameters and compressions of twenty-one substances to 50,000 kg/cm2," Proc. Am. Acad. Arts Sei. 74, 399-424 (1942).

139-3489.

"Pressure-volume relations for seventeen elements to 100,000 kg/cm2," Proc. Am. Acad. Arts Sei. 74, 425-440 (1942).

140-3505.

"Recent work in the field of high pressures," Am. Scientist 31, 1-35 (1943). "On torsion combined with compression," J. Appl. Phys. 14, 273-283 (1943). "Some irreversible effects of high mechanical stress," in Colloid Chemistry, ed. Jerome Alexander (New York: Van Nostrand, 1944), V, 327-337.

141-3541. 142-3553.

143-3565.

"The stress distribution at the neck of a tension specimen," Trans. Am. Soc. Metals 32, 553-572 (1944).

144-3588.

"Flow and fracture," Metals Technol. 11, 32-39 (December 1944).

145-3597.

Discussion of "Flow and fracture," Metals Technol., supplement to Technical Publication No. 1782, 2 pp. (April 1945). Discussion of Boyd and Robinson, "The friction properties of various lubricants at high pressures," Trans. ASM Ε 67, 56 (1945). "The compression of twenty-one halogen compounds and eleven other simple substances to 100,000 kg/cm2," Proc. Am. Acad. Arts Sä. 76, 1-7 (1945).

146-3599.

147-3601.

148-3609.

"The compression of sixty-one solid substances to 25,000 kg/cm2, determined by a new rapid method," Proc. Am. Acad. Arts Sei. 76, 9-24 (1945)'.

149-3626.

"Polymorphic transitions and geological phenomena," Am. J. Sei. 243a (Daly Volume), 90-97 (1945).

150-3635.

"Effects of high hydrostatic pressure on the plastic properties of metals," Rev. Mod. Phys. 17, 3-14 (1945).

151-3647.

"Recent work in the field of high pressures," Rev. Mod. Phys. 18, 1-93, 291 (1946).

CONTENTS

vü

152-3741.

"The tensile properties of several special steels and certain other materials under pressure," J. Appl. Phys. 17, 201212 (1946).

153-3753.

"Studies of plastic flow of steel, especially in two-dimensional compression," J. Appl. Phys. 17, 225-243 (1946).

154-3772.

"The effect of hydrostatic pressure on plastic flow under shearing stress," J. Appl. Phys. 17, 692-698 (1946).

155-3779.

"On higher order transitions," Phys. Rev. 70, 425-428 (1946).

156-3784.

"An experimental contribution to the problem of diamond synthesis," J. Chem. Phys. 16, 92-98 (1947).

157-3791.

"The rheological properties of matter under high pressure," J. Colloid Sei. 2, 7-16 (1947).

158-3802.

"The effect of hydrostatic pressure on the fracture of brittle substances," J. Appl. Phys. 18, 246-258 (1947).

159-3815.

"The effect of high mechanical stress on certain solid explosives," J. Chem. Phys. 15, 311-313 (1947).

160-3819.

"The compression of 39 substances to 100,000 kg/cm 2 ," Proc. Am. Acad. Arts Sei. 76, 55-70 (1948).

161-3835.

"Rough compressions of 177 substances to 40,000 kg/cm 2 ," Proc. Am. Acad. Arts Sei. 76, 71-87 (1948).

162-3852.

"Large plastic flow and the collapse of hollow cylinders," J. Appl. Phys. 19, 302-305 (1948)

163-3856.

"Fracture and hydrostatic pressure," in Fracturing of metals (Cleveland: American Society for Metals, 1948), pp. 246261.

164-3873.

"General survey of certain results in the field of high pressure physics," in Les Prix Nobel (Stockholm: P. A. Norstedt, 1948), pp. 149-166. Reprinted in J. Wash. Acad. Sei. 38, (May 15, 1948).

165-3891.

"The linear compression of various single crystals to 30,000 kg/cm 2 ," Proc. Am. Acad. Arts Sei. 76, 89-99 (1948).

166-3903.

"Viscosities to 30,000 kg/cm 2 ," Proc. Am. Acad. Arts Sei. 77, 117-128 (1949).

167-3915.

"Further rough compressions to 40,000 kg/cm 2 , especially certain liquids," Proc. Am. Acad. Arts Sei. 77, 129-146 (1949).

168-3933.

"Linear compressions to 30,000 kg/cm 2 , includng relatively incompressible substances," Proc. Am. Acad. Arts Sei. 77, 189-234 (1949).

ROUGH COMPRESSIBILITIES OF F O U R T E E N SUBSTANCES TO 45,000 Kg/Cm 2 BY P . W . BRIDGMAN

CONTENTS Presented October 13,1937

Received October 20,1Θ37

Introduction Technique and Corrections Detailed Results Lithium Sodium Potassium Rubidium Caesium Calcium Strontium Barium Indium Tin Lead Sulfur Carbon Dioxide Sodium Chloride Discussion

207 208 214 214 214 215 215 216 216 217 220 220 220 221 221 222 223 223 INTRODUCTION

In two preceding papers 1 the parameters of a number of transitions have been determined up to 45,000 kg/cm 2 . The method consists in determining at various temperatures the discontinuity in volume by measuring the displacement of the piston by which pressure is produced. If instead of determining the discontinuity in the motion of the piston, one plots the motion of the piston at constant temperature as a function of pressure, one obviously has a rough measure of the compressibility. Various corrections, however, reduce the accuracy of the method and restrict its applicability to the more compressible substances. I t probably will be possible to improve the method, and in fact I now have under construction an apparatus which should permit better values. But in the meantime, because of their intrinsic interest, I give in the following pages rough results for some of the more compressible substances, for which the results should be most accurate.

208

BRIDGMAN TECHNIQUE AND CORRECTIONS

If the contents of a cylindrical container are subjected to pressure by the thrust of a piston, the total displacement of the piston is evidently determined by the compression of the contents, the distortion of the container, and the distortion of the piston and packings. If the contents possess much mechanical stiffness, then friction on the walls produces a stress system in the contents which is not a hydrostatic pressure, and the interpretation of the piston displacement is not clear. The first requirement, therefore, is to make the pressure approximately hydrostatic. This was accomplished by enclosing the material under measurement in a lead sheath. The general arrangements are indicated in Figure 1, drawn to scale. They are practically the same as for the transition measurements. In the previous paper a discussion was given of the distortion of the container under pressure adequate for the purposes of that paper, but here the requirements are more exacting, and a more elaborate examination is necessary. Suppose, for example, that an incompressible substance is compressed in a cylinder to such a pressure that the increase of cross section of the container is 10 per cent. If now a transition occurs, and the change of volume is measured by measuring the displacement of the piston, a 10 per cent error will be made in the A F of the transition if no correction is made for the change of cross section. But on the other hand, before the transition occurs a 10 per cent compression would have been ascribed to the substance if no correction had been made for the cross section, whereas the actual compression was zero. That is, an infinite error in the compression against a 10 per cent error in the volume change of the transition is here the result of improperly correcting for the distortion of the container. An exact evaluation of the corrections is out of the question. Not only are the boundary conditions incapable of exact formulation, but the stresses are beyond the range in which linearity holds between stress and strain, and there is marked hysteresis. The latter effect should be approximately eliminated by using the mean of measurements with increasing and decreasing pressure. The elastic deformation was dealt with by computing it for idealized conditions, and then manipulating the results to secure agreement with certain check measurements. The idealized elastic problem is that of the infinitely long cylinder under external and internal hydrostatic pressure, the inner and outer radii being taken as those at mean positions along the axis of the cone. The external pressure can be evaluated, as explained in the previous paper, from measurements of the longitudinal

122 — 3254

ROUGH COMPRESSIBILITIES OF SUBSTANCES

a lead sheath for compressibility measurements.

209

210

BR1DGMAN

displacement of the cone into the sleeve, which gives the means for evaluating the friction. The idealized infinite cylinder fails to correspond to the actual case not only because of the conical figure of the actual container, but also because of the closures at the ends, one end carrying the freely moving plunger and the other end being closed by a screw plug which transmits a longitudinal tension to the walls of the container. On the outside of the container there is a longitudinal shearing force which gets transformed into a mean longitudinal tension inside. The distortion of an infinite cylinder under longitudinal tension can be calculated, and crude allowance made for these effects. Then there is the very important effect of finite length; the length of the cavity was on the average 2.5 times the diameter. This means that very effective support is afforded by the ends, which are not exposed to the internal pressure, although exposed to external pressure. As a result the cavity must become somewhat barrel shaped, and the cross section at the piston is different from that at the center of the cavity. In an infinite cylinder a simple application of Betti's theorem shows that the increase of cross section at the piston is only one half as great as that further down in the cavity. This means that the effective correction of the cross section that is to be used for computing the pressure from the thrust on the piston is of the order of only one half the correction on the cross section from which the total change of volume is to be computed. There are two independent measurements that can be made to check any computations. The longitudinal displacement of the container into the collar can be measured as a function of the thrust on the piston, and the internal change of volume can be measured when there is no internal pressure but the external pressure is made to be approximately the same as in the actual experiment by exerting on the whole container the same total thrust as that which in the actual experiment is exerted on the piston. This latter change of internal volume was measured by sealing a graduated capillary into the cylinder, which was filled with mercury, and observing the motion of the mercury column in the capillary as a function of thrust. The longitudinal displacement into the collar agreed exactly with that computed. The change of internal volume was 0.8 of that calculated for the infinite cylinder; the difference is to be ascribed to the effects due to the unknown distribution of longitudinal stress, departure from cylindrical figure, etc. The calculated corrections for the effect of internal and external pressure together were therefore reduced by this factor of 0.8. An additional reduction factor of 0.9 was guessed

ROUGH COMPRESSIBILITIES OF SUBSTANCES

211

at to allow for the difference of terminal conditions in the two cases, making a total reduction factor on the correction calculated for the infinite cylinder of 0.7. The final correction assumed for the maximum pressure (50,000 kg/cm2) was 2.7 per cent on the effective area from which the compression was calculated, and 1.5 per cent on the area from which pressure was calculated. These corrections were taken to be linear with pressure. As actually used, this was a differential method, similar to that which I had used to measure the compressibility of liquids,2 and which has been extensively used at the Geophysical Laboratory in Washington in measuring the compressibility of solids.3 The cylinder was filled with the substance under investigation in its lead sheath, and the displacement of the piston determined as a function of pressure. This was done on a careful time schedule. Pressure was first increased to the maximum in steps of 10,000 at intervals of 1 minute, released to 0 and again increased to the maximum on the same time schedule. This constituted the preliminary seasoning. Pressure was now released to 0 and increased back to the maximum in steps of 2,000 on a 1 minute schedule. This run down and up in 25 steps each way and in 50 minutes altogether constituted the essential part of the measurements. Pressure was finally reduced to 0 in 10,000 steps on the 1 minute schedule and the apparatus taken apart. It was now set up again with a core of soft steel replacing the previous substance, in a lead sheath of approximately the same size as at first. The same sequence of measurements was now made on the lead and steel. Next the differences of corresponding displacements of the two runs were computed, plotted on large size paper, and a single curve drawn as the mean of ascending and descending branches. A detailed discussion of the effects of friction, which I will not take space to give here, showed that it is better to take the differences of ascending and descending branches of the two curves, and then draw the mean curve of the loop thus obtained, rather than to draw the mean curves for the two loops and then take the difference of the mean curves. The upper end of the loops require somewhat special treatment. Figure 2 shows how the top of the loop runs horizontally on release of pressure during an interval corresponding to the friction on the piston. In taking the mean loop, this frictional effect was eliminated as best it might by extrapolating the curve AC beyond C graphically, and using the mean of this extrapolated curve and AB in the pressure interval CB. The maximum pressure listed in the following is 45,000 kg/cm2,

212

BR1DGMAN

corresponding roughly to the mean between the pressures a t C and a t B . T h e m a x i m u m pressure on the piston was more than 50,000, b u t friction reduced this in the material under measurement. I t would h a v e been easy to extrapolate from the results to an effective maxim u m pressure of 50,000, b u t there is no reason why the reader should not m a k e this extrapolation to suit himself.

C '

Β

/

Q_ - I CL CO

PRESSURE F I G U R E 2.

Idealized plot of piston displacement against pressure.

T h e final result was a smooth curve corresponding to the difference of compressibility between the substance under investigation and iron. Since the compressibility of iron is small compared with t h a t of the other substance, I assumed for the compressibility of iron values extrapolated from m y previous measurements to 12,000. I had formerly found b y direct measurement up to 12,000 a t 30° for the compressibility of iron: — AV/V0

= 5.87 Χ 10 - 7 p—2.37 X 1 0 ~ i 2 p 2 ,

ρ in kg/cm 2 . Since in the following all quantities of material were determined b y weighing, what is needed is the compression of iron in cm 3 per gm. T h e following were assumed to be the compressions in cm 3 of 1 gm of iron a t pressures of 10,000, 20,000, 30,000, 40,000, and

ROUGH COMPRESSIBILITIES OF SUBSTANCES

213

50,000 kg/cm2 respectively: 0.00072, 0.00137, 0.00196, 0.00250, and 0.00298. Since it was not usually convenient to use exactly the same amounts of lead in the actual and the blank runs, the compression of the differential amount of lead also entered as a correction. The compression of lead to 45,000 was determined by direct measurement by filling the container entirely with lead. The following are the values found for the compression in cm3 per gm at 10,000, 20,000, 30,000, 40,000, and 50,000 respectively: 0.0020, 0.0036, 0.0051, 0.00635, and 0.0075. The previous measurements up to 12,000 could be reproduced by a second degree formula. The previous measurements were 0.0019 at 10,000 and 0.0035 extrapolated to 20,000. The agreement is not bad. Beyond 20,000 the second degree formula representing the former results goes off badly, at 50,000 giving a change of volume of 0.0060 against 0.0075 experimental. The change of volume thus actually proceeds at a more rapid rate than the second degree formula would indicate. This is as is to be expected, because the second degree formula demands a minimum compression and a reversal at very high pressures. The useful life of one of the containers was rarely as much as ten applications of the maximum pressure. In the transition measurements 20 applications were not unusual. The conditions here were more exacting, however, and much closer track was kept of the progress of permanent distortion. A special arrangement was made for measuring the internal diameter of the container at different points along the axis to an accuracy of 0.0001 inch, and after every completed run the container was remeasured for permanent distortion, and discarded, or else reamed to a slightly larger size, when the permanent stretch got as high as 0.002 inch, which experience showed to be about the maximum tolerable. It would have been very convenient if it had been possible to make the blank runs on iron and lead on a single container once and for all, but this did not prove to be possible, since the containers were not sufficiently reproducible. This made it necessary to make a blank run with each new container. On the average a container yielded results for the compression of only one substance. If it had been possible to get reproducible containers, results could have been obtained twice as fast and with twice as great an economy in containers. A great deal of preliminary work was put into getting the best details of the various manipulations, such as the time schedules etc., to give most reproducible results. In the preliminary work a good

122 — 3259

214

BRIDGMAN

many measurements were made on the same substance, but after the method was established, one or two set-ups usually sufficed. A check on the accuracy of the measurements is afforded by comparing with the results previously obtained up to 12,000 and in some cases to 20,000. The low pressure end of the range was in general much less accurate than the high pressure end; in many cases the results were adjusted so as to agree with previous results over the first 5,000 kg/cm2. The detailed results now follow. DETAILED RESULTS

Lithium. One set-up was made for this substance, with the corresponding blank run. In Table I is given the compression at room TABLE

I

C O M P R E S S I O N OF T H E A L K A L I M E T A L S

Compressions Potassium Pressure Lithium Sodium Rubidium Caesium kg/cma cm8/0.534gm cm»/0.971gm cm3/0.870gm cm'/1.532gm cm3/1.88gm 0.182 5,000 .043 .071 .164 .116 .074 .183 .233 .271 10,000 .117 .230 15,000 .101 .148 .279 .326 .372 20,000 .182 .268 .316 .125 i.398 23,000 \.404* 25,000 .209 .301 .345 .145 .420 .165 .233 .329 .371 .438 30,000 .184 .464 35,000 .254 .353 .393 .202 .273 .413 .487 40,000 .375 .218 .431 45,000 .290 .396 .507 * Phase change temperature of that amount of material which occupies 1 Cm3 under normal conditions. Some check on the results can be obtained by comparison with previous measurements up to 20,000.4 Previous measurements of the compression at 10,000 and 20,000 were 0.073 and 0.123 against 0.074 and 0.130 found now. Sodium. Three different set-ups were made with three corresponding blank runs. One of the blanks was made with lead and gold instead of lead and iron, the idea being that gold might be so much softer than iron as to result in the pressure being appreciably more hydrostatic throughout the container, but no superiority of this run was found over that with iron, and gold was not tried in other blanks.

122—3260

ROUGH COMPRESSIBILITIES OF SUBSTANCES

215

There was no consistent difference between the results of the three runs; the one which gave the lowest compression at 20,000 gave the highest at 45,000. The results are given in Table I. The low pressure results were adjusted to agree with the former ones 6 at 10,000. At 20,000 the change of volume now found is 0.183 against 0.189 found before. The direction of deviation is the same as for lithium. The former results are doubtless to be preferred. I do not think, however, that this means necessarily an error in the same direction at the highest pressures of the range, but I think it probable that the effect is connected with hysteresis, and that the maximum error might be looked for a t the center of the range. This would mean that the relation found in all the work described in this paper between pressure and change of volume is probably a little too nearly linear, the actual compressibility dropping more rapidly at high pressures than found here. Potassium. One set-up was made, but runs were made at three temperatures: room temperature, 75°, and 125°, in an attempt to find the temperature coefficient of compressibility (or the pressure coefficient of thermal expansion). The method proved not to be sensitive enough, however, and after some experimenting I abandoned the attempt to get this sort of information out of the measurements. The blank run was made with tungsten and lead instead of iron and lead as usual. The compressibility of tungsten is less than that of iron, and for this reason it is ideally a better material for the differential measurements. But the second degree term in my previous measurements for tungsten 6 is perhaps not quite as certain as for iron, so that extrapolation from 12,000 to 50,000 is more hazardous. The compressibility of potassium is so high, however, that there should be no appreciable error here. The results are shown in Table I. The value a t 5,000 was made to agree with the former measurements. At 10,000 and 20,000 the present values of compression are 0.183 and 0.268 respectively against 0.189 and 0.277 found formerly. 7 Rubidium. Runs were made with two different set-ups; with the second set-up six different runs were made at temperatures between 0 ° and 75°. The important point at issue was whether rubidium has a transition like that which had just been found for caesium. At first, slight irregularities were found which were favorable to the interpretation of a small transition, but nothing was found that would definitely repeat, and I do not believe that there is a transition up to 45,000 with a volume change as large as 0.00015 cm 3 /gm.

216

BRIDGMAN

The two different set-ups gave fairly concordant results for the compression, the greatest discrepancy being a t 45,000, where the results were 0.433 and 0.428. The mean results of the two set-ups are given in Table I. The compression at 5,000 was adjusted to agree with the former value 8 at 50°, this being the only temperature at which measurements had been previously made. The present values for the compressions at 10,000 and 15,000 are 0.233 and 0.279 respectively, against 0.234 and 0.279 formerly. Caesium. Runs were made with a single set-up at room temperature. Caesium has a fairly small but perfectly clean cut transition a t 23,000 kg/cm 2 . At room temperature the transition pressure reached from above and below was not appreciably different. The mean change of volume differed by only 2 per cent from that with either increasing or decreasing pressure, namely 0.0064 cm 3 per 1.88 gm, or 0.0034 cm 3 /gm. (1.88 is the density under standard conditions). The results are given in Table I. Previous measurements 9 to 15,000 were made only a t 50°, so there is no exact basis for comparison. Present values for AF per 1.88 gm at 5,000, 10,000, and 15,000 are 0.182, 0.271, and 0.326 respectively against 0.184, 0.269, and 0.328 formerly. The present value at 5,000 was adjusted to agree with my estimate of what the previous value would have been corrected to room temperature. The transition pressure has also been determined by the discontinuity in resistance; the value found in this way was 22,000 against 23,000 above. Calcium. The material was some on which I had made compressibility measurements many years ago, 10 probably, although not certainly, from the General Electric Co. I t is not as pure as other material from the same source on which I have recently made resistance measurements, or as another sample formerly used also for compressibility. Runs were made with a single set-up at room temperature, 75°, and 125°. Runs were made at different temperatures in the search for a transition, which had been suggested by previous measurements of shearing strength; 11 in fact, the shearing measurements suggested two transitions. In this work persistent irregularities of the right character were found both with increasing and decreasing pressure a t all three temperatures, and it is highly probable that there are one or more transitions. The total change of volume is of the order of 0.0008 cm 3 /gm. The pressures of transition are between 25,000 and 36,000; the sensitivity was not great enough to definitely resolve the irregularities, and good results for the variation with temperature were not found. Previous shearing results indicated the mean pressure of the

217

ROUGH COMPRESSIBILITIES OF SUBSTANCES

transition or transitions as 30,000. Recent measurements of the resistance of calcium to 30,000 have shown no discontinuity up to this pressure; there is nothing inconsistent in this with the existence of a transition, because even if the transition exists below 30,000 it might have been suppressed by viscous resistance. The results are shown in Table II. No attempt is made in the TABLE II COMPRESSION OP THE ALKALI EARTH M E T A L S

Pressure kg/cm2 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 * Phase change

Calcium cm3/1.538 gm .031 .058 .082 .103 .122 .139 .155 .171 .188

Compression Strontium cm3/2.629 gm .047 .075 .099 .122 .136 .155 .172 .188 .204

Barium cm3/3.62 gm .045 .086 .121 .159* .186 .209 .230 .250 .269

Table to suggest any transition, but the results are smoothed right across the irregularities. The volume decrements at 5,000, 10,000, and 20,000 of the present work are 0.031,0.058, and 0.103 respectively. Previous results on the most nearly comparable sample were 0.029, 0.055, and 0.099 respectively. The present values are consistently higher than the old, the discrepancy thus being in the opposite direction from that of the alkali metals. Impurity of strontium or barium in the present sample would account for the direction of discrepancy. Strontium. The material was from Eimer and Amend, probably not of very high purity, and the same as that used in recent measurements of the resistance to 30,000. Runs were made with a single set-up at three temperatures: room temperature, 75°, and 125°. The runs were made on t h e one minute, 2,000 kg schedule. There is quite unmistakably a transition at all three temperatures, but it is unusually difficult to start the transition, the pressures at which the transition starts with increasing and decreasing pressure being separated by an unusually large amount. Furthermore, when the transition starts it

122 — 3263

218

BRIDGMAN

PRESSURE BARIUM Shows the transition temperatures of barium as a function of pressure in kg/cm2. FIGURE 3.

122 — 3264

219

BOUGH COMPRESSIBILITIES OF SUBSTANCES

runs very sluggishly, so that with the time schedule employed the transition is running through an unusually wide pressure interval. At the three temperatures, 25°, 75°, and 125°, the respective pressures at which the transition started with increasing pressure was 38,000, 34,000, and 33,000, and with decreasing pressure the corresponding pressures were: 19,000, 19,000, and 18,000. The mean change of volume is 0.0034 cm3/gm, or fractionally 0.0091 on the initial volume. The measured change of volume was less on increasing pressure than on decreasing, which means that the high pressure phase is more compressible than the low pressure phase, the normal direction of

.0020

.

Τ

0 Ο"

0

1 0 80°

»

1 ΙΟΟ"

1

1 150*

1

ZOO'

TEMPERATURE BARIUM

FIGURE 4. The volume changes when barium undergoes transition as a function of temperature along the transition line.

difference. The difference of compressibility is such that in the pressure interval from 17,000 to 43,000 the high pressure phase is compressed by 0.0066 more than the low pressure phase. The compressions of the low pressure phase are given in Table II; above the pressure of the transition the values are extrapolated with the help of the measured volumes of the high pressure phase. The data already given for the transition may be made to yield the volumes of the high pressure phase above the transition point. The compression at 10,000 was adjusted to agree with the former value.12 After making this adjustment, the volume at 5,000 is not in at all good agreement with the previous value, AV being 0.047 against 0.039 formerly. There is no reason to suspect, however, that this means that the high pressure values are any less reliable than usual.

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Barium. The material was from Mackay, and was the same as that used in recent measurements of the resistance to 30,000. Runs were made with a single set-up, and at room temperature, 75° twice, 125°, and 175°. Barium has a perfectly definite transition, running much more sharply and within much narrower pressure limits than strontium. A previous attempt to find a transition of barium with the volumetric apparatus had given negative results;13 the apparatus has since been very much improved. The transition pressures and temperatures are shown in Figure 3, the change of volume in Figure 4, and the transition parameters in Table III. T A B L E

III

T R A N S I T I O N P A R A M E T E R S OP B A R I U M

Pressure kg/cm2 17,500 16,400 15,300

Temperature 0° 100° 200°

dr

Δ~ν

Latent Heat

dp -0.0908 -0.0908 -0.0908

cm3/gm .00163 .00155 .00147

kg cm/gm gm cal/gm 4.90 .115 6.37 .150 7.65 .180

The compressions are given in Table II, the low pressure phase below 15,000, and the high pressure phase above. The compression was adjusted to agree with the former value14 at 5,000. The present values at 10,000 and 15,000 are 0.088 and 0.124 respectively, against 0.089 and 0.124, good agreement. Indium. The material was inherited from Professor T. W. Richards, and was of high purity. Runs were made with a single set-up at room temperature, 75°, and 125°. There were persistent irregularities at all temperatures that probably mean two or three small transitions; the highest transition pressure is probably in the neighborhood of 40,000, and the lowest around 30,000. The change of volume of the largest transition is probably not more than 0.0002 cm3/gm, with the others not more than half this. The volume compressions are given in Table IV; no adjustment was made in any of the low pressure values. For comparison there is only a measurement by Richards15 at pressures up to 500 kg/cm2, who found 0.0627 for the initial compressibility, consistent enough with the present values. Tin. Runs were made with a single filling at room temperature, 100°, and 125°. Previous measurements of shearing16 suggested a transition, but previous measurements in the volumetric apparatus17 had given negative results. The volume apparatus was now so much

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improved t h a t it seemed worth while to repeat the exploration, but no satisfactory evidence of a transition was found. The compressions are given in Table IV. No adjustment of values was made at low pressures. The present compressions at 5,000, 10,000, and 20,000 are 0.010, 0.020, and 0.038 respectively, against 0.009, 0.017, and 0.032 former 18 (the last value extrapolated with the second degree formula). The shape of the volume curve is thus somewhat different from t h a t found before. The compressibility of tin is so small t h a t the method is becoming incapable of such relatively accurate results as for most other substances; there is no question but t h a t the previous lower values are to be preferred. Lead. The measurements on this have already been described in connection with the blank runs. The compressions in terms of the initial volume (that is, cm 3 per 11.35 gm) are given in Table IV. TABLE

IV

COMPRESSION OF F O U R MISCELLANEOUS E L E M E N T S

Pressure kg/cm2 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000

Indium cm3/7.43 gm .012 .024 .035 .045 .054 .064 .073 ,0825 .091

Compressions Tin Lead cm3/7.30 gm cm3/11.35 gm .012 .010 .020 .023 .032 .029 .041 .038 .050 .048 .057 .058 .066 .065 .072 .075 .084j .079

Sulfur cm3/2.07 gm .049 .084 .110 .131 .148 .162 .175 .186 .195

Sulfur. Runs were made with a single set-up a t room temperature and 125°. Previous attempts to find a transition had been negative; 19 the present measurements were made with the idea t h a t perhaps with the improved apparatus a transition would now be found. There were irregularities in the neighborhood of 25,000 such as to make a transition not impossible, but I regard it as improbable. If there is one, its AV is not more than 0.0003 cm'/gm. The values of the compression are given in Table IV. Previously I have made measurements on the linear compressibility in different directions of the single crystal up to 12,000, from which the volume compression may be computed. Agreement with the present values

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is exact to two significant figures; the usual adjustment of the low pressure values to secure agreement at some point was not made. Carbon Dioxide. Measurements were made on this because of the desire of Dr. H. Sponer to secure experimental values of compression with which to check some theoretical calculations.20 Runs were made with a single set-up: two at solid COj temperature, one at 0°, and one at room temperature. The apparatus was filled at liquid air temperature, and an initial pressure of 10,000 kg/cm2 was applied at this temperature in order to get the COj into a region where it would not leak at higher temperatures. The first application of pressure at solid CO2 temperature seemed to go without any hitch, but after this there was internal evidence that there may have been slight leak at two or three places. The blank run from which the differential compressibility was determined was made at room temperature; at solid CO2 temperature the friction of the external surface of the cone is TABLE V C O M P R E S S I O N OF T w o

Pressure kg/cm2 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000

COMPOUNDS

Compressions C0 2 Na CI Fractional cm3/2.18 gm . 091 .020 .142 . 037 .177 . 052 . 206 . 066 . 226 . 078 . 246 . 089 . 262 . 099 .108 .118

much greater than at room temperature, so that there is possibly an error from this factor as well as from the difference of temperature. Furthermore, it was not feasible to determine the quantity of CO2 by weighing as usual, but it had to be found from measurements of the initial volume. There are several factors, therefore, making the accuracy of these measurements less than usual, but the absolute compressibility of CO2 is high, and since apparently there are no previous measurements at all, it seemed to me that the rough measurements were worth while. The numerical values of compression are given in Table V. These run to only 35,000 kg/cm2. There is no doubt that at high pressures,

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25,000 or higher, there is a transition. This runs sluggishly, and is spread over a considerable pressure range. The fractional AV may be as high as 0.003, or perhaps even higher. In view of the various uncertainties, I did not feel justified in attempting to force the results to give the compression of the high pressure phase above 35,000. Sodium, Chloride. Runs were made with a single set-up, at room temperature only. Previous explorations21 had made it pretty certain that there is no transition up to nearly 50,000, so that runs at other temperatures were not necessary. The compressions are given in Table V. The value at 5,000 was adjusted to agree with the previous value22 obtained when making measurements to 12,000. The present values at 10,000 and 20,000 are: 0.037 and 0.066 respectively, against 0.037 and 0.064, the latter value being extrapolated by the second degree formula. The agreement at 10,000 is exact, and at 20,000 the difference is in the direction to be expected in view of the fact that the second degree formula which fits the results to 12,000 gives a minimum in volume at 41,000. DISCUSSION

The methods of wave mechanics are now so far advanced that it is possible to make fairly satisfactory calculations of compressibilities, at least for the simpler substances. The value of any check of the calculations against experiment is greater the greater the range of the volume change that can be covered by experiment, so that these results should prove particularly useful in giving an idea of the relative importance of the various effects considered by the theory. Theoretical calculations of this sort have been made by Dr. J . Bardeen, and are now in course of preparation for publication. In the case of the alkali metals it is possible to obtain rather good agreement with experiment over the entire range; the agreement is best for caesium, and becomes less good as one moves toward lithium. It turns out that by far the greater part of the compression of caesium is a phenomenon involving the ionic forces in the metal, which are comparatively easy to compute, whereas as one proceeds towards lithium, the electronic interaction terms, which are more difficult to compute, become more important. I shall not attempt myself to go further into the theoretical significance of the results. There is, however, one matter of a more empirical nature which is of interest. Recently Murnaghan23 has modified the classical theory of elasticity in such a way that it is capable of dealing rigorously with the relation between stress and strain for finite strain. Of course

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when the functional relation between stress and strain is written out explicitly for any particular substance it is not possible to avoid the entrance of empirical constants, such as the coefficients of a power series expansion, but even with this limitation it seems that the form of the function which naturally presents itself in Murnaghan's analysis is better adapted to represent the relation between volume and pressure than many formulas which have been previously used, and therefore is more desirable if short range extrapolation has to be made. Murnaghan's relation between pressure and volume for those cases where two empirical constants are necessary is: ρ = a f + b f ,

where / = - { ( V 0 / V ) i - 1 j, and a and b are constants to be deterL· mined empirically. This formula may be checked as an extrapolation formula. I have made the calculations for caesium, lithium, and sulfur. The tables already given enable f to be determined as a function of pressure. Then a and b were determined so as to agree with experiment at 10,000 and 20,000 kg/cm2. The value of f at 45,000 was then substituted into the formula, and the corresponding value of ρ calculated. Perfect agreement would demand that the calculated ρ be 45,000. The values actually found were: 44,992,45,320, and 48,870 respectively for caesium, lithium, and sulfur. The agreement is astonishingly good for caesium and lithium, and still much better than I had expected for sulfur. Murnaghan's formula should, therefore, have much usefulness. I think, however, that too much theoretical significance cannot be attached to the success of the formula. The constants a and b have evidently only an empirical significance, and in fact a and b may have the same or opposite signs in order to fit the experimental points at 10,000 and 20,000. It seems probable to me that the formula in large part owes its success to its mathematical form, which is such that the volume goes to zero when pressure goes to infinity. Many of the equations of state of the past have represented the volume as approaching some finite value at infinite pressure. This is contrary to what we would expect now in the light of our knowledge of the structure of the atom, and is also definitely contrary to the experimental evidence, for the volume at high pressure almost always drops off more rapidly than would be indicated by extrapolation according to the usual formulas from experimental values at low pressures. This would suggest, therefore, that any extrapolation formula giving

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zero volume at infinite pressure would have a fair chance of success. I have tried a simple formula of this type for caesium, namely: ρ = a (Vc/V-l)

+

b(V.IV-lY.

If a and b are determined to agree with experiment at 10,000 and 20,000 and are then used in extrapolating, ρ calculates to 43,300 where it should be 45,000, not bad agreement. It is a pleasure to acknowledge financial assistance with regard to the execution of the experiments from the Rumford Fund of the American Academy, the Milton Fund of Harvard University, and the Carnegie Institute. I am also indebted to the Francis Barrett Daniels Fund of Harvard University for assistance with the publication. For most of the readings I am indebted to Mr. L. H. Abbott. RESEARCH LABORATORY OF PHYSICS, HARVARD UNIVERSITY, CAMBRIDGE, M A S S . REFERENCES 1

P. W. Bridgman, Phys. Rev. 48, 893-906, 1935. Proc. Amer. Acad. 72, July, 1937. 2 P. W. Bridgman, Proc. Amer. Acad. 49, 1-114, 1913. 3 L. H. Adams and E. D. Williamson, Jour. Frank. Inst. 196, 475,1923. 4 P. W. Bridgman, Proc. Amer. Acad. 70, 91, 1935. 6 Reference (4), p. 93. 6 P. W. Bridgman, Proc. Amer. Acad. 58, 181, 1923. 7 Reference (4), p. 95. 8 P. W. Bridgman, Proc. Amer. Acad. 60, 394, 1925. 9 Reference (8), p. 402. 10 Reference (6), p. 199. 11 P. W. Bridgman, Phys. Rev. 48, 837, 1935. 12 Reference (6), p. 201. 13 First reference under (1), p. 903. » P. W. Bridgman, Proc. Amer. Acad. 62, 215, 1927. » T. W. Richards. 16 Reference (11), p. 839. 17 First reference under (1), p. 903. 18 Reference (6), p. 211. 18 First reference under (1), p. 903. 20 H. Sponer and M. Bruch-Willstätter, Jour. Chem. Phys. 5, 745-751,1937. 21 First reference under (1), p. 906. 22 P. W. Bridgman, Proc. Amer. Acad. 64, 33, 1929. 23 F. D. Murnaghan, Amer. Jour. Math. 69, 235-260, 1937.

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POLYMORPHIC TRANSITIONS UP TO 50,000 Kg/Cm 2 OF SEVERAL ORGANIC SUBSTANCES B Y P . W . BRIDGMAN Presented October 13, 1937

Received November 8, 1937

CONTENTS Introduction 227 Detailed Data 229 Carbon Tetrabromide 229 Iodoform 232 Cyanamide 232 Urea (Carbamide) 233 Thiourea 236 Ammonium Thiocyanate 236 Nitro-guanidine 237 Ammonium Formate 239 Urea Nitrate 240 Methylamine Hydrochloride 240 Semi-carbazide Hydrochloride 242 Dichloro-acetamide 243 Iodoacetic Acid 245 Oxamide 246 Acetamide 247 Guanidine Sulfate 251 Quinone 254 p-Dichloro-benzene 255 Dichlorophenol 255 Hydroquinone 255 p-Toluidine 256 Naphthalene 256 d-Camphor 258 Menthol 261 Aniline Sulfate 263 Substances Giving Negative Results 264 Summary of Shearing Measurements on Substances not Investigated in Volume Apparatus 266 Summary 266 INTRODUCTION

This paper continues the subject already treated in Proceedings of the American Academy of Arts and Sciences, vol. 72, July 1937. In that paper the transitions of some 35 substances, all of them inorganic, were examined. In this paper the examination is extended to

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organic substances. The apparatus and the technique were the same as before, so that no new discussion is needed. In general comment on the new results, it appears that polymorphism is an even more common phenomenon among organic than among inorganic compounds in the temperature range of this work, solid CO2 temperature to 200°. This might be expected, because it has appeared that the chance that a substance will exhibit polymorphism is roughly greater the lower the melting point, and in general the melting points of organic substances are lower than those of inorganics. To compensate for the greater frequency of polymorphism with organics is the fact that the transitions are generally more sluggish and with smaller volume changes, so that they are much more difficult to measure experimentally; it results that they are of less interest. In fact, a number of cases will appear in the following in which I have not thought it worth while to take the great trouble that would be necessary to determine satisfactorily all the transition parameters, but have let the matter rest with a rather superficial statement of the existence of the transition and its order of magnitude. The scheme of selecting the compounds for examination in the following was simple. In the absence of any theory, polymorphism may be expected to be incident anywhere. The most significant cases are, in general, those occurring among the substances with simplest structure. After measuring a few common compounds in the Laboratory stock, I adopted the scheme of selecting from the list of organics in International Critical Tables those of the lowest molecular weight, and therefore simplest structurally, which were readily procurable commercially. Unless the contrary is stated, all the compounds used in the following were obtained from the Eastman Kodak Co., and were of their purest grade. In addition to the measurements with the regular volume apparatus, the shearing phenomena of a number of the substances were investigated as an auxiliary method of exploring for the presence of polymorphism. 1 These shearing phenomena have a certain intrinsic interest of their own, and since it is hardly worth while to write a separate paper describing them, some account will also be given in the following of the results of the shearing measurements. In general characterization, the shearing phenomena of organic substances differ from those of inorganic substances in the much more rapid rise with pressure of the shearing strength of the former. The rise is often linear with pressure, and even often more rapid than linear, so that the curve of shearing strength is concave upward, whereas for

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229

inorganic substances the curve is almost always concave downwards. Initially, organic substances are weak in shear, as is to be expected, but with increasing pressure the strength rapidly increases, and at the maximum pressure of 50,000 the strength averages about that of the usual inorganic compound. There are not, however, any cases of extreme strength corresponding to some of the exceptionally strong inorganic substances, and in general the range of shearing strength in organic substances under high pressure is much narrower than that of inorganics. The rapid increase of shearing strength of organics under pressure reminds one of the very great increase of viscosity of organic liquids under pressure. The mechanism of the two phenomena may well be related, involving an interlocking effect between molecules of complicated shapes. In the following the shearing measurements on those substances which exhibit polymorphism or which have been explored for polymorphism with negative results are described in connection with the discussion of the phenomena of polymorphism. In addition, the shearing phenomena have been investigated for a number of substances which have not been explored for polymorphism in the volume apparatus; these are described in a separate section. The presentation of detailed data now follows. DETAILED DATA

Carbon Tetrabromide. The phase diagram of this substance has been already investigated.2 There is a transition at atmospheric pressure at 47°, and there is a third form at higher pressures. In this work an additional form was found at pressures above 10,000, making four modifications in all. Runs were made with two different set-ups of the 50,000 apparatus, at temperatures from room temperature to 175°, eight runs in all. At temperatures below 130°, the dynamics of this transition are unique, there being an enormous asymmetry. On increasing pressure at temperatures below 130° the transition does not run even up to nearly 50,000, but on releasing pressure the transition runs, irreversibly of course, and with decreasing volume. This is highly paradoxical, and at first seems contrary to thermodynamics, that is, a transition with decrease of volume brought about by a decrease of pressure. There is, however, no violation of thermodynamics, the transition being irreversible. The phenomenon is doubtless connected in some way with nucleus formation. Nucleus formation takes time; on the first increase of pressure there was not time for sufficient for-

230

BBIDGMAN

mation of nuclei, and it was only after release of pressure that sufficient time had been spent in the critical region of nucleus formation to permit the formation of enough nuclei to make possible the transition. In nearly all the experiments the application and release of pressure was done on a careful time schedule, 1,000 kg/cm2 per minute. The pressure at which the irreversible transition runs with decrease of pressure becomes higher the higher the temperature. This is as would be expected, because at higher temperatures nucleus formation is easier, so that not so long a sojourn in the critical region is necessary, and a higher pressure means a shorter sojourn. At room temperature, the pressure at which the irreversible transition would run on release of pressure has dropped below the reversible transition line, and the transition does not run at all, up to 50,000 and back. At 150° and higher, the speed of nucleus formation has become sufficiently great so that the transition runs irreversibly, with volume decrease as normal, on the first increase of pressure. At 173° the velocity of nucleus formation has increased further, and now the super-pressure required is very much reduced. Figure 1 shows the phase diagram, and indicates the points at which the transition runs. The points obtained with the two different set-ups are rather consistent. This might not be expected of a thing as capricious as these inhibition phenomena usually are, and indicates that the results have a certain significance. The reverse transition, from IV to I I apparently runs normally enough. It is obvious that the location of the reversible transition line is in great doubt when the limits of indifference are as wide as they are here. I have drawn it with the same general slope as that of the line connecting the points marking the lower pressure of indifference, but this is evidently arbitrary, and in fact it can be argued that the line should be steeper than drawn, since usually the limits of indifference become wider at lower temperatures. It is hardly worth while giving a table for the transition parameters. The slope of the transition line is in such great doubt that no significance can be attached to any estimated latent heat. The change of volume is small and scattering, the extreme values being 0.004 and 0.009 cm8/gm. A mean value for A F is 0.0075 cm8/gm. There is no evidence for any significant variation of AV with temperature. A further study of the phenomena of nucleus formation would probably be of interest. I made one set of measurements that shows that the phenomena are not simple. At 100° pressure was increased to 50,000 without the transition running; then on decrease of pressure

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the transition ran irreversibly with volume decrease at 23,500, and then on further decrease ran in the opposite direction at 8,300. All this was on the regular time schedule, and was in duplication of the first run, and consistent with it. Pressure was now raised to 23,000,

PRESSURE Kg/cm2 CBr 4 F I G U R E 1. The transition pressures of the new high pressure modification of CBr< as a function of temperature. The dotted lines indicate that the transition ran with decreasing pressure after an excursion to 50,000. The transitions of II with I and III occur at pressures below 5,000, and have been studied previously.

14,000 beyond the reversible transition point, and left over night, temperature being maintained at 100°. No transition took place over night. This was a great surprise, since I thought that the rate of nucleus formation at 23,000 would be sufficiently great to start the transition in a time approximately 15 times as long as before. In the morning pressure was increased from 23,000 on the regular time schedule, 1,000 kg per minute up to 40,000, with no transition, then

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BRIDGMAN

released back to 14,000 (9,000 beyond the place where the transition had taken place on the first release) with no transition, and then back, the transition now starting and running to completion at 24,300 with increasing pressure. CBr 4 is known to decompose appreciably at its melting point at atmospheric pressure at about 90°, and in my former work decomposition was very troublesome. I t was apparently complete at 175° and pressures below 7,000. In this work no trace of decomposition was found after the run at 175°. Again we have evidence that pressure is effective in preventing a decomposition that proceeds with increase of volume. The shearing curve has a marked downward break at room temperature at 15,000 kg/cm 2 corresponding to the transition above. The high pressure modification thus has a lower shearing strength than the low pressure modification, a somewhat unusual fact. The shearing curve of the high pressure modification rises with general concavity toward the pressure axis. The shearing strength reaches 2,300 kg/cm 2 at a pressure of 50,000 kg/cm 2 . Iodoform. Three runs were made with this substance: the seasoning run at room temperature, one at 50°, and one at 150°. There appear to be three small but quite definite transitions. These could be established with greater certainty with increasing than with decreasing pressure, either an asymmetry in the transition or the greater curvature of the isotherm obscuring the effect with decreasing pressure. The lower transition, however, was picked up fairly certainly with decreasing pressure at 150°. The equilibrium lines are shown in Figure 2. Since the transition pressure was not established with decreasing pressure, except for the point mentioned, there is obviously no basis for an estimate of the most probable direction of the transition lines, which are schematically indicated by the dotted lines. The change of volume at the transition I—II is of the order of 0.0002 cm 3 /gm; that of the other transitions is perhaps one half as much. There is no point in attempting to calculate the transition parameters. The shearing curve has a gentle upward inflection in the neighborhood of 30,000, doubtless the transition at highest pressure of those found above brought down to room temperature. The shearing curve of the high pressure modification is concave upward, whereas below the transition the curve is concave downward. The shearing strength at 50,000 is 2,800 kg/cm 2 . Cyanamide. Two runs were made: the seasoning run at room temperature, and a run at 125°. There appears to be a very small transi-

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tion at 125°, at 25,300 kg/cm2, and with a volume change of the order of 0.0003 cm3/gm. Urea. (Carbamide). Runs were made with a single filling of the apparatus at room temperature, 80°, 90°, 150°, and 200°. This material has already been found to have two high pressure modifications.3 The transition line between I and I I I runs from 4,300 at 0° to 6,750 at 102.3°, the triple point, and the line I—II from the triple point to 7,070 at 160°. With the present set-up, these transitions

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metals undergo transitions at atmospheric pressure with rise of temperature, and these phenomena are most important in the practical use of the metals. When one adds pressure to temperature as a second variable, the phenomena become very much richer, and many new modifications become capable of existence which never occur at atmospheric pressure at any temperature. Unfortunately, even if some of the new high-pressure modifications had useful properties, it would not be possible to

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7

utilize them in practical applications, for these transitions are reversible, and the metal reverts to its normal form when pressure is released. In Fig. 3 are collected the phase diagrams of nine metals for which the transition data have been determined by the volume discontinuity method. These metals all have comparatively low melting points, or at least are mechanically soft. There is good reason why the diagram of just this sort of metal has been determined experimentally. There is almost always a considerable internal frictional resistance to the change from one modification to another, and the frictional resistance may be so high that the change does not occur even though pressure may be raised far beyond the point at which the new phase, according to thermodynamics, becomes capable of replacing the old. The viscous resistance is less the higher the relative temperature; that is, the nearer the metal is to its melting point. One may suspect, therefore, that there may be many other examples of pressure polymorphism, besides those shown in the diagram, among the harder and higher melting metals. This does indeed seem to be true for if the metals are examined by the method of shearing stress, which cannot be described here except to state that shearing stress is much more likely to overcome internal viscosity than hydrostatic pressure, distinct evidence is found that still other metals of higher melting points, such as lanthanum, cerium, thorium and vanadium, pass into other modifications at high pressures. We now discuss some of the individual metals shown in Fig. 3. Two of the most interesting examples of pressure polymorphism are bismuth and gallium. Both of these metals melt at atmospheric pressure with decrease of volume, a highly anomalous state of affairs, for which the only other well established example is ice to water. It has been known for some time that the anomalous relation between the volume of liquid and solid water is only more or less temporary and accidental, characteristic of low pressures, for at pressures above 2000 kg. per sq. cm. ordinary ice is replaced by a succession of more stable forms, all with greater density than the corresponding liquid. One would expect by analogy a similar state of affairs with bismuth and gallium, but until recently experimental search for the expected new forms had been unsuccessful. It appears that the reason was that the pressure had not been raised high enough. At pressures beyond 13,000 kg. per sq. cm. for gallium, and 25,000 for bismuth, the anticipated new forms have recently been found, so that at high pressures all substances now appear to have the normal relation between the volume of the solid and the liquid. Bismuth has at least three new high-pressure modifications; and, curiously enough, its phase diagram has rather striking resemblances to that of water. The three alkali earth metals, calcium, strontium, and barium, all show polymorphism under pressure, and their phase diagrams are not dissimilar. Close examination shows, however, that the similarity is

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8

N A T U R E OF METALS SHOWN BY PROPERTIES U N D E R

PRESSURE

not as far-reaching as at first appears, for the structure of the normal modification of barium is body-centered cubic, whereas that of calcium and strontium is face-centered cubic. Since the face-centered cubic arrangement is close-packed, it suggests itself that barium is forced by pressure into the close-packed arrangement already assumed by calcium and strontium at atmospheric pressure. The high-pressure forms of calcium and strontium must then be something else, perhaps involving a rearrangement of the electrons at levels below the valence level in the atom, since the atomic arrangement is already close-packed. In any event, it is evident that the pressure transition in barium cannot be of the same character as that in calcium and strontium. Among the phase changes listed above one would expect the most significant for theoretical purposes to be that of caesium, for this metal has a structure simple enough to enable calculations, which are of prohibitive difficulty for most other metals, to be carried through to a successful conclusion. This does, indeed, prove to be true, for Dr. John Bardeen, at Harvard, has succeeded in calculating not only that caesium should undergo a transition at high pressures, but has calculated also the approximate pressure at which the transition occurs and the magnitude of the volume change. A striking feature of the calculation by Dr. Bardeen was that it was made before the actual existence of the transition had been certainly established by experiment, and it was the stimulus of his calculation that led to the definitive experimental investigation. The structure of the atmospheric modification of caesium is body-centered cubic; at high pressure, calculation indicates that it is forced into a facecentered cubic arrangement, that is, a close-packed arrangement, which is what might be expected. The situation with regard to caesium is, however, very unusual. For many other substances, it is the low-pressure modification that has the close-packed arrangement—that is, the closepacked arrangement of spheres. One might perhaps think that the first task for a theory of any particular crystalline substance would be to calculate the crystal system in which the substance crystallizes, and that then, having established the system, on the basis of it other physical properties could be calculated. If this were true, the prediction of the pressure at which to expect new forms would become one of the easiest tasks of the theory, but it turns out that the prediction of the precise crystal system is, in the present state of theory, one of the most difficult things that can be asked. At present, theory usually has to assume the crystal system as known from experiment, and then, in terms of the known system, it is an easier task to calculate other properties, such as compressibility or electrical resistance. The reason for this is that the energy differences, and also the differences of thermodynamic potential, which determine the relative stability of different possible phases, are usually very small compared

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BRIDGMAN

9

with the total energy or thermodynamic potential, so that the total energy must be known with high precision in order to determine the differences of energy or potential, and so the transition parameters, with even moderate precision. Except for caesium, I do not know of any successful calculation that has been made for the metals. Even in the simplest case of all, that of the transitions of a number of ionic compounds from the NaCl to the CsCl type of structure, the calculations have proved too difficult to yield good values for the pressure of transition. The forces in ionic compounds are predominantly simple electrostatic inverse-square forces between the charged nuclei, superposed on repulsive forces when the ions get too close together. This repulsive force can be approximately calculated from other sorts of phenomena, but it turns out that assumptions about the repulsive forces which are adequate to account for the compressibilities, for example, fail when it comes to calculating the transitions. Thus, in Physical Review for August 15, 1937, May finds that in order to make his calculation eventually yield fairly satisfactory values for the transition temperatures of NH4CI and CsCl at atmospheric pressure it is necessary to alter arbitrarily one theoretically calculated force by a factor of 3.5 and another by a factor of 0.6. The phenomena of polymorphic transition thus appear from the theoretical point of view to be among the most delicate with which we are concerned. This delicacy is borne out from the experimental side by the observation that no other phenomenon shows such qualitative variation among substances closely related chemically, and which do show a high degree of similarity with regard to other properties. 2. Volume

Compression

We next consider the second group of phenomena; namely, simple volume compression. On the experimental side, one of the most interesting features is the mere magnitude of the volume changes that can be produced by experimentally attainable pressures. Under ordinary pressures the volume changes of solids are negligible for most practical purposes, but at high pressures they may become very appreciable. In fact, in my previous range of pressures, up to 12,000 kg. per sq. cm., the volume changes were materially greater than the change on cooling from room temperature to absolute zero at atmospheric pressure. Of course, at 50,000 the changes must be importantly larger, but not larger in proportion, because if the volume were to continue to decrease with increasing pressure at the same rate it would presently pass through zero and become negative. To take an extreme case, if the compression of caesium continued at its initial rate, it would be squeezed out of existence at only 14,000 kg. per sq. cm. It is evident, therefore, that in general at high pressures the plot of volume against pressure must be convex toward the pressure axis, and one may expect, at least for the more compressible

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NATURE OF METALS SHOWN BY PROPERTIES UNDER PRESSURE

substances, that the departure from linearity is considerable. An adequate theory must reproduce not only the initial slope of the curve of volume against pressure, but also the entire course of the curve as a function of pressure. The experimental determination of volume compressions up to 50,000 offers certain difficulties because of the various corrections for the distortion of the apparatus already suggested, so that up to the present acceptable measurements can be made only on the more compressible substances. I now have measurements for eleven of the more compressible metals, and for three other substances. In Table 1 are given the volumes of these TABLE 1.—Compression of Eleven Low-melting

Metals

AV/Vt

Sq. Cm.

Li

Na

Κ

Rb

Cs

Ca

Sr

Ba

In

Sn

Pb

5,000 10,000 15,000

0.043 0.071 0.116 0.164 0.182 0.031 0.047 0.045 0.012 0.010 0.012 0.074 0.117 0.183 0.233 0.271 0.058 0.075 0.086 0.024 0.020 0.023 0.101 0.148 0.230 0.279 0.326 0.082 0.099 0.121 * 0.035 0.029 0.032

20,000

0.125 0.182 0.268 0.316 0.372 * 0.103 0.122 0.159 0.045 0.038 0.041

25,000 30,000 35,000 40,000 45,000

0.145 0.209 0.301 0.345 0.420 0.122 0.136 0.186 0.054 0.048 0.050 0.165 0.233 0.329 0.371 0.438 0.139 0.155 0.209 0.064 0.057 0.058 0.184 0.254 0.353 0.393 0.464 0.155 0.172 0.230 0.073 0.066 0.065 0.202 0.273 0.375 0.413 0.487 0.171 0.188 0.250 0.082 0.075 0.072 0.218 0.290 0.396 0.431 0.507 0.188 0.204 0.269 0.091 0.084 0.079 * A polymorphic transition occurs in this interval.

metals as a function of pressure; the relative accuracy for the more compressible metals is naturally greater than for the more incompressible ones. These eleven metals include the five alkalies, which at present are of most interest to the theoretical physicist, and the three alkali earth metals, calcium, strontium, and barium, which also have a relatively high compressibility. The alkali metals are the most compressible of the metals; their compressibility increases with increasing atomic weight, reaching its maximum with caesium, which is compressed by a pressure of 45,000 kg. per sq. cm. to less than one-half its initial volume. One gets a rough idea of the departure from linearity by noticing in the table the compression at 20,000 as compared with that at 40,000; in general the compression at 40,000 is much less than twice that at 20,000. Among the alkalies, the deviation from linearity is greatest for caesium and least for lithium. This is a case of a general rule; namely, that the decrease of compressibility with rising pressure is greatest for those substances with the greatest absolute compressibility. In the alkali earth series the same sort of progression is found—compressibility increases with

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P. W. BRIDGMAN

11

increasing atomic weight and the relative decrease of compressibility with pressure increases also. It is to be noticed that the volume changes of caesium and barium listed in the table straddle a polymorphic transition. In both cases the volume change at the transition is small and the compressibility is not markedly affected by passing through the transition. In these two cases the change of lattice structure thus appears as a rather unimportant episode as far as other properties are concerned. This can be seen in another way from the fact that the energy difference between low-pressure and high-pressure caesium is only 3^20 of the binding energy of caesium. The theoretical calculation of compressibility has been attempted with varying degrees of success for a number of years. The first successful calculations were made for nonmetallic lattices of the simple NaCl type. A number of the simpler and more important properties of such lattices may be calculated from very simple assumptions about the law of force between the ions which occupy the points of the lattice; this force consists of a simple inverse-square electrostatic force between positive and negative ions, with a superposed repulsive force which increases very rapidly when the centers of the ions approach beyond a critical distance corresponding to what may roughly be called the size of the ions. This repulsive force was assumed for the simple calculations which were made at first to vary as some power of the distance to be determined empirically. For most of the simple ionic lattices it is approximately as the inverse ninth power. For recent wave mechanics this repulsive force is best represented by an exponential term. By means of this simple picture it is possible to calculate several of the more important properties of the lattice, such as the energy content and also the compressibility. However, it is only the initial compressibility that can be thus computed —the results are not at all in agreement with experiment when one attempts to calculate the change of compressibility with pressure; that is, the deviation from linearity of the curve of volume against pressure. More detailed considerations will be necessary therefore to reproduce the volume of the simple lattices as a function of pressure. When it comes to calculating the compressibility of the metals, the nature of the structure and of the forces is importantly modified, and other methods of calculation have to be adopted, which consider in much more detail the precise structure. The fundamental idea is not changed; namely, to find the energy of the lattice as a function of the lattice spacing. If one knows the lattice spacing at equilibrium at atmospheric pressure, and the energy at all spacings, one knows the difference of energy between the equilibrium spacing and some other. From this one can find at once the magnitude of the pressure necessary to increase the energy by this amount on compressing the lattice from the initial to the final spacing, and thus the volume as a function of pressure. At ordinary

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12

NATURE OF METALS SHOWN BY PROPERTIES UNDER PRESSURE

temperatures this calculation would have to be corrected for various temperature effects; these corrections are not easy to make, so that one is usually satisfied to calculate the compressibility at zero absolute, where the corrections vanish. This is usually good enough, because experiment shows that compressibility does not vary by a large amount with temperature. The numerical working out of the energy as a function of volume has up to the present been carried out for only a few of the simplest cases. One can guess that a rigorous mathematical solution is of absolutely prohibitive difficulty. It is known that in classical mechanics the problem of three bodies moving under their mutual forces of gravitation has not been completely solved; here we have the problem of 1022 atomic nuclei per unit volume, each nucleus accompanied by from 2 to 92 electrons. Obviously the only hope is in making certain approximations. The nuclei are at once dealt with by assuming that they are stationary at the points of the lattice; this practically means that the calculations are made for 0° Abs. The electrons are now to be dealt with by the equations of wave mechanics; into these equations enter the forces arising from the nuclei, and these forces are calculated from the positions of the centers of the nuclei by the old classical methods. That is, the nuclei are themselves not considered subject to wave mechanical treatment; in a general way the justification for this is that they are so much heavier than the electrons. The rigorous solution of the wave equations for even the electrons alone would be impossible. Rigorously, all the electrons should be treated together, each electron affecting every other. But fortunately this interaction is only slight on the average for pieces of material of ordinary size. This is shown by the fact that metals have specific properties—the density or the specific resistance determined from measurements on a piece containing 2 c.c. is the same, within experimental error, as that determined on a piece of 1 c.c. Corresponding to this, it proves possible in the first place to assign the vast majority of electrons to comparatively fixed positions near the individual nuclei, corresponding to the inner shells of isolated atoms. In general, the mutual interaction of these inner shells can be neglected except for the shells of contiguous atoms, when there is effectively a repulsive force opposing the penetration of a shell of one atom by that of another, as would be expected on purely intuitive grounds. This obviously permits an enormous simplification in the calculations. The electrons that remain after this approximation are the outer or so-called valence electrons. These also can be handled approximately, but by a sort of approximation opposite from that applicable to the inner electrons. The periodic structure of the entire lattice enters essentially into the solution of the wave equation for these electrons; these electrons are the possession of the entire lattice and cannot be associated with any

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P. W. BRIDGMAN

13

particular atom. As might be expected, the practical difficulties of working out the solution for these electrons depend on their number. It has been found possible to carry through the solution to a satisfactory conclusion for the simplest cases, that of the alkali metals, which have only one valence electron per atom, and in which the cores of the atoms are so small that the mutual interference of the cores of neighboring atoms can be mostly neglected. Other metals with only one valence electron per atom, such as copper, silver, and gold, can also be treated with some degree of success, but here the difficulties become greater because there is interference between the closed shells. If there are two outer electrons per atom, the difficulties become greater, and not so many of the properties have been subjected to successful calculation. It is perhaps unfortunate that theory is not yet in a position to make such successful calculations for most of the metals of industrial and technical importance. The solution of the wave equation for the outer electrons for the alkali metals corresponds to a distribution of electrons throughout the lattice which is nearly uniform except in the immediate neighborhood of the nuclei. It follows that to a first approximation an alkali metal can be regarded as positive point charges arranged at the points of the lattice, embedded in a uniform sea of negative electricity. The electrons distribute themselves so that on the average they occupy all parts of space uniformly, owing to the mutual repulsion between them. This means that on the average the immediate vicinity of each nucleus is occupied by only one electron at a time. From this is derived an approximate method of calculation originally due to Wigner and Seitz. In the space lattice imagine lines drawn from every nucleus to its nearest neighbors in all directions, and imagine planes erected perpendicular to these lines at their middle points. The whole lattice is in this way divided into polyhedra. The approximation consists in treating each polyhedron as containing a single positive charge at its center, surrounded by a uniform sea of negative electricity of such density that the total negative charge in the polyhedron is also one unit, so that the polyhedron as a whole is electrically neutral, and accordingly exerts very little field at outside points. It follows that the energy of the system can be found to a good approximation by neglecting the interaction of the polyhedra on each other, and merely summing the energies of the individual polyhedra. The energy of a single polyhedron is composed of the potential energy of the electron cloud, plus the kinetic energy of the electrons. In calculating these energies, a further approximation is made by replacing the polyhedra by spheres of equal volume. When the volume of the lattice is decreased by the application of pressure, the two contributions to the energy change also. The potential energy consists of two parts: the energy of the negative cloud in the presence of the nucleus, and the mutual energy of the cloud on itself. It is easy to see that both these parts vary inversely

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14

N A T U R E OF M E T A L S SHOWN B Y P R O P E R T I E S UNDER

PRESSURE

as the linear dimensions; that is, as assuming that when the lattice is compressed the cloud is compressed in the same ratio. The way in which the kinetic energy of the electrons varies with the dimensions of the lattice can be anticipated from the fundamental relation connecting the equivalent wave length of a free electron with its momentum, ρ = h/\. That is, the momentum varies inversely as the wave length, and therefore the kinetic energy varies inversely as the square of the wave length. In a block of metal the solution of the wave equation for the electron is a series of standing waves, the length of these waves being determined by the requirement that they shall fit without remainder into the dimensions of the block. If the block is changed in dimensions by pressure or

CALCULATED THEORETICALLY B T D R . JOHN BARDEEN.

otherwise, the wave length of each of the waves must change proportionally in order to maintain its fit. This means that the momentum of the electrons increases proportionally to the decrease of linear dimensions of the lattice, and the kinetic energy increases proportionally to the square of the decrease of linear dimensions, or proportionally to The signs of the two terms t ; - H and t>~H are opposite, potential energy being negative and kinetic positive. At large distances of separation of the nuclei one term preponderates, and at small distances the other. The two together give a curve for the energy which passes through a minimum. The position of this minimum determines the lattice spacing, and the variation of energy in the neighborhood of the minimum the compressibility. It turns out that rather good values for the lattice constant and for the initial compressibility can be obtained for the alkali metals by

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15

P. W. BRIDGMAN

this simple picture. However, for the other metals with one valence electron—copper, silver and gold—the agreement is not nearly so good. The explanation has been sought in the fact that the ion cores for these metals are much larger than for the alkalies, so that there are mutual repulsive effects due to relative impenetrability of the ions. These forces must also be active to a lesser extent with the alkalies. Calculations show that this force would be expected to vary inversely as the volume. Putting all three terms together, the energy of the metal would be expected to have the form: W = a/v +

b/vH

-

c/vH

With a formula of this type, Dr. Bardeen has reproduced the volume of the five alkali metals with a gratifying degree of approximation up to the limit of the experimental range. In Fig. 4 are shown the theoretical and experimental curves. It turns out that by far the most important term is the increase of kinetic energy of the electrons when the lattice is compressed. The other metals, however, have up to the present not been so successfully dealt with. 3 . RESISTANCE AT HIGH PRESSURES

We now turn to the third group of phenomena, the resistance of metals at high pressures. As already stated, the apparatus necessary for measuring resistance is larger and more complicated than that for the other two effects, so that it has proved possible up to the present to make measurements only to 30,000 kg. per sq. cm. Previously measurements had been made to 12,000, and in a few cases to nearly 20,000. These previous measurements had shown that the resistance of most metals decreases under pressure, but at a rate which becomes less as pressure becomes higher. There are, however, a fair number of metals whose resistance increases under pressure, and for these, surprisingly, the rate of increase of resistance becomes greater as pressure increases. In addition, three examples had been found in which the resistance passes through a minimum with increasing pressure. In all cases, the plot of resistance against pressure is convex toward the pressure axis. In general the changes of resistance are greater for the softer metals with low melting points. Furthermore, the order of magnitude of the changes of resistance with pressure is 10 times greater than that of the corresponding change of volume. In the new range, measurements were made first on some of the highmelting metals: copper, silver, gold and iron. The effects here are about what might be expected—smooth continuation of the results previously found at lower pressures. The plot of resistance against pressure continues convex toward the pressure axis, but any eventual minimum is so far away as to discourage extrapolation. The softer metals give more interesting results. One might expect the effects with the alkali metals to

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16

NATURE OF METALS SHOWN BY ΡΚΟΡΕΒΤΙΕΘ UNDER

PRESSURE

be large, and easiest for the theoretical physicist to handle. Lithium is different from the other alkalies in that its resistance increases with pressure from the very first. Up to 30,000 kg. per sq. cm., the increase continues at a continually accelerated pace, until at 30,000 the resistance is nearly 25 per cent greater than initially. The resistance of sodium, on the other hand, decreases rapidly, but with upward curvature. The resistance at 30,000 is about 0.4 of its initial value. Potassium is softer and more compressible, so that the effects with it might be expected to be larger. This in fact proves to be so, and the resistance of potassium at 30,000 is less than 0.2 its initial value. But the most interesting feature

PRESSURE.

B R E A K IN C U R V E S C O R R E S P O N D S TO P O L Y M O R P H I C T R A N S I T I O N .

of potassium is that the resistance passes through a minimum in the neighborhood of 25,000; this had been anticipated from previous measurements, but sufficient pressure had not been available at that time actually to realize the minimum. Rubidium at first decreases in resistance more rapidly than potassium, but then passes through a minimum in the neighborhood of 16,000, as had already been found. In the new pressure range resistance continues to increase, and at a constantly accelerated rate. Caesium had been previously found to have a minimum in the neighborhood of 5000, and above this the resistance became rapidly larger. One of the most interesting results to be anticipated in the new range was with regard to the new polymorphic modification of caesium formed at 22,000. The new high-pressure modification

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P. W. BRIDGMAN

17

has, of course, a smaller volume than the low-pressure modification, so that it would be expected in the first place that the resistance would decrease on passing to the new modification, since in all known examples of phase change the resistance follows the change of volume. In the second place, one might anticipate that the resistance of the new modification would decrease under pressure, since it is only the unusual metal whose resistance increases under pressure. Both these anticipations proved to be exactly wrong; the resistance increases on passing to the high-pressure phase with its smaller volume, and the resistance of the new phase continues to increase with increasing pressure. In Fig. 5 is shown the resistance of caesium as a function of pressure. In general not much disturbance in the resistance is produced by the change of phase, the curve continuing through the phase change without any marked alteration in its character. The alkali earth metals might also be expected to show large effects. The resistance of calcium and strontium was already known to increase with pressure—in the new range it continues to increase at a continuously accelerated rate. At 30,000 the resistance of strontium has grown to nearly 3.5 times its initial value, the largest increase of resistance measured for any substance. Barium had been previously found to pass through a flat minimum of resistance and then to increase. The question of interest here was the same as with regard to caesium; namely, how will the new high-pressure modification behave? The resistance proves in the first place to decrease slightly on passing to the high-pressure modification, thus obeying the rule with respect to volume to which the only exception thus far is caesium; but, on the other hand, the curve of resistance continues to rise beyond the transition, and the general effect of the transition on the resistance is only slight, as was also true for caesium. Mercury is a low-melting metal and fairly large effects might be expected. The freezing temperature of mercury is raised by 30,000 kg. per sq. cm. to above 100° C., so that in this range it is easy to make measurements on solid mercury. It turns out that the resistance of mercury decreases under pressure at a rate about 50 per cent greater than does that of lead, a result which feels reasonable enough. Interesting results are to be anticipated from the measurement of the effect of pressure on the resistance in different directions of large single crystals of the noncubic metals. Zinc decreases in resistance in all directions, but there is a curious dissymmetry of the pressure effects in different directions, so that at high pressures the relative resistances along the principal crystallographic axes are reversed. Single-crystal tin decreases smoothly in resistance over the entire pressure range and in all directions, and shows no reversals. Single-crystal antimony is the only example of a metal whose resistance at first increases with pressure but then passes through a maximum and then decreases; this anomaly

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18

NATURE

O F METALS SHOWN BY P R O P E R T I E S U N D E R

PRESSURE

holds only for certain directions. Tellurium is interesting because it is only semimetallic in its properties. It was already known that the resistance decreases enormously with increasing pressure. Measurements in two different directions of the crystal show that in the extended pressure range the resistance continues to decrease rapidly, until at 30,000 the resistance is only %oo of its initial value. There is not much difference between different directions in the crystal. The most interesting feature of the behavior of tellurium is with regard to its temperature coefficient. The resistance of all true metals increases with rising tem1.75

1.50

1.25

R IQ

1.00

0.15

0.50

0.25

0 0

5000

10,000

15,000

20,000

'5.000

3QOOO

Pressure,kg. per sq.cm. FIG. 6.—RESISTANCE OP BISMUTH AT 3 0 ° C . AS FUNCTION OP PRESSURE UP TO 3 0 , 0 0 0 KO. PER SQUARE CENTIMETER.

Different segments represent resistance of different polymorphic modifications.

perature, but tellurium betrays its nonmetallic character by a negative temperature coefficient of resistance. However, at high pressures, the temperature coefficient is found to reverse sign, becoming positive like the true metals, so that with a certain justification one may say that the effect of pressure on tellurium is to squeeze it more nearly into the state of a metal. Finally, bismuth would be expected to be of interest because of its two transitions in the range up to 30,000. Ordinarily bismuth is abnormal in that its resistance increases with pressure. The resistance is now found to increase in the new pressure range up to the first transition point, shown in Fig. 6. Here the resistance drops, as is to be expected because of the direction of volume change, and by a factor of 6, which is unusually large. The new high-pressure modification is now found to decrease in

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P. W. BRIDGMAN

19

resistance with increasing pressure, the first time that this expectation has been fulfilled. But now at the second transition point, the resistance jumps up again, in opposition to the change of volume and by a factor of 2.6. In this respect bismuth III (or perhaps rather bismuth II) is abnormal, but on the other hand, bismuth III, like bismuth II, has a negative pressure coefficient of resistance. The experimental situation in this new pressure range is thus somewhat complex; in the present state of theory one could reasonably expect that only the simplest features of the experimental situation could be reproduced. Even the theory which can deal with the simplest effects has to be much more complicated than the theory which was sufficiently good to give energies, lattice constants, and compressibilities. It is not possible in this lecture to attempt to give a complete account of the wavemechanics theory of electrical resistance; only the principal points can be suggested. It is in the first place to be considered that the electrons are not distributed over all velocities. The entire block of metal is to be regarded as in a certain sense a gigantic molecule, and there will be structure in the way in which the electrons are arranged in it, analogous to the structure with which electrons are arranged in shells in single atoms. In fact, one can get an idea of the nature of the energy structure of the electrons in the whole metal by imagining the metal assembled from the individual atoms at infinite dispersion, the shells in the individual atoms passing continuously into energy bands of closely packed energy levels in the assembled metal. Just as in the isolated atoms there is a structure for the energy which the electrons may acquire under external stimulation, as well as for the energy they possess when undisturbed, so in the metal there is a structure of the energy states to which the electrons may be excited as well as a structure for the energy states which they assume when undisturbed. The "zone" theory of metals is the theory which takes account of the energy structure of the electrons, and it is the properties of the zones which are primarily concerned in phenomena of electrical resistance. Under ordinary conditions the energy the electrons have in virtue of their wave character is much greater than the energy they would have because of temperature agitation. At 0° Abs. the electrons all settle down into the lowest possible energy states, filling all these states full, with unoccupied states of higher energy above them. When temperature increases, it is only a few of the electrons, near the top of the occupied energy states, which can acquire sufficient energy from the bombardment of the atoms to be raised to those higher energies which are permitted to them by the energy structure. This is the explanation of the fact that the electrons make a very much smaller contribution to the specific heat than would have been supposed by classical theory; the explanation of this fact was the first great striking success of the new point

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20

N A T U R E OF M E T A L S SHOWN B Y P R O P E R T I E S UNDER

PRESSURE

of view in explaining the properties of metals. Similarly, when an external electric field is applied to the metal, the electrons can acquire energy from the field—that is, move under the influence of the field so as to constitute a current—only when there are unoccupied states in the energy structure to which the electrons may move. According to the nature of the energy structure, we may have different sorts of behavior of the electrical resistance. It may happen that the topmost band in the energy structure which is occupied by electrons at all is only half filled by electrons; this is true of the alkali metals, which have only one valence electron per atom. In such metals there are unoccupied energy levels close at hand to each electron, to which it may be easily excited by an external field, so that the electrons in such metals respond readily to external fields, and the metal is a good conductor. The metal is not an infinitely good conductor because of continual dissipation of the energy absorbed by the electrons from the field by collisions with the atoms, which are moving irregularly because of temperature agitation. On the other hand, if the atoms each have two valence electrons, the uppermost occupied energy band is filled completely with electrons in their natural unexcited state. The only way in which the electrons of such a substance can acquire energy from an external field is to be advanced to positions in other unoccupied energy bands. If the next unoccupied energy band is some distance above the occupied band, the electron will not be able to acquire sufficient energy from the field to make the jump, and the material will be an insulator. This is the state of affairs with many nonconductors. If on the other hand, the next band is very close to the occupied band, or actually overlaps it, it will be easy for the topmost electrons to be excited by the field, and the material will be a conductor. This is the case with the bivalent alkali earth metals. When a material is compressed, the energy structure is going to be altered, and the resistance will be altered. In the detailed working out of the effects, several factors will have to be considered. The rate at which the energy acquired from the field is dissipated to the atoms is affected by pressure. Here it proves that analysis made before the advent of wave mechanics gives approximately the correct answer; the rate of dissipation is proportional to the square of the amplitude of atomic vibration. As pressure increases, the natural frequency of vibration of the atoms increases because of the greater intensity of the restoring forces at small volumes, and the amplitude decreases. This factor would therefore produce a decrease in the resistance with increasing pressure. This is probably the most important effect with most normal metals, and it is for this reason that the resistance of most metals decreases under pressure. There is another important effect. It is to be expected that the old picture of a free electron would not correspond exactly to the situation in wave mechanics. It turns out that if the electron is situated in the middle of an energy band the old picture is good enough, and the electron

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P. W. BRIDGMAN

21

can be thought of as having its normal mass, and its kinetic energy is the square of its momentum divided by twice its mass. But near the top of an energy band this simple relation between momentum and energy ceases to hold. Here for a time the energy does not change, although the momentum may be changing, and then there is a sudden snapping of energy to a higher value with no change in momentum. In this region the electron is not "free," as it is in the center of the band. The average behavior of the electrons in the band will be a sort of mean between that of those free and those not free; in other words, the "effective" number of free electrons will be less than the total number. The ratio of the "effective" number to the total number will depend on the detailed structure of the band. This will in turn depend on the pressure, so that we have the possibility of an effect of pressure on resistance which was not contemplated in classical theory; namely, an effect on the "effective" number of free electrons. Detailed calculation shows that this number may either increase or decrease with pressure, so that we have here a mechanism which may explain the increase of resistance with pressure observed in some metals. There is still a third factor, arising from interaction between the ions, which has been taken into account by Dr. Bardeen. It appears that this factor also may either increase or decrease with pressure. The detailed calculations of the relative magnitudes of these effects in any special case are difficult, but they cannot be avoided, because it is not possible to see intuitively whether the number of free electrons, for example, should increase or decrease with pressure for any special metal. Dr. Bardeen and Mr. Weiner have carried through the calculations for lithium and sodium, taking account of the variation of all three factors. For lithium it turns out that there is a decrease in the number of effectively free electrons with increasing pressure more than sufficient to overbalance the other factors, so that there would be expected to be a net increase of resistance with pressure, as is the experimental fact. The numerical agreement is not good, however. For sodium, on the other hand, detailed calculation shows that practically the entire effect arises from the change of amplitude of atomic vibration, and it is possible to compute the resistance with good approximation over the entire range of pressure. When more powerful methods of calculation are developed it will be possible to extend the calculations to other metals. In the meantime there is no reason to think that the fundamental equations are not capable of dealing with the situation, and that the difficulties are not entirely practical ones due to the difficulty of the calculations. One of the jobs which most obviously lies ahead of theory is to extend its calculations to single crystals in order to give some account of the variation of mechanical and electrical properties in different directions; this, theory has as yet hardly attempted.

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22

NATURE OF METALS SHOWN BY PROPERTIES UNDER PRESSURE

THEORETICAL

STRUCTURE

In conclusion, I want to comment briefly on the character of the theoretical structure that is growing up. It is yet too early to expect that the practical man can use theory as a tool with confidence that it will give him insight into new situations. It is true that many features of the new theory can be talked about in the easy intuitive way that made our old mechanical models so valuable, but I think if one examines the situation he will find that the intuition which is successful is a highly sophisticated intuition, and that without a previous detailed mathematical analysis by someone, intuition could not be safely followed. Thus we have come to talk intuitively of energy bands populated by electrons, and have learned how to use this picture to make many results appear plausible. But this picture cannot be handled with the thoroughgoing naivete with which we could handle our old mechanical models. Thus we may not ask: "Which are the particular electrons in the energy band which have the lowest energies, or in which part of the metal are they situated?" This question makes no sense from the point of view of wave mechanics, although the natural implications of language make it a very natural question to ask. The intuitions which the theoretical physicist is developing to meet these new situations are intuitions based only partly on our previous experience, and in any new case the proper intuition has to be found and developed by the difficult method of detailed mathematical analysis. In these early days of this new subject those of us who are not primarily theorists can only sit and be instructed by those who have tediously worked through the details.

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Reflections on Rupture BY P . W . BRIDGMAN Research Laboratory of Physics, Harvard University, Cambridge, Massachusetts

I

T

HE rupture of solid materials is one of the most common and most unpleasant of everyday experiences. As we see them, these ruptures almost always follow the application of too great loads of one kind or another. In fact the correlation between the application of a great load and rupture is so universal and inevitable that we have acquired an intuitive feeling for the "cause" of the rupture. This we associate with the action of a force, or, if we are a little more careful, the action of a stress, in the ruptured material. This concept, of rupture caused by a stress, like many other intuitive concepts, is seldom subject to critical analysis. Experience in other fields would, however, make it not too surprising if it should prove that this intuitive and uncritical idea breaks down outside the range of experience in which it has grown up. We almost always go further than to think that the rupture demands merely the presence somewhere of a stress or force, but, if the stress is to "cause" the rupture, we also usually demand that the direction of the force be properly related to the direction of the rupture. Thus, when we have a clean tensile break we demand that there be a force separating the particles acting perpendicular to the plane on which rupture occurs, or if the failure is by slip in shear, there must be forces tangential -to the plane of shear. Otherwise we feel that there is nothing to "make" the rupture take place. Let us look a little more carefully at what is involved in the idea of a "stress" or of a force acting on the atoms or molecules of a material. We shall, fortunately, not find it necessary to go to that degree of sophistication which considers a force as merely an aspect of the geometry of a four-dimensional relativity, but shall do our thinking with the old mechanical ideas. A force produces acceleration in the body on which it acts; if the body is stationary on the average,

then the total force acting on it is zero on the average. This applies to atoms or molecules or microscopic crystalline grains no less than to the heavenly bodies to which Newton first applied his analysis. Every atom in a body which is not in the act of accelerating as a whole or in part must therefore be subject to no net force, and every atom in such a body has found such a position that it is subject on the average to no net force. The effect of applying an external force to a body, even a force up to the verge of rupture itself, is to cause the atoms to find new relative positions in which the net force acting on them will still be zero. Because the atoms move when changing their positions and because any motion which begins and stops must involve accelerations, there must be net forces on the atoms during the rearrangement which follows the application of the external force. This force, however, is evidently only an incidental epiphenomenon, because it can be made to be as small as we please by applying the load slowly enough, and can have no essential connection with the rupture which inevitably occurs when the external force passes a certain limit, independently of how slowly it may be applied. When rupture does occur, the parts of the body, and the atoms with them, receive accelerations, and there are unbalanced forces acting on the atoms. This may be stated in paradoxical fashion as follows: "A body does not break because there are unbalanced forces acting on the atoms, but there are unbalanced forces acting on the atoms because the body breaks." The mechanism by which the atoms seek new positions when an external force is applied so as to be still subject to zero net force evidently involves a propagation of some action across the boundary of the body. When a load is applied to the body, the atoms in the surface layer on which the load acts are subject to an increased force on the side of the load which would be unbalanced

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518 if the surface atoms did not move in such a direction as to compensate this change in the force acting from one side by a change in the force exerted from the other side by the atoms in the next layer under them. The second layer of atoms in turn now finds itself solicited by an unequal force from the two sides and moves so as to equalize this, in turn throwing the third layer of atoms out of equilibrium, which in turn moves, and so on until the change of dimensions has propagated itself throughout the entire body. The direction in which the atoms move so as to recover positions of no net force evidently depends on the direction of the external force; if the external force is a tension, then the first layer of atoms moves away from the second layer until it finds at a greater distance a greater force of attraction toward the second layer, neutralizing the greater force in the other direction of the external tension. Or if the external force is a compression, the first layer of atoms moves toward the second layer until it finds closer to the second layer an increased repulsive force sufficient to neutralize the external compression acting in the other direction. II The language in which we describe the "causal" relations in this situation has to be chosen with care. Thus it is safe and profitable to say that the strain in the body (that is, the greater distance of separation of the atoms) is caused by the external tension, because the strain always follows the tension, and is quantitatively connected with it, being greater the greater the tension. But it is not so easy to describe this situation felicitously in ordinary causal language from the microscopic point of view of the individual atoms, for the unbalanced forces which are the immediate occasion of their motion to new positions of equilibrium have no fixed connection with the external tension, but may be large or small at will for the same tension and the same final strain merely by applying the tension rapidly or slowly. The interior of any body subject to the action of external forces across its free surface (we neglect the effect of "body" forces such as gravity) is the seat of stresses, and these stresses are ultimately defined in terms of the forces on the free surfaces. In general, as proved in any text-

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book on elasticity, the stresses are not determined solely by the external forces, but also by the elastic properties of the body. The stresses are not forces themselves, but are constructional quantities with six components, instead of the three components of a force. Given the stress, it is possible to calculate the force acting across any surface drawn in the body. The stresses are determined by the condition that the total net force on any isolated piece of the body must vanish. There is no simple connection between the stress and the net force on the individual atoms, because the latter is always zero at equilibrium, no matter what the stress. The total force acting across any plane drawn in the body is the sum of the forces exerted on all the atoms on one side of the plane by all the atoms on the other side. It is more like one-half the gross force on the atoms in distinction from the net force. The word "stress," as used in elasticity theory, for example, has meaning only from a large scale point of view. The elements of surface across which the forces determined by the stress act must be so large in extent that the statistical effect of all the atomic forces is steady. A stress is too blunt a tool to describe small scale happenings in which the detailed play of the forces acting on the individual atoms is determinative. It is similar with the strain. The strain which enters the equations of elasticity theory is, like the stress, an average over dimensions so large as to give smooth results. Conversely, if one works from the large scale equations of elasticity theory in the elastic range, or the similarly constructed equations of plastic flow in regions of plastic deformation, one can expect to obtain no inkling of nonuniformities on the atomic scale. Consider, for example, a cylinder of plastic material which is being extended along the axis. If the extension is uniform, every cross section which was originally plane remains plane after the stretching. That is, the deformation can be described from the large scale point of view by saying that every line of particles which was originally parallel to the axis remains parallel, but extended uniformly, and every line of particles originally perpendicular to the axis remains perpendicular, but uniformly contracted. Lines of atoms thus remain lines of atoms, but their centers change in distance apart. But in the original solid material the

atoms were already practically in contact—it is not possible to crowd them much closer together, whereas the description of uniform plastic flow just given envisages the possibility of indefinitely close crowding. Hence, in the small, lines of atoms cannot remain straight after the deformation, but they must crumple, or be otherwise distorted. Any crumpling of lines of atoms may be expected to modify profoundly the properties of the substance, particularly with regard to rupture, but it is something of which no suggestion is given by the large scale description in terms of stress and strain. "Stress" and "strain" are often used loosely, in an imperfectly defined sense, as applying when there are small scale departures from the normal regularity of atomic arrangement. This matter will be discussed again later. In this paper I use "stress" and "strain" in the precise sense of elasticity theory for large scale phenomena. m The idea is very common that fracture occurs when stress or strain reaches some critical value. Many attempts have been made to formulate some mathematical relation on stress or strain or both which shall serve as a universal criterion of rupture. Yet if fracture is initiated in the microscopic domain, as it seems it must, there appears to be no particular reason to expect any vital connection between such small scale happenings and stress and strain, which begin to have meaning only on a larger scale. Of course it may prove as a matter of experience, particul. rly in a narrow range, that the small scale happenings are determined by the larger scale stress and strain, but even so, there seems no reason to anticipate any general relation valid for all substances in all conceivable conditions of atomic disarray. Fracture occurs in a body when the external conditions are altered if all the atoms cannot find new positions, not far from the original positions, in which they will still be subject to zero net force on the average. We have already seen that the mechanism which procures the change of position need have no simple connection with the external force which initiates the change. The mechanism procuring change of position is something automatically provided, and we need not worry too much about the details. Every atom, even at 0°

519 Abs. is in incessant motion in a small region about its position of equilibrium, continually exploring the force field in its immediate neighborhood. Under normal conditions, before the solid breaks, every atom is in a stable force field, that is, the net force called into play when the atom is displaced from its position of equilibrium is in such a direction as to restore it to its initial position. When this condition fails to hold, the atom finds itself in an unstable force field, and will presently take up a new position of equilibrium at some distance from its original position. It seems plausible to suppose that every fracture must take its microscopic beginning from some such atomic instability. Whether the instability will then spread from microscopic to macroscopic dimensions will depend in part on large scale considerations, principally on the energy. In particular, the instability will tend to spread if in this way the potential of all the forces is diminished. It seems to me that any theory of rupture must involve as an essential element a consideration of this instability factor, for certainly if there is instability there will be fracture and conversely, fracture is an instability. However, this factor is not considered by any of the present important theories, 1 some of which involve such considerations as: "At what distance of separation will the atoms exert the maximum force on each other?" A complete theory of rupture would involve a formulation of all the conditions under which instabilities may arise. It is well known that the formulation of the conditions of stability is an extremely difficult mathematical problem. From the indifferent success of various attempts to formulate the conditions for such simple systems as regular crystal lattices it is to be expected that a general solution is at present beyond mathematical possibilities. The situation is further complicated by the probability that instabilities are almost always initiated at some imperfection in the structure, either internal or on the surface, as shown by the success of various well known recent theories of rupture. It is possible to see from certain very general considerations, however, that there are factors of instability present in any ordinary solid, even in the absence of imperfections in the structure. Under conditions of normal temperature the mean atomic forces in

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520 solids are attractive. One can see this from the thermodynamic formula:

(ϋ) =-,(*) \dp/ \dr/ T

p

\Bp/T

This formula states that when the dimensions of a body are uniformly reduced by the application of hydrostatic pressure, the internal energy of the body decreases at low pressures, or energy flows out of the body in the form of heat faster than it enters in the form of work done by the pressure. This means that the atomic forces do work when the distance between atomic centers decreases, which means that the forces are on the average attractive. The explanation of the fact that the solid under ordinary conditions is held distended so that the forces are attractive is to be sought in the kinetic energy of temperature agitation with which the atoms bombard each other. At very low temperatures the zero point energy may play the same role as ordinary temperature energy at higher temperatures. Imagine now the thermal energy removed from a small piece of the body and simultaneously a microscopic gap to open between two neighboring atoms. Then the strings of atoms terminating on the two sides of the gap will shorten because of the attractive forces, thus pulling away from each other and increasing the extent of the gap; in this way the potential energy of the atomic forces attains a lower value. Since the thermal energy in any part of the body is continually fluctuating, this factor making for instability is always present. From this point of view the problem becomes not to determine what it is that makes fracture occur, but how the body manages to hang together at all. Of course it must be, because bodies do hang together, that compensating fluctuations of thermal energy above the mean occur rapidly enough to annul the incipient fractures, and in fact one can see that the energy set free by the atomic forces when the incipient fracture occurs may be at once transformed into local temperature effects, just in the place needed to heal the fracture. But if the lines of atoms are too much extended, thus increasing the gain in potential energy when rupture occurs, it is to be expected that eventually large scale instability will set in. This is to be expected whether the body is extended uniformly in all

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three directions, or only in one or two directions. On the other hand, when the body is so much compressed that the forces are on the average repulsive, that is, when a pressure greater than — τ(βν/θτ)ρ/(θν/θρ)τ is applied, a fracture cannot spread at the expense of the energy of the atomic forces because the widening of a fissure means a compressing nearer together of the abutting atoms and so an increase of atomic potential energy. It is not at all inconceivable, however, that the external forces may be so disposed that a spreading of the rupture involves a decrease of energy of the external forces more than sufficient to balance the increase of energy of the atomic forces; in this case rupture may still occur. IV The conditions which favor stability can be seen in a general way from the nature of the forces between atoms or atomic nuclei. If the atom as a whole is neutral, then in almost every case we have reasons, other than the thermodynamic reasons above, to believe that two such atoms attract each other when separated beyond a critical distance, and repel when nearer. If the atoms are electrically charged, then at large distances the force is mainly electrostatic, and may be either attractive or repulsive, depending on whether the net charges on the two atoms are of opposite or the same sign, but even in the case of charged atoms the force at close enough distances of approach always becomes an intense repulsion, which increases more and more rapidly as the distance of approach becomes less. In fact, the increase of repulsive force is so rapid that for many purposes the atoms can be thought of as hunks of ordinary matter, with sharp boundaries, incapable of mutual penetration. It follows that in general atomic arrangements in which the atoms are in close contact on all sides are stable, because when any atom is displaced from its position of equilibrium it must approach more closely some neighboring atom and thereby receive from it a much intensified repulsion, driving it back toward its initial position. This is why rupture is not produced by hydrostatic pressure, no matter how high (at least so long as the pressure does not break the atoms themselves) and this applies whether the substance has the regular arrangement of the crystal, or the hap-

521

hazard arrangement of a liquid, or is a solid with crystal structure highly disorganized by drastic deformation. If on the other hand the atomic arrangement is one with a pronounced impressed anisotropy superposed on any natural anisotropy which may be a consequence of asymmetric atomic force fields, such as is often revealed in the lattice of the crystal, then new factors making for instability may be looked for. In the following, attention will be directed principally to one particular aspect of anisotropy, namely extensions, and the corresponding instability which results in a shortening of extended fibers, but this must not be taken to imply that the shearing aspect of anisotropy, which must accompany any elongation, may not, under the proper circumstances, be followed by a corresponding instability by shearing slip. Whether instability will manifest itself by tearing or slip will depend on the structure of the body; in general slip seems to demand the cooperation of more extended domains of atoms and occurs more frequently in bodies with a large element of crystalline regularity of arrangement. Anisotropy of distribution may be initially brought about by the action of anisotropic systems of forces on the body, either in the elastic or the plastic range. The character of the anisotropy depends not only on the external forces, but also on the atomic force fields. In particular, there is no simple connection between the direction of the external force and the resulting displacements. An example of this is the elastic lateral expansion produced in a block shortened by the action of an external axially applied compressive force within the elastic range. It is instructive to stop for a moment to analyze this situation. Let us suppose the material crystallizes in the simple cubic system. Initially, before the application of the load, the lattice automatically comes to equilibrium at such dimensions that the net force on each atom vanishes. We have already seen that this means that each layer of atoms takes up such a position that the repulsive and attractive forces of the next layer balance each other. If the lattice were completely static, symmetry would demand that the transverse spacing be uniform all the way across, up to and including the surface layer. Temperature bombardment, however, introduces an unsymmetrical element

in the surface layer, so that the transverse spacing changes in the surface layer. Now apply a compressive load; the body shortens in the direction of the load, because only in this way can the outer layer of atoms on the face on which the load acts receive from the next deeper layer of atoms the repulsive support necessary to balance the action of the external force. But there is also a change of transverse spacing, and this also depends on the nature of the forces. Let us suppose in the first place that only nearest neighboring atoms exert appreciable force on each other and that this force is in the direction of the line of centers. We also neglect temperature agitation. Then we see at once that there is no transverse change of dimensions, since the distance from its transverse neighbors at which the outer layer of the lateral face finds itself in the position of no net force from its next inner neighbor is the same as before. Suppose, however, that the next nearest neighbors also act, that is, Β and D act on A as well as C, still in the line of centers. If the force exerted by Β and D is attractive, while that by C is repulsive, the effect of decreasing the distances from Β and D to C will be to increase the component of the forces toward C exerted by Β and D, with the result that A will move toward C until the more rapidly increasing repulsive force from C balances the increased component of attraction exerted by Β and D. A material with forces like this would therefore contract laterally when compressed longitudinally, that is, it would have a negative Poisson's ratio. Such substances are very unusual; negative Poisson's ratios are known for certain directions in certain crystals, however, and there is nothing intrinsically im-

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522 possible in such behavior, in spite of the fact that it feels wrong intuitively. It is to be remarked that no metal crystallizes in the simple cubic system. Suppose now that the force exerted by Β and D on A is repulsive whereas that of C is attractive, as it is in the simple NaCl type of structure because of electrostatic action. Decreasing the distance from Β to C and from D to C now increases the component of repulsive force urging A away from C, and the distance of transverse separation of the first and second layer of atoms will therefore increase until the increased attraction exerted by C balances the increased repulsion of Β and D. Stability in the structure demands that the atoms be able to find new positions in which the attraction of C overtakes the repulsion of Β and D; if no such position exists the structure becomes unstable and breaks. Substances with atomic forces such as we have just discussed have positive Poisson's ratio, as is normal. It is important to notice that there is no component of stress acting in the direction of this transverse change of dimensions. Even if the distortion were pushed so far that the lateral separation is sufficient to enter the region of instability so that rupture occurs, still there would be no component of stress at the moment of rupture across the separating planes. V The idea of a strain component for which the corresponding stress component is zero is one which is widely accepted, and seems to cause no difficulty, but for some reason the natural extension of this to fractures with vanishing stress component is one which does cause great difficulty. The intuitive demand is very common and very strong for a stress component in the direction of fracture which shall "make" the fracture occur. It is of course evident, if the external force acting on the system is in the direction of rupture, that work is done by this force when rupture occurs, and so the mechanical principle is satisfied that systems move so as to decrease the potential energy of the forces. But the energy of the external forces is not the only energy involved— there is also the internal strain energy, and this may decrease by a pulling together of lines of atoms, as we have already seen, without the

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immediate accompaniment of work by the external forces. I think the intuitive demand that rupture be in the direction of the external force, or the stress, would not have arisen except for the restricted character of our ordinary experience; nearly all fractures encountered in ordinary situations, as well as those of engineering interest, are such that the direction of the fracture is the direction of the applied force. We have already remarked that both of the common manners of rupture, tensile and shearing, occur under the action of forces so applied as to increase the distance of atomic separation in the direction of fracture. But when the configuration of the external force assumes less familiar forms, one may expect the simple connection between direction of force and direction of fracture to fail, particularly if the forces are on the average compressive, so as to decrease the mean distance of separation of the atoms. When one stops to think of it, it appears that only an infinitesimal fraction of the matter in the universe is in a condition of comparative freedom or in the comparative " state of ease" of -the material from which we derive our ordinary experience of fracture. All the material of the crust of the earth, for example, as well as that of all the deeper layers of the earth, is subject to enormous mean compressive stresses, and the atomic arrangement is certainly on the average removed very far indeed from that of the perfect crystal. Matter in this condition is subject to fracture, as we know from earthquakes, or from experiments on combined pressure and shearing stress. 2 Matter in the condition familiar to us occurs only in a two dimensional skin. In my work at high pressures many examples of fracture under conditions different from the ordinary have been observed, and I shall now discuss some typical cases. The earliest and one of the most striking of such cases is the "pinching-off" effect.' A rod of glass or hardened steel or other brittle material passes into and out of a pressure chamber through two stuffing boxes; inside the pressure vessel it is exposed to the action of fluid pressure on the curved surface, while the ends are free. Under the action of the external pressure the rod lengthens along its axis, by exactly the same effect that produces the lateral expansion of a compressed

prism, only the effect is here doubled because the compressing force is applied along two axes instead of one. Since the ends are free there is no stress across the planes perpendicular to the axis, except inside the chamber, where there is an unimportant compressive stress because of friction as the rod elongates through the stuffing boxes. When the pressure on the outside of the rod, and accordingly the elongation along the axis, reaches a certain value, the rod suddenly breaks by a clean tensile fracture perpendicular to the axis, the two fractured pieces being expelled by the fluid pressure through the stuffing boxes. The same sort of fracture is also produced in ductile materials, but the expelling action on the fractured fragments is complicated by the necking down which occurs before rupture, thus giving rise to a component of fluid pressure in a direction to assist the completion of the break. This component of fluid pressure results in a tension in the necked-down region, exactly like the excess tension in the necked-down region in an ordinary tensile test. One of the surprising things about this phenomenon is the unanimity with which people, when they first see it, hunt for a longitudinal tensile component of stress or force, thinking that otherwise there would be nothing to "make" the rod break. For instance, one may set up the thesis that the fracture starts at surface fissures, and that at the bottom of these fissures there is a tensile stress due to the pressure exerted by the liquid on the walls of the fissure which is responsible for the fracture. Qualitatively there may be a tension of this kind, but quantitatively it is quite inadequate. Thus in the case of glass, the hydrostatic pressure necessary to produce the "pinching-off" effect is roughly equal to the ordinary tensile strength. Suppose, to be specific, that the ordinary tensile strength is 100,000 lb./in. 2 and that the pinching-off effect is produced by a pressure of 100,000 lb./in. 2 . In an ordinary tensile test there is an enhancement of tensile stress at the bottom of the surface fissures because of the geometrical relations at reentrant angles. Suppose, to be specific, that the maximum tensile stress at the bottom of the fissures is 125,000 lb./in. 2 . Then the thesis is that the rod breaks in ordinary tension because the tensile stress has risen in places to 125,000 lb./in. 2 , which

523 is more than can be supported. Consider now the pinching-off situation. Elementary analysis shows that the complete system of stresses is the sum of two systems of stresses—the stress under simple tensile load of 100,000 lb./in. 2 and the stress under uniform hydrostatic pressure over the entire external surface, including the ends, of 100,000 lb./in. 2 . But the latter stress system is a uniform hydrostatic pressure (all three principal stress components equal) of 100,000 lb./in. 2 throughout the interior of the body. It follows that the net tensile stress at the bottom of the surface fissures in the pinching-off experiment is 25,000 lb./in. 2 , only one-fifth of that required by hypothesis to produce a tension failure. Even in a structure without internal or surface imperfections, it is reasonable to anticipate that the fracture will eventually start in the microscopic domain because of some such instability as previously discussed, involving the appearance of lens shaped fissures perpendicular to the axis of the rod. Such lens shaped fissures would be unstable under a sufficiently high transverse load which tends to bow out the lens surfaces, increasing their curvature. Whatever the conditions may be in the microscopic domain in which rupture starts, and whether or not fracture starts at a flaw at the surface or in the interior, there can be no question, I think, but that from the point of view of a scale large enough to give the very concept of "stress" meaning, we have in the pinching-off effect an example of a clean rupture occurring in a direction in which there is no stress component. We obviously have to distinguish between an extension (strain) failure, and a tension (stress) failure. The stress in the pinching-off experiment can be analyzed into the sum of two stress systems: a uniform hydrostatic pressure equal to the pinching-off pressure over the entire exterior surface of the specimen, plus an ordinary tension on the ends also equal to the pinching-off pressure. The pinching-off pressure is therefore numerically equal to the tensile strength, suitably defined, which would be shown by the specimen if it were subject to a uniform confining pressure all over equal to the pinching-off pressure. This analysis holds whether or not the specimen necks down during rupture.

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524 VI Another striking example, which I have already discussed,4 is that of a ring of hard rubber, fitted over a closely fitting steel core, and immersed in a fluid to which pressure is applied. When pressure rises to a few thousand atmospheres, the ring splits off the core by a clean tensile break, exactly as if it had been stretched by driving a wedge into it. This is in fact the nature of the action; the hard rubber has a rather high compressibility, so that if it were not for the restraint of the steel core it would shrink by a rather considerable amount when fluid pressure is applied. But the steel core, by preventing it from shrinking as much as it otherwise would, effectively stretches it beyond its natural figure, and this stretch may be so great that rupture occurs. However, the steel is slightly compressible, so that the rubber, even when it breaks, is still somewhat smaller than its original dimensions. Furthermore, since Young's modulus for hard rubber is comparatively small, the extra force superposed on the hydrostatic pressure necessary to stretch and break it is still much smaller than the hydrostatic pressure. We have, then, the paradox of a substance in which every strain is a shortening and every stress a compression, experiencing a clean tensile break. The break here is against the direction of the stress. It seems evident that it is the distortions in the molecular arrangements which are effective, and the fact that every distance between molecules has been shortened absolutely at the moment of rupture is without pertinence. Other examples of this sort of rupture are common enough under hydrostatic pressure. Thus it is impossible to seal heavy platinum wires into glass without the seal cracking when hydrostatic pressure is applied, or a too closely fitting glass sleeve over a steel core will crack at high pressure, exactly like the hard rubber ring. It is easy to mention unequal compressibility, and to think that the explanation is the same as that for the familiar cracking that occurs when a seal of an unequally expansible metal and glass is cooled. But in this latter case net tensile stresses are produced on cooling, whereas in the case of breaking under hydrostatic pressure, the superposed tension which is necessary to stretch the

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glass over the metal is less than the hydrostatic pressure, so that the total resultant stress is compressive in every direction. Again it is evident that the character of the stress is not the determining factor, but the geometrical distortion must be a very important if not the unique factor. The relations are so paradoxical here that it may pay to dwell a little longer on the matter by means of an idealized experiment, not very far removed from what has actually been done in the laboratory. Imagine, then, a bar of hard rubber of 1 sq. in. section which can be loaded longitudinally by a load hung on it, enclosed, with the load, in a chamber filled with a fluid on which hydrostatic pressure can be exerted. We suppose the normal breaking strength is 5000 lb./in. 2 . The rod would then break under a load of 5000 lb. when the pressure in the fluid is zero. Now apply pressure to the fluid, up to 100,000 lb./in. 2 , to be precise. Then we may suppose, to be general, that there has been some change in the tensile strength of the rubber, but, in any event, we suppose that the increase in tensile strength is not as great as the applied pressure, that is, the strength is now less than 100,000 lb./in. 2 . If justification for this is felt necessary, it can be found in various experiments, in particular, the recent ones of Griggs on limestone; 6 he found an increase in tensile strength under pressure, but by an amount very much less than the increase of pressure itself. Suppose now that the strength of our hard rubber rod is 10,000 lb./in. 2 under 100,000 lb./in. 2 pressure. This means that the rod breaks when a weight of 10,000 lb. is hung on it, when immersed in the fluid under 100,000 lb./in. 2 . The rod thus breaks against a net compressive stress of 90,000 lb./in. 2 . In spite of this, the mechanical principle that the potential energy must diminish is not violated, because the work done by the fluid rushing into the fracture at 100,000 lb./in. 2 more than compensates the work done against the force of 90,000 lb./in. 2 on the end where the weight is applied. Superposed on this there is an additional work done by the fluid, because at the moment of rupture there is a net decrease of volume of the entire rod. Both of these examples, that of the pinchingoff effect and of the cored ring, are understandable from the point of view of atomic instability

525

as the determining factor in initiating rupture In our discussion of both these examples we found it suggestive to resolve the actual stress system into the sum of two systems, a hydrostatic pressure and a superposed tension, and we saw that qualitatively the fracture occurred as if the tension only were acting. That is, to a first approximation the effect of the hydrostatic pressure in producing rupture could be ignored. This is just what would be expected, because obviously if we imagine every atom exposed to additional forces directed radially at it and symmetrical from all sides, in addition to the forces which actually act on it, the superposed set of forces will be without effect on stability. To a first approximation, the effect of hydrostatic pressure is to superpose an additional system of forces of this character. But there are at least two factors which prevent this from being more than a first approximation. In the first place, an atom is not uniformly surrounded by neighbors on all sides, but the neighbors are situated at discrete points and so can only approximate a spherically symmetrical field. The approximation to a spherically symmetrical field is particularly crude at flaws. In the second place, when the structure is compressed, the atoms do not carry with them their original force fields undistorted (as is so often assumed in many approximate theories, and as we assumed above in our discussion of Poisson's ratio), but there is a distortion of the atomic force field which may have its own specific effect on the stability conditions. It is the combination of these two factors which determines the pressure coefficient of tensile strength, etc. VII Recently I have observed other kinds of fracture in connection with high pressure, and these have been so striking as to start me thinking again on this whole question of rupture, and to be the immediate occasion for this paper. The first example is that of a thick walled cylinder of hardened steel which was exposed to sufficient pressure on the outside to produce radial flow toward the center with permanent decrease of the diameter of the inside hole. On release of pressure, and after standing for some hours, a radial crack developed, starting at the inner wall and gradually working its way outward until it had prac-

tically reached the outside. The paradox in this situation is the development of rupture on release of the pressure that had produced the conditions of rupture. I had observed similar cracks in tubing collapsed by external pressure many years ago6 but had not then observed the gradual growth of the crack in time. It is natural to say "internal strains and internal stress" in connection with situations like this, in which a material has been previously subject to plastic deformation, but the mere words are not sufficient unless detailed examination shows that the internal stresses and strains are in the right direction. An exact specification of the distribution of strain after release of stress is at present impossible because we do not have sufficient knowledge of the general behavior of the material in the plastic range, but a rough qualitative picture is suggested by the known solution in the elastic range. From this point of view it seems plausible that after release of external pressure there should be a circumferential component of tensile stress in the inner layers, and a corresponding circumferential compression in the outer layers. The inner tension and the outer compression must always, no matter what the wall thickness, be related by the equilibrium condition that the integral along the radius of the tensile stress exactly balances the radial integral of the compressive stress. It is therefore not impossible to imagine that on first release of pressure the crack starts at the inner wall because of a high circumferential stress of tension at this point, but it is impossible to suppose that the crack spreads all the way to the outside under the action of this same tension, because this would demand in the final thin layer that separates the end of the crack from the outside surface a highly anisotropic distribution of tension and compression. If, however, one gives up the demand that rupture requires the presence of a certain stress component in the direction of rupture, the whole situation becomes understandable enough when one reflects that on release of external pressure there is a circumferential extension throughout the whole mass. Rupture occurs if this extension exceeds the limits within which stability is possible. The zero from which the significant extension should be calculated is obviously the configuration reached by plastic flow at the

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526 maximum external pressure. During plastic flow some lines of atoms must be crumpled and others extended, and some of the atoms permanently transported to new atomic environments. It is therefore not pertinent to consider that these atoms were once somewhere else, that is, to figure the strain from the initial configuration. Rupture under such conditions may thus occur on release of external load because by release of load a configuration is produced too far removed from the position of stability. The amount of plastic flow produced at the maximum pressure and responsible for rupture on release of pressure may be so small as not to be easily measurable. Thus I have observed many times, in closed glass cylinders with thick walls which have been exposed to the action of heavy external pressure, spontaneous fracture after release of pressure on the lapse of several days. There was no measurable change of dimensions after such exposure to pressure, but the mere fact of spontaneous rupture is itself peremptory evidence that some permanent change had taken place. The precise meaning to be attached to internal stress and strain in these situations evidently requires some analysis. The implication of the "internal" in these designations is that the external surface of the body is free and that one part of the body is acting against another. But we cannot define the internal stress in terms of the surface conditions unless we have knowledge of the properties of the body sufficient to enable us to integrate the stress-strain relations throughout the interior, and this we practically never have. We are driven to more indirect and hypothetical definition. Internal stress is comparatively easy to deal with—to find the internal stress at a point we may imagine a small piece of the body separated from the rest and find the forces which must be applied to the surface of this piece in order that its geometrical configuration shall be the same as when it was in its original position in the body. This is adequate to give unique meaning to the internal stress because it is known that the stress throughout the interior of a body is uniquely determined by the forces acting across the surface, independently of the elastic constants or other physical properties of the body, provided that the body is so small

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that the internal state of affairs can be treated as homogeneous. Whether the small piece of the body is actually reduced to the dimensions which it occupies in its original position must of course be determined by indirect means, such, for example, as by finding whether all such pieces into which the body can be imagined to be divided fit together so as to give the observed external shape to the body as a whole. This procedure for giving meaning to "internal" stress is the same as that for giving meaning in general to "stress at a point," and is unaffected by the previous history of the material or the stress in other parts. The internal strain at a point in a body is not so easy to deal with as the internal stress because of the complication of determining the appropriate zero from which to calculate the strain. We may, of course, calculate the strain from the initial configuration or from a condition of zero stress, but the results obtained by such definitions would have only a geometrical significance, and would not be especially revealing as to the internal state of the body. One can see this by reflecting that in reaching its actual configuration from its initial configuration lines of atoms are crumpled or otherwise permanently distorted, or that in releasing the element to a state of zero stress the element may rupture. In fact, the concept of internal strain does not seem to be a particularly valuable one when one is so far from the initial configuration that permanent alterations have been produced. But if one is so near the original configuration that all deformations remain within the elastic range, then internal strain becomes a useful concept, and it may be given simple experimental meaning, as in the case of transparent bodies by optical procedures. We have been using the words "stress and strain" in the technical sense in which they occur in the equations of elasticity theory, and we have already seen that in this sense they have meaning only from a large scale point of view. But we have already remarked that the words, particularly "strain," are often used in a less precise sense, which may give rise to confusion. In this less precise sense a body is said to be strained, or internally strained, if the atoms are in any sort of unnatural position which they tend to leave automatically. Such situations are very common, particularly in crystalline materials, as shown by the

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frequency with which recrystallization occurs after plastic flow. One may suspect that atomic rearrangements less complete than actual recrystallizations are very common, and that they may be easily initiated by a change in the external conditions. Atomic disarrangements are evidently capable of an almost unlimited complexity, and it is impossible to describe them with a few simple parameters. It is to be expected that fractures are often initiated at such disarrangements. It is evidently important to distinguish between large scale strain or strain proper and this sort of small scale strain, because when attempts are made to formulate conditions of rupture in terms of stress and strain it is the large scale strain which enters the formulations, whereas it is really the small scale strain which is operative. A very beautiful example of rupture on release of pressure and also against the stress is afforded by some recent experiments of D. T. Griggs.8 In these experiments he studied, among other things, the compressive strength of limestone as affected by a hydrostatic pressure, acting over the entire surface of the body, superposed on the compressive load. Very large effects were found— under high hydrostatic pressure a very much greater compressive load is required to crush limestone than is required at atmospheric pressure (600 percent more under 10,000 kg/cm 2 hydrostatic pressure), and before fracture very considerable plastic deformations in compression occur, whereas at atmospheric pressure the material is brittle. Griggs found in many cases that if the experiment were terminated by release of compressive load and then release of pressure before the occurrence of compressive rupture, but a/ter considerable plastic flow had taken place, the specimen was found, on removal from the apparatus, to be ruptured into discs on planes perpendicular to the original direction of compression. Although this sort of fracture was observed many times, Griggs for some reason did not describe it in his paper. The conditions in this experiment are particularly simple because the stress and deformation are homogeneously distributed throughout the mass. In particular, the component of stress across the plane prependicular to the axis of compression must be constant through the mass and must be equal to the

compressive force acting across the ends. This stress, therefore, is always a compressive stress, except at the moment of release, when it becomes zero. At no time can there be a tensile stress in any direction. In spite of the fact that the conditions on the stress are about as clean cut and unequivocal as it would be possible to devise, I think that many persons on seeing these fractures will find it difficult to resist the temptation to say "It pulled itself apart," so strong is the appeal of the old intuitive point of view. It is not difficult to see what must have happened in this experiment on limestone. During release of compressive load and hydrostatic pressure there is an extension of the body reckoned from the configuration which it had reached by plastic flow under the maximum load. This extension is greatest, of course, in the direction of the axis of compression. As long as the pressure is high, this extension takes place stably, because the atoms are still in sufficiently close contact in all directions. But when the pressure is reduced far enough, the corresponding extensions can no longer take place stably and the body ruptures across the planes on which the extension is greatest. The suggestion given by this example prepares us to expect many other examples of rupture on release of a state of stress which has been preponderantly compressive, but in which there have been sufficiently large differences between different components of stress to produce permanent deformations. Such conditions are not common in ordinary testing; if they had been more common we would not have our intuitive feeling that fracture must be produced by a corresponding component of stress. Although such conditions are not common in every day experience, they are nevertheless not infrequent. All through my high pressure experimenting I have been continually bothered by fractures that occurred during release of pressure. Or there is another sort of experience that many people must have had. Like other experimenters, I have made many attempts to form coherent bodies for compressibility or other measurements by compressing the powdered material into a cylindrical mold between pistons. Although some substances can be successfully molded in this way, there are many others which invariably fall apart on removal from the mold

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528 into disks, sometimes very thin, perpendicular to the axis. It is not necessary to argue after the analysis above that there can be no tensile stress producing these ruptures; it is sufficient to observe that on release of pressure there is an elongation in the direction of the axis. This elongation is obviously accentuated by the constraint exerted by the walls of the mold during release. Obviously the field, par excellence, in which to look for effects of this sort is geology. Many rocks have been plastically deformed at great depths, and then brought to the surface with release of mean stress. One would expect fractures of this sort to be common. It may, however, not always be easy to tell by mere observation of the fractured material that fracture must have been produced in this way. But there are examples in which this mechanism can be observed in actual operation. It is known that quarrying operations are often accompanied by fracture of the rock with extensions.' VIII In conclusion and summary, the problem of rupture is essentially a problem in stability; this has been too little appreciated in mathematical deductions of the conditions of rupture. The difficulties of a complete mathematical discussion of the conditions of stability seem at present to be prohibitive. But in any event it would seem that local irregularities, if of the right sort, may be expected to be important in initiating instabilities. The important part played by internal "Lockerstellen," or by surface imperfections, in the rupture of actual materials is therefore not surprising. Much of the recent work by various authors in discussing the conditions of rupture is thus of great value and applicable in many situations of practical importance. But I think that if one contemplates the whole field of all possible conditions of stress, and in particular the almost infinitely complicated atomic rearrangements that occur in plastically deformed material, one feels the need for the utmost generality of analysis. In particular, one would not expect any

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general criterion of rupture in terms of the large scale stress and strain of ordinary elasticity theory. The stability of every atom is determined by its position with respect to its neighbors; when its position relative to its neighbors is changed, as by the application of forces to the surface of the body, its stability will change also. Changes of relative position making for instability may be of various types. In this discussion the importance of one particular type has been especially dwelt on, namely, unusual extensions in particular directions and the corresponding rupture by separation of fibers. It is not intended to suggest that under proper conditions the accompanying shearing distortion may not result in a corresponding instability. The deleterious effect of relative extensions probably tends to be less when the substance is on the average in a compressed state, with the mean force between the atoms repulsive instead of attractive. Very roughly, it seems to be the extensions reckoned from a state of uniform compression which are the major factor in initiating this kind of instability. This appears not unreasonable. Cases occur, in substances elongated in one or more directions, of rupture with no corresponding stress component or of rupture against the direction of total stress. On release of mean pressure from substances plastically deformed under the action of stresses which are on the average compressive, elongations will occur, calculated from the configuration reached at the maximum pressure, which is the proper zero to use, and ruptures may therefore be expected on release of pressure and against the stress. Various examples of this sort of thing have been found. Bibliography 1. P. W. Bridgman, Rev. Mod. Phys. 7, 30 (1935). 2. P. W. Bridgman, J. Geol. 44, 653 (1936); J. App. Phys. 8, 328 (1937). 3. P. W. Bridgman, Phil. Mag. 24, 63 (1912); Proc. 2nd Internat. Cong. App. Mech. Zurich, 1926, p. 53. 4. Second reference under 3, p. 60. 5. D. T. Griggs, J. Geol. 44, 541 (1936). 6. P. W. Bridgman, Phys. Rev. 34, 16 (1912). 7. G. W. Bain, J. Geol. 39, 715 (1931).

SHEARING EXPERIMENTS ON SOME SELECTED MINERALS AND MINERAL COMBINATIONS. E S P E R S. LARSEN AND P. W. BRIDGMAN. ABSTRACT.

This paper presents a study of the effect of drastic shearing at room temperature under a mean confining pressure of 50,000 kg/cm s on various minerals or combination of minerals. Attempts to form the so-called "Stressminerals" were unsuccessful; other types of change were observed, however. In all cases the crystal structure was highly broken down, and many cases were found in which the product of shearing stress appeared under the microscope to be a perfectly transparent and isotropic glass with an index of refraction lower than that of the original material. The X-ray examination, however, gave no unambiguous evidence for the production of a true glass. Cristobolite inverts to a form with higher index, probably a new form of SiO. Opal is dehydrated and transformed in one case to quartz. Four pyroxenes are transformed to a phase with much lower index, possibly related to amphibole. Azurite is transformed to some substance with definitely different chemical properties. Gypsum loses water and is definitely changed. Siderite changes to a reddish substance, probably an oxide or hydroxide. Definite orientations are produced in many cases, many of these agreeing with results of Sander. INTRODUCTION.

In this paper a study is made of the effects of the combination of hydrostatic pressure and shearing stress at room temperature produced by the new apparatus of Bridgman1 on selected groups of natural minerals and mixtures, in the hope that it may throw some light on processes occurring in nature. We were encouraged in the expectation of positive results, because it had already been established that shearing stress is effective in producing certain reactions in inorganic compounds and also in initiating inversions at temperatures 100° to 150° lower than are effective without shear. The first set of experiments was made in an attempt to bring about some of the 1 Bridgman, P. W . : Phys. Rev. 48, 825-847, 1935, Jour. Geol. 44, 653-669, 1936, Proc. Amer. Acad. 71, 387-460, 1937.

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reactions that are believed by Harker and others to be favored or even determined by shearing stress. The second set was made in an attempt to bring about, by shearing, inversions and reactions from unstable to stable forms that are too sluggish under ordinary conditions to take place, even in geological time. The third set was designed for a study of the orientation of some minerals under shearing conditions. CONDITIONS OF T H E EXPERIMENTS.

The material under investigation takes the form of two thin discs, which are compressed between two hardened steel pistons and an anvil, as described in the papers of reference 1. The pistons are pushed against the anvil by a hydraulic press with any desired force up to the maximum of 50,000 kg/cm 2 on the pistons. Under this pressure the material of the discs flows out laterally from between piston and anvil until it is so thinned down that further extrusion is resisted by friction. A little consideration shows that, if the coefficient of friction is finite, the disc will ultimately come to an equilibrium thickness for any pressure, no matter how high. Because of deformation of the steel, the disc formed at high pressure is not of uniform thickness, but is lens-shaped, the center being thicker where the steel of piston and anvil is depressed more than at the edge. At the maximum pressure, 50,000 kg/cm 2 , the final thickness at the edge of the lens was of the order of 0.002 cm, and that at the center perhaps five times as much. The diameter of the disc is 6.35 mm. After the disc has reached its equilibrium thickness at any pressure and while pressure is still applied, shearing stress in addition is now produced by rotating the anvil between the pistons about the vertical axis. At pressures higher than perhaps 10,000 to 20,000 kg/cm 2 in these experiments the friction at the surface of the disc becomes greater than the internal plastic shearing strength of the material, the disc is frozen fast by friction to the surface of piston and anvil, and the rotation of the anvil is accompanied by internal plastic flow in the material of the disc. The shearing distortion accompanying this flow may be very high at the edge of the disc; with the usual thickness and usual rotation through 60° the shearing displacement at the edge of the disc is 120 radians. Toward the center the shearing distortion rapidly drops off, both because of the increased thickness of the disc and the smaller relative linear displacement of top and

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bottom surfaces of the disc. This is strikingly shown by the fact that by far the larger part of any transformations produced is confined to the outer parts of the discs. This in itself is sufficient to show that the effects are not produced by hydrostatic pressure alone, but shearing stress in addition is necessary. The fact that the affected material in most cases is confined to the edge of the disc enhances the difficulty of the analyses because of the very minute quantity of material available, which was of the order of 0.001 gm. The torque necessary to produce rotation was measured, and from this rough values of the shearing strength can be calculated. No attempt is made to reproduce the values of shearing strength in the following, however, because they showed too much variation to be of much significance. In general, the substances examined here are very strong in shear, and are usually brittle, so that the shearing displacement is accompanied by continual snapping and internal rupture; the smooth shearing shown by so many other substances is not often found. In fact, these materials put the utmost demands on the steel parts, which were more damaged than by most other materials. For this reason usually only a single double rotation forward and back through 60° was made at 50,000 kg/cm 2 , giving a total shearing distortion at the edge of the order of 250 radians. The total duration of application of shear was of the order of ten seconds. The shearing strength at the maximum pressure averaged between 10,000 and 15,000 kg/cm 2 . The materials were finely powdered, weighed and mixed, in those cases where mixtures in definite proportions were investigated, roughly formed by compression in a mold in an arbor press to discs coherent enough to stand careful handling, and then placed in position between piston and anvil. A number of the powders were prepared "wet," that is, the powders were wet with water before forming to the preparatory disc. Most of this water must have been squeezed out afterwards between piston and anvil, so that it is difficult to estimate how effective the wetting may have been. The temperature effects may be calculated from the energy required to produce rotation, which was performed at the rate of about 1 radian in 5 seconds, and the thermal conductivity of the steel parts. It turns out that under extreme conditions the rise of temperature is only 30° C., so that temperature can hardly play a part in whatever effects may occur.

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The samples were studied under the microscope both before and after shearing, and a selected group were studied by the X-ray powder method by Dr. Alden B. Greninger and Dr. R. R. Hultgren. The microscopic study showed that all of the discs were made up of a central part that is relatively thick and not much cracked and an outer part that is thinner and is broken into rings by numerous cracks concentric with the center of the disc. The central part has been less changed than the outer part; in most of the discs the minerals at the center show some granulation and shearing, but the particles are relatively large and can be easily identified as those of the powder before stressing. The outer rings show much more effect from the shearing, and the mineral particles are very small. In many of the discs in which more than one mineral was used, the individual minerals are too fine-grained and too intimately mixed to permit identification, and in some, these outer rings appear to be clear, isotropic glass. The X-ray analysis in general showed the patterns of crystalline material highly broken down. Doctor Greninger reports that he has never seen such highly distorted material—that it must be broken down "almost to the unit cells." Any positive results shown by the X-ray analysis are definite, and one may be sure that the indicated material is present. But negative results mean only that the suspected substance was not present in large enough quantities for detection and under the unfavorable conditions of these analyses this might mean 30 or even 50 per cent. In particular the X-ray analysis is incapable of distinguishing the presence of a rather high percentage of true glass. I. A N ATTEMPT TO FORM T H E "STRESS M I N E R A L S . "

The minerals we attempted to form were typical stressminerals, selected so as to be representative of those which under natural conditions are formed in the full temperature range corresponding to low- to high-grade metamorphism. The minerals used for the mixtures were in part amorphous or hydrous, as such minerals were thought to be more likely to react. The samples were all investigated in the "wet" condition, as water was necessary for some of the reactions, and it was believed that it might act as a catalyzer for others. None of the expected reactions or inversions to form stress-

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minerals took place, although several examples of other sorts of change were found. This failure is probably not entirely due to failure to carry on the shearing at temperatures within the range of actual metamorphism, since some of the expected reactions take place in metamorphism under so wide a range of temperatures that one may suspect that some capacity for reaction is left at room temperature. It cannot be denied, however, that a higher temperature, but still one low enough to be within the range of stability of the desired material, would have been more favorable. The use of higher temperatures was prevented by experimental difficulties. In further understanding of the negative results of this section it is to be considered that in nature most of these reactions are so sluggish that failure to reach equilibrium, even in geological times, is common among the metamorphic rocks. For example, andalusite may be only partially replaced by sillimanite. It is further to be considered that the natural conditions with regard to presence of water may not have been sufficiently well reproduced; it is well known that slowly moving solutions play an important part in bringing about metamorphic changes. The detailed results of the analyses are now given. In spite of the failure to produce any of the expected stress-minerals, there is probably enough interest in some of the other positive results which were found to justify this record in detail. The different experiments are distinguished by numbers. 1. Orthoclase and halloysite in the proportion to form sericite. The central part of the disc still shows the original orthoclase grains not much crushed. Nearer the edge the minerals form a sub-microscopic, fibrous aggregate that resembles the fine fibrous groundmasses of many rhyolites. The fibers are oriented radially and the high index of refraction (γ') is along the length. The mean index of refraction of this submicroscopic aggregate varies somewhat and averages about 1.535. This is about the mean index of refraction for the original mixture of orthoclase and halloysite; probably no new minerals were formed. There has been an orientation of the orthoclase. Greninger found that the sub-microscopic part of the outer ring of the disc showed the lines of orthoclase but that the lines of halloysite had disappeared. 2. Orthoclase and diaspore in the proportions to form seriate. The central part is still orthoclase and diaspore. The material of the outer rings is sensibly isotropic and has an index of refraction that varies from 1.57 to considerably less. 1.57

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is about the mean index of refraction of the original mineral mixture. The material with lower index of refraction may possibly represent the presence of some glass. However, probably no new minerals were formed and little or no glass. Greninger made X-ray photographs of the original mixture (not sheared) and of the outer nearly isotropic shell and reports: "The pattern of the sheared mixture shows the lines of both orthoclase and diaspore with diaspore predominating. For the original powder, diaspore gave the stronger lines." 3. Halloysite and K 2 C 0 3 . 2 H 2 0 in the proportions to form sericite. The outer part of the charge is made up of a fine aggregate with the following optical properties, which are the properties of an aggregate: mean index of refraction varies, but averages 1.54; birefringence rather strong; optically — ; 2V moderate. In many parts aggregate interference figures are in the field of the microscope. This is probably a mixture of halloysite and anhydrous K 2 C0 3 . The crystals have been rather well oriented. 4. Chlorite and sericite in the proportions to form biotite. The central part is made up of grains of green chlorite ( ω = 1.615) and colorless sericite. The outer part is a very finestreaked mixture of the two minerals. The sericite (and perhaps also the chlorite) are well oriented with y' normal to the concentric cracks. The aggregate interference figures of the sericite are in large part oriented with the acute bisectrix in the field of the microscope and about 90 per cent show the plane of the optic axis radial and normal to the concentric cracks. Some of the extreme outer part is sub-microscopic and has streaks of opaque dust, as if some decomposition had taken place. 5. Chlorite, K 2 C0 3 , and Si0 2 in the proportions to form biotite. The small amount of the charge adherent to the piston was nearly or quite isotropic and had an index of refraction of about 1.575. This might be a mixture of the original minerals. 6. Calcite and wood opal in the proportion to form wollastonite. It is a very fine mixture of calcite and opal. The calcite is biaxial and tends to be oriented with the optic axis normal to the cake. These data were obtained from aggregates of very fine grains. 7. Dolomite and wood opal in the proportions to form diopside. There was no reaction. Optical data on the dolomite aggregates are: biaxial, Bx a nearly normal to the disc. Some of the sheared opal has η = 1.52 + .

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8. Siderite and opal in the proportion to form FeO.SiO,. After shearing the siderite was changed to fibrous aggregates of a reddish material with a high index of refraction and rather strong birefringence. Particles of opal were still present in the central part of the disc. The siderite was broken down to some unknown material, but there probably was no reaction with the opal. 9. Andalusite. This yielded a thin layer of vitreous material so hard and tightly welded to the steel piston as to require a diamond point to separate it from the piston. The central part is very finely granulated andalusite. The outer part is chiefly finely crystalline to sensibly isotropic and has a mean index of refraction of 1.64. There are some patches and very tiny (up to 20μ) rounded globules of isotropic material, with an index of refraction as low as 1.56. It is probably glass, perhaps due to some impurity; it is in any event improbable that the highly refractory Al 2 Si0 5 was fused. Nothing that resembles cyanite was found. An X-ray study by Hultgren of the isotropic outer shell indicates a "probable change." The optical data are uncertain, but show that any new form cannot be sillimanite or cyanite. 10. Colorless diopside and H 2 0 . The inner part of the disc is diopside strained and crushed (γ =1.69). Some of the outer part is sensibly isotropic, but some is very finely fibrous and birefracting. The mean index of refraction of the isotropic part is near 1.62, that of the fibrous part about 1.64. The β index of refraction of the original diopside was 1.678 and y was 1.699. The microscopic data indicate that the outer fibrous aggregate is not diopside. The mean index of refraction of a tremolite with about the iron content of the original pyroxene but with some H 2 0 and a different ratio of CaO to MgO would be about 1.616. The fibrous aggregate is therefore not ordinary tremolite, but it might be an impure tremolite lacking H 2 0 and of somewhat unusual composition. However, Greninger found that the X-ray pattern of the outer part of the stressed diopside disc is the same as that of diopside. 11. Green augite from Iron Hill, Colorado and H 2 0 . (a = 1.688, β = 1.697, y = 1.719). The central part of the disc is crushed pyroxene. The outer rings are matted radial fibers with extinction angle, negative elongation, β ranging from 1.675 to 1.685. Hultgren found that the original pyroxene and the outer ring of the sheared pyroxene gave the same

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X-ray pattern. The same pyroxene sheared dry was like the original mineral except for a little material with low index of refraction. 12. Augite from Renfrew, Canada, and H 2 0 . (β = 1.725, y = 1.74). The central part of the disc is granulated pyroxene. The outer part is in radial fibrous aggregates with y normal to the disc and ο nearly radial. The mean index of this fibrous material is variable but averages about 1.69 and is lower in the very fine-grained and sub-microscopic parts. Hultgren studied the X-ray patterns of the original pyroxene from the central part of the disc and of the fibrous material of the outer rings and found the latter much more shattered than the former, but could detect no other change caused by the stress treatment. The pyroxene from Renfrew sheared dry has a thick inner part to the disc that is nearly opaque, due to its thickness, but appears to be unchanged pyroxene. The outer ring of the disc is thinner and is made up of matted fibers radiating from the center, with a = 1.697 parallel to the fibers and γ = 1.71. Some parts are nearly isotropic and have a lower index of refraction. 13. Bronzite from Stillwater Complex, Montana, and H 2 0 . (y = 1.681.) It yielded a disc with a central part not adherent to the piston and an outer part that was welded to the piston. The central part is sub-microscopic to isotropic and has η about 1.64. The outer part, welded to the plunger, resembles a clear glass and has η — 1.62. From the X-ray patterns of the original bronzite and the central part of the disc Hultgren concluded that there was probably no change. Another disc of bronzite had a central part made up of rather coarsely crushed bronzite separated rather sharplv from the outer rings that were made up of very finely crystalline to submicroscopic or isotropic material with an index of refraction of about 1.65. The bronzite sheared dry has a central part of the disc made up of finely granulated bronzite and an outer ring that is for the most part bronzite but has a little material in radial fibers with y parallel to the fibers and η = 1.645 to 1.655. Some clear parts are made up largely of the material with a low index of refraction. All four of the sheared pyroxenes studied above have much lower indices of refraction than those of the original mineral. This indicates an inversion to a new phase possibly related to amphibole. However, the X-ray data for all four pyroxenes are negative The outer rings of sheared clinopyroxene are

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made up of matted fibers with extinction angle and negative elongation. 14. Hornblende, dark green, (a = 1.679, β = 1.695, γ = 1.698.) Sheared dry it is much like the original hornblende except for some material in the outer shell that is sensibly isotropic and has η below 1.68. Sheared wet, the central part of the cake was not changed much. The outer part is made up of minute matted, radial fibers with γ parallel to the elongation. T h e mean index of refraction is 1.673. Hultgren reports that X-ray data on the original and the stressed hornblende show no change. 15. Garnet f r o m Bohemia, pale pink, isotropic crystals with η = 1.745. Sheared dry, it gave a fine aggregate of distinctly birefracting material even in the center of the disc with η about 1.72. Greninger states as a result of his X-ray study: " T h e original pattern showed very sharp lines. T h e pattern of the sheared garnet gave the same pattern as the original garnet, with practically no change in line sharpness. This material differs f r o m all others examined in that the shearing has had practically no effect on the quality of the X-ray lines." There was probably no change in the garnet in spite of the optical data. Greninger comments that the presence of sub-microscopic cracks is to be considered as an explanation of the low index of refraction. II. INVERSION A N D DEHYDRATION.

T h e first two investigations in this group were made on forms of silica, since they are promising minerals f o r the study of shearing as a catalyzer in mineral inversions. They have a simple and uniform composition, their stability relations are well known, and they are chemically stable. They have practically zero rate of inversion under ordinary conditions, as the unstable forms, tridymite and cristobalite, have persisted without appreciable inversion since Miocene time or earlier. Even at temperatures above 1000° C., without a flux, their rates of inversion are not appreciable in the laboratory. 16. Cristobalite. Cristobalite has a specific gravity of 2.34, while quartz has a specific gravity of 2.65 ; hence the difference in density is large and some change is to be anticipated. Artificial cristobalite made by heating quartz sheared dry became birefracting and had a mean index of refraction of 1.486. A f t e r subjecting a wetted sample to shearing the whole

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of the disc was made up of matted birefracting material. Most of the material has an index of refraction of about 1.515, but a small part has η greater than 1.53 and another small part has η less than 1.51. Greninger reports that "the X-ray pattern of the sheared sample shows considerably more resemblance to the tridymite pattern than to the original cristobalite pattern, although it is not possible to state definitely that the sheared material is tridymite. The pattern of the sheared material shows no resemblance to quartz. A fairly definite change was caused by the shearing." It appears, then, that both the microscopic and X-ray data for cristobalite show a change on subjecting to shear. The microscopic data was thought to mean a partial inversion to quartz. The X-ray patterns resemble that of tridymite, but the material cannot be tridymite, as the index of refraction of tridymite (n = 1.470) is somewhat lower than that of cristobalite, while the stressed material has a much higher index of refraction( η = 1.52). A reasonable interpretation is that a new form of Si0 2 not hitherto known has been formed. 17. Opal. This, the hydrous form of silica, also has a low density, so that again changes may be anticipated. A wood opal from Sonoma County, California, was originally sensibly isotropic, had an index of refraction of 1.452, and gave an X-ray pattern resembling that of cristobalite. It contained numerous microscopic tubes of air. After subjecting to shearing, without the addition of water, the inner part of the disc became a mass of matted fibers that are faintly birefracting and that tend to have their high index of refraction and elongation radiate from the center of the disc. The mean index of refraction varies ± 0.005 and averages 1.477. A powder that probably represents the outer part of the disc contains some opal but is made up for the most part of faintly birefracting matted fibers that have a somewhat variable index of refraction which is as high as 1.49 in some parts. Doctor Greninger examined both the original, unsheared wood opal and the central part of the disc of opal after subjecting to shear. He states, "The pattern of the original opal greatly resembles the cristobalite pattern, but is definitely not exactly the same as the cristobalite pattern. The sheared material has suffered no change other than a considerable shattering. The pattern of the sheared material is considerably different from that of cristobalite sheared (wet)."

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91

These data show that the original "opal" was made up chiefly of submicroscopic cristobalite with the addition of water and that shearing drove off most of the water but did not invert the cristobalite. Opal variety hyaline from Mexico. Under the microscope the original hyaline shows good birefringence and a fine radial structure. The fibers have negative elongation and an average index of refraction of 1.459. Greninger found that the X-ray pattern shows the sample to be very close to amorphous, with a few very weak and broad bands. After shearing, the inner part of the disc shows a mottled birefringence and an index of refraction that varies ± 0.01 but averages about 1.492. The outer rings are cloudy, nearly isotropic, and have an index of refraction of 1.51 ± 0.005 Greninger took an X-ray photograph of the outer rings and states: "The X-ray pattern shows the material to be at least partly crystalline. The lines are very weak but sharp; the pattern is almost identical with that of quartz. It is different from the stressed cristobalite, which appeared to be similar under the microscope (n = 1.52)." He regards the evidence of the transformation to quartz as perhaps the most unequivocal of all the X-ray results. 18. Azurite. Azurite sheared dry remains blue with some dark opaque streaks and a little green material on the borders. This sheared material effervesces actively in AsBr3 and leaves a brownish residue, while the original azurite is not acted on by AsBr3. There must have been some chemical change or inversion. 19. Goethite, sheared dry, was probably not changed. 20. Gypsum. The disc of sheared gypsum has a central part that is still gypsum. This part is made up of concentric layers that have different birefringences and are themselves made up of fibers across the layering. Another set of layers (twinning?) is at 35° to the main layering. X = Bx a (?) is normal to the disc, 2V appears large, and the extinction angle measured against the layering is large. The outer rings are filled with black iron( ?). They are made up of radial fibers with γ = elongation and X(Bx 0 ?) normal to the disc. They have a mean index of refraction of 1.56 and are not gypsum. Greninger found that "the central portion of the disc (gypsum) gives fairly good X-ray lines and the black portion (outer rings) gives faint lines, and the lattice has been greatly shat-

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Bridgman—Shearing

tered, but evidence is definite that the pattern is different from that of the white portion. The pattern of the black portion does not resemble the pattern of anhydrite nor that of plaster of Paris (hemihydrite). There is a fairly definite change." The outer rim (dark part) must be either the monohydride or soluble anhydride. A number of the substances examined in the attempt to form "stress-minerals" gave results bearing on the question of inversion and dehydration. The following brief recapitulation is therefore made of results already given in section I. Andalusite after shearing looks like an isotropic glass under the microscope, but its X-ray data indicates that andalusite is still predominantly present. The pyroxenes and hornblende after shearing have lower indices of refraction than the original minerals. The X-ray data give no positive indication of inversion. Garnet after shearing has become distinctly birefracting and has a lower index of refraction than the original mineral, but the X-ray data indicate no change in crystal structure. Siderite is changed by shearing to a reddish material, probably an oxide or hydroxide. III. ORIENTATION OF THE SHEARED MATERIALS.

As the sheared minerals are all in a very fine state of subdivision, all the optical data are approximate and are derived from aggregates. The orientations observed on these aggregates give only approximate petrofabric data. 21. Sericite. Sheared wet, the sericite plates have a good aggregate orientation. Bx a is normal to the disc, and the plane of the optic axis is about radial, which is normal to the rings. This makes the gliding plane of sericite the base and the direction of transport the normal to the optic plane and agrees with the data given by Sander.2 22. Calcite. Sheared dry, most of the fragments are aggregates. The aggregates appear to have a medium to small axial angle and the acute bisectrix is nearly normal to the disc for many of the plates. Calcite has recently been found to have at least two polymorphic transitions at pressures below 50,000 kg/cm 2 . Orientation phenomena may be connected with the transitions. A similar possibility is to be considered in specu' Sander, Bruno: Gefügekunde der Gesteine, Julius Springer, Wien, p. 323, Diagrammen 119, and p. 215, 1930.

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93

lating on the explanation of orientation phenomena in other substances. 23. Dolomite gave the same orientation as calcite—the optic axis nearly normal to the disc. The orientations of calcite and dolomite appear to agree with those found by Sander for these minerals in metamorphic rocks. 24. Quartz after shearing had a fair orientation with the c crystal axis in the plane of the disc and tangential to the outer ring of the disc. (η averages about 1.545.) This would make c the direction of transport, which is the common orientation in the quartz of some metamorphic rocks.3 The following three substances have already been described in another connection in the earlier sections. Hornblende after shearing yielded matted fibers that have positive elongation and that are oriented radially. The fibers, therefore, appear to be parallel to the b fabric axis. Pyroxenes after shearing tend to have the fibers radial and on extreme shearing give moderate extinction angles and negative elongation and y nearly normal to the disc. Orthoclase in mixture with halloysite after shearing yielded a finely fibrous mass. The fibers have positive elongation and are elongated radially (along the b fabric axis). In general summary of the orientation results, quartz is poorly but distinctly oriented, sericite and carbonates are well oriented, and all of these minerals appear to follow the laws of orientation given by Sander. After shearing, hornblende, pyroxene, and orthoclase tend to yield fibers elongated radially. SIGNIFICANCE TO GEOLOGY.

In nature, the various forms of mylonite, including pseudotachylite, are formed under conditions of compression and shearing that closely resemble the conditions of the experiments reported in this paper. Nearly all the types of mylonite-structures were reproduced in our experiments. The ultramylonites and pseudo-tachylites are much like the submicroscopic and isotropic materials produced in the laboratory. Attempts to form the stress-minerals were not successful. This is not surprising, since the temperatures of the experiments were not altogether favorable and the time of shearing 8

Sander, Bruno: loc. cit., p. 312, pp. 180-184, 306-307, and 312.

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was short. We know that many of the reactions during metamorphism are extremely slow, requiring geological time. Mica, carbonates, and quartz were oriented by shearing and in general, they follow the common types of orientation given by Sander. Many of the fibrous minerals were oriented with their elongation along the b-tectonic axis. Acknowledgment is made of a grant from the Milton Fund of Harvard University with which part of the expenses of this investigation were met. RESEARCH LABORATORY OF P H Y S I C S , HARVARD UNIVERSITY, CAMBRIDGE, M A S S .

THE HIGH PRESSURE BEHAVIOR OF MISCELLANEOUS MINERALS. P. W. BRIDGMAN. ABSTRACT. Calcite is found to have two new transitions at high pressure, one running at about 14,000 kg./cm." nearly independent of temperature between 0 e C. and 200° G, and the other running from about 17,000 at 0° to 28,000 at 200°. The compressibility is roughly measured up to 50,000. The compression of quartz glass is measured up to 50,000; it is found that the previously known abnormal increase of compressibility with rising^ pressure abruptly ceases at about 35,000, and from here on compressibility decreases with rising pressure as is normal. The compressibility of basalt glass becomes nearly constant between 25,000 and 50,000. _ Explorations up to 50,000 to find new transitions of a number of common minerals are described, mostly with negative results. Exploration for new modifications is also made by the shearing method; it is probable that there is a transition for pyroxenite. Finally, wurtzite is found to be irreversibly changed to sphalerite by shearing at room temperature. INTRODUCTION.

In this paper are collected the results of an examination in my new pressure range up to 50,000 kg./cm. 2 of a few of the physical properties of several substances of geological interest which I have not had opportunity to publish elsewhere. The properties examined are polymorphic transition, compressibility, and behavior under shearing stress. Many of the results were negative, and the accuracy of some of the measurements is low, but in spite of this I think the results are perhaps worth recording because of the extent of the pressure range. The general experimental methods have been sufficiently described in previous papers.1 THE TRANSITIONS OF CALCITE.

Five different set-ups in all were made for the measurements of this substance. The first two set-ups, made with the apparatus used previously in transition and compressibility measurements up to 50,000 kg./cm.2, and referred to hereafter as the first apparatus, were made on Solenhofen limestone and a pure white Vermont marble. Each substance was examined both at room temperature and at 150° C. The final run on marble was terminated by an explosion. Both of these calcite rocks exhib-

it 27—3363

8

P. W. Bridgman.

ited at both temperatures a somewhat sluggish transition, with volume change large enough to be easily determined. The sluggishness might be ascribed either to the small grain size or to impurities. The next two set-ups were made also with the first apparatus with clear crystals of Iceland spar. The transition found with Solenhofen limestone and marble was again found, at about the same pressure as before, and in addition another transition at somewhat lower pressures, and with a change of volume seven times smaller, so small that an accurate determination of it could not be made. The transition runs sharply, however, so that good values for the transition pressure could be obtained. With the first of the two set-ups with Iceland spar, measurements were made at room temperature, 75°, and 133°. This set-up was terminated by an explosion. With the second set-up runs were made at 105° and 167° ; the latter run also was terminated by an explosion. The fifth and final setup, also with clear Iceland spar, was made with a new apparatus not yet described in print. An improved method of external support of the pressure chamber reduces the distortion of the apparatus and also volume hysteresis, so that satisfactory measurements of compressibility can be made on substances of much less compressibility than could be measured with the first apparatus. An additional advantage of the new apparatus is that it is about three times as sensitive as the first apparatus. With this improved apparatus measurements were made at room temperature of the transition parameters of the smaller transition, the volume change being obtained with much greater accuracy than was possible with the first apparatus (however, the average of six determinations with the first apparatus agreed within one per cent with the value of the improved apparatus). The average deviation from the mean of a single determination of the change of volume of the larger transition (there were seven determinations in all) was about ten per cent. The transition pressures with the two pieces of apparatus were in good agreement. The essentially new results obtained with the improved apparatus were measurements of the volume over the entire pressure range up to 50,000 kg./cm. 2 The volumes of the low pressure phase are not particularly accurate, the apparatus being insensitive at the lower pressures, and previous measurements2 made with a more sensitive type of apparatus up to 12,000 are certainly to be preferred for the low pressure modification. The values obtained

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High Pressure Behavior of Miscellaneous Minerals.

9

with the present apparatus for the high pressure phase are of course new. The intermediate phase is stable over such a short pressure range that it was not possible to try for its compressibility. The results are collected in figures and tables. In Fig. 1 is shown the phase diagram, in Table I the transition parameters, and in Table II the volumes as a function of pressure up to TABLE

I.

Transition Parameters of CaCOs. Pressure kg./cm.2

Temperature Centigrade

15,000 14,500 14,000 13,500 13,000

0° 50 100 150 200

—0.1 —0.1 -0.1 —0.1 —0.1

16,700 19,570 22,440 25,300 28,170

0° 50 100 150 200

.0175 .0175 .0175 .0175 .0175

dT dp

Δν cm.'/gm.

Latent Heat kg. cm./gm. gm. cal./gm.

I-II .00135 .00135 .00135 .00135 .00135

3.68 4.35 5.03 5.70 6.37

.086 .102 .118 .133 .149

.00956 .00956 .00956 .00956 .00956

149.7 177.2 204.5 232.0 259.4

3.50 4.15 4.80 5.44 6.08

II-III

TABLE

II.

Volume Decrements of CaCOs, cm.8/2.711 g m . Pressure kg./cm.' 5,000 10,000 15,000

AV 0066 0130 0192 Transitions

20,000 25,000 30,000 35,000 40,000 45,000 50,000

077 082 087 092 096 099 102

50,000 kg./cm. 2 at room temperature of 2.711 gm. of calcite (that is, the quantity which occupies 1 cm.8 under normal conditions). The first three volumes, at 5,000, 10,000, and 15,000,

10

P.

W.

Bridgman.

are taken from previous work,2 and are given to one more significant figure than the results at 20,000 and above obtained in this work. The figures obtained in this work at 5,000, 10,000, 200f

LjJ

0

£

1

ι L

Qu

UJ Q_

\

ΊΓ

1

IOO-

1-

UJ

H

/ / π

/

50*

14

IftOOO

Ιβροο

20,000

26.000

PRESSURE CaC03 Fig. 1. The phase diagram of CaCOa, temperature in degrees Centigrade against pressure in kilograms per square centimeter.

and 15,000 were 0.006, 0.012, and 0.017 respectively, somewhat less than the previous values. An interesting feature of the compressibility is the large jump upward of compressibility on passing from phase I to

127 — 3366

High Pressure Behavior of Miscellaneous Minerals. 11 phase III, in spite of the fact that the volume of III is smaller. This jump is so large as to be beyond any possibility of experimental error. The compressibility of III drops with rising pressure, as is normal, but does not sink to the compressibility of I at the transition point until a pressure of the order of 40,000 is reached. The question of the nature of the transition is of interest. In general, two different sorts of transitions can be recognized ; in one, the new modification is generated from the original modification by a comparatively minor geometrical rearrangement, perhaps a rotation of molecules, or a displacement of planes as wholes, which disturbs the original structure to such a slight extent that when the reverse transition is allowed to run the primitive crystal orientation is recovered. A well known example of this is the low temperature inversion of quartz. In the second type of transition a much more drastic rearrangement is involved, so that when the reverse transition occurs the primitive orientation is not recovered, but what might originally have been one crystal is broken up into a multitude of grains with haphazard orientations. The distinction between these two sorts of transition could not be established in the apparatus with which transitions and compressibility were measured, because the specimen is so seriously distorted in any event by the medium by which pressure is transmitted (lead or indium) that any specific effect of the transition is obscured. But with another apparatus, capable of a maximum of only 30,000 instead of 50,000 kg./cm.2, pressure is transmitted by a true liquid, so that the mere act of applying and releasing pressure produces no distortion in the specimen. With this apparatus I subjected a small clear crystal of Iceland spar to 30,000 kg./cm.2 at room temperature, this being about 11,000 kg./cm.2 higher than the higher transition pressure. The original orientation was noted. Mr. D. T. Griggs was kind enough to make a microscopic analysis of the results. The specimen was found fissured by many cleavage planes, all in the direction of the original cleavage. New cleavages, artificially made after release of pressure, also had the original direction. It thus appears that after the four transitions, two with increasing and two with decreasing pressure, the original orientation is recovered. Both the transitions, I-II and II-III, must therefore be of the less drastic type. The volume

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P. W. Bridgman.

change of the larger of these two transitions is about 2.6 per cent, not large enough to make this result too unexpected. The transition II-III probably does not occur under geological conditions, the rise of temperature with pressure along the transition line being considerably less rapid than the accepted natural rise of temperature with pressure at depth in the earth's crust, so that in the crust the temperature is always too high at the prevailing pressure for the transition II-III. On the other hand, the transition line I-II is retrograde, so that unless some new transition occurs, at depths below 40 or 50 km. the transition I-II may be expected in the crust. COMPRESSION

OF QUARTZ

GLASS.

Si0 2 glass has the unusual property in the pressure range in which it has been previously studied,3 that is, up to 12,000 kg./ cm.2, that its compressibility increases with increasing pressure, so that the curve of Δ ν , plotted against pressure, is convex toward the pressure axis. This is the sort of behavior that would be exhibited by a structure containing lenticular cavities which are squeezed flat by the pressure, yielding more and more easily because of change of geometrical configuration as they get flatter. In such a structure, the effect would disappear as soon as the lenticular cavities had been squeezed completely flat, so that the opposite walls are in contact. The question suggests itself whether similarly the effect may not disappear in Si0 2 glass at a high enough pressure, above this pressure the curve of AV becoming concave toward the pressure axis, as is normal. The compression was measured at room temperature to 50,000 kg./cm. 2 in the new, improved apparatus. The proportional changes of volume, that is, AV in cm.3 per 2.206 gm. of Si0 2 glass, are given in Table III. The results of the direct measurements were adjusted by an additive constant amounting to one per cent of the maximum effect, in order to secure as good agreement as possible with previous results at 5,000 and 10,000, where the present method is not sensitive. As it is, the tabulated values are still somewhat irregular. Experimental accuracy does not justify the fourth decimal place given for the absolute volume decrement, but four figures are necessary to give smooth first differences.

127 — 3368

High Pressure Behavior of Miscellaneous Minerals. TABLE

13

III.

Volume Decrements of Si0 2 Glass, cm.3/2.206 gm. Pressure kg./cm. 2 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000

Δν 0137 0277 0421 0570 0724 0882 1040 1163 1281 1394

First Differences of AV .0137 .0140 .0144 .0149 .0154 .0158 .0158 .0123 .0118 .0113

The expected effect is found. At a pressure not far from 35,000 kg./cm. 2 , the upward curvature stops, there is a cusp or at any rate a region of abnormally rapid curvature, and at

PRESSURE Kg/cm2 Si0 2 GLASS Fig. 2. The deviations from linearity of the volume decrements of quartz glass plotted against pressure. The cusp in the curve marks the change from abnormal to normal behavior.

higher pressures compressibility drops with rising pressure, as is normal. The abruptness of the effect is well shown by plotting differences from linearity against pressure, in Fig. 2. Professor J. C. Slater has suggested that it might be profitable to search for an explanation of the effect in the behavior

127 — 3369

14

P. W. Bridgman.

of the bond Si — Ο — Si, which is known from work of Warren to be straight in quartz glass, but is bent at a definite angle in crystalline quartz. Pressure might perhaps be expected to force the bond in glass in the direction of the crystal, with progressively increasing loss of geometrical advantage. The return to normal behavior at high pressures may possibly signify an eventual freezing of the bond at the angle of the natural crystal. It was already known from work of Birch and Dow4 that at higher temperatures the abnormal increase of compressibility with pressure becomes less pronounced and presumably eventually disappears. This, combined with the result just found, makes it probable that under geological conditions the phenomenon is not of importance; it is, however, of great interest because of the light it throws on the structure. COMPRESSION OF BASALT GLASS.

Two sets of measurements were made on artificial basalt glass. The first, with the first and less accurate apparatus, gave irregularities at both room temperature and 150° that suggested the possibility of a small transition. The material was accordingly reexamined at room temperature with the new improved apparatus. The proportional changes of volume (cm.8 per 2.7 gm.) are given in Table IV, keeping one more significant figTABLE I V .

Volume Decrements of Basalt Glass, cm.8/2.7 gm. Pressure kg./cm.' 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000

Δν Olli 0210 0300 0385 0463 0543 0622 0701 0779 0858

ure than is justified by the absolute accuracy in order to give smooth differences. Up to about 25,000 it will be seen that compressibility drops with rising pressure, as is normal, but here the drop ceases almost abruptly enough to amount to a

127 — 3370

High Pressure Behavior of Miscellaneous Minerals.

15

cusp on the volume curve, and from here on the compressibility is approximately constant, independent of pressure. The irregularity found with the first apparatus, suggesting a transition, was doubtless connected with this cusp. In explanation, one is reminded of Si0 2 glass—some molecular adaptation to pressure that exhausts itself. It is to be remarked that we are again concerned with a glass, and such effects are more to be expected in a glass than in a crystal. The values of AV shown in Table IV at low pressures are notably higher than previous values® found for the same material. It is to be remembered that the present apparatus is inaccurate at low pressures, where results have to be obtained by a relatively uncertain extrapolation. MISCELLANEOUS TRANSITION EXPLORATIONS.

Polymorphism is known to be of such frequent occurrence among simple compounds that it must be recognized as an important factor in any speculations about the nature of the material in the earth's crust. The actual discovery in the laboratory of polymorphism in the constituents of the crust is therefore of much importance, all the more since our theoretical understanding of the solid state is not yet sufficiently advanced to permit predictions of the occurrence of polymorphism. A number of natural minerals were therefore examined. These examinations were made with the first apparatus, which is the apparatus used in collecting all my previously published results on polymorphism to 50,000. No large transitions, comparable with that described above for CaCOs were found, and in fact no absolutely certain evidence was found of any at all. All the minerals investigated are comparatively incompressible, and are mechanically rigid, with high internal friction. This means unusually great irregularity in the results, and unusually large hysteresis between increasing and decreasing pressure. Attempts were made to calculate rough values for the compressibility from the data, but the attempt was abandoned because of too great irregularity. The failure to find transitions must not be taken to mean that transitions do not occur in these substances under geological conditions, where the temperatures corresponding to pressures of 50,000 are very much higher than 150°, the maximum

127 — 3371

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P. W. Bridgman.

temperature of this work. It has already been found that transitions are much more frequent among substances with low melting points. The presumption is that the higher melting substances also have other phases, but that the transitions are suppressed by viscosity at the lower temperatures. A positive result of a transition exploration is at once applicable to geological conditions, but on the other hand a negative result in the laboratory does not mean that there is no transition under geological conditions. For the specimens I am indebted to Dr. Francis Birch, who placed at my disposal specimens that he had already used in determining the effect of pressure on rigidity; detailed descriptions of the specimens are given in his paper.6 The details of the explorations now follow. Gabbro, from Mellen, Wis. Two different set-ups were made. There were irregularities in the results which may possibly mean a transition of the second kind (discontinuity in the compressibility), or possibly an ordinary transition with very small volume change. The pressure of the irregularity was in the neighborhood of 23,000 kg./cm. 2 on the first set-up and 19,000 on the second. The transition pressure appears to be little affected by temperature. Diabase, from Vinal Haven, Maine. Two suspicious irregularities were found at 150°, at 28,000 and 15,000 kg./cm.2, the possible fractional volume discontinuity being of the order of .0005. This result, was not, however, checked by repetition, and in view of experience with other materials there is no positive assurance that the irregularities were not instrumental. Pyroxenite, from the Transvaal. Four set-ups in all were made with this material. The first was terminated by an explosion at room temperature during release of pressure after reaching the maximum. The second set-up gave successful runs to the maximum both at room temperature and 150°. It seemed to be perfectly certain at 150° that there was a transition on release of pressure at some pressure greater than 18,000 kg./cm.2 To check this, a repetition was made, but again there was an explosion at room temperature, just below the intended maximum. The fourth and final set-up gave two successful runs at room temperature and 150° up to 50,000 and back. Again at 150° unusually large irregularities were found, this time in the neighborhood of 25,000 and both with increasing and decreasing pressure, but the pattern previously found was

127 — 3372

High Pressure Behavior of Miscellaneous Minerals.

17

not followed. The existence of a transition cannot therefore be regarded as definitely established, but it seems highly probable that there is a transition with small volume change, and that the failure to obtain an exact repetition is due to viscosity, which may produce capricious results. This would be the explanation of the failure of the transition to be manifest with increasing pressure on the first application at 150°, and also for the failure to find it at all at room temperature. My feeling that there is probably a transition is strengthened by the results obtained by the shearing method, to be described later. Anorthosite, from New Glasgow, Quebec. Exploration was made with a single set-up, once at room temperature, and twice at 150°. There was an irregularity on the first application at 150°, which however, was not found on repetition. There is probably no transition large enough to detect with this apparatus. Dunite, from Balsam Gap, N. C. Runs at room temperature and 150° were made with a single set-up. The cylinder was found split on the termination of the run, so that a repetition would have demanded a new set-up. There is probably no transition. Granite, from Quincy, Mass. Nothing was found with a single set-up at room temperature or 150°. The only reason for trying this complex combination of minerals is its importance as a constituent of the crust. SHEARING EXPLORATIONS.

In addition to the explorations for transitions recorded above by the method of volume discontinuity, several minerals were also examined by the shearing method.7 This is a qualitative method, which past experience has shown discloses the existence of transitions in perhaps 90% of the cases in which the volume method also discloses them. In addition, transitions may be found by this method which are not detectible by the volume method, the reason being that the drastic deformation by shearing decreases the inhibiting effect of internal viscosity—in general one can expect to find transitions by the shearing method 100° to 150° below the temperature at which they become suppressed by internal viscosity for the volume method. The following substances were sheared by the conventional procedure: olivine, feldspar, obsidian, basalt (artificial), and pyroxenite. The first four gave negative results. The last

18

P. W. Bridgman.

was sheared twice, since the first measurements gave evidence of a transition. The effect was found again on the second application. It was the results of these shearing measurements that accounted for my persistence in making four set-ups with the volume apparatus. In general, the behavior of these minerals under shear was that typical of the harder minerals—great shearing strength at high pressures, so that the steel pistons were always badly damaged, and also failure by snapping, that is, internal rupture, as well as by plastic flow. All of these minerals showed both plastic flow and internal rupture. This question has been discussed in detail in another paper. Finally, I record here some hitherto unpublished results on the shearing of wurtzite, a form of ZnS which is known to be less stable thermodynamically than the ordinary cubic form, sphalerite. Since sphalerite has a higher density, 4.102 against 4.087, the transition from wurtzite to sphalerite is in the direction to be induced by pressure. It was a question whether under shearing the viscosity would be sufficiently overcome to permit the transition. The question was brought to my attention by R. K. Waring of the New Jersey Zinc Co., who supplied me with specially prepared pure wurtzite (precipitated powder), and who made an X-ray analysis of the results of exposure to shear. A complete transformation to sphalerite was found, thus checking the anticipation. The shearing curve as a function of pressure was smooth, showing that the transition did not take place abruptly at any particular pressure, but must have been a more or less gradual and continuous affair. REFERENCES.

1. 2. 3. 4. 5. 6. 7.

Bridgman, P. W . : Phys. Rev. 48, 893-906, 1935; Proc. Amer. Acad. 72, 46-136, 207-22S, 1937-38. : This Journal, 10, 483-498, 1925. : This Journal, 10, 359-367, 1925. Birch, F., and Dow, R. B.: Bull. Geol. Soc. Amer. 47, 1235-1256, 1936. Bridgman, P. W . : Proc. Amer. Acad. 70, 310, 1935. Birch, F., and Law, R. R.: Bull. Geol. Soc. Amer. 46, 1219-1250, 1935. Birch, F., and Bancroft, D.: Jour. Geol. 46, 59-87, 113-141, 1938. Bridgman, P. W . : Phys. Rev. 48, 825-847, 1935; Jour. Geol. 44, 653-669, 1936; Jour. App. Phys. 8, 328-336, 1937; Proc. Amer. Acad. 71, 387460, 1937; This Journal, 36, 81-94, 1938. R E S E A R C H LABORATORY OF HARVARD UNIVERSITY, CAMBRIDGE,

127 — 3374

MASS.

PHYSICS,

CONSIDERATIONS ON RUPTURE UNDER TRI AXIAL STRESS BY P. W . B R I D G M A N HARVARD UNIVERSITY

the three-dimensional case is without doubt to be explained by the fact that the conditions have not been realized experimentally. However, in spite of the difficulty of attaining in experiment the full three-dimensional variability of stress, the author believes that nevertheless by considering what sorts of phenomena might be anticipated in the full three-dimensional range we will obtain suggestive points of view with respect to some of the two-dimensional phenomena which are under control. GENERAL CONSIDERATIONS

INTRODUCTION

N ROUTINE testing of engineering materials the stresses which are most frequently employed are simple tensions or compressions. It is easy both to apply such stresses in the testing laboratory, and to calculate the resulting strains and distortions, so that it is simple to interpret the results. It is recognized, however, that materials in practical use arc often subject to more complicated sorts of stress, and accordingly there have been many efforts to make the stresses employed in testing cover a wider range of type than simple tensions and compression. Perhaps the simplest of these is testing under shearing stress by torsion; the principal stresses are here twodimensional rather than one-dimensional, that is, a tension and an equal compression at right angles to it. However, such a method of testing suffers from the disadvantage that the distribution of stress is by no means uniform, the stress being a maximum at the outside of the rod and zero on its axis in the ordinary method of testing by twisting a circular cylinder. It is generally recognized that methods of testing would be desirable in which the two principal stresses are each uniformly distributed throughout the material, and each independently controllable. It is not very easy to apply such an independently controllable pair of uniform principal stresses however, and in practice few experiments of this kind have been made. The special case of this sort of thing that is probably easiest to realize is when the two principal stresses are each compressive and numerically equal. This can be realized by exposing a cylindrical rod to fluid pressure on the curved surface, the ends of the rod projecting out of the pressure vessel through stuffing boxes. But even such a simple stress distribution as the negative of this, that is a hydrostatic tension on the curved surface, would be difficult to realize. When we come to the full generality of the next step, three uniformly distributed principal stresses, each independently controllable, the conditions are so difficult to realize experimentally that there have been practically no attempts. The simplest special case here is obviously when the three stresses are equal and compressive, that is, a hydrostatic pressure. This can be easily realized, but from the point of view of actual testing it is of minor interest, because rupture never occurs under hydrostatic pressure. The negative of this, hydrostatic tension, has not yet been realized, at least not up to magnitudes of stress sufficient to produce rupture, and the difficulty of realizing it is at present doubtless great. The fact that there has been so little discussion of rupture in

I

In this paper the author proposes to make such an analysis from the full three-dimensional standpoint. One reason that such an analysis is profitable is that it is sometimes possible to analyze a two-dimensional distribution of stress into a hydrostatic pressure or tension with a superposed one-dimensional stress. The introduction of a hydrostatic-stress component into the total stress is important because a wide experience has shown that although hydrostatic pressure modifies the properties and behavior of substances, the qualitative behavior re mains recognizable without great modification. A body which is a conductor of electricity under normal conditions continues to be a conductor when subjected to pressure, and the change in conductivity may be described with the help of a "pressure coefficient." If a fluid offers viscous resistance to flow under normal conditions it continues to offer viscous resistance when exposed to hydrostatic pressure, and the alteration in its behavior may be described with the help of a pressure coefficient of viscosity. If a metal wire breaks in tension when a sufficiently great weight is hung on it, then it may still be made to break by hanging a sufficiently great weight on it when the wire and the weight are together immersed in a fluid medium carrying hydrostatic pressure. The change in weight required to break the wire is to be described in terms of a pressure coefficient of tensile strength. Rupture, as well as any other physical behavior, is modified by the application of pressure, but not so as to become qualitatively unrecognizable, at least if the pressure does not vary too much, and the magnitude of the alteration of stress which produces rupture can be described in terms of a pressure coefficient. If any justification is felt to be necessary for this statement, it can be found in examples which the author has frequently observed during the course of his high-pressure experimenting of objects ruptured while exposed to a fluid medium carrying hydrostatic pressure. All this not only agrees with experiment, but also seems right from the theoretical point of view, because the hydrostatic pressures which can be ordinarily applied are not large enough to greatly modify the atomic forces—the compressibility and the other elastic constants are not greatly modified, so that we are still approximately in the range of Hooke's law. Let us now set ourselves the problem of discussing the behavior of a unit cube of some definite substance. To the opposite pairs of faces of this cube may be uniformly applied arbitrarily and independently variable normal forces, the forces of course being equal in pairs as demanded by mechanical equilibrium of the whole cube. That is, we suppose any required system of principal stress components applicable to the cube.

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2 Any particular stress system can be plotted as a point in a three-dimensional diagram, with three orthogonal Cartesian axes corresponding to each of the three axes of the cube. When the stress reaches certain values the cube will fail by rupture. The stress points in the three-dimensional plot corresponding to rupture will lie on a surface, the rupture surface, which we now discuss further. For the present, suppose we are dealing with a brittle substance which breaks suddenly when it breaks; otherwise rupture is not always clean-cut and the rupture surface would not be well-defined. If instead of rupture there is some other phenomenon which has a cleanly marked onset when stress passes some critical value, we could construct a

RUPTURE UNDER COMBINATIONS OF COMPRESSIVE STRBSS

Now allow the stress system to have two components, and for the present make these two components equal, so that the point in the stress diagram lies somewhere on the 45 deg line running from southwest to northeast. For some value of the two component compressive stress the cube will rupture; denote the corresponding stress by the point P. We might call this type of rupture the C2 type—two equal components of compressive stress. The simplest way of realizing this type of rupture, as already suggested, is to subject a cylindrical rod to hydrostatic pressure on its curved surface only, leaving the ends free through stuffing boxes. The author has referred to this kind of rupture in other places as the "pinching-off" effect ( l ) . 1 One can approximate to it in a plastic substance like putty by squeezing a roll of putty out endwise from one's clenched fist. The "pinching-off" effect may be readily produced in brittle materials like glass in the very simple apparatus shown in Fig. 2. The requisite pressure on the piston may be produced by a 5-ton arbor press. Study of the fractures produced in an apparatus of this kind will be found most instructive. What would one who had not experienced it expect this Cj type of fracture to look like? Probably like some sort of elaboration or modification of the simple compressive fracture, which in the case of glass frequently means crumbling or powΡ

Β

f

A

< c

\ L-l F1G. 1

corresponding surface for it. Such might be the beginning of permanent set, or the failure of the proportional limit, if only these phenomena could be sharply distinguished. We can in any event approximate to such surfaces by setting numerical limits. , Wc suppose that the substance is homogeneous and isotropic, so that its rupture surface is symmetrical with respect to the three axes. It will be convenient to map out the rupture surface by first marking its intersections with the coordinate axes, and then finding the curves which trace its intersection with various important planes. Take as typical the x-y plane, and take compressive stress as positive. Then the intersections with the positive x- and jy-axes denote the rupture point, or the strength of the cube under simple compressive stress. Similarly, the intersections with the negative axes mark the strength in simple tension. If the substance is like ordinary glass the strength in tension is markedly less than that in compression, as indicated in Fig. 1.

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FIG. 2

APPARATUS FOR PRODUCING THE " P I N C H I N G O F F - ' EFFECT

(The diameter of the rod is '/u in.; A is the solid glass rod to be ruptured; Β are tightly fitting red-fiber washers; C is a rubber tube loose inside and out, copiously smeared with molassas, to produce approximately hydrostatic pressure and reduce friction; and Ρ is a hardenedsteel piston forced in by an arbor press.) dering of the specimen. But as a matter of fact the fracture is like a typical tensile fracture under a tension acting along the third axis, that is, the axis along which by construction there is no component of stress. This means that for a brittle material like glass there is a clean rupture on a plane perpendicular to the axis of zero stress, or if the material is ductile like mild steel, the rod necks down and breaks with a conical pit exactly like an ordinary tensile break. The phenomenon of a rupture 1 Numbers in parentheses refer to the Bibliography at the end of the paper.

with all the characteristics which we are accustomed to associate with a break under tension occurring in a direction in which the component of stress vanishes is so paradoxical to many people that they arc unwilling to accept it, but must argue that in some w a y a component of tension in the direction of fracture has been smuggled in and is responsible. The point which the author wishes to make is that the phenomenon becomes understandable and to be expected from the point of view of the complete three-dimensional figure. Consider the section of the surface standing perpendicular to the plane of the paper of Fig. 1 on the 45-deg line. This plane, shown in Fig. 3, will contain the axis of hydrostatic pressure and tension, that is, the line equally inclined to the three axes, so that a point on the line denotes a stress with three equal components. Since rupture does not occur under pure hydrostatic pressure, at least for any ordinary pressure not great enough to break the atoms themselves, the rupture surface will be open in the direction of the axis of hydrostatic pressure, and w i l l stretch toward infinity without ever intersecting it. Fig. 3 shows at once that the stress at the point P, where the Ct type of fracture occurs, is the sum of the hydrostatic pressure represented by the point A and the simple tension along the g-axis represented by the length AP. That is, the two-dimensional

compression Ct may be described as a hydrostatic pressure of intensity equal to the intensity of the components of Ct, plus a tension, also numerically equal to the components of Cj. Expressed analytically, the stress system (Χ,Χ,Ο) is equivalent to the hydrostatic pressure ( Χ , Χ , Χ ) plus the tension ( 0 , 0 — X ) . Since the stress at Ρ by construction and hypothesis produces rupture, we are to expect, by our principle that hydrostatic stress does not essentially modify qualitative behavior, that the

3 character of the rupture will not be essentially different from ordinary tensile rupture produced by a one-component tension. Although the character of the fracture does not change, the magnitude of the superposed component of tensile stress required to produce it will be somewhat modified because of its pressure coefficient. General experience, which is consistent with the theoretical expectation that when a substance is compressed the atomic forces become somewhat greater, suggests that the pressure coefficient of tensile strength is positive. In accordance w i t h this, as shown in Fig. 3, AP has been drawn somewhat longer than 07", so that the trace of the rupture surface TP diverges from the hydrostatic-pressure axis in the direction of increasing pressure. This is also consistent with our previous observation that the rupture surface must be open in the direction of the hydrostatic-pressure axis. What is the character of the rupture surface in the immediate neighborhood of P? There seems no physical reason for any discontinuity here, so that we may expect the trace of the surface to be roughly linear through Τ and P, as shown in Fig. 3. This means that at points beyond P, at Ρ ' , for example, all three components of stress are compressive and correspondingly, if the point A is sufficiently beyond P, all three components of strain may be shortenings. But the stress can be described as the hydrostatic pressure A' plus the superposed tension A'P'j therefore, w e are to expect that the rupture will still be tensile in character. This at first sight appears perhaps even more paradoxical than the "pinching-off" effect, namely a tensile break with every stress compressive and every strain a shortening. The author has found that many people aggressively refuse to accept it. This sort of fracture has, however, been well substantiated by experiment. The author has realized it under simple conditions (1, 2), and there are the elaborate experiments at Illinois ( 3 ) of rupture of cylinders of concrete exposed to lateral hydrostatic pressure and longitudinal compression on the parts projecting through stuffing boxes. The photographs of the Illinois specimens show strikingly the tensile character of the fracture when the longitudinal compressive stress vanishes or is less than the lateral pressure, but apparently no great significance was attached to the character of the fracture by the experimenters. The same sort of analysis that we have just applied to the trace of the fracture surface with the 45-deg plane through Ρ may also be applied to the trace through C, shown in Fig. 3. Fracture on this trace may be described as fracture in simple one-dimensional compression with superposed hydrostatic pressure. The character of the fracture on this trace will therefore be that of a simple compressive fracture. The strength in compression may be expected to increase with hydrostatic pressure; for this there is dramatic experimental justification in recent experiments of Griggs (4). This means that the sheet through C w i l l also diverge from the axis of hydrostatic pressure, as is indicated in Fig. 3. The experiments of Griggs indicate that departures from linearity on this sheet w i l l soon come into evidence. The experiments at Illinois in which the longitudinal compressive stress was greater than the lateral pressure are also of this type.

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4

RUPTURE UNDER COMBINATIONS OF TENSILE STRESS

Consider next the prolongation toward the negative side oi the trace through C. Let us for simplicity suppose that the intersection of this sheet with the 45-deg plane continues straight, and denote its intersection with the x-y plane by R. The point R therefore indicates fracture under a system of two equal tensions, with zero principal stress along the third axis, that is, the ζ-axis in Fig. 3· We may denote this type of fracture by T2 to suggest two equal tensions. What is the character of the T2 rupture at the point R? Perhaps one's first impulse would be to say that it must be like an ordinary rupture in tension, only "more so." What "more so" means specifically is a little difficult to see—perhaps two systems of tension cracks at right angles. But now the three-dimensional representation makes a plausible suggestion. The stress at the point R is the sum of the hydrostatic tension represented by the point Β and the compressive stress given by the length RB, which is also numerically equal to the hydrostatic tension at B. If our principle is correct that hydrostatic tension does not qualitatively alter the phenomenon, we expect the character of the fracture to be like that of a compressive fracture rather than of a break in tension. The numerical magnitude of the crushing strength at R is obtained from that at C by applying a correction determined by multiplying the pressure coefficient of compressive strength by the pressure (negative) at B. For a substance like glass, for which we may expect a comparatively small pressure coefficient and for which the strength in compression is notably greater than that in tension, the distance RB will be greater than the distance OT but less than OC; it is so shown in Fig. 3. In order to have a name by which we may talk about it, we may call this T2 type of rupture the "rending" effect. It does not appear how one would realize this type of fracture with ordinary materials. A two-dimensional distribution of tension can be produced at the junction of the arms of a cross by applying tension to the arms, but if our expectation is right, rupture will occur by ordinary tension in the arms before sufficient stress can be built up at the junction to produce fracture there by the "rending" effect. If, however, the ordinary compressive strength be notably less than the tensile strength, one could hope to realize it in such a cross. In very weak materials one could realize it by cementing to the faces of the test cube tension members, provided the tensile strength of the cement is sufficiently greater than the rending strength of the material. What now happens to the rupture surface at hydrostatic tensions much greater than that at B? The author believes it is universally accepted that the rupture surface is closed in this direction, and that any substance could be ruptured by the application of a sufficiently great hydrostatic tension. A sufficient argument for this is that all substances are capable of assuming the vapor form, that vaporization requires energy, and that an indefinite amount of energy can be put into a substance by stretching it indefinitely in three dimensions. At the same time it is admittedly most difficult to realize such conditions in the laboratory, and the character of the corresponding rupture is for the present conjectural. Just to have a name to call it by we may call it the Τ» type of rupture. Rupture of this type will be said to be the "disruptive" effect, and the corresponding

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point where the rupture surface cuts the axis of hydrostatic tension will be denoted by D. As in the two-dimensional case, this may perhaps be realized in sufficiently weak materials by cementing tension members to the faces of the test cube. The author probably approximated to it on one occasion with glass. A solid sphere of glass was exposed to high hydrostatic pressure, when the pressure vessel accidentally ruptured with unusual violence. The glass was found reduced to an impalpable powder, supposedly by the inertia effect attending the sudden release which subjected the glass momentarily to a hydrostatic tension approximately equal to the previous hydrostatic pressure. This suggests the character of the fracture that may be expected. The author has not been able to repeat the experiment, however, in spite of several attempts. Fig. 3 shows that it is geometrically possible to pass on the rupture surface from the point C, through R and D, to T. This suggests the possibility of a continuous change in the type of rupture from compressive rupture at C to tensile rupture at T. The author's conclusion that the ' 'rending'' type of rupture at R is predominantly compressive in character is therefore probably not as secure as the conclusion that the ' 'pinching-off'' type of rupture at Ρ is predominantly tensile. However, the inference has a good degree of plausibility for ordinary substances in which there is no appreciable departure from Hooke's law up to the rupture point. It is to be considered that probably a high three-dimensional tension is necessary to rupture, so that the actual rupture surface may be much more extended in the direction of D than shown in Fig. 3. This allows chance for marked variation in the character of rupture between R and D; the possibility must also be considered that the curve may have breaks between R and D, and not be smooth as drawn. At points on the rupture surface sufficiently below R we may have a highly paradoxical state of affairs analogous to that already found in the neighborhood of P, namely, rupture which is predominantly compressive in character with a stress system whose three principal components are all tensions and a strain system whose three principal components are all extensions. THE COMPLETE RUPTURE SURFACE FOR MIXED STRESSES

Having now mapped out the section of the rupture surface which includes the axis of hydrostatic stress let us return to complete the discussion of the intersection with the x-y plane. We already have the points C, C, Τ, Τ, P, and R as shown in Fig. 1. We begin by inquiring what is the probable character of the intersection in the neighborhood of the point C on the praxis. At C we have compressive rupture under a one-dimensional stress C along the x-axis. This compressive rupture may take various forms for different substances; in addition to the crushing and powdering already mentioned, we may have "slabbing off" in the faces perpendicular to the y- and the siaxes, or the expulsion of shear wedges from these faces. Suppose we now apply a small compressive stress along the j-axis; then, the elongation parallel to the ζ-axis is increased, while that parallel to the^-axis decreases. Slabbing off and wedging out from the ζ-iace is facilitated, while that from the y face ceases. The rupture changes from taking place indiscriminately on the y- or ζ-face to taking place exclusively on the Zr

5 face. Furthermore, the main compressive stress C along the xaxis can now be reduced somewhat and still produce rupture, since it is assisted by the compression along the^-axis. That is, the initial slope of the intersection at C is into the second quadrant, as shown in Fig. 4. This is consistent w i t h the observation we have already made that the stress at the point Ρ in a substance like glass is notably less than the stress C. Since the rupture surface is symmetrical about the 45-deg line, the curve may be plausibly completed in the first quadrant as shown. Between the points C and Ρ we have a change in the charactcr of fracture from compressive to tensile. It is not to be expected that necessarily, or even probably for all substances, the rupture surface is smooth between C and Ρ as drawn, or that continuous transition occurs between the crushing and tensile types of rupture. However, such continuous transition is conceivable and doubtless occurs in materials like glass; as one passes from C to P, failure by slabbing off becomes more and more dominant, and failure by the expulsion of shearing wedges disappears. In fact, from this point of view, failure by slabbing off in compression, which is not so very common, is merely the premonition of the tensile failure into which the compressive failure is transformed.

Consider now the effect of adding a small component of tension along the _?-axis instead of the compression that we have just considered. There w i l l now be an additional extension along the j - a x i s w h i l e the extension along the ζ-axis w i l l be diminished. Failure w i l l now take place by slabbing off or the expulsion of shear wedges in the y-i&cc. Again the main compression along the x-axis necessary to produce rupture becomes somewhat less because of the assistance it receives from the other component, and the curve starts off below C in the direction of the third quadrant, as indicated. There is, then, a

cusp in the rupture surtace at C, corresponding to the discontinuous change in the fracture from a ζ-face to a j-face fracture. In the fourth quadrant, the curve must eventually land on the point T. Again, whether it is continuous in this quadrant doubtless depends on the type of substance. Continuity means continuous passage from compressive to tensile rupture; if the surface is continuous from C to Ρ it is probably continuous from C to T. It is so drawn in Fig. 4, which may perhaps be expected to apply to substances like glass. If, however, the substance readily flows by shear, as in the case of many ductile materials, then at some point in the fourth quadrant, where the shearing stress reaches a critical value, we may expect another discontinuity in the curve. The curve in the second quadrant is symmetrical w i t h that in the fourth. Next, how does the curve enter the third quadrant from the points T? At Τ rupture is a tensile break on planes perpendicular to the axis of tension. Additional small compression at right angles increases the extension along the main tension axis, and makes rupture by the main tension easier. On the other hand, an additional small tension along the perpendicular axis decreases the extension along the axis of main tension and makes rupture by the main tension more difficult. That is, there is no discontinuity in the character of rupture on going through T, and the rupture surface passes smoothly through this point without a cusp. At R the character of the rupture is compressive. If continuous transition is possible from tensile to compressive rupture, as we are supposing, then w e may fill in the curve continuously between Γ and R, as shown in Fig. 3· If, on the other hand, the substance is such that continuous transition in the type of rupture is not possible, and in particular if there is a discontinuous change from a tensile to a shearing type, then we may expect discontinuities between Τ and R, similar to the discontinuities in the other quadrants, whose possibility we have recognized, but have not attempted to represent specifically in the diagrams. We now have, in virtue of symmetry, six sections of the complete three-dimensional rupture surface, namely three sections made by the three coordinate planes, and three by the three 43-deg planes through the axis of hydrostatic stress. By filling in smoothly over these six sections it should be possible to get a fairly adequate idea of the complete rupture surface, even if there are still other discontinuities in the surface beside those whose possibility or probability has been indicated. For the scattering of actual experimental points in rupture experiments is usually so great that there is seldom adequate justification for drawing curves or surfaces w i t h discontinuities. When "filling i n " the surface it is to be kept in mind that it is only on the three 45-deg planes that the total stress can be analyzed into a hydrostatic stress plus a one component simple stress, so that it is only on these planes that our argument as to the character of rupture applies. On intermediate parts of the surface one may be prepared for considerable variations from material to material. It is to be remarked that if the material is one for which failure in shearing is important, it is possible to determine a "pressure coefficient of shearing strength" from the geometrical surface by a method entirely analogous to that

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6 used for "the pressure coefficient of tensile strength," and similar arguments may be expected to apply to it. CONNECTION W I T H CONDITIONS OF RUPTURB I N GENERAL

Finally, what is the connection between what we have been doing and the "conditions of rupture" or the "theory of rupture?" It is to be emphasized that up to now we have been concerned with the rupture surface which reproduces the experimental results on a particular material, in a particular shape, and with a particular manner of distribution of the surface forces. Common practice in dealing with rupture would suggest that we use this surface in the attempt to determine when rupture occurs under the most general conditions in the particular material by setting up the thesis that rupture always occurs in this particular material whenever the local stresses at any point of it reach values corresponding to any point on the rupture surface. It is, however, certain that there are cases in which rupture is determined not only by the stress conditions but also by conditions such as the nature of the surface of the specimen, and also probably by such other conditions as the way in which the distribution of stress departs from homogeneity. There is also the enormously important factor of repetition of stress application. Further, under some circumstances the general geometrical configuration seems to play an enormously important r61e; thus, the author has found that heavy-walled glass cylinders will support external pressures of 30,000 atm, which means a stress difference of 60,000 atm at the internal surface, far above the crushing strength under more normal conditions. The decisive rdle of surface conditions is established by the well-known experiments of Griffiths (5) on glass or of Orowan (6) on mica. A complete formulation of the conditions of rupture, even for a single material, depends on many more variables than merely the stress components, and is a much too complicated thing to reproduce by any such simple surface as we have been considering. At the best such a surface can be expected to be of value in determining rupture only for particular kinds of materials, or for particular ranges of stress. The metals of ordinary engineering practice do seem to be materials for which the surface conditions are relatively unimportant, so that we may expect the experimental mapping out of a surface such as we have considered to be important in indicating when to expect rupture under practical conditions, especially in those cases where the stress distribution is approximately homogeneous. However, the general application to metals is obscured by the fact that failure in metals is often not a clean-cut phenomenon. For substances like glass we should expect the applicability of such a surface to be obscured by the capriciousness of the results, because surface effects are known to be very important. CONCLUSION

The complexity of the whole subject is obviously enormous and baffling. The simplifying idea which this paper would chiefly emphasize is that a pure hydrostatic pressure or tension does not produce large qualitative changes, and that it is therefore of value to resolve, when possible, a stress system into a hydrostatic stress plus a superposed simple stress, and that the

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physical effects are qualitatively those of the superposed simple stress. BIBLIOGRAPHY 1 "Breaking Tests Under Hydrostatic Pressure and Conditions of Rupture," by P. W. Bridgman, Philosophical M*(/n.itu, vol. 24, July, 1912, p. 66. Also: "Some Mechanical Properties of Matter Under High Pressure," by P. W. Bridgman, Proceedings of the Second International Congress for Applied Mechanics, Zurich, Switzerland, 1926, p. 39. 2 "Theoretically Interesting Aspects of High-Pressure Phenomena," b y P . W . B r i d g m a n , Review of Midtm

Physics, v o l . 7 , 1 9 3 5 , p . 31.

3 "A Study of the Failure of Concrete Under Combined Compressive Stresses," by F. E. Richart, A. Brandtzaeg, and R. L. Brown, Engineering Experiment Station, University of Illinois, Urbana, 111., Bulletin No. 185, November, 1928. 4 "Deformation of Rocks Under High Confining Pressures," by D. T. Griggs, Journal of Geology, vol. 44,1936, p. 541. 5 "The Phenomena of Rupture and Flow in Solids," by A. A. Griffith, Philosophical Transactions of the Royal Society of London, vol. 221, 1920, p. 163. 6 "Die Zugfestigkeit von Glimmer und das Problem der technischer Festigkeit," by Ε. Orowan, Zeitschrift fir Physik, vol. 82, 1933, p. 235.

Absolute Measurements in the Pressure Range up to 30,000 kg/cm2 P. W.

BRIDGMAN

Harvard University, Cambridge, Massachusetts (Received November 20, 1939)

' I VHE first task for any program of accurate measurements in a new pressure range is the establishment of various landmarks. The most important of these are pressure fixed points, similar to the familiar fixed points of thermometry, for the reproduction and measurement of pressure. After the pressure scale is established perhaps the most fundamental sort of measurement that can be attempted is of compressibility. The most convenient method is a differential method, which assumes as known the absolute compressibility of a substance of reference. The establishment of one absolute compressibility is therefore the next task after the establishment of the pressure scale. In this paper I briefly summarize the results of recent measurements of these two kinds; full details are in course of publication elsewhere. In my previous measurements1 of various pressure effects up to 12,000 kg/cm 2 the working pressure gauge was a coil of manganin wire. A preliminary investigation with an absolute pressure gauge of the free-piston type had shown that the change of electrical resistance of manganin is nearly linear with pressure in that range, so that the manganin gauge could be calibrated by the determination with it of a single pressure at some pressure fixed point. For this pressure fixed point the freezing pressure of mercury at 0 e C was chosen. This was measured in the first place with the absolute gauge and taken in all my work to be 7640 kg/cm2. In extending the pressure range by a factor of 2.5 the first question to be answered is whether the manganin gauge continues linear. I have already made a preliminary investigation of this point,2 and had come to the conclusion, from a comparison of the way in which the resistances of various metals extrapolate together and from rough measurements of pressure in terms of the force on the piston, that the manganin gauge is not probably in error by more than one or two

percent at 25,000 kg/cm 2 . It appeared therefore that in extending the accurate calibration a single new fixed point near the end of the range would be adequate. Of the phenomena which might be used to determine such a fixed point it appeared that a phase change, as had been employed before, was by far the most convenient. Transition measurements in the pressure range up to 50,000 of some -60 substances afforded extensive material for selection.' Of all these substances bismuth is by far the most suitable. The transition between modifications I and II of bismuth occurs at about 25,000 kg/cm 2 at room temperature, it has a conveniently large volume change, about 4.5 percent, it runs fairly rapidly with little excess pressure in either direction to start the transition and with very narrow region of indifference, and the temperature dependence is so slight that thermostatic temperature control is not necessary. The exact transition pressure must be established by some sort of absolute procedure. An absolute gauge of the free-piston type operating with a liquid is probably not feasible, for I believe that difficulties set by leak and viscosity in the liquid will prevent the use of this type of gauge to pressures much exceeding my previous maximum of 13,000 kg/cm 2 . But some sort of measurement of pressure in terms of the force exerted on a piston probably remains the simplest. This can be done by directly compressing the bismuth undergoing transition with a piston, measuring the force on the piston, and determining when the transition occurs by the discontinuous change of volume. The errors in this procedure arise from friction and distortion of the vessel under pressure. Friction is minimized by using the minimum amount of packing, making the ratio of area to thickness of the bismuth as large as possible so as to minimize the piston motion during transition, and making readings with increasing and decreasing pressure.

1 P. W. Bridgman, The Physics of High Pressure. (Bell and Sons, London, and Macmillan, New York, 1931). ' P. W. Bridgman, Proc. Am. Acad. Sei. 72, 157 (1938).

* P. W. Bridgman, Proc. Am. Acad. Sei. 72, 46, 227 (1937-38).

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236

P . W.

BRIDGMAN

With proper precautions the mean of increasing and decreasing pressure is surprisingly constant, and the total difference between increasing and decreasing pressure may under favorable conditions be as little as 3 percent, meaning an absolute friction of not more than 1.5 percent and an error of the mean of much less. Correction for distortion of the pressure vessel is less than it otherwise would be because of the external support which is necessary in order to withstand rupture. The distortion of the cross section was only 0.5 percent at 25,000; this figure was checked in two ways. An approximate calculation by ordinary elasticity theory gave about this value, and a more rigorous evaluation of this correction was made with an independent piece of apparatus with which the distortion was measured with a sliding contact arrangement mounted within the cylinder, which was filled with an insulating liquid. The final values found for the pressure fixed points were: At 30°, At 75°,

25,420 kg/cm 2 . 23,350 kg/cm 2 .

The manganin gauge may now be calibrated against the previous mercury fixed point at 7640 and the new bismuth point, and the change of resistance expressed by a quadratic formula in the pressure. As previously surmised, the relation is very nearly linear. Pressures at 30,000 obtained by linear extrapolation from the mercury point are in error by only about one percent, and in an unexpected direction, the linearly extrapolated pressure being too low. This means that the pressure coefficient of manganin decreases with increasing pressure; in almost all other cases the coefficient increases. Different manganin gauges, even those cut from the same spool of wire, have slight differences in the second-degree term, so that every coil must be calibrated at two points for the most accurate results. With the manganin gauge calibrated in this way, the freezing pressure of mercury at 30° was found in two determinations to be 13,700 and 13,730 kg/cm 2 . The mean of these, 13,715 may be taken as a new fixed point, the freezing pressure of mercury at 30.0°C. Calibration with this instead of the former fixed point at 0° is

1 2 9 — 3382

somewhat more convenient because by putting suitable amounts of both bismuth and mercury in the apparatus the calibration may be made with a single set-up. It is also an advantage to have a point at approximately the middle of the pressure range. The pressure scale having been established, the absolute compressibility Of some one substance may next be determined. As in my previous work, the substance chosen was pure iron. The method demands a measurement of the relative change of length of an iron rod with respect to the pressure vessel by a sliding electrical contact device, plus a measurement of the distortion of the vessel. The latter was accomplished by using two probe rods reaching to nearly the interior wall of the pressure vessel through small drilled holes. The accuracy with which the second-degree term in the compressibility is determinable varies, other things being equal, as the square of the pressure range. The new determinations should therefore give this term more than six times as accurately as before. Part of this advantage is sacrificed, however, by the necessity for using a shorter specimen because of the more serious restrictions on the dimensions of the vessel. The effect to be measured is small, the maximum relative displacement being 0.05 cm. In spite of every effort, I did not succeed in eliminating capricious irregularities in the results, so that the only course was the accumulation of many observations and least-squares reduction of the results. Twenty-five different set-ups of the apparatus were made and some 400 individual observations, uniformly spaced over the entire pressure range, both with increasing and decreasing pressure. The new final result for the linear compressibility of pure iron at 24°C is: - Al/lo = 1.942 X10~ J p - 0.23 Χ ΙΟΠψ,

pressure in kg/cm 2 . The apparatus was not well adapted to a determination of the temperature coefficient. In the absence of new measurements, the best that can be done is to use my previous temperature coefficient. This would give for the linear compressibility at 75°C: —Al/h— 1.964X10~7/>—0.23X 10-12/»2.

ABSOLUTE

MEASUREMENT

The new second-degree terra is smaller by a factor 3.3 than the former one (23 against 75). This is the direction of change which several theoretical physicists have pointed out was probable. I can see no possibility, however, of reconciling with the present experimental data

OF

PRESSURE

237

reduction by a factor as large as 10 or even 100, as has been suggested. This work is indebted for financial support to the Francis Barrett Daniels Fund of Harvard University and to the Rumford Fund of the American Academy of Arts and Sciences.

129 — 3383

Compressions to 50,000 kg /cm2 P. W .

BRIDGMAN

Harvard University, Cambridge, Massachusetts (Received November 20, 1939)

T

HE object of this note is to present a compact summary of the numerical results obtained in series of measurements with new apparatus of the volume decrements of about 40 binary cubic compounds together with a few of the more compressible elements up to pressures of 50,000 kg/cm 2 . The detailed paper, to be published presently in the Proceedings of the American Academy of Arts and Sciences, will contain, in addition to the material to be expected in such a paper, such as a description of the apparatus and discussion of the methods of calculation and the probable errors, a tabulation of the compressions at pressure intervals of 5000 instead of 10,000 kg/cm2, and at approximately —80°C in addition to room temperature. The novel feature of the new apparatus is the more effective external support afforded the pressure vessel, there being now two stages of support instead of one as formerly.1 This materially increases the life of the vessels, permits the attainment of somewhat higher pressures, and decreases the distortion of the vessel and the error from uncertainty in the distortion. All results are the mean of two or more independent measurements, which usually did not differ by more than 5 percent. One more significant figure is given in Table I than would be 1

P. W . Bridgman, Proc. Am. Acad. Sei. 72, 207 (1938).

justified by the absolute accuracy; the retention of another figure is demanded if the differences are to be smooth. The method is such that the accuracy is less at the ends of the range; the relative values are probably most accurate in the range from 10,000 to 40,000. The probable error varies with the material. The nine compounds of calcium, strontium and barium are probably the least satisfactory. The compressibility of the sulfides of these is probably too high because of presence of a comparatively large amount of amorphous material, and the selenides and tellurides had a tendency to chemical instability. The figures given in the table are in cm' for a specified number of grams, and are ostensibly fractional changes of the volume at atmospheric pressure and room temperature. The volume decrements listed are for room temperature, which may be taken as 23°. The actual measurements were of volume decrements in cm1 of a known number of grams. To get the fractional volume changes the observed changes must be multiplied by a factor depending on the atmospheric density. The number of grams listed with each substance is the assumed atmospheric density, in most cases the x-ray density as given in Wyckoff. If better densities are later determined, the figures of Table I may be corrected by simple factors.

130 — 3385

238

P.

W.

BRI

A number of new polymorphic transitions were found. Among the compounds, the order of stability seems to be: ZnS structure, NaCl structure, and CsCl structure. That is, a compound of ZnS structure may be forced by pressure into the NaCl structure, and a NaCl structure into the CsCl structure. No polymorphic transitions have been found among the CsCl structures. All of the compounds given above are cubic except HgS, for which the figures refer to the red hexagonal modification. Measurements were attempted on the black cubic modification of HgS, but were found to be impossible over any extended range because the black modification is irreversibly transformed by pressure into the red. The compressibility of red HgS is about twice as great as that of the black in spite of its smaller volume. Measurements not given in the table were also attempted on HgTe. This is formed from the elements with increase

TABLE I.

DGMAN

of volume, and it was found to be unstable under pressure, slowly decomposing to the elements. Although no good measurements could be made of compression because of the decomposition, nevertheless the decomposition was slow enough to permit an approximate measurement of a transition at 12,800 kg/cm 2 with an 8.4 percent change of volume. In general, the curves of compression against pressure are strongly concave toward the pressure axis. The fractional decrease of compressibility with pressure is as a rule greater for those substances with an absolutely large compressibility, but this is by no means universal, and there are a number of cases of crossing of the curves. In particular the rapid decrease of compressibility of sulfur and selenium is to be noted. The curve of the compressibility of selenium against pressure has a sharp break in direction near 34,000 kg/cm 2 , that is, a discontinuity in

Volume decrements of various binary cubic compounds and of a few of the more compressible elements. The numbers are in cm* for the specified number of grams.

PRESSURE KG/CM»

NaCl 2.163 G

NaBr 3.205 G

Nal 3.667 G

KCl 1.988 G

KBr 2.750 G

KI 3.123 G

RbCl 2.849 G

RbBr 3.391 G

CsCl 4.031 G

10,000

0.0365

0.0430

0.0553

0.0478

0.0547

0.0648

0.1882

0.1879

0.1918

0.0479

0.0537

20,000

0.0664

0.0771

0.0974

0.0841

0.1989

0.1970

0.2184

0.2207

0.2315

0.0850

0.0949

30,000

0.0919

0.1047

0.1294

0.2225

0.2267

0.2296

0.2422

0.2462

0.2609

0.1146

0.1274

40,000

0.1130

0.1274

0.1538

0.2419

0.2479

0.2532

0.2612

0.2670

0.2831

0.1387

0.1532

50,000

0.1309

0.1464

0.1728

0.2579

0.2650

0.2715

0.2768

0.2848

0.3009

0.1596

0.1748

PRESSURE KG/CM*

Csl 4.547 G

NH.Cl 1.536 G

NH.Br 2.548 G

NH.I» 2.887 G

AgCl 5.589 G

AgBr 6.548 G

Agl 5.709 G

TlCl 7.029 G

Rbl 3.591 G

CsBr 4.478 G

d

,

TIBr 7.539 G

Til 7.435 G

CaS 2.617

10,000

0.0647

0.0489

0.0487

0.0590

0.0216

0.0215

0.1896

0.0383

0.0426

0.0510

20,000

0.1120

0.0818

0.0880

0.1019

0.0401

0.0404

0.2095

0.0688

0.0763

0.0891

0.0421

30,000

0.1485

0.1070

0.1203

0.1332

0.0562

0.0584

0.2257

0.0936

0.1026

0.1173

0.0555

40,000

0.1781

0.1278

0.1465

0.1570

0.0704

0.0743

0.2396

0.1139

0.1224

0.1387

0.0658

50,000

0.2025

0.1462

0.1676

0.1775

0.0838

0.0890

0.2525

0.1313

0.1377

0.1554

0.0740

* Transition a t 2 0 , 0 6 0 k g / c m 1 . Compressions a t transition 0 . 0 8 4 7 and 0 . 1 9 8 0 . * Transition a t 18.430 k g / c m * . Compressions a t transition 0 . 0 8 8 6 and 0 . 1 9 3 8 . « T r a n s i t i o n a t 18,200 k g / c m 1 . Compressions a t transition 0 . 1 0 4 9 and 0 . 1 8 9 9 . * Transition a t 5 0 0 0 kg/cm«. Compressions a t transition 0 . 0 2 9 5 and 0 . 1 7 0 1 . * Transition a t 4 6 0 0 k g / c m 1 . Compressions a t transition 0 . 0 3 3 0 and 0 . 1 6 5 5 . 1 Transition a t 4 0 5 0 k g / c m 1 . Compressions a t transition 0 . 0 3 4 9 and 0 . 1 6 1 4 . * Transition a t 3 0 2 0 k g / c m * . Volume decrement a t transition 0 . 1 6 3 0 . * T h e figures for NH Transition at 24,680 kg/cm*. • Transition at 43,320 kg/cm*. * Transition at 41,200 kg/cm*. • Transition at 38,470 kg/cm*. / Transition at 41,270 kg/cm1. 9 Transition at 7650 kg/cm1. » Transition at 40,130 kg/cm1. „ .... * Transition at 27,570 kg/cm*. to III. There is an intermediate i Transition at 40,740 kg/cm*.

Volume decrement at transition 0.0100+· Compressions at transition 0.0464 and 0.0663. Compressions at transition 0.0903 and 0.1067. Compressions at transition 0.0818 and 0.0912. Compressions at transition 0.0568 and 0.0607. Compressions at transition 0.0763 and 0.0812. Compressions at transition 0.0130 and 0.1090. Compressions at transition 0.1227 and 0.1724. Compressions at transition 0.0692 and 0.1538. (These figures are smoothed figures for direct passage from I form II, stable over a narrow range.) Compressions at transition 0.1676 and 0.1700.

( d h t / d p 2 ) ^ T h i s is t o b e d e s c r i b e d f o r m a l l y a s a

t h e F r a n c i s B a r r e t t D a n i e l s F u n d of

" t r a n s i t i o n of t h e t h i r d k i n d . "

University and to the Rumford

T h i s w o r k is i n d e b t e d for

financial

support to

Harvard

Fund

of

the

A m e r i c a n A c a d e m y of A r t s a n d S c i e n c e s .

130 —

3387

New High Pressures Reached with Multiple Apparatus It has been suggested a number of times that hydrostatic pressures of any magnitude could be obtained with a nest of pressure vessels, one within the other, exposed to progressively higher pressures. The practical complications of such a scheme are, however, obviously great. By the partial use of such a scheme, in which the most vulnerable part of the pressure vessel receives external support, I have been able to extend useful measurements to 50,000 kg/cm'.1 This note reports a more complete application of the idea, which has made it possible to reach pressures considerably higher. The gain in doubling the pressure apparatus may be considerably more than double because of the increase in intrinsic strength under high hydrostatic pressure. This was clearly foreshadowed by the experiments of Griggs,* who found that the crushing strength along the c axis of a sihgle quartz crystal was increased from 22,000 to about 120,000 kg/cm' by a confining pressure of 20,000 kg/cm'. I have now applied to a Carboloy piston without fracture a compressive stress of between 200,000 and 250,000 kg/cm«. The crushing strength of Carboloy under normal conditions is not more than 70,000 kg/cm*. The confining pressure was afforded by bismuth undergoing transition, so that the confining pressure was automatically kept at about 25,000 kg/cm*. Under ordinary conditions Carboloy is highly brittle, and breaks with practically no plastic deformation, but under a confining pressure of this magnitude the Carboloy piston was plastically and permanently shortened by 5.5 percent, and considerably bent, with no perceptible cracks or other obvious damage. Glass-hard steel under the same confining pressure similarly shows an increase of compressive strength and very considerable plastic deformation, and also an appreciable increase of compressive strength at atmospheric pressure after the cold working afforded by the plastic deformation while supported. I have verified Griggs' observation of the great increase of the strength of quartz single crystal under a confining pressure of 25,000, applying without fracture compressive stresses of the order of 150,000. The strength in the c direction is greater than at right angles, as was also found by Griggs.· The effective Young's modulus appears to be increased at this stress by something of the order of 25 percent. Quartz glass has its strength increased by something of the same order as the crystal. Quartz glass compressed in this way ruptures on release of pressure into characteristic disks perpendicular to the axis of compression, and Mr. Griggs finds that optical anisotropy has been developed, indicating

131

—3388

some permanent plastic flow. He finds no optical anisotropy in any fragments of quartz crystals ruptured at high pressures. A "one sided" compressive stress in a piston may be converted into an approximately equal hydrostatic pressure in a thin disk of softer material compressed by the end of the piston, lateral extrusion of the soft material being prevented by friction. In this way I have applied a hydrostatic pressure of between 200,000 and 250,000 kg/cm1 to a thin plate of single crystal graphite at room temperature with no conversion to diamond. This extends the negative result beyond the pressure of 100,000 kg/cm» which I have already reported.' Since the pressure of thermodynamically reversible transition is according to the most recent 4 thermodynamic evidence not far from 20,000, it is probable that no pressure, however high, will accomplish the conversion at room temperature. This is suggested by the theory of Tammann, according to which the speed of formation of nuclei of a new phase at first increases as pressure is increased beyond the thermodynamically reversible transition point, but then passes through a maximum and drops again. The experiments just described were mostly performed in my apparatus for 50,000 kg/cm', support being usually afforded by bismuth in transition, but sometimes by lead. My apparatus for 30,000 affords opportunity for support by a true liquid, for experiments on a somewhat larger scale, and for measurements of greater precision and complication. In this apparatus several exploratory measurements have been made on materials confined in a small cylinder of A inch bore and A inch outside diameter, compressed by a Λ-mch Carboloy piston. The cylinder of the 30,000 apparatus contains in addition to the transmitting liquid (iso-pentane) and a manganin gauge for measuring pressure a large block of bismuth, the function of which is to maintain pressure in the supporting liquid at 25,000 during the transition, during which the motion of the main piston, 0.5 inch in diameter, is approximately 0.1 inch. The initial quantity of liquid is so chosen, after preliminary trial, that the 0.5-inch piston makes up on the Α-inch piston at the moment that the transition pressure of bismuth is reached. The pressure on the lV-inch piston is then given roughly by the excess pressure on the 0.5-inch piston. In this way I have observed at pressures estimated to be between 125,000 and 150,000 kg/cm» an elastic volume compression in NaCl of something over 20 percent. The compression at 50,000 is known to be 13 percent,' and

LETTERS

TO

the relation deviates markedly from linearity. It is therefore probable that NaCl has no transition with important volume change to the CsCl type of structure, unlike the rubidium and potassium salts, and as predicted by Jacobs' on theoretical grounds. Sulfur has also been compressed to approximately the same pressure with about 30 percent loss of volume, and no irreversible change to a more metallic form, which is to be looked for in analogy with black phosphorus. Incidentally the possibility of reaching pressures so high in a cylinder of the above dimensions means an increase in strength of the cylinder for internal pressure (that is, in tension) markedly greater than would be accounted for merely by the additive effect of the supporting pressure of 25,000. Finally, preliminary exploration shows the feasibility of

THE

EDITOR

343

using inside the 30,000 apparatus and supported by uniform hydrostatic pressure, a miniature double container, supported by an external cone in the same manner as now employed in my 50,000 apparatus, with resulting further increase in the range of controllable and measurable hydrostatic pressure. P. W.

BRIDGMAN

Physics Laboratories. Harvard University, Cambridge, Massachusetts, January 18, 1940. • P. W. Bridgman, Phys. Rev. 48, 893-906 (1935) and Phys. Rev. 57, 237 (1940). 1 D . Griggs and J . B. Bell, Bull. Geol. Soc. Am. 49, 1723-174« (1938). • P. W. Bridgman, Phys. Rev. 48, 832 (1935). • F . D . Rossini and R. S. Jessup, Nat. Bur. Stand. J . Research 21, 491-514 (1938). 1 Second reference under (1). • R. B. Jacobs, Phys. Rev. 54, 468-474 (1938).

131 — 3 3 8 9

T H E M E A S U R E M E N T OF HYDROSTATIC PRESSURE TO 30,000 kg/cm 2 BY P. W . BRIDGMAN Presented Oct. 11, 1939.

Received Oct. 13, 1939.

TABLE OF CONTENTS Introduction Instrumental Details Corrections for Distortion The Material for Transition Determination of the Fixed Points The Manganin Gauge

1 2 3 5 5 8

INTRODUCTION

A part of the problem of the extension of the controllable pressure range from 12,000 kg/cm 2 to 50,000 for certain phenomena and to 30,000 for others, a problem on which I have been engaged for the past few years, is to provide some method for the accurate measurement of pressure in the new range. For such phenomena as polymorphic transitions high accuracy in the measurement of pressure is not of extreme importance, but for those phenomena whose chief interest lies in departures from linearity with pressure, such as compressibility or change of electrical resistance, a higher degree of precision in the measurement of pressure is obviously desirable. In the range of my earlier work, mostly up to 12,000 kg/cm 2 , pressure was usually measured in terms of the change of resistance of a coil of manganin wire.1 Before the resistance changes could be accepted as a satisfactory pressure indicator a preliminary study was made of the change of resistance against an "absolute" gauge of the free piston type. The resistance change of any one coil of wire proved to be linear in the pressure within 0.1 per cent up to 13,000 kg/cm 2 , but different coils cut from the same spool might differ in their constant of proportionality by 2 or 3 tenths of a per cent, and coils from different manufacturers might differ by several per cent. A calibration of each individual coil in terms of some easily reproducible standard which determines a pressure fixed point was therefore indicated. For this fixed point the freezing pressure of mercury at 0° C. has been used in all my work; this pressure was found by original measurement against the piston gauge to be 7640 kg/cm 2 . In work already published2 up to 30,000, and also in some earlier work to 15,000 and 20,000,

pressure has been measured with a manganin gauge, by linear extrapolation of the constant determined at 7640. There was various evidence that any error in such an extrapolation could not be large, but now that I have started on a measurement in this range of the compressibilities of the relatively incompressible metals the time has obviously come to make the measurement of pressure as precise as possible. One would naturally first try to merely extend the former procedure to higher pressures, but this is not feasible because the free piston gauge had about reached its limit at 13,000, due to rapidly increasing viscosity of the pressure transmitting medium, demanding forces to rotate the piston great enough to break it, and also due to the rapidly increasing distortion, the correction for which can only be calculated by the methods of the theory of elasticity in a range in which the fundamental assumptions of the theory are becoming rapidly inapplicable. However, the fundamental idea of the free piston gauge, namely the measurement of pressure by measurement of the thrust on a piston in equilibrium with the pressure, appears to remain the simplest and perhaps the only method. The errors to which this is subject are two: those arising from friction and those arising from geometrical distortion. If these two sources of error could be overcome, then an extension of the same procedure as before could be used, namely direct measurement of some easily determined pressure fixed point against which the manganin gauge could then be calibrated and used thereafter as a secondary gauge. This is the course adopted in the following. By suitable design of the apparatus the friction has been cut down to a low figure; the corrections due to distortion have been determined by direct measurements of the interior bore of the apparatus while under pressure; the pressure of a suitable transition between solid phases has been determined as a pressure fixed point; and the manganin gauge has been calibrated in terms of these, and its departure from linearity determined. A variant of the former arrangement is that now the piston on which the thrust is meas-

132 — 3391

2

BKIDGMAN

ured is in direct contact with the solid undergoing transition, with no liquid as intermediary; in this way the problem of leak past the piston is minimized. INSTRUMENTAL

DETAILS

The chief frictional resistance to the motion of a piston arises at the periphery of the piston, in the packing; other things being equal it is proportional to the ratio of the active area of the packing material to the area of the piston. This ratio can obviously be cut down by making the ratio of periphery to piston area small, and by making the packing as thin as possible. There is then an advantage in working on a large scale, because the larger the scale the smaller the ratio of periphery to piston area. The diameter of the free piston formerly used to 13,000 was only 0.0625 inch; for this work up to 30,000, 0.5 inch was used. In fact, the cylinder containing the material undergoing transition, the piston, and the presses for pushing the piston, were the same as previously used in measuring the effect of pressure on resistance up to 30,000, and have already been sufficiently described.8 The % inch piston producing the high pressure is pushed by a 3.5 inch piston, thus giving a multiplication of 49. The 3.5 piston is actuated by a hand pump connected to a calibrated 0.25 inch free piston gauge, similar to that used in much of my previous work. The pressure on the 3.5 piston does not rise above 10,000 lb/in 2 , so that the weights on the 0.25 free piston gauge do not get above 500 pounds, which is easily manageable. Friction occurs both on the 3.5, and mostly on the 0.5 inch piston. Friction on the 3.5 inch piston is cut down by making the bore of the cylinder of the press as smooth as possible, and by using for packing material a disc of "Duprene" only 1/16 inch thick, instead of the % inch thickness usually employed. The Duprene is held between brass discs Yg inch thick, which are a smooth sliding fit for the hole. The life of the packing is naturally cut down by using only 1/16 inch thickness, but it nevertheless is long enough to permit measurements with no inconvenience on this score. With these dimensions, the ratio of packing area to area of the piston is only 0.07. The 0.5 high pressure piston was of carboloy, as in all this work. I am very much indebted for it to the Carboloy Company. This piston was made 0.010 inch smaller than the hole, so that there is no friction at the carboloy, but only at the end, where it pushes a packing disc against

132 — 3392

the solid undergoing transition. The construction of this packing disc is indicated in Figure 1. It consists of a disc of hardened steel, an easy push fit for the hole, and only 0.020 inch long on the straight part, bevelled below to an angle of 45° and pushing a conical packing ring of either beryllium-copper or phosphor-bronze, itself 0.035 inch thick. The endeavor is to make the thickness of the packing ring as small as is compatible with its not blowing out past the hardened steel disc. Another most important factor in determining friction is the length of the slug of material undergoing transition. Before the transition occurs

FIGURE 1. Method of packing the substance undergoing transition so as to give minimum friction.

there is of course appreciable volume compression of this material, which demands that the material slide in an axial direction along the walls of the container. This sliding is accompanied by friction, which resists the propagation of pressure, so that the pressure in the lower end of the slug is less than that in the upper end immediately under the moving piston. The material immediately under the piston may therefore be undergoing transition while that at the lower end is still below the transition pressure. There is the converse situation when the transition is approached from the other side, with release of pressure. The difference of pressure between the top and bottom increases exponentially with the length of the slug. Furthermore, after every change of pressure the

T H E M E A S U R E M E N T OF HYDROSTATIC P R E S S U R E TO

volume does not immediately take up its final value, but there is a frictional creep, which simulates the transition, and which rapidly becomes more important the longer the slug. Because of these two effects a large amount of material, that is, a long slug, is disadvantageous, but on the other hand, the greater the amount of material, the greater the volume change during the transition, and therefore the greater the ease of following the course of the transition and making measurements. The solution is to be found in decreasing the amount of material and at the same time increasing the sensitiveness of the method of measuring piston displacement, and also, of course, in using a transition with as large a volume change as possible. In this work the volume change of the material used, bismuth, is about 5 per cent, the length of the slug was only 0.375 inch with a diameter of 0.5 inch, and the piston displacements were read with a 0.0001 inch Ames dial gauge, which is sensitive to 0.00001 inch by estimation of tenths of the smallest divisions. Even with this favorable combination, frictional creep after every change of pressure is perceptible; one cannot be sure that the transition is running unless the creep exceeds something of the order of 0.0001 inch per minute.

30,000

Κβ/cM2

3

the change of internal diameter of a similar container filled with a liquid, as in the previous measurements of change of resistance under pressure, instead of a solid. This was accomplished by a modification of the sliding wire method of measuring small changes of length already extensively used in measuring compressibilities. A forked spring, shown in Figure 2, pressing against the

\

CORRECTIONS FOR DISTORTION

The containers used in determining the fixed points were the regular "cylinders" used in previous work to 30,000. It will be remembered that these are somewhat tapering on the outside, and that simultaneously with the development of internal pressure they are pushed into a tapered collar fitting the outside, thus producing an external pressure which rises simultaneously with the internal pressure. The cylinder thus remains entirely within the elastic range and shows neither creep nor permanent alteration of dimensions after exposure to pressure. It is formally possible to calculate the change of cross section, but the calculations could be only approximate even if the equations could be solved exactly, because the boundary conditions are not well defined. Furthermore, the stresses are so high that deviations from the linearity assumed in elasticity theory may be suspected to be perceptible, so that some experimental check, even if rough, on the calculations is desirable. There seems to be no easy method of measuring the change of internal dimensions of the container while the transition is running, but it is possible to determine, as a function of pressure,

c7Π

J

FIGUBE 2. The sliding contact arrangement for measuring the change of internal diameter while under pressure.

walls of the container, carries across its end a transverse high resistance wire, fixed to one tine of the fork and sliding over a contact fixed to the other. Measurement with a potentiometer of the potential difference between fixed and sliding contact when a known current flows through the wire affords the method of determining small changes of dimensions. A number of small corrections are involved in reducing the measured potential differences to displacement; these had been previously determined.

132 — 3393

4

BRIDGMAN

A number of different set-ups were made with the apparatus for measuring distortion; most of the runs were incomplete because of one accident or another, but finally enough partial readings were obtained to give a satisfactory characterization of the behavior over the entire range. I t is to be expected that the distortion of the bore of the cylinder will not be uniform along its length, being a maximum at the center of the stressed region, and a minimum at the ends, including the moving piston, where support is afforded by the parts of the cylinder walls not exposed to internal pressure. An attempt was made to find the distortion immediately under the moving plug by mounting the fork so that the cross wire is almost in contact with the lower end of the moving plug. In this arrangement the fork slides along the cylinder axis, pushed by the piston as it advances to increase the pressure. On release of pressure the fork is left standing in its extreme position. Measurements with increasing pressure therefore give the distortion at the moving plug, and measurements with decreasing pressure approximately the distortion at the center. Or the distortion at the center can be obtained both with increasing and decreasing pressure by placing the fork initially at the center. The distortion determined in this way was in every case linear with pressure within limits of error. The distortion at the moving plug turned out to be 2 / 3 of that at the center. I t may be shown theoretically, by an application of Betti's reciprocal theorem, that the distortion at the ;packing of the moving plug should be only one half the distortion at the center, where it is a maximum, assuming conditions for a semi-infinitely long thick cylinder. That is, if it had been possible to measure the distortion at the packing instead of some distance away at the end of the plug, theory would demand a value % that at the center instead of 2 / 3 as found. I t would seem that the discrepancy is sufficiently accounted for by the difference of location, and in the following the factor % was therefore used in calculating the correction at the packing, which determines the effective cross section of the piston. The correction so found is a 0.57 per cent increase in area at 25,000 kg/cm 2 . The correction thus found has to be still further modified for the finite length of the slug undergoing transition, the correction determined under the experimental conditions above being for a semi-infinitely long cylinder. I t would probably be difficult to calculate this correction exactly, but a rough graphical estimate

132 — 3394

may be made of it. The radial distortion of an infinitely long cylinder under the distribution of internal pressure indicated in Figure 3 can be

the nature of the radial stretch at the internal wall under an internal pressure applied over the shaded region.

the radial stretch at the internal wall under an internal pressure applied over the shaded region. at once expressed in terms of the radial distortion of the same cylinder under the same internal pressure distributed along the whole of one semiinfinite axis as shown in Figure 4. If we assume for the latter that the radial displacement at a

T H E MEASUREMENT 0 Γ HYDROSTATIC PRESSURE TO

point on the axis situated at a distance of one radius from the end of the region where the pressure ceases is one half the displacement at the place where the pressure ceases (that is, if in Figure 4 DC — y 2 AB, where AC = V2 AE), a not unplausible assumption, then in Figure 3 the radial displacement OP is approximately 0.35 what it would be at the corresponding point in Figure 4. This makes the correction on the effective cross section of the piston 0.40 per cent at 25,000. The final correction for the cross section was taken as 0.5 per cent at 25,000. The uncertainty in the final result arising from uncertainty in this correction should not be more than 0.2 per cent at the most. The correction can be calculated from the dimensions of the cylinder and the elastic constants with the simplifying assumptions that the cylinder is infinitely long and exposed to internal pressure over its entire internal length, that the external figure can be taken as cylindrical with the mean external radius instead of tapering as it actually is, that the external pressure can be taken as uniform over the entire external infinite length, and that the longitudinal compressive stress arising from the thrust which forces the taper into its external collar in order to generate the external pressure is uniform along the axis. With these assumptions the calculated internal radial displacement comes out two thirds of that measured. The agreement is perhaps as close as could be expected in view of the extremely rough approximations that had to be made for the calculation. The effectiveness of the external support given to the pressure vessel is shown by the calculation to be very high, the radial enlargement under the actual conditions being only 0.26 of what it would have been if there had been no external support. Of course the uncertainty arising from the correction for distortion is correspondingly reduced, a great advantage of the method. A further rough and presumptive check on the calculations was obtained by measuring with a simple mechanical contrivance the change of internal diameter while the cylinder was exposed to external pressure only by thrusting it into its collar. The change of internal diameter calculated with the same simplifying assumptions mentioned above was 83 per cent of the measured change. T H E MATERIAL FOR TRANSITION

The demands on a transition adapted to serve for a pressure fixed point are exacting; it must occur at the proper pressure, the transition must

30,000

5

KG/CM 2

run rapidly and with large enough change of volume for easy manipulation with both phases present, the transition should start in either direction with the minimum amount of super- or subpressing, and there should be little or no region of indifference. This latter means that when the two phases are in contact at a fixed temperature, pressure should automatically come to a single final value, no matter whether that value is approached from above or below. This requirement of no region of indifference is automatically met when the phases are liquid and solid, as in the former method of calibration against freezing mercury, but it is a very restrictive requirement on the phase change of solids. There were available for selection some 65 or 70 substances whose phase diagrams have been mapped out up to 50,000 kg/cm 2 . Most of these may be summarily ruled out, chiefly on the ground of too great sluggishness of transition or too wide a region of indifference. Of the entire list only three were found sufficiently promising for further examination: CuaI8 with a transition near 15,000; KCN with a transition near 20,000, and Bi with two transitions in the neighborhood of 25,000. KCN was tried, but proved too sluggish and also to have an appreciable region of indifference. CuJ 2 was not tried, the measurements with bismuth having in the meantime shown that the mercury and bismuth fixed points would be adequate, but I do not believe that if Cu2Ia were tried it would prove any more satisfactory than KCN. Bismuth proved much easier to handle even than freezing mercury, and seems satisfactory in every way. The measurements of the rest of this paper are based on the use of bismuth. If in the future it should be necessary for someone else to use some other transition it would be worth noting that in some cases the secondary properties of the transition are very sensitive to impurity, so that it is not inconceivable that highly purified Cu2I3 or KCN could be used. DETERMINATION OF T H E FIXED POINTS

Determinations of the transition pressures were made with three different pieces of apparatus. Two of these were not as favorable as the third; the measurements with them must be regarded as in the nature of checks. Most of the measurements were made with the apparatus already used for a variety of measurements to 30,000. This is shown in Figure 5. External pressure on the pressure vessel is produced by thrusting it into a tapered collar with a 6 inch piston. Pressure on

132 — 3395

6

BRIDQMAN

FIGURE 5. General view of the pressure apparatus. The bismuth undergoing transition is at B. In use the piston A is in a more extended position than shown, and the piston Ρ is shorter.

132 — 3396

the bismuth is produced by a 3.5 inch piston, driving a carboloy piston varying from 0.485 to 0.515 inches in diameter in the various set-ups. In order to be able to use the experimentally determined values for the correction to the cross section it is of course required that the external pressure on the vessel during the determinations of the transition be approximately the same as during the determination of the correction. This external pressure does not need to be controlled with high accuracy, however, and it was sufficiently good to measure the pressure on the 6 inch piston with a commercial Bourdon gauge of 15,000 lb/in 2 capacity. Friction on the outside of the cone could be allowed for by determining the displacement into the collar as a function of pressure, both with increasing and decreasing pressure. The pressure on the 3.5 inch piston driving the carboloy piston, on the other hand, has to be determined and controlled with the greatest possible precision. For this purpose the pressure on it was measured with a free piston gauge connected in series in the line between pump and press. The response of such a gauge to changes of pressure is always somewhat sluggish in spite of continual rotation of the piston, so that after every increase of pressure by operating the hand pump, or after every decrease by opening the valve, the pressure on the 3.5 piston would at first overshoot the mark, slowly creeping back to the final value as the piston gauge assumed control. Since the progress of the transition itself has to be judged by observing the creep, this effect might seriously lower the accuracy of the readings. It was avoided by providing a valve in the line between piston gauge and 3.5 inch piston, which was closed before every change of pressure, not being opened again until the piston gauge had become stationary. Even at constant pressure it was necessary to pump at intervals because of the unavoidable leak in the piston gauge. These intervals were made longer than they would have been otherwise by attaching a chamber of considerable capacity in the line, the volume compression of the liquid in this chamber providing a reservoir partially neutralizing the leak at the gauge. By this means the necessary pumping intervals were made longer than the intervals necessary to discover the direction of the transition, so that there was no complication on this score if the manipulations were properly made. The bismuth had been highly purified by double electric deposition, and had furthermore been me-

T H E M E A S U R E M E N T OF HYDROSTATIC P R E S S U R E TO

chanically filtered in the liquid state and slowly crystallized. The procedure in determining the transition pressure was first to increase the pressure in large steps on 3.5 and 6 inch pistons simultaneously, making rough measurements for orienting purposes of piston displacement and of the displacement of the pressure vessel into its collar. From this latter the friction could be calculated and thus a check made that such an external pressure had been attained as was required to duplicate the conditions during the measurements of the bore correction. Having arrived at the approximate pressure of the transition, the external pressure was kept constant by maintaining the pressure on the 6 inch piston constant, and the further manipulations were made only with the pressure on the 3.5 inch piston, the changes of which were slight. Pressure was now increased in small steps of approximately 400 kg/cm 2 on the bismuth, until the transition had started to run, as shown by the rapid piston displacement on the 0.0001 inch gauge. The total piston displacement corresponding to complete running of the transition was approximately known from previous work. The transition was allowed to run until it was one third or one half complete, and then pressure was lowered by 400 kg/cm 2 , the transition then ceasing to run. Pressure was now increased again in steps of 80 kg/cm 2 (on the bismuth), pressure held at each point for three minutes, and the piston displacement noted during these three minutes as a function of time. There is always some creep after every change of pressure; the transition is shown by a larger creep which does not slow down with time. Having thus located the transition with increasing pressure, the reverse process was performed, giving thus a location of the transition with decreasing pressure to the nearest 80 kg/cm 2 . With a little practice three

30,000

7

KG/C'M 2

minutes was sufficient to adequately characterize the creep and definitely establish the presence or the absence of the transition. The mean of increasing and decreasing determinations was taken as the transition pressure. The ratio of the difference between increasing and decreasing pressure to the total mean pressure was defined to be the "total friction"; it includes ordinary mechanical friction and the natural width of the "band of indifference." The total friction varied considerably in the different set-ups. The minimum value was 2.9 per cent— this sets an upper limit to any possible region of indifference. The width of the region was established with much greater accuracy during the calibration of the manganin gauge, to be described presently. The question of whether the pressure determined by taking the mean of the increasing and decreasing pressures is the pressure of true thermodynamic equilibrium is after all of minor importance; the important point is how reproducible the mean is, and this question is answered by the consistency of the results with different set-ups. The results are summarized in Table I. Rough check measurements were made with two other pieces of apparatus. One of these was the regular apparatus in which compressibilities are being measured to 50,000, to be described in fuller detail in another paper. The piston diameter of this is only 0.260 inch. The distortion correction was determined by calculation, allowing as well as possible for end effects, and at 25,000 was 1.35 per cent on the cross section. The other apparatus was a preliminary one of 0.40 inch diameter, which had been used in checking the effectiveness of giving external support to the cylinder by making it conical and pushing it into a collar. The external support in this apparatus was produced automatically by the thrust of the

TABLE

I

PRESSURES OF THE I - I I BISMUTH TRANSITION

75°

30° Diam. of Piston inches .4934 .5332 .5334 .4918 .4958

Total Friction Per Cent 5.1 9.0 4.1 4.0 7.4

Weighted mean

Pressure kg/cm2 25,430 25,465 25,400 25,450 25,380

Diam. of Piston inches .5334 .4918 .4958

Total Friction Per Cent 2.9 4.3 11.2

Weighted mean

Pressure kg/cm' 23,420 23,330 23,160 23,350

25,420

132 — 3397

8

BRIDGMAN

high pressure piston, and not independently. The external support on this is much less than with the two others, the external pressure being only 0.105 of the internal pressure, so that the correction for distortion is much larger. This correction was calculated to be 2.5 per cent for the middle of an infinite cylinder with the same simple assumptions as those already mentioned. This is to be reduced by an uncertain amount due to two end effects. Probably multiplication by a factor of one half is the best that can be done to allow for these end effects. The transition pressures found at 30° in this way with the 50,000 apparatus and with the early apparatus were 25,880 kg/cm2 (total friction 8.2%), and 25,620 kg/cm2 (total friction 4.5%) respectively. The agreement can probably be regarded as satisfactory in view of the more unfavorable dimensions of these two other forms of apparatus, and the larger calculated corrections. In addition to the transition between the forms I and II, which is the one which has been just studied, bismuth has another transition between the forms II and III at pressures not much higher than I—II. With proper care the II—III point might also serve as a fixed point. The manipulations are somewhat less convenient, however, because in the first place the transition I—II has to be got out of the way before II—III can be measured, and the two transitions are so close together that this offers some inconvenience, and in the second place the volume change II—III is only two thirds that of I—II. I did not attempt therefore any determination of the transition I I III with an accuracy sufficient for calibration purposes, but I did make measurements with a single set-up with the good apparatus and obtained the Mowing results: At 30°, 26,960 kg/cm2 (total friction 4.5%); and at 75°, 25,850 kg/cm2 (total friction 3.1%). T H E MANGANIN GAUGE

The fixed points having been established, the manganin gauge can be calibrated in terms of them. Two such gauges have been calibrated at this writing, wound from wire from the same spool. The manganin was of American origin, obtained from the Driver Harris Co., of 0.0035 inch diameter, double silk covered, wound non-inductively into coreless toroids of about 70 ohms resistance. Similar coils were used in measurements previously published of resistance to 30,000, pressure being obtained by linear extrapolation from the 7640 kg/cm2 mercury point. The coils were seasoned

132 — 3398

by exposure for 8 hours per day for 6 days to a temperature of 140° C. with an interlude of 1 hour each morning at liquid air temperature, and also by several applications of 30,000 at room temperature. In general, the zero of these two coils has been noticeably more constant than that of other coils used in previous work to lower pressures. The first coil was calibrated at room temperature (23° C.) against freezing mercury at 0° C. (7640 kg/cm2) in the apparatus with which most of my measurements to 12,000 have been made. In this apparatus the upper cylinder in which the coil is located is at room temperature, while the lower cylinder, containing the mercury, is at 0°. After this calibration the coil was transferred to the 30,000 apparatus, in which was placed a cylindrical slug of the same electrolytic bismuth as that whose absolute transition pressure was determined above, weighing about 28.5 gm. The rest of the 30,000 container was filled in the regular way with iso-pentane, which is known not to freeze at 30° below 30,000. From previous measurements the approximate transition pressure and the displacement of the piston to be expected during the transition were known. To facilitate following the progress of the transition the displacement of the piston was read with an Ames dial gauge graduated to 0.001 inch. The procedure was to raise pressure nearly to the transition point, wait for thermal and other equilibrium, then increase pressure sufficiently to start the transition, which was then allowed to run about one half to completion, as indicated by the piston displacement. Pressure was now reduced to such a value that there was no secondary reaction. From here as a starting point, and with the transition known to be one half completed so that the two phases were certainly in contact with each other, pressure was raised until it started to creep back perceptibly. This creep was allowed to continue until it had sensibly stopped, which might take from 10 to 15 minutes. The pressure reached in this way was called the equilibrium pressure from above. Pressure was next lowered until it started to creep up again, and in a similar way an equilibrium pressure from below was obtained. The mean of these two was taken as the equilibrium point. These two pressures differ by at least the true width of the region of indifference, but may differ by more than this because of sluggishness of the transition. If the width of the region of indifference were being

THE MEASUREMENT OF HYDROSTATIC PRESSURE TO

determined for itself a different procedure would be adopted. However, since pressure is here transmitted by a liquid, the pressures reached from above and below should not differ because of any factor of solid friction, and in fact the two pressures found with the manganin gauge calibrations are much closer than in the absolute determination of the transition pressures already described. The first coil was calibrated against the bismuth I—II transition in this way at 26°, 30°, and 75°. The points at 7640 being already known from the measurements with freezing mercury (the 7640 point at 75° had to be obtained from previous measurements of the temperature coefficient), it was then possible to construct a second degree formula, giving pressure as a function of the measured displacement of the balancing point on the slide wire, reproducing the known points at 7640 and 25,000. If the relation were exactly linear, assumed in previous work, the second degree term would of course vanish. It did not vanish, but was small. At 30° the pressure of the bismuth point obtained by linear extrapolation from 7640 was 25,010 against 25,420 actual, or 1.6 per cent too low, and at 75° the figure was 23,120 against 23,300, or 0.8 per cent too low. The deviation from linearity is thus in an abnormal direction, shown by no other pure metal or alloy except single crystal antimony over a limited range. The procedure in calibrating the second coil was somewhat different. In the first place, the 7640 point was experimentally determined at both 30° and 75° in order not to have to rely on the temperature coefficient determined on another sample. The 7640 point was determined in two steps. First, the 7640 point at room temperature of a coil of German manganin 0.0055 inch in diameter, such as had been used in all my early work to 12,000, was determined against freezing mercury at 0° in the regular way. The constant of this coil having been thus determined, the 30,000 coil was then compared against it at two temperatures, the German coil being kept fixed in one cylinder at room temperature, and the 30,000 coil in the other cylinder, which was thermostatically maintained first at 30° and then at 75°. The two coils were compared against each other at intervals of 2000 kg/cm 2 over the pressure range up to 12,000. The ratio of the resistance changes of the two coils proved not to be a constant, but there is a slight drift with pressure. A smooth curve was drawn through the points thus found,

30,000

KG/CM 2

9

and the coefficient of the 30,000 coil at 7640 was taken from the curve. The 30,000 coil was next transferred to the 30,000 apparatus for calibration at the higher points. The arrangements for this were modified as compared with those of the first calibration. The amount of bismuth was cut in two, and the space thus made available was filled with a thin walled steel shell containing mercury. In this way both mercury freezing points and bismuth transition points could be determined with the same apparatus. It was not feasible to cool the 30,000 apparatus to 0°; otherwise a single set-up could have been employed for the complete calibration. With this arrangement the mercury and the bismuth points were determined at 30° and 75°. The freezing pressures of mercury at these two temperatures are approximately 13,700 and 23,000 kg/cm 2 . If the 13,700 point were accurately known, the 7640 point could be dispensed with. Theoretically, this point should be known from previous work, since the previous calibration of the manganin gauge against the free piston gauge had been made up to 13,000. Actually, however, the 7640 point was determined more carefully and a number of times, so that more confidence can be placed in it than in a value just beyond the previous range, it being well known that error is likely to pile up near the end of a range. At 75° the mercury point is in new territory, and is very close to the bismuth point; the determination at 75° is therefore to be taken in the spirit of a determination of a new fixed point. At 30°, the bismuth point extrapolated linearly from 7640 was 24,910 instead of 25,420, or 2.0 per cent too low, against 1.6 per cent with the first coil. At 75° the linearly extrapolated bismuth point was 22,920 against 23,300, or 1.6 per cent too low, against 0.8 per cent of the first coil. This indicates that the departure from linearity of pieces of wire from the same spool may vary, just as the absolute constants are known to vary. The 7640 constant of the second coil was 0.6 per cent greater than that of the first one. This means that for the highest accuracy a two point calibration for every individual coil will be necessary. It would be too early to draw the conclusion that in general the greater departure from linearity goes with the greater first degree coefficient. Two determinations at 30° of the bismuth point of the second coil on successive days gave identical results to the limit of sensitiveness of the readings, better than one part in 6,000. Determinations

132 — 3399

10

BRIDGMAN

of the bismuth and mercury points at 30° at an interval of two months gave an increase of 5/6000 of the bismuth point and 9/3700 for the mercury point. Taken at its face value, this would indicate a considerably larger secular change in the second degree term than in the first degree term, but it would be too early to draw this conclusion in general, because of the uncertainty in the bismuth point due to the region of indifference. As a further indication of the variation in magnitude to be expected in the second degree term for different grades of manganin may be mentioned the results of the calibration up to 12,000 of the 30,000 coil of American manganin against the coil of German manganin. The ratio of the change of resistance of the first to that of the second varied approximately linearly with pressure from an initial value of 1.694 to 1.679 at 12,000. The interpretation of these results is that the second degree term in the German manganin is of the opposite sign from that of the American, the numerical value being such that a linear extrapolation by the German manganin from 7640 to 12,000 would be in error by 0.4 per cent at 12,000. At 30° the measurements with the two coils gave values for the width of indifference for bismuth I—II varying from 60 to 100 kg/cm 2 , and at 75° from 15 to 50. The lower of these values are to be taken respectively as upper limits for the true width of the region of indifference. In contrast to the bismuth points, the mercury points showed no perceptible region of indifference at all, the sensitiveness of the measurements being about 3 kg/cm 2 . This is to be expected because of the different dynamics of a solid-liquid transition as compared with a solid-solid transition. In any event it affords a check on the sensitiveness of the method. The following values were obtained for the melting pressure of mercury: at 30°, 13,700 and 13,730 kg/cm 2 , and at 75°, 22,950 kg/cm 2 . At 30°, the value of my former measurements, obtained by a slight extrapolation, was 13,610. At 75° I have already published3 the value 22,570, obtained by a linear extrapolation of the manganin gauge. Correcting this by 1.6 per cent for lack of linearity of the manganin as determined above, gives 22,930, practical agreement with the present value. Extrapolation of my previous values from 20°,

132 — 3400

assuming a second degree relation in the temperature with the constants so chosen as to agree with the measurements in the range from 20° down to the atmospheric melting point, gives 22,600 at 75°. The melting line thus appears to have very slight curvature, but it continues in the normal direction over the entire range up to 75°. This is of some interest, because except for water, this is the highest pressure to which any accurate determinations of the melting parameters have been made. The curvature of the melting curve of water was also found to be normal, that is, the curve is concave toward the pressure axis. Before the method of using the transition of bismuth to give fixed points was adopted, I made various attempts to calibrate the manganin gauge directly from measurements of the force driving the piston. This method was eventually abandoned in favor of the method above because it appeared that the friction on a piston packed to prevent leak of a liquid must always be greater than the friction of a piston packed against leak of a soft metal like bismuth. However, if the other better method had not offered itself, it would doubtless have been possible to obtain fairly satisfactory results by sufficient repetition of this method, since the curves with rising and falling pressure were surprisingly reproducible with different set-ups. The total friction with this method was 24 per cent at 25,000 and was rapidly becoming greater, so that I did not try for higher pressures. The measurements by this method showed the same abnormal departure of the resistance of manganin from linearity in pressure, and roughly of the same magnitude, between 1 and 2 per cent at 30° at 25,000, as by the better method above. It is worth while to have confirmation by this more direct method, even although the accuracy is lower. I am indebted for financial assistance in this work to the Rumford Fund of the American Academy of Arts and Sciences and to the Francis Barrett Daniels Fund of Harvard University. REFERENCES

' P . W. Bridgman, Proc. Amer. Acad. 44, 201-217, 1909; 47, 321-343, 1912. * P. W. Bridgman, Proc. Amer. Acad. 72, 157-205, 1938 ; 70, 71-101, 1935. "First reference under (2), p. 192.

THE LINEAR COMPRESSION OF IRON TO 30,000 kg/cm2 BY P. W . Presented Nov. 8, 1939. INTRODUCTION

I have already published1 measurements of the linear compression of a number of substances up to 12,000 kg/cm 2 . Apparatus has now been developed by which this range can be extended to 30,000, and I am now starting a program of measurement of linear compressions in this higher range. There are two necessary preliminaries to such a program. The first is the establishment of the pressure scale by the establishment of pressure fixed points and calibration of secondary pressure gauges. This work has already been done and is being published. The second is the measurement of the absolute compression of some substance of reference; this is the task undertaken in this paper. This task is necessary because the method adopted for the measurement of the linear compression of most substances is a differential method—measurement of the difference of compression between the substance in question and a standard. Measurement by difference is used because it is very much more convenient and rapid, although it would be possible to measure the actual compression of many substances by the same method as that used here for the standard substance. As in the previous work, the standard substance is chosen as pure iron. METHOD

The general features of the method are the same as before,2 namely the change of length of a rod of iron is measured relative to the pressure vessel, and this relative measurement is converted into an absolute measurement by an independent and simultaneous measurement of the distortion of the pressure vessel. The whole experimental set-up is, however, so different from that used before that a fresh description of many of the details is necessary. The pressure apparatus now has to be in a single piece, separate pressure chambers connected by tubing no longer being feasible; this results in a much decreased length of the specimen with corresponding loss of sensitiveness. The length was less by a factor of about 5. However, the chief interest in pushing the results to a higher pressure range is in the departures from linearity. Other things being equal, the accuracy with which

BRIDGMAN Received Nov. 8, 1939.

the second degree term in the pressure can be determined increases as the square of the range. The range is here increased by a factor of 2.5 ( = \/6.25), thus somewhat overbalancing the unfavorable factor arising from decrease of length. The method by which the change of length of the iron rod relative to the pressure vessel was measured is practically the same as that used before.2 A shoulder on one end of the rod is kept pressed by a stiff spring against a shoulder in the pressure vessel. A high resistance wire is pressed against the other end; this resistance wire slides over a contact fixed to the pressure vessel. Potentiometer measurements of the effective resistance of the wire, made on a potentiometer in the way already extensively used and described, give, after suitable reduction, the mechanical motion. The arrangement is shown in Figure 1. The arrangement by which the change of length of the pressure vessel was determined had to be materially altered from that used before because of the drastic difference in the arrangements. Formerly the pressure vessel was a long geometrically perfect cylinder, and the change of length was measured with an optical magnifying device between points on the outside opposite the ends of the iron rod. But now the pressure vessel was conical in shape, and it was subjected to external pressure by being pushed into a heavy conical collar. The points on the exterior of the pressure vessel opposite the ends of the rod were therefore inaccessible. Even if these points had been accessible, measurement of the change of external length would probably not have been particularly pertinent because the proportions were such that appreciable warping of the cross section may be anticipated. Under the circumstances it seemed that the best that could be done was to determine the change of length of the vessel from two probe holes, drilled approximately parallel to the axis, as shown in Figure 2. These holes were % inch in diameter, and were situated about 0.5 inch from the axis, giving therefore about 0.25 inch of solid wall between the hole and the inner bore. So close to the center as this, warping would be ex-

133 — 3401

12

BRIDGMAN

pected to be very much less than at the exterior, since near the axis the warping must be of the second degree in the radial distance.

clearance for most of their length of 0.010 inch, but where they emerged from the cylinder they were fitted with collars with clearance of only 0.0005 inch in order to reduce play. The lower ends of the probe rods were bevelled at 60°, and the very ends rounded to spheres of small diameter and hardened. A sharply pointed depression in the cylinder to receive them was made with a punch. The relative longitudinal displacement of the probe rods was transferred for measurement to two heavy iron bars, bent as shown in Figure 2, and the relative motion of these bars ultimately determined with an Ames dial gauge, as indicated, graduated to 0.0001 inch. The weight of the bar for the lower probe was entirely taken up by a counterweight with ball bearing pulley, and the bar itself was pressed into firm contact with the probe by a spring, not shown in the figure, thrusting directly in the line of the probe. Contact of the other bar with the upper probe was maintained by the weight of the bar (about 2 kg.), which was not counterbalanced in any way. Three point contact between the two bars was maintained by steel balls rolling in polished V grooves or over polished flats in an obvious enough fashion. The bars were maintained vertical against the tendency of the weight of the upper bar to fall toward the left by a horizontal cord several meters long acting toward the right at the point A. This elaborate and somewhat clumsy arrangement was made necessary by the exigencies of construction of the press, by the fact that there is a total vertical displacement of the pressure vessel during the run of nearly 0.5 inch as it is forced into its supporting collar, and by the desirability of some sort of arrangement that could be immersed into the temperature bath along with the entire press to permit measurements at higher temperatures. Before this final arrangement was adopted a simpler but less satisfactory scheme of take-off from the probes by a lever arrangement was tried.

FIGURE 1. The sliding contact arrangement for measuring the change of length of the iron rod I with respect to the pressure vessel.

Apparently the cylinder was not appreciably weakened by the presence of these probe holes. One might have anticipated either an increased danger for the cylinder to rupture by splitting, or else a possible collapse of the holes under the external pressure, but neither effect was found. No permanent change of dimensions of the holes could be detected after use. The probe rods had a

133 — 3402

The maximum relative displacement of the ends of the probe holes was about 0.00400 inch, in the direction of an extension with increasing pressure. This extension therefore makes the shortening of the iron bar relative to the pressure vessel too large, so that the correction to the relative shortening is subtractive. The longitudinal correction is about one quarter of the measured relative shortening. An error of 0.00001 inch in the longitudinal shortening of the cylinder, which was the limit of sensitiveness of the Ames gauge, corresponds there-

THE LINEAR COMPRESSION OF IRON TO

30,000

Κβ/cM 2

14

BRIDGMAN

fore to an error of 1/1200 in the final result. The sensitiveness of measurement of relative shortening of rod and pressure vessel may be pushed considerably higher by suitably choosing the electrical constants, so that the limiting error, as far as sensitiveness of reading goes, is set by the longitudinal factor. The measured longitudinal distortion of the vessel is a resultant of several factors, of which the largest are probably internal pressure, external pressure, and longitudinal compression arising from the action of the pressure thrusting the vessel into the external conical collar. These three stresses are not simply related to each other, and the resultant is complex. Since the correction determined by these factors is one third of the final result, and is doubtless the factor limiting the accuracy of the final results, it will pay to discuss it in some detail. By far the largest of the three component effects just mentioned is that due to the external pressure on the vessel due to the thrust into the supporting collar. This effect is naturally an extension with increasing pressure. The effect of internal pressure is on the other hand a shortening. The third component, longitudinal compression due to the thrust, may be shown by simple calculation to be small at the most. Only the roughest qualitative calculation can be made of this, because this compressive thrust is variable along the length of the vessel, having its full value at the bottom, and dropping to zero, in a way not easy to specify exactly, at the top. The two main components in the distortion do not vary in a simple way over the pressure range. With increasing pressure, internal and external components both vary linearly and the resultant total extension is also approximately linear. But with reversal of direction of change of pressure on reaching the maximum, the component due to internal pressure at once starts to reverse itself, whereas external pressure remains constant for a while in virtue of friction in the collar, in spite of the decrease in longitudinal thrust. The result is that the net longitudinal extension continues to increase when pressure starts to drop, reaches its maximum between 20,000 and 25,000, and gives a hysteresis loop of the general form indicated in Figure 3. The amount of external friction and therefore the external pressure can be determined with fair accuracy from the measurements, which were always recorded, of the longitudinal displacement of the pressure vessel into the supporting collar. Given the external and internal pressure it is then pos-

133—3404

sible to reproduce, with an error of perhaps 5 per cent, the longitudinal distortion by a linear expression in these two pressures. A check can be obtained on the measurements of longitudinal distortion by measuring the relative motion of rod and vessel when external pressure only is applied. In this case there is no change of dimensions of the rod, so that the potentiometer measurements should agree exactly with the distortion measurements. Of course this could be done only over a comparatively small external pressure range, because the maximum external

FIGURE 3. Showing the general nature of the hysteresis loop in the relation between internal pressure (abscissas) and elongation of the pressure vessel measured at the probe holes (ordinates).

pressure with no accompanying internal pressure would have collapsed the vessel. The range of external pressure for this check was taken as about one half the maximum of the regular runs, corresponding to about 6,000 kg/cm 2 external (12,000 during regular run). The uncorrected results of the check made in this way were not good; the relation was not linear, there was hysteresis, and different set-ups gave different results. The extension measured by the potentiometer varied on three set-ups from 6 to 17 per cent greater than that measured at the probe holes. The irregularities are probably due at least in part to irregularities in the external friction. There are two conceivable reasons for the discrepancy, granting that the measurements themselves are correct. The

THE LINEAR COMPRESSION OF IRON TO 3 0 , 0 0 0 Κ β / c M 2

15

be due to warping of the cross section. This discrepancy of 1.0 per cent is on a correction of 25 per cent to the measured change of length, so that the maximum possible error in the final result that can be ascribed to warping is .25 per cent. Even this small possibility of error is much reduced by the procedure adopted for reducing the final observations, as will be explained below. This check gives confidence in the soundness of the calculation of the correction for change of inclination of the lower probe rod. Under the conditions of the pressure measurement, this correction is much less than above, where the pressure was external only and the conditions as unfavorable as possible, for in the actual experiment the radial displacement is much less than above because the internal pressure to a large extent neutralizes the external pressure. A correction of 0.53 per cent was applied to the final compressibility for this effect. The mounting of slide wire and contacts has already been shown in Figure 1. The wire was of "Nichrome IV," about 0.013 inch in diameter, with a resistance of about 0.13 ohms per centi1 T \ meter. The total relative motion was about 0.046 λ+ μ ra μ = cm, corresponding to a change of resistance of 0.0060 ohms. The constants of the electrical cir' i I λ+ μ μ cuit were so chosen that this gave about 50 cm displacement of the slider of the potentiometer. The external radius does not enter this expression. This could be read to 0.1 mm, or 1 part in 5000. Taking r. = 1.20, and r, = 0.57, and for the elastic So high a sensitiveness was greater than could be constants λ = 9.4 Χ 1011 and μ = 7.7 Χ 1011, used because of the irregularity of the readings, this gives u /u = 1.35. Now u is accessible which at the best amounted to 10 times as much, to direct measurement; this was done with a and usually was much more. simply constructed bore measurer under the same The slide wire was calibrated by measuring on conditions of external pressure. It should also the potentiometer the change of resistance for be possible to calculate uH directly from elasticity known displacements. The displacements were theory, assuming an infinitely long cylinder. The produced by a screw in an arrangement of obvivalue calculated in this way is 15 per cent less ous enough design, and the the amount of disthan that directly measured, giving a good enough placement was measured with an Ames 0.0001 check considering the crudity of the approxima- inch gauge, which itself was calibrated against tion. u H now being known, u, a can be at once standard gauge blocks. The potential and current calculated. To the u,a found in this way a small leads were of pure nickel, 0.008 inch in diameter, term amounting to 11 per cent is to be added for attached by electric welding by the discharge from the radial expansion of the bottom of the cylinder a condenser of suitable capacity charged to 110 under the thrust which generates the external pres- volts. In the previous work to 12,000 kg/cm 2 sure. The resolved component of this along the the terminals had been attached by soft soldering, axis can now be obtained, with the result that the but in this new high pressure range of 30,000 longitudinal extension of the vessel measured with soldered connections had been sometimes observed the probes corrects up to a value only 1 per cent to crack because of the high differential compresless than that measured with the potentiometer sion. Such cracks, even if the connection were directly on the inside, giving essentially a check, not absolutely broken, might introduce irregulariconsidering the irregularities. The outstanding ties because of indefiniteness of the point of effecdiscrepancy of 1.0 per cent might be argued to tive contact. In fact the results did show a first of these is warping of originally plane sections of the vessel, different in amount at the two ends. Under the conditions of these check measurements it is difficult to estimate even what the sign of this would be, but it would seem that its magnitude must be small. The second and the more important possibility is concerned with the fact that the lower probe hole is not parallel to the axis, but is inclined to it at an angle of 8.15°. This is a bad feature of the design that was recognized in the beginning, but the geometrical restrictions imposed by the rest of the apparatus made it almost impossible to avoid. If the angle 8.15° changes during the extension there is a resolved component along the axis which contributes to the measured longitudinal displacement. It is not difficult to get an approximate numerical value for the magnitude of this effect. In the first place there is the formula of elasticity theory for the ratio of the radial displacement at the radial distance r a to that at the interior wall r, in an infinitely long cylinder under external pressure only: |

u

ra

ri

Ti

t

1

H

1 3 3 — 3405

16

BRIDGMAN

notable improvement in regularity after changing from soft solder to the weld. The correction for the change of resistance of the slide wire under pressure over the entire range up to 30,000 was determined by direct measurement on a piece of wire contiguous in the original length to the piece used for the slide. This piece was 6 cm long, and 4 cm between potential terminals. The change of resistance proved to be linear with pressure over the entire range, with

final result arising from this term is about 5 per cent of the difference of compression between nichrome and iron. Previous measurements, not published, up to 12,000 had shown that this difference is one per cent of the compression of iron it-

Fiqure 4. The blank insulating plug with pack-

ing rings. a maximum deviation of any single observed point from a straight line of about 1 per cent of the maximum effect. The coefficients were: at 30' JR JR - - 6 . 5 5 X 10 _ T , and at 75» ρ Ä(0,30°) ' pÄ(0,75«) = —6.62 Χ Ι Ο - 7 . The correction to the measured change of resistance arising from the change of resistance of the slide wire with pressure is 12 per cent, so that any error in the final result arising from uncertainty in this correction should be well below 0.1 per cent. The compressibility of the slide wire also enters as a correction into the final result. The various dimensions are such that the correction on the 133 — 3406

Figure 5. Detail of the insulating leads used in

the plug of Figure 4. self. This was taken as sufficient justification for entirely neglecting this correction in the present work without further examination. In Figure 2 is shown the iron bar, I, mounted in the pressure vessel ready for measurement. I t will be noted that three springs are used to keep the various surfaces in contact. Spring A (see

THE LINEAR COMPRESSION OF IRON TO 3 0 , 0 0 0 KG/CM 2

detail in Figure 1) has to be materially stiffer than B, because Β pushes against it. These two springs were wound out of piano wire of suitable diameter. At first the spring at C (Figure 2) was not employed, but the iron rod was held in contact with the shoulder on the pressure vessel by a solid nut screwed tightly home. However, various irregularities seemed to have their origin in differential distortion of the rod and the pressure vessel at this point. These irregularities were removed by putting a very stiff helical spring, milled from a solid piece of tool steel, between the nut on the rod and the shoulder on the pressure vessel. During these compressibility measurements a much more satisfactory solution of the problem of electrically insulating the leads to stand these high pressures was arrived at than had been previously found. This had always been the limiting factor, since it takes much time to set up these insulating plugs and they used to fail either mechanically or electrically after one or two applications of the maximum pressure. Insulation is now provided by a cone of pipestone, A, only 0.005 inch thick, with an angle of about 15° (see Figure 5). The thickness is so small that the pipestone is prevented from shearing out by friction. The shearing stress in the pipestone diminishes exponentially along the length, so that at the apex of the cone, where the wire emerges, the stress is reduced to zero. There is therefore no tendency to blow out the fine piano wire lead, a great advantage over previous arrangements. This arrangement of the pipestone remains mechanically and electrically perfect for a number of applications of pressure. The angle is such that there is no disadvantageous sticking, and the cone can be removed and replaced without renewing the pipestone. The cone carrying the fine stem is of mild steel. The piano wire stem is knotted once to prevent pulling through. This scheme of knotting the lead wire was used at the Geophysical Laboratory a number of years ago, with fine copper wire, for a considerably lower pressure range. It would not be possible to knot a piano wire of much larger diameter than that used here, 0.013 inch. The knot on the wire in most of this work was buried in soft solder; this prevents it from cutting itself and also permits a longitudinal pull up to the breaking strength of the straight wire to be applied without cutting through at the knot. However, because of the relatively high differential compression at these high pressures, the solder has a tendency to pull away from the

17

steel, permitting leak past the stem after a number of applications. Toward the end of this work the wire was silver soldered into the cone with better results. In the previous design leak was prevented by the principle of the unsupported area, the pressure in the soft packing being greater than that in the liquid. Now, however, the expelling thrust on the wire is done away with by the action of the cone, and leak has to be prevented by the natural resilience of the soft packing with no help from any differential stress. Fortunately the compressibility of rubber and "Duprene" is low enough so that if the washers are initially cut as large as is possible to crowd into the hole without folding there is still some excess natural diameter left at 30,000 to prevent leak. Special measurements of the compression of an equivalent grade of soft rubber gave a volume decrement of 27 per cent at 30,000 kg/cm 2 , from which an idea can be obtained of the initial dimensions in the washer necessary to reach the maximum pressure without leak. However, when the washers are cut as large as they have to be to reach these high pressures, they are almost certain to fold and slip out of the hole unless some guidance is provided. This is done by the helical steel spring pressing down from above, as shown in Figure 5, the top part of the spring pushing against a stop clamped by a screw to the lead wire. Soft rubber and Duprene washers are used, the Duprene being on the side next the liquid to prevent the iso-pentane attacking the rubber, and the rubber doing perhaps the bulk of the packing because of its greater pliability. It is well to renew these washers after several applications of pressure, because they are likely to receive a set, which may lead to leak. Another improvement in the plug is the insulation around the fine stems where they come out through the plug. This was formerly of fine glass tubing, which was constantly breaking under the slight movements of the stems, and short circuiting. The glass is now replaced by silk; half a dozen turns of silk thread are wound around the wire at the mouth of the hole and these are then crowded to the bottom with a tube. The process is continued until the entire annular space, B, between stem and plug is filled with silk. No trouble has been experienced from short circuit in this location since this arrangement was adopted. One has to be sure that the silk initially is quite dry, and in assembling one has to avoid handling it with moist fingers. It is of extreme importance that all particles of dirt should be eliminated on assembling the

133 — 3407

18

BRIDGMAN

apparatus. As already mentioned, the maximum relative displacement is about 0.047 cm and the maximum deviation from linearity is about 0.0005 cm, so that an exceedingly small particle of grit between the bearing surfaces at any of the three crucial places may have a very large effect. The geometrical arrangement of the bearing surfaces was made as unfavorable as possible to the lodging of grit upon them, and all parts were cleaned before assembly by copious flushing with xylene and blowing out with an air blast. M E A S U R E M E N T S , CALCULATIONS, AND R E S U L T S

More than twenty-five different set-ups were made and measurements made to 30,000 kg/cm 2 at room temperature. In spite of every effort it was not possible to get rid of capricious irregularities. There probably was no one cause of these, but many of the necessary conditions of the experiment were favorable to such irregularities. Friction cannot be expected to be exactly reproducible, and the steel vessel, continually strained as it is beyond the elastic limit, would be expected to show irregular hysteresis and creep. There seemed nothing to do except to attempt to eliminate the effect of such capricious irregularities by a large number of observations. In marshalling the measurements a procedure was adopted calculated to eliminate any systematic error due to one effect hitherto not adequately discussed, namely warping of the cross section as a result of which the apparent change of length of the vessel measured at the probe holes is different from that at the interior where the rod is situated. It is evidently only differential warping at the two ends of the rod that is harmful. Warping may arise from various departures of the conditions from those in an infinitely long cylinder with internal pressure along the entire axis. One such effect arises at the two ends, where the internal pressure ceases at the upper and the lower plugs. This effect, however, is probably negligible because the plugs are several diameters removed from the critical region. It would seem that by far the most effective source of warping is tangential drag along the axis arising from friction at the outer and inner surfaces of the vessel. At the outer surface there is such a frictional force when the vessel is forced into its supporting cone, and at the interior there is such a force due to the friction of the moving plug with which pressure is generated. These effects, being different at the two ends, will produce just that differential warping that is es-

133 — 3408

pecially to be avoided. This warping reverses sign when the direction of friction changes, and therefore reverses when the direction of motion of the moving plug or of the vessel into its cone reverses. The existence of the effect may be demonstrated experimentally by just reversing the direction of motion of the moving plug or of the vessel into its cone at approximately constant values of internal and external pressure. The maximum magnitude of this warping effect amounts to about 1 per cent of the total effect at the maximum pressure. During increasing pressure the effect will be in one direction and during decreasing pressure in the other. It should be eliminated by taking the mean of runs with increasing and decreasing pressure. These considerations controlled the manipulation of the results. Readings were made at 13 approximately equally spaced pressure points, that is, at 0, 2,500, 5,000, 7,500, etc., both with increasing and decreasing pressure. The change of length of the iron rod was then calculated for each of these measurements, making all the corrections. These results for all the runs were then plotted, in one diagram for the measurements with increasing pressure and in another for those with decreasing pressure. The more discordant of the points at each of the 13 mean pressures were discarded; in a few cases as many as one third of the points were thus discarded, but usually about half as many. The remaining points were averaged, giving 13 approximately equi-spaced points for increasing pressure and 13 for decreasing pressure. A straight line was then passed by calculation through the initial and final points of each of these two groups, and the deviation from linearity, Δ , of the intermediate points calculated. A second degree curve in the pressure of the form J = a + bp + cp2 was then passed by least squares calculation through these deviation points, weighting each point according to the component number of observations which had been retained in the average. In this least squares calculation all 13 points with increasing pressure were retained, but the two highest points with decreasing pressure were not used, for the reason that friction had not entirely reversed itself at these points so that the warping could not be expected to have assumed the value characteristic of decreasing pressure. The total number of component observations used with increasing pressure was 154, and 172 with decreasing pressure. The "standard error of estimate" y j ^ d f / n of the points with increasing pressure was 0.36 per cent of the total

THE LINEAR COMPRESSION OF IRON TO 30,000 KG/CM2

change of length at the maximum pressure, and of the decreasing points 0.26 per cent. The average of the least squares deviation curves for increasing and decreasing pressure was then combined with the expression from which the deviations had been calculated, to give the final result. The deviation from the straight line of the midpoint of the curve joining initial and final points was 0.92 per cent of the maximum. The linear term in the final result that would have been calculated from the increasing points differed by only 1.2 per cent from that which would have been calculated from the decreasing points only. The second degree term, on the other hand, from the decreasing points only was 3.6 times greater than that from the increasing points only. The effect of warping is thus much greater on the second degree term, as would be expected. The final result for the change of length at a mean temperature of 24° is: -AHl0

= 1.942 X 10~7p -

0.23 X 10~12p2,

and for the change of volume: -

JV/V0

= 5.826 X 10 _ 7 p -

0.80 X 10- 12 p 2 .

Using only the three smoothest of the many runs and simple graphical methods of calculation, a linear term of 1.939 was found against 1.942, and for the second degree term 0.34 against 0.23. Or if all the measured points had been retained, making no discards, it was apparent without making the calculations that the result would not have been much different; the average compression to 30,000 would have been 0.3 per cent greater. The result found now is to be compared with my former value3 up to 12,000 at 24°, namely: -

tJ-/l0 = 1.953 X 10-7?) - 0.75 X 10~ 12 p 2

The linear terms do not differ greatly, but the second degree term now appears to have been formerly much too large. This is the direction in which the theoretical physicists have been insisting was probable. It is also in the direction demanded by the measurements of Ebert4 on an iron single crystal in the pressure range up to 5,000 kg/cm2; his second degree term is —0.4 X 10~12. Exact comparison of my former and present results is hardly possible, because of the difference of range and because there can be only a heuristic significance in the second degree expression used to represent the results. It would be hopelessly beyond the accuracy of either former or present measurements to search for any real departure from the second degree relation. The most natural point to seize on in at-

19

tempting to explain the difference between the second degree term found now and formerly is that now the second degree term in the manganin gauge is taken into consideration, whereas formerly a linear relation was used. The deviation from linearity found for the present manganin gauge is in the abnormal direction, the resistance increasing with pressure at a decreasing rate at the higher pressures. The result is that a linear extrapolation from the low pressure readings gives too low a pressure at the high pressures. Hence as far as the present gauge is concerned the linear compression of iron would have been found more linear than it is if a linear calibration had been used for the manganin. However the effect is small: at 30,000 the true pressure is 1.3 per cent greater than would have been obtained from a linear extrapolation of the manganin gauge from 15,000. Using a linear relation for the manganin would have given a second degree term in the compression of iron only one third that given above, which is in the wrong direction to explain the discrepancy. The situation, however, is by no means simple, and it is not possible to argue back with certainty from these results to the previous source of difference. The second degree term in the manganin has to be found by individual calibration of each coil, and differs appreciably for contiguous pieces from the same spool. The manganin used in the previous work was from an entirely different source from the present manganin. If the former manganin had a small second degree term of the normal sign the former larger value of the second degree term in the compression of iron would be accounted for. The possibility cannot be ruled out that the curvature of the relation between the resistance of manganin and pressure reverses on passing from a low pressure range to one more extensive. It must furthermore be remembered that because of the difference of range the accuracy of the second degree terms in the present work is, other things being equal, more than six times that of the previous work. It was my original hope to also measure the temperature coefficient of compression with this apparatus. In view, however, of the difficulties encountered in the measurements under the comparatively favorable conditions at room temperature it seemed hardly practical to try for the temperature effect. The best that can be done at present is to use the former value for the temperature coefficient. This would give at 75°: — Jl/l n =

1.964 X 10 - 7 p — 0.23 X 10~12p2.

133 — 3409

20

BRIDGMAN ACKNOWLEDGEMENTS

REFERENCES

I am much indebted to the skill of my mechanician, Mr. Charles Chase, in the difficult and tedious task of setting up the apparatus. For financial assistance I am indebted to the Rumford Fund of the American Academy of Arts and Sciences and to the Francis Barrett Daniels fund of Harvard University.

"P. W. Bridgman, Amer. Jour. Sei. 10, 359-367, 483-498, 1925; 15, 287-296, 1928; Proc. Amer. Acad. Arts and Sei. 58, 166-242, 1923 ; 59, 109-115, 1923; 60, 305-383, 1925 ; 62, 207-226, 1927 ; 63, 347-350, 1928; 64, 51-73, 1929 ; 66, 255-265, 1931; 67, 345-375, 1932; 68, 27-93, 1933; 70, 71-101, 1935; 70, 285-317, 1935. * P. W. Bridgman, Proc. Amer. Acad. 58, 169, 1923. "Last reference under (1), p. 312. Ή . Ebert, Phys. ZS. 36, 385-392, 1935.

T H E RESEARCH LABORATORIES OF P H Y S I C S ,

Harvard University, Cambridge, Mass.

133 — 3410

THE COMPRESSION OF 46 SUBSTANCES TO 50,000 kg/cm2 BY P. W. Presented Nov. 8, 1999.

Received Nov. 18, 1939.

CONTENTS Introduction Method and Apparatus Method of Calculation and Corrections Detailed Presentation of Data In . . . NaCl NaBr Nal . KCl . KBr . KI .. RbCl

31 31 32 32 32 32 33 33 34 34 36 36 35 35 35 35 30 36 37 37 37 38 38

Rbl CsCl CsBr Csl NH.I AgCl AgBr Agl .. T1C1 . TIBr Til .. CaS .

BRIDGMAN

CaSe . CaTe . SrS . . . . SrSe ... SrTe .., BaS ... BaSe . BaTe . PbS ... PbSe .. PbTe . ZnS .. ZnSe . ZnTe . HgS .. HgSe . HgTe . S Se Te Sb Bi Rubber

General Discussion

21 21 28 30 38 38 38 39 39 39 39 40 40 41 41 41 42 43 43 44 44 44 44 45 45 46 46 47

INTRODUCTION

Values for the compression of several substances up to 45,000 kg/cm 2 at room temperature have already been published. 1 In the following the method has been considerably improved and measurements made of the compression of 39 compounds which crystallize in the cubic system and whose structural constants are known from X-ray analysis, together with a few other substances, in the range up to 50,000 kg/cm 2 , and at two temperatures, room temperature and — 78.8°, the subliming temperature of solid C 0 2 at atmospheric pressure. METHOD AND APPARATUS

In brief the method is differential. The material to be measured is surrounded by a plastic

solid to transmit pressure approximately hydrostatically, and then compressed in a properly reinforced vessel by the motion of a piston. The displacement of the piston is measured as a function of pressure. Distortion of the vessel and other parts is eliminated by making the method differential, that is, by determining with a similar set-up the piston motion required to compress a very much less compressible substance whose compression may be assumed known with sufficient accuracy from previous measurements in a smaller pressure range. The difference of the two piston displacements gives the differential compression, the distortion cancelling out if it can be assumed to be the same in the two set-ups. The accuracy of the method evidently decreases rapidly as the compressibility of the' substance becomes smaller. The chief improvement in the new apparatus consists in the more effective external support given the pressure vessel. Whereas the maximum external pressure on the vessel was formerly somewhat less that 17,000 kg/cm 2 , in the new design it is 26,000. This more effective external support not only decreases the distortion of the vessel and so increases the accuracy of the results, since the corrections for distortion are somewhat uncertain, but also has the important effect of materially increasing the life of the vessel. Formerly, the vessel rarely survived twenty applications of the maximum pressure, whereas now survival of 70 or more applications is not uncommon. It would not have been possible with the previous arrangement to have applied 26,000 to the outside of the pressure vessel, for so high a pressure is considerably beyond the strength of the heavy tapered collar by which the external pressure is exerted. To reach 26,000 it is necessary to give the collar itself external support; this was done by making the collar double, the inner collar being tapered and supported externally by being thrust into an outer collar. That is, there are now three stages in reaching the maximum pressure, instead of two as formerly. The inner collar and the outer collar now function in the same way as the pressure vessel and its collar functioned in

134 — 3411

22

BBIDGMAN

the previous apparatus. In the new apparatus the external pressure is controlled independently of the internal pressure by means of a second hy-

FIGURE

1. General view of the apparatus.

134 — 3412

draulic press, instead of producing the external pressure automatically by the same press that produces the internal pressure. This arrangement of the two presses was adopted in the first instance as a matter of convenience and in spite of its greater complication, because of the greater resulting flexibility, allowing a greater range of choice in the angles of the pressure vessel and collar and in the ratio of internal to external pressure. In the end, however, it proved necessary, because with the angles needed to reach the proper pressure automatically with a single press the strength of the pressure vessel against extrusion would have been too low. The new arrangement is shown in Figure 1, in which the parts are given to scale. The piston, P, with which the high pressure is produced, is of carboloy, from 0.250 to 0.262 inches in diameter, driven by a piston D 3.5 inches in diameter operated by a hand pump, the connection to which is indicated by the arrow T. The piston Ρ rests on a carboloy block A 0.5 inch in diameter, which in turn rests on a hardened steel column B. The compressive stress in Β is therefore only one quarter that in P, so that even with a pressure of 60,000 kg/cm 2 in Ρ the steel column remains within its elastic limit. The high pressure vessel C is thrust into the conical steel collar H, which in turn is thrust into the external collar I by means of the 6 inch piston F, which is also actuated by a hand pump, the connection to which is indicated by the arrow U. The 3.5 inch piston D together with its cylinder, E, rides on F. The exterior of the pressure vessel C was given a much larger taper than in the previous work, the taper now being 4 inches to the foot (on the diameter) against 1.125 in the previous apparatus. At first a smaller taper was tried, but trouble was found from the pressure vessel tearing apart at the threads under the combined action of the force expelling the screw plug and the tendency of the vessel to extrude itself through the conical opening in H. This latter tendency is diminished by increasing the angle of the cone, allowing the walls to exert an increased longitudinal component in such a direction as to resist extrusion. The angle; finally chosen was satisfactory in this regard, and the vessels very seldom fail at the threads. The chief disadvantage of making the angle of the cone large is that now a higher pressure must be exerted on the 6 inch piston F in order to generate a given pressure on the outside of C. With the dimensions given the pressure on F at the maxi-

THE COMPRESSION OF 4 6 SUBSTANCES TO 5 0 , 0 0 0 KG/cM 2

mum was about 8,300 lb/in 2 , which means a total thrust of 235,000 lb on the thrust ring G, which has a total area of a little less than one square inch. This thrust ring was made of "Solar" steel; the stress is near the elastic limit and the rings sometimes cracked from radial expansion, but after some trial the proper heat treatment was found. The taper on the outside of the inner collar Η was 2.75 inches per foot. At the maximum the internal pressure on Η was 26,300 kg/cm 2 , and the external pressure 11,400 kg/cm 2 . With the dimensions this was fairly near the elastic limit of the steel (Solar), and a couple of these rings broke in the preliminary work. The behavior of this ring is capricious; one was used for some 400 applications of the maximum pressure before breaking. The outer collar I is also of "Solar," specially forged on a mandrel to give circumferential working to the fibres. The internal pressure on it is the same as the external pressure on H, namely 11,400 kg/cm 2 . It was given a preliminary treatment by a permanent stretching in two stages to a maximum of 17,500 kg/cm 2 internal pressure and then ground to final size. Three of these rings have fractured in use, all near the conclusion of the measurements. Since the fracture of this ring is accompanied by the explosive release of all the pressure on the 6 inch piston, the damage done may be considerable. Lubrication at the sliding surfaces between C and Η and between Η and I was done much as before. There was in the first place a wrapping of 0.002 inch lead foil, which was smeared on both surfaces with a paste made of flake graphite and a 5 per cent soap solution. Formerly glycerine and water had been used in making this paste, but at C0 2 temperature this becomes very stiff and the friction high. Although the water in the soft soap freezes, the internal plastic flow strength of the ice is less than that of the congealed glycerine mixture, and the friction was very materially less. The internal mobility which is the accompaniment of the various polymorphic changes in the ice doubtless helps to reduce friction. The displacements of C into Η and of Η into I were determined with two Ames gauges at J and Κ as part of the routine of the measurements. These displacements are not directly used in the final result, and need not be known with high accuracy, but they are a useful check on the proper functioning of all the parts. By plotting these displacements with rising and falling pressure the external friction on the cones may be found, and

23

in this way a value for the external pressure, which enters the calculation for the distortion of the vessel. In general, the friction was reproducible to an unexpectedly high degree, so that no appreciable variation from run to run in the distortion correction arises from this cause. Because of the blunter taper of the cones the friction was much less than with the previous apparatus. The crucial measurement is the displacement of Ρ into C. Any attempted direct measurement of this is going to be somewhat in error because of distortion of various parts of the apparatus. A good deal of preliminary work was put into finding the best point of attachment for the gauge with which this displacement is measured. At some of the more obvious points of attachment the distortion may be so great as to more than mask the effect sought, giving under some conditions retrograde readings. The requirements in the point of attachment are that it be such that the distortion be reproducible, that it be free from frictional effects, and if possible that it be small. The arrangement shown in the diagram was checked by a variety of preliminary tests which it is not necessary to describe in detail, and seems entirely satisfactory. The most important feature of the final arrangement is the use of the fine hardened steel probe rod, L, reaching through the screw plug with which the pressure vessel is closed at the bottom, resting on a carboloy closing plug M. The longitudinal distortion of the threads of the closure plug could not be made reproducible, so that many simpler schemes could not be used. The block Μ must be of carboloy; hardened steel in this place is compressed beyond its elastic limit and the results are not reproducible. Various blank runs showed that the total distortion of the parts of the measuring system at the maximum pressure is 0.016 inch. All the parts are well under their elastic limits, and there was never any evidence to suggest that this distortion was not reproducible to the limits of error, so that it drops out from the final difference. The gauge with which the displacement of the piston is measured via the probe rod is an Ames dial gauge, R, graduated to 0.0001 inch and read to 0.00001 inch. In the previous work the displacement was read with a gauge only one tenth as sensitive, but a lever magnifying arrangement was interposed with a magnification factor of 3. There is outstanding therefore a factor of about 3 in favor of the new apparatus. The order of magnitudes of the piston displace-

134 — 3413

24

BRIDGMAN

ments was as follows. In a calibrating run in must be increased by increasing the pressure on F. which the vessel was filled with iron and indium The internal volume of C is affected very mathe total measured displacement at 50,000 was , terially by the changes of external pressure, so about 0.065 inch. Of this, 0.016 was contributed that if pressure on F is not increased smoothly, by the distortion in the press, 0.011 by the actual and in the correct ratio to the increase of pressure compression of the iron, 0.022 by the compression on D, the resulting displacements will be irregular. of the indium, and the balance 0.016 by the in- At first various schemes of manual control of the crease of cross section of the pressure vessel. The pressure on the two pistons D and F were tried total measured displacement of the piston for a without sufficient success. Finally D and F were filling with a substance of average compressibility connected by a pressure multiplier, not shown in was 0.100 inch. The difference, 0.035, was there- Figure 1, so that the pressures on D and F were fore given to one part in 3500, reading the Ames maintained automatically in the correct proportion, gauge to its limit of sensitiveness. In spite of the which was found by a preliminary trial. This smallness of the displacements, the accuracy was pressure multiplier consisted simply of one piston not limited by this factor. pushing another of different area. There was, of In order to protect the Ames gauge from ex- course, some friction in the multiplier, but by plosions, the probe rod transmits its motion using the same packing technique as on D (and F) through a brass pin and a heavy weight, S, the this was kept to a sufficiently low figure. The brass pin shearing off if the probe rod is explos- capacity of the two cylinders of the multiplier was ively expelled. There is a further safety arrange- sufficient so that it was possible to reach the maximent, not shown in Figure 1, which limits the mum pressure by pumping only into the side of motion of the screw plug, if it should be expelled the multiplier connected to F; similarly pressure was released by opening a valve in the F side of in an explosion, to about 0.5 inch. The thrust of the 6 inch piston is transmitted the multiplier. The pressure on D was controlled by a 0.25 to the pressure vessel and from the collars supporting the pressure vessel to the frame of the press inch dead weight free piston gauge connected in by means of the thin sleeves Ν and 0 of hardened series between the multiplier and D. Pressure tool steel. These are made of as small cross sec- was increased in 30 equal steps from zero to the tion as is safe to keep them certainly below the maximum by succeessive addition of equal weights elastic limit. This is done in order that heat con- to the piston gauge, and similarly released by sucduction from the bath in which the pressure vessel cessive removal of weights. The procedure, after and its collars may be immersed may be as small one reading was completed, was to place the next as possible. In this work the can of sheet iron weight on the piston gauge, and then to pump Q was filled with solid C0 2 and alcohol for the by hand into F until the free piston gauge rose low temperature runs, and it was of course desir- because of the increased pressure transmitted to able to restrict thermal conduction to other parts it from the multiplier. The pipe connecting the of the apparatus as much as possible. piston gauge to D was constricted by a wire nearly The essential measurement, beside the displace- filling the bore, so that pressure was transmitted ment of the piston into the pressure vessel, is the only slowly from the piston gauge to D. In this pressure on the piston P. This was obtained di- way fluctuations in pressure were retarded and rectly from the pressure in the liquid driving the smoothed out so that pressure on D did not overpiston D. It is therefore necessary that D move shoot the mark while the piston gauge was overwith the least possible friction. The interior of coming the inertia of the weights and rising. the cylinder Ε in which D moves was finished as In spite of the external support, the pressure vessmooth as possible by grinding, and the packing sel is strained beyond the elastic limit at every apon the end of D was a smoothly cut disc of "Du- plication of pressure, and eventually breaks, prene" 0.125 inch thick held between retaining although this may be deferred for 70 to 80 applicadiscs of brass also 0.125 inch thick. The friction tions. The distortion of the vessel therefore shows with this arrangement is only a few per cent, and hysteresis and all the other phenomena to be exsmaller than the friction on the high pressure end pected beyond the range of elasticity. In order to of the piston P. Simultaneously with the increase obtain reproducible results it is necessary to proceed of internal pressure produced by increasing preson a rigorous time schedule. At each temperature, sure on D, the external pressure on the vessel C room temperature or carbon dioxide temperature,

134 — 3414

THE COMPRESSION OF 4 6 SUBSTANCES TO 5 0 , 0 0 0 KG/CM 2

a seasoning application of the maximum pressure was first made in six large pressure steps, and readings made with increasing and decreasing pressure to check that the apparatus was functioning properly and roughly to locate any polymorphic transitions, if there were such. The regular readings were then made in 30 equal steps up and 30 equal steps down on a time schedule of 2 minutes to the step, the gauge R being read on the conclusions of the 2 minutes and immediately before the next increase of pressure, the pressure in the meantime having been held constant by the piston gauge. Piston displacements (readings of R) were then plotted against pressure. The result is a loop, the decreasing readings never coinciding with the increasing readings because of friction in one place or another and because of hysteresis in the distortion of the pressure vessel. The greatest friction is at the end of the piston Ρ and in the material in the interior of the pressure vessel as it slides along the walls to take up the compression. As in the measurements already published, the material under measurement is enclosed in the pressure vessel in a capsule of a soft metal, by which pressure is transmitted to it approximately hydrostatically. In the previous work this metal was lead. Preliminary exploration before these measurements showed that indium is somewhat superior to lead for this purpose, being materially softer, and it was accordingly used in all this work. The amount of indium required is small, and it can be used a number of times, so that the expense was not an important factor. The total width of the loops of piston displacement against pressure, that is the difference between increasing and decreasing pressure for a fixed displacement, averaged about 12 per cent of the mean pressure at the maximum. The error in the curve median to the loop cannot therefore possibly be more than 6 per cent. The actual error in the median curve of course is much less than this, since it is determined by the failure of friction and hysteresis to be reproducible on the different runs. This 6 per cent is the net result of all the differences between the ascending and the descending branches. Friction at the various pistons produces a true hysteresis loop, the displacement with decreasing pressure lagging behind that with increasing. Paradoxically, however, friction on the external conical surface of the pressure vessel makes a contribution to the loop in which the displacement leads instead of

25

lags, because when pressure is too high on the exterior of the vessel the internal volume is too small and the piston has to be withdrawn to compensate. This effect may be very appreciable, and it was not at all unusual for the loop at C0 2 temperature to be narrower than at room temperature because of the greater friction on the conical surface between C and H. It follows that the narrowness of the loop cannot be used as an exclusive criterion for the satisfactory functioning of the apparatus, but this has to be combined with an examination of the friction at the various surfaces, which may be determined from the readings of J and K. In the previous work the median curve through the hysteresis loop was obtained by plotting against pressure the mean of the displacements with increasing and decreasing pressure. Since increasing and decreasing measurements were made at exactly the same pressures, this sort of average was very easy to obtain by calculation. However, a discussion of the way in which friction inside the high pressure vessel affects the mean compression showed that the other sort of averaging, that is, the mean of increasing and decreasing pressure at constant displacement, was preferable. Although this sort of averaging is considerably more inconvenient to apply, it was adopted in the following. The difference between the two methods of averaging is quite appreciable for some substances, and the superiority of this method of averaging was checked by the fact that the agreement between repetitions with the same substance was improved. The new method of averaging was applied graphically. The observed points were plotted on millimeter paper to a scale of about 30 centimeters range in abscissae to 40 centimeters range in ordinates, a smooth curve was drawn through ascending and descending points (60 points in all) with a "ship's" curve, then the loop was bisected at some 20 uniformly spaced displacement points with a simply constructed special drawing instrument for bisecting lines, and finally a smooth curve was again drawn through the mean points. The end of the loop at the maximum pressure, where the direction of pressure change is reversed, required special treatment. Obviously on reversal there is back lash in the various parts, so that the loop is closed with a rounded end in the familiar way. When pressure is reduced so far that backlash in all the parts has disappeared the ascending and descending branches differ by the whole frictional

134 — 3415

26

BRIDGMAN

effect, which is approximately proportional to the pressure. The difference between the two branches of the loop should therefore be proportional to the pressure over most of the range. This did indeed prove to be the case, showing incidentally that hysteresis in the pressure vessel makes only a small contribution. The constant of proportionality was determined graphically from the loop itself, and the descending branch was extended by calculation by means of this constant, as shown by the dotted line in Figure 2, and this dotted

FIGURE 2. The upper end of the hysteresis loop, and the method of extending the reverse branch to eliminate the effect of backlash. Ordinates are piston displacement and abscissas pressure. curve was used in getting the mean at the upper end of the loop. Backlash on reversal ceased to be perceptible when pressure had been released by something of the order of 20 per cent of the maximum. Because of friction it was necessary to run the maximum pressure on the piston to about 53,000 kg/cm 2 in order that the mean maximum pressure on the inside should be 50,000. Considerable preliminary work was put into funding the steel most suitable for the pressure vessel. The steel finally chosen was the "Omega" steel of the Bethlehem Steel Corporation. A typical analysis is: C, 0.55; Mn, 0.80; Si, 2.30; V, 0.25; Mo, 0.50; P, 0.015; S, 0.025. This is an oil hardening steel, and is somewhat less capricious in its behavior than "Solar," the water hardening steel used previously, and which is still used in other parts of the apparatus. The vessels were heat treated by quenching into oil from 885° C. and

134 — 3416

drawing back to a Rockwell C. hardness of 56-57. It is still possible to force a high speed steel reamer through the hole at this hardness if only a few thousandths of an inch is removed. The vessels were first made to 0.250 inch in diameter, and then subjected to a preliminary stretching to a maximum pressure of about 56,000. During this stretching the ratio of the pistons of the multiplier had to be changed to get the correct external pressure. This preliminary stretching was done in two steps: the first with the whole vessel filled with indium to stretch the body of the vessel, and the second with much of the indium replaced with a core of iron, to stretch the mouth of the hole. Under this preliminary stretching the bore increases to something of the order of 0.257 inches. It was then reamed to 0.260 inches and was ready for use. The first stage in use consists of a blank calibrating run in which approximately the same amount of indium is used as is to be used in the later measuring runs, and in which a core of iron of approximately the volume of the substance to be measured later replaces it. Unfortunately the different vessels, in spite of every effort, differed so much that such calibrating runs proved necessary for each individual vessel. The blank calibrating run demands the application of the maximum pressure four times: one seasoning and one regular at each temperature. The vessel is now ready for regular measurement with any substance. Again four applications of the maximum pressure are necessary. The vessel does not begin to give results therefore until it has withstood the application of the maximum eight times, not counting the preliminary stretching. In the previous work the vessel broke frequently before reaching eight applications, so that this was a most discouraging requirement, and in fact was not enforced. But the accuracy is much improved by it. After every set-up the bore of the vessel was freshly measured. In spite of the preliminary stretching it continues to slowly stretch. The current value of the diameter was of course used in the calculations. When it gets to as much as 0.263 inches the vessel is discarded, if it has not already broken. As already mentioned, vessels have been used for 70 to 80 applications (20 fillings). It is to be anticipated that the calibration will slowly change as the vessel stretches. For this reason the routine procedure was adopted of making a fresh blank calibration on every fifth set-up, thereby further improving the accuracy. As a matter of fact the successive calibrations were

THE COMPRESSION OF 4 6 SUBSTANCES TO 5 0 , 0 0 0 Κ β / c M 2

gratifyingly reproducible after due allowance was made for the slight stretch. As calibrations accumulated a mean of the calibrations was used in the calculations. The experiments were usually limited by two sorts of rupture, rupture of the pressure vessel and of the carboloy piston. Other places where rupture might be expected to occur are in the tapered supporting collars and in the tool steel sleeves supporting the temperature bath. The latter never ruptured, but in the initial design they were a little too thin, so that they took a permanent set of a few thousandths of an inch. This might be serious, because it is evident that the alignment of all the parts must be good if the carboloy piston is to receive an entirely straight thrust, which is essential. The sleeves were remade about 25 per cent thicker and have never given any further trouble except during one major explosion of another part. The present dimensions are a wall thickness of 0.187 inch and 6 inches diameter. The tapered collars have also given comparatively little trouble; three ruptures of the outer collar have occurred and three of the inner. The carboloy pistons, however, are another story. These are likely to break at any time, and a constant watch must be kept after every run for the appearance of fine longitudinal cracks, which are the prelude to complete failure, and the piston must be at once discarded. Final rupture of a piston may be a most violent affair, when it is often reduced to a fine powder. Such rupture occurs so rapidly that the multiplier has no time to function, with the result that the pressure vessel is exposed to the full external pressure with no compensating internal pressure. The result is that the vessel is appreciably collapsed, and has to be discarded. The strains set up in the vessel by this collapse are so severe that often the vessel spontaneously ruptures hours or perhaps days after the explosion. Loss of the pressure vessel means not only loss of the particular run but also loss of all the labor of calibration. After a few unfortunate occurrences of this kind, subsequent occurrences have, to a large extent, been prevented by keeping a most careful watch for the first appearance of fine cracks in the piston. Fracture of the piston was often initiated in the early work by slight chipping around the edges. This can be largely avoided and the life of the piston much prolonged by forcing the thin supporting disc of hardened alloy steel shown in Figure 3 around the end of the

piston. The other the pressure vessel walls of the vessel, occurs at this end.

27

end of the piston which enters is adequately supported by the and chipping practically never The carboloy piston is pushed

Figure 3. Reinforcement of the carboloy piston with a thin disc of heat treated alloy steel. by a carboloy block 0.5 inch in diameter, against which it directly rests, both surfaces being ground flat. This block has ruptured oftener than would be anticipated because of its dimensions, and a careful watch must be kept for the development of cracks. In spite of every endeavor both by myself and by the manufacturers, the performance of the pistons remains capricious, and the life may vary from 2 or 3 to more than 100 applications of the maximum. Attempts were made to correlate the life with the density and with Young's modulus. I am much indebted to Dr. Dennison Bancroft for measurements by his dynamic method of Young's modulus of a number of rods from which the pistons were cut. Probably there is some correlation with both density and modulus, long life

w

Figure 4. Two views of the pressure vessel with a system of three mutually perpendicular fractures.

134 — 3417

28

BRIDGMAN

having a tendency to go with high density and high modulus, but the correlation is not close enough to be a useful practical guide. One thing is certain, however. In cutting the pistons to length and in facing the ends the use of diamond charged wheels is necessary. The cutting must be free and without forcing; otherwise there is local heating and strains are set up which may initiate rupture of the whole piece. The method of rupture of the vessels is capricious; apparently the limit of strength in all possible directions is reached nearly simultaneously. The same vessel may show radial and circumferential rupture and also rupture perpendicular to the longitudinal axis, as suggested in Figure 4. The rupture is practically always an extension rupture; I do not remember ever having seen a shearing rupture. It is quite common for the crack to develop after the vessel has been standing for some time free from any external force.

M'Vo + m\ = lo's0 M'V„ + m'vj, = lP'ap = 1,'s, (1 + Δ)

(1)

There are essentially three unknowns here, Vr, Vp, and A, and two equations, the first equations for each set-up being merely check equations. It is not possible to provide a third equation from which these three quantities may be determined by making a third set-up with different relative quantities of the two substances, for the equations obtained in this way are only identities, useful only for check. By eliminating V, between the last two equations above one gets: 1+ A =

vrlmM' — m'M 1

(2)

s.lM% - Ml,']

Hence if vp, the volume of the second substance, which in this experiment was pure iron, is known as a function of pressure, the distortion of the cross section can be obtained in terms of measurM E T H O D OP CALCULATION AND CORRECTIONS able quantities. I have recently determined v, 2 2 The following simplified equations were used by direct measurement up to 30,000 kg/cm . in calculating the results. Imagine runs with two The deviation from linearity is so slight that there different set-ups; in each set-up the vessel is filled can be no hesitation about extrapolating to 50,000. with two different substances, the amounts of In fact the final value for the cross section that one obtains by extrapolating the new experimental which differ for the two set-ups. measurements of the volume of iron from 30,000 Let Μ and M' be the masses of the first substance to 50,000 differs by less than 0.1 per cent from (presumably indium) for the two set-ups re- the value obtained by an extrapolation to 50,000 spectively. of the former measurements of compressibility Let m and m' be the masses of the second sub- to only 12,000. stance (presumably iron) for the two set-ups It is also possible to calculate A by the methods respectively. of conventional elasticity theory. This method Let I. and I.' be the initial lengths of the pressure was used in the previous paper,8 to which reference vessel for the two set-ups respectively. is made for the details of the calculation. The Let I, and I,' be the lengths of the pressure vessel value calculated in this way for A at 50,000, by at pressure ρ for the two set-ups respectively. assuming the conditions of an infinitely long cylinLet s. be the initial cross section of the pressure der, was 0.026, whereas the experimental value vessel. was 0.0271. The agreement is most gratifying. Let 8, = s. (1 + A) be the cross section of the The value 0.0271 was used in all the reductions pressure vessel at pressure p. of this paper for the value at 50,000. For interLet V, and V, be the volumes of one gram of the mediate pressures it was assumed linear with presfirst substance initially and at pressure ρ respec- sure; the variation with temperature was neglected. tively. The quantity l r ' which enters equation (2) Let v. and vv be the volumes of one gram of the second substance initially and at pressure ρ re- above is not given directly by the measurements, nor is it determinable directly from I.' and the spectively. measured displacement of the piston, for the latThen we have the equations: ter involves the distortion of various parts of the press. These distortions were determined by variMV0 + mv0 = l TνJ ν ^ 100 Ε υ ο.

Ε £

0

ιοο

ο

0

1

2

3

4

0

1

2

3

4

0

1

Pressure ,kq. per sq.cm. χ 10"*

2

3

4

5

FIG. 8. The "phase diagrams" (temperature of transition against pressure) for a number of metallic elements.

ments of the volume compression in terms of the motion of the piston. But, fortunately, there is a great deal that can be usefully done in this range: the simplest thing is the study of polymorphic changes which many substances undergo. The thermodynamic parameters of the transitions of some 75 substances have been determined over this range ti3i. Figure 8 shows the transitions of some of the metallic elements, and Figure 9 those of d-camphor, the most complicated substance yet investigated. Polymorphism appears to be an increasingly common phenomenon as the pressure range is increased; almost any substance selected at random may be expected to exhibit it. It is paradoxical that this phenomenon, which is easiest to measure and which, one would think, involves the most fundamental

140 — 3524

Recent Work in High Pressures

21

of the properties of a substance, its space lattice, is theoretically the most difficult to predict or compute. This is because present methods of theoretical computation make the existence of the phenomenon depend on the small dif-

Fic. 9. The phase diagram of d-camphor, the most complicated yet discovered.

ference of large quantities. As a result this mass of experimental material on polymorphism, which anyone must concede has to do with fundamental things, has for the present to be stored like a collection in a museum, waiting for the later moment of illumination, just as spectroscopic data were collected for years before illumination came from later investigations. The compressibility of solids can also be measured over the range up to 50,000, although with more difficulty, and data have been collected for a considerable number of materials. Liquids too can be measured over that part of the pressure domain in which they are not frozen by the pressure, by the device of sealing them inside a mass of some deformable solid, such as lead, and measuring the over-all compressibility of the whole. In this way the change in compressibility when a substance freezes can be studied over a wide range m i . The accuracy, of course, is not so great as at lower pressures, since complications arise from the rapidly increasing friction and the distortion of the apparatus.

22

American Scientist

Some of the effects are capricious in sign, so that the accuracy could be increased somewhat if necessary merely by heaping up the measurements. The old problem arises as to just where to make the best compromise between accuracy and extensiveness; this will always be to a certain extent a personal matter, and will also vary with the development of theory and the interest of theoretical physicists in the results. It is fortunate that the error in determinations of compressibility, which have been among the most difficult measurements of all physics at the lower pressures because of the smallness of the effects, becomes less at high pressures with the increase in magnitude. The experimental arrangements which were used to determine the compressibility of the liquid and solid phases of one substance may also be used to determine the effect of pressure on melting temperature in the range up to nearly 50,000. Previously I had examined the same problem for some 30 or 40 substances in the range up to 12,000 kg/cm 2 , and had come to the conclusion that all melting curves are similar in that they rise to indefinite temperatures and pressures and neither end in a critical point nor reach a maximum temperature, as had at one time been supposed. Theoretical physicists had recently reopened the possibility of a critical point, so that it became desirable to reexamine the question over the wider pressure range now available. A number of the newly-determined melting curves are given in Figure 10. Although they are shown as ending in the diagram, this does not indicate a critical point, but merely that, because of experimental difficulties, the curve was not followed further. By combining a study of these curves with the other thermodynamic parameters of the melting, latent heat, and difference of volume, the trend of the phenomenon at pressures beyond those experimentally reached may be studied. The conclusion is a confirmation of that previously reached from measurements in the narrower pressure region, namely, there is no experimental indication that there will ever be either a critical point or a maximum temperature, but all the indications are that the melting curve rises

140 — 3526

Recent Work in High Pressures

23

indefinitely with pressure and temperature. This' is obviously an important conclusion for geology.

Pressure,

Kg/cm1

FIG. 10. Melting temperature against pressure for a number of substances. At 15,000 kg/cm 2 the order of substances, reading from top down, is chloroform, chlorobenzene, chlorobenzene (second modification), water (ice VI), η-butyl alcohol, carbon bisulfide, methylene chloride, η-propyl bromide, ethyl bromide, and ethyl alcohol.

If one is content with pressures below 50,000 it is possible to build more elaborate apparatus employing the same principle of conical support. A greater variety of phenomena may be examined with such an apparatus, and much greater accuracy obtained. I have built apparatus of this type with which pressures of 30,000 may be reached as a routine matter [ΐό], in which the volume is approximately IS cm 3 , and in which pressure is transmitted by a true liquid. The use of a liquid allows the introduction of electrically insulated leads, and this opens the possibility of many different sorts

140 — 3527

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American

Scientist

of measurement. A pressure of 30,000 is sufficiently high to justify the inauguration of an extensive program of measurement in this range, particularly since the frequency of breakage has been reduced by the new design to the dimensions of a minor inconvenience. Some of the questions of special interest in the 30,000pressure range demand considerable accuracy in the measurements. For instance, there is the change in compressibility of a solid with pressure. Born's theory of solids, as first formulated, had a certain degree of success in calculating the compressibility of salts, such as sodium chloride, but when it came to reproducing the curvature of the curve of volume against pressure it failed by a wide margin. For metals the curvature was so small as to be difficult to measure, but presently the theory was dealing with metals as well as with salts, and it became desirable to obtain data for all these materials with as much accuracy as possible. The accuracy with which a curvature can be measured increases, other things being equal, as the square of the pressure range, so that this effect can be determined at 30,000 six times as accurately as at 12,000. The "other things being equal" includes the accuracy of the measurement of pressure. A preliminary to entry into this new field was, therefore, just as with the former narrower field, the establishment of methods of measuring pressure with the requisite accuracy, and the location of pressure-fixed points to facilitate the future calibration of pressure gauges. The pressure scale having been fixed and made reproducible to an accuracy of 0.1 per cent, a somewhat similar task had to be done for the measurement of compressibility. The most convenient method of measuring compressibility is a differential method whereby the difference of compression of the substance in question and some standard substance is measured. To convert this sort of measurement into absolute measurement demands a knowledge of the absolute compression of the standard substance. Special methods are needed to determine this. These methods have been developed, and the absolute compressibility of a standard substance, iron, determined over the range to 30,000. The

Recent Work in High Pressures

25

final result of the determination over the wider range of the deviation from linearity of the compressibility of the common metals was a value considerably smaller than had been given by the previous measurements over the narrower pressure range. The new value was much more acceptable to theoretical physicists, who, in the meantime, had been pushing theory to a degree of perfection which gave them considerable confidence in the higher order term. Right here a significant change in the relation of experiment to theory has occurred since I began my work. At the time when I made my measurements of the effect of pressures up to 12,000 on the electrical resistance of metals or on the compressibility of solids, the theory of these two phenomena was in such a simple state that it was not a hopeless matter for me to attempt to make some contribution to theory in the light of the new experimental material. But by the time that I was measuring compressibility to 50,000 the wave-mechanics theory had developed to such a stage of complexity that it was not possible for me to make a theoretical contribution on the basis of my new data except at the price of completely dropping experimental work and embarking on the extremely problematical course of acquiring sufficient facility in wave mechanics. It is becoming increasingly difficult for the same person to combine theoretical and experimental productivity. For the experimenter this means that he must exert increasingly great care that his work does not degenerate into the hoarding of new data for their own sake. The problem of maintaining the pressure without rupture of the vessels or leak was not the only problem in extending accurate measurements to the new domain; the question of suitable electrical insulation for the leads was at first most troublesome, the methods of insulation suitable for the former narrower field not being applicable in the extended range. At first the best insulation that I could design usually failed either electrically or mechanically after about two applications of pressure. Under such circumstances the collection of results was very slow because of the necessity for continually taking apart and reassembling the ap-

140 — 3529

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American

Scientist

paratus. I had to decide whether to stop for a systematic development of a more adequate type of insulation or to continue with the measurements, making such changes in the method of insulation from time to time as occurred to me. The latter course, which I took, has, I think, proved to be the better tactics, for now after several years I not only have a considerable accumulation of measurements both on compressibility and on the effect of pressure on electrical resistance, but also have developed an improved method of insulation which permits a number of measurements before reassembly becomes necessary tiei. The method is shown in Figure 11. THE RANGE ABOVE 50,000 Kg/cm 2

FIG. 11. The method of msulating the leads to stand a pressure 2 Of 30,000 kg/cm . A i s a thin sleeve of pipestone, 0.00S inch thick, Β is the lead, of piano wire, 0.013 inch in diameter.

Work with the two types of apparatus, that for 50,000 with somewhat less accuracy and restricted to the measurement of simple volume effects, and that for 30,000 with greater accuracy and greater latitude in the effects studied, was carried on side by side for several years. During this time the problem of reaching still higher pressures was continually in the background. It was evident that 50,000 was about the pressure limit possible with the conical type of external support and the carboloy piston. The pressure vessel was just on the point of going to pieces in all directions, like the deacon's one-horse shay; instances were not uncommon in which the vessel ruptured simul,

,

A

11

taneously on three mutually perpendicular planes. Also the car-

,

.

.

boloy piston was near its limit

Recent Work in High Pressures

27

and broke more often than was pleasant. It was increasingly clear that the ultimate nest of pressure vessels could no longer be sidestepped. With the experience gained by several years, measurements in the new range this did not seem as hopeless as at one time, and the problem was again attacked with more optimism and more prospect of considerable extension of range than before, because it was now possible to utilize as the first supporting pressure 30,000 or 50,000 instead of the mere 12,000 that set the limit earlier. The first attempts were made with the support afforded in the 50,000 kg/cm 2 apparatus and were highly encouraging, for they indicated the possibility of reaching pressures of 200,000 or even more ti7]. So large an extension of range, by considerably more than the support afforded by the pressure itself, was perhaps more than might have been hoped for, but it was in line with my early experience that the usual theories of rupture of heavy vessels under internal pressure set too low a limit. This large extension was also in line with observations made by Mr. Griggs cisi in my laboratory in his geophysical studies of the increased strength and plasticity of rocks and minerals under the support afforded by hydrostatic pressure. He had found that the strength was much increased and that the higher the pressure the more rapid the rate of increase, so that it looked as though it might be exponential. My observations were consistent with this view, and I accepted them as confirmation. However, the accuracy possible at these new high pressures was so low that it was questionable whether there would be any great scientific purpose served by extending the measurements, or whether much would be found that could be accepted with as much confidence as a simple extrapolation from the lower domain. The reason for the marked decrease in accuracy was that the "liquid," by which the external supporting "hydrostatic" pressure was exerted, was itself a soft metal, such as lead, indium, or bismuth, and the friction effects were so large as to obscure everything else. It soon became evident that, in order to secure a satisfactory accuracy, the first stage of external

140 — 3531

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American

Scientist

support by a hydrostatic pressure would have to be provided in the 30,000 apparatus by a true liquid, in which there was the possiblity of accurate measurement through the use of electrically insulated leads.

I

1

MEASUREMENT OF PRESSURES

Before this was possible, a "compressometer" had to be developed to measure a thrust on a piston immersed in a fluid under high pressure. This was at last satisfactorily accomplished, and a compound pressure apparatus, consisting of a piston, a cylinder, and a pressure gauge, all completely imFIG. 12. The miniature apparatus for reaching 100,000 kg/cm 2 mounted in its mersed in the fluid of an supporting outer pressure vessel. The outer pressure apparatus, thrust on the small pistons is measured was set up. This is shown with the electrical device indicated at the bottom. in Figures 12 and 13. The inner piston was only He inch in diameter, again illustrating how the apparatus becomes smaller with higher pres-

1

1

FIG. 13. The miniature pressure apparatus, immersed in the fluid of a larger pressure apparatus to which a pressure of 25,000 kg/cm 2 or more is applied, with which pressures of 100,000 kg/cm 2 are reached. The charge is compressed from the two ends by two carboloy pistons. The "cylinder" of the apparatus is compound, consisting of an inner core of carboloy forced into an outer supporting ring of steel.

Recent Work in High Pressures

29

sures. Almost at once it appeared with the use of this more accurate apparatus that the previous estimates of the possibilities in a single stage of support had been set too high. The upper limit is not sharp, because rupture is always capricious, but it is probably not possible under any cir-

Fig. 14. The effect of pressure in increasing the ductility of steel. Above are shown two different grades of steel broken in tension at atmospheric pressure. Below are specimens of the same grades of steel broken while immersed in a liquid exposed to 25,000 kg/cm 2 . The approximately 100 per cent reduction in the size of the specimen on the right is especially striking.

140 — 3533

30

American Scientist

cumstances, with the materials available, to reach more than 150,000 kg/cm 2 in the interior of a cylinder with the thrust exerted by a piston, and 125,000 would be a more normal upper limit. With the hindsight afforded by the more accurate measurements, a reinspection of the previous results, in which support was provided in the 50,000 apparatus, indicated an equally plausible way of interpreting the results so that there was now no inconsistency with the new limit of 150,000. It also appeared in the light of the more accurate measurements that the supposed exponential increase of strength with supporting pressure was illusory, and that the increase of strength is at least approximately linear in the supporting pressure for the materials used for piston and cylinder, a result which ordinary physical intuition, I think, will find more congenial. In any event, there is an increase of strength under supporting pressure and there is, therefore, a gain in supporting the apparatus by external hydrostatic pressure of more than the supporting pressure itself. There is also a notable increase in ductility, as shown by the specimens in Figure 14. The limit of 125,000, just mentioned, has to be further cut down when accurate measurements are required because of the slow creep of the carboloy piston. Under high supporting pressure carboloy loses its ordinary brittleness and becomes capable of considerable plastic deformation. The latter is not noticeably accompanied by a work hardening, as in steel, but occurs under conditions more nearly approaching true viscosity, which permits indefinite yield when the pressure is continued long enough. For accurate measurement it has been found desirable to restrict the thrust on the piston to approximately 110,000 kg/cm 2 ; this corresponds to 100,000 on the contents of the cylinder when allowance is made for friction. USE OF CARBOLOY

The possibility is now open, therefore, of making simple volume measurements up to pressures of 100,000 and study-

140 — 3534

Recent Work in High Pressures

31

ing polymorphic transitions and compressions in this range. When I started on such a program, it soon developed that accurate results were going to be difficult for another reason, namely, the very large distortion of the cross section of the steel containers under pressure, which becomes greater than 10 per cent, with an unknown and increasing uncertainty as to the proper way to calculate the correction. The obvious remedy was to make the pressure vessel of some material with much higher elastic constants, so that it would be less deformable. For this purpose the only material with a sufficient gain in elastic constants appeared to be carboloy itself, but at first this seemed to me to be ruled out for two reasons: the impossibility of making carboloy cylinders and the fact that carboloy would be expected to rupture in tension more easily than steel, its superior strength normally being in the direction of compression. However, on reflection and inquiry it appeared that neither of these considerations might be decisive. Basset U9i in France had published results in which he had obtained high pressures in carboloy cylinders with external supporting jackets of shrunk-on steel. It also turned out that a technique had been developed in this country, just in time for my experiments, of drilling accurate holes in carboloy, so that the cylinders could be made. As far as the rupture of carboloy under internal pressure was concerned it was obvious that my conditions were more favorable than Basset's, because the external supporting pressure would, in virtue of differential compression between carboloy and steel jacket, afford an additional differential pressure on the carboloy cylinder. I hoped that this extra factor would be sufficient to give the additional strength needed to get beyond Basset's pressures by the amount desired. The first trial was successful, as it so seldom is. The distortion was found to be only one-third of that for steel, and this can be calculated with less uncertainty than in the other measurements. The over-all accuracy is perhaps about 2 per cent. As so often occurs, one has to put up with a diminished accuracy in extending the range, but the accuracy is great

32

American Scientist

enough to permit results of value and is probably within any present-day theoretical demands. With this apparatus

PRESSURE.

Kfl/cm*

FIG. IS. The volume compression of several elements up to 100,000 kg/cm 2 . The breaks in some of the curves indicate polymorphic transitions.

140 — 3536

Recent Work in High Pressures

33

I have started on a program of measurements up to 100,000 and already have values for the volume compressions and polymorphic transitions of some seventeen elements [201 and a number of simple compounds in the new range. The curves for several of these are shown in Figure IS. There are a number of new polymorphic forms. For example, bismuth has a new form, making its phase diagram strikingly

FIG. 16. T w o pieces of carboloy which have been pushed together with an intensity of stress of 400,000 k g / c m 2 on their area of contact. The radial cracks were produced on release of pressure.

similar to that of water, and antimony has a form looked for at lower pressures, but without success, because of the close resemblance between the lattice structures of the ordinary forms of bismuth and antimony. Still higher pressures are attainable, but the experimenter must be reconciled to increasing uncertainty in the values of the pressures themselves, and less scientifically useful results. In the literature there are fabulous estimates of the pressures that can be reached for very short intervals of time when a steel projectile is fired into a tapering hole in a massive block, but no results have ever been obtained under such conditions except a description of the distortion

140 —

3537

34

American

Scientist

or rupture of the steel itself. Study of rupture under such conditions might be of interest, but probably not much else could be done. Even a study of rupture would be of inferior value until the stresses were more accurately established; and our growing knowledge of the properties of matter under pressures up to 100,000 shows that the stresses attainable under such conditions have been much overestimated and are no greater than may be reached under better controlled conditions in other ways. It now appears that certain very limited studies can be made at controlled and maintained pressures materially above 100,000. It will be recalled that I subjected a miniature piece of graphite to a pressure of 100,000 in an apparatus entirely composed of steel. It is evident that higher pressures can be secured if a miniature form of such an apparatus is subjected to one stage of external support by hydrostatic pressure in the apparatus for 30,000, and that still higher pressures may be anticipated if the miniature apparatus is made of carboloy instead of steel. This is essentially what I have done, with certain modifications. Figure 16 shows two pieces of carboloy that were used in an experiment of this sort. Pressures of 400,000 kg/cm 2 or more can be reached in this way on minute flakes of various materials 1211; these flakes are large enough so that after exposure to such pressures they can be examined by Xrays to determine whether there has been any permanent alteration, such as the alteration from yellow to black phosphorus occurring at 12,000. Seven or eight substances selected as most likely to give positive results because of their position in the periodic table have been examined in this way but with negative results. Even at this pressure graphite is not changed to diamond. It is probable that T a m m a n n was right and that if a certain transformation is not effected by a moderate pressure in excess of the pressure of the thermodynamically reversible transition, it will not be effected by any pressure, no matter how high, the tendency to the transformation passing through a maximum with increasing pressure. Interesting examples of rupture take place under these

140 — 3538

Recent Work in High Pressures

35

very high stresses. It would doubtless be of value to study them systematically, because they can be measured with some accuracy, but as yet I have not had a chance to embark on such a program. The only other thing in sight to do with these very high pressures is to search for permanent transformations. In view of the negative results so far attained, I shall probably leave this field in abeyance until there are more positive indications from the theoretical side as to the most probable places to look for such effects. T h e next step in the direction of still higher pressures is obviously two stages of external support, but this at present seems an incalculable distance in the future. REFERENCES A general survey of the high-pressure field, up to the time of publication, will be found in my book, The Physics of High Pressures. Macmillan, 1931. 1. AMAGAT, Ε. H., Ann. Chim. Phys., 29, 68, 1893. 2. TAMMANN, G. Kristallisieren und Schmelzen. Barth, Leipzig, 1903. 3. BRIDGMAN, P. W. Phil. Mag., July, 1912, p. 63; Jour. App. Phys., 9, S17, 1938; Mech. Eng., Feb., 1939. 4. Jour. Am. Chem. Soc., 36, 1344, 1914; 38, 609, 1916. 5. JACOBS, R. B. Jour. Chem. Phys., 5, 945, 1937. 6. STAR», CHAUNCEY. Phys. Rev., 54, 210, 1938. 7. BRIDGMAN, P. W. Proc. Am. Acad., 59, 165, 1923. 8. BORN, MAX. Atomtheorie des festen Zustandes. Teubner, Leipzig, 1923. 9. Ε WELL, R. H., and EYRING, H. Jour. Chem. Phys., 726, 1937. 10. BRIDGMAN, P. W. Proc. Am. Acad., 68, 27, 1933. 11 . Phys. Rev., 48, 825, 1935. 12. ROSSINI, F. D., and JESSUP, R. S. Nat. Bur. Stds., Research Paper RP1141, 1938. 13. BRIDGMAN, P. W. Proc. Am. Acad., 72, 45, 1937; 72, 227, 1938. 14. Jour. Chem. Phys., 9, 794, 1941. 15. Proc. Am. Acad., 74, 1, 1940. 16 . Proc. Am. Acad., 74, 11, 1940. 17 . Phys. Rev., 57, 342, 1940. 18. GRIGGS, D. Τ. Jour. Geol., 44, 541, 1936. 19. BASSET, J . Jour. de Phys. et le Rad., 1, 121, 1940. 20. BRIDGMAN, P. W. Phys. Rev., 60, 351, 1941. 21 . Jour. App. Phys., 12, 461, 1941.

140 — 3539

On Torsion Combined with Compression P. W .

BRIDGMAN

Harvard University, Cambridge, Massachusetts (Received March 4, 1943) If a rod is twisted white subjected to longitudinal compression it will support without fracture angles of twist many-fold greater and maximum torques somewhat greater than is possible in the absence of load. Under compressional load the curve of shearing stress against shearing strain rises to a maximum and then sinks with a long drawn out tail to an approximate asymptote. Fracture is never complete, but some coherence always remains, probably due to cold welding. The maximum torque is not marked by any visible beginning of fracturing or other discontinuity. The strain hardening curve in torsion, therefore, under proper circumstances passes through a maximum. The whole mechanism of strain hardening appears to be different in torsion and in tension, and reasons are given for anticipating such a difference because of the difference of the atomic

kinetics in torsion and tension. It is shown in particular that the method of correlating tension and torsion through the "octahedral" coordinates which is applicable for small strains is not applicable to the (arge strains which are the subject of the present discussion. It is shown that the equations of conventional plasticity theory correctly reproduce certain qualitative aspects of the secondary longitudinal and radial flow which accompany twisting, but it is possible to establish large failures of isotropy not covered by the elementary theory. With regard to fracture, it is necessary to distinguish sharply between fracture in tension and in shear. The latter is not clean cut and it is probably possible to realize a continuous gradation of atomic disorganizations, culminating under proper conditions in complete shearing fracture.

INTRODUCTION

with a small hydraulic ram in such a way that longitudinal extension or shortening is free to occur. The measurements consist of the torque of the twisting force against the angle of twist. There are various advantages in giving the specimen the shape shown. One of the most important is that no end thrust bearings are needed and there is no frictional resistance to twist. Furthermore, there are two regions of twist, so that essentially two experiments are performed simultaneously, and the result, being an average of two, is correspondingly more accurate. By confining the twisted region to a narrow isthmus longitudinal stability is ensured under the joint action of twist and compression. By making the specimen hollow instead of solid and making the

F a bar is twisted while a longitudinal compressive load is simultaneously applied it is possible to twist the bar through much greater angles without fracture than is possible without the compressive load. At the same time the magnitude of the torque which the bar can support without fracture is increased. There are also other related phenomena, such as an alteration during twisting in the radial and longitudinal flow which would normally be produced by a pure longitudinal compression. In this paper some of these phenomena are examined.

I

EXPERIMENTAL METHOD

The torsion specimen is shown in Figs. 1 and 2. The central part is separated from the ends by two deep and narrow notches; the two ends are held from rotating and the center is twisted between the ends. The requisite torques are applied with the help of keyways milled in the three segments, not shown in the figure. A longitudinal compressive load may be applied at the same time as the twist. The compressive load is applied

FIG. 1. Section of the torsion specimen with central pin for stability.

141 — 3 5 4 1

274 wall thickness at the notch small, approximate uniformity of stress distribution is attained and

with part of the central pin.

the problem becomes approximately a two dimensional one. With the hollow specimens geometrical stability up to complete fracture was secured by inserting a hardened guiding pin in the central hole. Control experiments show that no appreciable error from friction is introduced by the pin. T h e central part was attached to a pulley of diameter 75 times greater than the notch diameter, and rotation of the central part against the ends was produced by a flexible wire cable which was wound off the pulley onto a drum actuated by a motor through variable gears so as to give a wide range of speed. The arrangement was essentially one, therefore, in which the velocity of twist was impressed—the requisite torque automatically adjusted itself. T h e effect of speed was studied in the range from 0.006 to 40.0 degrees per second. In this range there is an increase of torque with increasing speed of the order of five percent. This effect is so small that it was neglected in the following; the measurements of this paper were carried out with a speed of rotation of approximately 0.15° per second. Much preliminary work was done in selecting the best dimensions, starting with solid specimens j " diameter, then increasing to γ»" and finally to I " , and with several sizes for the hole, starting with j " up to 0.290", which proved too large,

141 — 3 5 4 2

settling back on 0.277". The final outside diameter at the bottom of the notch was 0.297". Different notch widths were also tried; that finally adopted was 0.010" at the bottom. The sides of the notch are inclined at 30° to each other. T h e early notches were made with rounded corners to avoid danger of fractures starting at sharp edges. T h e uncertainty in the effective width of the zone of flow introduced by the rounding was so great, however, that finally notches with sharp corners were tried, although with much misgiving. I t was a surprise to find that there is no tendency for the fracture to start at the corner, but the crack still usually appears in the central portion. It is evident that the effect of stress concentrations at corners is quite different under these conditions than in ordinary tension tests. T h e results were recorded photographically. T h e twisting force deflects a stiff spring which carries at the end of a long arm a source of light and a lens system by which a spot of light is thrown onto a revolving drum with photographic paper geared to rotate with the central part of the specimen. The apparatus is not sensitive in the elastic range. Arrangements are made for recording on the paper fiducial marks from which the absolute values of force and angle of twist may be obtained. In Figs. 3 and 4 are shown typical photographic records of twisting force against angle of twist with and without compressional load for two grades of steel. The great effect of compressional load is apparent. The records read from right to left. T h e long horizontal dimension is proportional to the angle of twist, the vertical one to twisting force. T h e initial part of the curve, corresponding to the elastic range, is straight. The elastic deflection is too small to show on the scale of the reproduction. The rectilinear part corresponding to elastic deflection is not at right angles to the horizontal line because of stretch in the twisting cable and lack of complete rigidity in other parts. The photographic record therefore gives stress against strain in oblique coordinates. On the record the second horizontal line is a fiducial line for a known force, made at the conclusion of the twisting experiment. The interruptions in the trace are fiducial marks for angle.

275

FIG. 3. Cold rolled steel—photographic record of angle of twist (abscissa, reading from right to left) against torque. The short graph on the right was obtained with zero compressional load, the long graph on the left under an average compressional load at the isthmus of 5700 kg/cm2. The total angular displacement of the long graph is 85°. METHODS OF CALCULATION

In order to reduce the records to characteristic properties of the material, the shearing stress and the shearing strain in the material corresponding to any point on the record should be determined. T h e mean shearing stress can be found at once from the torque and the dimensions. If it is assumed that the shearing stress, S, is constant across the section, which must be very approximately true under the conditions, the following equation holds:

or

cr° Torque — 2 5 1 2ir r2dr, Ju S=

3 Torque

, 4π fo3 — r3 in the range up to 12,000 kg/cm.2 The initial compressibilities calculated from these measurements are 4.9 and 4.3 Χ 10 - ' respectively, against 3.6 and 3.7 given by extrapolation of the values in Table IV. The discrepancy is much beyond the experimental error of the present method, and the explanation of it is not clear. However, it is probable that the previous measurements should be disregarded; these were made by a new method, which has been applied to only a few substances, and which has never been adequately checked. The method was especially devised to apply to substances which are acted on by kerosene, and employed smaller samples than usual, mounted in a complicated way under the surface of mercury.

between the ascending and descending branches in general being of the same order of magnitude as for the inorganic compounds. This is perhaps not too surprising, because it has already been found that under high pressures such organic compounds as rubber may acquire a high rigidity, greater even than that of mild steel under the same pressure. The results are collected in Table V. Under the name of each substance is the density assumed in the calculations. This density was obtained from the measurement of the dimensions of the charge after release of pressure and removal from the apparatus. It is likely to be slightly and consistently in error on the small side, because of a slight swelling in volume on removal from the apparatus due to the elastic springing back of voids not crushed completely flat by the high pressure. The assumed density enters the calculation in such a way that, if at some future time better values are obtained for the density of the perfectly compacted material, the relative compressions given in the table may be corrected by multiplying by the ratio of the corrected density 3. Organic Solids. to the assumed density. This means that in A. Definite Compounds. A few simple compounds general the volume compressions given in Table were investigated, with a range of types of com- V are probably slightly too low. position. They were taken from the regular Among these organic solid compounds the stock of the Harvard Chemical Laboratory. In compression at 25,000 kg/cm2; ranges from 0.1959 spite of the mechanical softness of organic solids for menthol to 0.0901 for dextrose, or by a factor in general under atmospheric conditions, the of 2.2. The initial compressibilities of these two indium sheath was used in all the measurements. substances, extrapolated to atmospheric pressure, This proved to be necessary, the difference are in the ratio 3.5. This is consistent with the

148 — 3619

20

BRIDGMAN ΐβ CO CO W 00

Ό Ό
-Ι

g

§fi

5

2

0

5,000

10,000

15,000

20,000

25,000

30,000

PRESSURE, kg/cm* Logarithm of relative viscosity of n-amyl alcohol, i-pentane, and η-butyl bromide as a function of pressure. See text for the symbols. FIGURE 3.

166 — 3909

124

BBIDGMAN TABLE

I

Log ίο (Relative Viscosity)

0 5,000 10,000 15,000 20,000 25,000 30,000

Methyl Alcohol

n-propyl Alcohol

i-propyl Alcohol

n-amyl Alcohol

0.000 0.650 0.890 1.200 1.482 1.810 2.152

0.000 1.014 1.684 2.328 2.966 3.708 4.500

0.000 1.168 1.990 2.960 4.116 5.490 6.986

0.000 1.290 2.224 3.150 4.096 5.100 6.192

TABLE

n-butyl i-pentane Bromide 0.000 1.004 1.722 2.548 3.326 4.228 5.146

0.000 1.026 1.720 2.342 3.122 3.980 4.930

II

VISCOSITY o r SEVERAL DIMETHYLSILOXANE POLYMERS

Logio (Relative Viscosity)

Pressure kg/cm2 0 2,000 4,000 6,000 8,000 10,000 12,000

Trimer

Tetramer

Hexamer

Octamer

0.00

0.00

0.00

0.00

0.86 1.50 2.13 2.94 4.19 6.39

0.94 1.63 2.40 3.53 5.26

0.98 1.73 2.66 4.05 6.46

1.01 1.83 2.87 4.52, 6.03 * at 9,000

TABLE

III

V I S C O S I T Y OP S E V E R A L " D O W - C O R N I N G F L U I D S "

Pressure kg/cm2

Logio (Relative Viscosity) 500-1.00

0 2,000 4,000 6,000 8,000 10,000 (a) at 7,000

0.00

0.86 1.50 2.13 2.95 4.26

500-2.00

500-12.8

200-100

0.00

0.00

0.00

0.98 1.73 2.63 3.91

1.13 2.15 ϊ

>

(b) at 5,000

1.05

2.87

VISCOSITIES TO 3 0 , 0 0 0 KG/CM 2

1

1

1

1

1

1

1

125 1

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!h β

/

£

1

/* /s

]/// °/d

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§

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1 1 1 5,000

1

1

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1 10,000

1

1

PRESSURE, kg/cm 4. Logarithm of relative viscosity of four dimethyl siloxane polymers. See text for the symbols. FIGURE

The results obtained with the mixtures of pentanes are not reproduced in detail here, since the material was not well enough defined to have scientific significance, nor were the measurements as complete over the full range. From the point of view of technique, however,

166 — 3911

126

BRIDGMAN

6 1

1

1

1

1

5

1

1

/''

in 8 (Λ >

is _i

1

/

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vy //

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PRESSURE, Kg/cm2 FIGURE 5 . Logarithm of relative viscosity of several "Dow-Corning fluids." See text for symbols.

it is worth mentioning that a mixture of equal parts of Eastman's i-pentane and "pentane" ("technical") is at 30,000 less viscous than Eastman's i-pentane by a factor of 2, and pure "pentane" is less viscous than i-pentane by a factor of 3.5. Furthermore, the "pentane" did not freeze under these conditions at room temperature, so that it may well replace i-pentane or mixtures as the pressure transmitting

166 — 3912

VISCOSITIES TO 30,000 KG/CM2

127

liquid. The absolute viscosity of i-pentane at 30,000 at room temperature is about 170 poises. In Figure 4 and Table I I the results are shown for four pure dimethyl siloxane polymers, the trimer through the octamer, and in Figure 5 and Table I I I for several "Dow Corning Fluids" of the 500 and 200 series, which are mixtures of the dimethyl siloxane polymers. The corrections for buoyancy and change of linear dimensions were so small for these liquids that they were not applied. The effect of pressure is so large on this class of substance that no attempt was made to carry the pressures above 12,000. Not only is the effect of pressure large, but the curvature is in all cases much greater than for any of the liquids of Table I, and the upturn begins at much lower pressures. This is all in accordance with results previously found, namely that the pressure effect and the curvature is greater for substances with more complicated molecules. This general trend is particularly well brought out in Figure 4 for the pure species. Another feature evident from the figures is that all members of the series have very approximately a common initial tangent at atmospheric pressure. The very large pressure effect makes these liquids unsuitable for pressure transmitting media at high pressures, in spite of other desirable characteristics. Thus at atmospheric pressure the lowest member of the series which does not freeze under pressure, the trimer, is five times more viscous than i-pentane, whereas at 10,000 kg/cm2 it has become 5,000 times more viscous. SUMMARY AND DISCUSSION

In this paper measurements of viscosity have been extended over a 2.5 fold increase of pressure range, from 12,000 to 30,000 kg/cm2. The trends formerly found continue in the new range. Ultimately the viscosity increases with pressure more rapidly than exponentially. The pressure at which the upturn occurs is lower for liquids with more complicated molecules and the rate of upturn is more rapid. The order of magnitude of the effect of pressure on viscosity is greater than that of any other known pressure effect, and would seem to indicate some essential difference in the mechanism. In viscous flow the molecules preserve their inviolability and must to a large extent function as individual wholes. In the case of long polymeric molecules, packed together like earth worms in a tin can, the phenomena of viscous flow must be quite different from those of specific heat or thermal expansion, for example, in which the parts of the molecules can function with a certain degree of independence. I have previously expressed this by saying that the pressure effect on viscosity involves an "interlocking" of the molecules. The accentuation of the effects

128

BRIDGMAN

now found on increasing the pressure range seem to me to only accentuate the necessity for some such mechanism. It would seem to me that some essential physical modification is necessary in the pictures back of analyses suph as those of Frisch, Eyring, and Kincaid, 4 for example, in which viscous motion is supposed to involve the passage of an activated complex from one equilibrium position over an intermediate potential hill to a new equilibrium position. Formally, it would probably be possible to include the new sort of thing by assuming, as they themselves indicate, that the activated complex itself is an aggregate of molecules, the degree of aggregation itself increasing rapidly with pressure. But physically it would seem that this is pretty close to the "interlocking" effect. I am indebted to my mechanic, Mr. Charles Chase, for skillful construction and setting up of the apparatus. LYMAN LABORATORY OF PHYSICS,

Harvard University, Cambridge, Mass. REFERENCES 1. P. W. Bridgman, Proc. Amer. Acad. 61, 57-99, 1926. 2. P. W. Bridgman, Amer. Scientist, 31, 1-35, 1943. 3. P. W. Bridgman, Proc. Amer. Acad, number following this. 4. David Frisch, Henry Eyring and John F. Kincaid, Jour. App. Phys. 11, 75-80, 1940.

166 — 3914

FURTHER ROUGH COMPRESSIONS TO 40,000 kg/cm2, ESPECIALLY CERTAIN LIQUIDS CONTENTS INTRODUCTION AND TECHNIQUE T H E MATERIALS COMPARISON WITH PREVIOUS MEASUREMENTS T H E RESULTS AND DISCUSSION

INTRODUCTION AND

129 134 135 138

TECHNIQUE

R e c e i v e d N o v e m b e r 13, 1948

In this paper former rough measurements1 of compression to 40,000 kg/cm2 at room temperature of a number of solids are extended to substances initially liquid, the measurements in many cases being carried through the freezing point and on into the solid phase. This extension to the liquid phase has been made possible by a small change in technique, by which the liquid is sealed inside a lead capsule, and the overall compression of capsule with its contained liquid determined. A similar technique was formerly used in measurements to 50,000 over a temperature range,2 but with a modification of detail. Formerly the lead capsule was sealed with a condenser discharge at the moment of impact of a lead plug pressed against the body of the capsule. With the present arrangement the walls of the capsule are so thin, the total thickness of the capsule being only 0.130 inch, as shown in Fig. 1, that the impact of the sealing plug would produce undue distortion and consequent mechanical extrusion of the liquid. Some less violent method of making the seal is therefore required. Ordinary soft soldering is ruled out for the same reason as before, namely too rapid heat transfer, with resulting thermal expansion and escape of the liquid. The new technique employs essentially a cold soldering. The lead sealing point is lightly amalgamated with mercury, then lightly pressed against its seat in the capsule at the same time that it is rotated so as to spread the amalgamation to the seat, and finally held pressed against the seat with light pressure for 18 hours or more. By this time the mercury has diffused into the lead, leaving a solid solution, which is strong enough to withstand without leak the distortion of the capsule incident to carrying it to 40,000 and back, one or even several times. Lead is unique among all the soft metals whose binary mixture diagrams are given in Hansen3 in the width of the range of composition in which the homogeneous solid solution is stable. Most soft metals

167 — 3915

130

BRIDGMAN

V

°50" F I G U R E 1. Scale drawing of the lead capsule for containing the liquid for measurements of compression. The seal is made by cold amalgamation under slight pressure of the conical plug.

break up into a liquid phase when amalgamated with mercury, so that the seal is not made. The cold amalgamation seal with lead was successful at once for nearly all the liquids tried. For some it was more difficult than for others, apparently the liquid itself forming some sort of surface film on the lead which was difficult to break through so as to obtain a contact sufficiently close for the solid sulution to grow across the surface. Several liquids were tried three or four times before success was attained, and there were one or two which were finally abandoned. Success was apparently easier to achieve if a slight amount of sodium was dissolved in the mercury, a practise long familiar in amalgamating copper for electrical contacts. The methods of computation were simple extensions of those used before. The measured displacement of the piston has to be corrected for distortion of the carboloy piston and the compression of the lead sheath and of the steel washers. The total corrections were of the general order of 25% of the measured displacement. The initial volume of the liquid was calculated from its weight and density, the latter obtained either from the International Critical Tables or by special measurement in a specific gravity bottle. It is characteristic of the compression of liquids that the initial increment of pressure is accompanied by a comparatively large volume change, the compressibility rapidly dropping at higher pressures. This means that the error from the friction exerted by the lead capsule is especially large at the low pressure end of the range. Furthermore, it is especially important to know the initial volume accurately, since this sets the fiducial mark from which all subsequent proportional changes of volume are calculated. The result was that it was neces-

167 — 3916

FURTHER ROUGH COMPRESSIONS TO 40,000 KG/CM ?

131

sary to supplement the measurements in the 40,000 apparatus with other measurements in an apparatus especially constructed for the initial range from atmospheric pressure up to 5,000 kg/cm2. The primary function of this supplementary apparatus for 5,000 was the same as that of the 40,000 apparatus, namely to permit rapid measurements with moderate accuracy, so that it can be used as a tool for exploration. The supplementary apparatus is shown in Figure 2. The liquid whose compression is to be measured is placed in the heavy steel cylinder A. Pressure is produced by advance of the piston, P, inch in diameter, and the volume change is given directly by the motion of the piston measured by a dial gauge graduated to 0.001 inch and reading by estimation to 0.0001 inch. This gauge is so connected to the cylinder and the mushroom plug as to minimize any distortion in the steel parts and so as not to include at all any compression in the rubber packing on the end of the piston, which operates on the unsupported area principle. The compressing piston Ρ is driven by a second piston B, 2.0 inches in diameter, thus affording a sixteen fold multiplication in pressure. The piston Β is driven by a conventional hand pump, connected through a dead weight piston gauge. The pressure is controlled by the weight on the piston of the dead weight gauge, the weight being adjusted and then the pump operated until the weight floats. Readings were made at eleven different pressures between atmospheric and 5,000, the spacing being nonuniform and closer at the lower end of the range. Readings were made with increasing and decreasing pressure, 20 in all, in order to eliminate error from friction. A special feature of this apparatus, not used in any other of my pressure apparatus, is the provision for rotating the pistons Ρ and Β before each reading to minimize the effect of friction. To this end the packing on the mushroom heads of both Ρ and Β is made unusually thin, only 1/64 inch thick on each. The packing material was usually neoprene, but for some liquids which attack neoprene, such as xylene, varnished cambric, such as is used in electrical insulation, was successfully used, in three thicknesses, each .007 inch thick. The washers must obviously be cut with care, using a sharp cutter to obtain a smooth edge. Use of such thin packing demands that the inner surfaces of the cylinders in which Ρ and Β play be well polished. Rotation was by hand, with a lever passing through a hole in the piston B, back and forth through an angle of 60°. Usually three double oscillations were made before each reading. It is not possible with this apparatus, in contrast to the 40,000 apparatus, to make readings as fast as the pressure manipulations can be made, but after every increase of pressure an appreciable time must elapse for dissipation of

132

BEIDGMAN

FIGURE 2. The apparatus for rapid determination of the compression of liquids up to 5,000 kg/cm2. Friction is minimised by rotation of the pistons Ρ and Β before the readings.

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the heat of compression. The time may be decreased by placing in the body of the liquid several strips of sheet copper to conduct away the heat. In this way the time between readings was reduced to two minutes. The readings were taken on an exact time schedule to make the conditions as reproducible as possible. By taking all precautions, the difference between readings with increasing and decreasing pressure was practically never as much as 0.001 inch, and often materially less, on a total stroke of 0.5 inch. Friction should be reduced from the mean of readings as close together as this to a value smaller than that of the other errors. The piston readings were converted to absolute compressions by means of blank runs with solids and liquids of known compressions in a way which need not be described in detail. The time required for a complete run was of the order of one hour, somewhat less than that required with the 40,000 apparatus. Operation so far has been confined to room temperature, which in the following may be taken as 25°, but there is no reason why temperature control and operation at other temperatures should not be added; in fact, a modified apparatus is now under construction for use at other temperatures. The time for a run will now naturally be increased by the time required for attainment of temperature equilibrium at each temperature. The apparatus may be used for determinations of the thermodynamic freezing parameters of those liquids which freeze within the range by placing the liquid in an inverted steel cup with mercury seal, with water to transmit the pressure to the mercury, after the fashion of my early freezing curve determinations.4 The apparatus was so used for a number of substances to be described in the following. By carrying the measurements beyond the freezing pressure up to 5,000, compressions of the solid phase are also obtained. The accuracy of these determinations is somewhat reduced as compared with that of the compressions of non-freezing liquids because of the reduced amount of liquid allowed by the presence of the water, mercury, and steel. In certain cases the freezing parameters had been previously determined in other apparatus better adapted to giving accurate values. In these cases the present data were adjusted to agree with the former results in the overlapping range, as will be described in detail later. There are also some cases in which compressions have been previously measured in the range from 5,000 to 50,000 kg/cm2, but in which the low pressure range was not measured. The new data supplemented with the old now can allow complete values of compressions from atmospheric pressure to 40,000 kg/cm2. The freezing temperatures and pressures given in the various tables have only an inferior accuracy, since the pressure steps were not made small enough to give good

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values, the smallest being 200 kg/cm2. The differences of volume between liquid and solid are the differences at the temperature (25°) and the pressure indicated, and should be fairly good for these conditions. They are not the volume differences for the correct equilibrium pressure at 25°, but differ from this by a term equal to the product of the pressure excess (or defect) and the difference of compressibility between liquid and solid. T H E MATERIALS

The materials measured in the following include in the first place 30 hydrocarbons. It was thought to be of interest to find whether the compressions, particularly at the high pressure end of the range, tend to assume any simple relation to the obvious properties of the molecule. The 30 hydrocarbons selected include all those listed in Eastman's catalogue of organic chemicals and procurable, including substances both liquid and solid under ordinary conditions. Most of these were of the "Eastman" grade of purity; the n-dodecane, n-hexadecane, and tetrahydronaphthalene were of "practical" grade, the amylene and fluorene of "technical" grade, and the styrene was "stabilized with tert.-butylcatechol." Next comes a group of 8 miscellaneous organic compounds. The first six of these were from my own stock, left from previous experiments, which seemed of interest for various reasons. In addition there are two of the fluorocarbons developed during the war, which I owe to the courtesy of Professor W. T . Miller of Cornell University. The first of these is perfluoroheptane, C7Fie, prepared by the vapor phase fluorination of heptane, utilizing the procedure of Cady, Grosse, Barber, Binger, and Sheldon.6 It boiled at 82°. The second is a "chlorofluorocarbon polymer oil." This was a fraction of "stabilized" chlorotrifluoroethylene polymer of approximate boiling range 100° to 200° at 0.3 mm, prepared as described by Miller, Dittman, Ehrenfeld, and Prober.6 Finally there is a group of 16 substances which I owe to the courtesy of Mr. Shailer L. Bass of the Dow Corning Co.. The first seven of these are the individual members of the dimethylsiloxane polymers from the dimer through the octamer, or in other words the compounds of the formula

(CH 3 ) 3 Si0-[(CH 3 ) 2 Si0] i -Si(CH 3 ) 3 where χ varies from 0 through 6. The next eight are commercial "Dow Corning" fluids of the 500 and 200 series of different viscosities. The members of these two series are composed predominantly of polymers of the type just described. In the following these liquids are identified in the regular manner by giving first the number of the series and then the viscosity in centistokes. Thus the liquid

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135

designated as 500-2.00 is the liquid belonging to the 500 series with viscosity 2.00 centistokes. Finally, there is a single member of the 550 series, which is a different type of compound than the others, in that a portion of the methyl groups are replaced by phenyl groups. COMPARISON WITH PREVIOUS MEASUREMENTS

The volume compression of liquid n-heptane has been previously measured7 by the sylphon method at 0°, 50°, and 95° in the range of the liquid below 11,000 kg/cm2. Exact comparison with the present measurements is not easy because of the incompatibility of temperature range. Linear interpolation of the previous results gives volume decrements at 500 and 5,000 kg/cm2 of 0.0544 and 0.202 respectively against 0.0502 and 0.198 found now. The difference is in the direction to be expected because of the inadequacy of a linear interpolation, and does not appear unreasonable in magnitude. The volume compression of liquid n-octane was previously measured8 in the same way as n-heptane in the same temperature range, but of necessity in a narrower pressure range because of the freezing. Linear interpolation as above gives for the volume decrements at 500 and 3,000 kg/cm2 0.0444 and 0.149 respectively against 0.0444 and 0.146 found now. The agreement at 500 is too good for the method of interpolation, and at 3,000 not unreasonable. The volume compression of liquid n-decane9 was determined under the same conditions as outlined in the two paragraphs above, the pressure range being correspondingly reduced. The volume decrements at 500 and 1,000 kg/cm2 by linear interpolation were 0.0417 and 0.0713 respectively against 0.0400 and 0.0683 found now. The difference is in the right direction, but somewhat larger than appears a natural consequence of the method of interpolation. Three previous sets of measurements have been made on benzene in the course of my high pressure work, not to mention work by other observers.10 The freezing parameters were determined with much care up to 12,000 kg/cm2. These values are doubtless better than those obtained with the present apparatus, and they were accordingly accepted and incorporated in Table II. The fractional change of volume on freezing with the present apparatus was about 5 per cent lower than the value accepted from the previous work. The volume compression of the liquid was measured in the former sylphon apparatus, but only at 50° and 95°. The decrement at 24° and 680 kg/cm2 (the freezing pressure at this temperature) was obtained by linear extrapolation from these two temperatures and is therefore rather uncertain. Finally, the volume decrement of the solid phase from 5,000 as the zero has been determined. The volume decrement

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between 5,000 and 40,000 formerly found was 0.141, against 0.144 found now and given in Table II. Exact comparison of these two results is not possible because the present results pertain to the low pressure modification of the solid, since no trace of the transition to a high pressure form was found which formerly occurred at 12,500 kg/cm?. In the present work the transition was doubtless suppressed because of the small size of the apparatus and the low temperature, which was at the lower edge of the range in which the transition was previously observed. The volume decrement at the transition formerly found was 0.008. In comparing the previous results with the present for the low pressure modification the volume decrement is therefore to be taken as probably 0.149 at the maximum (assuming the two modifications to have the same compressibility), or somewhat less than 0.149 if the high pressure modification is assumed to be less compressible, as is probable. In any event the agreement with the former high pressure values is not bad. The freezing pressure of cyclohexane at 25° listed in Table II, 355 kg/cm', is taken from Deffet11. There is no doubt that his value is better than the mean value 420 kg/cm2, given by the present work. It has already been explained that the pressure steps in the present work were so large that a minimum error of 100 kg/cm2 in the equilibrium pressure is always possible. The values above 5,000 given in the table are taken from my previous measurements12 to 50,000. Measurements above 5,000 were not made with the present apparatus because cyclohexane was one of the liquids for which the sealing technique made so much difficulty that it was abandoned. With regard to the previous work it is to be especially noted that the volume discontinuity at 7,500 listed there was incorrectly described as due to freezing; it is, as a matter of fact, due to a transition between two solid phases. The freezing pressure of p-xylene is so low that the values of other observers were used for the low pressure end of the range. The freezing pressure at 25° was taken as 343 kg/cm2 from the work of Deffet,13 and the fractional change of volume on freezing as 0.164 at the same pressure and temperature from the same author. The compression of the liquid at 343 kg/cm2 was assumed to be 0.0249 from the work of Richards and collaborators,14 this being their value at 20°. There should be a small correction for the difference of temperature, but the data for this do not exist. In connecting these low pressure values with the present measurements to 40,000 an extrapolation of the measurements on the solid of 1,000 kg/cm2 was necessary. Measurements have been previously made on the solid phase of this sub-

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stance in the range above 5,000 kg/cm2. The volume decrement between 5,000 and 40,000 formerly found was 0.113 against 0.116 found now. Methylene chloride (Table III) has been previously measured16 above 5,000, so that the essentially new contribution of the present measurements is the compression of the liquid up to 5,000. The former total volume decrement between 5,000 and 40,000 was 0.219 against 0.211 found now. The agreement above 15,000 is perfect within the number of significant figures. The former freezing parameters agree fairly well with the present ones. The freezing parameters of chloroform have been previously measured16 with considerable care; these former values are incorporated in Table III. The compression has also been determined from 5,000 as zero up to 50,000. The former value of the volume decrement between 5,000 and 40,000 was 0.204 against 0.203 found now. Ethyl acetate has been previously measured17 above 5,000. In the former measurements data were obtained for both liquid and solid phases up to the maximum pressure; the natural tendency is for the liquid to subcool over the entire pressure range, so that special manipulation was necessary to obtain the solid phase. With the present smaller apparatus and more rapid pressure variation the solid phase was not obtained at all. The former volume decrement of the liquid phase between 5,000 and 40,000 was 0.185 against 0.178 found now. The compression of the liquid phase of chlorobenzene has been previously measured18 at 0°, 50° and 95° up to 11,000 kg/cm2. Reducing to 25° by linear extrapolation gives for the volume decrement at 5,000 and 25°, 0.1406 against 0.1517 found now. The discrepancy is perhaps in the direction to be explained by the linear extrapolation, but is larger than usual and not obviously explainable. Further, the volume decrements have been determined up to 50,000 from 5,000 as zero. The former volume decrement between 5,000 and 40,000 was 0.177 against 0.175 now. The correct freezing pressure at 25° is probably nearer 5,000 than 7,500, the average figure given by this work. It is to be marked that in the former work a second phase of the solid was encountered at pressures above 13,000 and at temperatures of 75° or more; no trace of this phase was found in the present work. The compression of n-amyl ether has been measured19 up to 50,000 from 5,000 as zero. The total volume decrement between 5,000 and 40,000 was 0.197 against 0.187 found now. The former freezing pressure given for 25° was 7,500, very materially lower than that now given, 11,140; neither of these values makes any pretense to accuracy. The former volume decrement at the freezing pressure, 0.047, is much higher than that now given, 0.021, but is not inconsistent with it in

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view of the difference of pressures, and indicates a compressibility for the liquid phase materially higher than that of the solid, as is normal. T H E R E S U L T S AND DISCUSSION

The results for the normal straight chain paraffins, containing 7, 8, 10, 12,16, 18 and 28 carbons in the chain, are shown in Table I. The TABLE Ι COMPRESSIONS OF NORMAL STRAIGHT CHAIN

Pressure kg/cm 2

Δ V/Vo n-heptane

n-octane

n-decane

n-dodecane

.0000 .0502 .0835 .1073 .1266 .1428 .1567 .1688 .1796 .1893 .1982 .2659 .3394 .3616 .3789 .3937 .4057 .4163

.0000 .0444 .0751 .0982 .1170 .1326 .1460 .1579 .1686 .1782 .1868,, .2941 .3205 .3398 .3546 .3669 .3775 .3872

.0000 .0400 .0683 .0902 .1079 .1228 .1359

.0000 .0353 .0609 .0787

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5.000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 a b c d e

HYDROCARBONS

Freezes Freezes Freezes Freezes Freezes

at at at at at

.1869 c

.2319 .2694 .2948 .3141 .3293 .3418 .3524 .3615

.2158 .2516 .2769 .2961 .3115 .3244 .3359 .3464

Ο

n-hexadecane .0000 .1413® .1576 .1676 .1756 .1823 .1887 .1951 .2006 .2056 .2096 .2446 .2696 .2883 .3034 .3156 .3261 .3352

n-octadecane

n-octacosane

.0000

.0000

.0479

.0437

.0777 .1183 .1470 .1695 .1886 .2051 .2196 .2324

.0719 .1117 .1407 .1637 .1829 .1992 .2128 .2239

11,450. Δ V/Vo .2782 and .3202 5,510. Δ V/Vo .1863 and .2475 3,050. AV/Vο .1370 and .2107 1,700. Δ V/Vo .0839 and .1869 420. AV/V,.0300 and .1392 Δ V/Vo = .0192 at 250 and .1498 at 750

table exhibits definite regularities. The first five of the series are liquid at atmospheric pressure at room temperature, and are brought to freeze by the application of pressure. The pressure required for freezing decreases as the number of carbons in the chain increases. A plot of the freezing pressure against number of carbons yields a smooth curve, rising very rapidly at the lower end. The fractional discontinuities of volume on freezing are 0.0420, 0.0612, 0.0737, 0.1030, and 0.1092. If these values are plotted against number of carbons a curve rising with increase of carbon number will be obtained, but the curve is not smooth. A very considerable part of the rise with increasing carbon number is to be ascribed, not to an effect of structure, but to

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the incidental effect of decreasing freezing pressure, since the volume discontinuity of nearly every substance increases as the freezing pressure is lowered. The initial compressibility in the liquid phase decreases as the number of carbons increases, as shown, for example, by the row of compressions for 500 kg/cm2. This is in large part a reflecrion of the greater volatility of the lighter members of the series. The effect persists over the entire range, the compressions at 40,000 showing the same sequence. The initial effects reflecting the proximity of the critical point with the vapor might be expected to be wiped out at the upper end of the pressure range, where other sorts of structural effect might be expected to begin to become apparent. As a rough indication of this, the relative compression in the last 20,000 kg/cm2 may be taken, that is the difference between the rows for 20,000 and for 40,000 kg/cm2 in the table. The numerical values for the seven members of the series are respectively: 0.0547, 0.0474, 0.0474, 0.0503, 0.0469, 0.0629, and 0.0602. The tendency of the first five, for the paraffins initially liquid, is an irregular decrease with increasing carbon number. The last two, for those members initially solid, are on the average 25 per cent higher than the others. Part of this is to be ascribed to the fact that the initial Vo on which the compressions are calculated is the volume of the solid rather than the larger initial volume of the liquid. However, not as much as half of the difference can be explained in this way, the difference of volume between solid and liquid at the atmospheric freezing point not being much over 10 per cent. Taking due account of this factor, there seems to be no outstanding regularity left in the compressions at the upper end of the pressure range. This means that other factors become more important than the simple size of the molecule. In Table I I are collected the compressions of the other 23 hydrocarbons. The arrangement is by number of carbons in the molecule. This means that substances initially liquid occupy the first part of the table and those initially solid the last part, with some overlapping toward the center. Obvious factors which might be taken into account in searching for correlations with the compressions are: the carbon-hydrogen ratio in the molecule, the ratio of the number of double bonds between carbons to single bonds between carbons and the type of molecular structure, whether straight chain, single ring, or double ring. Search has disclosed no obvious correlation between any of these factors and the initial compressibility, the total compression under 40,000 kg/cm2, or the compression in the last 20,000 kg/cm2. There are, however, certain gross regularities in the behavior of the hydrocarbons as a group. The total compression under 40,000 kg/cm? for those substances initially solid clusters around 0.2, ranging from a

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