Collected Experimental Papers of P. W. Bridgman, Volume V: Papers 94-121

Table of contents :
Contents
94. Physical properties of single crystal magnesium
95. A New kind of e.m.f. and other effects thermodynamically connected with the four transverse effects
96. A transition of silver oxide under pressure
97. The pressure coefRcient of resistance of fifteen metals down to liquid oxygen temperatures
98. The compressibility of eighteen cubic Compounds
99. The effect of homogeneous mechanical stress on the electrical resistance of crystals
100. The pressure-volume-temperature relations of fifteen liquids
101. Compressibilities and pressure coefficients of resistance of elements, Compounds, and alloys, many of them anomalous
102. The effect of pressure on the electrical resistance of single metal crystals at low temperature
103. Two new phenomena at very high pressure
104. The melting Parameters of nitrogen and argon under pressure, and the nature of the melting curve
105. The compressibility of solutions of three amino acids (with R. B. Dow)
106. Theoretically interesting aspects of high pressure phenomena
107. Electrical resistances and volume changes up to 20,000 kg/cm2
108. On the effect of slight impurities on the elastic constants, particularly the compressibility of zinc
109. The melting curves and compressibilities of nitrogen and argon
110. Measurements of certain electrical resistances, compressibilities, and thermal expansions to 20,000 kg/cm2
111. The pressure-volume-temperature relations of the liquid, and the phase diagram of heavy water
112. Effects of high shearing stress combined with high hydrostatic pressure
113. Polymorphism, principally of the elements, up to 50,000 kg/cm2
114. Compressibilities and electrical resistance under pressure, with special reference to intermetallic compounds
115. Shearing phenomena at high pressure of possible importance for geology
116. Flow phenomena in heavily stressed metals
117. Polymorphie transitions of inorganic compounds to 50,000 kg/cm2
118. Shearing phenomena at high pressures, particularly in inorganic compounds
119. Polymorphie transitions of 35 substances to 50,000 kg/cm2
120. The phase diagram of water to 45,000 kg/cm2
121. The resistance of nineteen metals to 30,000 kg/cm2

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Gollected Experimental Papers of P. W. Bridgman

Volume V

P. W. BRIDGMAN

Collected Experimental Papers

Volume V Papers 94-121

Harvard University Press Cambridge, Massachusetts 1964

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

Distributed in Great Britain by Oxford University Press, London

Library of Congress Catalog Card Number 64-16060 Printed in the United States of America

CONTENTS Volume V 94-2559.

"Physical properties of single crystal magnesium," Proc. Am, Acad. Arts Sei. 67, 29-41 (1932).

95-2572.

"A new kind of e.m.f. and other effects thermodynamically connected with the four transverse effects," Phys. Rev. 39, 702-715 (1932).

96-2587.

"A transition of silver oxide under pressure," Ree. Trav. Chim. Pays-Bas 51, 627-632 (1932).

97-2593.

"The pressure coefRcient of resistance of fifteen metals down to liquid oxygen temperatures," Proe. Am. Acad. Arts Sei. 67, 305-344 (1932).

98-2633.

"The compressibility of eighteen cubic Compounds," Proe. Am. Aead. Arts Sei. 67, 345-375 (1932).

99-2664.

"The effect of homogeneous mechanical stress on the electrica! resistance of crystals," Phys. Rev. 858-863 (1932).

100-2671.

"The pressure-volume-temperature relations of fifteen liquids," Proe. Am. Acad. Arts Sei. 68, 1-25 (1933).

101-2697.

"Compressibilities and pressure coefficients of resistance of elements, Compounds, and alloys, many of them anomalous," Proe. Am. Acad. Arts Sei. 68, 27-93 (1933).

102-2765.

"The effect of pressure on the electrical resistance of single metal crystals at low temperature," Proc. Am. Acad. Arts Sei. 68, 95-123 (1933).

103-2795.

"Two new phenomena at very high pressure," Phys. Rev. 45, 844-845 (1934).

104-2796.

"The melting Parameters of nitrogen and argon under pressure, and the nature of the melting curve," Phys. Rev. 46, 930-933 (1934).

105-2801.

"The compressibility of solutions of three amino acids" (with R. B. Dow), J. Chem. Phys. 3, 35-41 (1935).

vi

CONTENTS

106-2809.

"Theoretically interesting aspects of high pressure phenomena," Rev. Mod. Phys. 7, 1-33 (1935).

107-2843.

"Electrical resistances and volume changes up to 20,000 kg/cm^" Proc. Nat. Acad. Sä. U.S. 21, 109-113 (1935).

108-2849.

"On the effect of slight impurities on the elastic constants, particularly the compressibility of zinc," Phys. Rev. 393-397 (1935).

109-2855.

"The melting curves and compressibilities of nitrogen and argon," Proc. Am. Acad. Arts Sei. 70, 1-32 (1935).

110-2887.

"Measurements of certain electrical resistances, compressibilities, and thermal expansions to 20,000 kg/cm''," Proc. Am. Acad. Arts Sei. 70, 71-101 (1935).

111 -2919.

"The pressure-volume-temperature relations of the liquid, and the phase diagram of heavy water," J. Chem. Phys. 3, 597-605 (1935).

112-2929.

"Effects of high shearing stress combined with high hydrostatic pressure," Phys. Rev. 48, 825-847 (1935).

113-2953.

"Polymorphism, principally of the elements, up to 50,000 kg/cm^," Phys. Rev. 48, 893-906 (1935).

114-2967.

"Compressibilities and electrical resistance under pressure, with special reference to intermetallic Compounds," Proc.

Am. Acad. Arts Sei. 70, 285-317 (1935). 115-3001.

"Shearing phenomena at high pressure of possible importance for geology," J. Geol. 44, 653-669 (University of Chicago Press, 1936).

116-3018.

"Flow phenomena in heavily stressed metals," J. Appl. Phys. 8, 328-336 (1937).

117-3028.

"Polymorphie transitions of inorganic Compounds to 50,000

kg/cm^" Proc. Nat. Acad. Sei. U.S. 23, 202-205 (1937). 118-3033.

"Shearing phenomena at high pressures, particularly in inorganic Compounds," Proc. Am. Acad. Arts Sei. 71, 387-460 (1937).

119-3107.

"Polymorphie transitions of 35 substances to 50,000 kg/cm^" Proc. Am. Acad. Arts Sei. 72, 45-136 (1937).

120-3200.

"The phase diagram of water to 45,000 kg/cm^," J. Chem. Phys. 5, 964-966 (1937).

121-3203.

"The resistance of nineteen metals to 30,000 kg/cm^," Proc. Am. Acad. Arts Sei. 72, 157-205 (1938).

Gollected Experimental Papers of P. W. Bridgman

P H Y S I C A L P R O P E R T I E S OF S I N G L E C R Y S T A L MAGNESIUM. B Y P . W . BEIDGMAN. Presented Oct. 14, 1931.

Received Oct. 16, 1931. INTEODUCTION.

THE compressibility, specific electrical resistance, and pressure and temperature coefficients of resistance of single crystal magnesium in the crystallographically independent directions have already been reported in a previous paper.^ To these are now added the five elastic constants, the thermo-electric properties, and the thermal expansion. Although the amount of this new material is not large, it has seemed better to give it in a small independent paper rather than to wait indefinitely until opportunity should present itself to publish it with related data for other materials. The specimens whose thermo-electric properties and elastic constants are measured in this paper were the same as those whose electrical resistance was determined in the previous paper. The thermal expansion was measured on the two compressibility samples of the previous paper. D E T A I L E D DATA.

Thermo-Electric Properties. Measurements were made simultaneously on six crystal rods of dififerent orientations in the same apparatus as previously used for thermo-electric measurements on a number of non-cubic crystals.^ The ends of the rods were in contact with two difPerent streams of rapidly circulating kerosene at diflerent temperatures, and the thermo-electromotive force between the magnesium rods and copper leads was measured as a function of the variable temperature of the one stream, that of the other being maintained fixed at about 15.7° C. The upper temperatures were 37°, 56°, 75°, 96°, and a return check reading was made at 57°. Smooth curves of e.m.f. against temperature were then drawn through the observed points for each specimen, and the differences taken between the smooth curves and the straight lines joining the extreme points. The differences were then reproduced analytically by a three constant expression in the temperature of the form at' + bt'^ + ct'^, where the temperature of the cold junction is taken as 15.7°, and t' is the excess of the temperature of the hot junction above this. A three constant expression was adequate to reproduce the results within experimental error, but

9 4 — 2559

30

BEIDGMAN

a two constant expression was very distinctly not adequate. For most of the previous metals two constant expressions had been adequate. The calculation of the constants a, b, and c was faeihtated by the fact that the maximum departure from linearity of the smooth eurves for all orientations occurred at the same temperature, 35°. The constants a, b, and c were then plotted separately against cos® 9, where 6 is the angle between the principal axis of the crystal and the length of the specimen. If the Kelvin-Voigt symmetry relations hold, these three constants should each be linear in cos® 6. The experimental evidence indicates that the Kelvin-Voigt relation is only an approximate relation, and that in Bi and Sn there are deviations beyond experimental error, although in Zn, Cd, and Sb the relation does seem to be satisfied within experimental error.® It would therefore have been most desirable to test the Kelvin-Voigt relation in magnesium also, but unfortunately the experimental accuracy was not great enough for this, and all that was possible was to assume the relation and to draw through the experimental points the best straight lines.

FIGURE 1. The constant " o " of the thermo-electric formula for rods of different orientations plotted as a function of the Square of the cosine of the angle between the length of the rod and the crystal axis.

94 — 2560

PHYSICAL PROPERTIES

OF S I N G L E C R Y S T A L M A G N E S I U M

31

.6 c o s ^

9

Figure 2. The constant "b" of the thermo-electric formula for rods of different orientations plotted as a function of the Square of the cosine of the angle between the length of the rod and the crystal axis.

o

ü

o .6 C O S ®

.0

1.0

e

Fiqube 3. The constant "c" of the thermo-electric formula for rods of different orientations plotted as a function of the Square of the cosine of the angle between the length of the rod and the crystal axis. In figures 1,2, and 3 the three constants a, b, and c are shown plotted against cos^ 0, together with the straight lines taken to best represent the results. The intercepts of the lines at cos^ 9 = 0 and 1 give the

94 — 2561

32

BRIDGMAN

values of o, b, and c for the parallel and perpendicular orientations. Finally, the origin of temperature may be changed to 0° C, giving the following fonnulas for the thermo-electromotive force in volts: (t.e.m.f.)x-cu = 1.65 X lO"»« + 12.5 X 1 0 - ^ - 3.8 X 10->¥, (t.e.m.f.)||_cu = 1.85 X lO"»« + 24.3 X lO-»«^ - 7.7 X lO-"««, where t is ordinary Centigrade temperature. From these expressions the Peltler and Thomson heats between the parallel and the perpendicular directions may be found by differentiating once and twice. P|l_i = •r[0.20 X 10-® + 23.6 X 10-»< - 11.7 X 10-"at22°.5 C. Perpendicular to the axis, 4.60 X lO"«; EflFect of pressure on resistance: Axis 73° to length: At 30°, At 75°, -

= 5-61 X 10-»p - 8.4 X 1 0 - ^ AR = 5.67 X 10-«p - 8.35 X l O - V R(0, 75°)

Axis 29° to length. At 30°, -

= 5.48 X 10-«p - 7.8 X IQr'Y-

At75°, -

= 5.99 X l O - ' p - 1 1 . 8 X I O - V -

94 — 2567

38

BRIDGMAN

Temperature coefRcient of resistance. Axis 73° to length, mean coefficient 0°-100° = 0.00439. Axis 29° to length, mean coefficient 0°-100° = 0.00420. A paragraph is also quoted from the discussion in the previous paper: "Magnesium is of interest because it is the first hexagonal metal measured in which the axial ratio corresponds to a packing of spheres in dose packed hexagonal array. The piling in Zn and Cd, for example, is that of dose packed ellipsoids. I t is, of course, well known that the dose packed hexagonal arrangement of spheres differs little from the dose packed face centered cubic arrangement. In fact, if the two arrangements are built up by piling over eaeh other layers perpendicular to the hexagonal axis, the only difference between the two arrangements is a slight relative displacement of the third layers, the first and second layers in the two arrangements being the same. Hence the forces on the atoms in the two arrangements can differ only by the contributions of the more distant atoms, which are unimportant because of the rapid falling off of atomic forces with increasing distance. I t follows that a dose packed hexagonal arrangement of spheres would not be expected to differ greatly in physical properties from a dose packed cubical arrangement, and in particular, the compressibility of the hexagonal arrangement would be expected to be nearly the same parallel and perpendicular to the axis, because the compressibility of a cubic crystal is the same in all directions." The expectation that magnesium would be like a cubic crystal in many respects is fulfilled in the first place by the linear compressibilities, which are the same in different directions within experimental error. Most of the elastic constants show the same sort of thing. Consider the "square" constants »h, »33, «12, and «13, called "square" because no shearing strains or stresses are involved, but these constants connect the elongations parallel and perpendicular to the axis with the normal stresses across the corresponding planes. For a cubic crystal these four square constants reduce to two, «n, »n, «u, and «12 respectively. We notice at once that the four constants for hexagonal magnesium reduce in exactly the same way to two, that is, «n = «33, and Sii = «12. and »33 measure the effective Young's modulus for rods cut perpendicular and parallel to the crystal axis, so that we see that the extensibility under a one sided extending stress is the same for directions parallel and perpendicular to the axis, just like the linear

94 — 2568

PHYSICAL PROPERTIES OF SINGLE CKYSTAL MAGNESIUM

39

compressibility. In the same way «u and Ä13 measure the effective Poisson's ratio for rods parallel and perpendicular to the axis, and these again are equal. As far as this type of deformation is concemed, therefore, magnesium behaves much like a cubic substance. The shearing constant, however, does not follow the type of the cubic crystal. In a cubic crystal the three principal shearing constants «44, »66 and SK are all equal. In a hexagonal crystal like magnesium, on the other hand, «44 and «55 are equal to each other, but See is different and identically equal to 2(«ii — Sn). Hence if the shearing constants of magnesium were like those of a cubic crystal we would have for it Su = 2(^11 — S12). As a matter of fact, the numerical values are 87.8 and 51.2 X respectively, so that the cubic relation fails by an amount far beyond possible experimental error. The failure of the cubic relation for the shearing constants reacts on the effective Young's modulus of rods inclined to the axis, and it will be found that the Young's modulus of rods neither parallel nor perpendicular to the axis is not quite the same as for these two directions, so that with regard to the complete reaction to tension, magnesium does not behave like a cubic crystal, although it does with respect to hydrostatic pressure. In view of the complete elastic symmetry with respect to hydrostatic pressure, it was a surprise to find the distinct failure of isotropy with respect to thermal expansion, which in the direction perpendicular to the axis is only 0.90 of the value parallel to the axis. This difference is consistent with the behavior of other metallic crystals, the thermal expansion usually being greatest across the basal plane, that is, the plane of easiest slip. For example, in Zn and Cd the ratio of the expansions perpendicular to parallel are 0.22 and 0.39 respectively. In the case of Zn and Cd, however, the ratio of the expansions is nearer to unity than the ratio of the compressibilities, whereas in Mg, the reverse is the case. The behavior of the thermal expansion is somewhat in line with other temperature parameters, for it has already been found that the temperature coefficient of compressibility is markedly different in different directions, as is also the temperature coefßcient of resistance. It is evident, therefore, that different effects are influenced in different degrees by the similarity of the structure of magnesium to the cubic structure. With regard to thermo-electric properties, magnesium is like all the other non-cubic metals studied exeept tin, in that the Peltier heat at 0° between the parallel and perpendicular directions of flow is positive.

94 — 2569

40

BRIDGMAN

but the effect is unusually small in magnesium, being only 0.55 X 10"^ against 4.90 X 10"^ for zinc, for example. In a cubic crystal the Peltier heat between any two directions is of course zero, so that with regard to Peltier heat magnesium again approaches a cubic crystal. The Thomson heat, however, is different, because a||_j. for magnesium has the value 6.43 X 10~®, and this is somewhat larger than for any of the other non-cubic metals except bismuth, where large effects are always to be expected. The sign of sy—i is the same for magnesium as for all the other non-cubic metals except bismuth. This confirms a conclusion previously reached on other grounds that there is not much similarity between the Peltier and Thomson heat mechanisms. The manuscript of this paper was ready for publication when a preliminary notice, without experimental details, was published by Goens and Schmid' giving the specific resistance, temperature coefBcient of resistance, and elastic constants of single crystal magnesium. The results of our two measurements are not as consistent as they ought to be. The greatest discrepancies are in the elastic constants. The values of Goens and Schmid are: sn = 22.3 X 10-",

S33 = 19.8 X 10-",

»12 = - T J X 10-",

«44 = 59.5 X lO"",

si3 = - 4.5 X 10-".

The method of Goens and Schmid was a dynamic method in distinction from the static method used here. The greatest difference in our constants is in su- The values of Goens and Schmid of the constants would demand that the curve of figure 4 have the Ordinate 22.7 at cos^ 6 = 0.5, and in figure 5 the Ordinate at cos' 9 = 1 would have to be 1.17; neither of these values seem possible for my material and my method. The specific resistance of Goens and Schmid, parallel to the axis, reduced to 22.5°, is 3.84 X 10"« against my 3.89 X 10-«, and perpendicular to the axis they had 4.63 against my 4.60. The value to be calculated for polycrystalline material from these figures is almost identically the same for both of us. Their mean temperature coefficients of resistance parallel and perpendicular are 0.00427 and 0.00416 against my 0.00413 and 0.00441 respectively, a reversal of Order to which they have already called attention, and which is not easy to account for. Their thermal expansions parallel and perpendicular, making a linear correction for the difference of temperature ränge, are 25.5 X

94 — 2570

PHYSICAL PEOPERTIES OF SINGLE CRYSTAL MAGNESIUM

41

10"® and 24.9 X 10"« respectively, against my 27.1 and 24.3. The caiculated values for voIume expansiona are 75.3 and 75.7 respectively. The discrepancies are not easy to account for. The first thing to suspect is difference of purity. They do not give in their preliminary communication the method of casting the crystal or the sort of mold used, but S t a t e that the purity of the initial material was 99.95%. The values given above for the specific resistance would indicate no difference in the purity of our respective material, while the temperature coefficients would indicate a slight superiority of mine. The discrepancy in the elastic constants may be due to the difference of methods. I t is to be noticed that their value for the shearing constant »44 is much more like that of a cubic metal than mine; it is important for theoretical reasons that the discrepancy be explained. 1 am indebted to my assistant Mr. L. H. Abbot for the measurements of thermal expansion. I am also indebted for financial assistance to the Milton Fund of Harvard University and the Rumford Fund of the American Academy of Arts and Sciences. The Jefferson Physical Laboratory, Harvard University, Cambridge, Mass. RBFEBENCES.

> P. W. Bridgman, Proc. Amer. Acad. 66, 255-271, 1931. 2 P. W. Bridgman, Proc. Amer. Acad. 63, 351-399, 1929. > P. W. Bridgman, Proc. Amer. Acad. 53, 305, 1918. * P. W. Bridgman, Proc. Amer. Acad. 64, 19-38, 1929. » E. Goens and E. Schmid, Die Naturwiss, 18, 376-377, 1931.

94 — 2571

A NEW KIND OF e.m.f. AND OTHER EFFECTS THERMODYNAMICALLY CONNECTED WITH THE FOUR TRANSVERSE EFFECTS BY P. W .

BRIDGMAN

R E S E A R C H L A B O R A T O R Y OF P H Y S I C S , H A R V A R D U N I V E R S I T Y

(Received January 11, 1932) ABSTRACT

The Hall e.m.f. attending a current in a magnetic field is subjected to a thermodynamic analysis like that for an ordinary battery, from which it appears that if the Hall e.m.f. has a temperature coefficient, there must be a reversible heating effect when a transversa current flows across a conductor carrying a longitudinal current in a magnetic field. Hut other arguments show that this heating effect vanishes, and furthermore, it could not be found experimentally. The consequent vanishing of the temperature coefficient of the Hall e.m.f. involves the existence of a new sort of e.m.f., that is, an e.m.f. in a conductor carrying a current in which the temperature is uniformly changing. Corresponding analysis may be made for the other transversa effects. A thermo-motiveforce connected with the Righi-Leduc coefficient existsin a conductor carrying a thermal conduction current when its temperature changes uniformly. Other relationsare deducedconnectingthe Nernst coefficient and the Ettingshausen coefficient with the new e.m.f. and thermo-motive force. It appears that the temperature dependence of all these quantities is simply connected, and in particular, that the temperature coefficient of the Hall coefficient vanishes at 0°K. The new relations show that certain relations suggested in a previous paper from general considerations of a nonthermo-dynamic character cannot be rigorously exact. A new account is given of the origin of the major part of the Ettingshausen temperature gradient, which is approximately checked by experiment. Finally, the order of magnitude of various smali effects isdiscussed. It isa thermodynamic consequenceof the existence of a temperaturee.m.f. that there is a temperature change when the current in a conductor changes in magnitude, but it is far below experimental reach. It must be recognized that the specific heat of a conductor is altered by the presence of an electric current. The specific heat is also altered by the presence of an ordinary thermal conduction current. Numerical considerations suggest that the proper velocity to be associated with the thermal current, whether ordinary conduction current, or thermal current convected by an electrical current, is the velocity of sound.

T;

^HERE has been so much speculation about the detailed functioning of the mechanisms which may be responsible for the four transverse effects, namely the Hall, Ettingshausen, Nernst, and Righi-Leduc effects, and the whole subject is still in such an unsettled State, that it is well to obtain by arguments of a thermodynamic or other general character all the Information which we can which must be independent of any special mechanism. It is not inconceivable that a better understanding of the thermodynamic connections between these effects may lead to a better understanding of the effects themselves. It is surprising how little this method of attack has been used in the past and there are still simple relations of a thermodynamic character which apparently have not been noticed. Practically the only previous applications 95 — 2572

TRANSVERSE

EFFECTS

703

of thermodynamics to this subject have been made by Lorentz and myself/ but there are still other relations not hitherto touched. Relations of a purely thermodynamic character may be obtained by constructing electromagnetic or thermodynamic engines utilizing the various effects to furnish energy. Consider first the Hall effect. An electric current flows in a toroid of mean radius a, breadth b, and depth d, breadth and depth being small compared with a. There is a uniform magnetic field of strength H perpendicular to the plane of the toroid. The magnetic field may be supposed produced by a permanent magnet with zero temperature coefficient. The circuit is supposed resistanceless, and in the following, irreversible effects arising from the Joulean heating are neglected. This is allowable, because by increasing the linear dimensions of the circuit indefinitely, keeping the total current I constant, the electromagnetic energy of the circuit, ^LP, may be made indefinitely large compared with the Joulean dissipation of energy in unit time, RP, since L increases in direct proportion to the linear dimensions, and R decreases in the same ratio. The inner and outer circumferences of the toroid are at a difference of Potential in virtue of the Hall effect. If we short circuit across from the inner to the outer circumference, a uniform radial current will flow; this current may be used to drive an external electromagnetic engine, and so energy may be taken out of the system. The external electromagnetic engine may be assumed perfectly efificient, so that the energy Output is the product of the Hall Potential difference and the amount of electricity flowing transversely. The source of the energy Output is primarily the energy of seif induction, §LP, associated with the primary current, and the mechanism by which this energy is tapped is the Hall e.m.f. associated with the transverse flow acting circumferentially in the toroid and opposing the primary current. This arrangement is for thermodynamic purposes indistinguishable from a battery, and the ordinary analysis for a battery applies. In particular, if the Hall e.m.f. depends on temperature, then, in analogy with the known behavior of ordinary cells, we may expect reversible heating effects when the transverse current flows. The analysis is so simple that it will pay to reproduce it from the beginning. Call I the total current, and i the current density, where I = bdi. Then the definition of the Hall coefficient at once gives: Transverse e . m . f . =

bHiR,

where R is the Hall coefificient, using the conventional notation. If a transverse quantity of electricity dqe flows, the work done is the product of quantity and e.m.f., or dW = bHiRdq,. The only variables in this system capable of external manipulation are temperature and transverse flow, which are therefore to be taken as the independent variables. The conservation of energy now gives at once: ' H. A. Lorentz, Report of the Fourth Solvay Congress, ConductibiIit6 ßlectrique des Metaux, 1924, pp. 354-360; P. W. Bridgman, Phys. Rev. 24, 644-651 (1924).

95 — 2573

704

P. W. BRIDGMAN dQ =

/dE\

j

/dE\ dr + {^—J dq. + bHiRdq dq,

where E is internal energy and Q heat absorbed. Now form dS=dQ/T, and write down the condition t h a t dS be a perfect differential, by equating the cross derivatives of the coefficients of dr and dq,. This gives a t once, neglecting the thermal expansion of the material of the toroid,

This indicates that when a transverse current flows in a conductor arranged to show the Hall effect there is a reversible generation of heat required to maintain the system isothermal. In Eq. (1), Q and q, are the total amounts of heat and flow of electricity respectively. If Q' is the development of heat per unit volume, we have approximately Q = 27raWÖ'. and if dq,' is the density of transverse flow, we have dq, = 2Trdadq,'. This gives:

an equation exhibiting the thermal effect in terms of intrinsic properties of the materials, independent of the dimensions of the circuit. We now have to consider the term d/dT{iR) q, on the right hand side of the equations. Expanded, thisisi{dR/dT)q,+R{di/dT)Numerically the proportional change of R for one degree for bismuth, for example, is 0.004. The term (di/dr) one would probably say on first impulse to be zero, since this denotes the change of current produced by a change of temperature acting so quickly t h a t the Joulean effects may be neglected, and with no transverse flow, t h a t is, with no extraction of work from the system. If the term were not zero, this would demand t h a t there be an e.m.f. in a circuit in wliich the temperature is changing, and this is an effect not usually considered. I believe, however, that this e.m.f. must exist. M y reason is t h a t there are a t least two arguments which demand t h a t the absorption of heat accompanying transverse flow be zero, and the only way in which this is reconcilable with the thermodynamic expressions above is that d, . 1 di l dR -(iR) = 0 , o r — — 0. dr i ÖT R dr T h e first argument is derived from the vector character of the current. T h e transverse and longitudinal currents combine according to the ordinary rules for vectors into a single current, and such a current flowing in a magnetic field is without heating effect, according to original assumption, as far as known experimentally, and also in accordance with the demands of symmetry. The relations here are somewhat simplified by imagining the conductor in the form of a cross, the longitudinal and transverse currents combining 95 — 2574

TRANS VERSE EFFECTS

705

at the center of the cross as indicated to a sufficient degree of approximation in Fig. 1. The only way of saving the Situation seems to be to assume that the heating effect is localized in the periphery of the central Square, where the direction of current flow changes, as indicated by the dotted lines, But this is inconsistent with the dimensions of the effect as shown by Eq. (2) which exhibits the effect as a heating per unit volume, whereas if the eflect were concerned with the change of direction, it would be an effect per unit area. The second argument is derived from the symmetry of the longitudinal and transverse currents. It is evident in the first place that the heating effect

Fig. 1.

of Eq. (2) can be exhibited as a heating effect per unit time per unit transverse current. But if the arrangement is geometrically symmetrical in longitudinal and transverse current, as may be accomplished by making the conductor in the form of a cross as in Fig. 1, then the same result should be obtained independently of which current is called transverse and which longitudinal. An inspection of the figure shows that the symmetry relations make this impossible, for calling the transverse current longitudinal and conversely demands that the effect reverses sign. The only quantity equal to its own negative is zero, showing again that the heating effect must vanish. There is apparently, therefore, an e.m.f. in a conductor in which the temperature is changing such that 1

di

i ÖT

1 dR R

dr

The partial derivative in i may be taken to have the general significance that no work is to be extracted from the system during the change of temperature; 95 — 2575

706

P. W. BRIDGMAN

the partial derivative in R may for practical purposes be taken to be the ordinarily determined temperature derivative. The experimentally determined values of (1/J?) J2/dr) are so large, 0.004 for bismuth, that the related e.m.f. cannot be treated as a negligibly small quantity. An approximate expression for this e.m.f. may be readily found. To get it, we neglect any interaction between the thermal and the electrodynamic energy of thesystem, setting the total internal energyequal tothesum of the ordinary internal thermal energy in the absence of the current plus the electrodynamic energy, j L P . This amounts to assuming that the specific heat of a conductor carrying a current is the same as that of the same conductor without the current. Later in this paper an estimate will be made of the order of magnitude of this small effect. Utilizing this approximation, the e.m.f. arising from a change of temperature changes only the electrodynamic energy of the system, and we have: ~[hLP]

= / X e.m.f.,

dt

whence at once: dl

dl

dt

dr dt

e.m.f. = L — — L But (l/Didl/dr)

= (l/i)(di/dT),

dr

so that a / / c 7 = - / ( l / J ? ) ( 5 i ? / 5 r ) , and /

1

dR\dT

\

R

d r ) dt

e.m.f. = - ( z /

)—•

(3)

That is, the temperature e.m.f. in a circuit in which the temperature is changing a t u n i t r a t e is

-LI{\/R){dR/dT).

One can see in a general way why there should be an effect of this kind. In the first place, it arises from the magnetic field of the current on itself, the external magnetic field having dropped out of the picture. That the external field ought to have no net effect is suggested by the theorem of elementary electrodynamic theory that there is no mutual energy between an electrical current and a system of permanent magnets. Some of the electrons which constitute the current will move perpendicular to the magnetic field of the current itself, and will thus experience an action in virtue of the Hall effect which will have a component along the original current. The intensity of this action involves the seif magnetic field, which explains how L gets into the picture. Furthermore, the number and distribution of the transversely moving electrons is a function of the temperature, so that there will be an interaction, manifesting itself as an e.m.f., when temperature changes. To give a detailed account of this effect from the Statistical point of view would probably be prohibitively complicated, and would involve Integration over the entire conductor of many terms, a number of which would drop out from the final result. An experimental attempt was made to detect the existence of the transserve heating effect, when I first noticed the analogy with an ordinary bat95 — 2576

TRANSVERSE

EFFECTS

707

tery, and had not yet realized that the relations between other quantities were such as to make this zero. Two crosses of bismuth like Fig. 1 were cast, the arms being about 1.2 by 0.6 cm in section. In casting, they were chilled rapidly from the molten condition so as to make the crystal structure as fine grained as possible. These crosses were mounted face to face, separated by a layer of cellophane for insulation, and the two junctions of a copper-constantan thermocouple were attached to the two centers of the crosses, indicated by 0 in the figure. The couple indicated, therefore, the differential effect at the centers of the two crosses. The electrical connections were such that the currents in the various branches could be varied independently, both as to magnitude and direction. The magnetic field was about 5000 gauss, and the maximum current density about 10 amperes per square cm. The difficulty with the experiment is in eliminating the effect of the finite size of the crystal grains. Because of the unequal resistance of the grains in different directions, the current experiences many internal changes of direction. Each of these is accompanied by a local heating effect, in virtue of the internal Peltier heat. This is changed by the application of a magnetic field, because of the effect of the field on the resistance. Effects of this kind exist with only a longitudinal current. However, by using all possible combinations of currents, and noting that some of the effects change sign when current direction changes and some do not, it was possible to show that if any heating effect of the kind corresponding to Eq. (2) exists it must be less than 10 percent of that part of the non-isotropic effects which is due to the action of the magnetic field. Numerically, this meant that any final shift of equilibrium of temperature due to the effect sought was less than 0.006°. This was much less than a preliminary calculation had indicated was to be expected on the assumption that di/dr = 0. This is probably as good a proof of the non-existence of the effect as can be given without very much more elaborate precautions. It was a great surprise to find that the magnetic influence on the internal non-isotropic effects was so large. It raises the question whether such effects have been sufficiently considered in previous measurements; measurements of the Ettingshausen temperature difference would be particularly susceptible to error from this source. Returning now to the relation (d/dT)(iR) = 0, we can derive a suggestion as to the behavior of R at 0° K. It seems highly probable that the e.m.f. arising from change of temperature vanishes at 0°K. We would expect this from general considerations suggested by experience with the third law, and the mechanistic explanation of this e.m.f. just given would suggest the same thing. For the transverse components of motion of the electrons which constitute the current would be expected to lose all their haphazard quality at low temperatures, and therefore their capacity for taking part in thermal effects. If di/dr vanishes at 0°K, this demands: lim

1

T=o R

dR

= 0.

dr

This relation appears to be consistent with the experimental results found 95 — 2577

708

P. W. BRIDGMAN

at Leiden,® although the experimental accuracy is not always great enough to give perfectly definite indications. The other transverse effects may now be subjected to an analysis similar to that above for the Hall effect. In doing this it will be convenient to introduce new coefficients in place of the conventional Nernst and Righi-Leduc coefficients, since the conventional definitions of these involve a lack of symmetry as compared with the Hall and Ettingshausen coefficients. The conventional Nernst coefficient, QK is to be replaced by Qw' where Qif' = Qs/k, k being the thermal conductivity, and the conventional Righi-Leduc coefficient SR is to be replaced by SR', where SR' = SR/k. These coefficients are written with subscripts N and R to avoid confusion with the thermodynamic symbols Q for quantity of heat and 5 for entropy. These altered definitions now give the following consistent scheme for the four transverse effects: (1) Hall transverse potential gradient with longitudinal electric current, i,=RHi.

(2) Ettingshausen transverse temperature gradient with longitudinal electric current, i, =PHi. (3) Nernst transverse potential gradient with longitudinal heat current, w, = Qff'Hw.

(4) Righi-Leduc transverse temperature gradient with longitudinal heat current, w, =SR'HW. i and w are here density of electrical and thermal current. Imagine now the toroid of the preceding analysis with a circumferential heat current replacing the electrical current. The ring will have to be split along some radius and the two sides of the slit maintained at a difference of temperature. This temperature difference is to be maintained irrespective of how the mean temperature of the whole system may change. The irreversible effects connected with thermal conduction in such a system may be neglected by making all changes in the system rapidly, so that the dissipation due to the thermal conduction is vanishingly small compared with other effects. The exact parallel of the preceeding analysis for the Hall effect may now be made. Allow a quantity of heat dq^, to flow transversely, and utilize this to drive a thermodynamic engine working between the temperature limits of the Righi-Leduc temperature difference. This difference is SR'ÖHW, and the work received from the engine is: dW =

T

—SR'bHwdq,,.

The source of this work is the work done by the longitudinal heat current in flowing through the longitudinal Righi-Leduc temperature difference accompanying the flow of the transverse heat current. A result exactly similar to that before follows at once on writing down the condition that the entropy change be a perfect differential, namely: ' Bengt Beckman, Leiden Communications, Suoolement, No. 40, 1915.

95 — 2578

TRANS VERSE EFFECTS

709

ÖtXT/

VÖOB,/,

or this may be written as heat per unit voIume in terms of densities:

Exactly the same arguments as applied before, namely one from combining longitudinal and transverse heat currents vectorially, and one from the effect of interchanging longitudinal and transverse currents, may be applied to this case, showing that this heating effect must vanish, giving the relation 3/öt(w5ä'/t) = 0 , or: 1 SR'

1 dw

d /SR'\ dr

\

T

/

w dr

It is to be presumed that SB'/T varies with temperature, and that therefore the term (1/w)(3w/öt) exists. This is the formal analogue of the expression (l/i)(di/dT), and denotes a change in a thermal current when the mean temperature is changed, no external work being taken from the heat current and the change being made so rapidly that the dissipation of the thermal stream against thermal resistance is negligible. Such phenomena connected with thermal currents certainly have not been detected, and the mechanism must be quite different from that in the electrical case. An electrical current is capable of coasting for a certain time after the e.m.f. has ceased, driven by the stored energy of seif induction. The strict analogue of seif induction does not exist for a thermal current. If, however, the thermal current is at all like ordinary currents in having a property analogous to velocity, it must also have a space density, so that the energy content and therefore the specific heat of a body carrying a thermal current is different from that of an equivalent assembly of infinitesimal elements with no thermal current. This Space density of energy may perform the same function as the energy of seif induction of an electrical current, and give meaning to the derivative dw/dr. An estimate will be made later of the order of magnitude of such effects. They are too small to be detected by direct experiment, but we may nevertheless recognize their existence and use them in theoretical discussion. The other two effects, the Ettingshausen and Nernst effects may be similarly analyzed. By allowing a transverse heat current to flow in the presence of a longitudinal electrical current, energy may be taken out of the system in virtue of the Ettingshausen transverse temperature difference, and by allowing electricity to flow transversely in the presence of a longitudinal heat current energy may be taken out in virtue of the Nernst transverse potential difference. The same analysis as before demands accompanying heat effects, which, written for unit volume, are respectively: 95 — 2579

710

P. W. BRIDGMAN

mr-m

We expect as before that these two effects are zero in virtue of other relations. The argument has to be somewhat modified, however. The first argument disappears entirely, because a heat current and an electric current do not combine vectorially. The second argument may, however, be appropriately modified. It is to be noticed in the first place that there is a reciprocal relation between the sources of the energy of the phenomena involved in Eqs. (6) and (7). The energy extracted by the transverse thermal flow of Eq. (6) is provided by the longitudinal electric current flowing against the Nernst e.m.f. acting longitudinally associated with the transverse heat current. Similarly, the energy extracted by the transverse electric flow of Eq. (7) has its source in the longitudinal heat current flowing against the Ettingshausen temperature difference acting longitudinally associated with the transverse electric flow. Eq. (6) now demands that dQ' be positive when the transverse heat current extracts energy from the longitudinal electric current, and (7) demands a positive dQ' when the transverse electric current extracts energy from the longitudinal heat current. But the Situation of Eq. (6) may also be described as a longitudinal heat current in the presence of a transverse electric current, and the energy relations demand that the transverse electric current give energy to the longitudinal heat current. We thus again have the dilemma of a quantity equal to its own negative, and the only way out is the quantity itself to vanish. Hence (8)

ör \ T /

and

^ W ) ÖT

=0.

(9)

The di/dr which occurs in (8) is the same as that which occurred in connection with the Hall coeflicient, and the dw/dr of (9) is the same as in the expression for the Righi-Leduc coefficient. Eliminating these derivatives gives:

P dArJ T

and 5Sh'/ T

Integration gives at once: 95 — 2.580

\ r /

Ö T dAr

1

dR

R

dr

Qn' Ojv'

dr

TRANSVERSE

EFFECTS

711

P

— = consti R, T

and 5B'

= consts Qh' .

T

The constants are independent of temperature, but may of course vary from substance to substance. Furthermore, Qn' = P/t, as was shown in the preceding paper to be demanded by the energy relations. We therefore have the relations: P

^R

R = Consta— — consta ÖA^' = const4 T T

/

\

(10)

T h a t is, R, P/t, Qn', and Sr'/t all depend on temperature in the same way, and therefore, in particular, all vanish in the same way at 0°K. In addition to the relation P/t = Qn' deduced in the previous paper from the first law of thermodynamics, two other relations were also deduced from much more doubtful premises, such, for example, as the assumption that the rotation of the equipotential lines is the fundamental feature of the Hall effect, and is the same whether the potential drop is an iR drop as in an ordinary conductor, or whether it somes from a Thomson effect in an unequally heated bar. These two other relations were :Qn' = ff/kpR, and P = cttSr', where a is the Thomson coefficient and p specific electrical resistance. Consistency of these relations with those above would demand that (r/kp = const, and -33) cos^ 7 + 25r23 cos ß cos 7 + 25^31 cos 7 cos a + 2Sri2 cos a cos ß. (F) Next consider the effect of a mechanical tension T applied along the rod. The stress system thereby produced within the rod must satisfy the following conditions: Xx cos a +

cos

Xy cos a +

cos i3 +

Xi cos a

and

+ X j cos 7 = T cos a cos 7 = T cos ß

(G)

Yi cos /3 + Z^ cos 7 = T cos 7

Xx cos a' + Xy cos ß' + Xi cos 7 ' = 0

Z^cosa'

+etc.

=0

X^ cos a '

+ etc.

=0

(H)

where a', ß', and y' are any direction angles satisfying the condition cos a' cos a + cos ß' cos ß + cos 7 ' cos 7 = 0.

(I)

The conditions (G) come from the requirement that the force across any plane perpendicular to the length of the rod must be T, perpendicular to this plane, and the conditions (H) from the requirement that there is no external force acting across any lateral surface of the rod. B y reflecting that the stress quadric in this case reduces to a couple of planes, the Solution may be found almost by inspection, and is: Xx =

r

cos" a,

Yy=T

COS»

ß,

Z, ^ T cos« 7,

Y, = T COS ß cos 7, Zx = r cos 7 cos a, Xy = T cos a cos ß

(J)

The 6r's now assume the values: irn = r[pii cos" a + pn cos" ß + pu cos" 7 + pu cos ß cos 7] &rM = r[pi2 cos" a + Pu cos" ß + Pn cos" 7 - pu cos j3 cos 7] Sr33 = r[pi3 cos" a + pn cos"^ + psa cos" 7] 5r23 = r[^pi4(cos" a — cos" ß) + ip44 cos /3 cos 7] Brii = T\\pii

(K)

cos a cos 7 + pu cos a cos ß\

Srn = r[pi4 cos a cos 7 + (pn — pn) cos a cos /S] . The material is now at hand for substituting in the expression (F) for R. Comparison with experiment will be simplified by introducing two new 99 — 2667

862

P. IV. BRIDGMAN

angles. Project the length of the rod on the basal plane and denote the angles between this projection and the X and Y axes by a" and ß", where cos a" = cos a/(cos ^a+cos and cos ß"=cos ß/(cos^a + cos'^ßy. Substitution gives, after some simple reductions, for the tension coefficient of resistance: Kt^

1 AR — T i?„ Pii sin^7+(p44+2pi3) cos'' 7 sin^ 7+P33 cos^7 —2pi4 cos 7 sin' 7 cos 3(3' rii sin^ 7 + f33 cos'' 7

.(L)

Notice that the constant p]2 has cancelled, and P44 and pn enter only through the combination p44 + 2pi3. Tension measurements are, therefore, not sufficient to exhaustively determine the coefficients, but at most only four relations between the six coefficients can be fixed by such measurements. Explicitly, by appropriately varying the orientation, the constants pn, Pas, and px4 may be determined, and the combination p44 + 2pi3. Furthermore, Kt is Seen to have three-fold symmetry about the Z axis, as insured by the term in cos 3/3". This, of course, is necessary, and constitutes one check on the correctness of the analysis. Another important feature is that Kt has complete rotational symmetry (that is, the term in ß" vanishes) both when the rod is parallel to the trigonal axis and when it is in the basal plane. That this must be the case when the length is along the trigonal axis is evident from most elementary symmetry considerations, but it is not so easily obvious that the coefficient should be independent of orientation in the basal plane. This latter fact was found experimentally by Miss Allen, and was looked on as one of the important results of the paper, although at the time it did not appear whether this was general, or only a fortuitous result for bismuth. The relation now appears necessary for any crystal of the same symmetry as bismuth. The two remaining relations necessary to completely determine the six constants must be determined by the imposition of other kinds of stress. The simplest is a hydrostatic pressure, and the calculations can be made at once for this case. The stress system Xx=Yy=Z z = —P, Yz = Z^ = Xy = Q. If the rod is cut parallel to the Z axis:

i?o/||

'•33

and when the rod is perpendicular to the Z axis, parallel to the basal plane: 1 AR\ \P

r J x

pii + P12 + pi3 rii

(N)

Examination shows at once that these two additional relations permit explicit Solution for the remaining coefficients, so that the six coefficients may be completely determined in terms of tension measurements on four orientations and hydrostatic pressure measurements on two orientations. 99 — 266S

ELECTRICAL

RESISTANCE

OF CRYSTALS

863

The detailed d a t a of Miss Allen permit further check of the above expression for KT. Such a check m a y be made in various ways. For example, a t constant y the Variation of KT with ß" m a y be studied. T h e formula demands t h a t the variable part of KT be proportional to cos 3/3". Miss Allen's Fig. 5 exhibits the coefficients in this way, and inspection will show t h a t within the limits of experimental error each of the curves of Fig. 5 has the shape of a cosine curve. (Her and d are the ß" and y of this paper respectively.) It may be taken, therefore, t h a t the geometrical theory checks sufficiently well against experiment. T h e numerical coefficients may now be computed. The tension coefficients are given in Miss Allen's paper. T h e pressure coefficients I have found^ to be 1.05X10-6 for 7 = 90°, and 2.03X10-« for 7 = 0°. T h e specific resistance I have also found to be ni = lU.OXlO"« and ^33 = 144.2X10-'. All these values are a t 30°C. T h e numerical coefficients are now found: Pii = - 7.7 X 10-9, P33 = _ 6 . 6 X 10-ä, pi2 = + 5 . 6 X 10-» P13 = + 1.8 X 10-^ pi4 = + 31.3 X 10-9, P44 = - 12.3 X 10"«. T h e stress unit is 1 kg/cm^. In this computation the corrections for change of dimensions and of angle with stress are neglected. These corrections are just about on the margin of experimental error. Finally, it is interesting to go back and examine the geometrical significance of the various coefficients by determining what sort of simple measurement would give the isolated coefficient. P33 and pn have already been dealt with, and are directly determined in terms of the tension coefficient of rods parallel and perpendicular to the trigonal axis. T h e coefficients pn and pu determine transverse components of e.m.f. when current flows lengthwise in a rod subjected to tension acting lengthwise. For example, if a rod is cut parallel to the Y (or X) axis, and a current passed lengthwise of the rod, then when a tension is applied along the rod, a transverse component of e.m.f. will appear along the X (or Y) axis which determines pn- T h e other cross coefficient pi3 has similar significance with a proper change of letters. The term Pi4 points to a formal analogy in crystals to the Hall effect in isotropic metals, the magnetic field being replaced by a compressional force. If a rod of rectangular section is cut with its length along the Z axis and with the X and F axes along the sides of the rectangular section, and if a current is passed lengthwise of the rod, then a transverse e.m.f. along the Y axis will appear if a compression along the X axis is applied between the opposite faces of the section. Finally, if a bar of rectangular section is cut along the X axis and a shearing stress Yz is applied to the sides of the bar distorting the cross section, and if a transverse current is led between opposite faces along the Z axis, an e.m.f. between the other two faces is produced by the shearing stress, the magnitude of the effect being determined solely by p u . > P. W. Bridgman, Proc. Amer. Acad. 63,351 (1929).

[The analysis is too special. See J. W. Cookson, Phys. Bev. 47, 194 (1935).]

99 _

2669

THE PRESSURE-VOLUME-TEMPERATURE RELATIONS OF F I F T E E N LIQUIDS. B Y P . W . BRIDGMAN.

Presented Dec. 14, 1932.

Kecelved Dec. 24.1932. CONTENTS.

Introduction DetaüedData Triethanolamine n-propyl chloride n-propyl bromide n-propyl iodide n-butyl Chloride n-butyl bromide n-butyl iodide n-amyl chloride n-amyl bromide n-amyl iodide Octanol-3 2-methyl heptanol-3 2-methyl heptanol-5 3-methyl heptanol-1 3-methyl heptanol-4 Discussion

1 3 3 6 6 7 8 9 9 10 12 13 15 16 17 18 19 20 INTRODUCTION.

This paper contains determinations of the volume of a number of liquids between 0° and 95° C and up to 12000 kg/cm^ by the sylphon method which has been applied and discussed in detail in two preceding papers.^ The new liquids investigated here fall into three groups. The first group consists of only a single liquid, triethanolamine. The reason for investigating this was that it was hoped that its structural similarity to glycerine would throw some light on the cause of incompressibility in liquids, glycerine bemg the most incompressible organic liquid yet measured. The second group consists of nine alkyl halides, namely the propyl, butyl, and amyl chlorides, bromides, and iodides. Halogen Compounds were chosen for investigation because previously interesting results had been found for mono-clorbenzene and mono-brombenzene as compared with simple benzene, and it seemed that the most promising method of investigating the effect of the halogen was to systematically examine a whole

100 —2C71

2

BRIDGMAN

series of Compounds. Finally, the third group, five of the isomers of octanol, was investigated in order to find more in detail the eflect of systematic structural changes.

The technique of the manipulations and the computations is almost exactly the same as before, particularly in the second of the two papers. The only significant differences are: (1) that readings of volume at atmospheric pressure were made at both 0° and 50°; this is preferable to obtaining the volume at 50° and atmospheric pressure by an extrapolation from readings between 200 and 1000 kg as was done in the previous paper: (2) in the case of the alkyl halides it was possible to make readings at 0° in most cases to 12000 without freezing, thus permitting more complete data than was possible for many of the previous liquids which freeze at lower pressures. The liquids of the first two groups were obtained from the Eastman Kodak Co. Several of these were further purified, as will be described in the detaiied presentation of data. Preliminary examination had shown that there is no important chemical action between these liquids and the solder and brass of which the sylphon is constructed. For the octanols I am much indebted to Professor E. Emmet Reid of the Johns Hopkins University, who has prepared the complete set of the 22 isomers of octanol, and who placed at my disposal the entire set. Many of the physical properties of these isomers have already been determined. From a study of them, and in particular the densities at atmospheric pressure, I selected the five which seemed most likely to have significant differences in compressibility, and the results for these are presented here. The freezing pressure of the isomers of octanol is much less than that of the other liquids of this paper, so that a fairly definite indication of where it is located was essential to avoid damage to the sylphon. A preliminary series of measurements was therefore made on the five isomers. The approximate freezing pressure at room temperature was determined by the method of piston displacement which I have previously applied in measuring freezings and Polymorphie transitions under pressure.^ The isomer was separated from the pressure transmitting liquid by mercury. The apparatus, which was specially constructed for these measurements, differed from that used before only in its small size, which was necessary because of the limited amount of the isomers available. Definite indications of freezing were obtained, but the freezing was never sharp, so that it did not seem worth while to try to get precise freezing curves or the change of volume on freezing. The melting temperatures at atmos-

100 — 2672

PRESSURE-VOLUME-TEMPERATURE RELATIONS OF LIQUIDS

3

pheric pressure had been determined by Professor Reid. This, together with the freezing pressure a t room temperature gave sufBciently good indications of the pressure ränge to be avoided with the sylphon. In Tables X I to XV the region in which the material is solid is indicated by the blank places; these should not be used, however, to get more than very rough coordinates for the melting curves. In addition to rough measurements of melting, other measurements were also made on the isomers of octanol at room temperature. Some question as to whether the Compounds may have experienced changes between the time of formation and the time of the compressibility measurements arose because of discrepancies between the densities provided me by Professor Reid and those which were demanded by the dimensions of the sylphons. This led to an independent determination of the densities of the five isomers by measurement in a specific gravity bottle containing about 4 gm., the weighings being made to a fraction of a milligram. These specially determined densities are given in the following, and were used as fundamental in reducing measured changes of total volume to fractional changes of volume. As an additional check, Professor Conant was so kind as to have measured in his laboratory the index of refraction for the sodium D line at 25°, from which the molecular refraction can be calculated by combining with my densities. These values are given in the following, as well as the indices and the molecular refractions supplied me by Professor Reid, which I understand are not yet published. The theoretical value for the molecular refraction for all five isomers, disregarding structural differences, is 40.79. DETAILED DATA.

Triethanolamine. This was most kindly purified under the direction of Professor J. B. Conant of the Chemistry Department by distillation in vacuum over BaO, in order to remove as much of the water as possible, which nevertheless in the opinion of Professor Conant was not completely accomplished. The produet of the distillation was a liquid, clear, but of a distinct yellow color. This became browner and cloudy by the end of the filling process. The liquid is extremely viscous and two days were taken in filling the sylphon; the final touches to the filling operation were given at 95° and at 3 mm. pressure. Düring the filling the liquid was kept under a bell jar or other closed Container with CaCla present in order to prevent the absorption of water from the air.

100 — 2673

4

BHIDGMAN

Because of the extreme viscosity and unknown liability to freezing the measurements were made in an unusual order: first at 50° to 1000 kg., without return, then immediately to 95° at 1000, and at 95° to 10000 and return with good check, then to 0°, first at atmospheric pressure, and then to 1000, where there was evidence of freezing, which persisted on releasing pressure to atmospheric. The probability is that this, like glycerine, will support great subcooling under ordinary conditions. The normal melting point is giveri in the Eastman Catalogue as 17° to 19°. Temperature was then raised to 50° with good check in spite of the apparent freezing at 0°, and T A B L E I. Triethanolamine.

Related Volumes

Pressure kg/cm^ 0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000

0°

50°

1.0000 .9835 .9699

1.0251 1.0075 .9921 .9786 .9666 .9464 .9302 .9163

95°

1.0130 .9978 .9851 .9637 .9463 .9308 .9176 .9057 .8944 .8848 .8758

finally at 50° pressure was raised to 5500 and back with good check and no further evidence of freezing. Discarding one point at 50°, the average departure from smooth curves of a single one of the 37 readings was 0.13% of the maximum effect. The relative volumes are given in Table I. The volume decrements are for 1.157 gm. The measured density at atmospheric pressure at 26.2° was 1.142, and the volume expansion of 1 gm. at atmospheric pressure between 0° and 50° was taken to be 0.0216 cm' from direct measurement in the sylphon. This substance is not listed in I. C. T., so no comparison with previous values is attempted.

100 — 2674

PHESSURE-VOLUME-TEMPERATURE RELATIONS OF L I Q U I D S

5

n-propyl chloride. Runs were made without incident at 0° and 50° to 12000 kg/cm^, but at 95° pressure was allowed to get too low, permanently deforming the sylphon and probably developing a small leak, which, however, was not diseovered until the completion of the run. A repetition was therefore attempted with a second sylphon, but this proved defective and leaked. A third sylphon was therefore used for the run at 95°; this gave a perfeet check on releasing pressure, and also on returning at 95° after excursions to 0° and 50°. ConnecTABLE II. N-PROPTIi CHLORIDE.

Pressure kg/cm^ 0 600 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Relative Volumes 0°

50°

95°

1.0000 .9555 .9261 .9024 .8833 .8541 .8319 .8138 .7987 .7852 .7732 .7625 .7526 .7440 .7366

1.0757 1.0046 .9645 .9357 .9134 .8790 .8531 .8324 .8155 .8003 .7875 .7759 .7658 .7563 .7476

1.0084 .9734 .9463 .9051 .8766 .8539 .8350 .8192 .8052 .7929 .7817 .7723 .7632

tion was established with the previous rims at 0° and 50° by measurements at 1000 and 5000 at both these temperatures. The average deviation from smooth curves of a single one of the 38 points obtained at 0° and 50° with the first sylphon was 0.06% of the maximum effect; the results with the third sylphon were equally as smooth. The numerical results are given in Table II. As explained, the relative volumes at 0° and 50° were obtained with one sylphon and those at 95° with another. The volumes obtained at 1000 and 5000 at 0° and 50° with the latter sylphon by way of check were not as good

100 — 2675

6

BBIDGMAN

as could be desired, and were on the average 0.0030 higher than those obtained with the first sylphon. I t is probable, therefore, that the 95° results for this liquid are not as good as usual, and less weight should be attached to them. The volumes of the table at 0° and 50° are for 0.9160 gm. The measured expansion of 1 gm at atmospheric pressm-e between 0° and 50° was 0.0823 cm', and the measured density at atmospheric pressure at 24° was 0.8839. I. C. T. gives for the density at 20° 0.890. n-propyl bromide. Two sylphons were used for this liquid. Rims were made in the regulär order at 0°, 50°, and 95°. There were irregularities at the maximum pressure at 0° with the first sylphon, which, however, seemed to have no effect on the later readings, checks being obtained between the readings with increasing and decreasing pressure. A check was not obtained, however, after the run at 95° at 0° at atmospheric pressure, and examination of the sylphon disclosed a leak. The complete series of runs was therefore repeated with a second sylphon. On working up the results, much greater irregularity was disclosed by the high pressure measurements at 0°, TABLE III. N-PROPTL BROMIDE.

Relative Volumes

Pressure kg/cm' 0 500 1000 1600 2000 3000 4000 5000 6000 7000 8000 9000 10000 HOOG 12000

100 — 2676

0°

50°

95°

1.0000 .9626 .9356 .9146 .8973 .8696 .8476 .8291 .8134 .8000 .7887 .7784 .7687 .7595 .7616

1.0655 1.0114 .9750 .9491 .9289 .8963 .8705 .8499 .8332 .8182 .8060 .7943 .7835 .7739 .7663

1.0561 1.0113 .9780 .9635 .9176 .8901 .8673 .8485 .8318 .8177 .8052 .7944 .7846 .7754

P E E S S U E E - V O L U M E - T E M P E E A T U K E EELATIONS OF LIQUIDS

7

the irregularity being so great that the results of the first run are doubtless to be preferred. It seems now that there can be little doubt that freezing took place at the highest pressures at 0° and that both sylphons were weakened at this time, but that the actual leak in the first sylphon developed only after release of pressure to nearly atmospheric at 95°. The following table is based on the results obtained with the first sylphon. The average deviation from smooth curves of a single one of the 61 readings was 0.11% of the maximum effect. The volumes given in Table III are for 1.3777 gm. The measured density at 25° was 1.3337, and the expansion of 1 gm between 0° and 50°, 0.0478 cm^. I. C. T. gives for the density at 20° 1.353. n-propyl iodide. This was prepared under the direction of Professor Conant by shaking with "hypo" and CaCl2 and then fractional distillation. It was kept in the dark after purification to avoid decomposition. TABLE IV. N-PROPYL IODIDE.

Preasiire kg/cm' 0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Relative VolumeB 0°

50°

95°

1.0000 .9656 .9412 .9214 .9055 .8795 .8581 .8409 .8262 .8128 .8012 .7906 .7810 .7715 .7625

1.0509 1.0085 .9775 .9528 .9336 .9027 .8792 .8594 .8435 .8289 .8163 .8049 .7945 .7850 .7761

1.0106 .9813 .9595 .9238 .8973 .8755 .8577 .8422 .8288 .8169 .8060 .7961 .7864

Measurements on this were made without incident; the conventional Order was followed, 0°, 50°, 95°, and then the retum check reading at 0°. The average deviation from smooth curves of a single one of the 51 readings was 0.04%.

100 — 2677

8

BEIDGMAX

The relative volumes are given in Table IV, which is constnicted for 1.778 gm. The observed density at atmospheric pressure at 24.5° was 1.7303, and the measured expansion of 1 gm. between 0° and 50°, 0.0319 cm\ I. C. T. gives for the density at 20° 1.747. n-butyl Chloride. Runs were made on this without incident except for a leak at the gauge plug, which was repaired without displacing the sylphon. The conventional nins at 0°, 50°, 95°, and retum check reading at 0° were made. At 0° the maximum pressure reached TABLE V. N-BUTTL CHLOBIDl!.

Pressure kg/cm® 0 500 1000 1600 2000 3000 4000 6000 6000 7000 8000 9000 10000 11000 12000

Relative Volumes 0°

60°

96°

1.0000 .9598 .9310 .9098 .8928 .8667 .8438 .8266 .8116 .7984 .7867 .7762 .7663 .7669

1.0614 1.0066 .9695 .9436 .9234 .8896 .8651 .8455 .8286 .8143 .8011 .7900 .7796 .7704 .7618

1.0526 1.0062 .9728 .9491 .9111 .8835 .8616 .8435 .8277 .8133 .8012 .7904 .7810 .7727

was only 10500 instead of the usual 12000. This restriction in ränge was not due to freezing, but was compelied by reaching the end of the stroke of the piston because of the leak at the gauge coil. It did not seem worth while to repeat the measurements in order to remedy the deficiency. The average deviation from smooth curves of a Single one of the 65 readings was 0.08% of the maximum efiFect. Relative volumes are given in Table V, which is constnicted for 0.9063 gm. The measured density at atmospheric pressure at 25° was 0.8796, and the measured expansion of 1 gm between 0° and 50°, 0.0675 cm'. I. C. T. gives for the density at 20° 0.884.

100 — 2678

PHESSUEE-VOLUME-TEMPERATUEE EELATIONS OF LIQUIDS

9

n-butyl bromide. The measurements on this substance went without accident or incident. The material was used without purification directly as received from Eastman. I t was especially noticed on emptying the sylphon at the end of the runs that the liquid remained clear and colorless. Runs were made as usual at 0°, 50°, and 95°, to 12000 at each temperature, and then the return check reading at 0°. The average deviation from smooth curves of a single one of the 60 readings was 0.016% of the maximum effect. TABLE VI. N-BUTTL BROMIDE.

Pressure kg/cm' 0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Relative Volumes 0°

50°

95°

1.0000 .9641 .9384 .9191 .9025 .8743 .8531 .8363 .8214 .8084 .7968 .7862 .7767 .7683 .7609

1.0613 1.0101 .9759 .9499 .9297 .8993 .8759 .8565 .8392 .8243 .8115 .8005 .7902 .7811 .7726

1.0512 1.0102 .9788 .9554 .9202 .8942 .8717 .8530 .8377 .8244 .8123 .8014 .7919 .7836

Relative volumes are given in Table VI, which is constructed for 1.3063 gm. At atmospheric pressure the measured density at 25° was 1.2685, and the expansion of 1 gm between 0° and 50°, 0.0452 cm'. I. C. T. gives for the density at 20° 1.275. n-butyl iodide. This was purified under the direction of Professor Conant in the same way as propyl iodide, and it was similarly protected from the action of light before use. The conventional runs at 0°, 50°, and 95° and the return check reading at 0° were made without incident. When the sylphon was emptied at the end of the

100 — 2679

10

BRIDGMAN

run a perceptible but small amount of reddish sediment was foxmd, which doubtless was stannic iodide, from the solder of the sylphon. The iodides always seem to have some chemical activity; they are always perceptibly colored by dissociated iodine, which doubtless is the active agent. However, the amount of such activity was very slight because the return check reading at 0° after the high pressure runs was as good or better than usual. The average deviation from smooth curves of a single one of the 53 readings was 0.08% of the maximum efFect. TABLE VII. N - B U m IODIDE.

Relative Volumes

Pressure kg/cm«

0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

0°

50"

95°

1.0000 .9687 .9453 .9258 .9104 .8841 .8630 .8463 .8317 .8183 .8062 .7955 .7859 .7765 .7686

1.0508 1.0094 .9785 .9545 .9357 .9069 .8827 .8639 .8474 .8331 .8206 .8097 .7995 .7905 .7822

1.0458 1.0104 .9821 .9606 .9249 .8995 .8792 .8616 .8462 .8331 .8212 .8106 .8007 .7922

Relative volumes are shown in Table VII, which is constructed for 1.6443 gm. At atmospheric pressure the measured density at 24.5° was 1.6043, and the measured expansion of 1 gm between 0° and 50°, 0.0308 cm\ I. C. T. gives for the density at 20° 1.617. n-amyl chloride.

A t 50° a n d 95° a n d a t t h e low p r e s s u r e e n d of t h e

0° run results went smoothly without incident. On the initial application of pressure at 0° it was difBcult to get readings above 6000 because of high resistance at the moving contact against the slide wire, and those readings which were obtained were very much more irregu-

100 — 2680

PHESSÜRE-VOLUME-TEMPERATURE RELATIONS OF LIQÜIDS

11

lar than usual. This was ascribed to an improper configuration of the flexible leads. After the first run at 0°, when a maximum of only 8000 kg was attained, the sylphon was removed from the press and the difläculty with the leads apparently remedied, as proved by the perfectly satisfactory subsequent readings at 50° and 95°. On repeating the 0° run however, after a perfect check at atmospheric pressure, there was again trouble of some sort, for the readings were again irregulär, although there was no difficulty with the contact as TABLE VIII. N-AMTL CHLORIDE.

Relative Volumes

Pressure kg/cm2 0 600 1000 1600 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

0°

60°

96°

1.0000 .9632 .9369 .9156 .8982 .8712 .8491 .8319 .8180 .8059 .7948 .7845 .7748 .7660

1.0617 1.0080 .9739 .9481 .9277 .8956 .8716 .8615 .8360 .8206 .8082 .7971 .7866 .7777 .7696

1.0064 .9766 .9526 .9165 .8891 .8678 .8498 .8346 .8213 .8093 .7987 .7883 .7792

before. The maximum pressure reached on the repetition at 0° was 10100. It is not unlikely that the irregularities were due to partial freezing. The average deviation from smooth curves of a single one of the 33 readings at 50° and 95° was 0.05% of the maximum effect, while at 0° the corresponding deviation for 25 readings was 0.27%. At 0° practically all of the irregularity occurred below 6000. Relative volumes are shown in Table VIII, which is constructed for 0.9143 gm. At atmospheric pressure the measured density at 25° was 0.8872, and the measured expansion of 1 gm between 0° and 50°,

100 — 2681

12

BRIDGMAN

0.0670 cm«. I. C. T . gives for the density at 20° 0.883, less than my value at 25°, and indicative of a real discrepancy, although a slight one. n-amyl bromide. This was purified under the direction of Professor Conant in the same way as the iodides. Two complete runs were made with this material with two sylphons. At 0° on the first nin pressure was pushed to 11700, which apparently froze the liquid. After the temiination of the 50° and the 95° runs the sylphon was TABLE IX. N-AMYL BHOMIDE.

Pressure kg/cm' 0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Relative Volumes 0°

50°

95°

1.0000 .9680 .9428 .9233 .9072 .8807 .8600 .8429 .8284 .8153 .8036 .7930

1.0573 1.0090 .9770 .9528 .9338 .9031 .8795 .8599 .8439 .8299 .8172 .8063 .7971 .7879 .7790

1.0101 .9803 .9588 .9241 .8975 .8766 .8590 .8438 .8301 .8182 .8081 .7990 .7905

found to have lost considerable weight, leak evidently having been produced by damage during freezing. The readings were therefore discarded, and the runs repeated with another sylphon. There was no special incident during the runs with the second sylphon, except that on the initial application of pressiu^e up to about 5000 at 0° a leak developed in the connecting pipe which made it necessary to release the pressure to zero, renew the washers on the pipe, and repeat the run. The maximum pressure at 0° was now restricted to 9000, at which there was no trace of any freezing phenomenon. Runs were

100 — 2682

PEESSURE-VOLUME-TEMPERATUHE RELATIONS OF LIQUIDS

13

made at 50° and 95° to the füll 12000 and return without incident, and then the return check reading was made at 0°. The check was not as good as usual, so that it seemed desirable to repeat the entire 0° run. This was done with a satisfactory check at all the points except atmospheric pressure. On taking down the apparatus, weighing the sylphon indicated no trace of leak. No certain explanation could be found for the unusually large discrepancies at 0° at atmospheric pressure; it is possible that unusually high friction in the internal guides of the sylphon may have been responsible. However, in view of the checks at all other pressures, there is no reason to fear important error. The volume assumed at 0° at atmospheric pressure was the mean of the two volumes on the first application, which diflered by only 0.1% from the mean. The mean of the two zeroes on the second application also agreed with the first mean. The mean deviation from smooth curves of a single one of the 50 readings (discarding the atmospheric readings at 0°) was 0.07%. Relative volumes are given in Table IX, which is constructed for 1.2505 gm. At atmospheric pressure the measured density at 24.5° was 1.2616; I. C. T. gives 1.223 at 20°. The expansion of 1 gm at atmospheric pressure between 0° and 50° was not obtained by direct measurement, but at 50° an extrapolation to atmospheric pressure was made from 100 kg; the ränge of extrapolation is so slight that there can be no important error. The value thus found for the expansion was 0.0456 cm®. n-amyl iodide. This was purified under the direction of Professor Conant in the same way as the other iodides and butyl bromide. The sylphon was filled in a darkened room to avoid decomposition. Regulär runs were made without incident at 0° and 50°. At 0° the füll 12000 was applied with no signs of freezing, although when the results were plotted on a large scale the irregularities beyond 9000 at 0° seemed somewhat larger than usual. One would have been prepared for freezing in view of the known freezing of amyl chloride and bromide; it may well be that the liquid subcooled and the irregularity of the high pressure points at 0° may have been due to the great viscosity of the subcooled liquid. On completing the run at 50° and passmg to 95°, a short circuit developed in the leads which made it necessary to take the apparatus apart, without, however, touching the sylphon. The apparatus was then reassembled, and the 95° run, up and down, made with satisfactory results, but on trying for the lowest reading at 95° trouble of some sort again developed in the connections, making the reading impossible. Neither was it possible

100 — 2683

14

BRIDGMAN

to get readings at 50° and 0°, so that the usual check could not be made. On hunting for the trouble after dismounting the apparatus the sylphon was found to have developed a leak, with a total loss of weight of 0.2 gm. I t was therefore necessary to repeat the measurements with a new sylphon, but in view of the regularity of the readings with the first sylphon up to the very end, the simple check was first made of determining the difference between the 0°, 50°, and 95° isotherms at atmospheric and 5000 kg/cm^ with the new sylphon. TABLE X . N-AMYL lODIDE.

Pressure kg/cm' 0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Relative Volumes 0°

50°

95°

1.0000 .9685 .9442 .9250 .9094 .8831 .8624 .8451 .8304 .8173 .8064 .7965 .7873 .7786 .7706

1.0529 1.0100 .9793 .9559 .9376 .9080 .8835 .8640 .8476 .8337 .8211 .8105 .8006 .7911 .7816

1.0093 .9806 .9585 .9247 .8994 .8783 .8607 .8453 .8312 .8192 .8085 .7987 .7896

These were found to check perfectly, so that further repetition was dispensed with. I t is evident that the leak in the first sylphon must have developed after the last reading at 95°. The average deviation from smooth curves of a single one of the 55 readings with the first sylphon was 0.10% of the maximum eflect. Relative volumes are given in Table X , which is constructed for 1.5683 gm. The measured density at atmospheric pressure at 24.5° was 1.5287; I. C. T. gives 1.517 at 20°, less than my value at 24.5°, indicating some discrepancy. I t would seem probable that any

100 — 2684

PRESSUEE-VOLUME-TEMPERATÜRE RELATIONS OF LIQUIDS

15

ordinary impurity would make the liquid lighter rather than heavier. The atmospheric volume at 50° was obtained, as for the preceding liquid, by an extrapolation from 100 kg. The expansion of 1 gm between 0° and 50° was found to be 0.0331 cm'. CHs Octanol-3. C — C — C — C — C — C — C — C. The initial attempt to get a run at 95° failed beeause of a ground on one of the connections. This was repaired without disturbing the sylphon, and TABLE XI. OCTANOL-3 Pressure kg/cm^ 0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Relative Volumes 0°

50°

1.0000 .9697 .9479 .9301 .9156 .8916 .8722

1.0480 1.0090 .9800 .9583 .9407 .9124 .8910 .8737 .8584 .8452 .8338

95°

1.0105 .9849 .9646 .9332 .9086 .8891 .8728 .8589 .8465 .8349 .8250 .8158 .8073

three successful runs obtained in the order 50°, 0°, 95°. The final points at 95° agreed with the initial ones before the short circuit developed, so that the usual check at 0° was not necessary. The average deviation from smooth curves of a single one of the 48 readings was 0.10% of the maximum effect. Relative volumes are given in Table X I , which is construeted for 0.8370 gm. At atmospheric pressure the measured density at 22.2° was 0.8177, and the thermal expansion of 1 gm between 0° and 50°

100 — 2685

BRISOMAN

16

0.0574 cm'. Professor Conant's index of refraction was 1.4251, which combined with my density gives 40.74 for the refraction constant. Professor Reid's vahies for index and refraction constant are 1.4209 and 40.41 respectively. All these are at 25°. CHs 2-methyl heptanol-S.

C — C — C — C — C — C — C . Runs were OH TABLE XII. 2-METHYL HEPTANOL-3.

Pressure kg/cm' 0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Relative Volumes 0°

50°

1.0000 .9690 .9469 .9283 .9140 .8897 .8707 .8544

1.0505 1.0078 .9789 .9565 .9394 .9216 .8891 .8714 .8568 .8435 .8318 .8213 .8117

95°

1.0121 .9851 .9647 .9428 .9080 .8888 .8719 .8569 .8441 .8331 .8232 .8139 .8049

made without incident at 50°, 0°, 95°, and the return check reading at 50°. The average deviation from smooth curves of a single one of the 51 readings was 0.08% of the maximum effect. Relative volumes are given in Table X I I , which is constructed for 0.8392 gm. At atmospheric pressure the measured density at 22.2° was 0.8211, and the thermal expansion of 1 gm between 0° and 50°, 0.0603 cm'. Professor Conant's index of refraction was 1.4255, which combined with my density gives 40.68 for the refraction con-

100 — 2686

PHESSURE-VOLUME-TEMPEEATUKE BELATIONS OF UQUIDS

17

stant. Professor Reid's values for index and refraction constant are 1.4246 and 40.31 respectively, all for 25°. CHs 2-methyl heptanol-6.

I

C — C — C — C — C — C — C. Runs were OH TABLE XIII. 2-mbthti, hbptanol-5

Pressure kg/cm' 0 500 1000 1600 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Relative Volumes 0°

50"

1.0000 .9679 .9449 .9269 .9122 .8882 .8698 .8538

1.0477 1.0071 .9774 .9549 .9375 .9099 .8887 .8716 .8561 .8425 .8305 .8198 .8102 .8023

95°

1.0085 .9815 .9612 .9297 .9054 .8855 .8696 .8556 .8433 .8318 .8220 .8127 .8038

made without incident at 50°, 0°, 95°, and the return check reading at 50°. The average deviation from smooth curves of a single one of the 49 readings was 0.05%. Relative volumes are given in Table X I I I , which is construeted for 0.8337 gm. At atmospheric pressure the measured density at 24.4° was 0.8147, and the thermal expansion of 1 gm between 0° and 50°, 0.0571 cm'. Unfortunately there was not enough of the material to permit a measurement of its index. Professor Reid's value for index and refraction constant are 1.4112 and 41.65 respectively.

100 — 2687

18

BRIDOMAN

CHa S-methyl heptanol-1.

C — C — C — C — C — C — C. Compressi-

OH bility measurements were made without incident at 50°, 0°, 95°, and the return check reading at 50°. The average deviation from smooth ciirves of a single one of the 50 readings was 0.03%. TABLE XIV. 3-METHTI, HBPTANOL-l.

Pressure kg/cm® 0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Relative Volumes 0°

50°

1.0000 .9714 .9499 .9323 .9181 .8946 .8760 .8605 .8468 .8341

1.0446 1.0065 .9791 .9585 .9422 .9147 .8939 .8764 .8616 .8482 .8366 .8260 .8167 .8083

95°

1.0090 .9834 .9642 .9342 .9105 .8912 .8748 .8611 .8487 .8371 .8270 .8179 .8098

Relative volumes are given in Table X I V , which is constructed for 0.8426 gm. The density measured at atmospheric pressure at 22.2° is 0.8265, and the expansion of 1 gm between 0° and 50°, 0.0530. Professor Conant's index of refraction was 1.4304, which combined with my density gives for the refraction constant 40.82. Professor Reid's values for index and refraction constant are respectively 1.4225 and 42.21.

100 — 2688

PRE8SUBE-V0LUME-TEMPERATURE KELATIONS OF LIQÜIDS

19

CH, S^ethyl

heptanol-4.

I

C — C — C — C — C — C — C. Compressi-

OH bility runs were made without incident at 50°, 95°, 0°, and the return check reading a t 50°. T h e average deviation from smooth curves of a Single one of the 54 readings was 0.09%. TABLE XV. 3-MBTHTL HEPTANOL-4.

Relative Volumes

Pressure kg/cm' 0 500 1000 1500 2000 3000 4000 6000 6000 7000 8000 9000 10000 11000 12000

0°

50°

1.0000 .9697 .9476 .9305 .9162 .8929 .8739 .8591 .8453

1.0506 1.0091 .9814 .9599 .9421 .9146 .8925 .8762 .8614 .8490 .8368 .8263 .8167 .8081

95°

1.0125 .9864 .9664 .9349 .9101 .8917 .8754 .8614 .8487 .8381 .8283 .8193 .8109

Relative volumes are shown in Table XV, which is constructed for 0.8455 gm. The density measured at atmospheric pressure at 22.2° is 0.8272, and the expansion of 1 gm between 0° and 50°, 0.0599. Professor Conant's index of refraction was 1.4286, which combined with my density gives for the refraction constant 40.92. Professor Reid's values for index and refraction constant are respectively 1.4211 and 39.61.

100 — 2689

20

BRIDGMAN DISCÜSSION.

This discüssion will not be concerned with general features of the pressiire-volume-temperature relations which are common to all liquids, for these have been sufBciently considered in previous papers, but we shall be interested only in features characteristic of these particular liquids. Triethanolamine (N(C2H60)3) was tried, as already stated, because experience with glycerine and similar Compounds had suggested that the three OH groups might give it unusual incompressibility. As a matter of fact the compressibility is about 50 per cent greater than that of glycerine, which thus retains its position as the most incompressible organic Compound, and is almost exactly the same as that of ethylene glycol. It is to be considered, however, that the rest of the molecule of triethanolamine is much more complicated than in the case of either glycerine or ethylene glycol, so that the OH groups occupy a proportionally smaller part of the total structure. The fact that the compressibility is so low in spite of the greater complication of the rest of the molecule is again evidence of the great eflect of the OH group in consolidating the entire molecular structure and imparting to it relative incompressibility. Consider next the halogen Compounds. The most outstanding effect of the addition of a halogen is that the substance is carried away from the gaseous condition toward incompressibility and liquidity. Propane and butane are, of course, under ordinary conditions gaseous, while pentane is one of the most compressible of liquids. The addition of the halogen lowers the vapor pressure and decreases the compressibility by a marked degree. At 0° the volume compression under 10000 kg/cm^ of the amyl halogens is roughly about 0.8 as much as that of normal pentane. The compression of amyl alcohol is about the same as that of the halogen Compounds, so that roughly the effect of a halogen is about the same as that of an OH group in decreasing the compressibility. If the relative volumes at 50° of the nine halogen Compounds are plotted against pressure in the same diagram, certain regularities stand out. In the groups containing a common halogen the compressibility decreases on passing from propyl to butyl to amyl groups, that is, in the direction of increasing molecular weight, and in the groups containing a common alkyl the compressibility decreases as the atomic weight of the halogen increases. An exception to this general trend are butyl and amyl iodides, which have almost exactly the same compressibility.

100 — 2690

PRESSURE-VOLUME-TEMPERATUEE RELATIONS OF LIQUIDS

21

If the volume increment on increasing temperature at constant pressure is plotted against pressure, curves will be obtained which drop rapidly with increasing pressure, as has been universally found before. The decrease of thermal expansion with increasing pressure is, however, not so large as has been previously found for other classes of Compounds. As a rough average the thermal expansion of these alkyl halides at 12000 kg/cm® is between one third and one fourth of its value at atmospheric pressure. Among other substances instances are not uncommon in which the drop is twice as rapid. In smaller detail, the curves of thermal expansion against pressure are not entirely smooth, but exhibit various episodes, as has been previously found for other liquids. Among the most striking of such episodes shown by the alkyl halides is a Stretch from 2000 to 6000 kg for butyl bromide, for which the thermal expansion between 0° and 50° is higher than is to be expected from the rest of the curve, and the last 6000 kg of the curve for butyl iodide, which shows a nearly constant expansion between 0° and 50°. Without doubt the most significant method of analysis for the nine alkyl halides is to compare the molecular volumes instead of the relative volumes as given in the tables. The molecular volumes are obtained at once from the data of the tables by dividing the figures there given by the number of grams for which the tables are constructed (that is, by the density at 0° C at atmospheric pressure), and multiplying by the molecular weight. The volumes thus obtained may be compared either by comparing the volume increments on changing the alkyl group, keeping the halogen fixed, or by changing the halogen, keeping the alkyl group fixed. The differences of molecular volume obtained in this way are given in Tables XVI and XVII. Table XVI gives the increments of volume on adding a CH^ group to the molecule. It is in the first place evident that this volume is a strong function of pressure, that is, the additional space required on forcing a CHa group into the molecule becomes less as pressure increases. This is naturally to be described as due to the compression of the CHj group itself. The absolute value of the volume of the CH« group varies considerably, depending on the kind of molecule to which it is attached, as may be seen by an inspection of the table, the ränge being from 17.09 to 15.36 at atmospheric pressure, and from 13.69 to 11.18 at 12000. The proportional loss of volume with pressure, as shown by the decrement in any of the columns of Table XVI, is more nearly constant. Disregarding the initial entry in the first column, which is abnormal and is connected with the abnormally

100 — 2691

22

BEIDGMAN

large volume of propyl chloride due to the nearness of the critical point, the volume of the CH2 group at 12000 varies from 0.72 to 0.79 of its volume at atmospheric pressure. The ratio of the total volume of the Compound at 12000 to that at atmospheric pressure varies from 0.72 to 0.75. The average compressibility of the CH2 is therefore approximately the same as that of the entire Compound, not a particularly surprising result. The increment of volume on adding a CH2 group to propyl chloride or iodide to form the butyl Compound is less than the increment on TABLE XVI. D I F F E R E N C E S OF M O L E C U L A R V O L U M E S AT

50°.

Pressure kg/cm^

Propyl chloride to butyl chloride

Butyl chloride to amyl chloride

Propyl bromide to butyl bromide

Butyl bromide to amyl bromide

Propyl iodide to butyl iodide

Butyl iodide to amyl iodide

0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

16.15 16.63 16.29 16.13 15.98 15.46 15.20 14.98 14.67 14.53 14.28 14.14 13.94 13.82 13.69

15.36 14.75 14.56 14.13 13.85 13.55 13.25 12.85 12.72 12,49 12.40 12.27 12.08 11.98 11.91

16.28 15.62 15.31 14.91 14.57 14.32 14.16 13.98 13.65 13.41 13.17 13.06 12.92 12.87 12.70

16.37 15.92 15.62 15.42 15.27 14.73 14.35 14.01 13.85 13.74 13.57 13.39 13.40 13.19 13.04

17.09 16.53 16.01 15.68 15.47 15.13 14.70 14.48 14.17 13.97 13.76 13.64 13.48 13.37 13.30

15.38 14.57 14.18 13.96 13.67 13.20 12.78 12.45 12.21 12.05 11.86 11.76 11.62 11.46 11.18

adding CH2 to butyl chloride or iodide to form amyl chloride or iodide. This means that as the molecule becomes more complex the increment of volume due to the addition of successive CH2 groups becomes less, as seems not unnatural. This sequence does not hold for the bromides, however. Examination shows that the sequence would be restored if the volumes of butyl bromide were increased somewhat. Table XVII, as will be shown in more detail presently, indicates the

100 — 2692

PEESSURE-VOLUME-TEMPEKATÜRE RELATIONS OF LIQÜIDS

23

same sort of thing, namely that butyl bromide has at all pressures a volume somewhat too small to fit in regularly with that of the other Compounds. Consider next Table XVII, which shows the differences of volume between chlorine and bromine and between bromine and iodine in the various Compounds. The State of affairs is entirely diflerent from that of Table XVI; here the columns at first increase with inTABLE

XVII.

Differences of Molbcitlar Volumes at 50°.

Pressure kg/cm«

0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 liooo 12000

Propyl Propyl Chloride bromide to propyl to propyl bromide iodide 2.80 4.19 4.36 4.51 4.63 4.64 4.56 4.50 4.45 4.44 4.43 4.40 4.31 4.24 4.23

5.46 6.11 6.42 6.37 6.30 6.32 6.38 6.31 6.28 6.20 6.11 6.04 6.02 6.01 5.90

Butyl Chloride to butyl bromide

Butyl bromide to butyl iodide

Amyl Chloride to amyl bromide

Amyl bromide to amyl iodide

2.93 3.18 3.38 3.29 3.32 3.50 3.52 3.50 3.53 3.32 3.32 3.32 3.29 3.29 3.24

6.27 7.02 7.12 7.14 7.20 7.13 6.92 6.81 6.80 6.76 6.70 6.62 6.58 6.61 6.50

3.94 4.35 4.44 4.48 4.64 4.68 4.62 4.66 4.56 4.57 4.49 4.44 4.61 4.50 4.37

5.28 5.67 5.68 5.68 5.60 5.60 5.35 5.25 5.16 5.07 4.99 4.99 4.80 4.78 4.64

creasmg pressure and then fall off somewhat. The total ränge of Variation is less than in Table XVI. A possible explanation is obviously that the volumes of chlorine, bromine, and iodine are not the same sort of functions of pressure, but the compressibility of chlorine varies rapidly with pressure, dropping off rapidly with increasing pressure at the low pressure end of the ränge, the compressibility of bromine is intermediate in behavior, while the compressibility of iodine remains more nearly constant over the entire pressure ränge. A simple graphical construction will show at once the plausibility of

100 — 2693

24

BBIDQMAN

such an explanation, which is, moreover, consistent with what other lines of evidence would lead us to expect. In all cases the diJference of volume betweeen bromine and chlorine is less than the difiference between iodine and bromine. This difFerence is much accentuated in the butyl Compounds. The butyl Compounds would fall more nearly into line with the others if the volumes of butyl bromide were somewhat increased, showing, as already suggested, that the volume of butyl bromide is anomalously low. TABLE

XVIII.

V O L U M E S AT 5 0 ° OP 0 . 8 3 9 2 GRAMS OP VABIOUS OCTANOLS.

Pressure kg/om^

Octanol-3

2-methyl heptanol-3

2-methyl heptanol-5

3-methyl heptanol-1

3-methyl heptanol-4

0 500 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

1.0508 1.0116 .9826 .9608 .9432 .9148 .8933 .8760 .8606 .8474 .8360

1.0505 1.0078 .9789 .9565 .9394 .9216 .8891 .8714 .8568 .8435 .8318 .8213 .8117

1.0546 1.0137 .9838 .9612 .9437 .9159 .8946 .8773 .8618 .8481 .8360 .8252 .8156 .8076

1.0404 1.0024 .9752 .9546 .9384 .9110 .8903 .8729 .8581 .8448 .8322 .8227 .8134 .8050

1.0428 1.0016 .9741 .9527 .9351 .9078 .8858 .8697 .8550 .8427 .8306 .8201 .8106 .8021

The difference between the volumes of the halogens in these Compounds is several fold greater than one would calculate from the atomic radii in solid Compounds as given by X-ray analysis. Finally, consider the volumes of the isomers of octyl alcohol. The comparison here should be of the volumes of equal masses. In Table XVIII are shown the volumes at 50° in cm» of 0.8392 gm, 0.8392 being very nearly the average density of the five isomers at 0°. The most striking feature is doubtless the approximate equality of the volumes of all five isomers at all pressures. The ränge of Variation becomes less as pressure increases, the extreme

100 — 2694

P R E S S U H E - V O L U M E - T E M P E E A T U E K EELATIONS OF LIQUIDS

25

Variation a t t h e maximum pressure being somewhat less t h a n half of t h e Variation a t atmospheric pressure, b u t t h e effeet is not striking because t h e Variation is everywhere so small. Furthermore, t h e volume of every pair of substances does not tend to become more nearly equal a t high pressure, as can be seen a t once from the table in the case of octanol-3 and 2-methyl heptanol-3. 2-methyl heptanol-1 and 3-methyl heptanol-4 are a pair whose volume curves cross. F u r t h e r study of the details of Table X V I I I does n o t appear profitable a t present. I t was a considerable disappointment to find t h e Situation so featureless. This, in addition to previous experience, has convinced m e t h a t the behavior of isomers under high pressure is so similar t h a t it will not p a y to examine t h e question experimentally f u r t h e r until there is some theory which will indicate j u s t w h a t t h e crucial effects m a y be.

One would expeet that the average compressibility of the octanols would be less than that of octane, according to the general rule that the addition of an OH group decreases the compressibility. This is in faet the case; for example, the compression of n-octane at 50° under a pressure of 7000 kg/cm^ (the highest pressure at which n-oetane is liquid at that temperature) is 1.16 times as great as the compression of octanol-3 under the same conditions. I am mdebted to my assistant Mr. L. H. Abbot for making the readings. I am also indebted for financial assistance to the Rumford Fund of the American Academy of Arts and Sciences for the purchase of supplies, and to the Milton Fund of Harvard University for the salary of my assistant. R E S E A K C H L A B O E A T O E Y OF P H T S I C S , H A B V A R D ÜNRVEESITY, CAMBEIDGE, M A S S .

REFERENCES.

1 P. W. Bridgman, Proc. Amer. Acad. 66, 185-233, 1931; 67, 1-27, 1932. 2 P. W. Bridgman, Proc. Amer. Acad. 47, 347-^38, 1912; 47, 441-558, 1912; 51, 55-124, 1915; 52, 91-187, 1916. Phys. Rev. 3, 126-141, 153-203, 1914; 6, 1-33, 94-112, 1915.

100 — 2695

COMPRESSIBILITIES AND PRESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS, COMPOUNDS, AND ALLOYS, MANY OF THEM ANOMALOUS. B Y P . W . BRIDGMAN.

Presented Dec. 14.1932.

Received Dec. 19,1932.

TABLE OF CONTENTS. Introduction DetailedData Elements Columbium Rhodium Ruthenium Chromium Arsenic Beryllium Compounds Gulonic Lactose Rhamnose Sucrose MnClj ZnCU AlsO, Cu.Cd, Alloys Gold-Silver Alloys Ag 25%, Au 75% Ag 50%, Au 50% Ag 75%, Au 25% Cobalt-Iron-Tungsten Alloys Fe 90%, W 10% Fe 80%, W 20% Fe 70%, W 30% W 10%, Co 90% W 20%, Co 80% W 30%, Co 70% Fe 60%, W 30%, Co 10% Discussion

27 28 28 28 29 30 82 39 49 51 51 51 52 54 55 56 60 62 63 63 66 69 70 71 74 77 81 82 83 85 87

INTRODUCTION.

This paper represents the accumulation of a year and a half or two years' measurements of compressibility and pressure coefficient of resistance by methods already extensively used and described.'

101 —2697

28

BBID6MAN

The particular feature of this work is the discovery of a number of highly anomalous effects. Some of the anomalies are large scale and striking, as in the case of AgsO, ah-eady published elsewhere,^ or of the element chromium. But most of the anomalies are small scale in character, and demand carefui use of the apparatus in order to be sure that they exist. In fact some of these effects might previously have escaped notice, and have been dismissed as merely due to accidental irregularities. My assistant, Mr. L. H. Abbot, has developed a great deal of skill in the use of the lever piezometer, and has furthermore had the patience to make the large number of closely spaced readings necessary to decide whether an irregularity in the data is due to a real anomaly characteristic of the substance, or is only accidental. Every precaution has been taken to be sure that these anomalies are real and not in the apparatus. The apparatus itself has been carefully studied and recalibrated. The fact that all the readings of compressibility given in the following have been obtained with the same apparatus, and the fact that anomalies of different substances are so entirely different in character is itself guarantee of the genuineness of the effects. The explanation of the effects is not yet obvious; there is no reason to think that a single type of explanation will apply to all the phenomena. It is to be remarked that similar anomalies are beginning to appear in many places, the anomalies of NH4CI first discovered by Simon' being perhaps the best known. Whatever the explanation, a new field is here opening before us, just on the threshold of the last decimal place, which will occupy us experimentally for a long tüne. DETAILED D A T A .

Elements. Columhium. This material was obtained from the Fansteel Co. of Chicago, and was a product of their Research Department. The measurements were made in 1929, and have been waiting since for a suitable opportunity for publication. The compressibility sample was in the form of a rod 2.6 cm. long and 3 mm. in diameter. The compressibility measurements were made as usual at 30° and 75° without incident. At 30° the average arithmetical deviation from a straight line of a smgle one of the 11 readings was 0.13% of the total effect, and at 75° the corresponding figtire was 0.25%. The results follow: At 30°, - AF/Fo = 5.700 X 10"'^ - 2.22 X 1 0 " ^ . At 75°, - AV/Vo = 5.778 X 10"'^ - 2.12 X l O - i y , P in kg/cm".

101 — 2 6 9 8

PRESSUKE COEFFICIENTS OF RESISTANCE OF ELEMENTS

29

I t is thus slightly less compressible than iron. The resistance specimen was in the form of wire 10 cm. long and 0.050 cm. in diameter. The resistance under pressure was measured on the Potentiometer, employing four terminals in the conventional way, the connections being made by spot welding. The specific resistance at 30° was 23.3 X 10~® ohms per cm'., somewhat high for a metal of this character. The average temperature coefficient of resistance between 0° and 100°, obtained by linear extrapolation of the readings at 30° and 75° was 0.00228. This is considerably lower than is to be expeeted for a pure metal, and is probable indication of not very high purity. The effect of impurity is known in practically all cases to be greater on the electrical properties than on the compressibility. The effect of pressure on resistance was measured at 30° and 75°. At eaeh temperature the resistance is sensibly linear; at 30° the average arithmetical deviation of a single one of the 11 readings from a straight line was 0.10%, and at 75° the corresponding figure for the same number of readings was 0.27% of the maximum effect. The coefBcients found were as follows: At 30°, average coefficient 0-10000 kg, - 1.21 X 10"«, At 75°, average coefficient 0-10000 kg, - 1.25 X 10*^. The coefficient is thus normal in sign and dose in numerical value to that of cobalt, which also has about the same compressibility. Columbium thus appears to be an unexciting, prosaic substance. Rhodium. Measurements had been made previously on this material;^ the point in repeating them was that I had now obtained material of considerably higher purity from Johnson Matthey and Co. of London. The compressibility measurements were made on a rod 2.5 cm. long and 2 mm. in diameter. The measurements went without incident, at 30° and 75° as usual. At 30° the average arithmetical departure from a straight line of a single one of the 17 readings was 2.9% of the maximum effect, and at 75° the corresponding figure for 14 readings was 0.7%. The results are: At 30°, - AF/Fo = 3.606 X 10"'^ - 2.73 X 1 0 " ^ , At 75°, - AF/Fo = 3.702 X lO-'p - 2.75 X 1 0 - ^ The thermal expansion was measured in a specially constructed apparatus used previously in measuring the expansion of single crystals. The apparatus is described in my paper dealing with single

101 —2699

30

BBIDGMAN

crystals.® The mean linear diflerential expansion between Rh and Fe in the temperature ränge between 12° and 30° was found to be 3.49 X 10-«, which, assuming 12.0 X 10"« for Fe, gives 8.5 X 10"« for Rh. International Critical Tables (I. C. T.) gives 8.4 X lO"«. The electrical resistance was measured on a swaged wire about 10 cm. long and 0.08 cm. in diameter. The potentiometer method with four terminals was used, the terminals being attached with soft solder. Two nins were made at 30°, agreeing within the limits of error, and a single run at 75°. At each temperature the relation between pressure and resistance was sensibly linear. The results were: At 30°, average coefficient between 0 and 12000 kg, - 1.764 X 10-^, At 75°, average coefficient between 0 and 12000 kg, - 1.708 X 10-«. The specific resistance, measured at 30°, was 4.95 X 10"«, which, corrected by the temperature coefficient, gives 4.35 X 10"« at 0° C. I. C. T. gives 4.69. The average temperature coefficient of resistance between 0° and 100°, obtained by linear extrapolation of measurements at 30° and 75° was 0.00462. This is much higher than my previous value, 0.00399, and is evidence of the much higher purity of this material; the same is also shown by the low specific resistance. The previous relation between pressure and resistance at 30° was: AR/Ro = - 1.738 X 10-«p + 9.7 X 1 0 " V , which gives for the average coefficient between 0 and 12000 - 1.62 X 10"«, against - 1.76 above. The difference is in the direction always found without exception to be the effect of impurity. The compressibility of the former sample at 30°, however, was: - AV/Vo = 3.72 X 10"'^ - 2.67 X lO-^^'p®, somewhat higher than the value found for this new specimen. This is somewhat unusual, but there is no universal rule here as for the resistance. I t would indicate an impurity of higher compressibility in the previous sample, such, for example, as Pd. Ruthenium. This has not been previously measured. I t belongs to the hexagonal system, so that the following results can only be a mean of some sort for different directions. The material was obtained from Johnson and Matthey at the same time as the rhodium. The compressibility specimen was in the form of a swaged rod 2.7 cm. long and 3 mm. in diameter. I t was not perfectly regulär in appear-

101 — 2 7 0 0

PRESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

31

ance, but appeared as if there might be seams in it. On the first application of pressure there was a large change of zero. This may have been due to seams, or to the fact that the crystal system is not cubic; large efifects of this nature are to be expected for non-cubic materials. Two more applications of 12000 were made before the routine measurements were attempted. Also at 75° an additional seasoning application of 12000 was made before the measurements. This seasoning seemed effective, for the change of zero during the measurements, both at 30° and 75°, was not more than the irregularity of the other points. At 30° the average arithmetical departure from a straight line of a single one of the 13 readings (after making one discard) was 1.3% of the maximum effect, and at 75° the corresponding figure for 15 readings was 0.64%. As in the case of Rh, the relative irregularity is greater than usual because of the smallness of the compressibility; the absolute irregularity is not greater, and in fact is even less than usual. There may be some significance in the fact that the discarded point at 30° was at the maximum pressure. This was off the curve by one third of the total effect; there is perhaps a possibility that this is a genuine anomaly like that of many of the other substances of this paper, but it would have been very difHcult to establish, because it was at the end of the pressure ränge, and the matter was not investigated further. The results for volume compressibility, assuming equal linear compressibility in all directions, are: At 30°, - AF/Fo = 3.42 X 10"^^ - 2.13 X 10" At 75°, - AF/Fo = 3.45 X lO-'p - 2.13 X 10"'VThe average compressibility is therefore slightly less than that of Rh, and fits in with what might be expected from the periodic table. The linear thermal expansion at atmospheric pressure was measured in the same special apparatus as used for Rh. The mean value between 32° and 13° was 6.75 X 10"«. I. C. T. gives 9.1; this very marked divergence is perhaps to be ascribed to the non-cubic symmetry of the crystal, for it is now pretty well established that measurements by different observers on different specimens of non-cubic metals are likely to give different results. The principal value of such measurements on multi-crystalline aggregates is in establishing Upper and lower limits for the constants corresponding to different directions in the crystal. The resistance was measured on the compressibility sample, the technical difficulties having proved too great to permit swaging it to

101 —2701

32

BBIDGMAN

a more slender rod, as had been possible with Rh. The current was led in through copper terminals making soldered connection over the entire flat ends. In this way the lines of current flow are straight from the beginning, and end effects are avoided. The current, about one half amp., was made as large as possible without introducing troublesome thermal effects. I t was supplied from a storage battery, through heavy manganin resistances in an oil bath. The resistance was very low, only 0.00022 ohms, so that the measurements could not be as accurate as usual, in spite of the large current. Pressure measurements were made at 0° and 95°. Within the limits of error the relation between pressure and resistance was linear. At 0°, the average arithmetical departure of a single one of the 16 readings from a straight line was 2.2% of the pressure effect, and the corresponding figure at 95° for 13 readings was also 2.2%. The results were: At 0°, average coefficient 0-12000, - 2.48 X 10"», At 95°, average coefBcient 0-12000, - 3.20 X lO"«. So large an effect of temperature is not usual. Other electrica! data were also obtained. At 0° the specific resistance is 7.64 X 10-®. I. C. T. gives 10 X lO"®, to only one significant figure. The temperature coefficient of resistance a t atmospheric pressure was determmed from readings at 0°, 24° 50°, and 95°. The relation between resistance and temperature is of the second degree in the temperature, namely: Ä = Äo [1 + .00494« - 3.64 X 10^"]. The negative sign for the second term is not usual for most metals, but seems to be of frequent occurrence in the metals of the platinum groups. This formula gives for the average coefficient between 0° and 100° 0.00458. There seems to be no previous value for comparison, but this is high for a metal of this character, considerably higher than for pure platinum, for example, and is in so far evidence of high purity. Chromium. The compressibility of this dement has been previously measured,® but the purity was not high, and repetition was desirable. The previous sample was highly brittle, and in appearance was like the metal which has been available for many years made by the Goldschmidt process. Its compressibility was not notable in any way, being 5.19 X 10"^ at 30°, somewhat less than for Fe. For the new measurements I was fortunate to obtain from Mr. P. H. Brace of

101 —2702

PKE88URE COEFFICIENTS OF RESISTANCE OF ELEMENTS

33

the Research Department of the Westinghouse Electric and Manufacturing Co. a swaged rod of Cr. Mechanically, this was soft enough to be readily filed; the hardness of commercial chromium plating is said to be due to occluded hydrogen. This specimen had been made in connection with a systematic study of the properties of the piire metal, and every efFort had been made to obtain metal of high purity; the fact that it was malleable enough to be swaged is evidence Ä a t it was much purer than the previous sample. In Order to further test the purity, Dr. Martin Grabau was kind enough to make a spectroscopic examination under the direction of Professor F. A. Saunders, and it was found to be of quite an exceptional degree of purity, the only detected impurity being a doubtful trace of magnesium. Only one piece of this chromium was available, a rod 4 cm. long and 2.5 mm. in diameter. The resistance was first measured, and then the length of the rod was cut to 2.7 cm. for the compressibility measurements. The resistance measurements suggested most unusual compressibility efifects, which were indeed found. Readings of compressibility were made at the usual 30° and 75°, and also at — 40°, since the resistance measurements had suggested the possibility of new effects at low temperatures. The temperature bath at — 40° consisted of about 5 gallons of alcohol, rapidly stirred, into which small pieces of solid CO« were dropped when required to maintain the temperature constant as indicated on a pentane thermometer. The regulation was done by hand, one observer continually watching the temperature bath, while the other made the compressibility readings. The results were highly unusual, as shown in Figure 1. In this figure the actual displacements of the slider of the potentiometer are recorded, midtiplied by such a constant as to reduce them approximately to changes of length relative to the steel of which the piezometer is made. At 30° and 75° Cr is on the average less compressible than Fe, but the difference is far from linear, and behaves in the complicated way shown. Except for one point which may have involved a Wunder in reading, although this is not likely, all the points at these two temperatures lie dose to a single curve, that is, there is no difference between increasing and decreasing pressure. In fact, the direction of alteration of pressure was changed several times in O r d e r to be sure that the curve is really characteristic of the metal, and does not involve its past history. At — 40°, on the other hand, the character of the phenomena is entirely altered; the compressibility is now greater than that of Fe, the sinuosities in the curve of change of

101

—2703

BRIDGMAN

34

O

2

4 O 8 P r e s s u r e , Thouaands of Chromium

LO

FIQTOE 1. Deviations from linearity of the linear compression of chromium. The open circles are for increaäng pressure and the solid circles for decreasing pressure.

101 — 2 7 0 4

PRESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

35

length have now disappeared, and there is a distinct hysteresis between the readings with increasing and decreasing pressure. It is possible that the hysteresis would have disappeared if the pressure run had been repeated, but because of the inconvenience of maintaining temperature at — 40°, this was not attempted, but the mean result, indicated by the curve, was used in the final calculations. The final results for change of volume are shown in Table I. Chromium is cubie, so that the volume changes can be accurately computed from the changes of length in a single direction. In making the calculations at — 40° the compressibility of iron was extrapolated Hnearly from the measured values at 30° and 75°. T A B L E I. RELATIVE VOLUME CRANGES OF CHROMIUM.

ure kg/cm' - 40° 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

.001320 2577 3717 4869 5940 6981

AV/Fo + 30° 000606 001167 1611 2109 2622 3129 3618 4044 4473 4938 5427 5910

+ 75' 000552 001089 1605 2049 2430 2826 3336 3876 4410 4878 5310 5772

The resistance was measured, as already stated, on the same rod as that from which the compressibility sample was cut. It proved not to be possible to soft solder this, and spot welding on so large a diameter was not practical with the equipment on hand. Current connections at the two ends were made by massive sleeves of copper driven tightly over the ends. Under pressure these become even tighter because of differential compressibility. The design of the current connections is thus such as to start the lines of current flow approximately straight, avoiding end effects. The potential term i n a l were fine springs. It was soon found that the behavior of resistance is so complicated as to make it desirable to extend the study of resistance over a wider temperature ränge than usual. In addition

101 —2705

36

BEIDQMAN

to the conventional measurements at 30° and 75°, runs were also made at 0°, - 20°, - 40°, and - 78.5°, the latter being the normal Sublimation point of solid CO2. The temperatures below 0° were obtained in an alcohol bath, cooled with solid CO2 and regulated manually by a second observer, as already explained. The greatest difficulty to be anticipated at low temperatures is the freezing of the pressure transmitting liquid. Of all the substances liquid under ordinary MO

U55

/

X

U30

/

.95

.90

/

.es -eo-

-ao

-40°

-20°

O"

20'

TemperaVu-ne Chromiam

40-

SO-

etf

Figtjre 2. The relative resistance of chromium at atmoBpheric pressure as a function of temperature.

atmospheric conditions, and therefore capable of being used without the introduction of complicated precompressors, as would be necessary in handling a gas, iso-pentane is that with the lowest freezing point, and this was accordingly tried. It proved gratifyingly successful. It allowed readings at — 78.5° to a maximum pressure of 8000 kg/cm^ before its viscosity became too great (or before it froze, which, was not determined), and at — 40° and higher, readings to the füll 12000.

101 —2706

PRESSUKE C0EFFICIENT8 OF RESISTANCE OF ELEMENTS

37

Not only is the resistance abnormal when measured as a function of pressure at constant temperature, but it is also abnormal at atmospheric pressure as a function of temperature, an effect apparently not observed before because pure enough metal was not available. At 0° at atmospheric pressure the specific resistance is 18.9 X 10"®. The only figure given by I. C. T. is 2.6 for the pure metal on the authority of Shukov. This cannot possibly be correct, but would indicate a misprint somewhere. The relative resistance as a function of temperature at atmospheric pressure is reproduced in Figure 2. The curve is very similar in character to the curve for the volume of liquid water, with an abnormality in the neighborhood of 0° C. of much the same kind. It is to be noticed that there is no hysteresis between resistance and temperature, but within the limits of error the relation is Single valued. The order of the readings was as follows: first, 3 points at 30°, made before and after the pressure run, then at 75°, 30° again, 0°, - 78.5°, - 60°, - 40°, - 20°, + 20°, + 30°, + 10°, and + 5°. The relative resistance as a function of pressure is reproduced in Figure 3, where all the experimental points are shown. The scale of the figure is not large enough to show any departure of these points from smooth curves. In practically all cases the points alternated between increasing and decreasing pressure, readings being made on the odd thousands with increasing pressure, and on the even thousands with decreasing pressure. There is no appreciable hysteresis, even at — 40°, although the compressibility measurements, made after the resistance measurements, did show hysteresis. The crossing of the curves means that there are regions, varying with the pressure, in which the temperature coefficient of resistance is negative. This, of course, is to be expected because such a phenomenon has already been found at atmospheric pressure. The curves for the resistance and the compressibility must speak for themselves, and I shall not attempt to make any comment except to emphasize that whatever internal change it is which is responsible for the anomalies occurs for the most part without hysteresis, and to remark that manganese, which occurs next to chromium in the periodic table, isknown tohave polymorphic transitions at atmospheric pressure and to have a highly complicated crystal structure with 54 atoms in the unit cell. It is also to be noted that internal changes like these of pure chromium may be suppressed by impurities, the previous measurements of compressibility having given no hint of the complications now foimd.

101 —2707

38

BRIDGMAN

0

2

4

6

8

Pressure, Thousands of l^'/sm." Resistance of Chromium

Figube 3. The relative resistance of chromium as a function of pressure at various temperatures. The open circles are for increasing pressure and the solid circles for decreasing pressure.

101 — 2 7 0 8

PRESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

39

Arsenic. Measurements have already been made of polycrystalline arsenic on two different occasions.' The second measurements were made on samples which were approximately Single grains, in that there was a strongly preferred direction of orientation. Surprising results were found; it appeared that there must be a polymorphic transition in the neighborhood of 5500 kg., and it was evident that there were very large differences in different directions. However, the results were not consistent, and in particular there were obscure effects on the first application of pressure for which no parallel in the behavior of other substances was known. It seemed evident that satisfactory results could not be expected until truly single crystals were available. Measurements have now been made on a number of single crystals, without even yet, however, leading to a completely satisfactory cleaning up of the Situation. The preparation of single crystals proved an unexpectedly complicated and difficult matter, and Dr. W. E. Danforth, as my assistant, spent a good part of an academic year working out the technique and producing the crystals. The original material was of the " Kahlbaum " grade. This proved to have a very appreciable fraction of non-volatile impurity, probably carbon or Silicon. The metal was first purified by a vacuum distillation in pyrex at 500° C, removing the non-volatile impurities, and also separating out the volatile AsaOs, the metallic arsenic condensing in the intermediate part of the tube. The final crystallization was in heavy quartz tubes. The powdered arsenic from the first purification was introduced into a bulb at one end of the tube, which was bent into several straight lengths to give different orientations in the final crystal. Düring the exposure to the atmosphere incident to getting into the quartz, more AssOs was formed, which had to be eliminated by a second distillation. This second distillation was at 300°, which drove the AS2O8 into an end of the tube left projecting from the furnace. This end was then sealed off from the rest of the tube, thus removing the AS2O3. The quartz was then lowered at about 30 cm. per hour from a furnace maintained at 950°, well above the triple point temperature. The pressure at the triple point is 36 atmospheres. The quartz is amply strong to hold this pressure if perfect seals are made. The Casting obtained after lowering out of the furnace was expected to be a Single grain, but experience proved that it usually was not. Accordingly, after the first lowering from the furnace the now empty bulb was sealed off, leaving merely the bent tube fairly well filled with arsenic. This was now run through the furnace again in the opposite direction, and this second crystallization usually produced a single grain.

101 —2709

40

BBIDGMAN

There is a very strong tendency for the principal hexagonal axis to lie in a horizontal plane (cleavage plane vertical), and in fact this proved to be practically invariable, so that the only way of getting other orientations was to bend the tube. Successful specimens of high orientations are extremely difBcult to get, however, because the thermal contraction across the cleavage planes is so high that if the cleavage plane makes mueh of an angle with the length the rod will break spontaneously into short pieces a few mm. long on cooling. The highest orientation that was obtained was 50° between cleavage plane and length, and this was exceptional, angles greater than 10° being rare. Crystals were made in two sizes: 3 mm. in diameter for measurements of compressibility and about 1 mm. for measurements of resistance. Resistance measurements were made on two samples of 90° between axis and length (cleavage plane parallel to length), one of 83°, and one of 73°. Compressibility measnrements were made on two 90° orientations, one 79°, one 56.5°, and one 40°. The results were highly abnormal; it is diflBcnlt to decide just how much should be reproduced here, since the abnormalities are in some respects not reproducible. In general characterization, it appears that the direction perpendicular to the axis, in the cleavage plane, is abnormal, but along the axis, the behavior is quite smooth and canonical. One might at first be inclined to expect the opposite behavior, looking perhaps for irregularities associated with the closing together of the atoms in the direction of greatest Separation, that is, across the cleavage plane. That the abnormalities are in the opposite direction indicates interpenetration effects in the direction of dosest packing, the fields of force being more symmetrical at larger distances of atomic Separation. The crystal arrangement of arsenic is much like that of bismuth and antimony, which are also abnormal in many particulars, but not to as extreme a degree as arsenic. One may suspect an imusual asymmetry in the arsenic atom. The two compressibility measurements on the two 90° orientations agreed in showing several ranges of pressure in which the change of length is approximately a linear function of pressiu-e, the different ranges running into each other continuously with a break only in the derivative, so that there is no evidence for a polymorphic transition of the ordinary kind, as was suspected from the previous measurements. But on the other hand, there is no exact correspondence between the results for the different samples. The first sample showed at 30° linear ranges from 0 to 4060, from 4060 to 6300, and from 6300

101 —2710

PRESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

41

to 12000 kg/cm^. This specimen showed no hysteresis at all on the very first application of pressure. Similarly at 75°, there were three ranges, from 0 to 3400, from 3400 to 7600, and from 7600 to 12000, and there was also no hysteresis except at the two lowest points, 700 kg. and atmospheric pressure. The second 90° orientation, on the other hand, showed at 30° on the first application of pressure very

30"

rc" - o . /

2

75'

4 6 8 10 PflESSURE, THOUSANOS As, SiNOLE C b y s t a l , CucAVAee paoallel t o l e n s t h .

12

Figuke 4. Differential linear eompression of Single crystal arsenic, clevaage plane parallel to length. The larger ciroles are for 30° and the smaller for 75°; open circles with increasing pressure, and solid ciroles with decreasing pressure.

marked hysteresis up to 5200, bat from here on the same perfectly linear hebavior up to 12000. Similarly at 75°, there was hysteresis, this time up to 8000, but from here on linear behavior. The low pressure episodes on this second sample were not linear like those of the first; they are reproduced infigure4. The straight lines indicated in this figure are obviously only a rough approximation, but they are sufiiciently good considering the failure of reproducibility, and it is

101 —2711

42

BHIDGMAN

the results given by the straight lines which are reproduced below. The 79° orientation gave essentially a linear relation at both temperatnres over the entire pressure ränge, except for slight curvature at the low pressure end. There was, however, marked hysteresis at 30°. The 56.5° orientation gave results of considerable irregularity, 1.05

1.04

lU

u z

1.03

f^ in VI

ui Cf^ F 1.02

1.01

1.00 6

B

10

12

PRESSURB, THOOSANOS OF ^^LAT" As., HexASONAL AXis 73° TO LKNGTH FIGUBE 5. The relative resistance at 30° C of Single crystal arsenic, hexagonal axis 73° to length, on the initial application of pressure.

with hysteresis. They can be fairly well reproduced by assuming at each temperature two linear ranges; at 30° from 0 to 7100 and from 7100 to 12000, and at 75° from 0 to 4800 and from 4800 to 12000. It is not certain, however, whether these effects are legitimate, because of difficulties in the preparation of the speeimen. Two pieces of this orientation were used, each only 2.3 mm. long, piled together with

101 —2712

P R E S S U R E C O E F F I C I E N T S OF R E S I S T A N C E OF E L E M E N T S

43

three steel separators to make up the length required by the piezometer. The ends were not perfectly flat, and the irregulär eifects may have been geometrical, due to rocking of one piece on another. The linear results are reproduced below, but the average compressibility, 0 to 12000, is much more secure than the results for the separate ranges. The 40° orientation gave results like those for any normal

2

^S.,

4 e a PRessuRe, T h o u s a n o s o f SlNSLE C R V S T A L , C u b A V A G E p a r a l l e l

To LEN6TH

Figtjbe 6. Deviation from linearity of the change of relative resistance of Single crystal arsenic, hexagonal axis perpendicular to the length, at 30° and 75°. The open circles are for increasing pressure and the solid eircles for decreasing pressure. material; there was no evidence of separate episodes, the hysteresis, althoughperceptible, was slight, and there were no importantseasoning efifects on the first applieation of pressure. The average deviation of Single points at both temperatures from smooth curves through the Centers of the hysteresis loops was 0.4% of the maximum eflect; the deviation would be much less if the two branches of the hysteresis loops were treated separately.

101 — 2 7 1 3

44

BEIDGMAN

The resistance samples covered a smaller ränge of orientations: there were two of 90°, one of 83°, and one of 73°. The resiJts of the resistance measurements agreed in that the whole pressure ränge breaks up into sub ranges, but did not agree with regard to the first seasoning effects of pressure. One 90° and the 83° orientation showed

0

2

4

As,

6

0

10

P ß E 9 S U R e , T h o u s a n d s o f ^•/c'^ S i n g l e C c y - s t a l , O - E a v a g e 7°+o L e n ö t h

Figtjke 7. Deviation from linearity of the change of relative resistance of Single crystal arsenic, hexagonal axis 83° to the length, at 30° and 75°. The open circles are for increasing pressure and the solid circles for decreasing pres-

no seasoning effects at all, but the other two specimens showed very large seasoning effects of the same general character. The effect of the first application of pressure on the resistance of the 73° specimen is reproduced in Figure 5. I t is the same sort of thing as was previously obtained with polygrained material, and accounts for the apparently positive coefficient at low pressures of the virgin specimen, followed

101 —2714

PRESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

45

by a permanent negative coefBcient. After the first application of pressure, there was very little hysteresis between resistance and pressure, but the behavior became steady almost at once. Unfortunately, the first 90° specimen, which showed no initial seasoning effects, did later develop irregularities, and on removing from the pressure cylinder feil apart into several pieces, so that the results had to be discarded. Within the somewhat wider limits of error, the results on it agreed with those of the other 90° orientation obtained after seasoning was complete. In figures 6 and 7 the deviations from linearity of resistance as a funetion of pressure for the second 90° orientation and the 83° orientation are given. I t is not difficult, knowing already from the compressibility measurements that there are linear ranges, to persuade oneself that there are linear ranges here, which are indicated in the figures. It must be remembered that in general resistance has proved much less sensitive to this sort of irregularity than compressibility. The numerical results now follow. Compressibility. First 90° orientation. 30° 0 - 4050, 4050- 6300, 6300-12000, Average,

- MIh = - 1.46 - AljU = 1.76 - MIU = 1.88 0-12000, 1.850 X

X 10"'? - 0.70 X 1 0 " V X lO"'?) - 0.70 X I Q - i y X lO-'p - 0.70 X 1 0 " V 10"^

75° 0 - 3400, - ällU = 1.41 X lO-'^p - 0.70 X I Q - V 3400- 7600, - MIU = 1.69 X IQ-'p - 0.70 X 10"»V 7600-12000, - MjU = 1.94 X lO-^p " 0-70 X 1 0 - ^ Average, 0-12000, 1.680 X 10"' Second 90° orientation. 30° 0 - 1850, - MjU = 0.43 X 10"^? - 0.70 X l O - ' V 1850- 5200, - MIU = 2.30 X IQ-'p - 0.70 X 1 0 " ^ 5200-12000, - AZ//o = 1.88 X - 0.70 X 1 0 " ^ Average, 0-12000, 1.786 X 10"'

101 —2715

46

BEIDGMAN

75" 0 - 4300, - Al/lo = 1.70 X 10"'^ - 0.70 X lOr^V 4300- 5300, - M/lo = 1.12 X lOr^p - 0.70 X 1 0 - > y 5300-12000, - Al/k = 1.90 X 10"^? - 0.70 X 1 0 " ' V Average, 0-12000, 1.771 X 10"' 79° orientation.

30°

- MIk = 1.826 X lO-'ß - 0.70 X 1 0 " V 75° - M/lo = 1.867 X lO-'p - 0.70 X 1 0 " ^ 56°.5 orientation. 0 - 7100, 7100-12000, Assuming 0-12000,

30°

- Al/lo = 5.87 X 10r''p - 0.70 X l O - ' V - Al/lo = 3.19 X 10"'? - 0.70 X 10->V no breaks: - Al/lo = 4.77 X lOr^p - 0.70 X 1 0 " » ^ 75°

0 - 4800, - Al/lo = 7.61 X 10r''p - 0.70 X lO'^Y 4800-12000, - Al/lo = 3.35 X 10"'^ - 0.70 X lOr'Y Assuming no breaks: 0-12000, - Al/lo = 5.04 X 10"'^ - 0.70 X 1 0 " ' ^ 40° orientation. At 30°, - Al/lo = 16.75 X 10"'? - 36.1 X l O ' V At 75°, - Al/k = 17.38 X lO-'p - 37.4 X l O - ' V The figures just given for the 40° orientation are only approximate, for the relation differs markedly from the second degree. The second degree fonnulas are so constructed as to give the correct changes of length at 0, 6000 and 12000. At intermediate points the actual changes of length can be obtained by combining with the second degree fonnulas a deviation curve. These deviation eurves can be drawn with sufBcient accuracy from the following specifications. At 30° the change of length is greater numerically at 3000 by 0.000177 than given by the second degree formula and at 9000 0.000164 less.

101 — 2 7 1 6

PHESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

47

At 75° the actual change of length is greater numerically at 3000 by 0.000239 than given by the fonnula, and at 9000 0.000164 less. The maximum deviation from linearity at each temperature comes at 4600 instead of 6000 as it would if the relation were second degree. Resistance: 90° orientation. Specific resistance at 30°, 27.5 X lO""® Average temperature coefficient, 0-100°, + 0.00479. 30° 0 - 5500, AÄ/Äo = - 1.74 X 10"-«^? 5500- 8200, AÄ/Äo = - 2.68 X 10"^? 8200-12000, AÄ/Äo = - 3.30 X 10-^2^ 75° 0 - 7100, AR/Ro = - 1.56 X IQr'p 7100- 9800, AÄ/Eo = - 2.08 X 10-«p 9800-12000, AÄ/iJo = - 2.58 X 10-«p 83° orientation. Specific resistance at 30°, 27.6 X 10"^ Average temperature coefficient, 0-100°, .00483 30° 0 - 4800,Aß/Äo = - 1.33 X 10"«^ 4800- 7400,AÄ//lo = - 1.81 X l ^ p 7400-12000, Aß/Äo = - 2.34 X 10"«? 75° 0 - 6100, AÄ/Äo = - 1.08 X 10-«p 6100- 8200, AÄ/i?o = - 1.43 X lO-^j? 8200-12000, AÄ/Äo = - 1.96 X 10"«? ientation. Specific resistance at 30°, 30.4 X 10"^ Average temperature coefficient, 0-100°, .00472

101 —2717

48

BRIDGMAN

30° 0 - 2550, AR/Ro = - 2.77 X lO^p 2550- 8200, AR/Ro = - 2.59 X 10"«? 8200-12000, AR/Ro = - 2.88 X 10-^p 75° 0 - 3000, AÄ/Äo = - 2.80 X 10"^? 3000-12000, AR/Ro = - 2.30 X 10-«p The thermal expansions were also determined as usual, and were as follows: Orientation 90°, Ist 90°, 2nd 79° 56°.5 40°

Mean linear expansion, 30°-75° Extreme values

Average

3.2 to 3.6 X 10-« 3.4 to 6.8 8.0 to 8.8 13.6 to 14.4 27.6 to 29.3

3.4 X 10-^ 5.1 8.4 14.0 28.4

Disregarding for the present the various abnonnalities, certain broad features stand out. There is great difference of properties in diflferent directions. In the cleavage plane the compressibility is less than that of iron, whereas across the plane the compressibility is more than ten tünes as high. This estimate is based on a rough linear extrapolation according to the cos^ law of the compressibilities of the orientations listed above, which gives for the average compressibility up to 12000 kg. the figure 19 X 10"' for the 0° orientation. The previous conclusion about large differences of compressibility in different directions is therefore verified, but the difference turns out to be more extreme than was surmised. In the same way the linear expansion for the 0° orientation may be estimated to be about 43 X 10~® against 5 or less for the 90° orientation, again showing an enormously greater deformability across the cleavage planes. The initial linear compressibility for the 0° orientation may be estimated by a similar linear extrapolation to be about 27 X 10"'. This would make the initial volume compressibility 31.6 X 10"'. The only previous measurement of this is by Richards,® on polycrystalline material,who found44 X 10"',so muchhigher than31.6as tobe beyond

101 —2718

PRESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

49

the possibility of experimental error. The difference is probably to be explained as an effect of internal strains arising from the very great differences of compressibility in different directions, and again emphasizes the conelusion that bulk measurements on haphazard aggregates of strongly non-isotropic crystals are of doubtful significance. The average volume expansion, calculated from the linear expansions in the 90° and 0° orientations is 53 X 10-«, er 17.7 X 10"« for the average linear expansion of the haphazard aggregate. I. C. T. gives for this 4.7 X 10"« from Fizeau, measured on sublimed mixed crystals. It would appear that Fizeau's orientations must have been almost exelusively the 90° orientation. Now consider the abnormalities. These are of two sorts: seasoning effects, and breaks in the direction of the curves after complete accomodation. The seasoning effects are not universally present; one 90° and one 79° compressibility sample, and one 90° and one 83° resistance sample showed no such effects. The seasoning effects are so striking in some of the other samples, however, that it is difficult to think that the effect is entirely spurious. It may possibly be connected with the rate of cooling, andmaymean that there is some other modification at high temperatures that gets carried down to room temperature into its region of instability by rapid cooling, and that the reaction then runs when the atoms are joggled, as it were, by an application of pressure. The matter requires further examination. The other abnormality, ranges in which the behavior is linear with sharp changes in direction but no discontinuities at the points separating the ranges, is doubtless a real phenomenon, for it is shown by all the high orientations, both in compressibility and resistance. The precise details are not consistent, however, which means that this is a sensitive phenomenon. In general there seem to be three linear ranges at the 90° orientation; as the orientation changes toward zero, these phenomena rapidly disappear, and the crystal becomes normal. Beryllium. This material I owe to the courtesy of Dr. R. Mehl, at the time Director of the Department of Metallurgy of the Naval Research Laboratory at Anacostia, D. C. The material was in the form of a lump approximately 2.5 cm. on a side; the original source was presumably the now defunct Beryllium Corporation of America. The method of formation of this lump is not known to me, but the result was a piece containing one large crystal grain, as could be established by the cleavage, which was quite perfect. This specimen was also distinguished from specimens made earlier in the art by its apparent complete homogeneity, no blow holes, slag inclusions, or

101 —2719

50

BEIDGMAN

other imperfections being evident. Two speeimens were worked out of the lump by grinding, one parallel and one perpendicidar to the axis, each about 7.5 mm. long. Beryllium crystallizes in the hexagonal system, and has therefore a single axis of six-fold symmetry. The compressibility results were unusual for a single crystal in that there was relatively large hysteresis between the readings obtained with increasing and decreasing pressure. The hysteresis was about the same for both speeimens at both temperatures. The width of the hysteresis loop at the maximum amounted to about 2% of the total deformation. The individual points on the ascending and descending branches for the parallel speeimen were regulär within at most one tenth of the width of the loop; the irregularity of the other orientation was three or four times greater. The sign of the hysteresis in the changes of length was the same in both directions, so that there is also a volume hysteresis of approximately the same amount. The direction of the volume hysteresis is normal, that is, a lag, as is demanded by thermodynamics. The numerical results follow: Hexagonal axis parallel to the length, At 30°, - Mjh = 2.20 X lO-'jj - .70 X l O - ' V , At 75°, - MjU = 2.30 X lO-'p - .70 X 1 0 - ' ^ . Hexagonal axis perpendicular to the length, At 30°, - ddjk = 2.82 X - 1.67 X 1 0 " ^ , At 75°, - MIU = 2.82 X lO-'p - 1.70 X lO-^VFrom these results the volume compressibility may be calculated to be: At 30°, - AF/Fo = 7.84 X 10"'? - 4.24 X lO-^V, At 75°, - AF/Fo = 7.94 X 10"'? - 4.31 X 1 0 - ^ I have previously found' for the volume compressibility of a polycrystalline rod 8.55 X 10"'^ - 3.88 X lOr^^p^ at both temperatures. The results are not far different from those above, but indicate that the orientation of the former sample was not completely random. The mean linear thermal expansion between 30° and 75° was found to be: Hex. axis parallel to length, 12.3 to 14.5, average 13.4 X lO""®, Hex. axis perpendicular, 15.2 to 17.0, average 16.1 X 10~®.

101 —2720

PEESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

51

This gives for the volume expansion 45.6 X 10~®. The thermal expansion of Be is not listed in I. C. T. The axial ratio of beryllium is known by X-ray analysis to be 1.585. The ratio for spheres in hexagonal dose packing is 1.63. It wouid be expected therefore that the compressibility of beryllium in the two directions would not differ greatly, as turns out to be the case. Compounds. Gulonic Lactose. This organie substance crystallizes in the orthorhombic system, so that measurements of the linear compressibility in three different directions are necessary to exhaustively characterize the behavior under pressure. I am indebted to Mr. Phelps of the Bureau of Standards for several large clear crystals which had been grown by slow evaporation from aqueous Solution. From these crystals rods varying in length from 6 to 9 mm. were cut in the three independent crystal directions " a , " " b , " and " c , " in the nomenclature of Dana, and the compressibility measured with the lever piezometer in the usual way. Pressure was transmitted directly to the speeimen with kerosene or petroleum ether, previous trijals having shown no perceptible amount of solubility. Regulär readings were made without incident at 30° and 75°. The average arithmetical departure from second degree curves of single readings at 30° and 75° were respectively: " a " direction, 0.22% (14 readings), and 0.29% (13 readings); " b " direction, 0.16% (13 readings), and 0.16% (15 readings);"c" direction, 0.05% (13 readings), and0.07% (13 readings) The results are as follows: 30° 75° " a " direction, -Al/k = 9.69 X 10"'^ - 10.3 X lO-^V; 10.66, - 11.9 "b"direction,°-A///o = 33.95 X 10"'? - 70.2 X 1 0 - ^ : 3 6 . 6 7 , - 81.5 " c " direction, -Al/k = 17.02 X lO-'p - 39.9 X 1 0 - ^ ; 17.36, - 40.1 and by caiculation, for the volume, - AF/Fo

= 60.66 X lO-'p - 132.0 X l O - ' V ; 64.69, - 145.7

Rhamnose. I owe this material like the gulonic lactose, to Mr. Phelps of the Bureau of Standards, who placed at my disposal several clear crystals grown from aqueous Solution. This is monoclinic and strictly specimens in four directions would be required to completely characterize the volume distortion under pressure. Unfortunately there was not enough material available to permit getting the four directions, but only the crystallographic " a , " " b , " and " c " directions

101 — 2 7 2 1

52

BRIDGMAN

could be obtained. However, judging by analogy with sucrose, to be described next, and which is very similar, the missing Y direction is so much like the " a " direction that little is lost by not making a measurement on it. The specimen in the " a " direction was 4 mm. long, in the " b " direction 1.0 cm. long, and in the "c" direction 1.1 cm. The average arithmetical deviations from second degree curves of Single readings at 30° and 75° were respectively: " a " direction 0.38% (16 readings), and 0.23% (15 readings); " b " direction, 0.25% (16 readings), and 0.13% (14 readings); and " c " direction, 0.15% (14 readings), and 0.16% (14 readings). The results follow: 30° 75° " a " direction, - M / k = 35.42 X lO-^p - 61.0 X 10-»V; 37.63, - 71.0 " b " direction,-AZ//o = 21.98 X lO-'j? - 38.4 X 1 0 - ^ : 2 4 . 8 2 , - 53.4 "c" direction, -Al/k = 13.78 X IQ-'p - 33.0 X 1 0 - V ; 14.66, - 35.3 and by calculation, for the approximate change of volume: - AF/Fo = 71.18 X lO-'p - 148.1 X 1 0 " ^ ; 77.11, - 1 7 8 . 1 Sucrose (Cane Sugar). The source of this material was the ordinary " rock candy " of commerce. In a pound a large number of clear Single crystals were found of sufBcient size. This crystallizes in the monoclinic system, like rhamnose, so that four orientations are necessary. The four orientations used were the three crystallographic axes " a," " b," and "c," and the direction perpendicular to b and c, the " Y " axis of Voigt. Since the a axis is inclined at 103° to the c axis, there is a difference of only 13° between it and the Y axis, so that not much difference in compressibility in these directions is to be anticipated. The runs on the four orientations were made without incident of any kind. The " a " sample was 5.0 mm. long, the " b " sample 9.4 mm., the "c" 7.3 mm., and the " Y " 5.6 mm. In spite of the small lengths, the compressibility is so great that large deflections were obtained, and the results are among the most regulär. The average deviations from smooth curves at 30° and 75° respectively were as follows: " a " direction, 0.40 and 0.21%; " b " direction 0.43 and 0.29%; " c " direction 0.37 and 0.32%, and " Y " direction 0.47 and 0.33%. In the following the results are reproduced by second degree formulas, the constants being so chosen as to pass through the end points, and to locate at 6000 kg/cm' the maximum deviation from linearity. But this does not always represent the results within experimental error, and in a number of cases small corrections must be applied; in

101 —2722

PRESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

53

general these corrections have the effect of somewhat increasing the compressibility at low pressures and decreasing it at high pressures as compared with the compressibilities of the second degree formulas. The corrections are given below in the form of deviations from the second degree formulas. " a " direction. 30°. The maximum deviation from linearity is at 5300 instead of at 6000. At 3000, MjU is greater numerically by 0.00005 than is given by the formula, at 6000 less by 0.00007, and at 9000 less by 0.00022. 75 As at 30°, except that at 9000 the compressibility is less by 0.00030 instead of 0.00022. " b " direction. 30°. The second degree formula is sufficiently good. 75°. The maximum deviation from linearity is at 5200 instead of at 6000. At 3000, AljU is 0.00011 greater numerically than given by the formula, and at 9000 less by 0.00017. " c " direction. The second degree formula is sufficiently good at both temperatures. " Y " direction. 30°. The second degree formula is sufficiently good. 75°. The maximum deviation is at 5500 instead of 6000. MjU at 3000 is greater numerically by 0.00014 than given by the formula, and at 75° less by 0.00026. The second degree results are: " a " direction. At 30°, - MIh = 32.74 X 10"'^ - 69.9 X IQ-'Y. At 75°, - Mßo = 33.80 X 10"'^ - 76.3 X 1 0 - ^ " b " direction. At 30°, - Mßo = 14.49 X lO-'p - 24.0 X lO-'VAt 75,° -

Alßo

=

16.98 X

lO-^p -

34.6 X

10"!^.

Alßo

=

22.81 X

lO-'p -

44.4 X

W Y -

" c " direction. At 30°, -

At 75°, - Alßo = 24.74 X 10"'? - 52.9 X lO-^V-

101 —2723

54

BRIDGMAN

" Y " direction. At 30°, - MjU = 32.00 X IQ-'p - 77.5 X At 75°, - MjU = 33.14 X lO-'p - 78.6 X 1 0 - ^ For the volume compressibility, from " b , " " c , " and " Y " : At 30°, - AF/Fo = 69.30 X - lül.l X 10"'V. At 75°, - AF/Fo = 74.86 X lO-'p - 184.2 X lO-'VThe results are seen to be numerically very dose to those for rhamnose, except for a curious reversal of the b and c directions. The thermal expansions were found to be: Direction a b c Y

Mean Linear expansion, 30°-75°. Extreme values 22.5 59.2 55.5 21.3

to to to to

23.3 X lO"« 60.4 58.5 25.3

Average 22.9 X 10^ 59.8 57.0 23.3

The mean volume expansion is thus 140.1 X 10"*. MnCh. This material crystallizes in the hexagonal system, but due to a misapprehension of some sort I originally supposed it to be cubic and it was measured with this idea. I probably would not have measured it if I had realized that it was hexagonal, for the values are only a sort of average, of somewhat indefinite significance. However, the measurements having been made, it seemed worth while to at least record them here. The material in powdered condition was obtained from Eimer and Amend. It was compressed into a slug in the split mold at room temperature. (See a preceding paper for a description of the technique of forming the compressed slugs.) The material is very hygroscopic, and although precautions were taken to prevent the absorption of moisture during preparation of the speeimen, treatment in the dessicator and weighing before and after heating indicated a water content of the compressibility sample of about 1%. Runs were made at 30°, 75°, and 30° again. There was a slight plastic deformation during the runs. This may have been due to two causes: in the first place there may have been some recrystallization, due to the fact that the crystal system is not cubic. In the second place, the water content

101 — 2724

PRESSURE COEFFICIENTS OF RESISTANCE OF ELEMENTS

55

may have allowed some plastic flow under the compressive force exerted by the lever of the piezometer, an effect shown very much more prominently by the copper halides, in connection with which it has been discussed in detail in a preceding paper. This plastic flow was greatest during the flrst run at 30°, and during the flrst two low pressure readings at 75°, and amounted to about 4 % of the maximum effect. I t had entirely disappeared from the second run at 30°, which was the only run at 30° used in the computations. The two first points at 75° were also discarded in the computations. Because of the distortions in the specimen it did not seem worth while to try for the thermal expansion, although this had been measured for most of the other compressed slugs. The average arithmetical departure from a smooth curve of a single one of the 14 readings of compressibility at 30° was 0.14% of the maximum effect, and the corresponding figure for 13 readings at 75° was 0.18%. The results for compressibility are: At 30°, - AF/Fo = 54.09 X 10-''p - 96.3 X 1 0 - ^ . At 75°, - AF/Fo = 55.62 X IQ-^p - 106.5 X 1 0 - V These volume compressibilities were calculated on the assumption of equal linear compressibility in all directions. ZnCh. This crystallizes with the same hexagonal structure as MnCla; I also thought at flrst that this was cubic, and measured the linear compressibility in that misapprehension. The results are recorded here in the same spirit as those for MnC^. ZnCU absorbs normally very large amounts of water. The water was driven off by heating as far as possible, until decomposition appeared to be just beginning, and after that it was kept in a dessicator and worked under Nujol. But according to Mellor's Chemical Handbook, it is impossible to remove all the water by heating, and the measurements bore this out. The material was formed into a compressed slug by the technique of most of the materials of the preceding paper. Measurements were attempted only at 30°. There were enormous permanent changes of zero after each application of pressure, of which three were made altogether. Whether the permanent changes are a regrowth phenomenon connected with the water still remaining and the compressive force exerted by the lever of the piezometer, or whether they are a consequence of the non-cubic nature of the crystal, I did not attempt to decide. I t seemed signiflcant, however, that the three sets of readings with increasing pressure agreed approximately, the permanent

101 —2725

56

BRIDGMAN

change taking place only on decreasing pressure. The readings on the second application of increasing pressure were made with the usual care, and showed an unusually high degree of regularity, the average arithmetical deviation from a second degree curve of a single one of the 8 readings being only 0.04% of the maximum effect. The volume change was calculated from the change of length by assuming equal compressibility in all directions, and is given for what it is Worth: At 30°, - AF/Fo = 41.40 X 10"'^ - 107.7 X 1 0 " ^ . AI2O3, Synthetic Sapphire. The material was obtained from G. Everett March, a dealer in synthetic jewels of Chicago, who specially selected it from his stock. I t was fumished in the form of a disc about 1.3 cm. in diameter and 3 mm. thick, the crystal axis being stated to be parallel to the plane of the disc. In appearance it was perfectly transparent and flawless. The Statement about the orientation of the axis was most kindly checked for me by Professor E. S. Larsen of the Department of Mineralogy of Harvard University by optical examination, and the precise position of the axis determined. The disc was then cut without incident with a saw charged with diamond powder into rods for the compressibility measurements, a Single rod 1.26 cm. long for the specimen parallel to the direction of the axis, and two pieces each 0.42 cm. long for the perpendicular orientation. These two pieces were placed end to end for the measurements. The compressibility of the parallel sample gave an irregulär curve, which could be reproduced within the error of measurement by a broken straight line, rather than the usual smooth curve. The experimental points at 30° and 75° are reproduced in Figure 8. At 30°, two complete runs were made, the first to 12000 and back with 12 readings, followed by the second with 30 readings. There was also an initial seasoning application of 12000, after which the change of zero was slightly less than after the third application of 12000, and within the limit of error of the other readings. It appears, therefore, that the effects are reproducible, approximately single valued and without hysteresis, and are not accomodation effects, but are truly characteristic of the material. At 75°, only a single application of pressure was made, but with the readings much more closely spaced than usual, 44 in all instead of the usual 14. There now appears to be a slight hysteresis between increasing and decreasing pressure, but it probably is not significant, and is of different sign at the higher and lower ends of the pressure ränge.

101 —2726

PEESSUBE COEFFICIENTS OF KESISTANCE OP ELEMENTS

57

I n Order to reproduce the results within experimental error, it is

sufficient to give the pressures at which the breaks in the curves of Figure 8 occur, and Üie changes of length at these pressures. Between the successive points of break the relation between pressure and change of length is linear.

0 ^ 0

^

+32.06

+13.86 X 10-

ELECTHICAL BESI8TANCK OF SINGLE METAL CHYSTALS

109

men was 1.2% of the maximum at CO2 temperature, and the maxiinum deviation by the 87° specimen 7% at liquid O2 temperature. The descending points only were used, as in the case of bismuth, and again the average deviation from a smooth eurve was inappreciable on the graphical scale employed, and was not more than a fraction of a tenth of a per cent. The results are given in Table V. Arsenic. I t has not yet been found possible to prepare single crystals of dimensions suitable for the low temperature apparatus in which the cleavage plane runs across the rod at any eonsiderable angle. These measurements refer to only a single orientation with the cleavage plane parallel to the length. In a previous paper® measurements have been given at 0° and 95° C for the resistance of single crystal arsenic up to 12000 kg/cm^. The specimen used here was the same as one of the pieces previously measured. Arsenic is highly anomalous; both compressibility and electrical resistance in the direction of the cleavage plane (that is, the direction measured here) showing breaks, the interval from 0 to 12000 kg/cm" consisting of ranges in each of which the dimensions or resistance vary linearly with pressure, with different slopes in the different ranges. These anomalous effects rapidly disappear as the orientation swings toward the perpendicular. Exactly the same phenomenon was found at CO2 and liquid O2 temperatures. One break in the slope of the curve giving resistance as a function of pressure occurs at each temperature in the pressure ränge up to 7000. Previously two breaks had been found up to 12000, which means three linear ranges. The middle ränge was shorter and somewhat more in doubt as compared with the two extreme ranges. It is not possible to say whether the two ranges found now at the lower temperatures correspond to the two low pressure ranges of the higher temperatures or whether the former middle ränge has been so displaced by temperature as to be absorbed by the low and the high pressure ranges. The latter seems to me somewhat the more probable. At CO2 temperature there were eonsiderable seasoning effects at the low pressures, as is usual, so that the points obtained with increasing pressure did not show a very distinct break. The pomts with decreasing pressure, however, lay without question on two rather well marked different lines. At liquid O2 temperature the seasoning effects were less, and the location of the break between the two separate ranges could be established with more certainty.

102 — 2779

G

I

TABLE V. ANTIMONT. Angle between axis and length

Temp. "C

0° 87°

-

78°.26

-182°.76

Relative Effect of Pressure on Measured Resistance

Average Coefficient of Measured Resistance 0-7000 kg/cm«

Relative Effect of Pressure on Specific Resistance

p

Rens

p

0 1000 2000 3000 4000 5000 6000 7000

1.0000 1.0055 1.0154 1.0290 1.0457 1.0651 1.0852 1.1057

0 1000 2000 3000 4000 5000 6000 7000

1.0000 1.0039 1.0122 1.0240 1.0391 1.0569 1.0753 1.0942

0 1000 2000 3000 4000 5000 6000 7000

1.0000 1.0032 1.0148 1.0393 1.0770 1.1240 1.1763 1.2344

0 1000 2000 3000 4000 5000 6000 7000

1.0000 l.OOlC 1.0115 1.0344 1.0704 1.1158 1.1664 1.2229

+15.10X10-»

+33.49

Resis

Specific Relative Resistance Specific ResistatO Pressure ance at 0 Pressure 38.63X10-« 1.0000 bd

2 24.67

.6390

8.70

.2251

ö Q

s. >

55

TABLE V.—Antimony.—Con«7iu«d. Angle between axis and length

Temp.

Relative EfiFect of Pressure on Measured Resistance

Average Coefficient of Measured Resistance 0-7000 kg/cm^

Relative Effect of Pressure on Specific Resistance

Rests 41°

-

78°.32

-182°.70

0 1000 2000 3000 4000 6000 6000 7000

1.0000 1.0115 1.0272 1.0475 1.0716 1.0985 1.1277 1.1593

0 1000 2000 3000 4000 dOOO 6000 7000

1.0000 1.0057 "1.0210 1.0490 1.0917 1.1430 1.2010 1.2636

+22.61

+37.66

Resis

33.28

1.0000

0 1000 2000 3000 4000 5000 6000 7000

1.0000 1.0133 1.0309 1.0530 1.0790 1.1077 1.1387 1.1722

21.20

.6374

0 1000 2000 3000 4000 äOOO 6000 7000

1.0000 1.0075 1.0247 1.0544 10991 1.1522 1.2120 1.2765

0°

90°

g

I

(o M 00

78°.30

Specific Relative Resistance Specific Resistat 0 Pressure ance at 0 Pressure

0 1000 2000 3000 4000 5000 6000 7000

1.0000 1.0039 1.0121 1.0239 1.0390 1.0567 1.0750 1.0940

w r

^ 2 o ^ w

t 2! O t?3 O

7.525

.2262

2! ffl s g

g 38.66

1.0000

24.69

.6390

o S) «!

s

I 00 to

T A B L E V.—Antimont.—Coniinued. Angle between axis and length 90°

Temp. "C

- 1 8 2 ° 80

Relative Effect of ^ s s u r e on Measured Resistance

Average Coefficient of Measured Resistance 0-7000 kg/cm'

Relative Effect of Pressure on Specific Resistance V 0 1000 2000 3000 4000 5000 6000 7000

Rena 1.0000 1.0016 1.0114 1.0343 1.0703 1.1157 1.1662 1.2227

78°.30

-182°.80

8.706

0 1000 2000 3000 4000 5000 6000 7000

1.0000 1.0228 1.0498 1.0823 1.1193 1.1590 1.2027 1.2510

0 1000 2000 3000 4000 5000 6000 7000

1.0000 1.0134 1.0378 1.0743 1.1275 1.1884 1.2573 1.3298

lo

.2251

W 29.23

0°

-

Specific Relative Resistance Specific ResistatO Pressure ance at 0 Pressure

1.0000

33 o s

>• 18.55

6.631

.6362

.2269

ELECTRICAL RESISTANCE OF SINGLE METAL CRYSTALS RELATIVE

(O Ol

•0

>> 7i

(O

0>

113

RESISTANCE

vo

00

ro

m in * (fl cö ^

0)

(O j i

m m Q o H

n

Ü1

yi

• »

0)

FIQURE 1. Relative resistance at — agonal axis perpendicular to the length.

8 2 . 8 ' of Single crystal arsenic, hex-

102 — 2783

114

BBIDGMAN

The experimental points at liquid O2 temperature are shown in Figure 1. The ranges and the coeflScients are as follows: As, axis perpendicular to length. -

78.3°, 0 - 3540, Aß/Ä (0, -

78°.3) = - 1.92 X 10"^^.

3540 - 7000, AR/R (0, -

78°.3) = - 3.24 X 10"^?.

- 182.8° 0 - 2360, Aß/Ä (0, - 182°.8) = - 3.34 X 2360 - 7000, AR/R (0, - 182°.8) = - 8.86 X lO^p. The relative resistances at atmospherie pressure at these temperatures were respectively .6501 and .2114 in terms of the resistance at 0° C at atmospherie pressure as unity. The pressure at which the first break occurs is a more or less well defined function of pressure. The numerical values are as follows: Pressure 7100 kg/cm2 5500 3540 2360

Temperature 75° C 0 - 78.3 - 182.8

If these points are plotted, a fair straight line will be obtained passing through 0° Abs. Tellurium. The crystals were made from "Kahlbaum" material. They were cast in pyrex tubes of about 1.2 mm. diameter like the other metals. One casting proved sufficient, so that the two pieces measured below are different orientations from the identical crystal. The furnace was filled with a protecting atmosphere of CO2 during the filling of the tube, and the rate of lowering was about 10 cm. per hour. The cleavage system of tellurium differs from that of the other metals of this paper in that there are three planes of easy cleavage, instead of one, each of the three planes being parallel to the trigonal axis, so that the intersections of the three planes form trianguIar prisms with edges parallel to the axis. Unless the axis is very nearly parallel to the length, one of the three cleavage planes will cut across the rod at a fairly high angle, which means, in rods of this small diameter, very easy fracture. The usual method of grinding away the glass tubes proved to be too severe, resulting in frequent breaking. The method finally adopted was to dissolve away the glass in hydrofluoric acid, the tellurium fortunately proving not to be attacked. The crystals obtained in this way were highly satisfactory in appear-

102 — 2784

ELECTKICAL KESISTANCE OF SINGLE METAL CRYSTALS

115

ance, with clean mirror-like cleavage planes, and were much better than I have ever obtained before. The improvement is probably to be ascribed partly to higher purity in the material, and partly to the smaller diameter. Some difBculty was encountered in attaching the leads. Tellurium cannot be soldered, but it is known to stick directly to copper or platinum, when these are heated hot enough to melt their way into the tellurium. Platinum leads were attached by fusing in this way, but although they proved satisfactory on the initial application of pressure, high resistance developed on subsequent applications, doubtless an effect of cracking due to differential compressibility between tellurium and platinum. Experiment showed that silver very readily alloys with tellurium, in fact, the alloying action is so rapid that fine silver wires cannot be fused into the tellurium, but melt back and drop off. Finally fine platinum wire (0.005 cm. in diameter) was first coated with silver by fusing the silver, and then melted into the tellurium with a diminutive loop of nichrome heated to incandescence. This was entirely satisfactory; apparently the thin layer of alloy on the surface of the platinum is so tenacious as not to be entirely cracked by the differential compressibility. The specific resistance of tellurium is so high that a modification of the regulär Potentiometer method of measurement was necessary. The simplest modification imaginable proved satisfactory. The potential drop across the tellurium under a known current was equalized to the Potential drop produced by the same current across a variable resistance. An easy modification of the regulär potentiometer connections proved feasible, which it is not necessary to describe in further detail. The effect of pressure on the resistance of single crystal tellurium has not been measured previously because suitable specimens had not been available. The usual measurements at — 78.3° and —182.8° were therefore supplemented by a run at 0° C in the low pressure apparatus, pressure transmitted with nitrogen, to a maximum of 7000 kg/cm^. The results obtained were so interesting, showing very large changes of resistance with both temperattire and pressure, that it appeared desirable to extend the pressure and temperature ränge. The specimens were therefore set up in the regulär high pressure apparatus, and the run at 0° repeated to 12000, petroleum ether transmitting the pressure, and a similar run was made at 95°. The effects are so large that the logarithm of the resistance may be conveniently shown as a function of pressure rather than the re-

102 — 2785

116

BRIDGMAN 1

.0


X

\

\ \

J - ' 1.0

\

\

S

V

\

\ \95-

\

-1.6

s.

\

-\ß

-2.0 4

6

8

10

12

Pressube.Thousanos of TFE,

AXIS

86°TO LEN6TH

Figubb 2. Logarith to the base 10 of the relative resistance of Single crystal tellurium, axis 86° to the length, as a function of pressure at several temperaturea.

102 — 2786

ELECTRICAL RESISTANCE OF SINGLE METAL CEYSTALS

117

1

-,2

v j

\

- 4

U

(n v> tu

-.8

\

-iszTs'

\

\

U

U u Cl^

s

\

§ -1.2

-14

\

-lÄ

\

\

\

\

\

-1.0 X -2.0

X 2

4

Pressure, TC., AXIS

O Thousanos 23.5°

TO

8

lO

12

of» LeNQTH.

Fiqube 3. Logaritbm to the base 10 of the relative resistance of single crystal teUurium, axis 23.5° to the length, as a function of pressure at several temperatures.

102 — 2787

118

BKIDGMAN

sistance itself. These are shown for the two orientations, axes at 86° and 23.5° to the length, in Figures 2 and 3. The ascending and descending branches lay so closely together in general that no attempt was made to separate them in the figures. The low temperature run of the 23.5° orientation does, however, show some divergence; the points with decreasing pressure are the high lying points. It is to be noticed that the two independent runs at 0° lie on the same curve T A B L E VI. Tellüeium. Pressure kg/cm«

logio (Ä/flo) (measured) -182°.8 -78°.3

0°

logio (p/po) (specific) 95°

-182°.8 -78°.3

0°

95°

-.032 -.079 -.127 -.177 -.229 -.286 -.350 -.418

.000 - .107 - .229 - .356 - .489 - .631 - .771 - .907 -1.037 -1.163 -1.289 -1.406 -1.518

- .541 - .702 - .853 - .990 -1.121 -1.244 -1.362 -1.477 -1.581 -1.680 -1.774 -1.863 -1.950

+.047 +.010 -.028 -.071 -.117 -.168 -.227 -.296

.000 - .111 - .229 - .350 - .478 - .610 - .738 - .864 - .983 -1.090 -1.198 -1.304 -1.408

- .582 - .722 - .853 - .979 -1.099 -1.212 -1.317 -1.416 -1.509 -1.601 -1.687 -1.765 -1.839

86° between axis and length 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

-.213 -.262 -.310 -.357 -.406 -.454 -.503 -.553

-.032 -.079 -.127 -.177 -.230 -.287 -.351 -.419

.000 - .107 - .229 - .356 - .490 - .632 - .772 - .908 -1.038 -1.164 -1.290 -1.408 -1.520

- .541 - .702 - .853 - .990 -1.122 -1.245 -1.363 -1.478 -1.582 -1.681 -1.776 -1.865 -1.952

-.213 -.262 -.310 -.357 -.405 -.453 -.502 -.552

23°.5 between axis and length 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

102 — 2788

-.135 -.175 -.215 -.255 -.295 -.336 -.376 -.416

+.047 +.005 -.038 -.086 -.137 -.193 -.257 -.330

.000 - .116 - .239 - .365 - .498 - .635 - .768 - .898 -1.022 -1.134 -1.246 -1.357 -1.465

- .582 - .727 - .863 - .994 -1.119 -1.237 -1.347 -1.450 -1.548 -1.645 -1.735 -1.818 -1.896

-.135 -.170 -.205 -.240 -.275 -.311 -.346 -.382

ELECTBICAL RESISTANCE OF SINGLE METAL CRYSTALS

119

indistinguishably. The numerical values of the logarithm of the relative resistance are given in Table VI in terms of the resistance at atmospheric pressure at 0° C of the two orientations. The table also contains the logarithms of the relative specific resistances, that is, the measured resistance corrected for the effeet of pressure on dimensions. The relative specific resistances at atmospheric pressure have not, however, been corrected for the effeet of thermal contraction. It will be noticed that the correction for distortion is almost negligible for the 86° orientation, but quite perceptible for the 23.5° orientation. T A B L E VII. TELLUKIDM.

Pressure kg/cm^

Logiop 0° between axis and length -182°.8 -78°.3

0 1000 2000 3000 4000 6000 6000 7000 8000 9000 10000 11000 12000

-.564 -.592 -.625 -.658 -.690 -.721 -.752 -.790

-.389 -.413 -.449 -.489 -.533 -.585 -.642 -.712

0°

95°

- .450 - .561 - .678 - .799 - .923 -1.053 -1.177 -1.300 -1.416 -1.519 -1.622 -1.723 -1.827

-1.046 -1.178 -1.303 -1.425 -1.541 -1.652 -1.752 -1.848 -1.935 -2.027 -2.111 -2.186 -2.257

Logio p 90° between axis and length -182°.8 -78°.3 -.417 -.466 -.515 -.562 -.610 -.658 -.707 -.757

-.236 -.283 -.331 -.381 -.434 -.491 -.555 -.623

0°

95°

- .204 - .311 - .433 - .560 - .693 - .835 - .975 -1.111 -1.241 -1.367 -1.493 -1.6X0 -1.722

- .745 - .907 -1.057 -1.194 -1.325 -1.448 -1.566 -1.681 -1.785 -1.884 -1.978 -2.067 -2.154

Table V I I contains the logarithms of the actual specific resistances for the 0° and the 90° orientations, caiculated by the same methods as for the other metals. DISCUSSION.

This discussion will at first not be concerned with tellurium, which is only partially metallic in character, reserving this for later. Considering now only the true metals, the general effeet of lowering temperature is the same as that found previously for the cubic metals.' In all cases, that is, for every orientation of every metal,

102 — 2789

120

BKIDGMAN

the pressure coefficient at liquid oxygen temperature is greater numerically than at CO2 temperature; this holds both for the more normal metals and for arsenic, the resistance of which decreases with pressure, and also for bismuth and antimony with positive pressure coefRcients. Excepting arsenic, the largest temperature effect is shown by the 90° orientation of antimony, the pressure coefficient of which at liquid O« temperature is more than double that at CO2 temperature. These remarks apply to the linear term in the power series development in those cases in which such a development is possible. The second degree terms do not show any such regularity, but may either increase or decrease with decreasing temperature. Arsenic is anomalous because of the breaks in its pressure coefficient. Its coefficient in the upper pressure ränge at liquid O2 temperature is of the Order of three times greater than in any other ränge. It is significant that in those cases in which departure from the second degree relation can be established the curvature becomes greater at increased pressure, provided the resistance decreases. On the other hand, bismuth and antimony, the resistance of which increases with pressure, have a decreasing curvature with increasing pressure. This result for the normal metals would suggest that the suspected minimum of resistance is nearer than would be indicated by an extrapolation of the second degree curves. The accuracy of the previous measurements for the cubic metals was not sufficient to indicate any such effect for them, and in fact most of the former results were linear. A question which could not be put with regard to the cubic metals now presents itself, the question namely as to the relative effect of pressure on resistance in different directions. Is the effect of pressme to make the resistance in different directions more nearly alike, or does it accentuate the difference? The question can be answered at once by forming the derivative:

F d p ~ — d p \ Pso" / Pw

dpo" Po° dj)

1 dpM" P9o° dp

We therefore have merely to take the difference of pressure coefficients in the two directions. When the ratio PoVPao» { —F) is greater than unity, a negative value for the right hand side of the equation means that the resistance becomes more nearly equal under pressure. The results are given in Table VIII.

102 — 2790

121

ELECTRICAL R E S I S T A N C E OF S I N G L E METAL CRYSTAL8 T A B L E

VIII.

E F F E C T O F P K E S S T T R E ON R A T I O OP R E S I S T A N C E I N D I F F E R E N T D I R E C T I O N S IN T H E CRTSTAI-.

1 dF

Substance

Temp.

Zn

- 78°.3 -182°.8

-4.05X10-«p+14.4X10-'y - 3.49 X 10-«p+11.5 X 1 0 - V

1.038

Cd

- TS'-.S -182°.8

- 3.35 X 10-«p+17.3 X l O - ' y -2.04X10-»p+4.8 X I O - V

1.207

Sn

- 78°.3 -182°.8

-0.22X10-«p+ 3.4X10-V -0.83X10--o'|o'.f2S?7'?acid 75 "C 25-C 25'C 75-C 25"C 75-C 1.0255 1.0148 1.0050 .9962 .9880 .9726 .9593 .9467 .9352 .9153 .8984 .8842

1.0300 1.0214 1.0130 .9967 .9824 .9689 .9566 .9359 .9187 .9039 .8905 .8784

1.0490 1.0370 1.0254 1.0149 1.0050 .9878 .9722 .9583 .9451 .9227 .9028 .8848

1.0747 1.0635 1.0533 1.0437 1.0344 1.0171 1.0016 .9873 .9739

1.0530 1.0426 1.0324 1.0143 .9981 .9836 .9701 .9460 .9258 .9079 .8921 .8780

had shown no iron before the run. However, the original material from which the acid was purified was known to contain some iron, so that it is perhaps possible that iron may have been initially present in the Solution in a form undetectible by the conventional test and then transformed by pressure into a detectible form. Any irregularities of this nature are, however, entirely too small to change appreciably the results when shown on the scale of magnitude of the figures, and any conclusions to be drawn here will not be affected. But a complete thermodynamic discussion of the properties of solutions under pressure, such for example as that recently given by Adams and Gibson' at the Geophysical Laboratory in deducing the solubility limits, demands that differentiations be performed with respect to the various variables, pressure, temperature and composition. Care should be used in subjecting the data of this paper to Operations of this sort, and conclusions drawn from such Operations should be carefully examined. The results were computed according to methods already described, which give immediately the relative volumes, the volume of each Solution at 25° at atmospheric pressure being taken as unity. For purposes of discussion the results may be presented in many ways, depending on the use to which they are to be put. It has seemed that perhaps the best general idea of the nature of the results is given by tabulating the volumes, as function of pressure, temperature and concentration, of thatamount ' L. H. Adams and R. E. Gibson, J. Am. Chem. Soc. 52, 4252 (1930). R. E. Gibson and L. H. Adams, ibid. SS, 2679 (1933). L. H. Adams, ibid. S3. 3769 (1931); 54, 2229 (1932).

2.0 Molal 25»C

75°C

1.1015 1.0909 1.0807 1.0713 1.0620 1.0442 1.0279 1.0141 1.0006 .9785 .9596 .9424

1.0822 1.0723 1.0628 1.0444 1.0277 1.0129 .9993

2.5 Molal Vol n f / ' S " ^ t "

1.1051 1.0954 1.0860 1.0683 1.0528 1.0394 1.0258 1.0039 .9845 .9666 .9501 .9350

1.1307 1.1191 1.1081 1.0978 1.0880 I.070S 1.0551 1.0409 1.0278 1.0045 .9838

1.1356 1.1254 1.1152 1.0969 1.0808 1.0664 1.0535 1.0296 1.0089 .9901 .9736 .9587

of Solution which contains one gram of water. In comparing solutions of dififerent strengths the water factor thus remains constant, and the difference is due to the dififerent amounts of acid. The results. are presented in this form in Table I for glycine. Table II for a-amino butyric TABLE II. Volume of a-amino butyric acid solutions.

Pressure kg/cra> 1 250 500 750 lOOO 1500 2000 2500 3000 4000 5000 6000 7000 8000

Pure W a t e r Vol. of 1 g 25"C 75 • € 1.0029 .9929 .9834 .9741 .9657 .9494 .9355 .9232 .9119 .8918 .8739 .8578 .8428 .8289

1.0055 .9969 .9885 .9729 .9578 .9444 .9325 .9117 .8938 .8777 .8698 .8509

0.5 Molal l g water 0.0537 g acid 25°C 75-C

Vol. of

1.042S 1.0301 1.0189 1.0094 1.0009 .9863 .9732 .9613 .9504 .9301 .9115 .8968 .8834 .8714

1.0449 1.0351 1.0263 1.0108 .9970 .9841 .9725 .9527 .9339 .9172

l.S Molal 1 g water 0.1751 g acid 25 »C 75 °C

Vol. of

1.1324 1.1213 1.1109 1.1016 1.0933 1.0784 1.0649 1.0518 1.0385 1.0141

1.1394 1.1298 1.1206 1.1038 1.0894 1.0764 1.0635 1.0387

acid, and Table III for «-amino caproic acid. In recalculating the results for presentation in this form in the tables the densities of the solutions at 25° and atmospheric pressure and the molecular weights were involved. It is possible to reconstruct the densities from the values given in the tables, but for convenience they are given here explicitly; they were originally determined in Dr. Cohn's laboratory, and are still partially unpublished.

0.5 1.0 1.5 2.0 2.5

Glycine M 1.01268 1.02822 1.04303 1.05775 1.07181

Densities a-amino 0.5 M 1.5

at 25°C. butyric 1.01075 1.03767

«-ammo caproic 0.5 M 1.01041 1.0 1.02338 1.5 1.03620 1.75 1.04221 1.04822 2.0 2.5 1.06016

105 — 2803

38

P.

W .

B R I D G M A N

T A B L E I I I . Volume

Pressure kg/cm>

1 250 500 750 1000 1500 2000 2500 3000 4000 5000 6000 7000 8000

Pure W a t e r Vol. of 1 B 25 °C

75-C

1.0029 .9929 .9834 .9741 .9657 .9494 .9355 .9232 .9119 .8918 .8739 .8578 .8428 .8289

1.0055 .9969 .9885 .9729 .9578 .9444 .9325 .9117 .8938 .8777 .8698 .8509

oj t-amino

R .

caproic

B .

acid

D O W solutions.

1.0 Molal 1.5 Molal 1.75 Molal 2.5 Molal 0.5 Molal 2.0 Molal 1 g water 1 g water 1 g water 1 g water 1 g water 1 g water Vol. of 0.0694 g Vol. of 0.1469 g Vol. of 0.2342 g Vol. of 0.2823 g Vol. of 0.3336 g Vol. of 0.4476 g acid acid acid acid acid acid 25 "C 75 •€ 25°C 75 »C 25«C 25 "C 75 " 0 75 «C 25'C 75-C 25 "C 75 °C 1.0583 1.0473 1.0369 1.0274 1.0181 1.0012 .9857 .9721 .9595 .9368

1.0632 1.0537 1.0448 1.0278 1.0118 .9972 .9840 .9616 .9432 .9275

1.1207 1.1073 1.0946 1.0827 1.0721 1.0537 1.0381 1.0237 1.0099 .9849 .9633 .9446 .9269 .9112

1.1281 1.1157 1.1043 1.0836 1.0663 1.0507 1.0363 1.0108 .9889 .9688 .9509 .9346

The molecular weights used in the calculations were, respectively, 75.047, 103.077 and 131.108. The "apparent molal volume" of the acid in Solution may be readily obtained from the data in the tables. The apparent molal volume is defined as the difference between the volume of that amount of Solution in which is dissolved one gram molecule of the acid and the volume in the pure State of the amount of water contained in the same Solution. T o illustrate the method of calculation, the apparent molal volume of glycine in 0.5 molal Solution at 25° is obtained by subtracting the volume of pure water listed in column 2 of Table I from the volume of the 0.5 M Solution listed in column 4, and multiplying the difference by 75.047/0.03847. The apparent molal volumes at 25°, calculated in this way, of the three solutions are shown in Figs. 1 to 3 as a function of pressure. If there were no interaction between the water and the acid in the Solution, that is, if our calculation of the apparent molal volume had been applied not to the Solution but to a Compound system containing pure water and the solid acid, the curves of apparent molal volume against pressure would have been the same for all concentrations, and would fall smoothly with pressure, the slope being a measure of the compressibility of the solid. The failure of the curves to possess this simple property is due to the interaction between water and acid in the Solution. The State of affairs in the Solution as revealed by these curves is most complicated, so complicated that it would be hopeless, in the present condition of the theory of solutions, to attempt

105 — 2804

A N D

1.1913 1.1818 1.1726 1.1637 1.1557 1.1403 1.1267 1.1143 1.1026 1.0822 1.0642 1.0490 1.0348 1.0218

1.1967 1.1873 1.1784 1.1629 1.1486 1.1356 1.1237 1.1022 1.0829 1.0663 1.0518 1.0391

1.2307 1.2204 1.2106 1.2018 1.1937 1.1790 1.1658 1.1535 1.1425 1.1225 1.1044 1.0884 1.0732 1.0572

1.2370 1.2281 1.2196 1.2047 1.1900 1.1764 1.1644 1.1432 1.1249 1.1084 1.0934 1.0797

1.2723 1.2610 1.2502 1.2407 1.230S 1.2130 1.1973 1.1838 1.1698 1.1463 1.1253 1.1057 1.0872 1.0697

1.2822 1.2706 1.2607 1.2419 1.2248 1.2098 1.1954 1.1713 1.1498 1.1301 1.1121 1.0940

1.3655 1.3S42 1.3435 1.3336 1.3240 1.3086 1.2914 1.2763 1.2646 1.2406 1.2206 1.2021

1.3712 1.3607 1.3506 1.3324 1.3156 1.3006 1.2870 1.2627 1.2417 1.2226 1.2065 1.1919

a detailed explanation of all the features; all that will be attempted will be a qualitative comment on a couple of the most striking features. In one important particular the behavior of these three acid solutions ander pressure is sharply different from that of all other solutions hitherto investigated. The curve of apparent molal volume against pressure of solutions of electrolytes and those few non-electrolytes which have been measured rises over the entire ränge of pressure, except possibly in a very few cases at the highest pressures. This result for ordinary electrolytes at first appears paradoxical, for it means that the apparent molal compressibility of the dissolved substance, defined as the negative pressure derivative of the apparent molal volume is negative. This paradoxical result receives qualitative explanation in Tammann's theory of solutions, which is that any aqueous Solution behaves approximately like pure water under some higher pressure. The essential role of the dissolved substance according to this picture is merely to increase the internal pressure of the solvent water by a fixed amount; except for this the dissolved substance acts as an inert addendum to the system with constant volume. T h e negative apparent molal compressibility of the dissolved substance is a consequence of this hypothesis, as a little algebra shows at once, utilizing the fact that the compressibility of water decreases with increasing pressure. A second approximation would add to the compressibility of the water at a higher pressure the compressibility of the dissolved substance, but this is small for such typical solutes as NaCl,

C O M P R E S S I B I L I T I E S

lUUÜ

2000

OF

A M I N O

3ÜÜU 4000 Pressure, Kg / Cm'

39

A C I D S

5000

6000

FIG. 1. The apparent molal volumes at 25°C of glycine as a function of pressure. The figures on the curves give the molal concentrations.

1000

2000

3000

4000 5000 Pressure. Kg jCm.'

6000

7000

8000

FIG. 2. The apparent molal volumes at 2S''C o( a-amino butyric acid as a function of pressure. The figures on the curves give the molal concentrations.

1000

2000

3000

4000 5000 Pressure, Kg / Cm'

6000

7000

8000

FIG. 3. The apparent molal volumes at 25°C of t-amino caproic acid as a function of pressure. The figures on the curves give the molal concentrations.

105 — 2805

40

P.

W.

BRIDGMAN

and the Situation is dominated by the water. Contrasted to this almost universal behavior is the behavior of these solutions of Zwitterions. The initial slopes at practically all concentrations of the curves of apparent voIume against pressure are negative, that is, the apparent compressibility of the dissolved substance is positive. Expressed in terms of Tammann's theory this would mean that the effect of the dissolved substance is here to decrease the internal pressure of the water, instead of to increase it. It seems not unreasonable that such a decrease of internal pressure is to be correlated with the dielectric behavior of these solutions. It has been established by the work of Wyman* and others that the dielectric constant of a Solution of a Zwitterion in water is higher than the already high dielectric constant of the water. An increase of dielectric constant means a decrease of the intensity of the forces arising from electric charges, and hence a diminution of that part of the internal pressure arising from forces between electric charges separated by distances so great that the intervening medium acts as an approximately homogeneous medium with the mean dielectric constant. This, however, can be only one of the features in the Situation, for it is known that solutions of urea, which are unusual in that they increase the dielectric constant of water, are normal in that the urea in Solution has a negative, although abnormally low, apparent molal compressibility. Furthermore, the second approximation, which takes account of the compressibility of the dissolved substance, may reasonably be expected to be important when the dissolved molecule is as large as it is here. Unfortunately the compressibility of none of these acids has been determined in the solid State; we may guess that the order of magnitude of the compressibility would not be far different from that of a number of other solid organic Compounds, which lose about 1.5 percent in volume at 1000 kg/cmK An effect of this magnitude would account for a large part of the initial slope of the curves for the more concentrated solutions. «Jeffries Wyman, Jr., Phys. Rev. 35, 623 (1930); J. Biol. Chem. 90, 434 (1931); J. Am. Chem. Soc. 56, 536 (1934). Jeffries Wyman, Jr., and T. L. McMeekin, J. Am. Chem. Soc. 55, 908, 915 (1933).

105 — 2806

AND

R.

B.

DOW

At low pressures the behavior of the more concentrated solutions approaches more closely to that of normal electrolytes than does that of the weaker solutions, that is, the apparent molal compressibility of the more concentrated solutions is less strongly positive. At concentrations beyond 1.0 molal there is a striking tendency for the curves of apparent molal volume to become relatively independent of concentration, and in fact to approach the behavior of a system in which there is no interaction between water and acid. But in the concentration ränge between 0 and 1.0 molal the behavior at constant pressure as a function of concentration is evidently highly complicated. In particular, the volume is very far from being a linear function of c*, and in fact this relation fails even at atmospheric pressure, although the relation is satisfied for practically all other substances. Neither is apparent molal volume any more approximately a linear function of c. Scatchard and Kirkwood' have recently verified the conclusion that in dilute solutions the effect of a Zwitterion should be proportional to the first power of the concentration rather than to its square root. Resemblances would be expected between the behavior of glycine and a-amino butyric acid because of the resemblances of structure. A glance at the structural formulas shows that the electrically active parts of the two molecules are identical, a-amino butyric acid diflering from glycine only in that it carries attached to it an inert tail; that is, the polar moments of these two acids must be nearly the same. At the 0.5 molal concentration the similarity in the behavior of these two substances is striking; both curves have a sharp initial drop, a rise to a maximum, followed by a drop to a second minimum, and ultimately at high pressures a continued rise, which means that the apparent molal compressibility ultimately becomes negative, which is typical of other substances. The curves at 1.5 molal, the only other concentration measured for the a-amino butyric acid, are much more featureless than the curves for 0.5 molal, and differ no more in absolute terms. Contrasted with these, the moment of c-amino caproic acid ' G. Scatchard and J. G. Kirkwood, Phys. Zeits. 33, 297 (1932).

COMPRESSIBILITIES

must be very materially larger, as shown by its structure, and one would therefore be prepared for qualitative differences in behavior. The most marked difference in behavior is seen to be a t the lowest concentration. Another line of comparison suggests itself. Glycine differs from a-amino butyric acid only in the presence of a C2H4 group. The difference of the molal volumes of corresponding solutions may therefore be described as the contribution to the volume of CjH«, and if the comparison is made a t different pressures, the volume of the C2H4 group is obtained as a function of pressure. A simple calculation shows t h a t in 0.5 M Solution the volume of the C 2 H 4 group decreases from 31.91 a t atmospheric pressure to 28.41 a t 3000 kg/cm^, whereas in 1.5 M Solution it increases from 31.70 at atmospheric to 36.05 a t 3000. Similar calculations may be made for other groups of Compounds. Thus from the compressibility of the propyl and amyl halides,® the volume of the CjH4 group may be obtained as a function of pressure by subtraction. I t turns out that in these Compounds the volume decreases with pressure by roughly the same amount in the chloride, bromide and iodide, which is as one might expect, and surprisingly enough the volumes are about the same as in the 0.5 M Solution. From this point of view the 0.5 M Solution is therefore more nearly normal than the 1.5 M Solution, although the apparentvolume curve against pressure of the 1.5 M Solution is much more regulär than t h a t of the 0.5 M Solution. A study of the thermal expansion discioses only complications which are probably too great to a t t e m p t to unravel a t present; such complications would be expected in view of the complications already found with respect to pressure. In very broad comment, the thermal expansion shows a very much smaller tendency to become less a t high pressures than it does for normal organic substances; this is a property of the water in the Solution which was already known. »P. W. Bridgman, Proc. Am. Acad. Sei. 68, 1 (1933).

OF

AMINO

ACIDS

41

Effects as complicated as these obviously demand something more specific in the way of explanation than such general considerations as, for example, the internal pressure in the Solution. In fact, from the point of view of internal pressure the variety and magnitude of the effects is very surprising. Thus, to take an extreme case, the initial slope of the curve of apparent volume of 0.5 M a-amino butyric acid has the largest negative value to be found anywhere in the series. A consideration of numerical magnitudes shows t h a t this means, according to T a m m a n n ' s picture, t h a t the water in the Solution is under a negative pressure of something of the order of 1000 kg/cm'. But the internal pressure in water under normal conditions is of the order of 10,000 or 20,000 kg/cm^ so t h a t the total internal pressure of the 0.5 M Solution is little affected by the dissolved acid. Externa! pressures would not be expected to produce important changes in the properties of such solutions until they become comparable in magnitude with the internal pressures already existing, or in this case, until a pressure is reached comparable with 10,000 kg/cm®. But actually an external pressure of only 800 kg/cm^ acting on this Solution reverses the sign of the apparent molal compressibility. Perhaps something in the nature of specific clustering or hydration effects, involving the possibility of multiple types of approximate order, would be competent to explain the complicated effects. But such effects must be surprisingly sensitive to changes of pressure which would be judged to be comparatively slight from the point of view of other phenomena. The great complication of these pressure effects suggests t h a t an experimental examination of other phenomena in these solutions might be profitably undertaken. For example, measurements might well be made of the effect of pressure on solubility and on the dielectric constants, on the compressibility of non-aqueous solutions and of solutions of other acids in the series, and of the compressibility of the solid phases of the pure acids.

105 — 2807

Theoretically Interesting Aspects of High Pressure Phenomena P. W. BRIDGMAN, Harvard University TABLE

OF

I. Introduction n . Atomic Changes Under Pressure III. Volume Changes and the "Law of Force" IV. Thermal Expansion and Entropy at Infinite Pressure V. P-V-T Retations in Liquids 1. Compressibility 2. Compressibility and cheitiical coniposition.. 3. Thermal expansion 4. The pressure coefficient and the mechanism of pressure 5. Small Scale irregularities VI. Periodic ReUtions

1 3 4 8 9 10 11 11 12 13

CONTENTS

v n . Compressibility of Single Crystals VIII. Two Phase Equilihrium 1. The melting curve 2. Polymorphie transitions between solids. . . . IX. Irreversible Transitions X. Discontinuities—Transitions of the Second Kind, etc. XI. Electrical Resistance Xn. Thermoelectric Phenomena. x m . Thermal Conduction XIV. Viscosity of Liquids XV. Conditions of Rupture XVI. Speculations XVn. BibUography

13 13 16 20 21 23 27 28 30 30 31 33

I. INTRODUCTION is rapidly becoming satisfactory, and in a sense HE invitatio!! of the Editors of Reviews of exhausted, so that an attack on the problem of Modern Physics to write some account of the the Condensed states is obviously next on the theoretical aspects of high pressure phenomena program. Indeed already a very considerable was one which I was glad to accept because it degree of success has rewarded theoretical atseems to !ne that the ti!ne is now approaching tack in this field, as, for example, in our rapidly when theoretical physics may hope to investigate growing theory of the metallic State in general the Problems of this field with good prospects of and of the electrical properties of solid conducsuccess. Until veiy recently the Condensed tors in particular. The Condensed State, par phases of matter, solid and liquid, have appeared exceUence, is obviously presented by matter under too complicated to make it worth while to high pressure, so that, to say the least, our underspend much effort in acquiring an understanding standing of the Condensed State cannot be reof them, particularly as long as the much more garded as satisfactory until we can give an acprofitable field of the investigation of matter in count of the effect of pressure on every variety its rarefied condition, as in vacuum tube phe- of physical phenomena. This we can at present nomena of all sorts, had not yet been fully ex- do in very few cases indeed. There are two aspects of theoretical concern ploited. But now our understanding of the atomic, as distinguished from nuclear, phe- with high pressure phenomena: a broader and a nomena presented by matter in its rarefied states narrower aspect. From the broad point of view

T

106 — 2809

P.

W.

BRIDGMAN

the eventual problem is to work out theoretical explanations of all known high pressure phenomena, and to predict the result of fresh extensions of experiment to pressures and groups of phenomena not yet reached. It must not be assumed too easily, I think, that this is a task of no particular interest, and that the problem is merely the problem of overcoming the complications of an analysis, the fundamentals of which are already completely understood. Such is without doubt the attitude of many theoretical physicists; in fact it seems to be a thesis of theoretical physics in its treatment of matter in bulk that there are no "emergent" properties, or in other words, that all the properties of Aggregates of atoms can be found from an exhaustive knowledge of the properties of the isolated atoms. There is a sense in which this thesis may be regarded as a mere tautology, because I suppose no one would deny that it would be possible to put enough parameters into the equations for the individual atoms or electrons to reproduce by some more or less complicated kind of theory all the properties of combinations of atoms in bulk. But the thesis does have real content if one understands it to mean that it is possible by experiments on isolated atoms, or atoms in the rarefied condition, to determine all the parameters necessary to describe all the properties of Condensed assemblages of atoms. No doubt the Impulse of many would be to say that in experiments involving nuclear bombardment and breakdown we are dealing with individual atoms under conditions of much greater intensity of force than are ever encountered in Condensed aggregates of atoms, so that there is no reason to think that such experiments will not give all the effective atomic Parameters. But on the other hand it must be remembered that in highly Condensed phases the character of the force to which the atom is subjected is different from that in collision experiments, the attack on the atom being now a more or less symmetrical and simultaneous attack from all sides, so that there may be a possibility of new kinds of effect. So far as I know no theoretical intimation was given, before the experimental evidence of astronomy, of the possibility of the existence of matter in conditions of density of the Order of 100,000. Our persistent difficulty

106 — 2810

in understanding superconductivity

of

metals

may also be significant. A t any rate, I believe that it must be conceded as a matter of pure logic that the thesis of non-emergent characteristics cannot be securely established until

at

least the possibility of a theoretical deduction of all the properties of matter in the Condensed condition

has

been

established;

what

one's

feeling will be as to the interest or profitableness of actually producing such detailed explanations will be largely a matter of taste and temperament. The narrower aspect of the high pressure problem concerns the extent to which we can understand

high

pressure

phenomena

in terms

of

recent wave mechanics pictures of atomic b e havior and interaction. This is the aspect of the problem which will serve as the background of Our present discussion. It would have been desirable if this paper could have been written b y someone who has made actual contributions to Our understanding in terms of wave mechanics of the behavior of Condensed phases, instead of by one whose qualification is merely an acquaintance with the nature of the experimental material. I shall have to content myself, therefore, with pointing out those aspects of the phenomena which are simplest and therefore where theoretical

attack

may

most

reasonably

anticipate

success, or those aspects which seem to me most suggestive and of intrinsic interest. I believe that Our theoretical mastery in this field is not yet so far advanced but that a careful pondering of the qualitative significance of various general types of pressure phenomena will be profitable. I have this feeling because a number of years ago I had arrived at various qualitative pictures, as of the phenomena of electrical conduction or of Polymorphie transition, which were somewhat at variance with the pictures common at the time, but which are becoming more and more justified b y wave mechanics. The experimental material which must form the basis of our present theorizing is almost entirely confined to the ränge from 10,000 to 20,000 kg/cm^, although a few data have been obtained at somewhat higher pressures and there is the possibility of more in the future. These pressures are of the order of magnitude of the internal pressures which various theories have agreed in assigning to ordinary Condensed phases;

HIGH

PRESSURE

such internal pressures vary from 3000 or 4000 kg/cm® for organic liquids and 10,000 or 20,000 for the more compressible metals, to a few hundred thousand for the most incompressible substances like iridium and diamond. Furthermore, the volume changes producible by pressures in the experimental ränge are materially greater than the volume changes due to temperature on cooling from room temperature to 0°K. One would appear to be justified therefore in anticipating that an adequate understanding of even the effects of pressure known at präsent would react beneficially on our general understanding of matter in the Condensed State. By the application of pressure we have the tool, as it were, for producing artificially a great variety of new Condensed states of matter. In the following I shall not attempt to give more than the very briefest possible indication of the nature of the experimental material and refer the reader to my book The Physics of High Pressure published by Bell in England and Macmillan in this country, whenever he feels the need of more detailed acquaintance with the data. I I . ATOMIC C H A N G E S U N D E R

PRESSURE

Perhaps the first and most important question that confronts one on entering this field is

PHENOMENA

whether it is legitimate to treat the atoms as fixed Units, or whether pressures in the experimental ränge produce important changes in the atoms themselves. A rough answer is suggested to this question by means of an important theorem, which has been much neglected, originally due to Schottky' and proved on the basis of classical mechanics. Later Born, Heisenberg and Jordan^ showed that essentially the same Situation holds in wave mechanics, and the theorem has recently been re-emphasized and applied to some molecular problems by Slater.® Schottky's theorem states that in any system controlled by internal electromagnetic forces, whether there are or are not in addition constraints imposed by quantum conditions, as for example, systems composed of molecules and atoms built of nuclei and surrounding electronic atmospheres, and on which in addition to the electromagnetic forces an external hydrostatic pressure, p, acts, the following relations hold: dr= -dE+3d{pv),

(1)

dV=

(2)

2dE-3d(pv).

Here T is the average internal kinetic energy and V the average internal potential energy, the averages being taken over a time interval long enough to give constancy, E is the total energy of the system and v the volume.

By thermodynamics we have: /ön

1

r /dv\

/dv\

1

Eliminating dE gives: (3)

(4)

Apply these equations to ordinary solid substances in the experimental ränge of pressure, and consider first the Variation of T with pressure at constant temperature, paying attention only to Orders of magnitude. T(dv/dT)p is evidently small compared with 3v and may be neglected. The most compressible solid metal

is caesium; at 15,000 kg/cm^ m d v / d p ) r has the value 0.6 and 3v is equal to 2, so t h a t (ßT/dp)r = 1.4 for Cs at 15,000. For lithium, on the other hand, the compressibility is much less, and {dT/dp), at 15,000 has the value 2.4, the derivative referring in both cases to that quantity of matter which occupies 1 cm' at atmospheric

106 — 2811

P.

W.

B R I D G M A N

pressure. Most soUds are much less compressible even than this, so that we would not be making an error on the average much more than 10 or 15 percent if we set dT/dp'^S in the experimental ränge of pressure. Hence at 20,000 kg/cm^ we have at once Tso.ooo—To=60,000 kg/cm = 3.5X10" electron volts. Expressed per atom, this becomes 3.5X10^X1.66X10-" Xat. wt./dens. »0.06 at. wt./dens., or rji).ooo-ro«0.06Xat. vol. in electron volts per atom.

(5)

For elements of high atomic volume this approximation is in general less good than for elements of low atomic volume, because compressibility is highest for high atomic volumes, and the actual value is less than the approximate value by a term proportional to the compressibility. In the ordinary ränge of temperature the specific heat of a solid is given approximately by Dulong and Petit's law, which ascribes three degrees of freedom to the kinetic energy of translational motion of the atom as a whole, and three degrees to the potential energy of position. Hence to this degree of approximation the kinetic energy of translation of the atoms is constant, independent of pressure, at constant temperature, and the change of kinetic energy with pressure which is given by Eq. (5) is change of internal kinetic energy of motion of the electrons inside the atoms. For lithium at 20,000 this is 0.8 e.V. per atom, for bismuth 1.3, for aluminum 0.6, and for iron 0.4. These energy changes are thus considerably smaller than the ionization energies of the atoms, but they are nevertheless of the same order of magnitude, being 18 percent for bismuth, and lead to the conclusion, I believe, that one should at least entertain the idea that appreciable internal changes may be produced by experimental pressures in the outer electron orbits of the atoms. It is to be noticed that an increase of the internal kinetic energy of the electrons in their orbits such as we have just found means a shrinkage of the orbits, that is, a compression of the atom, assuming the same relation to hold in the Condensed phase between atomic radius and electronic energy as holds for the isolated atom. The orbital shrinkage is evidently the theoretical Version of the "compressible atom" first insisted

106 — 2812

upon by Richards and which has seemed to me to be demanded by many qualitative aspects of my measurements of compressibility. The order of magnitude of the changes of internal kinetic energy just calculated shows that in the ränge of pressure at present realizable no very drastic rearrangements in the structure of the atom are to be anticipated, unless perhaps there may be a few cases in which the atom is already near some critical configuration. Drastic changes may, however, perhaps be expected at pressures of the order of 100,000 kg/cm^. Consideration of what the nature of these effects may be will be postponed until the end of the paper; in the meantime we shall be concerned with the present experimental ränge in which changes in the atom itself may be expected to be small, although appreciable. I I I . VOLUME CHANGES AND THE " L A W OF FORCE"

Doubtless the simplest of all the effects produced by hydrostatic pressure is the uniform change of volume of a fluid or an isotropic solid, and it is natural that theory should first attack this Problem. The simplest of all Condensed phases from the theoretical point of view is an ionic lattice of the NaCl type, and as is well known, theoretical attack on this problem, largely at the hands of Born,' has been successful Up to a certain point. The ionic lattice is held together by the electrostatic attractions of the ions and prevented from collapsing by a repulsive force due to ionic interpenetration. The attractive force can be completely dealt with in terms of the known lattice structure and the known magnitudes of the ionic charges. The repulsive force is more difücult. In Born's original discussion an attempt was made to give some account of the repulsive forces in terms of the structure of the atom as pictured at that time by Bohr's theory, but this was unsatisfactory because it gave stability only for certain relative orientations of the atoms. The final result was that the repulsive force had to be treated from an almost purely empirical point of view, and a repulsive force acting as some unknown inverse power of the distance between atomic centers was assumed, with an unknown coeflficient of

HIGH

PRESSURE

proportionality. T w o conditions, one on the size of the lattice at 0 ° K and the other on the compressibility, permitted a determination of the two Parameters of the empirical law of repulsion. For most of the alkali halides the repulsive force turned out to be approximately as the inverse ninth power of the distance between atoms. The complete law of force thus having been assumed and its parameters determined, it was possible to carry the computation further and find how the compressibility should vary with pressure. I t was calculated in this way that the compressibility decreases with increasing pressure, and to this extent there was agreement with experiment, but numerically the agreement was so far from satisfactory that it was obvious that a repulsive force of the form assumed could serve as an approximation over only a very narrow ränge when this type of phenomenon was concerned. The wave mechanics picture of the atom gives a more satisfactory basis than did Bohr's theory for calculating the repulsive force in terms of the mutual action of interpenetrating electron atmospheres, and Born, in recent revisions of his theory, has given the repulsive force an exponential form, which is the form that results most simply from the mathematics of the wave mechanics picture. But even this modification does not give the correct change of compressibility with pressure, so that again we have a comparatively short ränge approximation. Experimentally, the compressibilities of all the alkali halides except R b F , which does not crystallize properly, have been determined up to 12,000 kg/cm'. In this ränge the relation between pressure and volume may be represented by a two power expression in the pressure, the two Parameters determining the initial compressibility and the Variation of compressibility with pressure. In the case of such substances theory would at present have the task merely of reproducing these two parameters. There are, however, many substances for which the volume change in this pressure ränge is very definitely not representable by a two power series in the pressure, or even b y a three or four power series, as for example, the alkali metals, and there are even substances whose compressibility increases with increasing pressure instead of decreasing. For such substances theory will eventually have to

PHENOMENA reproduce a considerable number of parameters, or discover some type of function better adapted to reproducing the volume than a power series. In addition to the work of Born and others on the compressibility of ionic lattices there have recently been several calculations of the compressibility of the simplest metals, particularly the alkali metals.' Here again it has been found possible to reproduce the initial compressibility with some success, but the variations of compressibility with pressure are very wide of the mark.

One aspect of the method of treatment followed by Born is conventional in practically all derivations of an equation of State, whether or not intended to be applicable to high pressures and Condensed phases, nämely the assumption of a "law of force" between atoms, a function only of the distance of Separation of atomic Centers. In view of the failure of all attempts to reproduce more than the first derivative of volume with respect to pressure the question presents itself as to how far the action between atoms in Condensed phases under variations of temperature and pressure can be represented by " a law of force." In assuming a law of force of the form, for example, —o/r'-l-J/r", we are evidently maintaining that the behavior of the entire assemblage of atoms can be found by postulating that each atom of every pair of atoms acts on the other with the force given, irrespective of the presence of other atoms, in all orientations (orientation is not a factor for the type of ions just considered, which b y wave mechanics have spherical symmetry), and at all distances. The assumption of a law of force of the form given certainly corresponds to the facts from the j)oint of view of one very important first approximation. For two atoms acting on each other with a force of this character may be brought indefinitely dose together b y the action of sufficiently large forces, that is, such atoms are not rigid but are eflfectively deformable, as is demanded by many lines of experimental evidence. But the question is, how much further is the approximation represented by such a law valid. One may imagine oneself carrying through the detailed Solution of the wave-mechanical Problem of the NaCl crystal, for example, finding t h e complete tp function, Splitting this u p

106 — 2813

P.

W.

BRIDGMAN

into parts corresponding to p, s, d, etc., electrons associated with the different atoms, and then coalescing the results into a final law of force. Into this law of force will certainly enter the distribution of the electrons within the atoms. The law of force may remain good as long as the distribution of electrons remains fixed or as long as the electron distribution depends uniquely on the distance r, as when pressure is changed at constant temperature. But if the electron distribution is not fixed uniquely by r, a possibility which we must recognize if both pressure and temperature are allowed to vary, then we must be prepared to find that the interaction cannot be described in terms of constants and r only, that is, we must be prepared to find that there is no "law of force." Doubtless in a sufficiently narrow ränge the assumption of a law of force is a valid approximation. W e have to consider whether it is a valid approximation in the ränge of pressure and temperature now open to experiment. W e can obtain a qualitative answer to this question by means of Schottky's theorem. In Eqs. (3) and (4) write as an approximation that the total kinetic energy T is the sum of two parts: one, mass motion of the atom as a whole (T^t) and the other kinetic energy of the electrons inside the atom (Tei), so that T—T^t+Te\. W e could in the same way put 7 = 7 . t + Fei, where Fat is the part of the potential energy given by the "law of force" as in the discussion above, and Fei is the internal potential energy of the electrons inside the atom. This resolution into two parts should be a fairly good approximation for a simple ionic lattice; for complicated molecular lattices the resolution would be more questionable. W e assume further that the substance under consideration approximately satisfies Dulong and Petit's law, which means that (,dT.i/dp)r = 0, (ar«t/ÖT)p = Cp/2, neglecting the difference between Cp and C„, which is legitimate for Condensed phases. A t high pressure it is highly probable that the specific heat becomes somewhat less because of the stiffening of the atomic constraints, so that more exactly, {dTti/dp),2, at 30°C, p in kg/cm^

N the Physical Review for March 1, 1934, Hanson has published a careful determination by the method of the bending and twisting of cylindrical rods of the five elastic constants of zinc crystals from two different sources, both of purity higher than 99.99 percent, and has calculated from these constants the linear and cubic compressibilities. Considerable differences were found in some of these constants; for example, the calculated linear compressibility parallel to the axis of one grade of zinc was 40 percent higher than that of the other, and the cubic compressibility was 30 percent higher. These results were quite unexpected to me, both because of the opinion which seems to be quite widely held by experimenters on phenomena in crystals that the elastic constants are not "structure sensitive," and also because of my own personal experience. I had made measurements of the elastic constants by a more direct method and had found nothing to suggest as great a variability as found by Hanson. This was in particular true of my direct measurements of the linear compressibilities, which gave more clean cut results than for the other constants. Furthermore, all my experience with the compressibility of other materials indicated that it is not sensitive to slight impurity. The matter seemed important to me, since our opinions on "structure sensitive" properties of crystals are still hardly out of the controversial stage, and it would be desirable to get this

I

matter correct in the beginning if possible. I therefore suggested to Professor Tyndall, ander whose direction Hanson's work was done, the desirability of checking by direct experiment on the identical specimens some of Hanson's calculated compressibilities. Professor Tyndall cooperated in the readiest way by immediately placing at my disposal all of Hanson's samples of suitable orientation. Nine sets of measurements in my regulär pressure apparatus were made on these samples. On Consulting with Professor Tyndall as to the form which the results should take for publication, considerable difference of opinion developed as to the proper Interpretation, and it eventually appeared after considerable correspondence that conclusions satisfactory to both of US could be obtained only by the execution of fresh experiments. The main point at issue hinged on the effect of the handling which the specimens had received, since they were known in some instances to have been strained beyond the elastic limit. The effect of this strain was removed as far as possible by a process of annealing which at that time was believed to be effective in restoring the electrical properties to the original condition, although there was no proof that the elastic properties were similarly restored, and it has developed later that even the electrical properties are not equally well restored at all orientations. Professor Tyndall therefore undertook the preparation of fresh samples of zinc especially for this work, and every

108 — 2849

394

P.

W.

BRIDGMAN

precaution has been taken to avoid all possibility of overstrain. The freshly prepared zinc crystals were from three sources: (1) Evanwall "Rod" (E. R.) zinc made from material left by Hanson, originally obtained from the Evans Wallower Zinc Company; (2) Evanwall "Block" (E. B.) zinc from a fresh SO pound block of zinc from the Evans Wallower Zinc Company, the same as the zinc used by Cinnamon' in a recent paper, and (3) Horsehead Special (H.H.) zinc, from the same SO pound block as used by Hanson. Another sample of zinc from Evans Wallower showed by direct chemical analysis: Fe 0.0004 percent. Cd 0.0008 percent, Pb 0.0047 percent, Cu 0.0002 percent, As, Co, Ni, AI, 0.0000. Spectroscopic comparison of this with the E. R. zinc showed no detectible difference. Spectroscopic comparison with the H. H. zinc indicated somewhat more iron and somewhat less copper than the E. R. zinc. Spectroscopic comparison between E. R. and E. B. showed no iron at all in E. B. and slightly more copper. There were three samples of E. R. of orientations 5°, 90° and 8°, the angle being measured between the hexagonal axis of the crystal and the length of the rod. The 8° specimen had been strained in removing from the mold, and slip bands could be Seen on the central portion, but the ends appeared free from slip bands. There were two samples of E. B. of orientations 9.5° and 8S°. There were four samples of H. H. of 5°, 8°, 21°, and 89° orientations. The 21° orientation was really not pertinent for the present purpose, and was measured more or less by way of curiosity. These all were cast by methods already fully described^ into crystals about 8 cm long and of slightly trapezoidal section about 5 mm on the side. For the compressibility measurements it was necessary to form these into pieces about 2.7 cm long for the more incorapressible orientation and 1.3 cm long for the other more compressible orientation, with accurately flat and parallel ends. In order to perform the small amount of necessary machining, the specimens were first embedded in wax in a heavy brass tube of internäl diameter just sufficient to admit the rod freely. The wax was cast around the rod ' C. A. Cinnamon, Phys. Rev. 46, 215 (1934). 2 w . J. Poppy, Phys. Rev. 46, 815 (1934).

108 — 2850

TABLE I. Summary of linear compressibility measurements on fresh samples of zinc. -Ü/h

Qrsde of zinc

Orientstion

Linear compreaeion at 30°

at 10,000 kft/om*

E.R. E. B. H.H.

90» 85° 89°

LSTKlO-ip- 0.75X10-"V 1.96 - 0.75 1.58 - 0.75

0.0014» .00159 .00151

E.R. E. B. H.H. H.H.

5° 8.5° 8° 5»

E.R. 8° Strained H.H. 21°

-Wh

Widtli of liyatereeis leop

Average deviation from Bmootli curve l.JO% .83

13.39 13.03 13.5» 13.18

- 9.75 - 6.98 -10.95 - 6.01

.01270 .01243 .01249 .01258

0.83% 1.36 .75 .83

12.71

-

7.45

.01197

1.27

11.77

-10.35

.01073

1.40

.14 .50 .18 .21

Oi

by slowly lowering the mold containing the crystal surrounded by molten wax into cold water by a process very similar to my method for making single crystals. Pieces were then cut out of the mold of the requisite length with a fine jeweller's saw; the ends of the specimen were faced off in the lathe while still embedded in the wax, taking a very fine chip and using a keen tool, and finally the completed specimen was freed from the mold by melting the wax. In a few cases there were longitudinal ridges left from the Casting that had to be removed; this was done with a fine file, after part of the mold had been filed away, and while as much of the crystal as possible was still embedded in the wax. The results of the measurements of linear compressibility of these fresh samples are given in Table I. The method was the same as in all my previous work and has been fully described.' The measurements were made a t 30°C, over a pressure ränge of 12,000 kg/cm", readings being made a t equal pressure intervals with both increasing and decreasing pressure, making in all fourteen readings. The pressures in the tables are in kg/cm^ units. In addition to the regulär pressure run, an initial seasoning application of 2000 kg/cm® was made in all cases; this initial application was followed by no permanent change of zero within the regularity of the other readings, showing that there was no perceptible porosity in the spÄcimen. The results could in practically all cases be represented within the regularity of the readings by a second degree expression in the pressure. Space does not permit a reproduction of all the individual readings, which repay careful ä P. W. Bridgman, Proc. Am. Acad. S8, 166 (1923).

E F F E C T

OF

I M P U R I T I E S

ON

E L A S T I C

C O N S T A N T S

395

0.0130 study. The results were never entirely regulär within the limits of error of the method, b a t there were irregularities greater than would be 0.0125 shown under similar conditions by harder materials. The most important feature was that 1.0120 there was always perceptible hysteresis between pressure and change of length for the most compressible orientation, that is, parallel to the axis, while the other and relatively incompressible 0.0130 orientation showed no appreciable hysteresis. In Order to indicate the character of the results as fully as possible Table I contains, in addition 0.0125 aoo2C to the two power expression in pressure which best represents the results, the maximum width 0.0013 of the hysteresis loop expressed as a fractional part of the total displacement a t the maximum 0.0115 0.0010 pressure, and the mean departure from a smooth 0.00 curve of the individual points similarly expressed. F I G . 1. S h o w s in t h e u p p e r p a r t of t h e d i a g r a m t h e f r a c This latter gives an idea of the regularity of the t i o n a l c h a n g e s of l e n g t h a t 1 0 , 0 0 0 k g / c m ^ p l o t t e d a g a i n s t results; it will be seen that the average deviation c o s ' 6 f o r t h e f r e s h l y p r e p a r e d z i n c c r y s t a l s . I n t h e l o w e r is of the Order of a few tenths of one percent. p a r t of t h e d i a g r a m a r e s h o w n s i m i l a r d a t a f o r t h e e l a s t i c i t y s a m p l e s of H a n s o n . E l i s t i c i t y t h e o r y d e m a n d s t h a t I t is significant that by far the greater part of the t h e r e l a t i o n b e linear i n cos^ 9. average irregularity was contributed by the initial points at atmospheric pressure. A result point of this paper, and I believe establishes the of this would be that measurements made in only fact that there is at present no reason to believe a small pressure ränge would show mach greater that at any rate the compressibilities are sensitive irregularity, both relatively and absolutely, than to small impürities. measurements over a wider ränge. In order to It is instructive that the compressibility of the eliminate as far as possible the effect of small one sample known to have been strained in the local irregularities, I have chosen as giving the mold, which is also plotted in Fig. 1 and which best comparative indication of the true com- may be identified by comparison with Table I, compressibility the fractional change of length definitely does not fall in line with the others, in under 10,000 kg/cm^. This change of length spite of the fact that the sample was cut from should be a linear function of cos^ 9. The results what appeared to be an undamaged part of the are plotted in Fig. 1 against cos^ 9 giving only crystal. This suggests the extreme sensitiveness the parts of the diagram on a much enlarged of these efifects to strain. Doubtless the fact that Scale in the neighborhood of cos® 9 = 0 and the individual readings for all the other samples cos« 0=1. were not as regulär as those given by many other The diagram will leave no room for doubt, I mechanically harder materials is to be explained believe, but that the linear compressibilities of as an effect of slight strains introduced in spite these different grades of zinc are as dose to the of the greatest care in handling. same value as could be expected in view of The results listed in Table I for the 21° sample the experimental irregularity, and that no diflfer- should be given no consideration in comparison ence exists within experimental error which can with the others because the method is not be correlated with a difference in origin of the adapted to measuring the linear compressibility samples and therefore with minute differences in of such an orientation. The thickness of this purity. The extreme discrepancy between any sample was about one-half its length; calculation two samples is 1.2 percent, which is to be con- will show that under hydrostatic pressure there trasted with a discrepancy of 40 percent in is a change of angle for this orientation which in Hanson's averaged final results. This is the main specimens of these proportions produces an effect

108 — 2851

P.

396

W.

BRIDGMAN

far from negligible, giving too low an apparent compressibility. In fact, the compressibility of this sample was too low by 5 percent. I t is now instructive to compare these results, obtained on virgin unstrained specimens, with the measurements made on the specimens which had been previously used by Hansen in determining the five elastic constants, and which were known in a t least some cases to have been strained before the compressibility measurements. T h e results are given in Table II. They are distinctly more irregulär than those for the virgin material in Table I. This is particularly evident in the second degree terms which in two instances have a positive sign, a very abnormal State of affairs indeed. T h e relative changes of length a t 10,000 k g / c m ' are plotted in the lower part of Fig. 1. T h e very much greater scattering of the points is in the first place striking and also the fact t h a t a t the high orientations all the points lie above the line for the unstrained material and a t the low orientations all, with one exception, lie below it. The obvious Interpretation of this is that small strains act effectively like the introduction of other orientations; a t 90° the only other orientations possible are nearer 0°, and a t 0° the only possible other orientations are nearer 90°. Going back now to the results on the unstrained specimens, the present values of compressibility are -much to be preferred to those which I previously published;^ not only is the TABLE I I . Summary of linear compressibility on Hanson's elasticity samples.

Grade of sine

Orientation

Linear compression at 30^

-ai/lo at 10,000 itg/om! 0.00172

-U/h

measurements

Widtli of iiysteresia loop

Average devUtioo from smooth curve

E. R. i.a. E. R. a.a. H.H.

90»

1.38X10-'p+ 3.38X10-1V

90°

1.96

-

0.70

.00189

90°

1.49

+ 0.33

.00152

E°R. i.a. E. R. a.a. H.H. 6.a. H.H.

3°

13.91

-16.55

.01225

1.7%

.13

3°

13.60

-13.1

.01229

2.1

.25

H.H. a. 2Dda.

aa.

1.18% 1.86 .68

1»

13.40

-

4.22

.01298

1°

12.98

-10.40

.01194

2.1

.28

1»

12.91

-10.72

.01184

1.8

.29

.45

.09

b^., before anneRling, or "as received." a.a., after annealing, 380® for 8 to 10 houra. a. 2nd a., eecond annealing, 400® for 24 hours.

« P. W. Bridgman, Proc. Am. Acad. 60, 338 (1925).

108—2852

present material purer than mine, which we have Seen to be of comparatively minor importance, but the specimens were doubtless freer from strain. T h e average values given by the new measurements, weighting measurements on different specimens inversely as their average deviations from a smooth curve, and correcting for orientation, are a t 30°C pressure expressed in kg/cm^: At 90°, -AZ/;o = l.S7X10-V-0.7SX10-"/>>. At 0°, -A//;o = 13.SOX10-'/>-7.68X10-'y. From these the volume compressibility may be computed to be: - A 7 / 7o = 16.64 X 1 0 - ' ^ - 9.62 X lO-'^^. M y previous results were: At 90°, -Ai//o = 1.95X10-'^-l.llX10-iy. At 0°, -A//io = 12.98X10-'/.-5.32X10-»2i>^. Cubic, - Ay/7o = 16.87 X 10-^-8.08 X10"'^. I t will be noticed t h a t the difference between the two determinations is In exactly the direction that would be expected, that is, the linear compressibility of the strained 90° specimen is greater than t h a t of the unstrained specimen, because of the efTective introduction by the strain of other orientations, all of which have a greater compressibility, while for the 0° orientation the relations are reversed. T h e result is a comparatively large change in the ratio of the compressibilities in the two directions, the ratio being 8.6 for the unstrained specimen and only 6.65 for the strained specimen. I t is also to be noticed that the effect of strain is much larger on the 90° orientation, measured in percent, than on the 0° orientation; the absolute magnitudes of the effects are not greatly dissimilar. Interesting questions suggest themselves as to the mechanism by which strain simulates the effect of a change of orientation. T h e cleavage planes seem to be unchanged in orientation and as easily produced in strained as in virgin specimens. Perhaps the possibility is to be considered of a partial rotation of the atoms in Position in the lattice; it is probable t h a t the atoms cannot have complete spherical symmetry in a lattice as strongly anisotropic as zinc. T h e fact that annealing is comparatively successful in restoring electrical properties is not incon-

EFFECT

OF

IMPURITIES

sistent with an asymmetry in the atoms because the wave mechanics picture of electrical conduction represents the electron distribution as much more uniform than the atomic distribution. This is also suggested by the fact that the ratio of the electrical conductivities for the two independent perpendicular directions is only 1.055, against 8.6 for the ratio of the elastic constants. Leaving now the question of compressibility and passing to the other elastic constants as determined by Hanson, it seems to me that one may well question whether there is any longer ground to believe seriously that the other constants are sensitive to minute impurities. For I think it may be taken as now established that there is no such Variation in the compressibility as Hanson calculated from his other constants and this of course means an error in those constants. There are two factors which I think should be especially considered in appraising the Situation. There is in the first place the consideration that slight permanent strains may introduce systematic errors, changing the elastic properties for orientations near one extreme all in one direction, and those near the other extreme in the other. In the second place, there is the consideration that slight errors in the observational data may, because of the nature of the mathematical relationships, introduce very serious errors into some of the computed elastic constants. Thus it can be shown that by making a change of only 1 percent in the direct observational data from which 5ii, Ssa and 544 are computed, a change of 18 percent may be thereby introduced into5i2,22 percent into5i3,35 percent into the parallel linear compressibility, 81 percent into the perpendicular linear compressibility, and 47 percent into the cubic compressibility. If one examines the regularity of the experimental points in Hanson's diagrams, and further considers the possibility of systematic errors just mentioned and the fact that all the bending specimens consistently showed distinct hysteresis, I believe that the danger of an accumulation of errors like that just suggested must appear to be a very real one. The possibility of systematic errors arising from small strains offers the possibility of understanding how Hanson could have arrived at his

ON

ELASTIC

CONSTANTS

397

conclusion that very small diflferences in purity produce comparatively large differences in elastic constants. For the elastic limit is known to be sensitive to very slight impurities so that one grade of zinc may have been more susceptible to permanent strain than the other, and therefore more sensitive to systematic error. Something of this sort is definitely suggested by a study of the irregularities of the data. The spectroscopic analysis suggests that the H . H . zinc was slightly less pure than E. R. or E. B. and therefore less likely to receive permanent strains. Tables I and H both show a distinct tendency for the H. H. points to deviate less from smooth curves than the others which is what would be expected. There is also the fact that the compressibilities calculated by Hanson for the H. H. zinc are distinctly nearer the values directly determined above than are the others. In view of the various possibilities of error in the method of determination of elastic constants by bending and torsion, particularly when applied to substances with low elastic limits, it is pertinent to urge the great superiority of "direct" methods, that is, methods in which the specimen is subject to a homogeneous stress and strain corresponding to the constant to be determined. The constants 5ii and ^33 can be measured "directly" in terms of the shortening under compressive load, and so determined can be given more confidence than can be given to a determination by bending which involves a strain varying from positive to equal negative values across the section of a slender specimen. Similarly 5i2 and S n can be determined by direct measurements of the lateral contraction of suitably oriented specimens, and so determined are not susceptible to the possibility of large accumulated errors already indicated in the indirect method. Finally there can be no doubt but that directly measured compressibilities are to be preferred to compressibilities calculated by a combination of other constants. In a note following this Professor Tyndall presents the values of the elastic constants of zinc which he now thinks may be deduced with greatest probability from Hanson's data in view of these results on linear compressibility.

108 — 2853

THE MELTING CURVES AND COMPRESSIBILITIES OF NITROGEN AND ARGON. B Y P . W . BKIDGMAN. Received October 1, 1934.

Presented October 10, 1934.

CONTENTS. Introduction Apparatus Experimental Procedure Detailed Presentation of Data Ni trogen Argon Discussion

1 2 13 15 15 22 25

INTRODUCTION. DÜRING the last few years a revival of interest in the question of the possible existence of a critical point between solid and amorphous phases has been inspired by new measurements on several of the permanent gases, a particularly simple class of substance. These measurements are due primarily to Simon and his eollaborators,' who have followed the melting curve of helium to approximately 5500 kg/cm^, that of hydrogen to 5000, that of neon to 4900, that of nitrogen to 5000, and that of argon to 3400. However, there are also a number of measurements from the laboratory at Leiden,' over a much smaller pressure ränge, but with greater preeision. I t is the opinion of Simon that the melting curve will end in a critical point, but in no case has such a critical point actually been realized. In the failure actually to realize the critical point the course of the melting curve itself can give no basis for an extrapolation, which can be made only with the help of other independent data. Thermodynamically, the critical point is characterized by the simultaneous vanishing of the difference of volume between the two phases and of the latent heat of the transition. If a critical point is to be justifiably inferred from extrapolation from data in the experimental region, then the course of the curves for difference of volume and latent heat in the experimental ränge must be such as to indicate the vanishing of the volume difference and the latent heat within distances not too remote from the region of experi-

109 — 2855

2

BBIDGMAN

ment, and furthermore, the extrapolated vanishing pressure (or temperature) for volume change must be the same as the extrapolated vanishing pressure (or temperature) for latent heat. Simon did not make measurements of either change of volume or of latent heat, so that up to the present there is no basis for extrapolation, and no possibility of setting up a rigorous argument for a critical point, from the new data for the permanent gases. In this paper I present new measurements of the coordinates (pressure and temperature) of the melting curves of argon and nitrogen up to about 5500 kg/cm", and also measurements of the difFerence of volume. As is well known, the latent heat of the transition may be computed from the volume dilference and the coordinates of the melting curve by means of Clapeyron's equation, so that we now have the means of making an extrapolation toward a possible critical point for these two gases. Furthermore, in the course of the measurements of the volume difference it was necessary to know the volumes of the gaseous phase; these apparently have not been previously determined at temperatures below 0° C at pressures higher than 200 or 300 kg, so that it was necessary to determine a number of points on the surface of the gas in the new region. These determinations, which have an interest in themselves apart from the problem of change of phase, are also given in the following. APPAEATÜS.

The large features of the apparatus were determined by the general method, which was the same as that employed in my previous werk on change of phase of substances Uquid under ordinary conditions.' Pressure was produced by the motion of a leak-proof piston. Change of phase is accompanied by a discontinuity in the motion of the piston as a function of pressure. The pressure of the discontinuity at a given temperature gives the p-t coordinate of a point on the melting curve, and the amount of discontinuity gives the volume change. These new measurements differ from the previous ones in that gases are being dealt with instead of liquids, and by the low temperatures, running down to 77° K, so that appropriate changes in the apparatus were necessary. The apparatus already employed for the measurement of electrical resistance as a function of pressure at low temperatures^ could be adapted to the demands of this method with very few changes. The apparatus consists essentially of a couple of precompressors, by which

109 — 2856

THE MELTING CUEVES OF NITEOGEN AND AEGON

3

the gas is raised from the tank pressure of approximately 100 kg/cm^ to 2000 kg/cm'', an upper cylinder maintained at room temperature, in which pressure is produced by the motion of a leak-proof piston, and in which is installed the manganin gauge by which pressure is measured, a connecting pipe, and the lower cylinder, maintained at the desired temperature by a low temperature thermostat to be described later, in which the freezing of the gas takes place. The diameter of the hole in the upper cylinder was about 0.67 cm, and its length 8.6 cm, making a total capacity in the upper cylinder of about 2.8 cm'. The lower cylinder was also 0.67 cm in internal diameter, with a total capacity of about 3.8 cm'. The' connecting pipe was 30 cm long, with a total internal volume of 0.13 cm^, and an outside diameter of 0.48 cm. The upper cylinder carries only one side hole, that for the manganin gauge, instead of the four holes which were necessary in the previous experiment; this results in a very desirable simplification of construction and assembly. The screw plug by which the manganin gauge is retained against pressure is carried in a heavy ring, girdling the cylinder, and a push fit for it, as in the previous experiments. In my previous measurements of change of phase under pressure, the substance undergoing transition was usually separated from the pressure transmitting liquid, which was some light hydrocarbon, by mercury. This is now obviously impossible; furthermore, there seems to be no method of separating one fluid from another without mixing in the ränge of pressures and temperatures involved, so that the entire apparatus had to be filled with the substance whose transition was being measured. This necessity gave rise to considerable misgiving, for I had already tried without success to measure the compressibility of some of the permanent gases by the piston displacement method. The difficulty was the penetration of the steel by the gas, having the same eifect, as far as measurements of volume in terms of piston displacement are concerned, as a leak. It was the same penetration of the steel by the helium which set the maximum limit of 7500 kg/cm^ reached in my previous experiments on resistance at low temperatures. However, previous experiments had shown that penetration by nitrogen is usually not nearly so serious as penetration by helium, and on one occasion I had reached a maximum pressure of 12000 kg/cm^ with nitrogen, although this could not be permanently retained, so that the problem did not appear hopeless if one were Willing to restrict oneself to comparatively low pressures. It appeared.

109 — 28.57

4

BEIDGMAN

moreover, that Simon had been having no such difficulty as I from the Penetration of his steel. I therefore obtained, through the kind ofEces of Dr. Simon, for which I am very much indebted to him, from the German firm Bismarckhütte, Berlin, some of the same steel which he had been using. A test cylinder made from this withstood without rupture a maximum pressure of 12000 kg/cm^ exerted by helium, although the pressure was not permanently retained, but slowly dropped, thus showing some absorption by the steel. The Performance was very much better than that of any steel which I had previously tried, however, and the entire apparatus was therefore constructed from this German steel. I t is a chrome-nickel steel, the exact composition of which I do not know, but it is obviously low in carbon. I t is supplied in a heat treated condition, soft enough for ordinary machining Operations, with a tensile strength of about 150,000 Ib/in^. The upper and lower cylinders were machined from the steel as suppHed. The steel was too hard, however, to permit drilling the hole 30 cm long and 0.08 cm in diameter for the connecting pipe, so that the steel from which the pipe was made was first annealed and then reheat-treated after fabrication. The apparatus constructed from this steel was used in obtaining the results described in the following up to a maximum pressure of about 6000 kg/cm^ with no sign at all of penetration either by nitrogen or argon. One connecting pipe split during use, but the original upper and lower cylinder were used throughout. I have not yet had enough experience in handling gases at high pressures to know whether the superior Performance of this steel is due to its chemical composition, or to its superior homogeneity and freedom from various sorts of imperfections. This sort of steel is, of course, made in this country also, but I have not yet tried any of American manufacture. One or two metallurgists have suggested that the German steel may be intrinsically superior for this sort of Service because it is much freer from impurities of sulfur and phosphorus, the original Swedish ore from which German steels are made being known to be freer from sulfur and phosphorus than any American ores. Sulfur and phosphorus are said to be the most likely constituent of impurities which tend to segregate mechanically in the ingot, which one would expect to result in gas penetrability. If it should turn out that the employment of a CrNi steel, like that used here, is necessary in high pressure gas work, the pressures attainable with gases in experiments of this character would be definitely limited to about 12000 kg/cm^, the

109 — 28r)8

T H E MELTING CUBVES OF NITKOGEN AND ARGON

5

Stretch beyond this point in a steel not capable of being heat treated to higher figures becoming too great to permit accurate measurements of volume by the piston displacement method. However, up to pressures of this order it would seem that it is now possible to explore the p-v-t surface of gases by a technique distinctly simpler than that used in my previous work. It appears, furthermore, that there are several new possibihties which I have not yet explored in the way of homogenizing steels during the process of manufacture, so that it is not at all impossible that pressures still higher than this will presently be available for experiments of this character on gases. The motion of the piston which gives the change of volume was measured in two different ways. The first method was that ahready employed in measuring the compressibility of gases. The hardened plunger is pierced with a small axial hole, through which passes a wire made an integral part of the head of the moving packing plug. The Position of the upper end of this wire is read through a suitable peephole milled in the piston of the hydraulic press with a reading telescope and a scale attached to the upper cylinder. In this way the actual motion of the moving plug in contact with the gas is measured, and errors from compression or wear of the packing are eliminated. The second method measures the motion of the piston of the hyd rauhe press with respect to the upper cyhnder by means of two Arnes dial gauges of one inch stroke, graduated to 0.000.5 inch and easily read to 0.0001, mounted on opposite sides of the press. Calibrated extension rods were provided by which the ränge could be extended as required beyond the one inch capacity of the gauges. This scheme is much like that used by Adams at the Geophysical Laboratory in his measurements of various compressibilities by the piston displacement method, except that two gauges are used instead of one, thus making possible the more complete elimination of the effects of distortion in the press. The two gauges usually agreed to about 0.002 inch over the entire stroke. The gauges were calibrated over their entire stroke with gauge blocks, and the maximum error found was 0.0005 inch, although the error in a couple of gauges which were discarded was more than this. The mean of the readings of the two gauges should be free from the effects of distortion or other error within about the sensitiveness of the readings. The second method is very much more convenient than the other because the Ames dials are much easier to read than the telescope. After one or two runs had disclosed no perceptible difference between the piston displacements given by

109 — 2859

6

BKIDGMAN

the two methods, showing no perceptible wear in the packing, the Arnes gauges only were used after the initial measurement, when the telescope and Scale also was used in order to give the absolute position of the plunger and so a fiducial point from which could be calculated the absolute volumes which enter into some of the coreections. It proved on working up the results, however, that variations in the initial volumes affect the corrections only within wide limits, so that the Information given by the absolute position of the piston did not prove to be important. The Upper cylinder was not provided with a thermostat, but was at room temperature. A small oil bath was built around the cylinder above the ring carrying the screw plug of the manganin gauge, and the temperature was read a number of times during a run with a thermometer immersed in this oil bath. The Variation of temperature during a run was seldom more than a few tenths of a degree, and the corrections for this small Variation were so easy to apply that the complication of a thermostat was not justified. The manganin gauge was the identical one which had been used in the previous work on resistance at low temperature; it was wound from wire 0.003 inch in diameter, obtained from Driver Harris. It was however, now subjected to a fresh seasoning procedure, the zero drift having become, in the two years since previously used, somewhat larger than desirable. The seasoning consisted in maintaining it continuously at a temperature of 135° C for three days, except for two excursions for five minutes each to the temperature of solid C02. The resistance was lowered 0.45% by the seasoning, and the pressure coefficient dropped 1.79%. The pressure calibration was made in the usual way in terms of the freezing pressure of mercury at 0° C. The drift of the zero was very much reduced by the new method of seasoning; the change of zero in three months time now amounting to an increase of 0.005% of the total resistance. Because of the necessity of getting closely spaced pressure readings in the neighborhood of the transition points, the sensitiveness of the pressure readings was increased nearly five times beyond that of the previous work by increasing the size of the slide wire of the bridge. With the new arrangements, 1000 kg/cm^ corresponds to a slider displacement of about 24 cm, and it was possible to get readings consistent to 0.1 mm, or about a quarter of an atmosphere, over the entire pressure ränge. The absolute accuracy of the calibration, of course, does not correspond to this sensitiveness, but small differential effects could be obtained corresponding to this sensitiveness.

109 — 2860

T H E MELTING CUBVES OF NITROGEN AND AEGON

7

The lower cylinder, in which freezing takes place, has to be maintained at constant temperature at any desired point in the ränge from 77° K to 185° K, and this demanded the construction of a special thermostat. In the previous work only the temperature of boiling oxygen was used, so that formerly the problem was very simple. Boiling oxygen was also used as one of the fixed temperatures in this work, and to this was added boiling nitrogen. The liquid nitrogen was obtained by passing nitrogen from a tank of commercial nitrogen, "99.7% pure," through a copper coil immersed in liquid air, there being a throttle valve on the outlet end so as to maintain a pressure of at least five atmospheres in the gaseous nitrogen and thus permit its liquefaction at the temperatiu-e of liquid air. Corrections were made for the barometer when using either of these boiling baths, as had also been done in the previous work. Above the temperature of boiling oxygen there are no available substances boiling within the ränge desired, and some sort of stirred and thermostated bath seemed the only possibility in view of the necessity of raising and lowering the cylinder into the bath in order to control the freezing, as will be explained later. The problem of a stirred bath in this ränge of temperature is one which has been encountered by many other experimenters and has never proved easy of Solution. The conditions were in this case perhaps more exacting than usual because of the unavoidably large heat leak into the bath along the connecting pipe. I made a number of attempts before finding the Solution adapted to the needs of this particular ezperiment. The bath liquid finally used was liquid propane, obtained by passing the gas, sold commercially under various trade names in compressed cylinders for domestic use in places where there is no municipal gas supply, through a copper coil immersed in CO2 and alcohol. The liquefied propane is contained in a thin German silver can of about one half liter capacity, surrounded for heat insulation by a special thermos flask pierced with a hole through the bottom. The propane is stirred by a small turbine stirrer of conventional design. Passing through the propane bath are several turns of light walled copper tubing, connected at the upper end with a source of vacuum, and at the bottom end, through the bottom of the pierced thermos flask, with a source of liquid air. When the temperature rises too high, liquid air is automatically sucked up into the copper tubes, lowering the temperature of the surrounding bath, until the vacuum is again cut off. The temperature regulating member is essentially a hydro-

109 —

2861

8

BRIDGMAN

gen pressure thermometer. A thin walled copper bulb, of about 8 cm' capacity, connects through hypodermic steel tubing of 0.02 cm diameter with a mercury column provided with suitable contacts. The bulb also connects, through suitable reducing valves, with a tank of commercial hydrogen. The height of the mercury column is so chosen that the hydrogen in the bulb is under a pressure of about two atmospheres, thus increasing the sensitiveness. The contacts are made through a vacuum tube arrangement through a thyratron, so that the motor which runs the vacuum pump can be turned on and off with no sparking at the contacts; the sensitiveness is so great that the contact makes or breaks with no motion of the mercury column perceptible to the eye. The bidb was always carefully filled with hydrogen by flushing from the tank a number of times to remove the atmospheric air. It was found that use of hydrogen instead of air greatly improves the Performance, both because of the better heat conductivity of the hydrogen, and because of the diminished resistance in the connecting capillary. Sluggishness of response due to viscous resistance in the capillary limits the sensitiveness of this device; if the size of the capillary is increased too much, error is introduced by fluctuations in room temperature because of changes in the volume of that part of the gas exposed to the temperature of the room. In Order to avoid danger from ignition of the propane vapors which might escape from the bath into the room, a small ventilating hood was built around the lower end of the press and connected with a ventilating fan. Evaporation was prevented as much as possible by the use of a fairly tight Atting cover over the propane bath, but this had to be removed during the manipulations incidental to freezing, so that during a run of several hours perhaps as much as 50 cm' of propane was lost by evaporation. This was replaced several times during the run from a special source of supply, so that the level of the bath was maintained approximately constant, an important point in Order to avoid errors in the volume due to fluctuations in the temperature of the pipe. One anticipated source of danger was the explosion which might result from a mixing of propane with the liquid air if there was a rupture of the lower cylinder. Fortunately the lower cylinder remained intact during all the runs, but this source of danger was in any event minimized by surrounding the thermos flasks containing both propane and liquid air with heavy steel walls so that, if rupture of the lower cylinder did take place, only the small amount

109 — 2862

THE MELTING CURVES OF NITROGEN AND ARGON

9

of liquid air which might happen to be in the cooling spiral would come in contact with the propane. Before using propane I tried some of the non-inflammable liquids recommended for cryostats by the Bureau of Standards, which are described in International Critical Tables, vol. I, p. 61. It proved that although these might be practicable at the upper end of the temperature ränge as far as their behavior at that temperature only is concerned, they at once become of the viscosity of Vaseline on the wall of the cooling spiral when the liquid air is sucked into the spiral, and for this reason were totally unfit for use in my particular form of cryostat. Temperature was measured with a copper-constantan thermocouple, using a Standard cell and Leeds and Northrup potentiometer, Type K, for the measurements of voltage. One junction was maintained at 0° C in a thermos flask filled with ice, and the other junction was immersed directly in the propane of the bath at a point very dose to the wall of the pressure cylinder. The sensitiveness of the potentiometer corresponded to about 0.03°. The thermo-couple was calibrated at the boiling points of nitrogen and oxygen and at the subliming point of solid COj. The voltages at these temperatures were compared with those given by Adams for a copper-constantan couple in International Critical Tables, I, 57, and a smooth deviation curve was drawn through the points representing the difference of the readings. The temperatures corresponding to other voltages were obtained by a combination of Adams's tables with the deviation curve. The error in such a procedure shoiJd not be more than 0.05° at any point, which was sufficient for the purposes in hand. A second copper-constantan couple, connected to a sensitive millivoltmeter, served as a thermometer in giving a constantly visible indication of the temperature, but not with the accuracy of the potentiometer readings. The bath temperature, except of course when boiling oxygen or nitrogen was used, fluctuated back and forth through an extreme ränge of 0.5° C with a period of about two minutes. The extreme temperatures were read several times during the course of a run and the mean taken as the true temperature. At the interior of the pressure cylinder the temperature fluctuations of the bath were to a large extent wiped out, but nevertheless, sometimes when both liquid and solid phases were present together, the temperature fluctuations were manifest in a small oscillation of pressure lagging almost 180° behind

109 — 2863

10

BRIDGMAN

the temperature fluctuations of the bath. Under these conditions the mean temperature was taken as corresponding to the mean pressure. When only one phase was present the pressure fluctuations were too small to be perceptible. In addition to the measurements with the apparatus just described of the coordinates of the melting curve and the changes of volume, it was necessary also to know the specific volume of the gaseous phase in the ränge of pressure and temperature involved. The reason for this is that the measured discontinuity in the motion of the piston gives the change of volume on freezing of that quantity of the solid which occupies a known volume, that is, the volume of the lower cylinder, under the given conditions, whereas what is thermodynamically significant is the change of volume per gram. A knowledge of a specific volume is therefore necessary. I t has already been stated that no specific volumes are known in the ränge of pressures and temperatures involved here. However, it is very easy with this apparatus to make connection at any pressure between the volume at any temperature in the ränge below 0° C, and at temperatures in the ränge above 0°, merely by changing the temperature of the lower cylinder from the one value to the other and observing the amount by which the piston must be withdrawn to maintain pressure constant. Hence if the specific volumes are known over the requisite pressure ränge at some temperature above 0° C, the present apparatus readily süpplies the additional Information necessary. Now the specific volumes of nitrogen are known above 0° C, from the werk of Amagat up to 3000 kg/cm®, and from my own preA^ous work above 3000. No such information exists for argon, however; it is true that I have measured the change» of volume above 2500 kg, but these results cannot be converted into specific volumes until the volume is known at some one fiducial point in the ränge. To obtain the one fiducial point another simple piece of apparatus was necessary. This consisted merely of a small steel bottle of known volume which could be filled with argon to a known pressure and sealed off from the source of supply. The total weight of the bottle filled with gas was then measured, and again after the gas had been allowed to escape. The bottle was made of a stainless steel sold under the trade name of " Alleghany 44." I t is shown in Figure 1. The closure by the piece B was copper welded into place in an atmosphere of hydrogen, and was thus gas-tight. The capacity to the point C was then determined by weighing empty and filled with air-free distilled water. The interior

109 — 2864

T H E MELTING CURVES OF N I T R O G E N AND ARGON

11

volume was 1.26 cm'. A steel capillary of 0.008 inch internal diameter and 0.120 inch extemal diameter was then soft soldered into the piece B, the threads being first tinned carefully both inside and out,

FIGDKE 1. surface.

The steel bottle for obtaining a fiducial point on the p-v-t

and there being also an arrangement of steel retaining rings, not shown in the diagram, to prevent the extrusion of the soft solder by pressure. The other end of the steel capillary was connected to the high pressure apparatus by soft soldering into a cylinder shown in Figure 2, which replaces the lower cylinder of the freezing apparatus. The crux of the S i t u a t i o n is the piece of Wood's metal A, contained in the connecting cylinder. In use, the bottle was maintained at 0° C and filled with argon to a measured pressure. The connecting cylinder and the upper 10 cm of the steel capillary were then raised to the boiling point of water, melting the Wood's metal A. An excess pressure of 500 or 1000 kg/cm'' now forced melted Wood's metal into the capillary until it reached the cold part, where it froze. The connecting cylinder was now chilled, and the capillary cut off where it joins the cylinder, thus giving the bottle with gas sealed into it at known pressure. Weighing to the requisite accuracy was easily done

109 — 2865

12

BBIDGMAN

by attaching to the under side of the scale pan of a balance through a hole cut in the case. The actual filling was made at a pressure of

F I G U B E 2. Shows the connecting piece through which the bettle of Figure 1 is fiUed. The piece of Wood's metal A is melted after filling, thus sealing the gas into the bottle.

1070 kg/cm^, and the weight of the gas was 1.030 gm. An attempt to get a second fiducial point from a filling at 1500 kg/cm^ was unsuccessful because of leak around the soldered joint of the steel capillary. The interior of the steel capillary was found to be far from smooth; in places the cross section was roughly star shaped with sharp corners. This means that the absolutely tight sealing of the capillary with

109 — 2866

THE MELTING CUEVES OF NITROGEN AND ARGON

13

melted Wood's metal was not the perfectly simple thing that would be suggested by the description above, but additional manipulation was necessary, pinching the capillary nearly flat in places with a heavy clamp, and remelting and resolidifying several times the Wood's metal between the pinched places. A perfectly tight seal can at once be tested by immersing the cut end of the capillary in water, and it was only after a number of atteinpts that such a perfectly tight seal was obtained. There are a couple of small corrections to be applied; one for the thermal expansion of the steel of the bottle, for which the figure of the manufacturers (0.0000162 mean linear expansion between 20° and 100° C) was assumed, and a very small correction for the capacity of the capillary. The correction for the distortion of the bottle under internal pressure is too small to be appreciable. The measurements with the bottle just described give a fiducial point at 1070 kg/cm^ and the lowest pressure of my previous measurements was 2500. The interval between these two sets of measurements was spanned by making two sets of isotherms at room temperature, one with the same lower cylinder as that used in the melting measurements, and another with the same lower cylinder nearly filled with a known amount of steel. The difference of the piston displacements of the two isotherms gives the volume compression of the amount of gas occupying the volume of the steel, the various unkftown factors, such as the effect due to the compression of the packings, dropping out when the difference is taken. By this means the new point at 1070 kg/cm^ was connected with the previous work at 2500 and higher. EXPERIMENTAL PROCEDUEE.

The experimental procedure consisted mostly of perfectly straightforward adaptations and modifications of procedure used in previous measurements of phase change or of compressibility by the piston displacement method and need not be described in detail except for a few special points. The initial filling of the apparatus must be done in such a way as to get rid of most of the atmospheric air originally present, which otherwise will act as a dissolved impurity, depressing the freezing point and rounding the corners of the transition curve so as to obscure the true change of volume. In the case of nitrogen, of which a plentiful supply was available, this was accomplished by flushing out the apparatus three times from the original supply.

109 — 2867

14

BRIDGMAN

Since the pressure in the supply tank is of the order of 100 atmospheres, the original impurity is reduced by three flushings to 10~' of the total, a wholly negligible amount. In the case of argon (because of its greater value), this procedure was modified by initially exhausting the apparatus to about 1/100 atmosphere, filling once with argon at 100 atmospheres, exhausting again to 1/100 and finally filling again with argon to 100, thus again reducing the proportion of atmospheric impurity to 10~®. The approximate location of the freezing eurve was already known from the work of Simon. The freezing point was of course approached from the gas side, plotting the readings of piston displacement against pressure as each point was obtained. In this way the first beginning of freezing was at once caught. Special manipulation was now necessary in order to fill the lower cylinder with the solid phase and prevent freezing in the connecting pipe, which would have led to an incorrect and too small value for the change of volume. This was accomplished by lowering the bath from around the lower cylinder until only the lower part of the cylinder was dipping in the bath liquid, and then pushing the piston in by a number of small steps, perhaps 10 or 12 altogether, and at the same time raising the bath back until the cylinder was again completely immersed and also the connecting pipe up to the former mark. In this way the lower cylinder was forced to freeze solidly füll from the bottom up. After complete freezing had been accomplished, pressure was raised about 200 kg beyond the freezing point. Gare must be taken not to push pressure too far beyond the freezing point or eise the plug of solid in the pipe will yield, transmitting pressure to the solid in the cylinder, so that the change of volume measured will be that between the gas at the transition pressure and the solid at a somewhat higher pressure, which would give too large a change of volume. Readings were now made with decreasing pressure, perhaps at 40 kg intervals above the freezing point, several in the two phase region with varying proportions of the two phases, and then several in the gaseous phase, locating the first reading in the gaseous phase as dose as possible, usually within 40 kg, of the lower corner of the discontinuity, so as to minimize error by making only a short extrapolation necessary. It is obvious that having once filled the lower cylinder füll with the solid phase, no such precautions were necessary in lowering pressure as in raising it, and these readings could be made rapidly. The small size of the apparatus and increased thermal conductivity at low temperatures much facil-

109 — 2868

T H E MELTING CURVES OF NITROGEN AND ARGON

15

itates the procedure compared with previous transition measurements at higher temperature, and the whole series of readings with decreasing pressure could be made in less than an hour. Both the pressuretemperature coordinates of the melting curve and the change of volume were taken from the readings with decreasing pressure, these being more reliable than the readings with increasing pressure. The discontinuity in piston dipslacement given directly by the readings does not yield at once the change of volume on melting of the amount of solid which fills the lower cylinder, but includes also the thermal expansion of the gas on passing from the temperature of the lower to that of the upper cylinder. Because of the large temperature ranges, this correction is considerable. The füll details by which the correction was determined need not be described here. The general method, as already indicated, was to describe isotherms at various temperatures over the ränge of pressures involved, the difference of the isotherms giving almost directly the thermal expansions necessary. These isotherms were checked after a cycle of pressure and temperature changes by returning to the initial point. This check was almost always highly satisfactory, there being no evidence of leak, or of penetration of the gas into the steel, or permanent deformation of the cylinder. Only once was there a slight and temporary leak at the highest pressure; the character of the plot made so obvious the exact place where this had occurred that small corrections could be easily applied to it, so that it was not necessary to discard the run. The Parameters of the gaseous phase as such were determined only in so far as they were necessary to characterize completely the transition data, but nevertheless a considerable amount of .Information was thus incidently obtained of the p ^ t surface in regions not previously explored. This data is tabulated in the following, not at regulär temperature intervals, which would have involved interpolations and extrapolations which would perhaps not have been justified, but very nearly in the form in which it was obtained. I hope that at some time in the future this same apparatus may be used to give more systematic Information about the surface in this region. D E T A I L E D PRESENTATION OF D A T A .

Nitrogen. The nitrogen was obtained from a cylinder of 99.90% purity. I am indebted for this to the special courtesy of the Research Department of the Air Reduction Company. The labels as commercially supplied indicating the purity of nitrogen are highly misleading.

109 — 2869

IG

BRIDÜMAN

Thxis the true meaning of a label "99.90% pure" on a commercial tank is that the oxygen content has been tested and found to be 0.10%. In addition to oxygen, there is of course a considerable impurity of argon in nitrogen obtained from atmoapheric sources as is this, and this impurity is not at all indicated by the label. However, my cylinder was specially provided, and I have the statement of the Research Department that the actual nitrogen content of my sample was 99.90%. As always in making these transition determinations, the data themselves give internal evidence, by the sharpness of the transition, of the degree of purity, and the transitions were in fact in the final series of runs always gratifyingly sharp. In some of the early runs, however, sharp transitions were not always obtained, when various difficulties were encountered in sufBciently flushing out the atmospheric air originally filling the apparatus. Not only were the Corners sometimes rounded under these conditions, but after freezing had once taken place the impurities sometimes segregated, and did not immediately remix, by diffusion, when melting took place, so that there was the appearance of a discontinuity in the gaseous phase, due to the melting of the segregated impurity, superposed on the main transition. One might in this erroneous way receive the

140'

120'

i

100°

80'

60'

1000

2000

3000 4000 Pressure, Kg. / Cm.'

5000

6000

FIGURE 3. The melting temperature of nitrogen in degrees Absolute as a function of pressure.

109 — 2870

T H E MELTING C U K V E S OF NITKOGEN AND ARGON

.06

.04

\ \

\ o

\

17

\

OQ

.02

2000

4000

Pressure, K g . / C m . '

6000

FIGOTE 4. The change of volume of nitrogen on melting, in cm' per gm, as a fimction of pressure.

impression that there were degradation phenomena in the gaseous phase at high pressure and low temperature. In all, runs were made with ten different Allings of the apparatus, of which a few were completely discarded because of either insufficient purity, as shown by the rounding of the Corners of the transition, or because of imperfections in various parts of the apparatus, such as the tömperature measurements or measurements of piston displacement, before the final details of the apparatus had been worked out. There were about six jSllings which gave satisfactory results, either for the transition data or for the various isotherms. The experimental points for the pressure-temperature coordinates of the melting curve are shown in Figure 3, and the changes of volume in Figure 4. The -p-t points are suificiently regulär, but one could wish that some of the AD points had been better. This doubtless means that, in spite of the

109 — 2871

18

BRIDGMAN

precautions, the lower cylinder was not always completely filied with the solid phase. There are probably two reasons for this. In the first place, solid nitrogen seems to have considerable mechanical strength, so that, if the connecting pipe is once plugged with the solid, considerable excess pressure is necessary to force the plug through and build up the proper pressure in the lower cylinder. On several occasions, when the inanipulations of lowering the cylinder back into the bath and simultaneously building up the pressure were not made with great care, very nearly steady conditions were attained at pressures several hundred kilograms beyond the transition pressure at a piston displacement corresponding to only partial completion of the transition. That is, the pipe was plugged, and the plug was yielding with extreme slowness because of its mechanical strength. The second reason is probably connected with the fact that nitrogen apparently does not subcool under the conditions of the experiment, for freezing was always observed to start when pressure exceeded the transition pressure by the smallest observable amount. Since the pressure increases are transmitted through the pipe, a nucleus of solid may well have started to form in the pipe before freezing started in the cylinder itself, so that the formation of a plug is especially easy. One must not from this draw the conclusion that nitrogen will not subcool under any conditions; it is quite consistent with my previous experience that it might subcool when contained in a glass vessel, for instance, although it may not subcool in contact with steel. The most probable errors in A® appear to be in the direction of too small values, so that in Figure 4 the low lying points were entirely disregarded in drawing the curve. In Table I are shown the transition data, taken from the data of figures 3 and 4, smoothed and tabulated at intervals of 1000 kg/cm^. The freezing point at atmospheric pressure was obtained from Inter. dx . national Critical Tables. Table I also contains values of —, obtained dp from a plot of the first differences of temperature against pressure, and finally the latent heat of the transition, L, calculated by Clapeyron's equation, ^ = from the other data of the table. The last dp L significant figure in the latent heat is obviously in great doubt. A most important point to be settled with regard to the melting curve and the data of Table I is whether the melting parameters determined by these experiments refer to a-nitrogen, (low temperature

109 — 2872

19

T H E MELTING CUHVES OF NITBOGEN A N D ARGON

TABLE

I.

MELTING PARAMETERS OF NITROGEN.

Pressure kg/cm«

Temp. Abs.

(h dp

AF cmVgm

1 1000 2000 3000 4000 5000 6000

63°.2 82 .3 98 .6 113 .0 125 .8 137 .8 149 .2

.0209 .0176 .0153 .0135 .0124 .0117 .0112

.072 .058 .047 .040 .033 .029 .026

Latent Heat kg cm/gm 218 271 302 334 335 342 346

modification at atmospheric pressure) or to ß-nitrogen (high temperature modification). At atmospheric pressure the transition temperature between the two modifications is 35.5° K. The melting curve which is measured at low pressures, as for example in the recent work of Keesom and Lisman up to 110 kg/cm', is obviously that of the ß modification. If the high pressure coordinates given above are for the a modification, then there must be a triple point on the melting curve, with discontinuity in direction. The lowest pressure of my measurements was 750 kg; it seems that the assumption of a triple point above this pressure is not consistent with the experimental accuracy. If there is a triple point, therefore, it must be between 110 and 750 kg. In this ränge there are only the measurements of Simon, but when these are plotted on a large scale it appears that there is too much irregularity to settle the point. The argument must therefore be more or less indirect. If the thermodynamic parameters for the transition from a to ß were accurately known, the slope of the transition Ime could be computed and the question settled. This unfortunately is not the case; the latent heat of the transition is accurately known from the work of Giauque and Clayton,® but the values for the volume of the two solid modifications are very conflicting. Thus Dewar® gives for the density of the solid at 63° K 0.879 gm/cm^, Simon finds 0.906, and Keesom and Lisman find 0.947 by calculation from their own — and the latent heat of Giauque. There are X-ray dp measurements of the density of ß-nitrogen: 0.995 at 39° K by Ruhemann' and 0.982 at 45° by Vegard.® The crystal structure of anitrogen has been determined at liquid hydrogen temperature by de

109 — 2873

20

BRIDGMAN

Smedt, Keesom and Mooy,® who find that the structure is probably tetragonal with four atoms in the cell and density of 1.03. It would seem probable therefore that the density of a-nitrogen is greater than that of ß-nitrogen at the transition point, which meaas that the transition line rises, and that therefore a triple point on the melting line is a possibility. Further indirect evidence is contained in the data of Keesom and Lisman for the melting parameters up to 110 kg. Their initial slope is

dp

= 0.0222 against 0.0209, my extrapolated

value by drawing a smooth curve with no triple point, and their AO at atmospheric pressure, 0.092, is much higher Ä a n my 0.072, obtained by smooth extrapolation. These discrepancies are evidence of something the matter, but the disturbing feature is that the discrepancies at first appear to be in the wrong direction to be accounted for by a triple point, since my latent heat should be the sum of the melting heat of ß and the transition heat and therefore larger than the heat of Giauque, and my AD should be the sum of the AD of liquid — ß and a — ß and therefore larger than the value of Keesom and Lisman, instead of smaller. It appears to me that the Solution may be found in a very rapid Variation of the properties of ß-nitrogen in its domain of stable existence. That is, the slope

must drop rapidly along the dp

melting curve, and its A» must also fall rapidly. As far as the slope of the melting curve goes this is consistent with the data of Keesom and Lisman, for the formula by which they reproduce their results has initially a slope 6% greater than mine, which means that initially their temperatures lie above my smooth curve, but at 2000 kg their formula gives a melting temperature 6.7° lower than mine. A bit of confirmatory evidence is that at low pressures the temperatures of Simon are a trifle higher than mine, whereas at high pressures they become rapidly lower. It seems, therefore, probable to me that there is a triple point below 750 kg, that there is rapid Variation in the properties of ß-nitrogen, and that the parameters of the melting curve given in Table I are for the melting of the a modification. This Solution cannot be regarded as entirely satisfactory, however, and must wait for final confirmation for accurate measurements of the melting parameters in the pressure ränge below 750 kg, and for a good determination of the difference of density of the a and ß modifications at the atmospheric transition point.

109 — 2874

21

T H E MELTING CURVES OF NITEOGEN AND ARGON TABLE

II.

VOLUME OF 1 GM OF NITHOGEN.

VoJume, cm^

Pressure kg/cm^

+ 23°.5C

3000 4000 5000 6000

1.2374 1.161S 1.1061 1.0652

0° 1.2069 1.1391 1.0870 1.0487

-50°

-100°

-140°

1.1422 1.0881 1.0451 1.0117

1.0754 1.0327 .9997 .9729

1.0226 .9876 .9613 .9412

In Table II are given the volumes of the gas at regulär pressure and temperature intervals. This table is based on my previous values for the volume at pressures above 3000 kg/cm'' at 68° C, reducing these values to other temperatures by means of the thermal expansions determined in this investigation. My previous work, in turn, was based on the fiducial volume of Amagat^" at 3000 and 68°. Amagat also determined the thermal expansion at 3000 kg. His value for the mean expansion between 0° and 68° at 3000 kg differs by 2% of itself from the value found by me in the present investigation. The volumes of the gas given in Table II are not sufficient for all the reduetions necessary in Computing the parameters of Table I, since they do not extend below 2000 kg. Additional Information needed at the lower pressures was as follows: at the freezing point at boiling nitrogen temperature, that is, at 745 kg/cm^ and 77.5° K, one gram of gas occupies 1.138 cm'. At the boiling oxygen freezing point, that is, at 1472 kg/cm^ and 90.25° K one gram of gas occupies 1.123 cm'. Table II gives the means for finding the volume of the gas at various points of the freezing line; there were direct experimental values at three higher pressures as well as at the points just mentioned. The following appear to be the best values for the volume of one gram of the gaseous (amorphous) phase at pressures on the melting curve of 1, 1000, 2000, 3000, 4000, 5000, and 6000 kg/cm^ respectively: 1.140, 1,137, 1.094, 1.010, 0.980, 0.962, and 0.956. The sudden drop and point of inflection between 1500 and 3500 is unexpected, but the curve as given passes exactly, to the last significant figure, through my five experimental points and the point at atmospheric pressure determined by Baly and Donnan as quoted in Smithsonian Tables. An additional experimental point at 2500 to clinch matters would

109 —

2875

22

BRIDGMAN

have been desirable, but iinfortunately two attempts to put a point here were frustrated by leaks. The curve for the volume of the solid phase along the melting line may be found at once from the data just given and from the data of Table I, the shape of the curve is very much like that for the shape of the amorphous phase, except that the variations are not so pronounced. Argon. The argon was obtained from the Cleveland Lamp Division of the General Electric Company, to whom I am much indebted. It was purified by a process recently developed for use in directly filling lamps without further purification. The impurity is stated to be only 0.1%. I used it without further purification; the transitions were sharp, indicating suflficient purity. The measurements on argon were made after the apparatus had been perfected and after experience with the manipulations had been gained by the work on nitrogen, so that not so many runs were necessary; six fillings in all were made of the high pressure apparatus, and in addition several fillings of the bottle in order to get a fiducial point on the p-v-t siu^ace. 180'

160°

£ 140' 2

3 120'

1000

2000

3000 4000 Pressure, Kg./Cm.'

5000

6000

FIGUBE 5. The melting temperature of argon in degrees Absolute as a function of pressure.

109 — 2876

THE MELTING CURVES OF NITROGEN AND ARGON

23

The experimental p-t points on the melting curve are shown in Figure 5 and the experimental values of A® in Figure 6. It will be .08

.06

X

.04

.02

2000 4000 Pressure, Kg. / C m / FIOURE 6.

6000

The change of volume of argon on melting, in cm^ per gm, as a

function of pressure.

Seen that in general the A® points lie much more smoothly than for nitrogen. Neither of the reasons suggested for the irregulär results of nitrogen seem to be operative in the case of argon. In the first place, argon was several times observed to subcool, excess pressures of 100 kg or more being possible before freezing takes place. As already suggested, this characteristic would tend to result in the formation of the first nucleus of the solid in the cylinder itself rather than in the connecting pipe, with less likelihood of a plug of solid in the pipe.

109 — 2877

24

BEIDGMAN

In the second place, the mechanical strength of solid argon is apparently not as high as that of solid nitrogen, and no phenomena were observed with argon which would suggest the plugging of the pipe. In fact, on one occasion the change of volume on freezing was measured without taking any of the regulär precautions to ensure freezing from the bottom of the lower cylinder, and the point thus obtained lay smoothly on the curve with the others. The melting parameters, at regulär intervals and smoothed, are given in Table III; the melting point at atmospheric pressure was taken from International Critical Tables. TABLE

III.

M E L T I N G PARAMETERS OF ARGON.

Pressure kg/cm^

Temp. Abs.

d'z dp

AV cmVgm

Latent Heat kg cm/gm

1 1000 2000 3000 4000 5000 6000

83°.9 106 .4 126 .3 144 .9 161 .9 177 .8 192 .9

.0238 .0211 .0192 .0178 .0165 .0165 .0146

.0795 .0555 .0425 .0340 .0280 .0240 .0210

280 280 279 277 275 276 277

The volumes of the amorphous phase, at regulär pressure intervals and various odd temperatures determined by the accidents of the thermostat settings for the transition measurements, are given in Table IV. The values at 55° C are taken over directly from previous work, it now being possible to give the absolute volumes instead of only the volume changes, which alone was possible previously. Table IV provides the means by which the volume of the amorphous phase may be found at various points on the melting curve. There are also approximate experimental values for these same quantities; the experimental point at 750 kg/cm^ lies too high to fit in with the other points and the known value at atmospheric pressure; the experimental points at higher pressures lie fairly well on a smooth curve. The following seem to be the best values for the volume in cm' of 1 gm of the amorphous phase at various points on the melting curve: 1 kg, 0.702 cm«; 2000 kg, 0.656 cm'; 4000 kg, 0.638 cm'; 6000 kg, 0.628 cm'. The corresponding values for the volume of the solid are: 0.622,

109 — 2878

THE MELTING CURVES OF NITROGEN AND ARGON T A B L E

IV.

V O L U M E O F 1 OM o r

Pressure kg/cm« 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2500 3000 3500 4000 4500 5000 5500 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000

25

ABOON.

Volume, cm« + 55° C

.880 .831 .797 .772 .748 .730 .712 .698 .685 .663 .645 .630 .617 .607 .596 .588 .580 .573

+25°

0°

1.262 1.175 1.110 1.060 1.020 .989 .962 .938 .916 .898 .883 .870 .857 .846 .808 .773 .751 .729 .712 .695 .682

1.179 1.105 1.048 1.006 .970 .943 920 .899 .880 .864 .852 .840 .828 .818 .785 .753 .733 .713 .697 .681 .669

-90°.0

-101°.4 - 1 1 7 ° -135°.l

-1S3°.5 -171°.9 .724

.690

.697 .677 .657

.671 .661 .650 .641 .631 .624

.687 .667 .656 .642 .632

.653 .638

0.613, 0.610, and 0.607. This approximate constancy may be of 3ome theoretical significance. DISCUSSION.

A comparison of my p-t-v values of the gas with those of other observers is not possible, for there are no other determinations in this ränge; the only other values for the freezing parameters are those of Simon and collaborators for the p-t coordinates. Simon's melting curves for both nitrogen and argon nin mostly below mine, that is, at a given pressure his melting temperature is lower than mine. For

109 — 2879

26

BRIDGMAN

argon the discrepancy increases from 0 at atmospheric pressure to a maximum of about 2.5° at 1400 kg, between 1400 and 3400 the discrepancy is roughly constant, becoming less, if anything, at the higher pressures. For nitrogen the discrepancy is more serious. Up to 1400 his curve lies slightly higher than mine, by not more than 0.2° or 0.3°, but at 1400 it crosses, and from here on the divergence increases rapidly with increasing pressure, becoming more than 6° at 4900. The discrepancy is in the direction that would indicate impurity in Simon's material, but I believe that this is not the explanation and that the reason for the discrepancy can be found in Simon's method. This was the method of the stopping of a eapillary tubing first used by Keesom" in finding the freezing curve of helium. A eapillary tube filled with the gas connects at either end with a pressure gauge, the central part of the eapillary being maintained at the temperature at which the freezing pressure is to be determined. Pressure is increased by pushing a plunger into a cylinder connected to one end of the eapillary, resulting in a rise of pressure in both gauges as long as the substance remains fluid, but when the substance freezes the eapillary is plugged and only the one gauge responds to a further decrease of volume. A source of error in the method, apparently not discussed either by Keesom or Simon, is the fact that the plug of solid in the eapillary must be under a shearing stress, and it is known by thermodynamics that the freezing temperature is always depressed by a shearing stress by an amount proportional to the square of the stress and to the absolute temperature. The fact that the discrepancies are markedly greater with nitrogen than with argon fits in perfectly with the Observation made above that the pipe plugs much more easily with nitrogen than argon, involving a greater mechanical strength in the solid nitrogen and consequent greater shearing stress in it. The rapid increase of the discrepancy in nitrogen at high pressures is also consistent with this suggestion; the discrepancy would increase because of the increased viscosity or shearing strength to be expected in solid nitrogen in virtue of the increasing pressure, and it would also increase because of the absolute temperature factor in the thermodynamic formula. On the other hand, there would be a decreasing tendency because of the decreased strength to be expected at higher temperatures; in view of other experience at high pressures I would expect the first tendency much to preponderate. It would be an easy matter to find whether this is actually an important source of error if experiments by the method of Keesom are repeated in the future;

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THE MELTING CURVES OF NITHOGEN AND ARGON

27

if the effect is unimportant, the freezing pressure should be independent of the diameter of the capillary, whereas if the effect is important, the apparent freezing temperature should increase as the diameter of the capillary increases. Apparently the size of the capillary was not varied in previous experiments; the diameter of Simon's capillary was only 0.15 mm. The fundamental question raised by this investigation with regard to the existence of a critical point, crystalline-amorphous, must already have been answered by the reader from an inspection of Tables I and I I I . If there is a critical point, the curves of latent heats and volume differences must be such that they will extrapolate to a common vanishing point. For argon the latent heat is almost exactly constant, whereas for nitrogen it increases, comparatively rapidly at first (which may be an effect of the disregarded triple point), but it also is approximately constant between 3000 and 6000 kg/cm^. The volume differences on the other hand decrease, but the curve is convex toward the pressure axis in such a way as not to indicate vanishing at any finite pressure. Furthermore, if the changes of volume and the slope of the melting curve, —, are plotted agairst dp temperature instead of pressure, in every case the curve will be found to be convex toward the temperature axis. In all these respects the behavior of nitrogen and argon is not different from that of all other substances whose melting parameters under pressure have been determined, and there is still absolutely no evidence which would lead one to expect the existence of a critical point or to expect that the melting curve does otherwise than rise to indefinitely high pressure and temperature, with a curvature becoming continually less, a difference of volume between the two phases becoming continually smaller, and a latent heat tending on the whole to remain constant or to increase. In retrospect it is a little difficult to see why a permanent gas should be expected to give any more valuable evidence as to the character of the melting curve than other substances. Simon makes the point that in the case of helium, which unfortunately could not be investigated here, the critical temperature, gas-liquid, has been exceeded in his measurements by a factor of 8, whereas previously the maximum excess was only 20%, in the case of CO2. But what the precise significance of this is does not appear in the absence of any theory indicating a connection between the phenomena of passage from vapor

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28

BRIDGMAN

to liquid and passage from amorphous to crystalline phase, and in any event it does not appear why it should be more informing to exceed the critical temperature 8 fold than to exceed the critical pressure 165 fold, which had already been done. In fact, the great difference between the relative roles played by pressure and temperature on the vaporization and the melting curves, as shown by the difference between the factors 8 and 165, should itself indicate a vital difference between the phenomena of vaporization of the liquid and of crystallization of the liquid. There are a number of minor points which may now profitably be discussed. The latent heats of melting at atmospheric pressure given in Tables I and I I I , which were obtained by extrapolation from the last experimental point at 750 kg/cm', may be compared with the directly determined values of other observers. For nitrogen my extrapolated value is 218 kg cm/gm against 259 of Giauque. For argon my extrapolated value is 280 kg cm/gm against 287 of International Critical Tables. I t may be mentioned that all my computations and extrapolations were made before these previous values were consulted, and that no adjustment was made afterward. The better agreement in the case of argon is, doubtless, to be explained in part by the better values for A® which it was possible to obtain for argon, and in the case of nitrogen there is the unsettled point of a possible triple point. I do not believe, however, that all the discrepancy can be laid on my A® values, but I believe that there may be error in the previous values at atmospheric pressure. Simon comments on the well known inaccuracy on the density of the solid phase at atmospheric pressure, a datum which enters the latent heat. The difference of energy, A £ , between liquid and solid is of interest as well as the latent heat. The energy difference is obtained by subtracting from the latent heat the mechanical work during melting, or pAv. The term pAv is given in Tables I and I I I . Plotted against pressure or temperature it rises continuously, concave toward the pressure or temperature axis, with continually decreasing curvature. The AE curve has much the same character as the Av curve, falling with increasing pressure or temperature, but convex toward the axis in such a way as not to indicate vanishing at any finite pressure or temperature. The character of the pAv curve also gives some insight into the behavior of Av itself as a function of pressure. If Av vanishes at a finite pressure or temperature, the pAv curve must cross the axis at the corresponding point and there is no indication of this.

109 — 2882

THA MELTING CURVE8 OF NITEOGEN AND ARGON

29

Furthermore, if A® vanishes at infinite pressure, and if the p ä v curve continues to rise, as it does in the experimental ränge, then A® must vanish with infinite pressure less rapidly than it would if the relation between p and Av were of a simple hyperbolic type. In setting up a theory of the melting curve and its ultimate course it would seem that some significance should be attached to the volumes of liquid and solid phases along the melting curve. Such Information has been available in only a few cases hitherto, there being very few substances whose p-v-t surfaces have been determined for both liquid and solid phases. In the case of water and mercury it was known, however, that volume of both liquid and solid decreases with rising temperature and pressure along ^ e melting curve. We now add to this the information that the volumes of nitrogen and argon also decrease. I t would therefore appear not unlikely that this may be the general State of affairs. In fact Simon drops the remark that the volume of the liquid " m u s t " decrease along the melting curve. Such a State of affairs is, doubtless, consistent with our rough general expectations, because as the disorienting effect of temperature increases it would seem natural that the molecules should have to be brought into closer contact to induce crystallization. But this can be only a partial picture, because we know from thermodynamics that freezing is not produced by any condition in the liquid phase alone, but takes place only when there is a proper relation between both phases, a consideration which does not enter the crude picture just presented. I believe that in the absence of any general theory the expectation that the volume of the liquid phase always decreases along the melting curve is premature. In fact, the data obtained above suggest that theory might take as a rough first approximation the assumption that the volume of the liquid is constant along the melting line. Tuming now to the new data for the gaseous phase alone, the determination of the volume of argon at one fiducial point makes it possible to compute the p-v values at high pressures using data previously found. The relative pv values at 0° C and 55° C are given in Table V. In Computing these values, the volume of 1 gm of argon at 1 kg/cm® at 0° C was taken to be 580.3 cm', and the perfect gas law was assumed to hold at atmospheric pressure between 0° and 55°. At high pressures the curve of pv against pressure is normal, being slightly concave toward the pressure axis. Compared with nitrogen at 68°, hydrogen at 65°, and helium at 55°, the only other gases for which pv is known at high pressures and which will be found in Figure

109 — 2883

30

BBIDGMAN T A B L E V. R e l a t i v e V a l u e s o r PV t o b A k g o n .

Pressure kg/cm2 1 1000 2000 3000 4000 6000 6000 7000

PF 0° 1.000 1.733 2.818 3.89 4.91 5.87

55' 1.00 2.52 3.43 4.29 5.10 5.89 6.65

Pressure kg/cm'' 8000 9000 10000 11000 12000 13000 14000 15000

PV 0"

55° 7.40 8.14 8.85 9.58 10.26 10.97 11.65 12.33

4 of my previous paper/^ yv for argon at 55° is between that of nitrogen and hydrogen, and is roughly twice that of helium. At pressures below 2000 kg/cm^, pv for argon starts out by being convex toward the pressure axis; this convexity is much more marked at 0° than at 55°, and is of course a result of the fact that at 0° argon is relatively much nearer its critical temperature than the other gases at the temperatures mentioned. The data contained in Tables II and IV give much better values for the thermal expansion of nitrogen and argon than were obtained in my previous measurements, which were only very rough, and in fact I did not venture to give the values in detail. One check on the values now obtained has already been mentioned, namely that at 3000 kg/cm'' my thermal expansion of nitrogen agrees within 2.5% with that of Amagat. At higher pressures there are no previous values for comparison. It is seen that thermal expansion regularly decreases with increasing pressure and is less by a factor of several fold than it would be for a perfect gas. In fact it is smaller than for many liquids, such as alcohol, under normal conditions. Thus for nitrogen the thermal expansion at 0° C at 3000 kg/cm' is less by a factor of 3.4 than for a perfect gas, and at 6000 is less by a factor of about 5.5. Similarly, the thermal expansion of argon at 0° at 2000 is less by a factor of 2.82 than for a perfect gas, and at 5000 is less by a factor of 5.9. •pv, on the other hand, diflfers more from the perfect gas values for nitrogen than for argon. This means that the compressibility of nitrogen differs more from the perfect gas value than does that

109 — 2884

T U E MELTING CURVES OF NITROGEN AND ARGON

31

of argon, but its thermal expansion differs less. The relatively high thermal expansion of nitrogen, as compared with that of argon, tends to become more marked when extrapolated to higher pressures. It is known that a small thermal expansion means a law of force between the molecules which is nearly linear, exact linearity leading to zero thermal expansion, so that the forces in nitrogen at high pressures are not so nearly linear as in argon. This might be expected of a diatomic substance as compared with a monatomic one. It is of interest to find the change of internal energy with pressure along an isothermal of the two gases at high pressures. This is given L , , , /dE\ /dv\ /dv\ /dE\ . by the tormula ( — 1 = ~ ~ 1 ~ — 1 " 1 — ) is zero for a W p Vap/x perfeet gas, but for Condensed phases is initially negative, and changes sign at some high pressure. The pressure of the change of sign is the pressure at which the attractive and repulsive forces are in balance. A rough calculation shows that in the case of nitrogen the pressure of reversal is between 4000 and 5000 kg/cm^ at room temperature, and between 5000 and 6000 at - 120° C. The volume at the reversal point is markedly higher at the higher temperature. The minimum of E is very flat however, and its exact location is therefore subject to experimental error, so that possibly the Variation just stated in the pressure of reversal with temperature is not significant. For argon, on the other hand, the reversal has not yet been reached in the ränge covered in Table IV. It is also known that the reversal point of helium must occur at pressures probably above 15000 kg/cm^ at 55°; this suggests a possible essential difference between diatomic and monatomic substances. I am indebted to Mr. Charles Chase for assistance in setting up the apparatus, and for financial assistance to the Milton Fund of Harvard University and the Rumford Fund of the American Academy of Arts and Sciences. R E S E A R C H LABORATORY O F P H Y S I C S

Harvard University, Cambridge, Mass,

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BRIDGMAN

REFEEENCES.

' F. Simon. M. Ruhemann, und W. A. M. Edwards, ZS. f. Phys. Chem. B, 2, 340, 1929; 6, 62, 1929; 6, 331, 1930. 2 W. H. Keesom, Leiden Comm. No. 184b, 1926. W. H. Keesom and J. H. C. Lisman, Leiden Comm. No. 224, 1933; 232b, 1934. J. H. C. Lisman, Smeltlijnen van Gecondenseerde Gassen, Leiden Thesis, 1934, published by Eduard Ijdo, Leiden, 1934. > P. W. Bridgman, Phys. Rev. 3, 126, 1914; 6, 1, 94, 1915. * P. W. Bridgman, Proc. Amer. Acad. 67, 305, 1932; 68, 95, 1933. ' W. F. Giauque and J. O. Clayton, Jour. Amer. Chem. Soc. 66, 4875, 1933. «J. Dewar, Proc. Roy. Soc. 73, 251, 1904. ' M. Ruhemann, ZS. f. Phys. 76, 368, 1932. »L. Vegard, ZS. f. Phys. 79, 471, 1932. • J. de Smedt, W. H. Keesom, and H. H. Mooy, Proc. K. Amst. Akad, 32, (6) 745,1929. >» E. H. Amagat, Ann. Chim. Phys. (6) 29,1,1893. " First reference under 2 above. » P. W. Bridgman, Proc. Amer. Acad. 69, 173,1923.

109 — 2886

MEASUREMENTS OF CERTAIN ELECTRICAL RESISTANCES, COMPRESSIBILITIES, AND THERMAL EXPANSIONS TO 20000 kg/cm^ B Y P . W , BHIDGMAN. Received December 14, 1934.

Presented December 12, 1934.

CONTENTS. Introduction Apparatus and Technique DetailedData Resistance of Gold, Silver, and Iron Resistance of Black Phosphonis Resistance of Single Crystal Tellurium Resistance of Copper Sulphide Compression and Thennal Expansion of Lithium Compression and Thermal Expansion of Sodium Compression and Thermal Expansion of Potassium Discussion Summary

71 73 80 80 82 85 89 91 93 95 96 99

INTRODUCTION.

A number of the phenomena which have presented themselves in a rather extensive survey of the properties of matter up to 12000 kg/cm^ have proved to have features of sufficient significance and interest to justify the serious attempt to extend materially the pressure ränge. In this paper measurements are presented of such phenomena up to 20000 kg/cm'. The electrica! resistances of black phosphonis and of tellurium are studied; both of these substances had been found to have an abnormally high decrease of resistance with increasing pressure.' It was of interest to find whether the resistance of these materials could be forced by sufficiently increasing pressure to approach the resistance of the true metals. An investigation of other semi-conductors suggests itself in view of recent advances in our theoretical understanding of the nature of the mechanism of conduction; it would appear that in general there is some ground for the expectation that at least some semi-conductors can be forced into something like the metallic state by very high pressures, and that therefore a systematic investigation of such substances to the highest

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BRIDGMAN

attainable pressures should be of interest. There are very few measurements on such substances O v e r the lower pressure ränge, so that the grounds do not exist for selecting those substances which most probably will show significant high pressure effects. Furthermore, the difBculty of the investigation is increased by the fact that not many semi-conductors can be obtained in a geometrical form suitable for the measurements. The only course is, therefore, the empirical one of trying all the feasible semi-conductors. A beginning of such an exploration is presented here in measurements on CuSj, which is easy to obtain in massive form. Finally, measurements have been made on the volume as a function of pressure and temperature of the three alkali metals, lithium, sodium, and potassium. In the last few years theoretical understanding of the metallic State has advanced sufficiently to permit a calculation of the compressibility with some success, so that a knowledge of the behavior of these especially simple metals is desirable over as great a ränge of pressure as possible. For some time it has, furthermore, been evident that a knowledge of the thermal expansion also of these metals would be useful, but such determinations have ofifered the greatest experimental difficulties, and hitherto I have not succeeded in making any good measurements for these substances, even in the lower pressure ränge. The primary purpose of the present measurements was to yield reliable values for the thermal expansion, and now after many attempts I believe that I have obtained values which give the essential broad features of the behavior of thermal expansion up to 20000, although the accuracy is not greater than a few per cent, and there are finer details which it would have been desirable to establish. In comparing the present compressibility measurements over the wider pressure ränge with those previously made, a serious error was uncovered in my early published values for compressibility.'' The correction for the second order effect in Converting linear into volume compressibility was applied with the wrong sign in nearly all the measurements published through 1923. The compressibility at low pressures is unaffected by this error, but the volume changes at the maximum pressure were too large by a fractional amount equal to twice the change of linear dimensions themselves. The error is thus largest for the most compressible materials and for the highest pressures; at 12000 kg/cm' the error varies from 1 per cent for iron to 14 per cent for potassium. The corrected values are to be given in detail in another paper.

110 — 2888

MEASUREMENTS OF ELECTEICAL EESISTANCES

73

A P P A R A T U S AND T E C H N I Q U E .

A number of modifications were necessary in the apparatus and technique. In the first place, a hydrostatic press of larger capacity for producing the pressure was necessary. The new press was of about twice the capacity of the old one, the diameter of the piston being 3.5 inches, against 2.5, yielding, with a maximum working pressure of 15000 Ib/in^ on the 3.5 inch piston, a total force of about 140000 Ib. This could be concentrated on a high pressure piston usually about 0.5 inches in diameter, thus allowing a maximum pressure in the high pressure cylinder of the order of 50000 kg/cm^, making no allowance for friction. Formerly the high pressure part of the apparatus consisted of three parts: a cylinder in which pressure was produced and in which was situated the manganin pressure gauge, a connecting pipe, and a cylinder containing the particular specimen under measurement. The apparatus now consisted of a single cylinder, turned with a Shoulder on the Upper end, by which it was retained in the lower head of the press, the bulk of the cylinder projecting beyond the press as indicated in Figure 1. The temperature bath was brought up around the

FIGUBE 1. Section of the high pressure cyhnder mounted in the lower end of the press.

cylinder, the liquid in the bath standing nearly to the top of the cylinder and covering the lower head of the press and the lower ends of the tie rods. The cylinder, except for a by-pass at the upper end by which it was charged as usual to an initial pressure of 2000 or

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74

BEIDGMAN

3000 kg/cm^, was pierced with a single longitudinal hole. This is a departure, made necessary by the demand for maximum strength, from the previous design, in which the manganin gauge was let in through a hole at the side. The leads for the manganin gauge were now brought in at the bottom, along with the leads necessary for the Potentiometer measurements, as will be described later. An alloy steel was used for the cylinder, capable of giving higher physical properties than that which had been formerly used. Formerly a Cr-Va steel of approximately the analysis SAE 6150 was used, giving a maximum tensile strength of 225,000 Ib/in-. This was now replaced by a steel made by the Carpenter Steel Co. under the designation "S-M," and analyzing approximately 0.60% C, 0.75% Mn, and 1.90% Si. It may be heat treated to give a tensile strength as high as 320,000 Ib/in^, and has the remarkable property of showing considerable elongation even when treated to give as high a tensile figure as this. For the high pressure cylinder this steel was quenched into water from a temperature of 900° C, and then drawn at a temperature of 400° C, when it showed a Rockwell C hardness of 48, just soft enough to permit enlarging the hole with a reamer after the usual preliminary stretching. The stretching was usually done with lead, as before. The maximum pressure of the preliminary treatment was about 30000 kg/cm- for a cylinder to be used regularly to 20000, and the Stretch of the interior under this preliminary treatment might be as much as 0.06 inch on an initial internal diameter of 0.44 inches and external diameter of 3.8 inches. After the preliminary stretching one or two of the cylinders were subjected to a low temperature anneal, without any very distinct evidence of improvement. The life of the cylinder was capricious, cylinders having broken after only a few hours use at 20000, while one or two have had a life of about 30 hours total exposure to the extreme pressure of 20000. Rupture may occur at pressures materially less than the maximum previous exposure. In all, five cylinders were used in the measurements to be described here. The pistons were made of a special chrome ball bearing steel, left glass hard; and seldom gave trouble. Because of the violence of the failure of glass hard steel under compressive load, however, it is necessary to use adequate protecting shields in case of failure of the piston. The high pressure piston was packed with a plug of the same mushroom design, using the principle of the unsupported area, as has been used previously.' Failure of these packing plugs by pinching-off

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MEASUHEMENT8 OF ELECTBICAL RESISTANCES

75

of the unsupported stem was at first fairly frequent, but has been minimized by the use of a steel made especially for cold chisels, possessing great toughness combined with high strength, by avoiding reentrant sharp angles, and by avoiding the use of soft solder in attaching the soft packing washers of brass or copper to the mushroom. This last seems to be an important point; apparently tin ultimately gets forced by high pressure into the pores of the steel, the process being assisted by the natural chemical affinity of tin and steel, and failure ultimately occurs by the analogue of the amalgamation failure previously found with mercury at a pressure of a few thousand kilograms. The packing of the pistons is beeoming one of the more serious Problems in considerably extending the pressure ränge, and some simple device which will avoid the pinching off effect is desirable. I have had no luck with the simple solid rubber plug used by Poulter and by Imperial Chemical Industries Limited. This may be suitable if the transmitting liquid is highly viscous, but if the liquid is of low viscosity I have found that leak invariably occurs in the neighborhood of 10000 kg/cm''. In the present experiments it was necessary to use a liquid of the lowest possible freezing point and lowest possible viscosity; iso-pentane was the liquid so employed. It has a high initial compressibility, but this disadvantage was obviated by the initial charging through the by-pass. The details of the method of bringing in electrically insulated leads had to be modified. The leads were now all brought through a single plug at the bottom of the cylinder; there were four such insulated leads, one for the manganin gauge coil, and three for leads to the Potentiometer by which the resistance of the specimen was measured, the fourth potentiometer lead and the other lead to the gauge coil being grounded to the cylinder. The insulated leads were made of piano wire 0.010 inches in diameter. The mica washers previously used were now replaced with Solenhofen limestone, as has been used at the Geophysical Laboratory in Washington, for greater strength; furthermore the limestone cylinder was embedded in a brass sleeve which flowed suflSciently around it to prevent cracking by concentration of stress at the unavoidable local geometrical irregularities. The rubber washers by which the liquid was prevented from leaking around the stem were now replaced by a double washer, artificial rubber (Duprene) at the end next the liquid, and soft natural rubber below it. The Duprene is not attacked by iso-pentane, but is not

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BBIDGMAN

quite soft enough to give complete freedom from leak at the lower pressures, which is ensured by a thin layer of natural rubber. The soft packing on the mushroom plug has also been made of Duprene in these experiments with advantage, there being a marked improvement in the wearing qualities. The general design of the plug carrying the insulated leads was radically altered; the proportions of the holes carrying the packing around the piano wire stems were so changed as to give a considerably greater ratio of length to diameter, and the plug itself was not made integral, as before, with the screw by which it was retained in the cylinder, bat was a separate piece. This permitted the plug to be made much shorter, a change which greatly facilitated construction by avoiding the long accurately placed holes of small diameter demanded by the former method of construction. The measurements of electrical resistance described in the following were made by the same potentiometer method that has been used in much of my previous work, and no further description is necessary. The changes of dimensions of the alkali metals were measured in a piezometer of the same general design as that formerly used, but differing in detail. Attached to the specimen is a fine wire of high specific resistance, which moves over a contact fixed to the envelope containing the specimen as the dimensions of the specimen change under changes of pressure and temperature. Potentiometer measurements of the resistance of the wire between a point fixed to it and the sliding contact permit a calculation of the amount of motion, and thus the changes of dimensions of the specimen relative to the envelope. The distortion of the envelope is assumed to be known from previous measurements. Actual measurements of the compressibility and thermal expansion of steel have been made only up to 12000 kg; the results assumed here up to 20000 were obtained by extrapolating with the same second degree formulas which were adequate to represent the results over the 12000 kg ränge. This procedure seems safe enough in view of the small departure from linearity in the ränge up to 12000, and the smallness of the volume changes in steel compared with the alkali metals. One very serious source of difBculty was permanent changes in the dimensions of the specimens, the transmitting medium becoming viscous enough under pressure to deform permanently metals as soft as these alkalies. The difficulty was minimized by changing the pressure very slowly, and by suitably varying the dimensions of the

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MEASUREMENTS OF ELECTEICAL RESISTANCES

77

specimens. The specimen of lithium, which is mechanically the hardest of the three, was 5.8 cm long and 6.0 mm in diameter; the sodium intermediate in softness, was 2.5 cm long and 8.7 mm in diameter, and the potassium, softest of the three, 1.27 cm long, and 8.7 mm in diameter. The compressibility increases from lithium to sodium to potassium, so that in spite of the shorter length of the potassium, the relative change of dimensions of all three was roughly the same. From the point of view of simplicity of manipulation it would have been very much to be preferred to obtain the thermal expansion as a function of pressure from the difference of isotherms, each described Over the entire pressure ränge. Measurements were desired at five temperatures, 0°, 30®, 52.5", 75°, and 95°, so that this would have involved describing five isotherms to 20000 with practically perfect recovery of the zero, if thermal expansions were to be obtained by difference. In spite of many attempts, such perfection was not obtained. It was not diflBcult to describe a single isotherm with sufRciently small permanent distortion to give the isothermal change of volume with small error, but successive isotherms always involved sufßcient permanent distortion to introduce large percentage errors into the relatively small differential thermal expansions. Two different procedures were therefore finally adopted for getting compressibility and thermal expansion. The compression at 0° C was first determined by describing an isotherm over the entire pressure ränge, up and back, at this temperature. There was an advantage in working at 0° because the metals were mechanically least deformable at this temperature. The thermal expansions at four mean pressures, 5000, 10000, 15000, and 20000 were then obtained by successive readings at the five temperatures, up and down, the position of the piston being held fixed during a temperature excursion and therefore the pressure constant, except for the small changes due to the thermal expansion of the transmitting liquid. Distortion of the specimen under these conditions was practically eliminated, because of the very small movement of the transmitting liquid; and the recovery of the initial reading on returning to 0° was always very dose. In any event, the mean of the readings with increasing and decreasing temperature should give the thermal expansion with sufficient accuracy. The manipulations involved in this procedure were slow, demanding for each reading the changing of the temperature of the bath and then waiting for temperature equilibrium; about six hours were necessary for the determinations of thermal expansion at a single mean pressure,

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78

BRIDGMAN

as compared with two or three hours sufficient for an isotherm over the entire pressure ränge. Such long manipulations were undesirable, particularly at the higher pressures, because of shortening of the life of the cylinder and the possibility that the entire series of meaaurements would be ruined by an explosion. There seemed no way of avoiding this proeedure, however, and most fortunately all the final thermal expansion measurements on the three metals, as well as the calibrating blank runs, were made with the same cylinder. This cylinder showed, however, toward the end of the measurements, unmistakable evidences of approaching failure. The thermal expansions as directly determined were the differential expansions with respect to the steel envelope. In reducing to absolute expansion, the values of the thermal expansion of iron implicitly contained, but not expUcitly stated, in the former measurements of compressibility at two different temperatures were assumed to be correct, and furthermore, as already explained, the results were extrapolated from 12000 to 20000 by the same second degree formula that had sufficed in the ränge up to 12000. This precise assumption is not a matter of much importance, however, because the thermal expansion of iron is small compared with that of the alkali metals, and the Variation with pressure is relatively small. The figures assumed for the linear expansion of iron were 0.0000120 at atmospheric pressure and 0.0000110 at 20000. In making the final computations it was necessary to use corrections which had been determined from a run in which the specimen of alkali metal was replaced by a piece of pure iron. The reason for this was that it would not have been safe to assume that the thermal expansion of all parts of the envelope, which consisted of hard and soft steel and in addition a thin mica washer for insulation, was the same as that of pure strain-free iron. The corrections were so determined as to make the results with the blank run agree with the results assumed for pure iron. As a matter of fact, the corrections so found were of little importance. In addition to permanent distortion in the specimens, another serious difficulty in getting accurate measurements was in the slight fluctuations in the manganin gauge. The difiiculty was probably accentuated by the fact that the gauge was subjected to the same changes of temperature as the specimen. In the former measurements to 12000 the gauge was mounted in a separate cylinder, and maintained continually at room temperature, independent of the temperature of the specimen. The necessity for making the apparatus all

110 — 2894

MEASUHEMENT8 OF ELECTRICAL BESISTANCES

79

in one piece now demanded that the gauge have the same temperature as the specimen. This demanded in the first place a determination of the pressure coefficient of the gauge as a function of temperature. This was done by comparing the gauge at each of the five temperatures against a Standard manganin gauge, which had been calibrated in the regulär way against the freezing pressure of mercury at 0° C and which was maintained continuously at room temperature. This comparison was made up to 12000 kg/cm'. In this ränge the high pressure gauge was linear against the Standard gauge at each temperature. The pressure coefficient is not, however, quite a linear function of temperature, but increases less rapidly at the higher temperatures. The coefficient was found to increase by 1.30 per cent from 0° to 50°, and by 2.04 per cent from 0° to 95°. Partly, perhaps, because of the temperature changes, partly because of the greater pressure ränge, partly because the wire was of smaller diameter than that which had been previously used, 0.076 mm in diameter instead of 0.134, so that viscous drag by the transmitting medium is greater, and partly because the manganin itself is from a different source, being of recent American manufacture rather than of German manufacture of 40 years ago, the permanent zero changes after application of pressure were inclined to be much greater and more capricious than in the previous work. In fact, the changes found at first were sufficiently great to affect seriously the accuracy of the thermal expansion measurements. A special process of seasoning was therefore adopted; this consisted in maintaining the wire at a temperature of 130° C continuously for a week, except that for a few minutes every morning the coil was cooled to the temperature of solid COj. This treatment was effective in reducing the zero wandering to a harmless amount. Thus, after the series of thermal expansion measurements of lithium and potassium, the zero had changed by an amount equivalent to 17 kg/cm^, 0.085 per cent of the maximum ränge. The zero change after the runs with sodium was greater, but there was internal evidence showing that the change had mostly occurred at one definite place, so that correction could be easily applied for it. The extension of the pressure scale from 12000 to 20000 by linear extrapolation of the manganin gauge readings is an unsatisfactory feature, but one which appeared necessary. However, it was possible by two lines of attack to convince oneself that the error so introduced is probably of negligible importance. The problem here is somewhat like that of finding a suitable method of extending temperature

110 — 2895

80

BRIDGMAN

measurements into the region dose to 0° Abs. and the methods adopted are also somewhat similar. If the extrapolated scales given by different phenomena agree, one may have considerable confidence in the results. The first method adopted consisted essentially in a comparison of the extrapolated scales given in terms of the effect of resistance on the resistance of several diflferent metals. The metals chosen were iron, silver, and gold. Extrapolation of the results is complicated by the fact that the resistance changes of these metals are distinctly not of the first degree, nor even of the second degree within the errors of measurement. An ideal procedure would be to show that the same analytical expression represents the change of resistance as a function of pressure over the ränge up to 20000 that had formerly served to represent it up to 12000, assuming the linearity of the manganin over the entire ränge. One might feel considerable confidence if such an extrapolation were possible, because it would be highly improbable that deviations of all four metals would exactly conspire. As a matter of fact the Situation could not be handled in quite this simple way, but this suggests the general idea of the method of approach. The details of the comparison will be found in the detailed presentation of data, and an estimate of the possible error of the linear extrapolation. The second presumptive evidence as to the legitimateness of the extrapolation was obtained from the blank runs with pure iron. The results obtained from these runs were linear to a high degree of approximation at each of the five temperatures over the entire pressure ränge, with no hint of a change of trend between 12000 and 20000, so that for this additional reason considerable confidence may be feit in the extrapolation. DETAILED DATA.

Resistance of Gold, Silver and Iron. As already stated, the primary purpose of these measurements was not to find how the resistance of these metals varies with pressure over the new pressure ränge, but rather to obtain some suggestion as to the legitimateness of measuring pressures above 12000 by assuming that the relation between pressure and the resistance of manganin, which had been shown by reference to a primary pressure gauge to be linear below 12000, continues to be linear between 12000 and 20000. For this purpose it was sufficient to make the measurements at a Single temperature, 30°. The specimens measured were the identical samples which had been measured in 1917;^ they had been kept since that time in cork stoppered test tubes, and showed no perceptible change. The wires were double silk covered,

110 — 2896

MEASUREMENTS OF ELECTRICAL RESISTANCES

81

wound non-inductively into open coreless toroids; the resistance of gold, silver, and iron were respectively 18, 21, and 75 ohms. The three toroids, together with the manganin gauge, were attached one each to the four terminals of the four terminal plug, all coils being grounded in common to the cylinder. Measurements of resistance were made on the same Carey Foster bridge with which the pressure is regularly determined in terms of the ehange of resistance of the manganin. It was not possible to get as clean cut results as had been hoped because of very perceptible hysteresis in the resistance of all three metals against manganin. Readings with increasing and decreasing pressure in all cases differed consistently by much more than the irregularity in the individual readings; the maximum differences between increasing and decreasing readings, in terms of the maximum change produced by pressure, were 0.74 per cent, 0.72 per cent, and 0.55 per cent, respectively, for gold, silver, and iron. Associated with the hysteresis were permanent changes of zero of the same order of magnitude. In view of the long period of rest since previous exposure to pressure, and the very elaborate seasoning of the manganin, and the further fact that the manganin did not show changes of zero, it is plausible to suppose that the hysteresis was not connected with the manganin, but with the other metals. The mean resistance, that is the average with increasing and decreasing pressure, definitely could not be represented within the error of the readings by second degree relations in the pressure; but there were consistent departures always in the same direction, namely the maximum departure from linearity occurs at a pressure less than half the maximum pressure, and the curvature is greater at the low pressures than at the high pressures. The departures from a second degree relation were, however, in all cases slight, being greatest for iron, where the maximum departure of any observed point from that given by the second degree relation was 0.14 per cent of the maximum pressure effect. In view of the hysteresis, it did not seem worth while to attempt to reproduce the divergences by an analytical formula. The following are the second degree relaaons which best reproduce the actual results over the entire pressure ränge. The constants in these formulas are so chosen that the observed changes of resistance at 10000 and 20000 are exactly reproduced. Gold

A /? ^ = - 3.017 X 10-5p + 1.05 X lO-i'p'^ Ro

110 — 2897

82

BRIDGMAN

Silver

^

Iron

^ = - 2.377 X Ko

HQ

= - 3.575 X 10-^p + 1.90 X + 0.71 X 10"!^'

These results are all at 30" C, and pressure is in kg/cm^ The best comparison with previous results is afforded by comparing the fractional changes of resistance at 12000 obtained now with those obtained formerly. The present fractional changes at 12000 for gold, silver, and iron, respectively, are — 0.0351, — 0.0402, and — 0.0275 against the previous values - 0.0346, - 0.0412, and - 0.0275. Finally the question of the possible error in the extrapolation was crudely answered in the following way. The best second degree curve was passed through the experimental points up to 12000, that is, the constants in a second degree relation were so determined as to give the observed changes of resistance at 6000 and 12000. With the constants so determined the change of resistance at 20000 was calculated and compared with the measured value, which of course involved the linear extrapolation of the manganin. The changes of resistance calculated in this way were too small by 1.58 per cent, 0.95 per cent, and 1.24 per cent for gold, silver, and iron respectively, which means that the pressure calculated from a second degree formula made to fit approximately the observed changes of resistance of gold, silver, and iron in the ränge of direct pressure measurement up to 12000 would give pressures too large at 20000 by the amounts mentioned. In view of the known failure of the second degree relation to exactly reproduce the results in the ränge up to 12000, the discrepancies just found must be very generous upper limits to the true error; and I believe that we may finally conclude that the pressure obtained by a linear extrapolation of the manganin resistance is probably in error at 20000 by not more than a small fraction of one per cent. Resistance of Black Phosphonis. This material was from a batch freshly prepared in the conventional way from white phosphorus at 200° C and 12000 kg/cm', the pressure transmitting medium being water. The original dimensions of the white phosphorus were 1.4 cm diameter and 10 cm long. The transition is accompanied by a 33 per cent decrease of volume. The structure of the resulting black phosphorus is coarsely granular at the upper end and at the lower end very fine grained and distinctly filamentary in character, the direction of the filaments presumably being the direction of relative motion

110 — 2898

MEASUREMENT8 OF ELECTRICAL RE8I8TANCES

83

during the transition. The fracture at the lower end is very similar to that of hematite in the form of the so-called "peneil ore." The specimen was out from the lower end; some selection was necessary in Order to obtain a piece free from cracks. The specimen was in the form of a rod of rectangular section, 2.1 x 1.7 mm, and about 2.5 cm total length. Measurements were made by the potentiometer method, using four terminals. The distance between potential terminals was 1.36 cm. The current terminals were bands completely girdling the specimen and making approximately uniform contact all around, so as to minimize end efifects. The specific resistance at 30° C at atmospheric pressure was 0.484 ohm cm; this is somewhat smaller than two values previously found which were 0.588 and 0.773.® The difference is perhaps not more than might be expected in view of the pronounced structural differences of different specimens. The temperature coefEcient at atmospheric pressure is negative, the resistance at 75° being 35 per cent less than at 30°. This is not very different from the temperature coefficient shown by the two previous samples; the temperature coefEcient varies less from sample to sample than does the specific resistance itself. Two unsuccessful attempts to determine the pressure effect were made before the final successful attempt; one of these was terminated by rupture of the cylinder and the other by rupture of the insulating plug. The partial results obtained during the unsuccessful attempts were not inconsistent with those finally obtained. Successful runs were made at 30° and 75°. The initial application of pressure at 30° was accompanied by seasoning effects, the readings with decreasing pressure falling below those with increasing pressure and the zero resistance being permanently depressed by 16 per cent. The seasoning was practically complete with the first application of pressure; on the second application points agreed with increasing and decreasing pressure, the zero shift was only 0.5 per cent, and no point lay off a smooth curve by more than 2.3 per cent of the resistance at that point, the average deviation being much less. The basis of estimation of the smoothness of the results is necessarily different here from that usually employed because of the very large changes of resistance; the meaning of the statement just made is that when logio R/RO is plotted against pressure the maximum deviation from a smooth curve of any Single point was O.Ol, the total Variation in the logarithm being more that 2.00. Log R/RQ is given as a function of pressure at 30° and 75° in Table I.

110 — 2899

84

BRIDGMAN

TABLE

I.

R E S I S T A N C E OP BLACK PHOSPHORÜS.

Logio, Ä//fo

Pressure kg/cm=

30-95° C

0

(.000071)

2000

.0295

4000

.0652

55a

6000

.0779

49.

62j

8000

.0981

45,

10000

.1165

40,

12000

.1332

37o

14000

.1488

33,

16000

.1632

30o

18000

.1767

26.

20000

.1894

23,

linear thermal expansion obtained from the smooth curve of Figure 6 drawn through the experimental points. The general character of the agreement with the results previously obtained' is sufficiently indicated by a comparison of the results at 10000. Linear extrapolation to 0® of the results previously obtained at 30° and 75°, making the correct reduction from AZ/^o to AF/Fo gives A F / F o at 0° and 10000 kg/cm'' equal to 0.1134, against 0.1165 found now. The previous published value, in which the reduction was incorrectly made, was 0.1228. The mean thermal expansion at 10000, to be deduced from the former results, correctly reduced, was

110 — 2910

M E A 8 U R E M E N T 8 OF ELECTRICAL R E S I 8 T A N C E S

95

0.000034 against 0.000041 found now. There is no question but that the present value is to be preferred. Compresaion and Thermal Expansion of Potasaium. The material was obtained from Kahlbaum. I t was melted under Nujol, filtered through a fine hole, cast into a coherent perfectly clean rod of diameter somewhat greater than the final diameter, and reduced to the diameter of the finished specimen by extrusion. The final diameter was 0.87 cm and the length 1.77 cm. More or less complete runs were made with six different set-ups of the apparatus. The first of these was TABLE

V.

V O L U M E COMPRESSION AND T H E R M A L E X P A N S I O N OF POTASSIUM.

Pressure kg/cm'

Mean Linear Volume Compression Thermal Expansion - A F / F o at 0° C 0°-95° C

0

(.000083)

2000

.0571

67o

4000

.1002

53s

6000

.1347

42,

8000

.1640

33e

10000

.1890

26o

12000

.2108

22,

14000

.2300

18,

16000

.2472

15.

18000

.2626

13,

20000

.2767

12,

terminated by an explosion after a fairly complete determination of three isotherms; the results of four others were not sufficiently good to calculate, irregularities being due both to fluctuations in the gauge and to mechanical distortion of the specimen, which is particularly hard to avoid with potassium because of its great softness. The final run gave satisfactory results both for the isotherm at 0° and for the thermal expansion at four approximately constant pressures. The volume compression at 0° and the linear thermal expansion are given in Table V. The volume compressions so tabulated are the weighted means of the two successful isotherms at 0°, giving the results with the two runs a weight inversely as the average departure of the readings from a smooth curve. These departures were 0.0034 and 0.0015, expressed as fractional parts of the total effect, the

110 — 2911

96

BRIDGMAN

second run giving the best results. The diflPerence between the results of the two runs, expressed as a fraction of the maximum effect, was 2 per Cent at 10000 and 1.8 per cent at 20000, the better run giving the lower values for decrease of volume. The thermal expansions given in Table V were obtained from the smooth curve of Figure 6, drawn through points representing the mean of the results for the four temperature ranges, weighted as already described. There was no consistent Variation of thermal expansion with temperature at constant pressure, and it appears to be justified to retain only the weighted mean in the final results. The measured displacements at the high pressure end of the ränge, from which the thermal expansions were calculated, were smaller than for the two other alkalies, both because of the shorter length of the specimen and because of the absolutely smaller value of the thermal expansion. This was reflected in a greater irregularity of the results for the four temperature ranges; the apparently greater regularity of the experimental points for potassium as compared with sodium shown in Figure 6 is probably to a certain extent fortuitous. The volume compression was previously determined only at 45° and up to 12000.'° Using the value for the thermal expansion found now in Order to extrapolate from 45° to 0°, and correcting the reduction from M to AF, the volume compression at 10000 formerly found was 0.1877, against 0.1892 found now. The published value, in which AI was incorrectly reduced to A F , was 0.2150. The discrepancy due to the incorrect reduction is at its maximum for potassium, since it increases at an accelerated rate with increase of AF/Fo. The mean thermal expansion formerly found at 10000 was 0.000020, against 0.000027 found now. In general, the new values are better than the former values. DISCUSSION.

The principal points with regard to electrical resistance have already been discussed in the detailed presentation of data. In general comment, the resistance of black phosphorus and tellurium approaches that of the metals in so far as the reversal of sign of the temperature coefBcient is concerned. If the reversal of sign of the pressure coefficient is considered to be a characteristic of all metals, as it is known to be for the alkali metals, then it is highly probable that black phosphorus and tellurium are metallic in this respect also at pressures not far beyond those actually reached. But the absolute value of the specific resistance, even at the highest pressures, still remains in the

110 — 2912

MEASUREMENTS OF ELECTRICAL RESISTANCES

97

non-metallic ränge, being, for example, 20 times greater for tellurium at 20000 kg/cm^ than for bismuth under normal conditions. With regard to the alkali metals, it is to be remarked in the first place that there are none of the abnormalities in compressibility at high pressures, particularly for potassium, which were previously found and which were entirely due to the erroneous reduction from LljU to A VjVa.

The two compressibilities i ( — J and — ( — J both V\dp/r Va\dp/r decrease smoothly with pressure, even for potassium, up to the highest pressure. For potassium the " instantaneous" compressibility, — I — 1 has dropped at 20000 to about one third its value at atmosv\dpjr pheric pressure, and the " actual" compressibility, — ( — ) , to about Vo\dp/r one quarter its initial value. Furthermore, there is now no crossing of the compressibility curves, but both "instantaneous" and "actual" compressibility increase from lithium to sodium to potassium over the entire ränge of pressure. The thermal expansions, however, do show reversals of order. The thermal expansion drops with increasing pressure by a factor which increases from lithium to sodium to potassium, and the increase is more than sufRcient to wipe out the initial superiority of potassium. The result is that above 3500 kg/cm^ the expansion of sodium is greater than that of potassium, and above 15000 it is less than that of lithium, and above 5700 the expansion of potassium is less than that of lithium. This means that above 15000 the order of the alkali metals, arranged according to decreasing thermal expansion is: lithium, sodium, potassium; exactly the reverse of the order at atmospheric pressure. One is strongly reminded of the reversal of the order of the melting points of the alkali metals at high pressures already found; the two phenomena are doubtless intimately related. Another feature is that the thermal expansion at 20000 of all three metals has dropped by a materially larger factor than has the compressibility. This is the exact reverse of the behavior usually found with organic liquids, the compressibility of which in the ränge up to 12000 decreases by a factor two or three times greater than the factor of decrease of thermal expansion. A knowledge of thermal expansion is involved in an interesting speculation of G. N. Lewis as to limiting behavior at infinitely high pressure. Lewis has suggested" that it may be that the entropy of a

110 — 2913

98

BRIDGMAN

crystalline phase tends toward zero at infinite pressure at all temperatures. In virtue of the thermodynamic relationf — J = — ( — j wehave:

S (0,

" ^

=

^P-

S (0, T) may be determined by measurements at atmospheric pressure of specific heat as a function of temperature, assuming in accordance with the third law that entropy at 0° Abs vanishes. S(0, T) has been so determined for a large number of substances and may be found in I. C. T. Lewis's hypothesis then demands that J '

dpcannot

be larger than S (0, x), so that ( — ) must decrease with increasing /P

pressure fast enough to fulfill this condition. The integral may be approximately evaluated graphically. The result for potassium is that S (0, 0° C) - S (20000, 0° C) = 2.03 kg cm/°C gm. The value given in I. C. T. for -S (0, 0° C) is 17.3 in the same units. Similarly for sodium S (0, 0° C) - S (20000, 0° C) = 2.56 kg cm/'C gm, and S (0, 0° C) =22.1. The value for S (0, 0° C) is not tabulated for lithium, so that there was no particular point in caiculating the change of entropy out to 20000; it is evident from the graph that it will be between that of sodium and potassium. The conclusion for sodium and potassium is that the change of entropy with pressure at 20000 at 0° C fails by a factor of about 8.5 to reach the theoretical limiting value. The state of zero entropy at 0° C must then occur at excessively high pressures.

Even if ( — ) for potassium should reVÖT /p main constant beyond 20000, zero entropy would not be reached below a pressure of 450,000 kg/cm^. The general conclusion is that the zero State of entropy at ordinary temperatures is so very remote as probably not to impose any useful restriction on speculations as to behavior in the experimental ränge. With the more accurate values of thermal expansion now available, it is possible to calculate more accurately than before the pressure at which the internal energy passes through its minimum with increasing / dE\ / dv\ pressure at constant temperature. Smce I — ) = — t I — ) — \op / T \ot/p

110 — 2914

MEASUREMENTS OF ELECTRICAL KES1STANCE8

p ( — ) , thispressureisgivenbyp = — t — / — . \ dp /r ÖT / dp

99

Probably the

easiest way to find this pressure is to plot t —and — p — against presöi dp sure and determine the point of intersection of the curves. It was found in this way that at 0° C the minimum energy of lithium occurs at about 5000 kg/cm', that of sodium at 4000, and that of potassium at 2300. These pressures are much lower than the corresponding pressures for harder metals such as iron, and furthermore are somewhat lower than obtained previously on the basis of earlier values of thermal expansion. The volume at which internal energy passes through a minimum is roughly the volume at which mean attractive andrepulsive forces are in equilibrium, and this again should be roughly the same as the volume at 0° K at atmospheric pressure. This latter volume has not been determined with much accuracy, but there seems to be no question but that it is significantly larger than the volume at 0° C at the pressure of the minimum of internal energy. This seems to be the universal rule, and is doubtless connected with the compression of the force fields of the atom by external pressure. At pressures beyond the minimum of internal energy the term dv dv — p — becomes increasingly dominant over x — , so that at the highest dp dl pressures nearly all the mechanical work of compression is permanently retained as increase of internal energy, the energy flowing out as heat to compensate for the temperature rise produced by the compression becoming unimportant. This phenomenon is most marked, of course, with potassium; at 20000 kg/cm^ all except 8 per cent of the mechanical work of compression is permanently retained. I have calculated approximately the total increase of internal energy of potassium at 0° C up to 20000 kg/cm® by a simple graphical integration, and it proves to be about 14.5 kg m for that amount of potassium which occupies 1 cm' at 0° C at atmospheric pressure. The total mechanical work of compression of the average organic liquid is not far from this. SUMMARY.

The modifications in technique necessary in extending the pressure ränge from 12000 to 20000 kg/cm^ are described. The electrical resistance of silver, gold, and iron is found to extrapolate smoothly from 12000 to 20000, in such a way as to make it very

110 — 2915

100

BRIDGMAN

probable that the maiiganin resistance gauge may be safely used up to 20000 kg/cm', assuming a linear relation between pressure and change of resistance, and obtaining the pressure coefficient from a Single calibration at 7640 kg/cm'^, with a maximum error of a few tenths of one per cent. The electrical resistance of black phosphorus and of single crystal tellurium in the 23.5° and 86° orientations is measured to 20000 at 30° and 75° C. Both of these substances show very large decreases of resistance, the resistance at 20000 being less than O.Ol of its value at atmospheric pressure. The temperature coefficient of black phosphorus reverses sign near 12000 kg/cm^, and above 12000 is positive, like that of the metals. The temperature coefficient of tellurium (both orientations) also decreases markedly with pressure, but does not reverse sign, having a value at 20000 kg/cm' about one third of its value at atmospheric pressure. The rate of decrease of resistance with pressure drops very markedly with increasing pressure. With black phosphorus the drop is so rapid that a short extrapolation indicates that the resistance will probably pass through a minimum between 23000 and 24000 kg/cm^. The extrapolation for tellurium is not so certain, but it is probable that at a pressure not much above 30000 its resistance will also pass through a minimum. The resistance of CujS at 30° decreases with pressure, with a discontinuity in the direction of change near 2500 kg/cm^, above 2500 the rate of decrease being only about one tenth as large as immediately below 2500. Above 2500 the curve of resistance against pressure is concave toward the pressure axis, a very unusual phenomenon. The phenomena at 30° are approximately reversible. At 75° the same qualitative features as at 30° are shown on the first application of pressure, but above 10000 irreversible changes begin to take place, and the resistance with decreasing pressure does not retrace its former path, but lies below it, and the low pressure discontinuity is suppressed. The change of volume of lithium, sodium, and potassium is measured at 0° C. The compressibility of these three metals drops smoothly, both with respect to pressure and with respect to each other, over the entire ränge. The relative drop of the compressibility of potassium is the greatest and that of lithium the least; at atmospheric pressure the compressibility of potassium is three times that of lithium and at 20000 kg/cm« 1.65 times. The mean linear expansion between 0° and 95° C of the three alkali metals has been determined up to 20000 kg/cm''. The expansion

110 — 2016

MEA8UHEMENT8 OF ELECTEICAL RESISTANCES

101

drops with increasing pressure by a factor considerably larger than does the compressibility. The drop for potassium is so much greater than that for sodium and lithium that there is a crossing of the curves, with the result that at 20000 kg/cm^ the order of the expansions of lithium, sodium, and potassium is exactly the reverse of what it is at atmospheric pressure, potassium at 20000 appearing as the "hardest" and lithium as the "softest" metal. The same phenomenon is shown by the melting points. The decrease of entropy of these three metals with pressure at constant temperature may be evaluated in terms of the thermal expansions. It appears that any vanishing of the entropy must occur at pressures excessively beyond the present experimental ränge. I am indebted to my assistant Mr. L. H. Abbot for making the readings, which have often demanded a high degree of skill, to the Rumford Fund of the American Academy of Arts and Sciences for financial assistance in purchasing supplies, and to the Francis Barrett Daniels Fund of Harvard University for financial assistance with respect to the salary of Mr. Abbot. RESEAKCH LABORATOBY OF PHYSICS,

Harvard University, Cambridge, Mass. REFERENCES.

' P. W. Bridgman, Proc. Amer. Acad. 66, 126, 1921; 68, 114, 1933. ' P. W. Bridgman, lUd, 68, 166, 1922; 69, 109, 1923. »P. W. Bridgman, The Physics of High Pressure, G. Bell and Sons, 1931, Chapter II. * P. W. Bridgman, Proc. Amer. Acad. 62, 573, 1917. ' P. W. Bridgman, First reference under 1, and Jour. Amer. Chem. Soc. 36, 1344, 1914. «P. W. Bridgman, Proc. Amer. Acad. 62, 216, 1927; 64, 75, 1929. ' P. W. Bridgman, lUd, 68, 114, 1933. » First reference under 2, page 202. • First reference imder 2, page 203. First reference under 2, page 206. " G. N. Lewis, ZS. f. Phys. Chem. 130, 532, 1927.

110 — 2917

The Pressure-Volume-Temperature Relations of the Liquid, and the Phase Diagram of Heavy Water P. W. BRIDGMAN, Research Laboralory of Physics, Harvard

Universüy

(Received July 11, 1935) The pressure-volume-temperature relations of both liquid DjO and H j O are measured between - 2 0 ° and 95°C and up to 12,000 kg/cm', and t h e transition Parameters of t h e liquid and solid modifications of DjO in the ränge between - 6 0 ° and + 2 0 ° C and up to about 9000 k g / c m ^ An unstable modification of solid DsO, for which t h e designation IV is proposed, is found in t h e field of stability of V. Reference to t h e original work on H j O shows t h a t t h e corresponding modification of H j O also exists. In general the properties of H2O and DjO covered by these measurements

are very much alike, and differ in the direction suggested by t h e greater zero-point energy of HaO: t h e molar volume of D j O is always greater than t h a t of H j O a t the same pressure and temperature, and t h e transition lines of DjO always run a t higher temperatures. In finer detail, however, the differences between t h e two waters do not vary regularly, and probably other considerations than of zeropoint energy alone are necessary for a complete explanation.

T

compressibility of ordinary water was redetermined in the same sylphon and with all other parts of the set-up unchanged. The Order of the measurements was as follows: first, measurements with H2O at 0°, - 5 ° , - 1 0 ° , - 1 5 ° , - 2 0 ° , and check at 0°; second, measurements with D2O at +30°, 0°, - 5 ° , - 1 1 ° , - 1 6 ° , +52.5°, + 75°, +95° and check at 30°; and third, measurements with H2O again at +52.5°, +95°, and 0°. The smoothness of 'unctioning of the apparatus can be estimated from a comparison of the volumes of HJO at 0° with the two Allings of the sylphon. The maximum discrepancy between the two determinations of the volume was at 4000 kg, where the first run gave 15.875 for the molar volume and the second run 15.892. At 6000 kg the difference between the two runs had dropped from 0.017 to 0.009. In calculating the volumes listed in the tables the first step was, in principle, to draw smooth curves through the experimental points at each constant temper-

H E following measurements of some of the simpler properties of heavy water under pressure were made on 99.9 percent heavy water which I obtained through the courtesy of Professor Urey. My conventional high pressure apparatus was used in the measurements; the pressure ränge was up to 12,000 kg/cm^ and the temperature ränge from —60° to -f95°C. PRESSURE-VOLUME-TEMPERATURE

RELATIONS

OF THE LIQUID

The measurements of the volume of the liquid as a function of pressure and temperature were made by the sylphon method fully described in other places.' A new sylphon was used, calibrated as usual. Since the principal interest of these measurements is in the difference between the properties of ordinary and heavy water rather than in the absolute values, the » P . W. Bridgman, Proc. Am. Acad. 66, 185 (1931); 68, 1 (1933).

111 —2919

598

P.

flcs/cm') 1 500 1000 1500 2000 2500 .1000 3500 4000 5000 6000 7000 8000 9000 10000 11000 12000

-20'

16.380 16.155

-15»

16.660 16.410 16.188 15.987 15.807

-10»

16.974 16.685 16.440 16.221 16.025 15.843

(kg/cm') 1 500 1000 1500 2000 2500 3000 3500 4000 5000 6000 7000 8000 9000 10000 11000 12000

-20*

16.579 16.324

-15»

16.880 16.600 16.357 16.140 15.948

-10°

16.898 16.624 16.389 16.173 15.982 15.802 15.486

0'

-5»

18.122 17.692 17.328 17.014 16.741 16.501 16.287 16.094 15.915 15.600 15.352

17.308 16.994 16.712 16.468 16.255 16.061 15.879 15.567

TABLE

- 5 -

17.234 16.924 16.658 16.423 16.213 16.019 15.843 15.532

B R I D G M A N

I. Molecvlar mlume of liquid DiO.

TABLE PRESSURE

W.

40-

50'

60-

80"

lOO-

18.200 17.835 17.512 17.235 16.982 16.751 16.543 16.353 16.178 15.870 15.597 15.358 15.140 14.944 14.767 14.606 14.452

18.270 17.904 17.585 17.306 17.054 16.827 16.617 16.428 16.252 15.949 15.671 15.427 15.207 15.010 14.827 14.663 14.508

18.363 17.985 17.665 17.385 17.130 16.905 16.693 16.503 16.330 16.015 15.740 15.494 15.272 15.074 14.885 14.718 14.563

18.570 18.174 17.850 17.562 17.302 17.067 16.850 16.657 16.477 16.150 15.875 15.625 15.402 15.198 15.007 14.835 14.677

18.400 18.048 17.753 17.486 17.250 17.028 16.824 16.634 16.310 16.023 15.763 15.533 15.328 15.137 14.961 14.807

II. Molectdar mlume of liquid H^O. 0-

20»

40»

50-

60«

80»

100-

18.018 17.601 17.251 16.951 16.684 16.452 16.241 16.050 15.875 15.564 15.293

18.048 17.690 17.352 17.072 16.805 16.573 16.366 16.185 16.012 15.698 15.430

(18.157) 17.800 17.485 17.204 16.949 16.722 16.514 16.326 16.152 15.847 15.575 15.340 15.125 14.930 14.748 14.575 14.422

(18.233) 17.865 17.554 17.275 17.025 16.796 16.587 16.397 16.224 15.918 15.645 15.405 15.188 14.990 14.807 14.636 14.480

(18.323) 17.941 17.630 17.352 17.100 16.871 16.661 16.469 16.294 15.986 15.712 15.469 15.249 15.050 14.866 14.695 14.538

(18.539) 18.129 17.805 17.518 17.262 17.030 16.816 16.620 16.440 16.122 15.842 15.599 15.374 15.172 14.985 14.812 14.653

(18.800) 18.345 18.002 17.701 17.437 17.195 16.977 16.776 16.589 16.265 15.982 15.730 15.501 15.295 15.106 14.930 14.771

ature, and then to compute and tabulate the volume at regulär pressure intervals from each of these curves. The graphical representation used was on a very lange scale. To give greater accuracy, not the actual observations were plotted, but the difference between the actual observations and points computed by a simple logarithmic formula with two constants that could be so adjusted as approximately to fit the experimental curve over the entire ränge. At each constant pressure of this first tabulation curves were then drawn, also on a very large Scale, giving volume as a function of temperature, and from these curves were constructed the final Tables I and II, of volume at regulär intervals of pressure and temperature. The quantities of water used in filling the sylphon, which were of the order of 5 grams, were determined by weighing. The density of HiO at atmospheric pressure was taken from International Crüical Tables. The molecular volume of D2O was based on the value of Taylor

111 —2920

20' 18.125 17.739 17.404 17.110 16.854 16.620 16.411 16.215 16.040 15.730 15.465 15.215 15.001 14.803

and Sherwood^ for the molecular volume at 25°, 18.127. The values at other temperatures below this were obtained by combining this value with the values of Lewis and Macdonald' for the thermal expansion. The molecular volumes at higher temperatures at atmospheric pressure were obtained directly from the sylphon readings; these are not as accurate as the values under higher pressures, the sylphon not being particularly well adapted to readings at low pressures. THE

PHASE DIAGRAM OF THE SOLIDS

The method and the apparatus were very similar to those used for the corresponding measurements of H2O in 1912.'' The DjO, about 13.5 grams in amount, was placed in a steel Shell, completely surrounded by the pressure 2 H. S. Taylor and P. W . Sherwood, J . Am. Chem. Soc. 56, 998 (1934). » G . N. Lewis and R . T . Macdonald, J . Am. Chem. Soc. 55, 3057 (1933). ' P. W . Bridgman, Proc. Am. Acad. 47, 441 (1912).

P H A S E

D I A G R A M

TABLE I I I . Parameters

(kg/cm')

TEMPERATURE C O

dr dt

0 400 800 1200 1600 2000 2400

+ 3.82 + 0.82 - 2.74 - 6.76 -11.14 -15.82 -20.70

-.00665

PRESSURE

VOLUME

O F

H E A V Y

of ihe transiüon lines of D2O.

LATENT HEAT

(craVmole) (kg cm/mo!e) (cal/mole)

PRESSURE

(kg/cm«)

TEMPERATURE (°C)

dr dp

I^I 950 1055 1135 1195 1238

-65,000 59,600 57.000 56,300 56,600 56,800 56,600

-1523 1396 1335 1319 1326 1331 1326

-18.90 -17.37 -16.04 -14.90 -13.96

0.860 .730 .620 .530 .460

.00409 356 310 268 230

53,500 52,400 51,400 51,100 51,800

1253 1228 1204 1197 1214

IV-L

4000 4500 5000 5500

-17.90 -13.40 - 9.30 - 5.50

.00946 856 790 736

3000 3500 4000 4500 5000 5500 6000 6500

-18.90 -14.98 -11.34 - 7.99 - 4.91 - 2.09 + 0.57 + 3.08

.00812 .00754 .00698 642 590 546 514 494

5000 5500 6000 6500 7000 7500 8000 8500

-10.01 - 5.40 - 0.91 + 3.41 7.57 11.53 15.26 18.74

.00936 914 880 848 812 769

2250

2285

2325 2360

1.710 1.633 1.556 1.478

46.100 49,600 52,000 53,700

1080 1162 1218 1258

1.647 1.498 1.372 1.264 1.173 1.095 1.026 0.967

51,500 51,300 51,500 52,200 53,300 54,400 54,600 54,100

1206 1202 1206 1223 1249 1274 1279 1267

1.920 1.825 1.738 1.659 1.589 1.528 1.475 1.430

54,000 53,500 53,800 54,100 54,900 56,500 59,000 62,500

1265 1253 1260 1267 1286 1324 1382 1464

-20.0 -30.0 -40.0 -50.0

-.270 -.270 -.270

-.270

transmitting medium, in the lower cylinder, the temperature of which was thermostatically controlled, and which was varied for these measurementB from + 2 0 ° to —60°. The phase diagram was not followed beyond + 2 0 ° and 8600 kg because I did not want to risk the loss of such a large quantity of DjO; there is, however, no reason to think that there are any significant features beyond the ränge actually covered. The bath for temperatures below 0° was ethyl alcohol, about five gallons in amount, into which the temperature regulating arrangement admitted, when necessary, a stream of alcohol from a reservoir maintained at — 75° by solid CO2. The commercial availability of solid CO2 made the low temperature manipulations very much more convenient than in 1912. The lower cylinder connected through a heavy pipe with the upper cylinder, maintained at room temperature, in which was situated the manganin gauge. The

3,330 3,150

78

74 70 66

2,980 2,810

5,290

121 IIS 112

.380 .344

216 283

.313

9.200 12,100 14.200 15,200

356

-0.712 0.712

14,500 14,300

340 335

2240 2185

.1815 .1815 .1815

2400 2800 3200 3600

-29.69 -26.08

.01137 775

-3.9,S0 .3.925

0.431

520

3540 3800

-21.5 -24.7

-.0124 -.0124

3555 3540

-14.5 -21.5

.468

5410 5402

- 6.2 -14.0

.94 .94

6405 6401

+ -

3.900

S,0»0 4,790

II-III

-23.40 -21.20

605

333

N-V

III-V

.468

-

.985

-540 -560

-

12.7 13.1

0.352 0.310

-100 -100

-

2.3 2.3

0.696

100 95

-1.029 IV-VI

VI-L

721

LATENT HEAT

I-II -.W.O

V-L

668

-3.553 3.503 3.453 3.403

-40.0 -50.0

2295

III-L

2200 2600 3000 3400 3800

VOLUME

(cmVmole) (kg cm/mo!e) (cal/mole) I-III

1.56 1.79 2,01 2.23 2.45 2.64 2.77.

823

599

W A T E R

V-VI

2.6 5.0

1.90

1.90

0.670

2.3 2.2

Position of the piston by which pressure was generated in the upper cylinder was read to 0.0001 inch by two Ames dial gauges, so mounted as to compensate for any slight warping of the press. The position of the piston was determined at constant bath temperature as a function of pressure; a phase change is shown by a discontinuity in the position of the piston. The change of volume is determined at once by the amount of the discontinuity and the cross section of the piston. The cross section has to be corrected for the elastic Stretch of the cylinder under pressure. This correction was calculated from the elastic constants; it is proportional to the pressure and at 10,000 kg is 1.35 percent. There is in addition a correction for the thermal expansion of the transmitting liquid, isopentane, on passing, during a phase change, from the temperature of the lower to that of the upper cylinder. A few of the changes of volume, on the I I - I I I

III —2921

600

P .

W .

B R I D G M A N

Computing the results, the slope of the upper end of L - I curve, between 0° and +3.82°, was so determined as to be consistent with this value, 496.5, for the melting pressure; the other two points at + 2 ° and + 3 ° were not quite so regulär, perhaps because of inferior temperature control. The measurements were completed without accident, with a single set-up of the apparatus for all the points above 500 kg, and with a single set-up of the special low pressure apparatus for all the points below 500 kg. There was no perceptible rounding of the corners of the melting curves, indicating adequate purity. The equilibrium points (temperature as a function of pressure) are shown in Fig. 1. In Fig. 2 are shown the corresponding changes of volume, in

and the II-V curves, were determined by the method of varying bath temperature and plotting pressure against temperature at constant volume. This change in procedure was made necessary by the smallness of these volume changes; the method was essentially the same as followed in the previous work on HaO. A special apparatus was made for the determination of the points on the freezing curve of the ordinary ice between 0° and +3.82°, since the high pressure apparatus is not sensitive in this ränge. This special apparatus was constructed of mild Steel and was the same in principle as the other. Pressure was read on a Bourdon gauge, calibrated against an absolute free piston gauge. Two independent determinations of the freezing pressure at 0.00° were 496 and 497 k g / c m l In

TABLE IV. Triple points of the system water-ices. D.O

L-I III-L III-I

PRESSURE (kg/cm')

TEMP. (•C)

VOLUME CHANCE (cmVmole)

(kß c m / m o l e )

LATENT HEAT

2245

-18.75'

2.713 .847 3.560

-56.600 53,300 3,300

(cal/mote)

-1326 1249 77

PRESSURE (kg/cm>)

TEMP. CC)

2115

-22.0°

-

VOLUME LATENT CHANCE (cmVmole) (kg c m / m o l e )

2.434 .839 3.273

-43,100 39,100 4,000

-

HEAT (cal/mole)

-1010 916 94

-

I^III-V

III-L V-III V-L

355S

-14.5»

.498 .985 1.483

50,900 500 51,400

1192 12 1204

3530

-17.0»

.434 .985 1.419

47.100 700 47,800

1103 17 1120

6380

+

.949 .700 1.649

53,800 ISO 53,950

1260 4 1264

2170

-34.7-

3.532 .387 3.919

3510

-24.3*

.261 .721 .982

I^IV-VI

IV-L VI-IV VI-L

5410

-

6.2»

1.492 .352 1.844

53,500 100 53,600

1253 2,3 1255

L-V-VI

V-L VI-V VI-L

6405

+

2.6'

.978 .696 1.674

-

54,100 100 54,000

-

1267 2.3 1265

0.16»

I-II-III

III-I II-III II-I

2290

-31.0»

3.498 .449 3.947

-

3,100 8.400 5,300

-

73 197 124

-

1,700 9,400 7,700

-

40 220 180

II-III-V

II-III V-II V-III

111 —2922

3540

-21.5°

.317 .712 1.029

15,100 -14,600 500

-

353 342 11

13,000 -12,300 700

-

304 288 16

PHASE

/

i

/

OF

H E A V Y

^ M

601

W A T E R

, t-B

f\

V •

D I A G R A M

\

\

L

\

Y' tf 1 "v •

/H

(

n

Df

X

•

.

FIG. 2. T h e change of volume for the various transitions of the D2O system, plotted as ordinates in cm' per mole, against temperature as abscissa. The observed values are shown as circles; the crosses are the values computed at the triple points. FIG. 1. The transition lines of the systetn DjO. Prolongations of transition lines into regions of instability are dotted. Observed points are shown by circles. The triangles are the triple points in the H2O system.

cm' per mole, as a function of temperature on the transition lines. The smoothed resuits are given in Table I I I ; this table gives the pressuretemperature coordinates, the volume difference, the slope dT/ip of the transition line, the latent heat of the transition, the latter calculated by Clapeyron's equation and this latent heat in calories per mole calculated with the conversion factor, 1 kg cm = 0.02343 mean calorie. In finding the smoothed resuits there are several conditions that must be met at the triple points of which there are six: namely, the three independently determined transition lines must pass through a common point, the three independently determined changes of volume must satisfy the additive relation, and the calculated latent heats must also satisfy the additive relation. These three conditions are so interrelated as to leave very little freedom in drawing the best curves through the experimental points, the latent heats being determined by the slopes which are tied down by the conditions that the curves pass through a triple point. One may therefore feel considerable confidence in the resuits, since any important error would be expected to manifest itself in the impossibility of satisfying the triple point conditions. In Table I V are collected the triple points parameters, with the values for H2O also given for comparison. T h e qualitative characteristics of the transitions are very much like those of H2O. Perhaps the most striking characteristic is the enormous velocity of the transitions between the solid

phases I - I I I , I I I - V and V - V I at the upper end of the ränge, immediately below the triple points with the liquid, and the enormously rapid decrease of this velocity with falling temperature. The phenomena with regard to subcooling and Prolongation of transition lines into regions of instability are essentially the same as for H j O ; as indicated in Fig. 1 the line L - I may be unstably prolonged into the region of instability of I I I , the line L - V into the region of I I I , the line L - V I into that of I V or V, and I - I I I into that of II. The reluctance of V to appear from the liquid phase is again noteworthy, making possible the very marked extension of the L - V I line into the region of V. But just as in the case of H2O, if V had been recently present in the apparatus it was easy to make it appear again, even if in the meantime the system had been completely melted. The probable explanation is the persistence in the liquid phase of some sort of nuclei from which V is readily formed. A difference compared with the H2O system is that the Prolongation of the I - I I I line into the region of I I apparently does not have a vertical tangent; in fact the I - I I I line is straight within the limits of error instead of being markedly curved toward the temperature axis as in the H2O system. In one important respect Fig. 1 differs from the phase diagram published for H2O, namely, in the presence of the phase I V and the two transition lines L - I V and I V - V I . I V is totally unstable with respect to V, and once V has been produced, I V disappears. I V was found in the early part of these measurements, after the determination of points on the L - V I line at 0° and -|-10°, and before V had yet appeared. The

111 — 2 9 2 3

602

P.

W.

BRIDGMAN

first point found involving IV was on the IV-VI line. Since there was no analog for this in the diagram of HjO, it apjjeared a t first as if the phase diagram of D2O must be entirely different from that of H2O, and for a while there was considerable confusion in identifying the transitions as they were found. The confusion was increased by the fact that the melting Hne L - I V is not greatly different from the unstable Prolongation of L-VI. The decisive factor in fixing the Identification was the volume changes, the change L - I V plus IV-VI adding to L-VI, as it should, and the change L - I V being markedly different from L-VI. After the phase diagram of D2O was completed it was found on Consulting again the original work on H2O that the phase IV had also been found in the H2O system, and in fact on page 529 of my 1912 paper will be found an explicit Statement of the probability of the existence of another unstable form. The existence of this form was made probable both by the location of the pressure-temperature points, and by the values of the change of volume. The reason that the existence of the phase was not regarded as a certainty and the phase listed in the final results was that the transition IV-VI was not found. With the discovery of this transition for D2O, however, the whole Situation is cleared up, and the phase diagrams of D2O and H2O appear very similar in all respects. The designation IV is given to the new unstable phase, thus completing the sequence I to VI. When I chose the designations V and VI for the new high pressure ices beyond II and III, which had been previously found and named by Tammann, I left the designation IV blank because of uncertainty with regard to some unstable forms, the existence of which was suspected by Tammann. None of the suspected forms of Tammann have turned up, however, in the 40 years or more since he did his work, so t h a t there seems no reason for holding this designation open any longer, and it is now employed to complete the scheme of nomenclature. DISCUSSION

Accuracy of the results The absolute accuracy of the volumes of the liquid phase listed in Tables I and II is not as

III

—2924

high as could be desired for a substance like water for which very slight departures from regularity are significant in disclosing conditions of varying association. Five different determination of the p - r - ^ surface of liquid H2O have now been made in this laboratory, either by myself or by others using my apparatus, utilizing three different methods: the Aim6 piezometer, the piston displacement method, both in 1912,' and the sylphon method in 1931,' 1934,« and now again in 1935. The maximum discrepancy between any of these determinations a t any pressure is about 0.002 on the relative volume; for example, for the relative volumes a t 3000 kg and 0° the values 0.901 and 0.899 occur. T h e maximum discrepancy occurs a t an intermediate pressure and tends to become less a t the highest pressures. A great deal more work would be necessary before the p - r - ^ surface of water is known with an accuracy corresponding to the accuracy of our knowledge of volume as a function of temperature a t atmospheric pressure. With regard to the values below 0°, this is the first time since 1912 t h a t the volume has been measured in this region. The results now found do not check in fine detail with those found before; in particular the minimum and maximum of volume as a function of temperature on the isobar at ISOO kg found in 1912 and shown in Fig. 40 of the 1912 paper, has not been found this time. Irregularities are now found suggesting the maximum and minimum, but not so pronounced. The sylphon method is not particularly accurate a t the lower pressures, and in the present case suffers from the additional disadvantage that it is not safe to carry the liquid into the subcooled region because of danger of destroying the sylphon if freezing should occur. The measurements of 1912 represent considerable excursions into the subcooled regions, so t h a t the chance of losing a maximum or minimum by the smoothing process a t the end of the ränge was less. On the other hand, these new measurements, both on H2O and D2O, are the first in which the same apparatus and the same filling of the apparatus has been used to make measurements both above and below 0°. The present

' Second part of reference 1. ' P. W. Bridgman and R. B. Dow, J. Chem. Phys. 3, 35 (1935).

PHASE

D I A G R A M

measurements should give a more reliable picture of the complete ränge of the phenomena than the former measurements. Further, the present measurements should give considerably greater accuracy for the comparative volumes of H2O and D2O than can be claimed for the absolute accuracy of either. In making any comparative study of the properties of D2O and H2O from the volumes of Tables I and II it must be remembered t h a t the volumes of H2O at 0°, 50°, and 100° are doubtless somewhat more accurate than the values a t 20°, 40°, 60°, and 80°, since the observations were made only a t 0°, 52.5°, and 95°, and the volumes at other temperatures were obtained by a graphical Interpolation, which may have been subject in some cases to slight doubt because of lack of linearity. The measurements for D2O on the other hand, were made a t four temperatures above 0°, and so the interpolation is more certain. The accuracy of the phase diagram is perhaps sufficiently indicated by the smoothness of the experimental points in Figs. 1 and 2. All the p-T points obtained are shown, but not all the Av points, since a perfectly satisfactory value of Av cannot be obtained unless the transition is allowed to run to completion in both directions, and this was frequently inconvenient, either because of slowness of the transition, as on the lower end of the I - I I and I - I I I lineS, or because of the probability of completely losing one of the phases, as a t some points on the melting curves of I I I and V. The measurements of the volume changes of the two transitions I - I I and I - I I I were the most difficult, and are open to the greatest possibility of error. In the tables more significant figures are given for the temperatures, for dr/dp, and sometimes for Av than are justified by the direct measurements. However, the differences of temperature and pressure could often be obtained with a greater accuracy than the absolute values themselves. Furthermore, the conditions a t the triple pwints give a greater certainty than could be obtained from the absolute values; the values listed in the tables with a greater number of significant figures than apparently are justified have been smoothed and adjusted to satisfy the conditions a t the triple points and give relative accuracy of the Order suggested.

OF

HEAVY

603

WATER

A Word should be said about the normal melting parameters of D2O. The melting temperature (triple point with the vapor) was taken as 3.82°, as given by Bartholom^ und Clusius.' T h e latent heat given above, 64,950 kg cm per mole is equivalent to 1523 g cal. per mole, against 1522 recently determined by Bartholom^ and Clusius. The agreement is in part fortuitous, since my measurements could hardly distinguish between a volume change at atmospheric pressure of 1.56 (the value used) and 1.57. Bartholom^ and Clusius quote in their paper for the volume change 1.58, determined by Megaw from measurements of the lattice spacing in the crystals by x-rays. Relative behavior of D2O and H2O The molecular volume of liquid D2O is greater at all pressures and temperatures than that of H2O at the same pressure and temperature. This is consistent with the frequently expressed idea that "association" is greater in liquid D2O than H2O. The general tendency is for the volume excess to become less with both rising temperature and pressure, the maximum difference, 0.104, occurring at 0°C and atmospheric pressure. This again is what would be expected, because it is known that H2O becomes more normal both with increasing temperature and pressure. However, the details of the Variation of the volume excess are not altogether regulär. If the excess is plotted as a function of pressure at constant temperature, a flat minimum will be found a t the higher temperatures, the pressure of the minimum rising with increasing temperature. Thus at 40° the minimum is about 0.015 at 8000 kg, while at 100° the minimum is 0.030 a t 10,000 or 11,000 kg. On the other hand, if the excess is plotted as a function of temperature a t different constant pressures, a minimum will be found not far from 40° a t all pressures Up to about 8000, the depth of the minimum decreasing to about 0.015 a t 8000, but beyond 8000 the temperature of the minimum increases to perhaps 70° a t 12,000, where the depth of the minimum is of the Order of 0.025. This complication in fine detail is doubtless indicative of slight differences ' E . Bartholome a n d Chemie B28, 167 (1935).

K.

Clusius,

Zeits. f.

physik

111 — 2 9 2 5

604

P.

W.

BRIDGMAN

in the details of the "association." This is further indicated by the fact that the greatest departures from smoothness in the isotherms of H2O are found in the general neighborhocxl of 0° and at low pressures, whereas the greatest irregularities in liquid DsO are found at 5000 kg in the neighborhood of 50°. Perhaps the most sweeping characterization that can be made with regard to the phase diagrams is that the triple points in the D2O diagram all occur at higher temperatures, and the transition lines, except those running approximately vertical, all run at higher temperatures than in the HjO diagram. This is what would be expected in view of the usual explanation of the higher melting point of DjO in terms of its lower zero-point energy; the vo of DjO is less than that of H2O in consequence of the greater mass of the DjO molecule, so that a greater temperature energy must be added to shake the molecule of solid D2O out of its trough into the liquid phase, the implication being that zero-point energies have largely disappeared in the liquid phase. This explanation demands the approximate equality of the specific heats of solid D2O and H2O, and this does seem to be the fact experimentally. Going now to finer details of the phase diagrams, the differences at the triple points are not uniform, but in general the differences become less at higher pressures. Thus the excesses of the absolute temperatures of transition in the D2O system over the H2O system for the successive triple points L-I-Vap, L - I - I I I , L - I I I - V , and L - V - V I are, respectively, 1.40,1.40, 1.02 and 0.86 percent. The variations of the ratio of pressures at the triple points are greater than the variations of temperature; the pressure in the D2O system is always greater, the excess varying from 6.0 percent at the I - I I - I I I triple point to only 0.31 percent at the L - V - V I triple point. The fact that the variations of pressure and temperature at the triple points are irregulär shows that there can be no law of corresponding states for corresponding phases in the two systems. This is perhaps not surprising when the liquid phase is involved, but one might perhaps expect a closer approximation in the solid phases. The pressure in the D2O system exceeds that in the H2O system at the I-II-III triple point by 6 percent,

111 —2926

whereas at the I I - I I I - V triple point the excess is only 1.14 percent. The latent heat of melting of all the ices at the low pressure end of the ränge is greater in the D2O system than in the H2O system. The sign of the difference is again what would be expected in view of the difference of zero-point energies discussed above; the magnitude of the difference is, however, somewhat surprising. The melting heat of I at the triple point with the vapor is 6 percent greater in the D2O system than in H2O. This difference rapidly increases with increasing pressure along the melting curve of I, and at the triple point L - I - I I I the excess of latent heat in the D2O system has become 31 percent. A t the same triple point the latent heat of L - I I I is 37 percent greater for D2O than for H2O. This marks the extreme—from here on with increasing pressure the differences become smaller, until at the L - V - V I triple point the latent heats in the two systems are the same within experimental error. Exact equality of the latent heats in the two systems would not be expected according to the simple zero-point energy explanation, for ice VI in the two systems must differ in the same direction with regard to zero-point energy as ice I. Another consideration also suggests that other factors besides zero-point energy must be of importance, because it is usual experience that those substances with the higher natural frequency (higher characteristic temperature) have the higher melting temperatures, whereas here it is the D2O system, with the lower natural frequency, which has the higher melting temperature. The relative volume changes in the two systems are significant. In general, the volume change on melting is greatest in the D2O system; it is greater by about 4 p)ercent at the atmospheric melting point, increases to about 12 percent at the L - I - I I I triple point, and from here decreases with increasing pressure, remaining 1.5 percent for V I - L at the L - V - V I triple point. In finer detail, the difference of volume between VI and the liquid in the H2O system when plotted against temperature is concave toward the temperature axis up to 20°. This is abnormal. Above 20°, the curvature reverses, and H2O becomes convex toward the temperature axis like other liquids. The abnormality does

PHASE

DIAGRAM

not occur at all in the D2O system, but the difference of volume between L and VI is convex toward the temperature axis over the entire measured ränge. The Situation is reversed with regard to the phase I. In the H2O system Ao is linear against temperature, whereas in the D2O system it is abnormally concave toward the temperature axis. It is to be questioned, however, whether H2O is not realiy more abnormal on its L - I line than D2O, since the numerical magnitude of the Variation of A» is very much greater in H2O. An accompaniment of this is a much greater Variation of the latent heat along the L - I line for H2O than for D2O. The greatest qualitative difference with regard to volume is shown by the phases I and III. At the triple point L - I - I I I the decrease of volume when I changes to III is 9 percent greater in the D2O system, whereas at the I - I I - I I I triple point, only 12° lower, it is 1 percent less. The Variation is perhaps in small part due to experimental error, the volume determinations on the I-III line being the most uncertain of the measurements, but the triple point conditions did not seem to allow any important divergence from the values given, and the difference must be mostly real.

OF

HEAVY

WATER

605

The conclusion seems forced, I believe, by this detailed examination of the differences in the two systems that abnormalities occur not only in the liquid but also in the solid phases, and particularly in the phases I and III. In fact, I have been of the opinion ever since making the original measurements in 1912 on the H2O system that the p - r ^ surface of ice I would be found to deviate markedly from that of a normal solid, particularly in the neighborhood of the L - I - I I I triple point. This subject has never been investigated experimentally, and would, I believe, be well worth while. Measurements should be made if possible on single crystals. Not only is it highly probable that the ices I and III are abnormal, but the abnormalities must differ in the D2O and the H2O systems. More elaborate considerations than simply zeropoint energy appear to be necessary to satisfactorily explain the Situation. I am indebted to my assistant, Mr. L. H. Abbot, for making all of the readings with the sylphon and many of the readings of the transitions. I am also indebted for financial assistance to the Joseph Barrett Daniels Fund of Harvard University and to the Rumford Fund of the American Academy of Arts and Sciences.

111 — 2 9 2 7

Effects of High Shearing Stress Combined with High Hydrostatic Pressure P. W. BRIDGMAN, Harvard

Universüy

(Received September 3, 1935) Mean hydrostatic pressures up to 50,000 kg/ctn' combined with shearing stresses up to the plastic flow point are produced in thin disks confined between hardened steel parts so mounted t h a t they may be subjected to normal pressure and torque simultaneously. Qualitative and quantitative studies are made of the effects of such stresses. Among the qualitative effects it is found t h a t many substances normally stable become unstable and may detonate, and conversely combinations of substances normally inert to each other may be made to combine explosively. Quantitatively, the shearing stress at the

plastic flow point may be measured as a function of pressure. The shearing stress at plastic flow may rise to the Order of 10 or more times greater at 50,000 kg/cm^ than it is normally at atmospheric pressure; this is contrary to the usually accepted results in a narrower ränge of pressure. If the substance undergoes a polymorphic transition under these conditions of stress, there may be a break in the curve of shearing stress vs. pressure. This gives a very convenient tool for the detection of transitions. 57 elements have been explored in this way, and a number of new polymorphic transitions found.

INTRODUCTION

described as "work hardening." It is known that this work hardening cannot proceed beyond a somewhat nebulously defined upper limit, sand that there is a roughly defined "upper yield point" and a maximum shearing stress supportable by any material. In an ordinary tensile test the tension is accompanied, on planes at 45° to the direction of the principal tension, by a shearing stress numerically equal to one-half the tensile stress, so that under these conditions rupture or plastic flow occurs when the shearing stress reaches one-half the tensile stress limit. This quantity has been measured for many metals and rises higher than a few thousand kilograms per Square centimeter for relatively few substances. Engineers have found that under the limited conditions of engineering practice the maximum shearing stress is not greatly affected by a superposed hydrostatic pressure, so that ordinary engineering experience would suggest that it would be impossible under any conditions to apply to a material a shearing stress of much more than one-half its ultimate tensile strength. This opinion is sometimes explicitly expressed in criteria of rupture. This expectation, however, rests on a narrow ränge of experimental conditions, and it turns out that by sufficiently raising the mean hydrostatic pressure the maximum shearing stress may be very considerably increased. In the following are described experimental means by which this may be accomplished, as well as some of the effects of such high shearing stresses. This paper must be regarded only as a suggestive

T

H E experimental study of high stresses has hitherto been confined almost exclusively to high hydrostatic pressure. The distortion produced by hydrostatic pressure is simply describable, and the physical effects are specifiable in terms of a few parameters. Greater complications may be expected if shearing stresses are allowed to act in addition to the hydrostatic pressure. It is, I think, the general feeling that these additional complications are probably of inferior physical significance, but that this may be too narrow a point of view is suggested by the fact that the forces between molecules are in general certainly not central forces, so that on the molecular scale any except the simplest solids must be the arena of shearing forces of high intensity. Furthermore, if such a phenomenon as molecular disintegration by high stress is possible, it is probable that shearing stresses will be much more affective than hydrostatic pressure. The intensity of the shearing stresses hitherto realizable in practice has been restricted to a rather low value; there is no intrinsic upper limit to the hydrostatic pressure to which a substance may be subjected, but the shearing stress may not exceed a certain limit set by plastic yield of the material. The first plastic yield point in shear may be very low, as shown by the behavior of single crystals of many of the metals. The effect of initial plastic flow is to raise the resistance to plastic flow, a phenomenon

112 — 2929

826

P.

W.

B R I D G M A N

introduction to the subject; given the method of producing the stress, many sorts of experiment will occur to any one, some of which I have tried and will publish later, and some of which I have not yet had time to try. The results described in this paper fall into two parts; first a purely qualitative description of the behavior of a number of chemical Compounds, and secondly a quantitative examination of the behavior of all the available elements. I t is characteristic of the method t h a t it is applicable to very small quantities of material, so t h a t it has been possible to examine more of the elements than is often possible. DESCRIPTION OF METHOD

The principle of the method is suggested by Fig. 1. A represents a thin disk of the material under examination, squeezed between two cylinders B and C of hardened steel, with accurately ground plane ends. If the material A is softer than the hard steel it will, if its initial thickness exceeds a critical value, flow out laterally until the thickness of the disk is reduced to such a value that the friction against the steel near the outer edge of the disk is sufificient to balance the mean hydrostatic pressure exerted on the central parts of the disk. I t is obvious t h a t if friction is finite, lateral flow must eventually cease, no matter how great the pressure exerted by the cylinders B and C. When the equilibrium thickness has been reached for a given mean pressure, a couple is applied to the cylinders B and C with respect to each other. T h e initial effect of the couple is to produce a slight angular displacement, resisted by elastic distortion in the cylinders and in A, but if the couple is high enough, B rotates with respect to C with uniform angular velocity. There is thus applied to the disk A a shearing stress, the maximum magnitude of which is determined by the force necessary to produce uniform rotation of B and C. Under this maximum shearing stress there may either be slip at the surfaces of Separation of A from B and C, or more usually plastic flow throughout the interior of .4. In the following only the effects of the maximum shearing stress, t h a t is, the effects when there is uniform rotation of B with respect to C, are studied.

112 — 2930

B c

< B P

p FIG. 1.

FIG. 2.

FIG. 1. Idealized apparatus for exerting pressure and shearing stress simultaneously on the thin disk at A, FIG. 2. Scheme of the actual apparatus. The material in the form of a thin disk at A is squeezed by a hydraulic press pushing the steel cylinders B against the anvil C, which is rotated, while the cylinders B are held stationary by friction against the press.

In actual application, the apparatus is considerably modified from the simple scheme represented in Fig. 1. In the first place the maximum pressure attainable with the scheme of Fig. 1 would be limited to very materially less than the maximum compressive strength of the steel as given by ordinary compressive tests because of longitudinal Splitting of the cylinders due to friction of A as it flows out laterally. By projier design of the steel parts, it is possible, however, to exceed very materially the ordinary compressional limit of the steel. Local intensities of stress, which are very much greater than the intensities attainable under more normal conditions, are often reached in parts of a system which receive proper support from surrounding parts. Consider, for example, the Brinell method of measuring hardness by measuring the dimensions of the indentation produced by a hardened steel ball. Formulas will be found in the engineering handbooks for the stresses in the ball under working conditions. I t appears t h a t steel balls are regularly used on hard materials u p to a compressive force a t the point of contact of 75,000 kg/cm'', about twice the compressive strength under ordinary conditions of test. I t is obvious in this case t h a t the area of the ball receiving the maximum thrust is supported by surrounding parts of the ball and of the material with which it is in contact, and rupture prevented. The arrangement adopted in the following by which the surrounding parts support the most

SHEARING

STRESS

AND

HIGH

highly stressed parts, is something like that of the Brinell hardness test. The upper cylinder B of Fig. 1 is replaced by a very short boss projecting from a very much larger piece of steel. This boss is referred to in the following as the "piston"; in most of the experiments the diameter of the face of the piston was 0.25 inch, although 0.375 and 0.50-inch pistons were also sometimes used. The lower cylinder C of Fig. 1 is replaced by a large block of steel with a perfectly flat face, referred to in the following as the "anvil," and the material A is placed between the two. Finally, in order to eliminate frictional resistance to the rotation when the couple is applied, the whole arrangement is doubled, as shown in Fig. 2, and the anvil is rotated between the two pistons, which themselves do not rotate. The two pistons are compressed together with any desired force with a hydraulic press, and the force required to rotate the anvil is measured with a simple strain gauge on the handle of the rotating wrench. By doubling the apparatus, not only is end thrust eliminated, but each experiment is made virtually the mean of two, with a corresponding greater certainty in the results. In setting up the apparatus it was necessary to use various auxiliary devices to ensure accurate centering and proper placing of the material of the disk, which need not be described in detail. Suffice it to say that the apparatus must be well made; all the parts must be accurately centered and aligned. As a matter of routine the mean pressure exerted by the pistons was carried in all the following experiments to a maximum of 50,000 kg/cm^. The success of the piston in withstanding this pressure depends to a certain extent on the nature of the compressed material; many of the softer materials produce no perceptible effect on the piston except a slight rounding of the very outer edge, whereas the harder materials may produce much greater damage, grinding scratches in the surface, and sometimes chipping pieces off the edge along shear planes at approximately 45°. There was almost always some perceptible permanent alteration of the piston, so that a fresh set of pistons was used for every experiment, either completely new pistons or pistons reground after a former experiment. A freshly ground part of the anvil was also alwavs used for each new

HYDROSTATIC

PRESSURE

827

experiment. The necessity of fresh parts for every experiment makes the small size of the apparatus a very real advantage. The maximum force to produce rotation, and therefore the maximum shearing stress applicable to the disk, varied greatly from substance to substance; the maximum reached for any substance was 18,000 kg/cm''; the force on the end of a 1-meter lever to produce this was about the limit of what one man wanted to exert. The actual distribution of stress and strain in the disk is evidently very complicated, and must diflfer greatly from the mean values just discussed. An exact Solution of the problem would be impossible to give, both because of mathematical difficulties arising from the finite size of the strains, and because of physical difficulties arising from the fact that the constants of the material vary in an unknown and important way at such high stresses. However, some qualitative idea of the distribution of stress and strain can be obtained from the conventional Solution of Hertz by the methods of classical elasticity theory, assuming small strains and unaltered elastic constants. This Solution will be discussed in more detail in another paper, which will go into all questions of technique in greater detail. The Solution shows that the originally plane surfaces of the anvil do not remain plane, but it becomes relatively depressed at the center, so that under stress the disk assumes the shape of a double convex lens, sometimes as much as five times as thick at the center as at the edges. The actual thickness of the disks in these experiments after exposure to a mean pressure of 50,000 kg/cm'' was of the order of a few thousandths of an inch, being greater than 0.005 inch at the center only for a few of the hardest materials. Not only is the strain distribution far from uniform, but the normal pressure is not uniform, being greatest near the outer edge of the disk. Since the greater part of the area is concentrated near the outer edge, the assumption of mean values for normal pressure and also for shearing stress, the latter calculated on the assumption of a constant coefficient of friction all the way across the disk, gives a rough idea of what is happening. The attempt to get more accurate values than that

112 — 2931

828

P.

W.

BRIDGMAN

corresponding to mean values must be left until later, if indeed it proves feasible at all. EXPERIMENTAL RESULTS

1. Qualitative results This whole study of the effect of shearing stresses was the outgrowth of the extension of measurements on polymorphic transitions to 50,000 kg/cm^, which will be described in a subsequent paper, and in particular was at first directed to the attempt to produce in other substances irreversible and permanent changes analogous to the change from white to black phosphorus. It seemed not unreasonable that if the atoms or molecules could be forced to slide over each other by a shear they might take up new positions which they would be less likely to assume under the uniform distortion of a hydrostatic pressure. It seemed that perhaps sulfur was the most likely candidate for an irreversible change to a metallic modification, because of its chemical similarity to phosphorus. An irreversible transition from graphite to diamond was also an attractive possibility, made plausible by the magnitude of the voIume change, and the fact that the diamond structure can be approximately obtained from the graphite structure by a shear and an axial compression. The antidpated permanent changes were not produced, however. It then suggested itself that substances in which the molecular and atomic forces are not as intense as in sulfur and carbon, as in the more loosely knit organic Compounds, might show permanent changes; the first substance tried of this kind was rubber. Positive results were at once obtained; r u b b e r is derubberized t o a h a r d

translucent material, not unlike horn in appearance. Paper was also transformed into a translucent horn-like mass. By control experiments it was established that the paper was not transformed by the action of a pure hydrostatic pressure of 50,000, but the rotation was necessary for the effect. Wood and linen cloth next showed a similar sort of transformation. Celluloid was then tried; it detonated violently, blowing off the edges of the piston. One disk detonated spontaneously when a pressure of 25,000 was reached without rotation, but the füll 50,000 and rotation in addition was necessary to detonate the other

112 — 2932

disk. This result was perhaps not surprising in view of the known unstable character of celluloid. The detonation of celluloid brings up the question of temperature changes, there must of course be a local rise of temperature during rotation; the question is whether it is large enough to be important. An upper limit to the rise of temperature can at once be found from the known Solution of the following problem in one-dimensional heat flow: The X axis is maintained at temperature 0 for all negative values of time. At the origin of time a source emitting Unit quantity of heat per unit time is installed at the origin and constantly maintained for positive times. The known Solution gives for the temperature at the origin (