Collected Experimental Papers of P. W. Bridgman, Volume II: Papers 12-31

Table of contents :
Contents
12. The technique of high pressure experimenting
13. Über Tammanns vier neue Eisarten
14. Change of phase under pressure, I. The phase diagram of eleven substances with especial reference to the melting curve
15. High pressures and five kinds of ice
16. Two new modifications of phosphorus
17. Nochmals die Frage des unbeständigen Eises
18. The coagulation of albumen by pressure
19. Change of phase under pressure, II. New melting curves with a general thermodynamic discussion of melting
20. Polymorphic transformations of solids under pressure
21. The effect of pressure on polymorphic transitions of solids
22. On the effect of general mechanical stress on the temperature of transition of two phases, with a discussion of plasticity
23. Further note on black phosphorus
24. Polymorphic changes under pressure of the univalent nitrates
25. The velocity of polymorphic changes between solids
26. Polymorphism at high pressures
27. The electrical resistance of metals under pressure
28. The resistance of metals under pressure
29. Note on the elastic constants of antimony and tellurium wires
30. Theoretical considerations on the nature of metallic resistance, with especial regard to the pressure effects
31. Thermo-electromotive force, Peltier heat, and Thomson heat under pressure

Citation preview

Collected Experimental Papers of P. W. Bridgman

Volume II

P. W. BRIDGMAN

Collected Experimental Papers

Volume II Papers 12-31

Harvard University Press Cambridge, Massachusetts 1964

® Copyright 1964 by the President and Fellows of Harvard College AÜ 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 II 12-593.

"The technique of high pressure experimenting," Proc. Am. Acad. Arts Sei. 49, 627-643 (1914).

13-611.

"Uber Tammanns vier neue Eisarten," Z. Phys. Chem. 86, 513-524 (1914).

14-624.

"Change of phase under pressure, I. The phase diagram of eleven substances with especial reference to the melting curve," Phys. Rev. 8, 126-141, 153-203 (1914).

15-693.

"High pressures and five kinds of ice," J. Franklin Inst. 177, 315-332 (1914).

16-712.

"Two new modifications of phosphorus," J. Am. Chem. Soc. 36, 1344-1363 (1914).

17-732.

"Nochmals die Frage des unbeständigen Eises," Ζ. Chem. 89, 252-253 (1914).

18-735.

"The coagulation of albumen by pressure," J. Biol. Chem. 19, 511-512 (1914).

19-737.

"Change of phase under pressure, II. New melting curves with a general thermodynamic discussion of melting," Phys. Rev. 6, 1-33, 94-112 (1915).

20-789.

"Polymorphic transformations of solids under pressure," Proc. Am. Acad. Sei. 61, 55-124 (1915).

21-859.

"The effect of pressure on polymorphic transitions of solids," Proc. Nat. Acad. Sei. U.S. 1, 513-516 (1915).

22-863.

"On the effect of general mechanical stress on the temperature of transition of two phases, with a discussion of plasticity," Phys. Rev. 7, 215-223 (1916).

23-873.

"Further note on black phosphorus," J. Am. Chem. Soc. 38, 609-612 (1916).

Phys.

i

CONTENTS

24-877.

"Polymorphic changes under pressure of the univalent nitrates,^".Proc. Am. Acad. Arts Sei. 51, 581-625 (1916).

25-923.

"The velocity of polymorphic changes between solids," Proc. Am. Acad. Sei. 52, 57-88 (1916).

26-955.

"Polymorphism at high pressures," Proc. Am. Acad. Arts Sei. 52, 91-187 (1916).

27-1053.

"The electrical resistance of metals under pressure," Proc. Am. Acad. Arts Sei. 52, 573-646 (1917).

28-1128.

"The resistance of metals under pressure," Proc. Nat. Acad. Sei. U.S. S, 10-12 (1917).

29-1132.

"Note on the elastic constants of antimony and tellurium wires," Phys. Rev. 9, 138-141 (1917).

30-1137.

"Theoretical considerations on the nature of metallic resistance, with especial regard to the pressure effects," Phys. Rev. 9, 269-289 (1917).

31 -1159.

"Thermo-electromotive force, Peltier heat, and Thomson heat under pressure," Proc. Am. Acad. Arts Sei. 53, 269-386 (1918).

Collected Experimental Papers of P. W. Bridgman

CONTRIBUTIONS FROM T H E J E F F E R S O N

PHYSICAL

LABORATORY, HARVARD UNIVERSITY.

T H E TECHNIQUE OF HIGH P R E S S U R E E X P E R I M E N T I N G . BY P. W. BRIDQMAN.

Presented, Jan. 14, 1914.

Received, Dec. 29, 1913.

IN this paper I propose to collect the results of several years' experience in designing apparatus and conducting experiments at high pressures. The rather unusual magnitude of the pressures, from 12000 to 30000 kgm / cm2, has made necessary the development of methods different from those which have hitherto sufficed for more moderate pressures, up to perhaps 3000 kgm/cm2. I shall endeavor to present enough of the details of manipulation so that any one may construct apparatus for experimenting in this as yet almost untouched field of higher pressures. It is not claimed that the methods presented furnish the only solution of the problems of high pressure technique; all that is claimed is that the methods given are possible solutions which have stood the test of constant use for a number of years. The plan of presentation is to indicate the essential parts of a piece of high pressure apparatus, and then to describe in detail the peculiar features of construction of each of the parts. The apparatus consists essentially of a chamber in which pressure is produced by a plunger, a mechanism for pushing the plunger into the chamber, a tube connecting the chamber in which pressure is produced with a second chamber adapted to the particular investigation, and a pressure gauge. The second chamber is the only part of the apparatus that need be varied for different experiments. The other parts will be described in detail here. PACKING.

Obviously an absolute essential to the success of any high pressure apparatus is some reliable method of packing. I shall describe here the broad principle of this packing, leaving for further description the numerous modifications for special uses. All the packing used in this work is so designed that at high pressures it is made tighter by the action of the pressure itself. Figure 1, showing the

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PROCEEDINGS OF THE AMERICAN ACADEMY.

packing for the piston will make the principle clear. The piston Ρ pushes the plug A through the medium of the hardened ring R, the cupped washer of soft steel, C, and the rubber packing B. The liquid compressed is below A at L. The plug A is provided with a stem which is long enough to reach into the ring R, but not long enough to reach to the piston P. If now we consider the equilibrium of A, we see that the fluid pressure over the lower end of A must be balanced by the pressure exerted by the packing Β on an area less than that of A by the area of the unsupported stem. The result is that the hydrostatic pressure in the packing Β per unit area is always a certain percentage higher than that in the liquid, so that the liquid can [ ν / Ι

Fig. 1.

Fig. 2.

Shows the general principle of the packing by which the pressure in the packing Β is always kept higher than that in the liquid at L. The scale of the diagram is § actual size. FIGURE 2 . Shows a common previous type of packing for high pressures. The packing is compressed by a powerful screw into a confined space. This packing leaks when the pressure in the liquid rises as high as that initially applied with the screw. FIGURE 1.

never leak past the piston. This principle is capable of manifold modification and adaptation, but it will always be found that there is somewhere an area unexposed to the action of pressure, so that the hydrostatic pressure in the packing itself is always higher than that in the liquid. It is instructive to compare this packing with that formerly used for high pressures, by Amagat, for instance, up to 3000 kgm. His packing is compressed initially by a powerful screw into a confined

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629

space. Reference to Figure 2 will show that such a packing must leak as soon as the pressure in the liquid reaches the pressure applied initially to the packing by the screw. We proceed to the detailed consideration of the various parts of the apparatus.

T H E MECHANISM FOR MOVING THE PISTON.

This mechanism, of course, may be anything that will furnish a force of the required intensity and exert it over a long enough distance. It has been usual in previous high pressure work to use a screw to drive the piston. When the pressure to be produced becomes high, the screw becomes very inefficient, and it is highly desirable to replace it with a hydraulic press. In my early work up to 6000 kgm., the piston (I inch in diameter) was driven by a screw. This screw had a pitch of 8 threads to the inch, and needed a six foot wrench to turn it. Its efficiency was less than 5%. Furthermore, even when made of nickel steel, the screws, which were one inch in diameter, finally broke down and had to be replaced. The hydraulic press which I have been using for the last six years has never given the slightest trouble. To avoid bulky apparatus, it is desirable to actuate the press with liquid at a fairly high pressure. For this purpose a pump of the Soci^te Genevoise is convenient, giving 1000 kgm/cm2 with a lever. The diameter of the piston of the hydraulic press is 2 | inches, which permits, therefore, of a pressure of 25000 kgm/cm2 on a § inch piston, the size usually used. The barrel of the press is made of mild steel, 4 inches in outside diameter. The piston is threaded over the entire length and provided with a heavy nut by which the piston may be maintained in any desired position, even when the pressure on the low end is relieved. This arrangement has proved an indispensable convenience in operation. Opposed to the main hydraulic press is a smaller press with a f inch piston, connected to the larger piston by tie rods and a yoke pressing against the nut. By this auxiliary press the piston of the large press can be rapidly returned to its initial position after completion of a stroke. It is essential that the press be accurately constructed so that the thrust on the high pressure piston shall be exactly centered; otherwise the piston will buckle. The packing on the low pressure piston of the press embodies the principle shown above. It might be possible to use a cup leather,

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PROCEEDINGS OF THE AMERICAN ACADEMY.

but this would probably last for only a short time, for my experience has been that even so low a pressure as 1000 kgm. is sufficient to rapidly mechanically disintegrate the fibrous structure of the leather. Figure 3 shows the packing. The end piece A with stem Β plays in the hole C in the end of the piston. The packing is a disc of | inch soft rubber between two washers of ^ inch red fibre. The rubber washers will wear away in time, but the fibre washers will have then become so adapted as to give the necessary tightness. In six years of constant use, this packing has been renewed only once, and then only as a FIGURE 3. Shows a section of matter of precaution, when the press the cylinder of the hydraulic was dismantled for another purpose. press with the packing on the end of the piston P. Pressure In order to make absolutely sure that up to 1000 Kgm. per sq. cm. is the end of the stem Β is always free exerted on the piston by means from stress it is well to drill a small of a liquid at L. The scale of lateral hole at the bottom of C to allow, the diagram is } actual size. any liquid to flow away that might percolate around the packing when it is relaxed, as it is when there is no pressure behind it.

T H E HIGH PRESSURE

PISTON.

It has been found best to make this in two distinct parts; a piston proper by which pressure is transmitted from the press, and a packing plug driven by the piston into the cylinder. The piston proper is a cylindrical piece of steel with perfectly plane ends. It is made of tool steel, first turned between centers to the approximate dimensions, then hardened glass hard and left with the temper undrawn, ground to the final size between centers, and finally the center marks ground out, leaving the ends plane. If the center holes are not ground out, the piston is much more likely to crack. For pressures up to 15000 kgm. any high grade of carbon tool steel is good enough. For higher pressures it will be well to use one of the special tool steels that admit of being made especially hard. I have found chrome or silicon steels very suitable. One of these broke at 50,000 kgm/cm2. It has been

BHIDGMAN.— HIGH P K E 8 8 Ü B E EXPERIMENTING.

631

my experience that the new high speed steels are not so good for this· purpose as the old fashion carbon steels. It is the hardness that counts — and brittleness is no disadvantage. After prolonged use, the pistons may be expected to show longitudinal cracks. I have, never had a piston fail in actual use, although I have used pistons a. number of times after the appearance of the cracks. The piston must not be too long, or it will buckle. About 4 inches is a good length for a diameter of § inch. In use, of course, the piston is partially supported by the cylinder when high pressures are reached. A cylinder I inch in diameter may easily support 25000 kgm. with an unsupported length of inches, provided that it is properly centered. Some sort of face plate must intervene between the hardened piston and the soft steel piston of the press. The form shown in Figure 4 is convenient. This is made of tool steel, hardened, and drawn to a blue. If not drawn, it is quite likely that it will crack, or even that

ί-ί-) —

/

~3

A

Fig. 4.

F i g . 5.

4. Shows the face plate of hardened steel between the half inch high pressure piston and the piston of soft steel, P, of the hydraulic press. The scale of the diagram is § actual size. F I Q U B E 5 . The packing plug on the movable piston for use up to the highest pressures in thefinallyseasoned apparatus. The scale of tne diagram is f actual size. FIGURE

the center will be sheared through. A thin (0.01 inch) copper washer at A ensures uniform seating of the piston. The piston, it may be mentioned, is most likely to crack longitudinally when the ends press against something soft that may flow out laterally, carrying the piston with it by friction. It is well, therefore, to make the center hole in the face plate a good fit for the piston. The principle of the packing plug at the end of the piston has been described, but there are a number of details of construction. This plug may have two forms, one for use in the apparatus as finally set

632

PROCEEDINGS OF THE AMERICAN ACADEMY.

up ready for experiment, the other for use in giving the preliminary seasoning. I describe first the plug for regular use. Figure 5 shows the dimensions. It is particularly important that the corners at A should be left slightly rounded. The plug may be made an easy fit, say 0.001 of an inch too small, for the hole in the cylinder. The plug is further provided with a washer of copper, Β, of an inch thick, a force fit for the hole. For convenience in handling, it is well to solder the washer Β to the plug. Above Β is the packing washer, C. Ί of an inch is thick enough for this rubber washer if only a few strokes of the piston are to be made, but since the enormous friction rapidly wears away the rubber, the packing should be made thicker if longer use is contemplated. It is an advantage to keep the packing as thin as possible, for in this way the total friction is reduced. Above the packing is another copper washer, D, identical with the lower one, and above this a washer, E, of the same dimensions, of soft Chrome Nickel steel. Finally, above the soft steel washer, is a hardened steel ring, F, against which the piston bears. This ring is likely to crack. If pressures not over 12000 kgm. are to be used, the ring may be made of tool steel, hardened, and drawn to a black. But if pressures to 25000 are to be used, the ring must be left glass hard, and one may expect to renew this ring with each new setting up of the apparatus. The packing plug just described is one of the few parts of the apparatus almost certain to give way after long use. Fortunately the results of failure are nothing more serious than the projection of the severed stem against the piston, and sometimes, though not usually, leak. Failure takes the form of separation of the stem from the head at the corner A by the " pinching-off" 1 effect. The grade of steel used for the plug is therefore, important; a peculiar sort of toughness is necessary. I have found best for this a Krupp Chrome Nickel steel, grade E. F. 60.0. The New York agents are Thos. Prosser and Son, 15 Gold St. It is strange that another grade of steel with a higher tensile strength, and better adapted for the construction of the cylinders, is not so good for the plug. The plug is to be hardened in oil, and the temper left undrawn. The degree of heating during the hardening is important, slight differences having a great effect on the resistance to the "pinching-off" effect. The precise temperature of heating can best be told by experiment. The size of the rubber washers used for packing is also important; these should be as much larger than the hole as can conveniently be 1 P. W. Bridgman, Phil. Mag., 24, 68 (1912).

BRIDGMAN.— HIGH PRESSURE EXPERIMENTING.

633

used. The reason is that under high pressure rubber becomes rigid and brittle like glass, and under the right conditions may even crack. If the rubber is initially so small that under the high pressure its natural volume compression would make it smaller than the hole, then it would certainly leak if it were not for the excess pressure in the packing over that in the liquid. But the rigidity of the rubber may become so great that the excess pressure is not sufficient to force it tightly against the walls of the cylinder, unless the rubber would of t-A itself completely fill the hole at the high pressure. The form of plug to be used during the preliminary seasoning of the apparatus is essentially the FIGURE 6. Piston form described above so modified as to allow it to packing for high pressures for use in follow the stretching of the cylinder. It could be seasoning the cylinused under all circumstances, except that the fric- ders when provision be made for tion is considerably higher than that of the other must stretch of the cylinform. It is shown in Figure 6. The possibility der without leak of distension of the head to follow the stretching The scale of the diagram is $ actual of the cylinder is provided by a coned ring of size. copper, A, backed with solder, B, and the possibility of stretching at the upper end is provided by using a washer of soft steel, C, rather deeply cupped, the groove of the cup being filled with a solder. With such a plug, a pressure of 25000 kgm/cm. 2 may be maintained in a cylinder which has stretched ^ of an inch.

THE CYLINDERS.

The cylinders, or "bombs," need to be subjected to a seasoning process, because the pressures at which they are to be used are beyond the natural elastic limit of the steel. It is, therefore, necessary to raise the elastic limit by the application of a stress beyond the original elastic limit. But since the application of a stress great enough to permanently raise the elastic limit produces a permanent distortion of the cylinder, the cylinder must be machined again to the final size after the preliminary stretching. The choice of steel for the cylinder is a matter of much importance. A high tensile strength, combined with a moderate elongation before rupture is essential. The Krupp Chrome Nickel steel mentioned for the piston is satisfactory for this purpose, or somewhat better is a

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PROCEEDINGS OF THE AMERICAN ACADEMY.

Chrome Vanadium steel, "Type D," made by the Halcombe Steel Co. of Syracuse, Ν. Y. This latter steel may show a tensile strength as high as 300,000 lb. per sq. in. Before the stretching process, the cylinder should be hardened by heating to from 870° to 1000°, and quenching in oil. The temper should not be drawn at all after this hardening. It is not possible to get either of these two steels glass hard like tool steel, unless by case hardening, so that it is possible to enlarge a hole by reaming in a piece of steel so hardened, or even to drill it. The dimensions of the cylinders are capable of some variation. It has been my experience that the outside diameter of the cylinder should be from six to ten times that of the inside hole. Not much is gained by making it heavier than ten times, and it is likely to break if made much less than six times. Several cylinders of four times the diameter have eventually broken at 12000 kgm. although they withstood a seasoning pressure of 25000 kgm. Choice of dimensions must furthermore be influenced by the consideration that there is a distinct advantage in keeping the absolute dimensions of the apparatus small, because hardening by quenching cannot reach to the interior of a large piece of steel. I have found it convenient to use a diameter of about § of an inch for the piston, and an outside diameter for the cylinder of from 4 to 4 J inches. If the chrome vanadium steel is used, the hole may be made initially § inch in diameter, and the stretch after seasoning to 25000 kgm. will be small enough so that the hole may be reamed to a final size of of an inch. If the Krupp steel is used, a slightly greater allowance for stretch must be made, but it will still be less than χ^ of an inch on a diameter of § an inch. The actual details of the seasoning require little comment. Pressure should be increased gradually, stopping after every increase long enough for the viscous yield to entirely disappear. The length of the steps by which the pressure is increased may be so chosen that the maximum is reached in from ten to fifteen steps. Pressure should be maintained at the maximum for several hours. One application of the seasoning pressure is sufficient, unless the stretch should be so great as to make a second stroke necessary to reach the maximum pressure. The seasoning pressure should be as high as can be reached without permanent deterioration of the steel. With the grades of steel mentioned above, this pressure may be safely as high as 25000 to 30000 kgm. A mixture of f (by volume) glycerine and \ water is suitable for transmitting the pressure during the seasoning. The necessary length of stroke may be reduced by filling those parts of the

BRIDGMAN.— HIGH PRESSURE EXPERIMENTING.

635

interior of the cylinder which will not be reached by the piston with a core of brass or steel, thus reducing the volume and the compression of the liquid. One must always be prepared for disappointment after constructing one of these cylinders, for in spite of the greatest care of the manufacturer one cannot at the present day be sure that the steel will be free from flaws. These flaws may develop during the preliminary seasoning, but are much more likely not to show themselves until the piece has been reamed to the final size. For example, one cylinder had been used for a year before finally a seam opened in a wall 2 | inches thick, letting through a very fine stream of liquid. It is a matter of pure chance whether a flaw will be found or not; of two pieces from the same bar, one may have a flaw, and the other may be sound. It has been my experience that about three out of every four pieces are sound. CONNECTING P I P E S .

The proper construction of connections from one piece of apparatus to another has been until recently the most serious problem of all this high pressure work, and the cause of almost every explosion. The problem has at last, however, been satisfactorily solved. Diferent types of connection may be used, depending on the pressure to be carried. We begin with the connections for the lower pressures. For low pressure transmission, such as for the low pressure end of the press up to 1000 kgm., the most convenient connection is copper tubing. The size I have used is \ of an inch outside diameter and of an inch inside diameter. This may be used either in its hard drawn state or else annealed. It will stand a single application of 1500 kgm. and may be used almost indefinitely to 1000 kgm. For coupling together two pieces of pipe, a cone coupling with right and left handed thread will be found very convenient. (See Figure 7.) The hollow cone may be best made of steel, since it is subjected to greater strain than the other, which may be made of brass. The copper tubing is attached to the cones by threading and soldering. The thread may well be as long as § inch, and the unthreaded part another § inch. If the soldered length at the end of the pipe is much less than 1 inch long, solder will be slowly extruded through the threads by the pressure, and there will eventually be leak. For making connections to the cylinder the coupling shown in

12—601

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PROCEEDINGS OF T H E AMERICAN ACADEMY.

Figure 8 is useful. It will be seen that this is an application of the packing principle described above. Here the projecting pipe itself is the area unsupported, so that the rubber packing, A, exerts its pressure on an area less than that acted on by the liquid by an amount equal to the area of the cross section of the pipe. Brass washers, Β and C, are strong enough for the end of the tube. These brass washers should fit the hole within one or two thousandths of an inch,

Fig. 8.

Fig. 7.

Figure 7. Coned coupling for copper tubing up to 1000 kgm. The scale of the diagram is ? actual size. Figure 8. The packing for copper tubing, or, with slight modifications, for commercial steel tubing up to 4000 kgm. The scale of the diagram is f actual size.

so that the rubber may not be blown through the cracks. Occasionally, after several years' use, a copper tube may fail by the "pinchingoff " effect at the rubber packing. For pressures higher than 1000, up to 6000 or 7000 kgm., it is possible to get commercial steel tubing. The National Tubing Co., Pittsburg, Pa., draws a size of " Shelby" tubing f g of an inch outside diameter, and of an inch inside diameter, which I have found suit-

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able. This may stand as much as 9000 kgm. on the first application of pressure. The tubing should not be softened, but left hard drawn. I t is likely to have flaws in it, but these can be usually detected by a careful examination of the outside of the tubing. For pressures up to 4000 kgm. it is safe to use with this tubing a connection like that shown above (in Figure 8) for the copper tubing. But the right and left hand thread connection (of Figure 7) cannot be used, since for one thing a soldered joint will not stand the pressure, the solder being eventually pushed out. The washers, of course, should be of steel, and it pays to cup the upper steel washer, filling the groove of the cup with solder. At pressures in excess of 4000 kgm. the tube is likely to fail by the " pinching-off" effect, if the rubber type of packing is used. This "pinching-off" effect almost invariably takes place at the bottom of the thread, the weakest part of the tube. For higher pressures than 4000, up to 6000 or 7000, a connection must be used which prevents the packing from coming into contact with the thread. The cone packing of Figure 9 answers this purpose. The cone, A, screwing over the end of the tube is of hardened nickel steel. The liquid is kept from coming into contact with the thread by a ring, B, of soft steel, protected by solder, C, above. A hollow cone of soft steel, D, cut at a slightly more acute angle than the solid cone is the packing. To ensure initial tightness, before pressure has been pushed high enough to make the cones conform to each other, a thin piece of rubber, or a ring of copper may be placed between the cones. This packing has never been quite satisfactory, since FIGURE 9. Coned often rupture did ultimately occur at the base packing for use with of the threads. At the Geophysical Laboratory tubing up to 7000 kgm. The purpose in Washington a method has been developed by is to keep the presDr. John Johnston for packing commercial steel sure from the threads tubing that will doubtless be found more con- on the outside of the tubing, where rupvenient than the above. 2 He has tested the ture is particularly method to 8000 kgm., but whether the tubing likely to occur. The will stand the continued application of 8000 I scale of the diagram is § actual size. do not know. For continued use to pressures higher than 7000 I have not been 2 John Johnston and L. H. Adams, Amer. Jour. Sei., 31, 505 (1911).

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PROCEEDINGS OF THE AMERICAN ACADEMY.

able to use any commercial drawn tubing, but have found it necessary to drill the tubing from the solid rod. The same grade of steel as that used for the cylinders should be used for the drilled tubing. The inside diameter of the tubing is of an inch, and it is quite possible with a little practise to drill pieces at least 17 inches long. The drill should be cut on the end of a long piece of drill rod; it does not pay to try to braze a long shank onto a short drill. Two essentials in successfully drilling a long piece of tube are to start with the drill accurately central, and to use as homogeneous stock as possible. The drill need not be expected to run more than § of an inch out of center on a piece 17 inches long. After getting the drill accurately started for two or three inches it will be found convenient to put the drill in a hand tool holder and force it in by hand. This arrangement makes it much simpler to run the drill in and out of the hole to remove chips. Great care must be observed that the drill does not become clogged with chips. I have found that it pays to carefully clean out the hole with a swab after drilling not more than § of an inch. It is easy, if all precautions are observed, to drill a hole of an inch in diameter 17 inches long in from seven to eight hours. After drilling, the rod is to be turned off over the hole to the final size, so that the whole may be concentric, and then hardened in oil and left undrawn, exactly as are the cylinders. The problem of the proper connections at the end of the pipe is one that has given great trouble. The coned connection described above was used for some time. The only change necessary from the form used for lower pressures is the interposition of a hardened steel washer between the soft cupped washer and the retaining screw. I have successfully reached 12000 kgm. a number of times with this packing, but ultimately rupture always occurred at the bottom of the threads. It may be that rupture at this point is not a pure pressure effect, but that the cylinders are too heavy for the tubing, so that there is some slight bending at the thread under the unavoidable hard handling of setting up the apparatus. Be that as it may, the cone packing is unsatisfactory for long continued service, particularly at temperatures much above that of the room. The packing for the connecting tube finally adopted, and which has proved entirely satisfactory, is shown in Figure 10. The main improvement of this over the cone form is that it leaves the tube much heavier, the minimum outside diameter at a point exposed only to internal pressure being f of an inch in the new form against about £ of an inch at the bottom of the thread in the cone form. The end of

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the tube has a heavy thread cut on it, and is provided with a milled head, H, for a wrench. The packing is composed of three rings; a thin ring of Bessemer, A, a ring of lead, Β, of an inch square in cross, section, and a ring of Bessemer, C, of Ye i n c h square section. These rings fit over the end of the tube in an annular space of an inch wide between the tube and the walls of the cylinder. On screwing up the the tube, the rings are forced against a conical shoulder, D, on the tube. It will be noticed that the Bessemer ring C supports the hydrostatic pressure over the entire area of one face, but that at the rear face there is a vacant space, E, so that the pressure must be balanced by the force exerted by the cone on the corner of the ring. This means that the intensity of pressure in the steel at the corner is much greater than the pressure in the liquid, so that leak cannot occur. Here again, we have the principle of a packing with an unsupported area, packing of rings of soft steel for Tightness at the outside of the ^ S V Ä ^ ^ Bessemer ring is secured by the size, stretching of the ring over the cone. The lead washer merely serves the purpose of giving initial tightness, and the thin Bessemer washer is to keep the lead washer in place. The projecting ledge against which the washers bear opposite the cone is shown in the figure as the rim of a nickel steel cup, F, resting loosely in the hole. This construction is convenient, because it provides a way of withdrawing the packing rings after use by inserting a threaded rod through the bottom of the cup and pulling the cup out. It is, however, quite possible to use part of the cylinder itself as the ledge, since the removal of the washers, even without the device of the cup, does not present serious difficulties. The lead ring and the heavy Bessemer ring cannot be used more than once, but the thin Bessemer ring for retaining the lead may be used several times. This packing has, at the date of writing, been in continuous use for nearly a year, up to 13000 kgm. and 200°, without a single rupture or

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PROCEEDINGS OF THE AMERICAN ACADEMY.

leak of any kind. It has not been tested higher, but there is no reason why it should not hold until the steel cylinder stretches enough to leak. It is a satisfaction in using this connection to feel that this part of the apparatus is at least no weaker than any other. THE PRESSURE GAUGE.

Without doubt the most convenient means of measuring high pressure is to measure the change produced by the pressure in the electrical resistance of some such alloy as manganin. The details have been given in a previous paper.3 The only structural difficulties with the method are those incidental to getting electrically insulated leads into the cylinder. The principle of the insulating plug has also been described in a previous paper, but not in much detail, and since several improvements have been introduced, it will pay to redescribe it. The plug is shown in Figure 11. It consists essentially of an outer shell, A, to which one electrode is silver soldered, and running through it and insulated from it, a thin steel stem, P, which forms the other electrode. The outer shell of the plug, A, is made of Krupp Chrome Nickel steel, hardened in oil. The packing of the shell used at present is soft rubber, after the same design as that used for the tubing at lower pressures. This packing is not shown in the diagram. There is no weakening of the plug here by a thread on the outside, FIGURE I I . The so that the "pinching-off" effect is not nearly so lead!n t i n 6 electrical

connections To^the interior of the pressure chamber. The scale of the diagram is f actual size.

t r o u b l e s o l n e as in the case of the packing for the tubing. Moreover, by making the shell with a taper shoulder, and placing over this a soft steel

a g a i n s t which the rubber bears, thus provid' ° ' , , l n g for the possibility of sup ot one m e t a l p a r t over c o n e

.

the other in the locality where the "pinchingoff" effect would be most likely to occur if the metal were of one solid piece, and by using rubber washers only 5 of an inch thick, the danger of "pinching-off" is reduced to a minimum. However, this design 3 P. W. Bridgman, These Proceedings, 47, 321-343 (1911).

BRIDGMAN.— HIGH P R E S S U R E EXPERIMENTING.

641

does not entirely do away with the effect; it is safe to count on a rupture about once a year if the apparatus is used continually to 12000 kgm. Failure of the plug need not result in complete rupture. Once or twice I have been troubled with an obscure leak which I finally traced to a crack at the base of the cone of A, where the " pinching-off " effect might be expected to occur. If ever occasion should arise to make new plugs, I intend to redesign them so as to use the ring packing of steel now used for the connecting tubes. The insulating properties of the plug are provided by two layers of mica washers, Β and C, turned (not punched) so as to be a force fit for the hole. Tightness against leak is provided by a layer of rubber, D, between the two layers of mica. The fine stem, F, is insulated from A for the rest of its length by a thin glass tube, G, slipping into the annular space between F and A. A small cylinder of hard rubber, H, at the outer end completes the insulation. The insulating properties of the plug are improved if all the parts are dipped into paraffine heated to from 120° to 140° immediately before assembling, and if they are kept hot enough during the assembling so that the paraffine remains melted. The insulation resistance is at least 100 megohms, the limit of the measuring instrument used. It will be noticed that the insulating packing uses again the principle of the unsupported area, the central stem in this case being the unsupported part. But the area of the stem is so slight that the excess pressure provided by it may not be sufficient to overcome the friction in the mica washers against the side of the plug. It is therefore necessary to make the rubber washer initially considerably larger than the hole, or else the tightness will not be permanent. A washer initially |-§ of an inch to go into a hole xg of an inch in diameter is not too large. The steel disc at Ε is necessary to prevent the rubber blowing out past the mica washers along the stem. This disc should be of hardened nickel steel. The stem F passing through the washers is also of hardened nickel steel. It, together with the head at its upper end, must be made from one piece. Attempts to braze or screw the head onto a piece of wire have uniformly failed. This thin stem is also likely to fail by the "pinching-off" effect, where it passes through the rubber, or if the friction of the washers is too great, it may be torn apart by the tension afforded by the expansion of the washers during decreasing pressure. Several times I have observed rupture from this cause at 6000 kgm. after decreasing pressure from a maximum of 12000.

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PROCEEDINGS OF THE AMERICAN ACADEMY.

The pressure of 6000 kgm. is still sufficient to project the fine stem with considerable violence after rupture takes place, so that one must be particularly careful not to yield to a false feeling of security in handling the plug during decreasing pressure. The insulating plug as thus constructed is at present the part of the apparatus most likely to fail. The mica washers eventually fail along a cone of shear reaching from the hardened disc to the hole in the stem. Slipping of the mica on the shear planes is likely to be accompanied by unsymmetrical yielding of the rubber and the hardened disc, so that the fine stem may be bent or even sheared off by the tilted disc. It would probably pay in designing new apparatus to experiment with a form of insulating plug developed at the Geophysical Laboratory. 4 Soapstone instead of mica is the insulating material, and the rubber washer is dispensed with, so that it is simpler in construction. It has not been tested over so wide a range as the form described above, but has given perfect satisfaction up to 8000 kgm. The form described above has been used to 21000 kgm., although it would not stand this many times. VALVES.

I have as yet not been able to construct satisfactory valves. However, it may be worth while to describe a substitute which has been found useful for one particular purpose. In the absence of valves the desired final pressure must be reached with one stroke of the piston. But if the apparatus connected to the cylinder is of more than two or three times the capacity of the cylinder itself, it will not be possible to do this because of the compressibility of the transmitting liquid. But since the greater part of tlje compression of a liquid occurs in the first few thousand kilograms, it would in many cases be sufficient if an initial pressure of a few thousand kilograms could be produced in the cylinder before the stroke begins. This is accomplished by the use of a small by-pass at the upper end of the cylinder, so situated that it is just uncovered when the piston is withdrawn to its extreme position. Initial pressure to the desired amount is produced in the apparatus by an auxiliary pump through the by-pass, which is then cut off by the descent of the piston. It is necessary to make this by-pass very minute, so that the rubber packing of the piston may not be blown out through it as the piston passes by. One convenient way of doing this 4 John Johnston and L. H. Adams, Amer. Jour. Sei., 31, 507 (1911).

12 — 608

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643

is to drill and tap a convenient sized hole at the upper end of the cylinder, say for a 10-32 thread, j of an inch long, and then to screw tightly into the tapped hole a carefully cut screw, across the threads of which (that is, parallel to the axis) a fine scratch has been made. This scratch is the channel by which the transmitting fluid gains access to the interior of the cylinder; its size may be regulated at pleasure by varying the size of the scratch. The screw may be made of soft tool steel, since the pressure it has to withstand is not high, thus permitting the end projecting into the cylinder to be reamed off. The use of a by-pass necessitates the use of an auxiliary pump giving several thousand kilograms. I have found it convenient to use a second pump of the Geneva type,coupled to an intensifier of readily suggested design, stepping up the pressure four times. PLUGS.

In adapting pieces of apparatus to new uses it will often be necessary to plug holes previously used for connections. This may be done with a plug packed according to the simple method of rubber washers used for the connecting pipes at low pressures (see Figure 12). If the stem and the head, A, are turned from one piece of Krupp Chrome Nickel steel and hardened, the "pinchingoff " effect will seldom be troublesome. One should realize, however, that the "pinchingoff" effect is treacherous, and likely to come at the most unexpected times. All parts liable to this effect should either be shielded, or else they should be pointed in such a direction that they can do no damage if projected by an explosion. J E F F E R S O N PHYSICAL LABORATORY, HARVARD UNIVERSITY, CAMBRIDGE, M A S S .

FIGURE 12. The plug for closing holes against high pressures. The plug A is packed with a rubber washer B, a soft steel washer D cupped and filled with solder at C, and the hardened washer E. The scale of the diagram is i actual size.

Über Tammanns yier neue Eisarten. Von

F. B. Bridgman'). (Mit 2 Figuren im Text.) (Eingegangen am 6. 11. 13.)

In einer kürzlich erschienenen Arbeit hat T a m m a n n 2 ) wieder die Frage der gegenseitigen Beziehung der drei Eismodifikationen I, I I und I I I , aufgenommen, die früher zunächst von ihm 1899 3 ) und unlängst 1911 von mir 4 ) behandelt worden sind. In seiner neuen Arbeit ist es ihm gelungen, die Gleichgewichtskurve I i — I I I zu finden. Seine Leugnung der Existenz dieser Kurve war der Hauptpunkt der Nichtübereinstimmung zwischen seinen frühern Arbeiten und den meinigen. Die von ihm gefundene Gleichgewichtskurve I I — I I I hat nicht ganz die gleichen Koordinaten wie die von mir gefundene, aber der Unterschied zwischen seiner und meiner Kurve scheint nicht grösser als der mögliche Versuchsfehler zu sein. Ausser der Auffindung mehrerer Punkte auf der I I — I I I - K u r v e hat Tammann eine Anzahl von Punkten auf den andern Gleichgewichtskurven neu bestimmt. Diese wieder bestimmten Punkte sind nicht immer unter sich in Übereinstimmung und stimmen nicht mit den Punkten seiner frühern Arbeit überein. T a m m a n n findet, dass er seine Abweichungen weitgehend erklären kann durch Annahme der Existenz von vier neuen Eisarten, drei neue Arten der Gruppe des gewöhnlichen Eises, des Eises I, und eine neue Varietät von der Gruppe des Eises III. Es wird postuliert, dass die verschiedenen Eise der gleichen Gruppe nur wenig voneinander abweichen. verschiedene Kristallformen

Es wird angenommen, dass sie

besitzen, aber sich unmerklich in ihrem

Volumen unterscheiden, und die Drucke und Temperaturen, bei denen irgend eine der Modifikationen einer Gruppe mit irgend einer der Varie' ) Aus dem Englischen übersetzt von W . N e u m a n n . η Zeitschr. f. physik. Chemie 84, 257—292 (1913). 3)

Tammanns

frühere Angaben

sind in seinem Buch „Kristallisieren

und

Schmelzen", Ambros. B a r t h , Leipzig 1903 zusammengestellt. *) Proc. Amer. Acad. 47, 441, 558 (1912).

13 — 611

514

P. Β. Bridgman

täten einer andern Gruppe im Gleichgewicht steht, sind im allgemeinen nur wenig Verschieden. Eine Hypothese dieser Art kann man experimentell unwiderleglich machen nur durch das Postulat, dass die Unterschiede zwischen den verschiedenen Varietäten ausreichend gering sind. Um andere von der Richtigkeit einer so eigenartigen Hypothese zu überzeugen, obliegt aber dem Beobachter gleichzeitig in ungewöhnlichem Masse die Verpflichtung, jede Möglichkeit eines experimentellen Irrtums auszuschliessen. Nun scheint es, dass Tarn man η die peinliche experimentelle Sorgfalt, die erforderlich ist, um uns von der Wirklichkeit eines so verwickelten Zustands der Dinge zu überzeugen, nicht beobachtet hat, und ich beabsichtige, im folgenden zu zeigen, dass in der Tammannschen Arbeit mehrere Fehlerquellen von der gleichen Grössenordnung wie die Unterschiede zwischen den hypothetischen Eisvarietäten enthalten sind. In erster Linie ist bedauerlich, dass die Tammannsche Methode des Auftragens seiner Punkte die augenscheinliche Abweichung zwischen seiner und meiner Arbeit erhöht hat. Eine seiner Versuchsmethoden bestand in der kontinuierlichen Änderung der Badtemperatur. Die wirkliche Temperatur des untersuchten Eises hinkte, wie sich fand, ungefähr 1-5° hinter der Temperatur des Bades nach, aber Tarn mann trägt die beobachtete Badtemperatur an Stelle der korrigierten Temperatur mit meinen Punkten in die gleiche Figur ein. Ferner scheint er durch seine eigene Figur irregeführt worden su sein, denn im Texte vergleicht er seine nicht korrigierten Koordinaten mit denjenigen meiner Kurve. Fig. 1 wird dies klarer machen. T a m m a n n s beobachtete und korrigierte Punkte sind durch die Kreuze angegeben, die meinigen durch die Kreise. Man wird sehen, dass die grösste Abweichung zwischen den Tammannschen Punkten und meiner Kurve 2-7° beträgt, und die mittlere algebraische Differenz ist 1-6° anstatt 3 oder 4°, wie er angibt. Weiterhin betrachtet Tammann meine Kurve als unwahrscheinlich, wegen „ihrer auffallend starken Krümmung". Es wäre von Interesse gewesen, die Kurve zu sehen, die T a m m a n n durch seine eigenen drei experimentellen Punkte gezogen haben würde. Aber das verabsäumt er zu tun; in der Tat trägt er nirgends in seiner Ahhandlung den dritten dieser Punkte graphisch auf. Seine Figur (bei ihm Fig. 3) reicht nur bis 2550 kg, so dass sie nur die beiden ersten seiner Punkte einschliesst. Er nimmt an, dass sein Fall bewiesen ist, weil eine durch die beiden ersten dieser Punkte gezogene gerade Linie durch einen vermuteten Tripelpunkt geht, und er sagt: „Es harmonieren also die neuen Bestimmungen miteinander in befriedigender Weise". Das hier wieder-

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Über Tammanns vier neue Eisarten.

gegebene vollkommene Diagramm tut in überzeugender Weise dar, dass die Taiömannsche Methode der kontinuierlichen Änderung der Badtemperatur nicht imstande ist, genaue Resultate zu liefern, und sehr erhebliche Zweifel aufkommen lassen muss, ob er es überhaupt wahrscheinlich gemacht hat, dass seine Umwandlungskurve und die meinige wirklich verschieden sind.

•

X

/

y>

Aο

/

r

< 2500

3000

3500

Fig. 1. Die Gleichgewichtskurve zwischen Eis II und III. Die Kreuze sind Tarn m a n n s korrigierte Punkte, die Kreise die meinigen. Die beiden vollen Kreise an jedem Ende der Kurve sind die beiden Tripelpunkte, die diese Kurve abschliessen. Diese Tripelpunkte sind nicht direkt beobachtet worden, sondern involvieren die andern, in der Figur nicht wiedergegebenen Gleichgewichtskurven.

So viele der T a m m a n n sehen Daten sind nach der Methode der kontinuierlichen Änderung der Badtemperatur und Beobachtung der Druckänderungen gewonnen worden, dass eine eingehendere Kritik angebracht ist. T a m m a n n selbst erkennt an, dass die Temperatur des Eises innerhalb des Stahlzylinders hinter der Temperatur des Bades nachhinkt, aber er scheint nicht erkannt zu haben, dass dieses Nachhinken nicht immer das gleiche zu sein braucht. Wenn die Temperatur erhöht wird, während nur eine Phase anwesend ist, so rührt das Nachhinken nur von der langsamen Leitung der Wärme durch die Zylinderwandungen her. Wenn indessen während der Temperaturerhöhung eine Umwandlung von einer Phase in eine andere stattfindet, kann das Nachhinken, wegen der Umwandlungswärme, die abgeführt werden muss,

13 — 613

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P. Β. Bridgman

stärker sein. Das Nachhinken wird daher mit der Natur der Umwandlung variieren. Zum Beispiel wird man ein stärkeres Nachhinken auf der I—Ii-Kurve als auf der I—III-Kurve erwarten, weil die latente Umwandlungswärme im erstem Falle grösser ist. Den Fehler infolge des Nachhinkens der Temperatur kann man besonders schwerwiegend erwarten, in einem Falle des Schmelzens (d. h. des Überganges in die flüssige Phase) das wegen Verunreinigungen vorzeitig beginnt. Ausser dem Nachhinken der Temperatur wird die Möglichkeit des Nachhinkens des Drucks von Tammann nicht genügend berücksichtigt. Dieses kann zu ernsten Fehlern Anlass geben, besonders bei niedrigen Temperaturen. Der Grund hierfür ist, dass die Umwandlung von einer Phase in eine andere Zeit erfordert, so dass wenn die Gleichgewichtsbedingungen gestört werden, das Gleichgewicht sich nur langsam wieder herstellt Es ist einleuchtend, dass, wenn die Temperatur kontinuierlich geändert wird, der Druck nie derjenige sein kann, der der gegebenen Temperatur entspricht, selbst wenn die Korrektion für das Nachhinken der Temperatur angebracht wird. Dieser Fehler wird von viel grösserem Gewicht bei den niedrigen Temperaturen sein, bei denen die Reaktion langsam verläuft. Tammann gibt zu wenige Daten über die Geschwindigkeit seiner Änderungen an, als dass eine Schätzung des möglichen Fehlers aus dieser Ursache angängig wäre. Indessen zeigt seine Fig. 3 a, um einen besondern Fall zu erwähnen, bei der niedrigem Temperatur eine Abweichung von 7° zwischen zwei Bestimmungen der Temperatur des maximalen Drucks der I—III-Kurve. Es kann keinem Zweifel unterliegen, dass die Methode der kontinuierlichen Änderung der Badtemperatur für eine rasche Übersicht über das Feld von grossem Wert ist, aber sie sollte nicht benutzt werden, wenn genaue Werte der Gleichgewichtskoordinaten notwendig sind. Die beste Methode ist, die Temperatur konstant zu halten, und dem Druck Zeit zu lassen, sich dem Gleichgewicht sowohl von unten als von oben zu nähern. Die von Tammann benutzten Druckmesser waren metallene Deformationsdruckmesser vom Bourdonschen Typus. Die absolute Genauigkeit dieser Manometer ist sicherlich nicht sehr gross, denn zwei von Tammann benutzte Druckmesser dieser Art, der eine 1899, der andere 1910 1 ) differierten um ungefähr 100 kg bei 2000. Diese beiden Manometer kamen von S c h ä f f e r und B u d e n b e r g und wurden ursprünglich mit ihrem Manometer mit beweglichem Stempel geeicht. Zu einer Zeit in ihrer Geschichte müssen daher die beiden Manometer übereingestimmt haben, aber im Verlauf der Zeit sind sie um 5°/0 ver*) Zeitschr. f. physik. Chemie 72, 609 (1910).

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517

schieden geworden. Ferner ist es wohl bekannt, dass Manometer dieser Art Fehlern infolge von Hysteresis und „elastischen Nachwirkungen" unterliegen. T a m m a n n macht einige Angaben über den Betrag der „elastischen Nachwirkung" seines Manometers von 1899 Er sagt, dass, wenn dieses Manometer von 1140 auf 3500 kg gebracht, bei 3500 kg eine Stunde lang gehalten und dann wieder auf ungefähr 1140 kg erniedrigt wurde, es eine „elastische Nachwirkung" von 20 kg zeigte. Nun sind einige der Tarn mann sehen Kurven unter Bedingungen erhalten worden, die der Entwicklung elastischer Nachwirkungen besonders günstig sind. Seine Kurve I—III', die sich nur um 20 kg von seiner I'—III'-Kurve unterscheidet, wurde erhalten, nachdem das Eis sehr langsam von — 8 0 ° aus erwärmt worden war, während der Druck die ganze Zeit über in der Nähe von 2000 kg lag. Es ist sicherlich nicht unbegründet, zu vermuten, dass in a c h t Stunden bei 2000 kg eine elastische Nachwirkung von 20 kg aufgetreten sein mag, wenn wir wissen, dass der Fehler aus dieser Ursache in einem Falle 20 kg nach einer Stunde bei 3500 kg betrug. Aber Tarn man η ist nicht geneigt, diesen Fehler von 20 kg Manometerfehlern zuzuschreiben, weil er sagt, dass 20 kg das Zehnfache der „Empfindlichkeit" des Manometers sind. Es ist sicher ein kühner Standpunkt, zu behaupten, dass ein Instrument keine in sich selbst übereinstimmenden Fehler von grösserem Betrage, als seine Empfindlichkeit zeigen kann. Ausser den „elastischen Nachwirkungen" ist praktisch jedes Manometer vom Bourdontyp mit Hysteresisfehlern behaftet. T a m m a n n hat offenbar nicht versucht, den Betrag dieses Fehlers zu bestimmen, aber er macht Angaben, aus denen man seinen Betrag schätzen kann. Die Reaktionsgeschwindigkeit zwischen den beiden Varietäten von Eis I und III bei — 2 5 ° ist so ausserordentlich gross, dass ich in meinen eigenen Versuchen niemals eine Änderung des Drucks von 2 kg eine Minute nach einer Erhöhung oder Verminderung des Volumens beobachten konnte. T a m m a n n hat sich auch über die explosive Reaktionsgeschwindigkeit verbreitet, aber er hat immer nach einer vorausgehenden Druckerhöhung einen höhern Gleichgewichtsdruck gefunden als nach einer Verminderung. Diese Wirkung ist genau diejenige der Hysteresis. Der Betrag der Hysteresis wird mit dem Betrag der vorangehenden Druckerhöhung variieren, die T a m m a n n nicht angibt. Bei — 2 5 ° indessen bewegen sich seine Unterschiede in den von oben und unten erreichten Drucken von 5 bis 25 kg. Es hat daher den Anschein, dass ») Ann d. Phys. [3] 68, 559 (1899;.

13 — 615

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P. Β. Bridgman

unter manchen Bedingungen das Manometer einen Hysteresisfehler von 25 kg zeigen kann. E s bestehen immer Möglichkeiten geringer Unregelmässigkeiten bei der Bestimmung der Gleichgewichtsdrucke zwischen zwei festen Phasen, denn wenn eine Form in die andere umgewandelt wird, kann sie um dieselbe eine Schutzschicht bilden, so dass der Druck im festen Stoff in dem Punkte, in dem die Umwandlung vor sich geht, nicht der gleiche zu sein braucht, wie derjenige in der Flüssigkeit, die mit der Aussenfläche des festen Stoffs in Berührung steht. Diese Unregelmässigkeit kann gross sein, wenn man die Substanz in unmittelbare Berührung mit den "Wandungen des Druckzylinders kommen lässt. T a m m a n n gibt ein Beispiel, in dem der Gleichgewichtsdruck wegen dieses Einflusses 100 kg zu hoch erschien. Die Unregelmässigkeit kann sehr vermindert werden, indem man die zu untersuchende Substanz in eine allseits unter Druck stehende dünne Stahlhülse einschliesst, aber die Annahme scheint nicht berechtigt, dass jede Unregelmässigkeit auf diese Weise verhütet werden könnte. Ich habe selbst mehrere Male ausgesprochene Unregelmässigkeiten bei der Benutzung einer dünnen Stahlhülse gefunden, das eine Mal eine solche von der beträchtlichen Höhe von 200 kg bei 6000 kg. Diese Erklärung scheint die plausibelste für die beiden unregelmässigen Punkte zu sein, von denen T a m m a n n annahm, dass sie auf der I—III- oder der I—III'-Kurve lagen. In einem dieser Fälle wurden nach fünf aufeinander folgenden Volumverminderungen an Eis III bei — 25° die folgenden Gleichgewichtsdrucke gefunden: 2165, 2165, 2080, 2060 und 2050 kg. Die T a m m a n n s c h e Erklärung geht dahin, dass er von einem Gemisch von Eis III und III' ausging. Die beiden ersten Punkte bei 2165 sind der Gleichgewichtsdruck zwischen III' und I. Das Eis III' wurde dann erschöpft, und die drei andern Punkte sind die Gleichgewichtspunkte zwischen Eis I und dem übrigbleibenden Eis III. Wenn der Druck wieder erhöht wurde, fand sich nur ein Wert für den Gleichgewichtsdruck, bei dem höhern der obigen Werte. Dies erklärte T a m m anu durch die rasche und unvermeidliche Bildung von Kernen des Eises III' in I bei Druckerhöhung. Aber seine eigenen Versuche und die meinigen zeigen, dass sich III' nicht immer notwendig bildet, wenn I über den Gleichgewichtsdruck gebracht wird, und auf jeden Fall hätte T a m m a n n imstande sein müssen, den Gleichgewichtspunkt I—III von oben her zu erreichen, wenn er sich bei der Druckerhöhung über 2050 bemüht hätte, den Druck nicht ganz bis auf 2165 zu erhöhen. Die viel wahrscheinlichere Erklärung ist, dass die letzten drei niedrigen Punkte bei

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2080, 2060 und 2050 gefunden wurden, nachdem sich eine Schutzschicht von Eis I über Eis III (oder III') gebildet hatte, wobei die Dicke der Schicht mit fortscheitender Reaktion zunahm, so dass der Druckunterschied stieg. Yerunreinigung des Wassers durch die den Druck übertragende Flüssigkeit ist eine weitere mögliche Quelle kleiner Abweichungen. Das schlagendste Beispiel hierfür liefern die Tarn man nschen Versuche, die Existenz zweier noch unbekannter Varietäten von Eis I zu zeigen. In diesen Versuchen war die Flüssigkeit, die den Druck an das Eis vermittelte, Pentan. Die Tammannsche Methode war diejenige der kontinuierlichen Änderung der Badtemperatur. Er fand, dass der Druck mit steigender Temperatur bei einem Punkte 15° unter dem normalen Schmelzpunkt zu fallen begann, was er durch die Angabe erklärte, dass das Wasser zweifellos genug Pentan absorbiert hatte, damit sein Gefrierpunkt um 15° erniedrigt worden sei. Unregelmässigkeiten von 1 oder 2° in der Gefriertemperatur dieses zugestandenermassen sehr unreinen Wassers sind die Stützpunkte, auf die Tammann seine Hypothese von den beiden neuen Arten von Eis I gründet. Es scheint schwer, zu glauben, dass das Wasser genug Pentan absorbierte, um seinen Gefrierpunkt um diesen enormen Betrag zu erniedrigen. Ich habe ein Verhalten genau gleich dem von Τ am man η beobachteten gefunden, wenn die druckvermittelnde Flüssigkeit nicht Pentan war. Dies schien mir ein möglicher Hinweis auf einen negativen Ausdehnungskoeffizienten von Eis I in dieser Gegend zu sein, eine Hypothese, die auch durch die Änderung von A V auf der Umwandlungskurve kräftig zum Ausdruck gebracht wird. Gleichzeitig scheint es fraglos, dass Pentan und Wasser bis zu einem gewissen Grade gegenseitig löslich sind, und dass daher einige Erniedrigung des Schmelzpunkts stattgefunden haben muss, weil in einigen meiner Versuche der' Gebrauch von Pentan aufgegeben werden musste, da es genügend Wasser absorbierte, um die Manganinspule, mit der der Druck gemessen wurde, kurz zu schliessen. In diesem Falle muss deshalb der Fehler der Tammannschen Methode besonders gross gewesen sein, wegen des unregelmässigen Nachhinkens der Temperatur, das durch das vorzeitige Freiwerden der Umwandlungswärme hervorgerufen wurde, wie bereits erwähnt. Ob nun die Erniedrigung des Gefrierpunkts tatsächlich 15° oder weniger betrug, so ist es jedenfalls von Bedeutung, dass Tammann zur Annahme und Veröffentlichung von Beweisen geneigt war, welche sich auf Angaben über eine Substanz gründeten, deren Gefrierpunkt, s e i n e r A n s i c h t n a c h , durch Verunreinigungen um 15° erniedrigt

P. Β. Bridgman

520

war. In dem übrigen Teil der Tammannschen Arbeit war die druckvermittelnde Flüssigkeit nicht reines Pentan, sondern ein Gemisch von ο

Fig. 2. T a m m a n n s Diagramm für die Gleichgewichtskurven zwischen den verschiedenen angenommenen Eismodiiikationen. Seine beobachteten Punkte sind durch Kreise bezeichnet. Das Diagramm zeigt nicht seine Punkte, die nach der Methode der Temperaturänderung auf der I—III'- und der I—Ii-Kurve erhalten worden sind, und auch nicht einen Punkt auf der II—III'-Kurve bei 2890 kg.

55°J0 Toluol, 30°/o Schwefelkohlenstoff und 15°/0 Pentan. Wir haben keine Gewissheit darüber, dass das Wasser nicht in allen andern Versuchen etwas von dem Pentan aus dem Gemisch absorbiert haben mag.

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521

T a m m a n n s vollständiges Gleichgewichtsdiagramm ist in Fig. 2 wiedergegeben. In diesem Diagramm sind alle experimentellen Punkte, für die er die Koordinaten angibt, eingetragen. Die Einzelpunkte mehrerer Reihen von Ablesungen mit kontinuierlich variierender Badtemperatur sind nicht wiedergegeben. Eine eingehende Erörterung der verschiedenen Gleichgewichtskurven in dem Diagramm wird einen allgemeinen Begriff von der Wirkung der eben besprochenen Fehler auf die Tammannsche Beweisführung geben. Es ist im Auge zu behalten, dass der Kern der ganzen Angelegenheit darin liegt, die Existenz der verdoppelten, nahezu parallelen Gleichgewichtslinien zu beweisen. Auf jeder der Ο-III- und Ο-III'-Kurven befindet sich nur ein Punkt. Diese Punkte wurden nach der Methode der Änderung der Badtemperatur bestimmt, von der wir gesehen haben, dass sie bei der Ermittlung der Schmelzkurve einer etwas verunreinigten Flüssigkeit einem besonders grossen Fehler ausgesetzt ist. Es ist richtig, dass der eine von T a m m a n n auf der O-III-Kurve angegebene Punkt das Mittel aus drei getrennten, um 1-5° differierenden Bestimmungen ist, und der eine Punkt auf der Ο-III'-Kurve ist das Mittel aus drei um 0-3° differierenden Bestimmungen. Aber so weit nach dem Tammannschen Bericht geschlossen werden kann, sind alle drei Bestimmungen des O-Ill-Punkts an derselben Wasserprobe angestellt worden, und die drei Bestimmungen des 0-ΙΙΓ-Punkts an einer einzigen andern Probe. Etwas verschiedene Mengen gelöster Verunreinigungen würden den Unterschied und die verhältnismässige Harmonie der Bestimmungen erklären. Um die Überzeugung von der getrennten Existenz der beiden Kurven zu gewinnen, brauchen wir mehr Punkte über ein weiteres Druckbereich. Es sollte ferner möglich sein, mit der gleichen Wasserprobe Punkte auf beiden Kurven zu erhalten. Auf der O-I- und der O-I'-Kurve versuchte Tammann nicht, Punkte in dem in dem Diagramm dargestellten Gebiet zu finden, weil der zu erwartende Unterschied so klein ist, nur 0·2°. Aber bei 50Ö kg fand er zwei Punkte, die er auf diesen beiden Kurven liegend annahm, um 0'5° voneinander verschieden. Die benutzte Methode war die der Änderung der Badtemperatur, die grössere Fehler als dies geben konnte, insbesondere wenn das Wasser etwas verunreinigt war. In diesem Zusammenhang finde ich einen Irrtum in seiner Fig. 5, in der die Schmelzkurve ungefähr 2-5° zu hoch liegt. Die Wirkung dieses Fehlers besteht darin, die offenbare Wirkung des Nachhinkens der Temperatur auf ein Mindestmass zu beschränken. Natürlich würde der bindendste. Beweis für die Existenz zweier besonderer Arten von gewöhnlichem Eis durch

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ihre Hervorbringung bei Atmosphärendruck geliefert werden. Die von Tarn mann ins Feld geführten Gründe für die Unmöglichkeit hiervon (das Sublimieren der unbeständigem zur beständigem Form) scheinen nicht wichtig genug zu sein, um es zu rechtfertigen, dass er ihre Hervorbringung bei Atmosphärendruck nicht wenigstens versucht hat. Auf den Kurven I-III und I'-III sind nur zwei Punkte, die möglicherweise um 4 0 k g differieren, beide bei — 2 5 ° . T a m m a n n konnte nicht entscheiden, welcher der beiden Kurven diese Punkte angehören konnten. Diese beiden Punkte sind offenbar nur ein Beispiel für das abnorme Verhalten, das auftritt, wenn eine Varietät eine Schutzschicht über der andern bildet. "Weitere Beispiele hierfür sind sowohl von Tarn mann, als von mir gefunden worden, aber es ist ihnen in andern Fällen keine Bedeutung beigelegt worden. Dass dies fast sicher die Erklärung ist, zeigt sich an dem Umstand, dass es unmöglich war, diese Kurven mit der Methode der Temperaturänderung bis zu andern Temperaturen zu verfolgen, eine Tatsache, für die T a m m a n n keine Erklärung gibt. Die Erklärung kann sicher nicht in der freiwilligen Bildung von Kernen von Eis III' gefunden werden, welches die Erklärung T a m m a n n s dafür ist, dass das Gleichgewicht bei diesen beiden Punkten nicht von höhern Drucken aus erreicht werden konnte. Über diese beiden Punkte ist oben mehr gesagt worden: Es möchte daher scheinen, dass der Beweis dieser beiden Punkte vollständig zu streichen ist. Auf der I'-II-Kurve gibt T a m m a n n keine Punkte an, mit der Begründung, dass das Verfolgen dieser Kurve von geringem Interesse wäre, da sie um so wenig, 25 kg, von der I-II-Kurve abweicht. Er sagt, dass es wahrscheinlich nicht schwer sein würde, diese Kurve zu realisieren. Es scheint mir, als ob das gesamte Interesse der T a m m a n n · sehen Arbeit gerade in der Existenz eben solcher kleiner Druckdifferenzen läge. Es werden keine Punkte auf der II-III-Kurve angegeben, und T a m m a n n behauptet, die Eigenschaften der verschiedenen Modifikationen seien derart, dass derzeit geringe Möglichkeit vorhanden sei, die Kurve zu realisieren. Dies ist äusserst bedauerlich, weil der Unterschied zwischen dieser Kurve und der II-III'-Kurve grösser ist als der Fehler der Tammannschen Methode, so dass ein bindender Beweis der Existenz der beiden getrennten Kurven II-III und II-III' einen der unmittelbarsten und überzeugendsten Beweise, die für die Richtigkeit der Tammannschen Ansichten beigebracht werden können, darstellen würde. Auf der II-III'-Kurve sind drei Punkte nach der Methode

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Über Tammanns vier neue Eisarten.

523

der Änderung der Temperatur bestimmt. Einer derselben liegt ausserhalb des Bereichs der Figur und ist nicht wiedergegeben. Die drei Punkte dieser Kurve sind in einem andern Massstabe in Fig. 1 eingetragen. Aus ihrer Unregelmässigkeit geht klar hervor, dass hier beträchtliche experimentelle Fehler vorhanden sind. Soweit ist der Beweis für irgend eine der verdoppelten Linien tatsächlich äusserst dürftig. Tammanns ganze Behauptung muss mit dem Beweis der getrennten Existenz der beiden Linien Ι-ΙΙΓ und Ι'-ΙΙΓ stehen oder fallen. Hinsichtlich des tatsächlichen Verlaufs dieser Gleichgewichtskurven finde ich Abweichungen in Tammanns eigenen Koordinaten, die' ihre Lage einigermassen zweifelhaft machen. So finden wir auf Seite 273, dass der Druck auf der Ι-ΠΙ'-Kurve bei 30-0° 2180 beträgt, aber auf der nächsten Seite, dass er 2195 ist. Diese Abweichung macht mehr als die Hälfte des angenommenen Unterschieds zwischen den Kurven Ι-ΙΙΓ und Γ-ΙΙΓ aus. Es kann sich nicht um einen blossen Druckfehler handeln, weil der niedrigere Wert derjenige ist, den die ausdrücklich angeführten Koordinaten des Tripelpunkts erfordern, während der höhere "Wert der in der Figur wiedergegebene ist. Ferner unterscheiden sich die tabellierten Drucke auf der Ι-ΙΙΓ- und Γ-1ΙΓKurve bei — 2 2 ° nur um 10 kg, während die in der Figur wiedergegebenen um 20 kg differieren. Hier handelt es sich um einen Fall von Nachlässigkeit in den Angaben, bei dem die Hälfte der fraglichen Differenz in Betracht kommt. Ich habe die Figur (Fig. 2) in Übereinstimmung mit T a m m a n n s Figur gezeichnet und nicht in Übereinstimmung mit seinen tabellierten Punkten, weil seine Zeichnung seinem Gesichtspunkt günstiger ist. In diesem Diagramm finden sich einige Punkte auf der Ι'-ΙΙΓ-Kurve, erhalten nach der Methode des von unten und von oben erreichten Gleichgewichts. Die Abweichungen bei den niedrigem Temperaturen sind sehr gross, von der Höhe von 80 kg. Auf der Ι-ΙΙΓ-Kurve sind keine Punkte bei den niedrigem Temperaturen angegeben, weil diese Kurve fast vollständig nach der Methode der Änderung der Badtemperatur bestimmt worden ist. Die einzige Ausnahme bilden zwei Punkte bei den höhern Temperaturen, die nach einer Reihe von Beobachtungen über das System I-II bei den niedrigem Temperaturen, bestimmt worden sind. Die über mögliche Fehler infolge von „elastischen Nachwirkungen" gemachten Bemerkungen gelten für diese Punkte. Der Beweis für das getrennte Bestehen von Ι-ΙΙΓ und Γ-ΙΙΓ ist daher nur der folgende: dass zwei verschiedene Methoden Kurven geben, die um 20 kg oder 1 °/0 des gesamten Drucks voneinander abweichen. Sicherlich ist dieser Beweis zu dürftig im Hinblick auf die

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Komplikationen der zu beweisenden Theorie. Wir haben wenigstens das Recht, zu verlangen, dass T a m m a n n zum Beweis der getrennten Existenz der beiden Kurven dieselbe Methode benutzen möchte. Um zusammenzufassen, so scheint es mir, als ob es T a m m a n n durchaus nicht gelungen sei, die "Wahrscheinlichkeit der Existenz seiner neuen hypothetischen Eisvarietäten darzutun. Es ist insbesondere bedeutungsvoll, dass die von ihm angegebenen Daten selbst von seinem eigenen Gesichtspunkt aus nicht vollständig sind. Er konnte nur diejenigen Kurven realisieren, die um seinen möglichen Versuchsfehler differieren, und diejenigen Kurven, die sich um mehr als seinen möglichen Yersuchsfehler unterscheiden, vermochte er nicht zu verwirklichen. C a m b r i d g e , Mass., The Jefferson Physical Laboratory, Harvard University.

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CHANGE OF PHASE UNDER PRESSURE, I.

CHANGE I.

OF

PHASE

UNDER

PRESSURE.

T H E PHASE DIAGRAM OF E L E V E N SUBSTANCES WITH ESPECIAL R E F E R E N C E TO THE M E L T I N G BY P. W .

CURVE.

BRIDGMAN.

CONTENTS. Introduction Summary of previous work and present state of the problem Apparatus and experimental method Details of experiment and computations. Discussion. Summary.

126 127 130

INTRODUCTION.

' I "HIS paper is the first of a projected series of papers dealing with the -*· various problems offered by the phenomena of change of phase under pressure. A t high pressures we are concerned with phase changes of only two types, from the fluid to the solid (or crystalline) phase, and from one solid phase to another, since at high pressures the gaseous phase no longer has an independent existence. It is the first of these changes, that from the liquid to the solid, that is to be the special subject of this paper. The problem presented by the change from liquid to solid involves for its complete solution a description of the molecular arrangement of the liquid and the crystal and of the nature of the forces that produce crystallization. Hitherto one narrow aspect of this problem has received almost exclusive attention, the question as to the general shape of the melting curve. Evidently an answer to this question would go far in pointing the way to the essential difference between a liquid and a crystal. Two answers to this question have been regarded as most probably correct; the first is that the liquid-solid curve ends in a critical point, and the second, directly opposed to the first, is that the melting curve passes through a maximum temperature, so that if pressure is raised sufficiently high at constant temperature we may first freeze the liquid to the solid and then melt it again to the liquid. The more particular object of this paper is to settle definitely, with the help of new data, this long discussed question as to the shape of the melting curve. The data hitherto available have covered a pressure range of about 3,000 kgm. These data are mainly due to Tammann, who measured

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the relation between pressure and melting temperature over this pressure range, and also measured for some of his substances, with considerably less accuracy, the difference of volume between solid and liquid along the melting curve. The data presented here cover a pressure range up to 12,000-13,000 kgm. per sq. cm., and a temperature range from o° to 200°. Over this entire range the relation between melting temperature and pressure has been measured, and the difference of volume between solid and liquid has also been determined. These two kinds of data are necessary and sufficient from a thermodynamic point of view to settle the point at issue. Eleven substances have been experimented on, including simple and complicated organic compounds and three elements. These all indicate the same answer to the question in hand. For the immediate purposes of this first paper those substances were selected which had only one known modification of the solid, in order not to complicate the study by the entrance of a second solid phase. But four of the substances studied have been found to have new solid modifications at high pressures. It may be, therefore, that polymorphism at high pressures is a common instead of an exceptional phenomenon. The data given in this paper include data that will be used later in the discussion of the relation between different solid modifications. And similarly, some of the data to be presented in future papers may be expected to have a bearing on the narrower question to be discussed here. SUMMARY OF PREVIOUS WORK AND PRESENT STATE OF THE PROBLEM.

It is proposed to quote here only those papers bearing on the question at issue, the true character of the melting curve. This will omit a few papers giving measurements only, and also much of the earlier work, which was occupied with experimental proof of the validity of the formulas deduced by thermodynamics, at a time when complete confidence apparently was not felt in thermodynamic arguments. Most of the early speculators on the true nature of the melting curve seem to have been guided mostly by analogy with the then recently established critical point between liquid and vapor, and assumed the existence of a similar critical point between liquid and solid. Poynting 1 was one of the earliest of these. He predicted by analogy between water and its vapor that there were two critical points between water and ice; one at — 120° and 16,000 atmos., the other at + 140 and some high negative pressure. Practically no experimental evidence was given. Planck 2 thought that there was a critical point, and deduced some thermodynamic relations which must hold if such a point exists. Peddie 3 also gave thermodynamic relations for a critical point if it exists, and quoted observations

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of Bunsen on paraffine suggesting the possible existence of such a point. Amagat 4 then contributed some actual observations up to 1,100 atmos. on the solidification of CC14, and stated that the appearance was as if a second liquefaction took place at a higher pressure than that required to produce solidification. In his opinion a critical point seemed likely. Two papers by Damien6 with new experimental data gave the subject new impetus from the experimental side. His results reached to 200 atmos. and he claimed to have found for several organic substances, not a critical point, but a maximum melting temperature. A t temperatures below the maximum the continually increasing application of pressure first freezes the body to a solid and then melts it again. This seems to have been the first suggestion in the literature of such a phenomenon. Barus8 in 1892 published investigations up to 2,000 atmos. on a number of organic liquids, but his results did not become known until later. He found no evidence of a maximum up to 2,000 atmos., but there was a certain cyclic character in the transformation solid-liquid which reminded him of the unstable part of the isotherms of James Thomson. He seems to have been of the opinion that at high enough pressures there is a critical point. Amagat 7 then published data on water, obtained with the same apparatus as for CCI4, up to 1,000 atmos. He was of the opinion, although his results do not suggest it particularly strongly, that at high enough pressures there might be an inversion point beyond which ice is more dense than water, so that at high pressures the melting point of ice would be raised by pressure instead of lowered; that is, a minimum point, the reverse of Damien's maximum. Demerliac8 in two papers next subjected Damien's results to further experimental scrutiny up to 300 kgm. Demerliac's results are usually quoted as supporting Damien's theory, but only because of a misunderstanding. Demerliac found that for the lower pressures of his range his results could be very accurately represented by a formula which predicts a maximum, but that at the higher pressures the results no longer fitted the formula, the temperature tending to approach more and more closely to a limiting value. Demerliac's opinion, therefore, was that the melting curve tends to approach a horizontal asymptote. He nearly reached the asymptote for several substances. The years 1898-99 marked great activity in this field, several of the results appearing without knowledge of the others. Heydweiller9 published results showing that there could not by any possibility be a maximum at pressures as low as Damien supposed, and was of the opinion that there must be a critical point at high enough pressures. He chose substances to investigate that might be expected to be near their critical points, but he could find no critical phenomena up to pres-

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129

sures estimated to be between ι,οοο and 3,000 atmos. At the same time he observed effects of another kind on menthol which he thought were indicative of a critical point. Mack 10 published results up to 2,100 atmos. on several organic substances, and could find evidence of neither a critical point nor of a maximum. His melting curves were nearly linear. Hulett 11 ), inspired by Ostwald who was of the opinion that there was a critical point, investigated liquid crystals up to 300 kgm. It seemed natural to suppose that liquid crystals might be near the critical point, but he found on the contrary that the difference between liquid crystal and the liquid became more strongly accentuated at increasing pressure. If there were a critical point, it could exist only at negative pressures. About this time Tammann12 began to publish his experiments and theory, and he has since then almost monopolized the field. His results cover a range of 3,000 kgm., higher than had been reached hitherto. One of his first services was to explain the remarkable discrepancies between previous experimental results by calling attention to the effect of dissolved impurities. Damien provides a particularly striking example of this; his medium of compression was air, which is dissolved more and more at high pressures. The cycles found by Barus are also similarly explained by the action of impurities. Tammann's theory is well known, and will be described again only briefly. It is, in part, that all substances show a maximum melting point, but this maximum is very much higher than supposed by Damien. Tammana himself was never able to reach it, but supposed that it might be in the neighborhood of 10,000 kgm. for a number of substances. In support of this theory, Tammann shows that we must consider all the thermodynamic elements of the phenomena of melting, the change of volume and the latent heat, as well as the melting curve itself. His data show that the change of volume decreases along the melting curve, while the latent heat increases or remains nearly constant. Now at a critical point the change of volume and the latent heat must vanish together, but at a maximum the change of volume vanishes, while the latent heat remains finite. The data are unquestionably more favorable to the second than to the first of these alternatives, and this constitutes the evidence for a maximum. Still the evidence, even from Tammann's own data, is by no means conclusive, and there have been at least two upholders since then of the idea of a critical point. Weimarn13 in 1910 argued from the behavior of colloids to the probable existence of a critical point. His argument is briefly as follows. A t any pressure, no matter how high, the temperature may be raised so high that the dispersive forces due to the intense molecular agitation overcomes the orienting

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I30

P.

W.

BRIDGMAN.

forces, so that the substance can exist only in the form of very finely disperse crystals. When the crystals become molecular in dimensions we have achieved continuous passage between the two states, or have reached the critical point. Van Laar 14 also, from an entirely different point of view, has deduced a theory demanding a critical point. This has been described in greater detail elsewhere; briefly, the difference between a liquid and a solid consists in an association of the molecules in the solid, which produces a second loop in the isotherm of James Thomson, with the possibility of a critical point. For substances which contract on freezing, this theory demands that there shall always be a critical point solid-liquid, but never a maximum. Because of an error in one of the figures of the original article, the author stated in a previous summary of van Laar's theory that under some conditions a maximum might occur. In 1911 the author published two experimental papers bearing on this subject, 15 over a pressure range considerably higher than previously reached. The evidence of the first paper, on mercury to 12,000 kgm., was against the existence of Tammann's maximum, but left open the question of a critical point. The second paper, on water to 20,000 kgm., did not give so valuable evidence because of the many abnormalities of water. However, all the evidence suggests that these abnormalities disappear at high pressures. If water can be regarded as really normal at high pressures, then the evidence of water is that there is neither critical point nor maximum, but that the melting curve continues rising indefinitely. Van Laar 16 has since this published a short paper in which he regards the evidence of the mercury as on the whole favorable to his theory, but apparently regards water as too abnormal to make its evidence of much value. APPARATUS AND EXPERIMENTAL

METHOD.

Apparatus.—The apparatus is in essentials the same as that used in previous work 16 and needs only brief description. Some slight changes have been necessitated by the higher temperature reached here, 200° instead of 8o°. The apparatus finally used consists of an upper and a lower cylinder, connected by a heavy piece of tubing. The upper cylinder contains the moving piston, actuated by a hydraulic press, by which pressure is produced. The motion of the piston, measured with a micrometer, may be combined with the cross section to give the change of volume of the substance under investigation in the lower cylinder. The upper cylinder also contains the coil of manganin wire, from the change in the resistance of which the pressure is determined. The upper cylinder contains one feature not found in the previously used apparatus. The

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CHANGE

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PRESSURE.

compressibility of some of the substances was so high that a single stroke of the piston would not have given the maximum pressure desired. The difficulty was avoided by starting the experiment with initial pressure. To accomplish this, a very minute by-pass was provided at the upper end of the cylinder connecting the interior of the cylinder with an auxiliary pressure pump. The by-pass connects with the interior of the cylinder only when the piston is withdrawn to the extreme position. In this position, pressure was raised to the desired amount, 2,000 or 3,000 kgm., by the auxiliary pump acting through the by-pass, and then the auxiliary pump cut off by advancing the piston slightly beyond the by-pass. It is necessary that the by-pass be very small indeed, otherwise the rubber packing on the moving piston gets blown into it as the piston moves by. A sufficiently minute hole was made by drilling and tapping a hole through the side of the cylinder, and then screwing into the hole a tightly fitting screw, across the threads of which a lateral scratch had been made. The upper cylinder, together with the lower part of the hydraulic press, was placed in a thermostat maintained at about 350. In this way all temperature corrections of the manganin coil were avoided. A temperature as high as 350 was necessary because the conduction of heat along the connecting tube from the lower cylinder sufficed (when the lower cylinder was as high as 200°) to keep the upper thermostat at nearly 350. The lower cylinder contained the substance to be investigated. It was held suspended in another thermostat by the connecting tube, led through a water-tight stuffing box in the bottom of the upper thermostat. The temperature of the lower thermostat was systematically run to 200°. For the higher temperatures, "Crisco," a substitute for lard by the Proctor and Gamble Co., was chosen for the bath liquid, because of its comparative freedom from odor. The temperature regulation was by means of an ordinary mercury contact device. This worked well for the few hours occupied by a single run, but at the higher temperatures trouble might arise if longer runs were necessary, because of a slow drift of temperature due to the very gradual distillation of mercury from the temperature regulator. The difficulty can be largely avoided by carefully designing the mercury bulb. The substance to be investigated, if it was such as not to be attacked by the kerosene which transmitted the pressure, was placed in an open cup, or if it were attacked by the kerosene, it was placed in a steel bulb with a mercury seal, of exactly the same design as was used in investigating the thermal properties of twelve liquids.17 The dimensions of the various parts of the apparatus were as follows. The upper cylinder: length 8 inches, outside diameter inches, inside

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BRIDGMAN.

diameter 17/32 of an inch, length of stroke of piston 3 ^ inches. The connecting pipe: length inches, outside diameter i}/2 inches, inside diameter 1/16 of an inch. The connections at the end of this tube were especially heavy, the minimum outside diameter at places where the pressure was entirely internal was % of an inch. The lower cylinder had the dimensions: length I O ^ inches, outside diameter inches, inside diameter 11/16 of an inch, depth of interior cavity 9 inches. All parts of the apparatus were made of the Halcomb Steel Co.'s electric furnace chrome-vanadium steel, which has proved itself the best yet found for the purpose. The apparatus in the form just described was not the form first used. In the first form there were three pressure cylinders and two connecting pipes. In the one cylinder the pressure was produced by the moving piston, in the second was placed the manganin coil with which pressure was measured, and in the third was the liquid under investigation. There was only one thermostat, around the third cylinder. Conduction of heat to the second cylinder was avoided by a water jacket with running water around the connecting tube. The temperature fluctuations in the second cylinder were not large and could be readily corrected for. The fatal weakness in this original apparatus was in the connecting pipes. The connections were of a type in which the end of the tube was turned down to 5/16 of an inch and threaded with a 32 thread, bringing the minimum outside diameter of points where there is only internal pressure to about y i of an inch (the inside diameter was 1/16 of an inch). The result was that the tubes were invariably torn apart at the connections, sometimes at pressures as low as 7,000 kgm. The high temperature has a perceptible weakening effect on the tubing, since the same type of connection had been previously used to 12,000 kgm. in the work on mercury at 20°. Various other types of connection were tried with this first form of apparatus, but none with permanent success. Finally, after six explosions, the attempt to use this form of apparatus was entirely given up, since for one thing, the labor of drilling each new piece of tubing with a hole 1/16 of an inch in diameter and 16 inches long is considerable. However, the data obtained at the lower pressures with this apparatus are perfectly reliable, and form an important part of the data of this paper. To prevent rupture of the connections, a piece of apparatus much like that finally used was constructed, but which had no connections, everything being made out of one piece of steel. This necessitated drilling a hole 1/8 of an inch in diameter through a piece of steel 30 inches long and 5 inches in diameter, turning the steel to 1 i n c h e s over the middle third, and to the dimensions given above for the cylinders at the two ends,

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133

hardening in oil, seasoning by subjecting to 17,000 kgm. at 200°, and finally machining to the final size after the preliminary stretching. Some measurements had already been made with this apparatus when a flaw developed in the steel which made the whole apparatus valueless. The flaw developed rapidly into a crack through which the kerosene could be forced in a stream. The risk of flaws in the steel, as exemplified by this accident, is one which is apparently unavoidable in work at very high pressures. Several pieces of Krupp's best chrome nickel steel have previously developed flaws under high pressure, but it was a great surprise to find a flaw in this apparently perfectly homogeneous product of the electric furnace. That the flaw was very small is shown by the fact that the steel had withstood the first application of 17,000 kgm. at 200°. Rather than run the risk and lose the time of making another piece of apparatus, an attempt was then made to design a form of connection which should not have the weakness of the other, and the attempt was entirely successful. The packing is a thin ring of lead confined between two Bessemer rings. The lead gives the initial tightness, and at the high pressures the soft Bessemer rings become sufficiently deformed to give tightness. The connection has not leaked or broken once in several months of use. Besides the two forms of apparatus described above for high pressure a third form was used to find points at approximately atmospheric pressure. The necessity of this was not contemplated in the original plan of the work, but an examination of the existing data showed rather large discrepancies in the values for the change of volume (Δ V) on melting at atmospheric pressure, so that a redetermination of these data became necessary. The chief possibility of error in previous work, apart from impurity, seems to have been the formation of unfilled cracks, and uncompensated capillary effects. To avoid this, these determinations were made at a slight pressure, about 60 kgm., and then extrapolation made from 60 to X kgm. The change of Δ V with pressure is so small that this can be done without danger. The readings with this apparatus may also be used to give by extrapolation an approximate value of the freezing temperature at atmospheric pressure, but the extrapolation is sometimes uncertain, and the freezing point determined in this way is not so good as that directly measured. However, the freezing point so found may be of some value, and it is given in those cases where it was not determined by direct measurement. The apparatus for the low pressure measurements is in essentials the same as that used for high pressures. First there is a cylinder of known

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P. W.

BRIDCMAN.

cross section in which there is a moving piston. This piston was actuated by a screw instead of by a hydraulic press, and the connection between the screw and the piston was a positive one, so that the piston could be either advanced or withdrawn. The position of the piston was measured as usual with a micrometer. T o avoid error from the distortion of the piston or the wearing away of the packing, the piston was made hollow, and a rod was led through the piston and through the packing to the washer retaining the packing at the inner end. The position of the free end of this rod evidently gives directly the position of the upper surface of the liquid in the cylinder. This cylinder connects with a pressure gauge (a Geneva Bourdon gauge was accurate enough) and a second cylinder, containing the substance to be investigated, which was placed in a thermostat. The procedure in making measurements was to vary the temperature at constant pressure, instead of to vary the pressure at constant temperature as in the high pressure measurements. T h e data give the means of plotting volume against temperature, from which the discontinuity of volume at the freezing temperature may be found graphically. Because of the low pressures used with this apparatus, it was possible to enclose the liquid under investigation in a glass bulb with a mercury seal, instead of a steel bulb, as was necessary at the higher pressures. In this way somewhat greater purity was ensured. The use of the glass also allowed examining the liquid after the experiment, to be sure that none of the transmitting fluid had found its w a y to it. In no case had this happened. T o further ensure purity, no glass bulb was used more than once. The bulbs were filled by boiling the liquid into them under reduced pressure, in the same way as for the steel bulbs. The liquid transmitting pressure in this low pressure experiment was a mixture of water and glycerine, instead of kerosene, which was used at the high pressures. Corrections for the thermal expansion of the glycerine and water on passing from one clyinder to the other were determined and applied in the same way as for the kerosene at high pressures. Procedure.—This was in most respects like that used either in the work on ice18 or on twelve liquids 17 . A brief summary will suffice. The purified liquid was boiled into the bulb under reduced pressure to exclude all air, and its quantity determined by weighing. The apparatus was then assembled, the upper thermostat adjusted to 35°, the zero of the manganin coil determined, initial pressure of 1,000-2,000 kgm. applied through the by-pass, the by-pass shut off by pushing in the piston, and then the lower thermostat adjusted to the desired temperature. Pressure was now increased beyond the freezing point sufficiently far to ensure complete freezing, and then the pressure decreased, and readings made

14 — 632

CHANGE

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PRESSURE.

135

of the position of the piston for about 700 kgm. on each side of the melting point. Ordinarily four points were found above the melting point and three below it, with two determinations of the equilibrium pressure, one from above and one from below, with the liquid about two thirds melted. The results were plotted on a large scale, and the change of volume calculated from the discontinuity at the melting point. The temperature was then changed and the next point found in a similar manner. Ordinarily the points were obtained with increasing pressure and temperature. During one experiment on a single substance the apparatus was left with the pressure continuously at least as high as the initial value. This might be for three or four days. The procedure in finding the point at approximately atmospheric pressure has been indicated, the temperature being varied a few degrees at a time at constant pressure, instead of the pressure being varied at constant temperature. Corrections.—Several corrections were to be applied, but these have been so carefully described in previous papers that a mere enumeration will suffice; a correction for slight variations in temperature of the man· ganin coil (in the final form of apparatus there was no such correction), a correction for the distortion by pressure of the cylinder containing the moving piston, a correction for the thermal expansion of the transmitting fluid on passing from one cylinder to the other,* a correction necessary only with the first form of apparatus for slight variations of temperature of the cylinder containing the manganin coil, and finally corrections not peculiar to this particular work, such as corrections for the lack of uniformity of the bridge wire, or corrections for the thermometers, which were mercury thermometers, calibrated at the Reichsanstalt or at the Bureau des Poids et Mesures. Accuracy.—The accuracy of the melting curves, i. e., the curves showing the relation between melting temperature and pressure, was limited only by the accuracy with which pressure could be determined with the manganin coil. This was as good as .1 per cent, at the higher pressures. The coil was calibrated several times during the course of the experiment by determining with it the freezing pressure of mercury at o°, the coil being at 350. There was no change in the coil of so much as 0.1 per cent, during the experiment. The freezing pressure of mercury at 0° was taken as 7,640 kgm., and the relation between pressure and change of resistance was assumed to be linear. (For further particulars on this matter see Proc. Amer. Acad., vol. 47, No. 11, Dec., 1911.) The accuracy of the values for Δ V is not so high as that for the equi* This is the most important correction, and may be as high as 6 per cent.; it was entirely overlooked by Tammann.

14 — 633

136

P. W.

BRIDGMAN.

librium pressures, chiefly because it is seldom possible to entirely eliminate a slight rounding of the corner at the discontinuity of the curve of volume against pressure. This source of error has also been always present in all previous determinations of AV at atmospheric pressure. All the indications are that the special form of apparatus used here avoids this effect at atmospheric pressure more successfully than has yet been accomplished. Of course the error varies greatly with the nature of the substance. Several substances were tried and discarded because they could not be obtained sufficiently pure. Some of the substances show no perceptible rounding of the corners. The order of accuracy can be judged for each separate liquid from an examination of the curves in detail. The general accuracy of the results is further vouched for by the fact that we have here three independent pieces of data, obtained with different pieces of apparatus at different times; the first with the original high pressure apparatus up to 7,000-10,000 kgm., the second at nearly atmospheric pressure with the low pressure apparatus, and the third with the final high pressure apparatus up to 12,000-13,000 kgm. The inconsistency between the three sets of data is not greater than the discrepancies between readings with the same apparatus. In addition to the directly measured quantities p, t and AV, there are tabulated the latent heat of the change of state and the difference of internal energy between solid and liquid. T h e latent heat, AH, was computed from Clapeyron's equation,

dp The computation involves, therefore, the slope of the melting curve. Now the slope of an experimental curve is known with somewhat less accuracy than the points of the curve themselves. T o avoid as much as possible error in finding the derivative, two independent methods were used; first the derivative was obtained directly graphically from a large scale drawing, and secondly the melting curve was approximated to by two straight lines, the difference curve drawn, the slope of the difference curve found graphically, and combined with the slope of the straight lines to give the slope of the original melting curve. The two methods agreed very well, usually better than 0.5 per cent., so that we may feel confident that there is no large error in computing the derivatives from the actual melting curves. But aside from the error usually met in finding a derivative, there is here a special source of error operative only at

14 — 634

CHANGE

OF PHASE

UNDER

PRESSURE.

I 37

the low pressures. The curvature of the melting curve decreases rapidly as pressure increases, so that to find the initial curvature as accurately as the curvature at high pressures, a large number of observations would be necessary at the lowest pressures. But the form of apparatus used made it impossible to obtain points at much less than 1,200 kgm. This was due to the sticking of the piston and has been alluded to elsewhere. To avoid it, especially constructed apparatus would be necessary. As a result, the slope at atmospheric pressure of all the curves, and hence the latent heat, is much more in doubt than at any higher pressure. The agreement between the latent heat at atmospheric pressure, computed in this way, and that found by other experimenters by direct experiment, is not very good. In those cases in which reliable direct measurements of the latent heat exist, they have been accepted, and the most probable value of the initial slope computed backward from the accepted value of the latent heat. But unfortunately, the latent heat has been directly measured for only a few of the substances used here. For the other substances it must be borne in mind that the initial latent heat listed here may be subject to correction. The numerical details are given under the separate substances. The change of internal energy differs from the latent heat only by the external work (P&V) during change of state. This involves only quantities directly measured, so the errors in the change of energy are the same as those in the latent heat. In particular, the latent heat and the change of energy are practically the same at atmospheric pressure. In order to avoid the troublesome work of changing units, and to permit the direct substitution of the values given here in Clapeyron's equation, the latent heat and the change of internal energy are given here in mechanical units, kgm. m. per gm. instead of the familiar gm. cal. per gm. To change kgm. m. to gm. cal. multiply by 2.3442. Materials.—It is of the utmost importance that the materials be as pure as possible; erroneous results by other experimenters have been obtained because of this, as for example when Tammann announced two solid modifications of carbon dioxide, but later found the effect was due to impurity. The materials to be used were selected by running through a catalogue of chemicals and choosing those which were not prohibitively expensive, which it was known could be obtained fairly pure, which had freezing points within the desired range, and for which only one solid modification was known. These were then subjected to further purification, either by fractional distillation or by crystallization from the melt, or in those cases that were practicable, by both methods. The details of the purification by distillation do not require comment. The purification

14 — 635

138

P. W.

BRIDGMAN.

by crystallization was performed with more care than is perhaps usual. The substance to be purified was placed in the melted condition in a closed glass vessel, within a larger glass vessel, which dipped into a bath kept at constant temperature by a thermostat. The thermostat was then adjusted to a temperature a few tenths of a degree, or perhaps as much as 1.5° (depending on the purity of the substance) below the freezing point of the pure substance. After temperature equilibrium had been attained and the substance was in a slightly subcooled condition, it was inoculated with a minute crystal, and crystallization allowed to take place. Transfer of heat from the bath to the substance took place across an air space, and was therefore slow. Crystallization might continue in some cases for a couple of days. The remaining liquid was then drained off by inverting the glass vessel. The draining occupied several hours. During the draining the temperature of the thermostat was raised a few tenths of a degree in order to melt off more perfectly any layer of impurity clinging to the crystals. The advantages of the method are the very slow crystallization, and the fact that one can be perfectly sure that there is not enough impurity present to depress the freezing point as much as the depression artificially maintained by the thermostat. No special analysis is necessary to show the amount of purity finally attained, because the conditions of the experiment themselves impose one of the sharpest tests that could be applied. If the substance is perfectly pure it will all freeze sharply at one temperature, but if it is impure, the impurity will remain in the liquid as crystallization progresses, becoming more and more concentrated, so that the freezing temperature will drop as freezing proceeds. Or if the freezing takes place at constant temperature, as here, the freezing pressure will increase as the liquid approaches complete solidification. This will be shown by a rounding of the upper corner (where melting begins) of the curve of volume against pressure. It has been already stated that in only a few cases was it possible to entirely get rid of the rounding, but it was never allowed to become large enough to raise doubt; if it did the liquid was discarded, or further purified. It was very seldom that the rounding was perceptible more than 200 kgm. beyond the freezing point, and the curve from which extrapolation was made was usually run 700 kgm. beyond the point. One other effect of impurity is to greatly slow the reaction, so that it may be necessary to wait hours for equilibrium. The reason for this is evident. As the liquid crystallizes the pure substance separates, leaving an excess of impurity in the neighborhood of the freshly formed crystal. Further freezing cannot now continue until the excess of impurity has

14 — 636

CHANGE

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UNDER

PRESSURE.

139

been removed by diffusion into other parts of the liquid. But at high pressures the diffusion takes place very slowly because of the greatly increased viscosity. One striking example of this was found while working on monochloracetic acid. After setting up the apparatus the acid was found to become gradually impure by attacking the steel envelope. Three points at high pressure were determined. The progressive gain of impurity was shown not only by the much greater rounding of the corners at the last reading (which was at lower pressure than the first two), but by the exasperating slowness of the reaction. The impurity of this one substance finally became so great that it was not worth while to attempt any more readings. The slowness of the reaction furnishes, therefore, a further rough test of the purity of the substance. T h u s Tammann mentions that he was troubled by the slowness of freezing of a number of his substances, while no such trouble was found here. The presumption is that Tammann's materials were impure. An example is the case of sodium. Tammann found a very slow reaction, while in the present work the reaction ran as rapidly and as cleanly as one would expect from a metal, as rapidly as for mercury, for example. In some cases actual experiment showed that the commercial materials were pure enough. Examples are phosphorus and sodium. The details of the purification are to be found under the data for the separate liquids. Unsuccessful attempts were made to purify acetophenone and para-xylol. T w o crystallizations of acetophenone did not raise the freezing point more than 0.50, from 19.1 0 to 19.6°, although the pure substance melts at 20.50. T w o distillations of para-xylol failed to give a liquid that approximated to a constant boiling point. An attempt was also made to purify acetone. This was Kahlbaum's best, "from bisulfite," and would have been judged to be perfectly pure from the constancy of the boiling point, but the freezing under about 10,000 kgm. was spaced over a wide pressure interval. Monochloracetic acid was also tried and discarded because it collected impurities from the pressure apparatus, not because it could not be sufficiently purified initially. Depression of Freezing Point under Pressure.—One question of interest in this connection is as to the variation of the depression of the freezing point by impurity with pressure. It admits of simple thermodynamic treatment as follows. W e shall find it easy to deduce this relation by considering first the equilibrium between pure liquid and pure solid, both being at the same temperature, but the hydrostatic pressure on one being different from that on the other. Let us suppose that the liquid (1) and the solid (2) are in

14 — 637

140

P. W. BRIDCMAN.

equilibrium under normal conditions a t p and t. T h e temperature of both phases is now raised b y At, and the pressure on the liquid kept at its original value. W e require to find the increment of pressure (Ap) on the solid, so that the liquid at p and t + At may be in equilibrium with the solid at p + Ap and t + At. T h e relation may be found b y an obvious thermodynamic cycle to be At Äp

=

— Vit AH '

where AH is the latent heat of transformation. of opposite sign.

At and Ap are, therefore,

W e now apply this formula to determine the depression of the freezing point. Given pure (1) and (2) in equilibrium at p and t, and impure (1) in equilibrium with pure (2) at p and t — At. W e require to find At. T h e direct contact between pure (2) and impure (1) may be separated b y an intermediate step. Impure (1) at p and t — At shall be in equilibrium with pure (1) a t p — Ap and t — At, and the pure (1) at p — Ap and t — At shall be in equilibrium with pure (2) at p and t — At. Under these conditions we shall evidently also Fig. 1. have impure (1) at p and / — Δ/ in equilibrium Diagram for the depreswith pure (2) a t p and t — At. T h e decrement sion of the freezing point by of pressure is evidently the osmotic pressure of impurities. the dissolved impurity. Now the formula deduced above gives a relation between Ah and Ap (see Fig. 1). W e have, therefore, the two equations Ati Vtt Ap = AH' and dr Ah = At - Ap —. ap Whence At iht dr Vit +dp = Äp=ÄH AH' and finally, Vit At = AP. This gives the depression of the freezing point in terms of the osmotic pressure of the dissolved impurity. Now Ap does not change much with

14 — 638

CHANGE

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PRESSURE.

141

increasing pressure, since for impurities of slight concentration it is equal to the pressure that would be exerted by the impurity in the form of a gas occupying the same volume. AH changes only slightly on the melting curve, as will be shown later, vi decreases and t increases as pressure increases; the two partly neutralize each other. We need expect, therefore, that the depression of the freezing point due to a given quantity of dissolved impurity will not change markedly on the freezing curve, what change there is probably being in the direction of an increase.

14 — 639

CHANGE I.

OF

PHASE

UNDER

PRESSURE.1

T H E PHASE DIAGRAM OF E L E V E N SUBSTANCES WITH REFERENCE TO THE M E L T I N G BY

P. W .

ESPECIAL

CURVE.

BRIDGMAN.

DETAILS OF EXPERIMENT AND COMPUTATIONS.

The detailed presentation of data follows. Besides giving the data actually found in this present investigation (which in most cases are shown with sufficient accuracy by the points on the diagrams), the attempt has been made to collect all previous data bearing on the point, and to give some discussion of the most probable values. This would not be necessary if it were the only object of this paper to find the most probable course of the melting curve. In addition to numerical data, any details of manipulation or of computation peculiar to the individual substances are given; in particular the extent of the region through which search was made for other solid forms. Potassium.—The potassium was obtained from Eimer and Amend. The first sample used was very carefully purified by the following method. The commercial lumps were placed under gasolene in a glass receiver, the gasolene removed with an air pump, and the potassium melted and run into a connecting vessel. This connecting vessel was constructed so as to form part of a still, from which the potassium was distilled at high vacuum into a third vessel. The third vessel was then sealed off from the still and placed in the thermostat, where about two thirds of the potassium was allowed to crystallize slowly. The liquid metal was then drained off and the pure crystals used for the first run. But subsequent work showed all these precautions to be unnecessary; the commercial metal is pure enough if the scum of oxide is removed by the first of the processes described above. 1

Continued from page 141.

14 — 641

CHANGE OF PHASE

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155

TABLE I. Potassium. Proiiure.

Temperature.

AC, cm. 8 /gm.

Latent Heat, kgm. m./gm.

Change of Energy, kgm. m./gm.

1 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000

62°.S 78 .7 92 .4 104 .7 115 .8 126 .0 135 .4 144 .1 152 .5 160 .1 167 .0 173 .6 179 .6

0.02680 2368 2105 1877 1676 1504 1347 1205 1073 950 838 738 642

5.51 5.81 6.02 6.15 6.22 6.21 6.12 6.00 5.85 5.67 5.43 5.16 4.83

5.51 5.58 5.60 5.59 5.54 5.44 5.31 5.15 4.98 4.80 4.58 4.34 4.09

These results may first be compared with others at atmospheric pressure. For the freezing point we have: 62.1° by Hägen19, 62.5° by Holt and Sims20, and 62.5° by Kurnakow and Puschin21. The two present experiments at low pressures gave by an extrapolation 63.3° and 62.8°. As already stated this method does not give accurate results, but the high value is at least evidence of the purity of the metal. The two measurements of the change of volume at atmospheric pressure gave 0.0266 and 0.0262 cm.s per gm. This is considerably lower than the only other values we have 0.0313 by Hägen19 (this seems to be incorrectly quoted as 0.029 by Tammann22, and 0.030 by Toepler23. The agreement of the two new results makes it probable that they are better than the others. The low value of the melting point given by Hägen would suggest that his potassium was impure, and in all Toepler's work there is one very serious source of error not taken account of. Toepler used a dilatometer method, in which the bulb containing the substance under investigation and its projecting stem were at different temperatures. No correction was made for the thermal expansion of the substance on passing from the one temperature to the other. The effect of the correction would be to decrease Toepler's value. There seems to be only one direct determination of the latent heat, 15.7 gm. cal. per gm. (or 7.00 kgm. m. per gm.) by Joannis24. This is considerably higher than the value that was computed from the present data (5.51 kgm. m.), but since the initial slope admits of less adjustment here than for many of the other substances, no attempt was made to bring the two values into agreement. The presumptive error in latent heat measurements is so great that 7.00 could not be accepted without corroboration in any event. 14 — 643

P. W.

154

BRIDGMAN.

Three sets of measurements were made; one with each of the three pieces of apparatus. The first set comprises observations to 7,800 kgm. and 150°, the second two observations at atmospheric pressure, and the third five observations between 7,400 kgm. and 12,000 kgm. The direct experimental results are shown in Fig. 2 and the computed values of

2

3

4

6

6

7

8

9

Pressure, kgm./cm.2 χ 10J Potassium

10

11

12

Fig. 2. Potassium. Freezing curve and the change of volume curve. The observed freezing temperatures are shown by circles, and the observed changes of volume by crosses.

the latent heat and the change of internal energy in Fig. 3. ical values of these quantities are given in Table I.

1 2

3.

4

6

6

7

8

9

Pressure, kgm./cm.2 χ 101 Potassium

10

The numer-

1112

Fig. 3. Potassium.

14 — 642

The computed values for the change of internal energy and the latent heat when the solid melts to the liquid.

156

P. W.

BRIDGMAN.

The results at high pressure differ markedly from those of Tammann2®, whose specimen must have been very impure, as shown by its low freezing point, 59.50, and very slow freezing. Tammann says that he found it particularly difficult to obtain sharp settings with this substance, and had to modify somewhat his usual method. Tammann's results run to only 3,000 kgm. At this pressure he finds an equilibrium temperature nearly 8° lower than that found here. Tammann predicts from his data that a maximum melting point will be found at 10,000 kgm. and 130°. Both of these values are considerably exceeded here, with no indication whatever of a maximum. Tammann's results must also appear low because of error in his pressure measurement. That this error may be considerable is shown by the fact that he has in his recent work26 used a gauge giving results at 2,000 kgm., about 100 kgm. lower than the gauge of his previous work. Tammann apparently regards the new gauge as the more reliable of the two. It is unfortunate that he himself had no direct means of calibrating these gauges, but had to rely on the word of the manufacturer. In the search for other solid modifications, pressure was raised to 12,000 kgm. at room temperature, and to 12,500 kgm. at 1420, but none was found. A comparison of the curves for the change of volume and the latent heat with those for other liquids shows that the behavior of potassium is a little unusual. The change of volume has become an unusually small fraction of its initial value, and the latent heat decreases

Sodium Fig. 4. Sodium. The freezing curve and the change of volume curve. The observed freezing temperatures are Shown by the circles, and the observed changes of volume by the crosses.

14 — 644

CHANGE

OF PHASE

UNDER

157

PRESSURE.

at the high pressures more than is normal. Both of these considerations would seem to suggest that a new modification of the solid may be at hand. Sodium.—The material was obtained from Eimer and Amend. That used in the first set of experiments was carefully purified by distilling in vacuo, but this precaution proved unnecessary, and in subsequent work the commercial material, freshly cut under oil so as to avoid all oxide, proved entirely satisfactory. Three sets of measurements were made. The first was with the original apparatus up to 6,400 kgm. This series was terminated by an explosion. The second set comprised two measurements at low pressure, and the third nine measurements with the final apparatus over the entire range up to 12,000 kgm. The experimental results are shown in Fig. 4 and the computed latent heat and the change of internal energy in Fig. 5. The numerical values are given in Table II.

Sodium Fig. 5. Sodium.

The computed values for the change of internal energy and the latent heat when the liquid freezes to the solid. TABLE

II.

Sodium. Preoure.

Temperature.

1 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000

97°.6 105 .9 114 .2 121 .9 129 .1 13S .8 142 .5 148 .9 154 .8 161 .0 166 .7 172 .2 177 .2

cm.»/gm.

Latent Heat, kgm. m./gm.

Change of Energy, kgm. m./gm.

0.02787 2555 2362 2203 2072 1968 1873 1790 1711 1634 1556 1476 1398

12.90 12.46 12.16 12.00 11.93 11.94 11.99 12.10 12.22 12.35 12.48 12.60 12.72

12.90 12.22 11.70 11.33 11.08 10.93 10.85 10.83 10.85 10.88 10.92 10.96 11.00

14 — 645

P. W.

BRIDGMAN.

There are the following data for comparison at atmospheric pressure. For the melting point, 92.00 (evidently a misprint) by Holt and Sims20, 96.7° by Hagen19, 97.50 by Kurnakow and Puschin21, and 97.8° by Tammann27, against the values 97.62° and 97.63° found here. This evidence makes still further probable the high purity of the sodium used here. For the change of volume we have 0.0264 c m · 8 per gm. by Toepler23, and 0.0256 by Hägen19. But here again, the low value of Hagen's melting point makes impurity probable in his specimen, and the error already mentioned runs through all Toepler's work. In view of this uncertainty two measurements were made at 60 kg., giving by extrapolation 0.02785 and 0.02789. The agreement of these two values is very good, but is no better than would be expected from the self-consistency of the two individual experiments. There is only one value for the latent heat at atmospheric pressure, 31.7 gm. cal. per gm. (13.53 kgm. m.) by Joannis.24 The value computed at first from the initial slope of the melting curve, without reference to any other value, was 12.00. But as already explained, the initial slope is open to considerable uncertainty, and therefore it was adjusted, without doing violence to the slope at higher pressures, so as to give 12.90 for the initial latent heat. This is the value shown in the curves. At high pressures the values of Tammann28 agree much better with the present values than did those for potassium. At 3,000 kgm. his melting temperature is about 2° below that found here; this is to be explained in part by error in his high pressure measurement. Tammann also gives very rough values for AV, with a probable error of 20 per cent., according to his own estimation. Within this limit his values agree with those found here. But Tammann makes a rather daring linear extrapolation from these rough values for AV, and hints at a maximum melting point at 8,000 kgm. These data show no evidence whatever of such a point up to 12,000 kgm. At 40° pressure was raised to 12,000 kgm. and at 170° to 13,000 kgm. but no new solid modification was found. Carbon Dioxide.—The carbon dioxide was obtained from one of the commercial drums used to supply soda fountains. It was collected in the well-known way in the form of snow by placing a heavy bag over the open valve. The condensation to the solid in this way from the compressed gas acts as a further purifying process, and the carbon dioxide used gave sharper freezing curves than any of the organic substances, almost as sharp as a metal like mercury. A special form of bulb was necessary in placing the carbon dioxide in the apparatus. It is shown in Fig. 6. In general appearance it is much like the bulbs used for other

14 — 646

CHANGE

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PRESSURE.

159

substances except that it is much heavier. The problem was to provide a means of retaining the carbon dioxide in the bulb initially at considerable pressure. This was accomplished as follows. The lower part of the stem was closed by a lead cone A , covered with a disc of steel B. The cone was driven with a hammer against the conical seat so as to be gastight. The bulb was then filled by putting in the snow at the open end, and tamping it into a solid mass with a steel rod. The cap D was then screwed into place. This cap was made tight by a ring of solder at C, which was forced tightly into all the crevices. When the filling was complete, the entire bulb was of course at the temperature of solid carbon dioxide at atmospheric pressure, — 790. As the bulb warmed to room temperature, the carbon dioxide liquefied and exerted a pressure, which under the conXI ft/ ditions probably rose to 500 kgm. There was at first a slight leak of gaseous carbon dioxide, but this was soon stopped by expansion of the solder gasket. The quantity iF·^A of carbon dioxide was now determined by weighing the steel bulb. It was about 7.5 gm. The stem of the bulb Ε was then screwed into the mercury cup, E, and then Fig. 6. The receptacle placed in the pressure cylinder. Now when pressure in excess of the internal pressure was applied to the exterior for containing the carbon dioxide. of the bulb, the lead cone was forced into the bulb, and perhaps dissolved by the mercury. The rest of the experiment was exactly the same as for other substances. Of course after the lead cone was once dislodged, the pressure could not be allowed to fall below the initial value of about 500 kgm., but in this form of apparatus the friction of the moving piston automatically provided for this. In filling the bulb, some care was necessary to prevent condensation of moisture from the air onto the carbon dioxide. This was prevented by placing the closed bulb in a vessel surrounded by solid carbon dioxide, until it came to temperature. The cap was then removed and it was filled from a large funnel fitting the bulb closely. Only the carbon dioxide in the lower part of the funnel passed into the bulb, and there was no chance for condensation on the lower part of the carbon dioxide, since it was protected by the layers above from direct contact with the air. Only one set of observations was made on carbon dioxide, with the high pressure apparatus, from 3,400 to 12,000 kgm. The results were perfectly regular. It would not have been possible to reach temperatures much below zero without considerable trouble, or even redesigning the apparatus. Since the evidence given by this substance on the main

14 — 647

ι6ο

P. W.

BRIDGMAN.

question at issue is perfectly unmistakable, the trouble of reaching lower temperatures did not seem worth while. The experimental results are shown in Fig. 7 and the computed results in Fig. 8. The numerical values are given in Table III.

3 4 5 6 7 8 9 10 Pressure, kgm./cm.' χ ΙΟ3 Carbon Dioxide Fig. 7. Carbon Dioxide. The freezing curve and the change of volume curve. The observed freezing temperatures are shown by the circles, and the observed changes of volume by the crosses.

There are no results for comparison at low pressures, except a determination of the triple point at 5.2 kgm. and - 56.7° by Villard and Jarry. 2 · This value has been used in determining the probable course

0

Carbon Dioxide.

14 — 648

1

2

3

4 6 6 7 8 9 10 Pressure, kgm./cm. J χ Ifr 1 Carbon Dioxide Fig. 8.

1112

The ooaiputcd values for the change of internal energy and the latent heat when the solid melts to the liquid.

CHANGE

OF PHASE

UNDER

PRESSURE.

ϊ6ΐ

of the curve below o°. There are no values at present known for the latent heat or the change of volume at atmospheric pressure, and an extrapolation from the values found here would be too daring. All the indications are, however, that the change of volume at the pressure of the triple point will be found to be unusually high. TABLE I I I . Carbon Dioxide. Pressure.

Temperature.

1 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000

—56°.6 - 3 7 .3 - 2 0 .5 - 5 .5 8 .5 21 .4 33 .1 4 4 .2 SS .2 65 .8 75 .4 84 .6 93 .5

ΔΚ. cm.*/gm.

Latent Heat, kgm. m./gm.

Change of Energy, kgm. m./gm.

.1071 .0979 896 822 755 697 644 602 564 531

19.92 20.77 21.39 21.77 21.90 21.84 21.90 22.06 22.28 22.54

16.68 16.88 16.89 16.79 16.55 16.30 16.10 16.03 16.04 16.12

Comparison with the results of Tammann at high pressures is of little use, because Tammann had no adequate means for keeping the carbon dioxide pure. In his first experiment, described in " Kristallieren und Schmelzen",80 a solid cylinder of carbon dioxide was wrapped in a piece of parchment paper, and placed directly, with no other protection, in the mixture of glycerine and water serving to transmit pressure. The fact that after release of pressure the paper was found not wet by the glycerine was taken as evidence that there was no contamination of the carbon dioxide. With this apparatus Tammann found irregularities which he accepted as evidence of the existence of another modification of the solid, and carbon dioxide was accordingly listed by him among the polymorphic substances. Later, however, because a recently developed theory of Tammann's indicated that there should be only one solid modification, he repeated his experiment,31 and came to the conclusion that there was only one solid modification, and that the effects which he had previously explained by two modifications were in reality due to dissolved water or glycerine. His new data are not at all selfconsistent, and he represents them within the limits of error between a,ooo and 4,000 kgm. by a straight line. This gives a lower melting point at 2,000 than that found here, and a higher one at 4,000. Tammann did not measure AF.

14 — 649

162

P. W.

BRIDGMAN.

No evidence whatever was found here of the existence of a second solid phase. Search for such a modification was made at 25 0 to 12,000 kgm. and at 67° to 12,600 kgm. It is interesting to note in passing that the freezing temperature at pressures above 6,000 kgm. is higher than 31°, that is, higher than the critical temperature between liquid and vapor. It is possible, therefore, by the application of pressure alone to change a gas directly into a crystalline solid. This is the second case for which this has been realized, Tammann32 having previously shown that such is the case for phosphonium chloride at pressures above 75 kgm. Chloroform.—This was obtained from Eimer and Amend and purified by fractional distillation just before using. Only one distillation was necessary. The purity was sufficient, as shown by the sharp freezing curve. Two sets of measurements were made on chloroform. The first set was with the form of high pressure apparatus made entirely of one piece. Three points were obtained with this before the flaw developed that made it necessary to discard the apparatus. The second set was made with the modified high pressure apparatus with connecting tube, and comprises six points between o° and 107.7 0 . The quantity of chloroform used was about 25 gm. The experimental results are shown in Fig. 9

Chloroform Fig. 9. Chloroform. The freezing curve and the change of volume curve. The observed freezing temperatures are shown by the circles, and the observed changes of volume by the crosses.

14 — 650

CHANGE

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163

and the computed values of latent heat and change of volume in Fig. 10. The numerical values are shown in Table IV.

Chloroform Fig. 10. Chloroform.

The computed values for the latent heat and the change of Internal energy when the solid melts to the liquid. TABLE I V . Chloroform.

Pressure.

1 1,000 2,000 3,000 4,000

5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000

Temperature.

—61°.0 - 4 5 .7 - 2 8 .3 - 1 2 .1 3 .4 18 .2 32 .4 45 .6 58 .6 71 .3 83 .7 96 .1 107 .9

Δ V, cm. a/gm.

Latent Heat, kgm. m./gm.

Change of Energy, kgm. m./gm.

0.0530 498 467 438 412 389 368 350 334 321

8.70 9.10 9.43 9.65 9.81 9.93 10.00 10.08 10.20 10.35

7.11 7.10 7.08 7.01 6.93 6.82 6.70 6.60 6.56 6.59

It had already been shown in another paper that chloroform could be solidified by pressure,33 and two rough values for the solidifying pressure at 40° and 8o° have already been given, which agree rather well with those found here. These two instances, however, seem to be the only previous record we have of the freezing of chloroform under pressure, so there are no other results for comparison at high pressures. As in the case of carbon dioxide, it was not feasible to make observations below o°. The freezing of the mercury seal, apart from any other consideration, would demand an essentially different apparatus for readings much below o°. Over the range investigated, however, the

14 — 651

164

P. W.

BRIDGMAN.

results are just as significant in their bearing on the main question as were the results for carbon dioxide. There are very few observations on chloroform at atmospheric pressure. For the melting point Beilstein's Handbuch gives — 63.2° and Niescher34 — 6i°. The latter has been accepted for use here as more probably accurate, because higher. For the latent heat at atmospheric pressure we have only the value 19.2 gm. cal. per gm. (8.19 kgm. m.) by Niescher,84 obtained by indirect means. An examination of the values found here for pressures above 3,000 kgm. shows that they may be extrapolated without great violence to Niescher's value at atmospheric pressure. Pressure was pushed to 12,000 at 250 and to nearly 13,000 kgm. at 107° in the search for another solid modification, but none was found. Search to 12,000 at a temperature much lower than 250 was not feasible because of the freezing of the mercury. It might be expected by analogy with CCU, that chloroform, CHClt, a substance of much the same chemical constitution, would also show several modifications. It may still be that such is the case, for a glance at the melting curve will show that the explored region is after all comparatively restricted, and that there is room in the unexplored region for several solid modifications of much the same relationship to each other as the modifications of CC14. This possibility is still further increased by the rather large subcooling of 2,000-3,000 kgm. that chloroform may support, so that the domain of a new form may have been actually entered, but not far enough to compel its appearance.

Anilin Fig. 11. Anilin. The freezing curve and the change of volume curve. The observed freezing temperatures are shown by the circles, and the observed changes of volume by the crosses.

CHANGE

OF PHASE

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PRESSURE.

165

Anilin.—This substance, Kahlbaum's purest, obtained from Eimer and Amend, was purified by distilling, then by crystallization, and then again by a second distillation immediately before making the readings. Measurements on this were made in three series: the first at six temperatures with the first apparatus, the second at approximately atmospheric pressure with the low pressure apparatus, and the third at five pressures up to 12,000 kgm. with the final high pressure apparatus. About 15 gm. of anilin were used. The experimental results are shown in Fig. ι X, and the computed latent heat and change of internal energy in Fig. 12. The numerical values are shown in Table V.

Pressure, kgrn./cm.' χ I0J Anilin Fig. 12. Anilin.

The computed values for the latent heat and the change of internal energy when the solid melts to the liquid. TABLE V . Anilin.

Preeeufe.

1 1.000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000

Temperature.

-

6 e .4 13 .1 31 .6 48 .7 64 .5 79 .0 93 .2 106 .5 119 .1 131 .5 143 .2 154 .7 165 .3

cm.*/gm.

ΛΚ

Latent Heat, kgm. m./gm.

Change of Energy, kgm. m./gm.

0.0854 784 724 673 631 594 561 530 502 476 451 427 405

11.20 11.94 12.66 13.33 13.95 14.48 14.93 15.36 15.73 16.06 16.38 16.60 16.69

11.20 11.12 11.21 11.38 11.45 11.50 11.55 11.62 11.70 11.80 11.87 11.90 11.83

14 — 653

P. W.

BRIDGMAN.

There are only a few results at atmospheric pressure for comparison. For the melting temperature we have — 8.o° by Lucius,38 — 6.1° by Tammann, 36 — 6.0° in Beilstein's Handbuch, and — 6.45° found here by an extrapolation over about 1.5 0 . There is only one determination of the latent heat, 20.9 gm. cal. per gm. (8.91 kgm. m. per gm.) by de Forcrand. 37 But the author himself recognizes that the experiment on which this value was founded is probably in error, as is shown by the fact that a specific heat for the solid was found greater than that for the liquid. De Forcrand, from apparently slightly justified theoretical grounds, prefers to replace the experimental value 20.9 by 39.9, rather a large change. The value found here from the initial slope is 11.20. kgm. m. (26.4 gm. cal.), and has been retained, as probably the most accurate value we have. The results of Tammann 38 up to 2,500 kgm. are somewhat lower than those found here; 1.90 lower at 2,500, 1.1 0 lower at 2,000, and o.i° lower a t 1,000. This difference may be almost all explained by error in Tammann's standard of pressure. Tammann predicts from his curve to 2,500 a maximum melting point at 9,080 kgm. and 87.2°. Both of these values have been very considerably surpassed here without any sign of a maximum. Tammann does not give values for AV.

0

1

2

3

4

5

6

7

8

9

10

11

1_

Pressure, kgm./cm. 7 χ 10 1 Nitrobenzol Fig. 13. Nitrobenzol.

T h e freezing curve and

the change of volume curve.

T h e observed

freezing temperatures are shown b y the circles, and the observed changes of volume b y the

14 — 654

CHANGE

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167

In the search for another solid modification the pressure was raised to 12,000 kgm. at 250 without result. Nitrobenzol.—This was Kahlbaum's purest, further purified by fractional distillation, crystallization, and redistillation immediately before using. Three sets of observations were made; the first set comprises six observations with the first apparatus to 7,840 kgm., the second a single observation at approximately atmospheric pressure, and the third four observations with the high pressure apparatus to 10,780 kgm. About 17 gm. of nitrobenzol were used. The experimental results are shown in Fig. 13, and the computed values of latent heat and change of volume in Fig. 14. The numerical values are shown in Table VI.

0

1

2

3

.4 5 6 7 8 9 10 Pressure, kgm./cm. J χ ΙΟ1 Nitrohenzu

1112

Fig. 14. Nitrobenzol.

The computed values for the latent hent and the change of internal energy when the solid melts to the liquid. TABLE V I . Nitrobenzol.

Pressure. 1

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000

Temperature.

U.V. cm .'/gm.

Latent Heat, kgm. m./gm.

Change of Energy, kgm. m./gm.

5°.6 27 .2 48 .1 68 .3 87 .6 105 .5 122 .3 138 .1 153 .8 169 .3 184 .5 198 .6

0.08136 7326 6639 6052 5552 5172 4885 4641 4415 4210 4028 3864

9.60 10.00 10.36 10.66 10.92 11.21 11.58 11.91 12.16 12.39 12.59 12.73

9.60 9.26 9.01 $.84 8.71 8.64 8.63 8.64 8.62 8.60 8.53 8.47

There are a number of values for comparison at atmospheric pressure. For the melting point there is 5.82° by Meyer3*, and 5.67° by Tam-

14 — 655

P. W.

BRIDGMAN.

mann40. The directly determined freezing point of the nitrobenzol used in this experiment was 5.67°. For the latent heat we have 30.2 gm. cal. per gm. by de Forcrand37 (this is certainly greatly in error), 22.30 by Pettersson and Widman41, and 22.46 by Meyer3·. The corresponding values in the kgm. m. units of this paper are 12.89, 9-51 and 9.58. The value computed from the present data without any regard to the above values was 10.14. But since, as already explained, the initial slope, and hence the initial latent heat, is open to considerable uncertainty, the slope was corrected so as to give 9.60 for the initial latent heat, which is the value shown in the curves. For the change of volume on freezing there is one value by Meyer5·, 0.0808 cm.* per gm., against 0.0814 found above. The agreement is better than usual. Tammann's0 results at higher pressures run a little low, as we have always found them, the greatest discrepancy being between 2,000 and 3,000 kgm. At 3,000 his curve is 2.00 lower than that given here, at 2,000 it is 0.20 lower, and at 1,000,0.90 higher. Tammann predicts a maximum melting point at 10,100 kgm. and 1240. The curve has been carried in this work to 11,000 kgm. and 197.8°, with no approach to this supposed maximum. No other modification of the solid was found. The region explored lies between the melting curve, the isothermal at 250, out to 12,000 kgm., the isothermal at 200° from the melting curve to 12,800 kgm., and the straight line connecting the point (12,000 kgm., 250) with the point (12,800 kgm., 2000). Analogy with benzol would lead one to expect that possibly another modification is not far away. Diphenylamine.—The substance used was Kahlbaum's purest, provided by Eimer and Amend. It comes in the form of fine flakes, such as those familiar naphthalene preparations used for moth preventives. It is of a most dazzling whiteness, but there is some impurity present as shown by the yellow color of the melt. The material used here was further purified by slow crystallization at constant temperature in the thermostat. It was found possible in this way to obtain beautiful perfectly colorless and transparent crystalline plates, sometimes 2 or 3 cm. across. Three series of observations were made. The first comprises six points with the first apparatus up to 200°. An explosion wrecked the apparatus while obtaining the highest point. The second series consists of two observations at low pressure, and the third of two observations at the upper end of the curve with the high pressure apparatus. In addition, several unsuccessful attempts were made in which the diphenylamine became contaminated with kerosene by the collapse of the steel bulb. The manipulation of starting the experiment required some

14 — 656

CHANCE

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PRESSURE.

169

care, as pressure should not be applied while the diphenylamine was solid because of danger of collapse, and the temperature must not be raised so high in the preliminary melting as to allow any of the diphenylamine to escape from the bulb by temperature expansion. The experimental results are shown in Fig. 15, and the computed values of the latent heat

Diphenylamine Fig. IS. Diphenylamine.

T h e freezing curve and the change of volume curve.

T h e observed

freezing temperatures are shown b y the circles, and the observed changes of volume b y the crosses.

and the change of internal energy in Fig. 16.

The numerical values are

P r e s s u r e , k g m . / c m . J χ I fr3 Diphenylamine Fig. 16. Diphenylamine.

T h e computed values for the latent heat and the change of internal energy when the solid melts to the liquid.

given in Table VII. The rapid rate of rise of temperature with pressure on the melting curve is worth noticing. 14 — 657

P. W.

17°

BRIDGMAN.

TABLE

VII.

Diphenylamine. Pressure.

1 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

Temperature.

A V, cm .'/gm.

Latent Heat, kgm. m,/gm.

Change of Energy, kgm. m./gm.

54°.0 79 .1 103 .0 124 .7 144 .9 163 .6 180 .9 197 .3 212 .9

0.0958 807 708 638 586 541 504 472 448

11.24 11.47 11.78 12.23 12.77 13.25 13.63 13.92 14.18

11.24 10.67 10.33 10.29 10.40 10.49 10.54 10.55 10.57

There are the following data for comparison at atmospheric pressure. For the melting point Heydweiller43 gives 52.6°, Stillman and Swain44 54.00, and Block4® 53.40. No direct determination on the purified substance was made in this experiment, but the crystallization from the original impure diphenylamine took place in the thermostat at 53.50, so that the melting point of the finally purified substance must have been somewhat higher. For the latent heat there are three values. 23.97 gm. cal. per gm. by Stillman and Swain44, 25.3 by Battelli and Martinetti46 (because of an obvious misprint this number is quoted in tables of constants as 21.3), and 26.3 by Bogojawlensky 47 . The corresponding values in kgm. m. are: 10.23, 10.79, and 11.18. The number found by computation from the present work was 11.24. Because of the somewhat wide variation of the values by different observers shown above no attempt was made to so adjust the initial slope as to bring this into agreement with the mean of the values above. For the change of volume Block46 gives 0.0905 cm.8 per gm. The first determination of the present work gave a number somewhat higher than this, and the measurement was repeated for greater security. The two values found were 0.0960 and 0.0955, in rather good agreement. The mean of these two was used in the computations. Tammann's48 results to 3,000 kgm. are from 2° to 30 lower than those found here; this is probably in part due to impurity, as he himself recognizes that his material was somewhat impure. For the change of volume he gives one value at 455 kgm., 0.0838 cm.3 per gm., against 0.0880 found here. As usual Tammann represents his results to 3,000 by a parabolic formula, but in this case does not venture to guess from the constants of the formula what the maximum temperature may be. At 250 and at 200° the pressure was raised to 12,000 kgm., but no new solid modification was found. 14 — 658

CHANGE

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PRESSURE.

I7X

This completes the presentation of data for those substances for which only one solid modification was found. Benzol.—Kahlbaum's purest benzol was purified by distillation, by crystallization, and be redistilling immediately before use. The original benzol, when tested with sulphuric acid, showed no thiophen, the most likely impurity. Four sets of observations were made on benzol. The first two were with the first piece of apparatus and include eight points; these two sets were both terminated by explosions. There was one obser-

1

2

3

4

5

6

7

8

9

10

1112

Pressure, kgm./cm.J χ ΙΟ3 Benzol Fig. 17. Benzol. The phase diagram, showing the equilibrium curves between the liquid and two varieties of the solid, and the change of volume between the liquid and solid I. The observed transition temperatures are shown by the circles, and the observed changes of volume by the crosses. Ρ be.013

Temperature Benzol Fig. 18. Benzol. The change of volume between solid I and II as a function of the temperature. The curve of transition between these two solids runs so nearly at constant pressure that it would not have been feasible to plot the change of volume as a function of the pressure.

14 — 659

172

P.

W.

BRIDGMAN.

vation at low pressure, and Anally eight observations with the new apparatus.

T h e experimental results are shown in Figs. 17 and 18 and

the computed values for latent heat and change of internal energy in Figs. 19 and 20.

T h e numerical values are given in Table V I I I .

4 5 6 7 8 9 10 Pressure, kgm./cm.' χ I0 J Benzol Fig. 19. Benzol.

The computed value of the latent heat and the change of internal energy when the liquid melts to the solid I. TABLE

VIII.

Benzol.

Liquid—I. Preuure.

Temperature.

Δ V, cm.'/im.

1 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000

5 e .4 32 .5 56 .5 77 .7 96 .6 114 .6 131 .2 147 .2 162 .2 176 .7 190 .5 204 .2

0.1317 1026 872 759 675 614 564 522 485 451 422 394

Latent Heat, kgm. m./gro. 12.88 12.94 13.06 13.24 13.47 13.70 13.90 14.05 14.15 14.20 14.21 14.20

Change of Energy, kgm. m./gm. 12.88 11.89 11.27 10.93 10.72 10.60 10.47 10.36 10.23 10.10 9.97 9.82

I-II. 12,260 12,080 11,950 11,860 11,810 11,840

14 —

660

100" 120 140 160 180 200

0.01048 1110 1168 1219 1262 1281

-3.7 -3.4 -3.0 -2.0 -0.5 1.4

-16.6 -16.9 -16.8 -16.5 -15.5 -13.8

CHANGE

OF PHASE

UNDER

PRESSURE.

173

Benzol has a second modification of the solid, stable at the very highest pressures reached here. In fact, the transformation line so nearly marks out the arbitrary limit of pressure that had been set for this work that the discovery of the modification can be regarded only as a piece of good fortune. The transformation curve runs nearly vertically (showing low latent heat), convex toward the temperature axis. This seems to be the first example of a curve of this type; the other nearly vertical transformation curves, such as those between the different varieties of ice or the two kinds of phenol,44 are concave toward the temperature axis. The fact that a transformation between two solids shows such a distinct curvature at so high a pressure seems a bit surprising. It seems natural to think that the properties of a solid at high pressure would vary nearly linearly with temperature and pressure; under these conditions the transformation line would be nearly straight. In fact, it is in any event rather surprising to find a vertical transformation curve, because this means that Temperature one solid changes into another of smaller Benzol Fig. 20. volume with increase of internal energy, and that almost all the work done by the Benzol. The computed values external pressure is stored up within the of the latent heat and the change substance. The internal forces would seem of internal energy when the solid I changes to the solid II, as a to have become forces of repulsion instead function of the temperature of of forces of attraction. It may be that transition. Observe that the inthe increased temperature energy of the ternal energy of the form with the smaller volume is greater. molecules, corresponding to a greater number of degrees of freedom in the new modification, may account for the absorption of energy. But this seems unlikely, because the indications are that at atmospheric pressure benzol is entirely normal, that is, entirely dissociated into single molecules. In the later part of this paper a possible explanation is given of this increase of energy. The reaction velocity of the two solid forms shows the same rapid variation with temperature that has been found for the modifications of ice. A t the highest temperature, 201.6°, the reaction runs almost immediately, while at the lowest temperature, 990, the reaction runs so slowly that it was not feasible to wait for complete equilibrium, but the point was approximated to from the two sides. The difference of the two pressures reached from above and below was 100 kgm. The slowness of the reaction increases so rapidly with decreasing temperature that it was not feasible to try for points below 990, especially since the pressure

174

P. W.

BRIDCMAN.

rises more and more rapidly with falling temperature. Along with the slow reaction velocity at low temperatures goes the possibility of considerably passing over the transformation line without the reaction running. Within the pressure limits set here it was not possible to obtain the second modification at 99 0 ; temperature had to be raised to 135° before it appeared, and the temperature was then lowered to 990 and the readings taken. A t 25°, pressure was raised to 12,500 kgm., but no other modification was found. The triple point between the two solids and the liquid would apparently lie at about 216° and 12,000 kgm. The temperature was too high above the limit set to make it seem worth while to take the risk of reaching it. A t the triple point the transformation line between the two solids has reversed its slope of the lower temperatures, so that pressure and temperature rise together. There are a large number of data for comparison at atmospheric pressure, inasmuch as benzol has been a favorite substance for investigation because of the comparative ease of obtaining it pure. For the melting temperature we have 5.430 by Demerliac60, 5-35° by Heydweiller, 43 5.430 by Ferche, 61 5.440 by Meyer, 39 and 5.420 by Lachowicz, 62 . The value found here by extrapolation from the determination of A V at 60 kgm. was 5.430. For the latent heat we have 30.38 gm. cal. per gm. by Demerliac, 50 29.43 by Pickering, 63 30.18 by Ferche, 51 29.09 by Pettersson and Widman, 64 30.39 by Meyer, 39 30.08 by Fischer,65 and 30.6 to 31.0 b y Bogojawlensky 56 . The corresponding values in kgm. m. are: 12.96, 12.55, 12.87, 12.41, 12.96, 12.83, a n d 13-05 to 13.22. The value given by these data from the uncorrected initial slope was 12.33. The initial slope was so corrected as to bring the latent heat to 12.88. For the change of volume there are the values 0.1304 cm.3 per gm. by Heydweiller,43 0.1316 by Ferche, 61 and 0.1333 by Meyer 39 . The result found here was 0.1316, and is in unusually good agreement with the mean of these three. Tammann's, 67 results up to 3,000 kgm. are considerably lower than those found here; 4.5 0 lower at 3,000 and 3 0 lower at 2,000. The discrepancy is not to be entirely explained by impurity. Tammann as usual fits a parabolic curve to his results. T h e maximum of the parabola would lie at about 7,100 kgm., although Tammann does not explicitly predict this as the pressure of the maximum point. T h e data here reach to 12,000 with no tendency to a maximum. Benzol is one of the few substances for which Tammann attempted measurements of the change of volume over his entire pressure range of

14 — 662

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PRESSURE.

175

3,000 kgm. His results above 1,500 are considerably lower than those found here, doubtless due to leak around the piston, while his results below ι ,500, although showing considerable irregularity, agree with the present ones within the limits of error. Carbon Tetrachloride.—This was obtained from Eimer and Amend, and was purified b y a double fractional distillation. T h e second distillate showed a constant boiling point. Observations were made in three series; the first with the original apparatus to 183° includes seven points, the second, one point at low pressure, and the third nineteen points with the final high pressure apparatus. T h e experimental points are shown in Figs. 21 and 22, and the computed values of latent heat and internal energy in Fig. 23. T h e numerical values are given in Table I X .

Carbon Tetrachloride Fig. 21. Carbon Tetrachloride.

The phase diagram of the liquid and three solid forms. transition temperatures are shown by the circles.

The observed

Three solid modifications of CCl* were found, two of them not known before. This was the first of the four substances studied here for which more than one solid form was found, and the discovery of this was b y accident. A t 35 0 , when the experiment was performed for the third time with the high pressure apparatus, pressure was pushed several thousand

14 — 663

176

P. W.

BRIDGMAN.

kilograms beyond the freezing pressure to ensure complete freezing, because the curve for the change of volume liquid-solid had been showing some irregularities. In this way the second modification was found. The third modification was found while working on the transformation curve I-II. The first data in which III appeared were puzzling until the existence of the new phase had been made certain, because by chance the first readings were taken at almost exactly the temperature of the triple point. TABLE I X . Carbon

Tttrachloride.

Liquid—I. Pressure.

Temperature.

1 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000

—22°.6 14 .2 45 .9 75 .8 102 .7 126 .8 149 .5 171 .0 192 .1 211 .9

cm .'/gm.

4K,

Latent Heat, kgra. m./gm.

0.02580 2006 1653 1401 1197 1019 862 730 622 538

1.67 1.72 1.77 1.78 1.76 1.72 1.65 1.56 1.46 1.37

1.67 1.50 1.41 1.34 1.27 1.20 1.13 1.04 0.95 0.88

3.17 3.43 3.68 3.87 4.02 4.12 4.16

2.68 2.72 2.76 2.78 2.79 2.77 2.71

4.60 4.75 4.87 4.94

2.55 2.52 2.47 2.39

0.27 0.30 0.33 0.36 0.38

-0.09 -0.09 -0.08 -0.08 -0.08

Change of Energy, kgm. m./gm.

I.-II. 2,000 3,000 4,000 5,000 6,000 7,000 8,000

-

5°.9 13 .8 32 .8 51 .2 68 .6 86 .0 102 .8

0.02429 2343 2246 2147 2042 1929 1816 I.-III.

9,000 10,000 11,000 12,000

120°.0 139 .4 158 .9 178 .4

0.02259 2229 2187 2132 II.-III.

6,500 7,000 7,500 8,000 8,500

14 i— 664

- 4 21 48 75 101

e

,9 .8 .5 .2 .9

0.00555 562 562 555 543

CHANGE

OF PHASE

UNDER

PRESSURE.

177

There are no special peculiarities shown by the reactions between the different solid forms. CCI4 proved itself throughout a particularly pleasant substance to work with because of the sharpness of freezing,

0

0

1

2

3 4 6 6 7 8 9 10 Pressure, kgm./cm.J χ I0 J Carbon Tetrachloride

lite

Fig. 22. Carbon Tetrachloride. The change of volume curves for the liquid and the three solid modifications. The observed values are shown by the crosses.

and of the speed of reaction, both between solid and liquid and between the two solid phases. We are by this time accustomed to high reaction velocity at high pressure between two solid forms, but in all previous

ΙΒ •

Ö ^ ^ ^ M i 8

9

10

11

Pressure, kgm./cm.2 χ 103 Carbon Tetrachloride Fig. 23. Carbon Tetrachloride. The computed values for the latent heat and the change of internal energy for the various transitions between the liquid and the three solid forms.

cases the high velocity has been associated with very small latent heat, and the transformation curve has been nearly vertical. In the case

14 — 665

I ;8

P. W.

BRIDGMAN.

of these new modifications of CCI« the reaction between solids is noticeably rapid, much more rapid than between solid and liquid, but nevertheless does not approach the explosive rapidity that we have found previously. The reaction velocity between II and III is notably less than that between I and II or between I and III. Evidently the fact that there is here considerable heat of reaction is sufficient to prevent the reaction from becoming explosive, because time must elapse for the heat of reaction to be conducted away. But the converse, namely that explosive rapidity is brought about by zero heat of reaction, is not true, as is shown by the enormous slowing down of an explosive reaction by lowering the temperature a few degrees. The reaction velocity between these modifications of CC14 remained sensibly independent of temperature over the extent of the transformation curve investigated here. This is contrary to the behavior of those solids which show explosive velocity. This suggests, as will also be suggested by the behavior of o-kresol, that the explosive rapidity of reaction between two solids is something that is essentially brought about by the nearness of the liquid phase; we never find it except in the neighborhood of a triple point with a liquid. It was found possible to superheat III with respect to II; in this respect, therefore, two crystalline phases are essentially different from a liquid and a solid. Previous examples of this are not common. But no case was found of the superheating of either II or III with respect to I. The phase diagram of CCI4 is different from that of most other substances with which we are familiar in that the various reactions from one solid to another go on with no apparent relation to the liquid. It is usual for the new solid form to replace the original solid at high pressures, forming a new equilibrium with the liquid, so that the new solid has the appearance of having been made necessary in some way by new conditions in the liquid. But in the case of CCI4 it is quite different; it is evident that if there is a triple point between the liquid and I and III it is probably at pressures at least twice as high as those reached here. The necessity for the new solid forms seems to have been here brought about almost solely by the action of forces operative within the crystalline phase, independent of the liquid. It should be possible to realize the phase II at atmospheric pressure at low enough temperatures. Such an attempt was made by cooling CCI4 in carbon dioxide snow to — 8o°, but the depression of temperature was not sufficient to overcome the viscous resistance to the reaction. The two forms found here at high pressures seem to be entirely new, but there are hints by Tammann and Amagat, who have both worked with CCI4 under pressure that there are other solid forms. Amagat 88

14 — 666

CHANGE

OF PHASE

UNDER

179

PRESSURE.

used an apparatus with glass windows, and was able to obtain photographs of the

CCI4 crystallizing under pressure.

He found crystals of different

shapes, and assumed the existence of allotropic forms.

But such an

inference, without careful measurements of the crystalline angles, is dangerous, as shown by the varied appearance of snow flakes, for example. Amagat certainly did not obtain a modification of CCI4 with a freezing point different from that of the ordinary variety, which makes it exceedingly probable that his crystals of different shapes were only crystals of the same crystalline system, but of different crystalline habit from the common form.

Tammann's69 evidence for other forms is also by no

means convincing, being chiefly certain inconsistencies that he found in his determinations of AV.

He was not able to find two distinct melting

temperatures at the same pressure, as would be expected if he really had two distinct forms of the solid, but apparently he found exactly the same equilibrium temperature and pressure for two supposedly different forms. Tammann's inclination to explain these discrepancies by new allotropic modifications apparently is a bias left from his interpretation of some erroneous results that he had obtained in 1898.60

His original experi-

ment was performed on a very impure specimen of CCU with a melting point 30 below that used here.

An error in recording the temperature

had led Tammann to think that his specimen was unusually pure.

Irreg-

ular results were obtained with this impure liquid that were explained by the existence of three polymorphic forms.

But the properties of

these supposed modifications were so remarkable, such as ability to exist indefinitely in contact with the liquid without the reaction running, that Tammann reexamined the question, and in " Kristallieren und Schmelzen" retracted his former results.

He still explained the out-

standing irregularities, however, by the existence of two polymorphic forms.

But there now seems to be some doubt in Tammann's own mind

as to the reality of the existence of his second modification, for in a recent paper61 he marks it with an interrogation point. There are few other data for comparison at atmospheric pressure. For the melting point there is a value — 24° by Niescher,84 and — 22.6° by

Bugarszky.62

Tammann's specimen melted at

— 22.96°.

The

specimen used in this work melted at — 22.6°, determined by extrapolation from data at 60 kgm.

There seems to be only one value for the

latent heat, 4.2 gm. cal. per gm. or 1.79 kgm. m., determined by Niescher84 by an indirect method.

The value computed from these data is

1.67, in close enough agreement with Niescher's somewhat doubtful value to make unnecessary any adjustment of the initial slope of the melting curve.

The exceptionally small value of the latent heat should

14 — 667

ι8ο

P. W. BR1DGMAN.

be noticed. No other values of Δ V at atmospheric pressure are known; 0.0258 cm.3 per gm. was found here. As might be expected from the probable impurity of Tammann's 63 sample, his results up to 3,000 kgm. are considerably lower than those found here, 6.6° lower at 3,000, 5.40 lower at 2,000, and 3.50 lower at ι,οοο. The change of volume was measured by Tammann at three points. The change found at 700 and at 2,000 for his supposedly second modification is not in violent disagreement with the values found here, but his value at 700 for the so-called first modification is much too high. O-Kresol.—This substance was Kahlbaum's purest, supplied by Eimer and Amend. It was further purified by twice crystallizing at constant temperature in the thermostat. The crystals were obtained in the form of large transparent needles. The original substance came in the form of a powder of about the same coarseness as granulated sugar, and was somewhat impure, as shown by the yellow color of the melt. Three series of observations were made; the first with the original apparatus comprises 15 points up to 7,500 kgm., the second one point at low pressures with the low pressure apparatus, and the third nine points with the final apparatus. The experimental results are shown in Fig. 24, and the computed latent heat and change of internal energy in Fig. 25. The numerical values are given in Table X .

2

3 4 5 6 7 8 9 Pressure, kgm./cm.' χ

10-

10

1112

Orthokresol Fig. 24. Orthokresol. The phase diagram for the liquid and two forms of the solid, and the change of volume curves between the liquid and the two solid forms. It was not possible to find experimentally values for the change of volume between the two solids, because of the extreme slowness of the reaction. The observed transition temperatures are shown by the circles and the observed changes of volume by the crosses.

14 — 668

CHANCE

OF PHASE

UNDER

TABLE

PRESSURE.

l8l

Χ.

Orthokresol. Liquid—I. Prenure.

Temperature.

Δ y, cm.»/gm.

Latent Heat, kgm. m./gm.

Change of Energy, kgm. m./gm.

1 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

30°.8 47 .4 61 .9 74 .2 81 .8 94 .5 102 .9 110 .8 118 .1

0.0838 678 557 471 406 359 319 288 264

14.38 14.10 14.10 14.28 14.50 14.61 14.60 14.61 14.72

14.38 13.41 13.00 12.94 12.88 12.80 12.70 12.61 12.59

14.88 15.57 16.08 16.43 16.73 17.05 17.42

11.50 11.85 12.07 12.12 12.14 12.22 12.33

Liquid—II. 6,000 7,000 8,000 9,000 10,000 11,000 12,000

102°.7 116 .4 129 .3 141 .4 153 .7 164 .6 175 .9

0.0559 529 499 475 454 436 422

O-kresol has two solid modifications.

T h e second modification was

not found during the first set of experiments, although two equilibrium points between the liquid and solid I were found in the domain of stability of solid II. to appear.

T h e new modification requires a good deal of urging

A t 8o°, pressure on solid I was raised to 12,500 kgm., 6,500

1

2

3

4 5 6 7 8 9 10 Pressure, kgm./cm. 1 χ 10 3 Orthokresol

1112

Fig. 25. Orthokresol. The computed values for the latent heat and the change of internal energy when the liquid melts to one or the other of the two solid forms.

14 — 669

182

P. W.

BR1DGMAN.

kgm. beyond the transformation point, without the appearance of II, which was obtained only by raising the temperature at 12,500 kgm. to 1950 and waiting for some little time. All of the reactions with o-kresol were abnormally slow, both between the liquid and either modification of the solid or between the two solids. A high degree of subcooling of the liquid was also possible. On one occasion pressure on the liquid at 130° was raised to 12,500 kgm., 4,500 kgm. beyond the freezing pressure, and 50° below the freezing temperature, without solidification. The temperature had to be lowered at this pressure to induce solidification. The sluggishness of the reaction between the two solids was so great that only one point could be found on the transformation curve I - I I . A t 95.4°, 7.8° below the triple point, the reaction was so slow that absolutely no progress of the reaction within a region 500 kgm. wide could be detected in four hours, while 5.40 higher, 2.40 below the triple point, the reaction velocity had become great enough so that it was possible to shut the equilibrium point in between two values differing by only 70 kgm. in the course of an hour. This is the most striking example yet found of the enormous variation of reaction velocity between two solids as the triple point with the liquid is approached. The sluggishness of the solid reaction is not to be explained by the heat of reaction, because the transformation line between the two solids is almost vertical and the latent heat abnormally low. During the experiment, pressure was raised to 12.500 at 250 without the appearance of any other solid form. The two points found in the first series of observations in the domain of stability of II are interesting as the second example we have of the possibility of prolonging a transformation curve between solid and liquid to higher temperatures into the region of another solid. The other example is the prolongation of the ice III—water curve into the domain of ice V, but the effect was not nearly so persistent there as here; in fact it was obtained only once, by accident. On the other hand, several cases are known in which it has not been found possible to so prolong the curve to higher temperatures into an unstable region. The following seem to be the best values at the triple point: pressure, 6,100 kgm. and temperature, 103.20; Δ V{L-T) = 0.0317; Δ V(I-IJT) = 0.0238, AV(I-II) = 0.0555 cm.3 per gm., and (dr/dp) r - n = 0.700. That is, the transformation curve I - I I rises 700° for an increase of pressure of 1,000 kgm. O-kresol is a substance for which Tammann64 claims two solid modifications. His solid form has no relation with that found here, but entirely disappears beyond 640 kgm. and 38.8°, and at atmospheric pressure at tem-

14 — 670

CHANGE

OF PHASE

UNDER

PRESSURE.

183

peratures below 22.50. (See Fig. 26 for the domain of existence of this supposed modification.) This means that if liquid o-kresol is cooled at atmosheric pressure, it solidifies at about 30° to a solid which has a very limited region of stability, passing over at 22.50 to the form stable throughout the most of the phase diagram. Tammann gives the coordinates of five points on the transformation curve between the two solid forms. However, he apparently did not measure the magnitude of the change of volume between the two phases, and gives no hint as to what order of magnitude to expect, as he might if the reaction had been clean cut. Most careful search wa3 made during this present investigation for such another modification, but none was found. Two different methods were employed in the search. First, the equilibrium pressure and temperature was determined at eight points at pressures both above and below the supposed triple point, but no discontinuity in the curve could be found. These points are shown in Fig. 26 together with the points of 0 1000 Tammann. Secondly, measurements Pressure, kgm./cm.J were made on the solid at 60 kgm. from Orthokresol 15° to the melting point at about 31 0 . Fig. 26. Absolutely no discontinuity was found on Orthokresol. Equilibrium tempassing over the supposed transformation peratures a t low pessures (circles), point at 22.50. The evidence seems un- together with Tammann's points questionable that at least in the present (crosses). I t will be noticed that in this work no trace could be found of work there was only one low pressure a second solid form at low pressures. variety present. If there are really two low pressure varieties, then the measurements given here must have been on the second of Tammann's varieties (that is, the low temperature variety). But this possibility is ruled out by the high melting point of the modification used here. The melting point of Tammann's variety should be about 26°. There seems little room for doubt that Tammann's two varieties are only the apparent effect of impurities. The melting point of his o-kresol was about 1.2° lower than that used here. One is the more inclined to accept this explanation since Tammann has himself retracted announcements of new modifications which he later found to be due to impurities. Examples of this are CC1 Ο dp

if Av > o. This condition may be readily proved to be equivalent in all cases to the condition d IAH\ T h a t is, the latent heat increases more slowly than the absolute temperature. This condition, if drldp > o, is equivalent to ι „ dr -ACP— - Aß τ ap

o. This condition, which is equivalent to / dAa \ 1άτ\21ΘΑβ\ „d2r is of no immediate help to us here, because it gives the variations, instead of the actual values of Aa and Aß along the curves. In view of our inability at present to give precise values to Δα, Aß, and ACP, it becomes of interest to inquire if we cannot with the help of these inequalities find at least the order of magnitude of the several quantities. In general, we expect that Δα, Aß, and ACV are all positive, or that the compressibility, thermal expansion, and specific heat of the liquid are greater than the corresponding quantities for the solid. So far as I know, at atmospheric pressure, Aa is universally positive, even for

19 — 774

CHANGE

OF PHASE

UNDER

PRESSURE.

99

water where the liquid occupies less bulk than the solid. Aß is almost always positive; the only exception I know is for water, and even here Aß becomes positive at higher pressures. And the only authentic example I know of a negative value for ACP is that of sodium, recently measured by Griffiths. 34 We will assume in the following that these quantities are in general positive. We rewrite the inequalities obtained so far dr Act-—Αβ dr dp'

Aß — -

ACpidr\2

f U I dpi )

>

ACP

Ο,

(dp)

>

O,

dr

" ^ Δdp/ 3 +

ΔΟΟ.

T h e terms entering these inequalities seem to be in general of the same order of magnitude, so that the inequalities usually can give us genuine information. As an average, for these experiments, Δα is of the order of o.ooooi, drjdp of the order of Δ* 0.015, a n d τ of the order of 350°. This means that Aß is of the order of 0.0006, and ACP of the order of 10, or 0.2 cal. T h a t is, Δα, Aß and ACP are of the same orders as the compressibility, expansion, and specific heat of the liquid alone. The inequalities may be represented graphically, as shown in Fig. 22. T h e three quantities are arranged in descending order of magnitude, as shown. Fig. 22. T h e experimental fact that d2r/dp2 < ο is equivaGraphical representalent to the condition that the difference A to Β is tion of the relative maggreater than the difference Β to C. nitudes of the thermodyThe diagram makes clear what must happen in namic quantities deterthose exceptional cases when Δα, Aß and ACP are mining the freezing curve. not all positive. .

If Δα < ο, solid more compressi-

These

Native magnitudes

are determined by experi-

ble than liquid, then we must also have Αβ < ο, m e n t and ACP < o. That is, Δα cannot be exceptional without all three being exceptional. Now if Αβ < ο, we must also have ACP < o, but there is no necessary condition as to sign thereby imposed on Δα. Finally, if ACV < 0 , there is no necessary condition of sign thereby imposed either on Δα or Aß. W e may therefore say, since the normal state of affairs is for Δα, Aß and ACP all to be positive, that the probability of negative values is greatest for ACP, intermediate for Aß, and least for Δα.

ΙΟΟ

P. W.

BRIDCMAN.

Besides these inequalities, the equations we have written down give us numerically the distances between A and B, and between Β and C. Suppose now that we assume a probable value for one of the three quantities, and then compute the other two with the help of the known differences Α-B and B-C. It is obvious that we shall make the smallest percentage error in the other two if we assume ACP, and the largest if we assume Δα. The numerical values that we give in the following will be computed in this way. We shall assume that ACP = o, and then compute with the help of the above known differences the values of Δα and Δ/3. If, as is usually the case, ACP is really positive, the values we find will be minimum values for Δα and Aß. T h e values for Δβ so found will not do much good, but the values for Δα will be somewhat better, and are perhaps worth giving. The values for all the eighteen liquids listed in this and previous papers will be computed in this way and tabulated. In addition, where the results are available, the more accurate results will be given for atmospheric pressure. These accurate values a t atmospheric pressure, combined with the rougher values a t high pressures, will in some cases give us a better hold on the values under pressure. It should, however, be borne in mind that a direct experimental determination of either ACP or Aß is a matter of unusual difficulty, even a t atmospheric pressure, because of the disturbing influence of premature melting due to very slight quantities of impurities. A striking example of the possibilities in this direction is shown in the discussion following under " sodium " of Griffiths' recent values. In particular, direct determinations of ACP seem susceptible to error, as is shown by the very wide divergence of independent direct observations. In some cases, it is probable that the value of ACP computed from the value of Aß is better than the direct value. There seem to be practically no direct values of Δα, either a t atmospheric or higher pressures. In a few cases, I have, from my own d a t a for determining AV at low pressures, been able to find a fairly good value for the difference of thermal expansion a t atmospheric pressure, but in most cases the temperature range was not great enough to give satisfactory values for this. DIFFERENCE OF COMPRESSIBILITY, EXPANSION AND SPECIFIC HEAT BETWEEN SOLID AND LIQUID.

In Table X I . are given these values of Δα a t pressure intervals of 3,000 kgm. In addition, the values of Aß a t atmospheric pressure are listed. These values for Aß should not be used without consulting the discussion, where the sources of information a t atmospheric pressure are given and the most probable values indicated for each substance in detail. 19 — 776

CHANGE

OF PHASE

UNDER

ΙΟΙ

PRESSURE.

TABLE X I . D i f f e r e n c e of E x p a n s i o n ( = Δβ).

Difference of C o m p r e s s i b i l i t y ( = Λα). Substance. I

3,000

6,000

g,ooo

13,000

1

Potassium

0.0.47

0.0.34

0.0*27

0.0(21

O.O5I6

0.0,75

Sodium

0.0.33

0.0.18

0.041

0.0.8

0.0.8

0.0,89

C a r b o n dioxide

0.0,10

0.0.9

0.066

0.0.35

Chloroform

0.0.37

0.0.39

0.0j30

0.0.16

0.0629

0.0.30

0.0,3

0.0,8

0.0.241

0.0.11

0.0,6'

0.0.28

0.0,39»

0.0.48

0.0,81

Anilin

0.0.82

0.0.48

0.0,36

Nitrobenzol

0.041

0.067

0.0632

O.O s 27

Diphenylamine

0.0,24

0.0.7

0.0.4

0.0b32

Benzol

0.0,50

0.0,13

0.0.6

0.0544

C a r b o n tetrachloride

0.0,12

0.0.33

0.0.33

0.044

0.0,19

Ο.Ο58

0.0536

0.0ä21

0.0,30

0.0627

O-Kresol

jj''

Phosphorus

0.0.43

Bromoform

0.0.49

Silicon tetrachloride

0.0.28

O.O5I4

0.0.381

19,000

? 0.0.4 0.0,6 0.0,4

0.0.12 0.0,41 0.0.14

0.0.4 0.0.10

0.0.38

0.0.28

O.O5I9

0.0.16»

0.0.87

0.0.37

O.O5I7

0.0.121

0.0,46

0.0,54» 0.0,21»

Chlorobenzol

O.O4II

0.0.58

0.0.36

0.0626

0.0.15

0.0,13

0.0,4

Bromobenzol

0.0,13

0.0.49

0.0S34

O.O5I7

0.0.10

0.0.21

0.0,4

Benzophenone

0.0,29

0.0,13

0.067

0.0,32

0.0.47

p-nitrophenol

0.0,20

0.0,16*

0.0426

p-toluidine

0.0,31

0.0,13

0.069

0.067j

0.0.44

0.0482

M e t h y l oxalate

0.0,67

0.0.99

0.0J6

0.067

0.0.41

0.0.19s

Bismuth

0.07S7

1

11,000 kgm.

* 8,000 k g m .

0.0.11

0.0,8 3

9,000 k g m .

4

2,000 k g m .

» 4,000 k g m .

If there is no discussion for any substance, the value of Aß was computed, assuming ACP = o. T h e Table also gives in most cases, for purposes of orientation, the values of Aß at 12,000 kgm., computed on the assumption that ACP = o. Potassium.—There are two experimental values for Aß at atmospheric pressure; 0.0484 b y Block, 1 8 and 0.0464 b y Hägen. 62 If we assume as an average value 0.0475, we find Δα = 0.0547, and ACP = 0.046 cal. (1.95 kgm. cm./gm.). T h e difference of the specific heats found in this w a y is considerably less than either of two direct values that we have; 0 . 1 5 cal. b y Bernini, 63 and 0.08 cal. b y Joannis. 6 4 T h e probability seems to be that 0.046 is nearer the truth; the value of Bernini seems improbably large, and doubt is cast on the value of Joannis b y the fact that his value for the latent heat is without doubt too high, as is suggested b y the recent work of Griffiths 6 1 on a similar substance, sodium, for which Joannis' value is certainly too high. T h e value found for Aß, assuming ACP = o, is undoubtedly not good, for it is negative ( = — 0.0425), but the value for Δα on this assumption 5 2 . Ε . B . H a g e n , W i e d . A n n . , ig, 4 3 6 - 4 7 4 , 1 8 8 3 . 5 3 . A . B e r n i n i , N u o v . C i m . ( 5 ) , 10, 5 - 1 3 . 1 9 0 5 . 5 4 . A . J o a n n i s , A n n . C h i m . e t P h y s . (6), 12, 3 5 8 , 1 8 8 7 .

19 — 777

P. W. BRIDGMAN.

I02

is 0.0534. W e see, as was proved above, that Aa is not very sensitive to the value of AC„. In the table, the value for Δα is assumed 0.0547 at atmospheric pressure, and at 12,000 kgm. the value given is on the assumption that AC ρ = ο. A t intermediate pressures, the initial difference of the two values (0.0547 — 0.O534) is distributed proportionally to the pressure. Sodium.—There are values for both ACP and Aß at atmospheric pressure. W e have two values for ACP, both negative; — 0.07 cal. b y Bernini, 53 and — 0.06 b y Griffiths. 61 Neither of these values are explicitly stated b y the original authors, but have been estimated b y me Ε' be u · 4> ^Q. .31

s..30 ε

/

J-

/

τ

e.

Ο

.28

0° 20° 40° 60" 80"

Temperature Sodium Fig. 23.

The recent values of Griffiths for the specific heat of solid and liquid sodium at atmospheric pressure. In the discussion it is pointed out that a very small quantity of impurity is sufficient to produce the deviation of the specific heat of the solid from linearity.

from curves plotted from their data giving Cp as a function of temperature above and below the melting point. In spite of the agreement of these values, careful examination of the data leaves the conviction that the agreement is accidental, and even leaves doubt as to whether the negative value for ACP has been proved. T h e matter is of such importance that it will pay to dwell on it a little. In Fig. 23 are reproduced Griffiths' values for Cp above and below the melting point. It will be seen that the curve for Cp of the solid takes a sudden rise in the neighborhood of 70°. T h e question suggests itself whether this m a y not be due to a premature melting because of slight impurity. T h e amount of melting to account for this change of direction of the specific heat curve is very slight. If we suppose that the actual curve is really the dotted straight line, then the area between the dotted line and the curve through Griffiths' points represents the total heat set free in premature melting. This total heat is one fifth of a calorie which, combined with the latent heat, indicates that only two thirds per cent, of the total quantity of sodium need have melted prematurely to account for

19 — 778

CHANGE

this.

OF PHASE

UNDER

I03

PRESSURE.

T h e total amount of impurity needed to produce this slight amount

of melting is evidently much less than two thirds per cent., and m a y well be so small in amount as to resist most careful attempts to remove it. T h i s consideration, of course, has been known for a long time to apply to determinations of differences of specific heat near the melting point, b u t this example of sodium shows in an unusually striking manner how very slight the amount of impurity need be in some cases to vitiate the result. I t should be said that even if we assume the total variation of Griffiths' curve from linearity to be due to premature melting, the error so introduced into his value for the latent heat will be less than 1 per cent. If we grant for the present the negative value for ACP, and take the average of the two values, — 0.065 cal. ( = — 2.78 kgm. cm.), we calculate Aß = 0.0424.

N o w the value of Aß determined b y direct experi-

ment is 0.0483 b y Block, 1 8 and 0.0465 b y Hägen. 6 2

These values are both

considerably higher than that found b y using the negative value for ACP, and make improbable the validity of the negative value.

If we compute

backwards with the average of the two experimental values for Aß ( = 0.0474) w e shall find a v e r y small negative value for ACP, cal./gm.

— 0.0004

B u t it is to be noticed that the same causes which make ACP

appear negative will make the experimental values for Aß too small, and it is significant that the later, and presumably more accurate value for Aß is the larger.

I t seems to me that the safest course a t present is to

assume ACP = o.

T h i s is the assumption made in getting the values of

the table.

I t gives 0.0489 for Aß, close to Block's value, and o.o 6 33 for Δα.

A s this paper was going to press, I have come upon a recent paper b y Rengade (C. R., 156, 1897-1899, 1913), in which he finds that the specific heat of the liquid is greater than that of the solid b y 0.045 cal. and the melting point of the pure metal is 97°.90.

Beyond stating that great

precautions were taken to obtain the metal especially pure, no detail is given. Diphenylamine.—The

experimental value for Aß b y Block, 1 8 0.0328,

agrees well with the value computed above, 0.0324, assuming ACP = o. T h e r e are, however, two direct determinations of ACP; 0.043 cal. b y Batteli, 28 and 0.134 b y Bogojawlensky. 6 6

T h e values of Aß computed with

these values of ACP are 0.0338 and 0.0368 respectively. considerably higher than the experimental values.

Both of these are

Apparently Batteli's

value for ACP is much more nearly right than Bogojawlensky's.

Ace

is not appreciably changed b y using Block's value for Aß instead of 0.0324. Benzol.—The

experimental value of Block, 1 8 0.0347, agrees unusually

well with that found assuming ACP = o, 0.0346. ACP is small.

T h e presumption is that

There are three widely v a r y i n g experimental values for

55. Bogojawlensky, quoted by Tammann in " K . und S.," p. 45.

19 — 779

I04

P. W. BRIDCMAN.

ACP; 0 . 1 3 1 cal./gm. b y Ferche, 66 0.003 by Fischer," and 0.078 by Bogojawlensky. 66 If we assume the intermediate value, we find Aß = 0.0381, which seems too much above the experimental value. Very recently, since the writing of most of this paper, Essex 68 has published data for the effect of pressure and temperature on the liquid and solid forms of benzol. His value for Aß calculated by a linear extrapolation from his data for the solid at ι ,500 and 2,500 kgm. is 0.0350. There seems room for little doubt as to the approximate value of Aß at atmospheric pressure. Phosphorus.—There are three experimental values for Δ/3; 0.0310 b y 18 Block, 0.0310 by Leduc, 69 and 0.0465 b y Kopp. 60 We shall assume the value 0.03I0. This is without doubt better than the value, which is o, calculated assuming ACP = o. If we assume o.o 3 io for Aß, we find Aa = 0.0543, against 0.0514, calculated from ACP = o. This is an exceptional case where Aa is sensitive to the value assumed for ACP. In the table, the values of Δα are adjusted at high pressures as they were in the case of Potassium. T h e value of ACP calculated assuming Aß = 0.0310 is 0.027 cal./gm., which is in remarkably good agreement with the direct value, 0.026, found b y Person. 61 Monobrombenzol.—No direct experimental values are known for Aß or ACP, but this is the substance mentioned for which consistent experimental values of Δα were obtained over the pressure range. These values, at the pressure intervals of the above table, were 0.04II, 0.056, 0.053, ο.ο 6 ι, O.O05, respectively. T h e agreement with the values computed assuming ACP = ο is fairly good, and gives some confidence in the values for the other substances. It has been stated that the approximate values of the table are to be expected to be minimum values, but it will be noticed that the experimental values above are in most cases lower than the computed values. T h e reason for this is probably the unavoidable slight rounding of the corners of the freezing curve. Benzophenone.—Block's18 direct experimental value for Aß is 0.0347, against 0.0319 assuming ACP = o. There is no doubt that the direct value is better. T h e change in Δα, however, is not so large; 0.0429 using Block's value, and 0.0421 assuming ACP = o. T h e values at higher pressures are adjusted as in previous cases. Using 0.0347 for Aß, we calculate ACP = 0.075 cal./gm., as compared with 0.096, the direct experimental value of Tammann. 62 56. 57. 58. 59. 60. 61. 62.

19 — 780

J . Ferche, Wied. Ann., 44, 265-287, 1891. W. Fischer, Wied. Ann., 28, 400-432, 1886. H. Essex, Diss. Gött., 1914, Leopold Voss, Leipzig and Hamburg. A. Leduc, C. R „ 113, 259-261, 1891. H. Kopp, Trans. Roy. Soc., Vol. 155, 71-202, 1865. C. C. Person, Ann. Chim. et Phys. (3), 21, 295-335, 1847. G. Tammann, " Κ . und S „ " ρ. 240.

CHANGE

Paratoluidine.—For

OF PHASE

UNDER

PRESSURE.

Aß there is the direct value 0.0330 b y Block, 1 8

o.o 3 22 calculated assuming ACP = o, and 0.0344, a direct value of m y own.

T h e range of values of Δα, letting Aß v a r y from o.o 3 22 to 0.0344,

is only from 0.0331 to o.o 3 37, showing again the comparative insensitiveness of Aa. cal./gm.

T h e value of ACP, using the extreme value of 0.0344, is 0.068

T h i s is considerably lower than 0.146, the only experimental

value there is, b y Batteli. 28

T h i s is apparently much too high, because

if we compute back to Aß, assuming 0.146, we find Aß = 0.0375, which seems impossibly high.

T h e value given in the table assumes Aß — 0.0344.

Methyl Oxalate.—For

Aß a t atmospheric pressure there is the value of

Block, 1 8 w h o gives 0.000236.

I find 0.000405.

It is evident that the

same impurity which invalidated Block's value for the change of volume will also affect the difference of expansion, and in the same direction as the difference between Block's value and mine. m y own value in the computations.

I have, therefore, used

T h e values at the higher pressures

have been calculated on the assumption that ACP = o.

It is to be

remarked that, using m y initial value for Aß, the initial value for ACP is negative ( — 1 5 kgm. cm.), an unusual and questionable result. result depends on the large initial value for dAV/dp

This

rather than on the

value for Aß; it is quite probable that the initial value given above for dA V is really too large.

There is a direct measurement of the difference of

specific heats b y Bruner, 34 who found that at the melting point the specific heat of the liquid was 1.41 kgm. m. greater than that of the solid. B u t Bruner's sample w a s unusually impure, as has been stated.

In

a n y event, this appears to be a substance for which the assumption that ACP = ο is of more doubtful validity than usual. Bismuth.—For

this substance there are a number of data, none of

which are v e r y concordant, from which we m a y get some idea of Aa, Aß and ACP at atmospheric pressure.

For the specific heat of the solid there

are the following values, shown in T a b l e X I I .

A questionable extra-

polation from all these values would indicate 0.0313 cal. as a probable value a t the melting point. only the value of

Person, 42

For the specific heat of the liquid there is 0.0363.

T h e value of ACP from these data is

0.0050 gm. cal. or 0.213 kgm. cm. per gm.

For the thermal expansion

there are two widely differing measurements.

Vicentini and Omodei 43

find the average dilatation of the liquid between the melting point and 300° is 0.03120, the liquid increasing regularly in volume between these limits.

Their value for the average expansion of the solid, presumably

from room temperature up to the melting point, is 0.04395.

Lüdeking, 4 7

on the other hand, finds that liquid bismuth has a maximum density a t about 270°, just as water has above the freezing point.

T h e freezing

19 — 781

io6

P.

W.

TABLE CT for Solid Temperature.

Cp

-186° - 79° 18° 17°- 99° 22°-100° 0°

.0284 .0296 .0303 .0304 .03035 .03013

Observer.

Giebe

63

, as it is in those cases to which we wish to apply the dp

20 — 795

62

BRIDGMAN.

formula. Conversely, of course, the formula for the pressure shift does not apply at a horizontal part of the transition line, where ®1 — ®2 = 0. These formulas have been subjected to no restriction in the derivation except that the phase (1) is that in which the impurity is dissolved. This might, if we liked, be the phase stable at the higher pressure or the lower temperature, instead of as we have shown it. The formulas show that in all cases the effect of impurity is to shift the transition line into the region of the pure phase. For a given concentration of the impurity, that is, for a given osmotic pressure, the displacement is greatest for those substances with a small latent heat and a small change of volume. These are much smaller for the solids investigated here than for liquids, so that one would expect in general the displacement of the transition lines to be greatest for the substances investigated here. But as has been remarked, very few of these substances contain dissolved impurities (form mixed crystals), so that most of the transition lines are unaffected by what impurities there may be. If the impurity is soluble in both phases, we get for the pressure

This shows that if the total amount of impurity is slight, and if it is so distributed between the two phases that ®i Api = ®2 Δ ^ , then there is no shift of the transition line. The phenomena in the neighborhood of a triple point offer no particular difficulty. It may be shown directly by substitution that the displaced transition lines must pass through a triple point as well as the original lines, no matter what the relative amounts of impurity dissolved in the three separate phases. This of course is what we know must be the case from other considerations. It should be noticed that although these formulas are entirely valid when the impurity is dissolved in more than one phase, nevertheless the conditions under which they are derived are not always close to the conditions of practise. We have assumed a knowledge of Api and Ap2. This demands that we know the way in which the impurity is divided between the two phases. In practise this problem of the distribution of the impurity must usually be solved first, since the

20—796

POLYMORPHIC TRANSFORMATIONS OF SOLIDS.

63

practical conditions usually give us the total amount of impurity present in the two phases together. The distribution problem is not touched above; to solve it would require a knowledge of the heat and volume effects of solution.

T H E EQUATION OF THE TRANSITION LINES.

This equation has already been developed in a previous paper.1 The equation is

0, the curve may rise to a vertical asymptote, or may rise to a maximum and fall to a vertical asymptote, or rise to a maximum and fall to an inclined asymptote, or fall to a vertical asymptote, or fall to a minimum and rise to a vertical asymptote, or fall to a minimum and rise to an inclined asymptote. And if Δα20

y s

1

Π

/

160

I

CC
4)2 has been described in a separate section. It is likely that both of these transitions are really decompositions to the simple salts, rather than a true polymorphic change. An attempt to make KNH4SO42H2O anhydrous by heating for a number of hours at 150° in vacuum was without success. SUBSTANCES WITH UNSTABLE FORMS.— Benzophenone, has four modifications including a monoclinic and a rhombic form; Para-nitro phenol; Acetamide*, trigonal; Menthol; Acetophenone; Monochloracetic Acid, has several unstable forms; Propionic Acid; SM3, trigonal; Sulfur*, has a stable rhombic and monoclinic form, and numerous unstable forms; Phosphorus,* cubic, trigonal; Antimony, trigonal; Selenium, two monoclinic and a trigonal form; Arsenic, cubic, trigonal; Iodine, rhombic, monoclinic. The first seven of these substances have already been commented on, either in this or in earlier papers; the melting curves of several of them have been determined. Phosphorus B has been made the subject of a special paper. Antimony, besides being very near phosphorus in the periodic table, forms a number of stable and unstable

26 —1024

POLYMORPHISM AT HIGH PRESSURES.

161

modifications at low temperatures. It was somewhat of a surprise that there were no new forms under pressure. Sulfur is known to have a number of modifications, both stable and unstable, several of them more or less obscure in character, but there are at least two well defined forms that stand to one another in the relation of enantiotropy. I found no other well defined forms to 12000 at 20°, 100°, or 200°. It is possible, however, that a small percentage of the form insoluble in CS2 was formed by pressure, because the specimen which had been subjected to pressure was not completely soluble. One might possibly expect a new modification of sulfur by an irreversible transition, like that of black phosphorus, because of the proximity of the two elements in the periodic table. On one occasion a piece of sulfur was kept at 12500 kgm. and 2000, for six hours, but with no permanent change. The runs on selenium were started with the amorphous variety, which had been fused immediately before the experiment. It showed no transition to 12000 at room temperature. Pressure was maintained on the amorphous selenium at 7000 for 16 hours with no effect. At 7000 kgm. the selenium was then heated to 200°. There was a transition with decrease of volume somewhere between 20° and 200°, which was doubtless due to the formation of the crystalline phase. At 200°, the new phase showed no transition to 12000 kgm., and also showed none between atmospheric pressure and 12000 after cooling again to room temperature. On releasing pressure the selenium was found to have a density of 4.69. The density of the metallic modification of Se is given as 4.79, and that of the amorphous as 4.29 by Saunders.3® (It may be mentioned incidentally that several wildly inaccurate values for the density have found their way into some Tables. The Chemiker Kakendar, for instance, gives the density of the amorphous variety as 5.68, and that of the crystalline form as 6.5). There seems little reason to doubt that the substance formed above was metallic selenium, the somewhat small density might easily be due to fissures or occluded kerosene. It is known that ordinary amorphous selenium will crystallize slowly at atmospheric pressure at 200°; the effect of high pressures seems, therefore, to be to lower somewhat the temperature of crystallization. This is as one would expect. Before trying the experiment it seemed plausible to me to expect a new form stable at atmospheric pressure analogous to black phosphorus, because of the similar position of these two elements in the periodic table. 36 A. P . Saunders, Jour. Phys. Chem., 4, 491 (1900).

162

BRIDGMAN.

Arsenic, again, is near phosphorus in the periodic table, and I thought that there might be another form like black phosphorus, but none was found. The substance used was distilled arsenic; pressure was transmitted to it by mercury, so as to avoid the possibility of poisonous compounds with the kerosene. After the run, the surface of the arsenic was found wet with mercury, and the appearance was that of amalgamation. The mouth of the steel shell was also amalgamated, a thing which I have never observed before under similar conditions of pressure and temperature. Iodine was tried at 30° and 200° to 12000 kgm. without result. At 200° a much rounded melting point was found near 5000. Because of the great chemical activity of Iodine it was placed in a steel shell beneath water, instead of being allowed to come in contact with kerosene or mercury, as usual. In this way chemical action was largely reduced, but at 200° the Iodine apparently goes slowly into solution. SUBSTANCES EXISTING AS MINERALS IN TWO F O R M S . — P b ( N 0 3 ) 2 ;

HgS, trigonal, cubic; CaC0 3 , rhombic, trigonal. Pb (NOa)2 is said by Morel 3 7 to have two mineral forms. HgS crystallizes in a black and a red form; the black is very unstable. Both of these substances have been commented on in previous sections. The CaC0 3 was investigated in the form of calcite. In nature CaCC>3 occurs in two forms, as calcite and arragonite, the latter being the more dense. There has been considerable speculation as to the relation of these two forms, but it seems to have been finally settled that at ordinary temperatures calcite is the stable form, the reversible transition from calcite to arragonite running at fairly high temperatures. This means that the phase diagram must be of the ice type. There is, therefore, a possibility that a permanent change from calcite to arragonite might be brought about by increase of pressure, if the pressure could be carried far enough into the region of stability of the arragonite to force the reaction from calcite to run, and the pressure then released in a region where the reverse transition from arragonite to calcite does not run because of viscosity. The experiment was tried of maintaining pressure on calcite at 12500 kgm. for six hours at 200°, cooling it, and then releasing pressure, but there was no permanent change of density. Since the reaction from arragonite to calcite does not run at atmospheric pressure and room temperature, it would run 37 J. Morel, Bull. Soc. Min. France, 13, 337 (1890).

POLYMORPHISM AT HIGH PRESSURES.

163

still less at higher pressures at room temperature. Therefore, if arragonite had been formed at all in this experiment, the reverse transition would not have run, and we infer that 12500 kgm. at 200°, is not a high enough pressure to bring the calcite into a region where the reaction to arragonite spontaneously runs. The specimen used was not large enough to enable me to tell whether there was any reversible change in the calcite itself up to 12000 at 200°. SUBSTANCES WITH REVERSIBLE TRANSITIONS AT HIGHER TEMPERATURES.— K2C1O4, rhombic, triclinic; K2C1O7, two triclinic forms;

CU2I2*, cubic. These all have transitions near a red heat; it is not known to what type they belong. If they were of the ice type, a high pressure might bring the transition down to the range of this work. Reason has been given for supposing that the transition found at 200° for CU2I2 is not the same as the previously known high temperature transition. ORGANIC ACIDS.— Carbolic*; Acetic*; Monochloracetic; Stearic; Tartaric, monoclinic; Benzoic, monoclinic; Oxaljg, rhombic; Citric; Propionic; Formic. Pressure was transmitted to all of these substances by mercury. I have already mentioned we would expect from Tammann's theory of polymorphism that enantiotropic transitions would be particularly common among the organic acids. Out of ten substances tried, only two examples were found, and these were not new examples, but were known before. If ten is a sufficient number of instances to give the law of chances a fair test, this is not favorable to the theory. In the above list, monochloracetic acid, which has been previously mentioned, has unstable forms, but this sort of transition is not contemplated by Tammann's theory. Oxalic acid has also been mentioned; it was tried with and without the water of crystallization. Citric acid is listed as crystallizing with water, but as I could produce no change in its appearance by heating to 100° in vacuum for several hours, I assumed that it had been supplied in the anhydrous condition. The tartaric acid was dried in vacuum at 100°. At 12000 kgm. it showed no change on heating from room temperature to 200°, but on releasing pressure at 200°, decomposition began at 5000 with an increase of volume large enough to bring the pressure back to at least 7100. The product of decomposition was a sticky putty-like mass, which swelled up and overflowed the mouth of the tube when the apparatus was opened after cooling. The Nickel steel shell was split. Professor Kohler was kind enough to examine the substance, and found that it was one of the anhydrides of tartaric acid.

26 — 1027

164

BRIDGMAN.

E L E M E N T S : Hg, cubic; Κ , tetragonal; Na, tetragonal; Sn*, rhombic, tetragonal; Bi, trigonal; Tl*; S*, rhombic, monoclinic; P*, cubic; I*, rhombic, monoclinic; As*, cubic, trigonal; Sb*, trigonal; Se*, monoclinic (2), trigonal. The investigation of mercury was concerned primarily with the melting curve. Its freezing behavior is known to be abnormal, but since the freezing temperature is a much smaller fraction of the critical temperature than it is for most other substances, one would not perhaps expect the abnormality to result in polymorphism. Sodium and Potassium show nothing unusual. Perhaps, from the rather rapid approach of Δ® toward zero, Potassium might be regarded as a candidate for polymorphism at some pressure beyond the range of this work. Bismuth would be expected to have another form because its melting is of the ice type; it is a great surprise that it does not. Thallium has another known form; the change of volume is so small that I could not make accurate measurements. The reason for trying Tin was that it is known to have a transition point at 20°, with a large change of volume, the low temperature phase (gray tin) being the less dense. A phase diagram like that of Agl might be expected. The transition from white to gray tin is known to be enormously viscous, so that one could not expect to observe this, but there was a possibility that the reaction to Tin III, if there is such, might run more readily. No such transition was found. It would be of interest to start with pure gray tin, and subject this to pressure at a low temperature. Werner 38 has recently given a provisional location for a transition line between two varieties of white tin. The transition point at atmospheric pressure is at about 160°, and at 200°, it is 500 kgm. The change of volume is extraordinarily small, so small that I could hardly expect to detect it with my apparatus at a pressure so low as 500 kgm., where it is most insensitive. The other elements have been described in a previous section. MISCELLANEOUS S U B S T A N C E S . — H 2 0*, trigonal; CO2; K N O 2 * ; K4P2O7; K4S2O7; K 2 C O 3 ; KHCOs, monoclinic; Potassium Acid Tartrate, rhombic; Methyl Oxalate, monoclinic; Urethane*; Naphthaline, monoclinic; Cane Sugar, monoclinic. H2O has a phase diagram exceeded in number of phases only by N H 4 N O 3 , and possibly by camphor. CO2 was at first thought by Tammann, to have a triple point with the liquid near 4000, but he

38 M. Werner, ZS. Anorg. Chem., 83, 275 (1913).

POLYMORPHISM AT HIGH PRESSURES.

165

later withdrew this. I could find none to 12000. KNO2 shows a transition line of rather large and unusual curvature; it is unfortunate that the substance was so impure. The reason for trying the six substances from KNO2 to Potassium Acid Tartrate was merely that polymorphism seemed to be rather more common among the compounds of Potassium than of other elements, and it seemed worth while to try a number of examples. If this surmise is correct, these six substances were not such as to bear it out. K4P2O7 was tried only at 20°, because it had some water in it. K4S2O7 was tried at 20° and 200° as usual. Both were without result. Several runs were made with K2CO3. The first showed a small transition near 6500 kgm. at 200° and at a somewhat higher pressure at 185°. This was found unmistakably with two different fillings of the apparatus. B u t after standing in the apparatus for three days, the transition at 185° had entirely disappeared, and that at 200° had a smaller change of volume. An attempt to repeat the measurements after six months showed no trace of the transition. The result is hard to explain. I am inclined to think that the transition may be a genuine one, but that 200° is in the very viscous region, so that sometimes the transition will run, and sometimes not. The effect may, however, be due to moisture; the first specimen may possibly have been a trifle moist, but the second was carefully dried in vacuum. Methyl Oxalate was tried because Tammann 3 9 has announced two modifications. I could find no other form; the matter has been discussed at considerable length in the paper on melting. There was no particular reason for trying Urethane, except possibly its rather interesting method of decomposition on heating, and its polymorphism seems to have no suggestive connection with that of other substances. Naphthaline and Sugar offered no special promise of polymorphism; they are simply substances readily available for miscellaneous exploration. DISCUSSION.

A compact summary of the nature of the effects for all the polymorphic transitions investigated to date is given in Figures 30 and 31. These diagrams show the location of the transition lines between the several phases, which are indicated by Roman numerals or by L for the liquid; the arrows on the lines show the direction in which At 39 G. Tammann, Kristallisieren und Schmelzen, p. 265.

26 — 1 0 2 9

IΜ

ι

_

L

j L

ι

/

ι

/ι

/I

I

ι

'

y "

kcio,

ι

/

7*

/

1 . Λ

ι

n

-·»• KNOj ι

Ic

/

Phosphorus 1 1 l/i

\\ 1

"

/

1

1

!

c c i

1

1

1

1

CB rH 1 1

D Μ

111

/

1

11/ /

/

-/

1

*

•' / I

1

1

I

120" 80'

/ ν - Ύ / hy

/

/L

mo

1

· L

120'

/

C^l,

1

1

A

1

L

sr

I

Benzol

ν

II

ι

O-kresol

J T \ I.n a

^ ^ ^

80«

D

~*>1 ^ -k, I /*

.yf Phenol /f/

L _ 160 . -"'*' 120* 80*

Π

2

4

J

/

'V y

L

111

/ Carbamide iL 1 1 1 6

8

r 1 Aoetamlde

Acetic Aeld

.

I Q

1

D

10

0

j ^y ,4 1

2

4

6

Urethan 1 1 1 8

10

π

0

Ϊ tu

•11 f I β' ^ 1 2

4

® Camphor 1 1 1 6

8

Pressure lit Thousands of Kilograms per Square Centimeter. FIGURE 31.

Collection of Results.

167

10

168

BRIDGMAN.

decreases numerically, an α, β, or Cp to one side of the line indicates that on that side of the line the compressibility or the thermal expansion or the specific heat is the greater, and the crystalline systems have been indicated in those cases where known by letters. The abbreviations used for the crystalline forms are: C, cubic; Q, tetragonal or quadratic; R, rhombohedric or trigonal, including hexagonal; O, orthorhombic, or rhombic; M, monoclinic; T, triclinic. The diagrams bring out the fact, which was also brought out by the general survey, that mere chemical similarity is not sufficient to ensure similarity of phase diagram. A polymorphic change cannot be regarded, except from certain restricted thermodynamic view points, as a special case of a chemical reaction, but involves different and undoubtedly more mechanism. Similarity of the phase diagram of two substances involves a much more far-reaching correspondence of mechanism than similarity of chemical behavior. There are, as a matter of fact, only two groups of phase diagrams in the collection above which are equivalent. They are RbN0 3 , CsN0 3 , T1N03, with a remote possibility of KNO3 on the one hand, and NH4CI, ΝΗ4ΒΓ, NH4I on the other. In these cases it seems to be a first prerequisite for similar phase diagrams that the corresponding phases form complete series of mixed crystals in the range of temperature in which corresponding modifications of both pure components are stable. It would seem, however, that thorough going correspondence of phase diagrams demands a higher order of identity than simply ability to form a continuous series of mixed crystals at some one temperature and pressure. A probable example of this is KHSO4 and NH4HSO4. It is very likely, although not definitely proved, that the ordinary rhombic form of NH4HSO4 is identical with the form of KHSO4 above 180°, and that at pressures and temperatures in the region of stability of KHS04(I) the two salts form a continuous series of mixed crystals, unless indeed it should chance that one of the melting points is too low. On the other hand, it is conceivable that two substances should have corresponding phases with corresponding diagrams, but, because of special relations of the transition temperatures, no region of continuous mixed crystals. For instance, if the entire phase diagram of TINO3 were lifted to higher temperatures so that the transition from trigonal to rhombic takes place at say 160°, there would be no region in which the trigonal forms of CsN0 3 and TINO3 are completely miscible, but nevertheless the two phase diagrams would be closely corresponding. Whether cases of such large displacements of corresponding transition points occur in nature is a matter for experiment.

26 —1032

POLYMORPHISM AT HIGH PRESSURES.

169

It is evidently useless to try to generalize from only the two groups found here. This conclusion does seem justified, however; similarity of phase diagrams between corresponding phases is evidence of identity of structure of a higher order than is concerned in the ordinary run of chemical or crystallographical phenomena. In general, the identity of structure must be complete enough to allow continuous series of mixed crystals, but this identity is not necessarily far reaching enough. Instances of such far reaching identity must be rare; it is all the more important to investigate other cases. Similarity of phase diagrams means not only an identity of structure so complete that similarly arranged edifices are possible, but also means that the fields of force surrounding the elements are so similar that corresponding edifices are stable. This has a bearing on the custom of many crystallographers of classifying a substance as dimorphic if it can crystallize in limited proportions with another substance of different symmetry. Such a "dimorphism" cannot be of broad significance; it merely means that the similarity of the building stones of the two substances is great enough so that if sufficient compulsion is applied to the one set they may combine in limited proportions in the edifice appropriate to the other. A very wide range of similarity or dissimilarity is evidently included in a classification so elastic as this. It is also the custom, or rather a matter of definition, to class a substance as polymorphic if it has more than one modification, stable or not. This again, has no well defined significance. Given a number of identical building blocks, it would evidently be possible to build these with our hands into a large variety of assemblages corresponding to different crystalline systems. Most of these arrangements would be very unstable, but all would persist for a small interval of time. This means that in this sense every substance is polymorphic in a very complicated way. In practise, however, not very many substances under ordinary conditions happen to form assemblages that are comparatively stable. But it is conceivable, and likely, that under different conditions of inoculation or subcooling the number of substances with unstable polymorphic forms (monotropic polymorphy) should be very largely increased. The point is that this kind of polymorphism is not of absolute significance, and the more we extend the list of polymorphic substances by increased skill in manipulation, the less significant does it become. There is no denying, of course, that the easy and persistent polymorphism shown by phosphorus, for example, is significant — it is merely impossible to draw a sharp line. Further-

26 — 1033

170

BHIDGMAN.

more, many cases now classified as monotropically polymorphic would turn out to have larger significance if certain lines of conjecture prove to be justifiable. Many investigators have thought that forms unstable under atmospheric conditions would become stable at higher pressures. In this case such substances would become as significant as those enantiotropically polymorphic under ordinary conditions. The experiments above have shown, however, that in none of the cases examined have forms ordinarily unstable become stable at higher pressures. This is, after all, not surprising, because the majority of unstable forms are less dense than the stable forms. Their region of stability, if it exists, is at negative pressures. The example of MgS047H20, mentioned above, is a case on the other hand where the unstable form is more dense, but is not formed at high pressures, even when inoculated. The dense unstable form of MgSC^HO may be obtained in the pure state by crystallizing from the supersaturated solution on inoculation with a crystal of FeSCWEkO. Cases have been found, however, in which a phase unstable at high pressures becomes stable at relatively higher pressures. Water below 0° and near 6000 kgm. crystallizes most readily in the form of ice VI, which is unstable, in preference to the stable form, ice V. Ice VI is the denser form and becomes stable at higher pressures. Acetamide is another similar example. The case of o-kresol is of the opposite kind. Above the triple point the unstable modification I is very much more likely to crystallize from the melt than the stable form II. I is the less dense form, and it has a domain of stability at lower pressures, corresponding to negative pressures for ordinary substances. Although there are these examples showing the possibility in some cases of an unstable modification acquiring a region of stability, it is likely that in the majority of cases the unstable forms have no region of stability within experimental reach. It seems preferable on the whole, therefore, in this discussion to confine the use of the word polymorphic to those substances with two or more phases which are capable of reversible transitions. It is of interest to inquire what is the frequency of occurrence of polymorphism. I have already emphasized that an examination like that above of many substances cannot possibly disclose all cases of polymorphism; a number of stable forms will not appear because of viscous resistance. The phase diagrams afford several cases where the new phase would not have been discovered if the exploration had been confined to the low temperatures. Examples are KHSO4, Hgl2, and o-kresol. It is not possible to give any general rule that will show

26 —1034

POLYMORPHISM AT HIGH PRESSURES.

171

in what region a transition will become so viscous that it cannot be observed, because the behavior of different substances is very different. As a general rule, however, the viscous resistance to transition becomes· greater at greater distances from the liquid phase. Substances with high melting points would be expected to show less frequent polymorphism. Now in all the above list of substances with polymorphic forms, the highest melting point is 628°. Not one of the substances examined which has a higher melting point shows polymorphism in my range. The only example among substances which I did not examine is CU2S with a melting point of 1100°. There are, however, numerous examples known of polymorphism at higher temperatures; several of the substances examined above belong here. It is therefore likely that many of the substances would show polymorphism if examined over a wider range. It is, furthermore, significant that the nitrates, among which polymorphism is widely prevalent, are all low melting, as are also the iodides. The organic compounds all have low melting points; in the above list there are 39 organic compounds, of which 11 are polymorphic. This does not include Substances with unstable forms. Of the inorganic substances with known melting points below 650°, 25 out of 42 are polymorphic. Polymorphism seems of more frequent occurrence with inorganic compounds. As a general average, perhaps one out of three substances are polymorphic. We next examine the relative frequency of occurrence of the different crystalline systems. I have not yet been able to determine the system of any of the new forms stable at higher pressures; we cannot yet tell whether all substances tend to any one simple type under high pressures. The known forms include 17 cubic, 3 (or 4) tetragonal, 8 trigonal, 11 rhombic, 4 monoclinic, and 1 triclinic. The relatively high frequency of the rhombic system is perhaps surprising. The number of cases in which the cubic form, which has the highest symmetry, is of greater volume than a neighboring more unsymmetrical form is striking. It would perhaps be natural to expect that the forms stable at the higher temperatures, with the greater energy of temperature agitation, and in many cases the greater volume, would have fewer elements of symmetry. However, in 10 of the above 17 cases, the cubic crystal may be transformed by propter change of pressure and temperature to a phase of smaller volume and also of lower symmetry. It is evident that the cubic arrangement in these cases cannot be the arrangement of closest packing. There is, of course, no especial reason to expect it when the crystal is built up of different kinds of atoms. Out of the five cases above in which a trigonal form

172

BRIDGMAN.

adjoins a known form, four are cases in which the trigonal form adjoins another either of smaller volume and lower symmetry, or larger volume and higher symmetry. The general rule seems to be the reverse of what we would expect, the phase of higher symmetry in the majority of cases has the larger volume. In this connection it is also interesting to note that there are several cases in which the same crystalline system occurs in more than one phase of the same substance. NH4NO3 has two tetragonal forms (possibly these are identical), RbNOs has two trigonal forms, probably KHSO4 two rhombic, and of course NH4I, NH4B1·, and NH4CI are a striking series in which the different modifications belong to the same sub-group. This shows that there is no restriction placed on the total number of possible polymorphic forms of any one substance by considerations of this character. As far as this goes, we might have more than 32 modifications. It would seem that in our present state of knowledge the specification of the crystalline system of different polymorphs is without special significance, but is of value chiefly as a means of identification. And probably when we are able to give a more detailed description of the structure, specification of the crystalline system will be superfluous. We now turn from crystallographical considerations, and discuss the general thermodynamic aspects of the phase diagrams. The enormous complexity of the phase diagrams of solids as contrasted with the melting diagrams is apparent. There are only two known melting curves that fall in temperature with rising pressure, those of water and bismuth; all others rise. The rising melting curves rise indefinitely, with no suggestion of a maximum or a critical point. All the melting curves, whether rising or falling, are concave toward the pressure axis. On every one of the curves Δι decreases with rising temperature, and on every curve where accurate enough measurements can be made, the curve plotting Δ® against pressure is convex toward the pressure axis. Furthermore, the liquid is universally more compressible, and of a higher specific heat than the solid, and only one case is known in which the liquid has a smaller thermal expansion, that of water over a restricted range. None of these uniformities hold for polymorphic changes. Retrogressive transition lines are of fairly common occurrence. Wallerant makes the statement in his Cristallographie that there are only four known transitions of this type; Agl, NH4NO3, Boracite, and Calcium Chloraluminate. In all, sixteen such transitions have been examined above, fourteen of them not known to Wallerant. It appears, then,

26 —1036

POLYMORPHISM AT HIGH PRESSURES.

173

that nearly one quarter of all the transition curves are of the ice type. The persistence of the curves for AgNOä and HgL· suggests that an ice type of transition may be as capable of continued stability over a wide range of pressure and temperature as an ordinary transition. In the early stages of this work I was inclined to regard the existence of an ice type of transition as ä prion evidence that there must be at higher pressures a normal transition to supplant it, as on the melting curve of ice I. This surmise did not prove fruitful. A summary of all the transition lines examined is shown in Table XIV. This shows the number of various classes of lines grouped according to important characteristics. Thus, for example, out of 69 lines examined, there are 3 rising curves whose direction of curvature is abnormal, and whose direction of variation of Av is also abnormal. In drawing up this table, normal behavior has been called that which is like that on the melting curve. In detail, normal curvature is concavity downward, normal variation of Av is decrease with rising temperature, a and β are normal if the phase of larger volume is the more compressible or expansible, and Cp is normal if the phase stable at the higher temperature has the higher specific heat. In drawing up the table all those lines which are sensibly straight, 33 out of 69, were not tabulated as of either normal or abnormal curvature, but their other properties were tabulated under the normal branch. The results for Hglä have not been included at all, because its curve both rises and falls. In general the normal type of behavior preponderates, but the possibilities that have been discovered are so numerous that one would be prepared to admit that after extensive search probably representatives of every one of the divisions could be found. It is certainly evident that the mechanism of polymorphic transitions in different substances does not possess any one notable characteristic which expresses itself in a common type of behavior on all the transition lines, as is the case for melting. Two significant features of the table call for comment. In the first place, abnormal curvature means that the factor by which the change of volume is multiplied to give the change of internal energy becomes smaller at higher pressures. This factor is called by some writers the internal pressure, and is taken as a measure of the internal cohesion. It is at first surprising that this cohesion should become less as the substance is compressed so as to occupy less volume. It is difficult to imagine the possibility of such an effect in a substance composed of spherical molecules. The effect must be due to the configu-

174

BRIDGMAN.

Tation of the molecules and the location of the centers of force — when the new modification is formed the centers of force are torn farther apart, but the geometrical centers come closer together. In the second place, the number of cases in which the compressibility is abnormal cannot but be significant; there are 17 abnormal cases against 10 TABLE

XIV.

SUMUARY OF BEHAVIOR OF TRANSITION L I N E S .

Ν. 34

Ν. Δν Normal

Ab.

1

8

I 7

4

4

4

5

1

1

2

2

18 Ν.

Curvature Ab. Δ®