RECENT WORKS IN THE FIELD OF HIGH PRESSURES*)

P. W. Bridgman

Introduction.
Experimental technique. 1. Extension of the pressure range.
2. Measurement of pressure. 3. Various technical questions.
Mechanical effects. 1. Volume changes in gases.
2. Volume changes in liquids. 3. Volume changes in solids.
4. Phase transformations under pressure in one-component systems. 5. Phase changes under pressure in multicomponent systems. 6. Influence of pressure on viscosity. 7. Influence of pressure on elastic constants. 8. Influence of pressure on plastic flow and similar phenomena. 9. Various mechanical effects of hydrostatic pressure.
Influence of pressure on thermal effects.
Electrical effects of high pressure.
Magnetic effects at high pressure.
Optical effects of high pressure.
Influence of pressure on chemical reactions.
Influence of pressure on biological effects.

INTRODUCTION

The aim of the present review is to summarize works in the field of high pressures published since the appearance in 1930 of my book The Physics of High Pressure**) up to June 1945.

Activity in this field, as in many other fields of physics, is increasing. The number of papers published during the last fifteen years is approximately equal to the total number of articles printed during the entire preceding history of this question.

Activity is increasing at both ends of the pressure scale. On the low-pressure side, industrial applications—for example, the cracking of petroleum to obtain gasoline—have stimulated intensive study of the properties of gas mixtures and gas reactions at pressures up to several hundred atmospheres. On the other hand, it has become possible to carry out quantitative measurements at pressures of 100,000 atmospheres, which constitutes a fivefold increase in comparison with the quantitative measurements carried out fifteen years ago.

*) P. W. Bridgman, Rev. of Modern Physics 18, No. 1, 1 (1946). Translation by D. Gamburg and D. Tsiklis, edited by Prof. I. Krichevsky.
**) P. Bridgman, Physics of High Pressures, Russian translation, ONTI, Moscow, 1935.

Any division of pressure into “low” and “high” is to some extent arbitrary. We shall, naturally, not touch upon phenomena connected with vacuum; by “high” pressure is meant a pressure higher than atmospheric.

We shall, however, confine ourselves to phenomena that can be successfully investigated only with close attention to questions of experimental technique, which means the use of especially strong metal vessels and the adoption of measures to prevent leaks.

In other words, we leave outside the scope of our consideration the region where one can make do with sealing wax and glass capillaries. Roughly speaking, the pressures that interest us are measured in thousands of atmospheres. This means that we shall not dwell in detail on such phenomena as, for example, critical phenomena, which for most substances lie within a few hundred atmospheres. On the other hand, there are certain phenomena whose study may be carried out up to a thousand atmospheres, but which, nevertheless, because of one circumstance or another, have so far been investigated only up to a few hundred atmospheres. We shall devote attention to such phenomena in our survey.

Despite the increasing activity in the field of high pressures, this work has until now been concentrated in a comparatively small number of centers, since the average laboratory does not possess the special equipment necessary for carrying out investigations in this field.

During the last fifteen years several new centers have appeared in which work with high pressure is being conducted. Michels’s laboratory in Amsterdam, which in 1930 was relatively young in this field, has produced a considerable number of works, in which a significant number of researchers took part. The range of pressures in these works is several thousand kg/cm², and their most characteristic feature is high precision and an ingenious improvement of experimental technique.

About fifty works have come from Basset’s laboratory in Paris, and only two of them belong to the period before 1930.

These works are little known to our physicists; many of the communications are very short, and a considerable majority of the works are qualitative rather than quantitative in character. Basset’s work usually has a certain industrial orientation. Apparently, the initial aim of the research was an attempt to synthesize diamond, as a result of which these works had industrial support, and a number of the papers published by him are devoted to this question. Basset was also interested in the production of apparatus and issued a catalogue of apparatus which he can supply for research in the field of high pressures. In addition, in fourteen of his works, mostly with collaborators, a qualitative investigation of various biological phenomena is given. The most remarkable feature of the work is the magnitude of the pressure

…achieved in his experiments. One of his most recent articles describes apparatus in which he succeeded in attaining pressures of \(100\,000\ \mathrm{kg/cm^2}\). There is a brochure, issued without a date, probably a private publication by Basset, summarizing all his publications up to 1942. It was printed by Imprimerie Moderne de Dreuk 9, Grande Rue Dreuk (Paris?) under the title: “Description of a laboratory for scientific investigations at ultra-high pressures up to \(100\,000\ \mathrm{kg/cm^2}\), and a summary of the scientific works of James Basset.”

Activity in the field of high pressures in Russia is evidently great; however, it is difficult to find details of the work. It is known that there is a laboratory intended primarily for investigations at high pressures, and a certain number of articles published in Russian journals have reached us.

However, it should not be thought that our present information is in any way complete. At present there are no indications that results have been achieved there in the experimental field which would surpass the capabilities of the technique described by me in 1931.

In England, Imperial Chemical Industries carried out a series of serious investigations of chemical reactions under pressure and published the results of many investigations conducted at pressures of \(12\,000\ \mathrm{kg/cm^2}\).

In our country the most significant new works have been investigations in the field of geophysics at Harvard, undertaken by the Geophysical Committee and directed during the first several years by Zisman, and beginning in 1933 by Francis Birch. The research program included, along with other questions, the application of pressures up to \(12\,000\ \mathrm{kg/cm^2}\) in combination with high temperature to problems of geophysical interest. About twenty-five articles have already appeared concerning various pressure effects. The work of Griggs at Harvard (some of it commissioned by the Geophysical Committee) also to a considerable extent concerns the application of high pressures to geophysical problems.

At Pennsylvania State University, Dow founded a high-pressure laboratory, which has carried out about twenty works, chiefly concerning the influence of pressures up to \(5000\ \mathrm{kg/cm^2}\) on changes in the volumes and viscosity of various hydrocarbons and oils of industrial significance.

On the West Coast, intensive work financed by the American Petroleum Institute is being carried out in Pasadena and is associated mainly with the names of Sage, Reamer, Olds, and Lacey.

Investigations are being conducted of the viscosity and volume changes of various hydrocarbons and their mixtures, which have important industrial significance, at pressures of several hundred \(\mathrm{kg/cm^2}\).

The field of high pressures is attracting the attention of industry, and some industrial laboratories have begun to work in this direction; however, it is probably still too early to set forth the details of their work.

Of the laboratories that were active in 1930, the Geophysical Laboratory in Washington, the laboratory of the Massachusetts Institute of Technology headed by Keyes, and my laboratory at Harvard are continuing their activity.

Of those investigators who had distinguished themselves before 1930, Tammann, who contributed greatly to the development of this field of science, brought his activity to a close, having carried out after 1930 only a few works, and died at the end of the period described in the present report. The same applies to Ernst Cohen in Utrecht, who completed his activity and published during the period described only those works.

Poulter, who had been very active in this field and had carried out a number of important works at the end of the preceding period and in the first few years of the present period, turned to other work, although there are indications that recently he is again returning to this field of work.

The order of presentation here will be approximately the same as in my book. We shall first touch upon the technique of work with high pressure, then the mechanical effects of pressure, of which volume effects are the simplest and therefore the most important, then phase transformations, thermal, electrical, magnetic, and optical effects, and finally we shall turn to chemical and biological phenomena.

TECHNIQUE OF EXPERIMENT

We shall touch here only upon questions of general technique, transferring the description of special apparatus to the corresponding sections.

1. EXPANSION OF THE PRESSURE RANGE

Probably the first problem that we encounter in the technique of experiment is the expansion of the pressure scale. The obvious and direct method of expanding the pressure scale is the use of stronger materials. In this direction two important improvements have been achieved. At present, for the manufacture of steel vessels there are steels with an ultimate strength of approximately \(24\,500\ \mathrm{kg/cm^2}\) and an elongation of several percent, as compared with steels with an ultimate strength of \(17\,500\ \mathrm{kg/cm^2}\), used earlier. For pistons of high-pressure apparatus, carboloy is now used, with a crushing strength under atmospheric conditions, according to my measurements, of up to \(67\,000\ \mathrm{kg/cm^2}\), and, according to Basse, up to \(75\,000\ \mathrm{kg/cm^2}\). This is more than twice the pressure that steel can withstand without excessive plastic deformation. An even more important advantage of carboloy is its very low elastic deformation; moreover, the elastic constant of carboloy is three times greater than that of steel. Carboloy, however, under ordinary conditions is not so strong under

tension, like steel, and, moreover, it is exceptionally brittle. It can be used for the manufacture of high-pressure vessels, unlike the manufacture of pistons, only in special designs that give carboloy a noticeable superiority over steel.

The pressures that can be attained at the present time are obtained by using the best of the materials indicated above, in combination with special design methods.

The traditional methods of such design of high-pressure apparatus are the use of compressive reinforcing rings, wire wrapping, and cold working (autofrettage). These methods are described in detail in three English books: by Macrae¹, Tong², and Newitt³.

Fig. 1. Schematic representation of the method of automatically creating external compression of a vessel.

By such methods it is possible to achieve almost a doubling of the normal resistance of vessels. The upper limit is then determined by the attainment of the yield point under compression of the inner wall of the vessel under the imposed external stress. A more advantageous method of external reinforcement is such an external strengthening of the vessel as would vary in proportion to the increase of the internal pressure, instead of applying the maximum external reinforcement when the internal pressure is zero.

A simple way of realizing these conditions is to make the outer surface of the vessel under pressure conical, and to press the entire vessel into a conical recess in the outer supporting block.

The simplest method of carrying out this task is to let the pressure applied to the piston itself press the inner vessel into the block, as is shown in Fig. 1.

By this method⁴, in a vessel having an internal diameter of 0.25 inch, I attained pressures of 50,000 kg/cm² and measured a number of volume effects. However, there are geometrical limitations of this pro—

of this method of obtaining pressure, and it is better to increase the external stress independently of the increase of pressure on the piston. I had two arrangements for fulfilling this condition: in one of them⁵ the external pressure was directed opposite to the internal pressure. With such apparatus it was possible to attain pressures of 30,000 kg/cm² with an internal vessel diameter of 0.5 inch and a length of 6 inches. An electrode could be introduced into this vessel and complex electrical measurements carried out.

According to another method⁶ both pressures act in one and the same direction; the external strengthening device serves as a multiplier for increasing it; here volume measurements can be performed up to 50,000 kg/cm². With this method the apparatus is preserved considerably longer and undergoes considerably less plastic deformation than in the case of creating the external pressure by the piston itself. 50,000 kg/cm² is the limit that can be attained by this method of strengthening. The steel vessel is at the limit of failure because of the possibility of rupture in a plane perpendicular to the axis, owing to the flow effect. The vessel is also destroyed in a radial plane by the usual rupture under internal pressure.

To attain still higher pressure, a more complicated external strengthening of the vessel had to be arranged. I did this⁷ by immersing the entire high-pressure apparatus, both piston and cylinder, in a liquid that can be hydrostatically compressed to a pressure of 30,000 kg/cm².

The advantage of this method of strengthening is greater than a simple increase of the hydrostatic pressure, since the physical properties of the steel and carboloy from which the apparatus is made improve under the action of hydrostatic pressure. Under pressure of the order of 20,000 kg/cm² to 30,000 kg/cm², carboloy loses its brittleness⁸, permits elastic deformation under compression, and can withstand the internal stresses developing in a high-pressure vessel, so that under these conditions it becomes suitable for making not only the piston but also high-pressure vessels.

Under such conditions carboloy considerably surpasses steel, both because of its higher strength and because of its significantly smaller elastic deformation. With apparatus of this kind, shown in Fig. 2, many volume measurements were made up to pressures of 100,000 kg/cm². Thus, still higher pressures can be attained; however, under these conditions it is difficult to carry out volume measurements owing to the slow creep of the piston material.

Independently of these works, successes were achieved in parallel in the geophysical laboratory under the direction of Goranson⁹; however, these works were interrupted during the war. Goranson also strengthened his high-pressure vessels by immersing them in a liquid on which

acted as hydrostatic pressure. Only a preliminary communication on this was published. The supporting pressure was lower than in my experiments (not above \(20\,000\ \mathrm{kg/cm^2}\)), and Goranson reports that he reached a pressure of \(200\,000\ \mathrm{kg/cm^2}\). Until this work has been confirmed, I think that the pressure of \(200\,000\ \mathrm{kg/cm^2}\) indicated by Goranson is exaggerated. In the first stage of my work I myself estimated the pressure attained too highly.

The difficulties in determining pressure lie in friction, for which it is difficult to introduce a correction and which obscures the result. Goranson was to some extent predisposed to overestimate the pressure he had achieved, since he proceeded from his theory of the influence of supporting pressure on the temporary resistance

Fig. 2. Piezometer for volume measurements up to \(100\,000\ \mathrm{kg/cm^2}\). The diagonally hatched regions are made of carboloy; the horizontally hatched regions are the substance whose compression is being studied. The unhatched material is steel.

to compression by the piston. According to his theory, the temporary resistance under compression increases at a greater rate beyond several thousand \(\mathrm{kg/cm^2}\), turning into infinity, according to one of his diagrams\(^{10}\), at a pressure of less than \(15\,000\ \mathrm{kg/cm^2}\).

My direct measurements\(^{8}\), up to a pressure of \(30\,000\ \mathrm{kg/cm^2}\), did not reveal such a phenomenon; the increase in temporary resistance under compression remains approximately linear with supporting pressure over the entire range of pressures, with a maximum increase in temporary stress under compression of \(25\%\). The same qualitative picture was found for certain strong minerals, such as quartz, sapphire, tourmaline, and diamond. These direct measurements of temporary resistance under compression as a function of the true hydrostatic supporting pressure also refute the results of some earlier observations by Griggs, who supposed that he had established the acceleration in the growth of temporary resistance expected by Goranson.

I myself, in my preliminary observations, was convinced that Griggs’s conclusion was confirmed.

The explanation in all cases is evidently the obscuring effect of friction. The chief reason why a pressure of \(100\,000\ \mathrm{kg/cm^2}\) and more can be attained in a carboloy vessel probably lies not in any real increase of strength under the supporting pressure, but, rather, in the loss of brittleness and the increase of viscosity—effects observed at high pressure in many materials.

Basset[^11] published a description of apparatus for reaching \(100\,000\ \mathrm{kg/cm^2}\). He did not use supporting pressure, but instead cooled the apparatus in liquid air, and in doing so found that the temporary resistance to compression of a carboloy piston increased from \(75\,000\) to \(100\,000\ \mathrm{kg/cm^2}\). The high-pressure vessel was made by Basset of carboloy and had a compressing steel jacket. However, he published no results obtained with this apparatus; apparently, the range of application of this apparatus is limited.

At such high pressures the stresses are only approximately hydrostatic, since practically every liquid, or even gas, freezes; and one should expect differences in stress of the order of the plastic shear stresses in solids. The shear strength of metals such as tin or indium, however, amounts to only a few hundred \(\mathrm{kg/cm^2}\), even under high pressure, so that the stresses may be sufficiently close to hydrostatic pressure.

With appropriate equipment it is possible to attain considerably greater stresses in compression over very small areas that are reinforced by massive, less strongly compressed surrounding regions. In this way a higher, approximately hydrostatic pressure can be attained by placing small pieces of plastic metal between opposing parts of the apparatus. With a short truncated cone of carboloy, pressed into a massive carboloy block and reinforced by a supporting hydrostatic pressure of \(30\,000\ \mathrm{kg/cm^2}\), I reached a pressure of \(425\,000\ \mathrm{kg/cm^2}\) with small pieces of materials such as graphite or sulfur. Only qualitative permanent changes could be detected under these conditions, but so far only negative results have been obtained.

At times it seemed that the field of studying phenomena at high pressures and very low temperatures must be exceptionally difficult, owing to the reason indicated above, namely the freezing of any pressure-transmitting substances. Lazarev and Kan[^12], however, gave a method by means of which certain results can also be obtained in this field. They froze water in a closed vessel at a temperature of \(-30^\circ\) or \(-40^\circ\) and obtained a maximum pressure of about \(2000\ \mathrm{kg/cm^2}\), determined by the transition between ice I and II. At

at the temperature of liquid air the transition ceased, but they found that, when the apparatus was cooled to the temperature of liquid hydrogen, a large part of the pressure attained at the higher temperature was preserved.

The pressure was determined from the elastic increase in the external dimension of the high-pressure vessel.

In this way the authors measured the effect of pressure up to \(1700\ \text{kg}/\text{cm}^2\) on the superconductivity of tin and indium wires enclosed in ice. This method, evidently, can be applied to the investigation of phenomena that occur without significant changes in volume. The authors express the opinion that, by using the effect of the phase transformation of bismuth, it is possible to attain pressures of the order of \(10\,000\ \text{kg}/\text{cm}^2\) at low temperatures.

LITERATURE

1. A. E. Macrae, His Majesty’s Stationary Office, London, 1930. Stresses in metals and their application to autofrettage of cylinders and the manufacture of guns.

2. Harold Tongue, Chapman and Hall Ltd., London, 1934. Design and construction of high-pressure installations.

3. Dudley M. Newitt, Clarendon Press, Oxford, 1940. Design of high-pressure installations and properties of liquids and gases under high pressure.

4. P. W. Bridgman (a), Phys. Rev. 48, 893 (1935). Polymorphism, chiefly of the elements, up to \(50\,000\ \text{kg}/\text{cm}^2\).
   (b) Proc. Nat. Acad. Sci. 23, 202 (1937). Polymorphic transformations of inorganic compounds up to \(50\,000\ \text{kg}/\text{cm}^2\).
   (c) Proc. Am. Acad. Arts Sci. 72, 45 (1937). Polymorphic transformations of 35 substances up to \(50\,000\ \text{kg}/\text{cm}^2\).
   (d) Proc. Am. Acad. Arts Sci. 72, 207 (1938). Approximate values of the compressibility of 14 substances up to \(45\,000\ \text{kg}/\text{cm}^2\).

5. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 72, 157 (1938). Resistance of 19 metals under pressure up to \(30\,000\ \text{kg}/\text{cm}^2\).

6. P. W. Bridgman, Phys. Rev. 57, 237 (1940). Compression up to \(50\,000\ \text{kg}/\text{cm}^2\).
   Proc. Am. Acad. Arts Sci. 74, 21 (1940). Compression of 46 substances up to \(50\,000\ \text{kg}/\text{cm}^2\).

7. P. W. Bridgman, Phys. Rev. 57, 342 (1940). New high pressures attained in a complex apparatus;
   Phys. Rev. 60, 351 (1941). Compression and polymorphic transformations of seventeen elements up to \(100\,000\ \text{kg}/\text{cm}^2\);
   Proc. Am. Acad. Arts Sci. 74, 425 (1942). Pressure–volume relation for seventeen elements up to \(100\,000\ \text{kg}/\text{cm}^2\).

8. P. W. Bridgman, J. Appl. Phys. 12, 461 (1941). Investigations of the limit of usable pressure.

9. R. W. Goranson and E. A. Johnson, Phys. Rev. 57, 845 (1940). Production of high hydrostatic pressures.

10. R. W. Goranson, Sci. Mo. 51, 524 (1940). Physical effects of extreme pressures.

11. James Basset, J. de phys. et rad. [8] 1, 121 (1940). Attainment of very high pressures between \(50\,000\) and \(100\,000\ \text{kg}/\text{cm}^2\).

12. B. Lazarev and Ya. Kan, ZhETF, 14, 439 (1944). Measurements at low temperatures and high pressures.

2. MEASUREMENT OF PRESSURE

The basic method of measuring pressure, which serves as the standard for other methods, consists in measuring the force acting on a piston of known area.

The instrument par excellence for this purpose is a free-piston manometer. Careful investigations have been carried out in the range of several thousand kg/cm². The principal problem is the introduction of corrections for the change in the cross section of the piston that occurs as a result of the application of pressure. For an accuracy of the order of 0.1% and even better, it is sufficient to take the effective area as the mean of the areas of the piston and cylinder and to calculate approximately the deformations of the piston and cylinder from the theory of elasticity. A rigorous calculation of the deformations cannot be made because of the uncertainty in the external forces arising from leakage of liquid between the piston and the cylinder, and methods that check the calculations become necessary.

Free-piston manometers found very wide application in the laboratory of Keyes at the Massachusetts Institute of Technology, where over the course of more than twenty years fifty measuring instruments were used. They were described in the communications of Keyes¹³˒¹⁴.

Careful investigations were carried out by Beattie and Edel¹⁵ and by Beattie and Bridgman¹⁶. These investigations concerned the effect of pressure on the calibration constant and the permanent changes in the calibration constant due to a shift of the internal equilibrium in steel, and the influence of the viscosity of the oil on the accuracy of the manometer reading. The construction developed by them is such that there are no changes in the calibration constant up to 600 kg/cm². Permanent changes up to 0.1% were found only after ten years had elapsed, with a decrease to one fifth of this value in the following ten years. No effect of the viscosity of the oil was found. Michels¹⁷ used a column of mercury for calibration up to 40 kg/cm² and achieved a reproducibility of 1/50,000 and a sensitivity of 0.5 g for a total load of 300 kg. Ebert¹⁸ determined the dependence of the cross section of the piston on pressure up to 3000 kg/cm² by comparison at every 500 kg with a multiplying device, which was sealed in such a way that the correction for deformation of the multiplier was given simply by measuring its internal diameter. The cross section of Ebert’s manometer increased by \(2 \cdot 10^{-6}\) for each kg/cm².

There are no new determinations of any fixed pressure points, made with a free-piston manometer above 5000 kg/cm², and the principal value obtained by me, 7640 kg/cm² for the freezing point of mercury at 0°C, remains without any confirmation from other investigators. In Russia, Vereshchagin and Aleksandrov¹⁹ in the main reproduced my free-piston manometer ...

them and used it to measure pressures up to \(10\,000\ \mathrm{kg/cm^2}\). However, instead of carrying out with it an independent determination of the freezing point of mercury, they took my value of 7640 for calculating the effective cross section.

It still seems to me that very serious technical difficulties will arise in the use of a free-piston manometer for pressures considerably greater than the \(13\,000\ \mathrm{kg/cm^2}\) achieved in my initial calibration. Accurate pressure measurement in a range higher than this will probably require sealing the piston with the greatest possible reduction of friction. This can be accomplished by improving the mechanical design, in particular by reducing the thickness of the seal to a minimum. In this way I determined the transition parameters between bismuth I and II at \(30^\circ\mathrm{C}\), which are conveniently taken as a permanent pressure point. The difference between the readings on increasing and decreasing the pressure, i.e. under the doubled influence of friction, was \(3\%\); the mean value should have had a considerably higher accuracy. As the mean value of 5 determinations ranging between 25 380 and \(25\,465\ \mathrm{kg/cm^2}\), I adopted for the pressure of the transition of bismuth I to II at \(30^\circ\mathrm{C}\) the value \(25\,420\ \mathrm{kg/cm^2}\). The accuracy should be of the order of \(0.1\%\). In carrying out these determinations it is necessary to introduce a correction for the deformation of the cylinder by the internal pressure.

The correction was determined directly by measuring the change of the internal diameter under pressure with the aid of a contact sliding along the wire, instead of by a risky calculation of these deformations from the theory of elasticity.

If permanent pressure points have been established by a free-piston manometer or its equivalent, then it is possible to construct secondary manometers that are more convenient to use and in which the leaks inherent in free-piston manometers are eliminated. The change in the resistance of manganin remains the most convenient and is often used for constructing a secondary manometer. In the field of studying other alloys suitable for the same purpose, little work has been done. Schulze \(^{21}\) proposed using an alloy of \(15.9\%\) Mn, \(84.1\%\) Ag, having a higher pressure coefficient and a low temperature coefficient; however, apparently this alloy was not seriously tested.

There are a number of investigations on the best designs of the parts of a manganin manometer, especially those ensuring the stability of the zero. Michels and Lenssen \(^{22}\) investigated manganin manometers up to a pressure of \(3000\ \mathrm{kg/cm^2}\); the coils were wound freely along grooves on a porcelain cylinder. The accuracy of the readings was \(0.05\ \mathrm{kg/cm^2}\) at pressures of about \(1000\ \mathrm{kg/cm^2}\), up to 0.1 between 1000 and 1500, and up to 0.2 between 1500 and 2500. A small pressure hysteresis can be eliminated by stabilization with a pressure 25% higher than that used in the experiments. The resistance of their manganin was appreciably not—

linearly with pressure, the coefficient changing within the limits of 0.25% for each 1000 kg/cm².

Adams, Goranson, and Gibson²³ compared a manganin manometer with a free-piston manometer up to 1300 kg/cm² and studied its behavior after it had been subjected to a pressure of 12,000 kg/cm². It is important to achieve the absence of stresses in the winding. As a consequence of improper winding, deviations in the constancy of the coefficient of up to 2.5% per 1000 kg/cm² may arise. Their coil gave exactly linear readings over the interval they investigated. If, after its stabilization, the coil is subjected to random temperature changes of the order of 60°, permanent changes in the pressure coefficient may amount to as much as 0.4%. Aleksandrov and Vereshchagin²⁴ studied a manganin manometer up to a pressure of 10,000 kg/cm²; they found that the stresses caused by coating the wire with a light layer of insulating enamel, in addition to the usual loose silk insulation, are not harmful.

In my own work I have used manganin manometers for about ten years at pressures up to 30,000 kg/cm². I found that under these conditions the zero is appreciably more stable than it had been earlier, when the pressure did not exceed 12,000 kg/cm². The reason for this is probably a combination of the greater effectiveness of stabilization carried out at higher pressure with a changed procedure of temperature stabilization, in which the coil is held alternately at 140° and −80° for several days. When the range is increased from 12,000 to 30,000 kg/cm², the most important point is the preservation of the linear dependence. From the character of the change in the electrical resistance of a whole series of different metals up to high pressure, I found that some deviation from linearity for manganin cannot be significant. The linear dependence could be checked quantitatively with the aid of the constant pressure point at the transition of bismuth, and it was found²⁰ that the pressure obtained by linear extrapolation of the straight line obtained at 7640 kg/cm² gives no error greater than 1% up to pressures of 30,000 kg/cm². Calibration of a manganin manometer at two points is therefore sufficiently accurate for determining its behavior up to 30,000 kg/cm². The term of the second degree varies from coil to coil. Even in those cases where adjacent parts are cut from a single hank of wire, a separate calibration of each of the pieces is necessary. It must be emphasized that this favorable result was established only for my grade of manganin. It is quite possible that manganin from other sources may show a considerably greater deviation from linear dependence, as indicated by Michels’s results at lower pressures. The deviation from linear dependence for my manganin had an unexpected direction—the extrapolated pressure was too low.

LITERATURE

1. Frederick G. Keyes, Ind. Eng. Chem. 23, 1375 (1931). High-pressure technology.
2. Frederick G. Keyes, Proc. Am. Acad. 68, 505 (1933). Methods and techniques used in carrying out the Massachusetts Institute of Technology program for investigating the \(P—V\) relation for water up to \(460^\circ\mathrm{C}\).
3. Jones A. Beattie and Walter L. Edel, Ann. d. Physik, 11, 633 (1931). On measurements with a piston manometer. I. The effect of pressure on the manometer constant.
4. J. A. Beattie and O. C. Bridgman, Ann. d. Physic 12, 827 (1932). On measurements with a piston manometer. II. The effect of aging and the viscosity of oil on the manometer constant; the relation between the true and effective diameter of the piston.
5. A. Michels, Proc. Roy. Acad., Amsterdam 35, 994 (1932). Calibration of a piston manometer in absolute units.
6. H. Ebert, Phys. Zeits. 36, 385 (1935). Investigations up to a pressure of \(5000\ \mathrm{kg}/\mathrm{cm}^2\).
7. L. Vereshchagin and B. Aleksandrov, Zhurn. Tekhn. Fiz. 9, 348 (1939). A manometer for \(10\,000\ \mathrm{kg}/\mathrm{cm}^2\) of the free-piston type.
8. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 74, 1 (1940). Measurement of hydrostatic pressure up to \(30\,000\ \mathrm{kg}/\mathrm{cm}^2\).
9. Alfred Schulze, Chem. Zeits. 67, 228 (1943). Materials used for manometers and resistance thermometers.
10. A. Michels and M. Lenssen, J. Sci. Inst. 11, 345 (1934). An electric manometer for pressures up to 3000 atm.
11. L. H. Adams, R. W. Goranson and R. E. Gibson, Rev. Sci. Inst. 8, 230 (1937). A manganin manometer for high pressures.
12. B. Aleksandrov and L. Vereshchagin, Zhurn. Tekhn. Fiz. 9, 843 (1939). An electric resistance manometer for high pressures.

3. VARIOUS TECHNICAL QUESTIONS

In addition to these basic advances, a considerable number of improvements were carried out which had a more specialized field of application. Ramsauer \(^{25,26}\) discussed quantitatively the question of the possibility of obtaining very high pressures over short intervals of time by means of sharp compression when firing a projectile fitting tightly into a tube. Calculations indicate very high pressure values; however, an attempt at experimental realization of this method shows that carrying out measurements is a very difficult task, and nothing useful was obtained or measured.

Adams \(^{27}\) gave a description of comparatively simple apparatus for pressures of \(12\,000\ \mathrm{kg}/\mathrm{cm}^2\) or higher, in which the Poulter seal with an inverted rubber stopper at the end of the piston is used. This sealing method undoubtedly has a quite real field of application. Boyd \(^{28}\) and Schmidt \(^{29}\) described a method for measuring small pressure differences at very high pressure. Their instrument is essentially a U-shaped tube filled with mercury, with a corresponding contact arrangement for determining the difference of levels in the two chambers of the tube. Poulter with

with his collaborators, published several papers,^30–33 in which he described further details of his method of inserting ends without a seal, also described in my book.

The puzzles and contradictions in the behavior of inserted ends at the present time apparently are clear, and arise from the penetration into the glass, under pressure, of such liquids as water, or other similar liquids—for example, alcohol—that are in contact with the end. As a result, destruction of the glass occurs; whereas, if the pressure-transmitting medium is oil, no dissolving action is observed, and in this case a considerably higher pressure can be attained. Oil, however, has the unfavorable property of freezing. To avoid the dissolving action, Poulter proposed and made a diamond window, which successfully withstood the action of pressure at \(21\,000\ \mathrm{kg/cm^2}\), transmitted by means of a medium of alcohol and water. Roebuck and Miller^34 made and used transparent bakelite tubes, which made it possible visually to observe the interior of a high-pressure vessel up to a pressure of \(400\ \mathrm{kg/cm^2}\).

For general technique one should consult the books of Tong and Newitt, which may be recommended for reference. There is also a series of papers devoted to special questions of technique. Craze^35 in 1930 wrote an article entitled “Technology of High Pressures and High Temperatures,” devoted to the industrial application of pressure in large apparatus, weighing up to \(200\ \mathrm{t}\) and operating under pressures up to \(1000\ \mathrm{kg/cm^2}\). Berthelot^36 in 1941 wrote about the design of high-pressure autoclaves, and also about their industrial application in the same pressure range. Berthelot dealt chiefly with the creep effect at temperatures up to \(500^\circ\mathrm{C}\). Basset’s trade catalogue, undated (but not later than 1937),^37 gives many photographs of high-pressure apparatus designed by Basset. The same author^38 in 1934 described laboratory apparatus for obtaining pressures up to \(25\,000\ \mathrm{kg/cm^2}\) at the Congress of Industrial Chemistry. Keyes^13 published an article, “High-Pressure Technique,” describing mainly the apparatus used in his laboratory for investigations of the properties of steam at pressures up to \(1000\ \mathrm{kg/cm^2}\).

Korndorff^39 published a review article on the apparatus of a modern high-pressure laboratory, in which he describes some of the Russian improvements.

In addition to this, there is a considerable number of other publications on high-pressure technique that do not require detailed explanation. These papers will be cited by me chronologically. Tong^40 described the high-pressure equipment of the chemical laboratory at Teddington; the laboratory apparatus is intended for work with gases and liquids under pressures up to \(1000\ \mathrm{kg/cm^2}\). Basset^41 described apparatus for work with gases at pressures up to

6000 kg/cm²; this description was repeated to one degree or another in his later papers. Adkins ^42 described apparatus for studying reactions in the liquid phase up to pressures of 400 atmospheres and temperatures of 250°. Wartenberg ^43, with his four collaborators, found that the resistance of glass tubes to internal pressure remains practically just as high up to the transformation temperature as at room temperature.

Washburn ^44 described a double-bomb method for accurately determining \(P — V — T\) data and gave a simple method for the precise measurement of high pressure without using a precision manometer; the method is limited to pressures for which deviations from the ideal-gas law are not substantial. Wertheim ^45 published a review article describing compression methods for pressures from 42 to 37,500 kg/cm². Velbergen ^46 described a method of introducing electrical leads into a high-pressure vessel by means of a conical sleeve of Pyrex glass, accurately ground and inserted while hot. These leads withstand pressures up to 3000 atm and a temperature of 200°.

Beatty ^47 described in general terms apparatus used for measuring the compressibility of gases up to 500 atm and 325°. Frevel ^48 described a method of X-ray analysis of powders through the walls of a glass tube withstanding pressures up to 1000 kg/cm². Burnett ^49 described a method for carrying out precise determinations of compressibility without measuring volumes; the method consists in expanding gas from one vessel into another. It requires accurate pressure measurements with a dead-weight manometer and is suitable up to pressures of 125 atm.

Cohen and Lisso ^50 described a dilatometer for use under pressure, in which the volume was determined by measuring the resistance of a platinum wire in a capillary as the mercury rose, and used it to study transformations of tin up to 200 atmospheres.

Rebuc and Krem ^51 described a multistage tubular mercury manometer up to 200 atm with a measurement accuracy of 0.0014%. Cawsen ^52 investigated, with the aid of a special machine, the bursting strength of glass bottles under static and rapidly applied internal pressure up to 49 kg/cm².

The Journal of Scientific Instrument ^53 describes commercial apparatus of the firm Kipf en Zonen for obtaining pressures up to 1000 kg/cm² by heating a vessel in which one of the permanent gases has been condensed at the temperature of liquid air. Morey and Ingerson ^54 described the design of a stainless-steel bomb for experiments at several hundred atmospheres and 700°. Sage and Lacey ^55 described apparatus used in connection with carrying out the program of the American Petroleum Institute for studying the dependence \(P — V — T\) in gases and liquids at pressures up to 700 kg/cm² and 600°.

A distinguishing feature of this methodology is a carefully developed method of checking and varying the weights in a manometer with a free-

with a piston. Bomshtein^56 discussed the design of valves for pressures up to 900 atmospheres.

Aristov^57 described a differential manometer for high pressures with magnetic transmission. Ipatieff and Munro^58 described a rotating apparatus that ensures mixing of the contents, which they used to determine the solubility of gases in liquids at pressures up to 75 atm. Vintish^59 gave a detailed calculation, based on the mathematical theory of elasticity, for the design of autofretted and multilayer steel vessels for pressures up to 10,000 kg/cm^2. Krupp^60 patented an alloy containing 2–4.5% Cr, 0.15–0.7% Mo, not more than 0.3% C, the remainder being iron, which is specially intended for the manufacture of high-pressure vessels, especially for the chemical industry.

REFERENCES

1. Carl Ramsauer, Phys. Zeits. 34, 890 (1933). On a new method for attaining very high pressures and temperatures.

2. Carl Ramsauer, Chem. Fabrik, 391–393 (1937). Technical limits of high pressure and vacuum.

3. L. H. Adams, Rev. Sci. Inst., 7, 174 (1936). Simplified apparatus for creating high hydrostatic pressure.

4. James H. Boyd, Jr., J. Am. Chem. Soc. 52, 5102 (1930). A manometer for measuring small pressure differences at high pressures.

5. E. Schmidt, VDI 80, 635 (1936). Measurement of small pressure differences at high pressures.

6. Thos. C. Poulter, Phys. Rev. 35, 297 (1930). A glass window withstanding pressures up to 30,000 atm.

7. Thos. C. Poulter, Phys. Rev. 40, 860 (1932). Apparatus for optical investigations at high pressures.

8. Thos. C. Poulter and Carl Benz, Phys. Rev. 40, 872 (1932). Lens effect in high-pressure windows.

9. T. C. Poulter and F. Buckley, Phys. Rev. 41, 364 (1932). Diamond windows withstanding very high pressures.

10. J. B. Roebuck and E. E. Miller, Rev. Sci. Inst. 10, 179 (1939). Inspection tubes for high pressure.

11. Norman W. Krase, Chem. Met. Eng. 37, 530 (1930). Technology of high pressures and temperatures.

12. Ch. Berthelot, Rev. Mét. 35, 13 (1941). Design of high-pressure apparatus. Strength of steel and design of high-pressure autoclaves.

13. James Basset, Paris, Materials and complete installation for high pressures. The James Basset installation for scientific or industrial research.

14. James Basset, 14th Congr. Chim. Ind., Paris, October (1934). Laboratory equipment for research at ultrahigh pressures up to 25,000 kg/cm^2.

15. B. A. Kornorf, Izvestiya Akad. Nauk SSSR, chemical series 6, 997 (1940). Apparatus of a modern high-pressure laboratory.

16. Harold Tongue, Inst. Chem. Eng. 8, 1 (1930). Chemical-engineering high-pressure equipment in the chemical research laboratory at Teddington.

1. J. Basset, Comptes Rendus 191, 928 (1930). Apparatus for experimenting with gases at pressures up to 60,000 kg/cm².

2. Homer Adkins, Ind. Eng. Chem. Anal. Ed. 4, 342 (1932). Apparatus for reactions in the liquid phase at elevated temperatures and pressures.

3. H. von Wartenberg, Zeits. Techn. Phys. 13, 479 (1932). Resistance of glass tubes to pressure at high temperatures.

4. Edward W. Washburn, Bur. Stand., J. Research 9, 271 (1932). A double-bomb method for precise determinations of the values \(P—V—T\) and a simple method for the precise measurement of high pressures.

5. F. E. Wertheim, Heating, Piping a. Air Conditioning 4, 469 (1932). Geometrical joints at pressures from 600 to 550,000 pounds/in².

6. H. J. Welbergen, J. Sci. Inst. 10, 247 (1933). A new method of insulating electrical leads in high-pressure apparatus.

7. James A. Beattie, Proc. Am. Acad. Arts Sci. 69, 389 (1934). Apparatus and method used for measuring the compressibility of several gases in the temperature interval from 0° to 325° C.

8. Ludo K. Frevel, Rev. Sci. Inst. 6, 214 (1935). Technique of x-ray investigations of substances at high pressures.

9. E. S. Burnett, J. Appl. Mech., December (1936). Determinations of compressibility without measuring volume.

10. E. Cohen a. van Lieshout, K. Akad. Amsterdam, Proc. 39, 586 (1936). Electrical dilatometer for use at high pressures.

11. J. R. Roebuck a. W. Cram, Rev. Sci. Inst., 8, 215 (1937). Mercury manometer for 200 atm.

12. Arnold Cousen, J. Soc. Glass Tech., Trans. 21, 187 (1937). Rupture testing of glass bottles.

13. J. Sci. Inst. 14, 34 (1937). Thermal compressor for pressures up to 1000 atm.

14. George W. Morey a. Earl Ingerson, Am. Min. 22, 1121 (1937). Vessel for use in hydrothermal investigations.

15. N. H. Sage a. W. N. Lacey, Am. Inst. Min. and Metal. Eng., Tech. Publ., No. 1127 (1939). Apparatus for studying the \(P—V—T\) relationship of liquids and gases.

16. E. I. Bomshtein, Khim. mashinostroenie 8, 10 (1939). Rational designs of closures for high-pressure apparatus.

17. G. E. Aristov, Zhurn. khim. prom. 16, 45 (1939). Differential high-pressure manometer with magnetic transmission.

18. V. N. Ipatiev a. G. S. Monroe, Science 95, 423 (1941). Apparatus for determining the solubility of gases at high pressures and high temperatures.

19. H. von Wintsch, Schweiz. Arch. angew. Wiss. Tech. 9, 81 (1943). Design of cold-drawn thick-walled high-pressure cylinders and tubes.

20. Krupp A.—G. Fried, German patent 737 678, June 10 (1943). Alloy withstanding high pressure.

MECHANICAL EFFECTS OF HIGH PRESSURE

1. VOLUME CHANGES IN GASES

Owing to necessity, most of the works devoted to this question are limited to pressures of several hundred kg/cm², and therefore a review of them goes beyond the scope of our principal interests. Consequently the substance of these works will be noted only briefly. The main centers

activity in this direction were concentrated in the laboratory of Michels in Amsterdam, at Keyes’ laboratory with his coworkers at the Massachusetts Institute of Technology, in the Fixed Nitrogen Laboratory in Washington, and in the group working under the program of the American Petroleum Institute in Pasadena. In this field a high accuracy was attained, and the various laboratories obtained concordant results. Of particular interest is the joint investigation of the isotherms of nitrogen up to 400 kg/cm² by Otto at the Reichsanstalt, on the one hand, and by Michels and Wouters in Amsterdam, on the other, where agreement of the values of \(PV\) to the fourth decimal place was achieved \(^{61}\).

The greatest activity was shown by Michels and his collaborators, who published seventeen papers \(^{62–78}\). The range of these studies was from 0° to 150° C and up to 3000 kg/cm². In this interval \(P—V—T\) data were obtained for hydrogen, deuterium, nitrogen, carbon dioxide, and ethylene.

In addition to this, methane was investigated up to a pressure of 400 kg/cm². The results of the measurements were given by power series with six or seven coefficients, computed by the method of least squares to the sixth significant figure.

Michels and Nederbragt also measured \(P—V—T\) for methane–ethane mixtures up to a pressure of 60 kg/cm².

The work at the Massachusetts Institute of Technology \(^{79–87}\) was usually carried out within the limits from 0° C to 200° C and 1000 kg/cm². Keyes published data for ammonia, while Beattie and his numerous coworkers investigated various hydrocarbons: ethane, propane, normal and iso-butane, heptane, and mixtures of ethane and normal butane. A large amount of data covers the regions of two-phase equilibrium or liquids. In the gas phase the equation of state of Beattie and Keyes reproduces the results well, and the constants for this equation are given for many substances.

The published works of the Fixed Nitrogen Laboratory appeared mainly at the beginning of the period described \(^{88–92}\). The usual range of investigation was 70° to 200° C, although in some cases a temperature of 300° C was reached, at pressures up to 1000 kg/cm². Data were published for hydrogen, helium, nitrogen, carbon monoxide, methane, and nitrogen–hydrogen mixtures.

The group working in Pasadena \(^{93–99}\), including Lacey, Olds, Reamer, and Sage, was mainly interested in industrial hydrocarbons. Their investigations were carried out up to 250° C and 700 kg/cm². They published data for methane, ethane, \(n\)-butane and mixtures methane—water, ethane—water, methane—\(n\)-pentane, methane—carbon dioxide, methane—decane, and \(n\)-butane—water. The data cover two-phase equilibrium and the region above the critical point.

There is a series of Russian works from various laboratories, chiefly concerning gases of industrial importance. Kazarnovskii \(^{100}\) investigated ammonia up to 1600 kg/cm² and 300° C and proposed

equation of state for gas mixtures. Russian works dealt chiefly with ternary mixtures.

Krichevskii and Markov \(^{101}\) investigated binary and ternary mixtures of hydrogen, nitrogen, and carbon dioxide up to \(500\ \mathrm{kg}/\mathrm{cm}^{2}\) and \(200^\circ\). Bolshakov and Lebedeva \(^{102}\) investigated ammonia—nitrogen—methane mixtures from \(-20^\circ\) to \(50^\circ\) and up to \(560\ \mathrm{kg}/\mathrm{cm}^{2}\). Kazarnovskii, Simonov, and Aristov \(^{103}\) investigated ammonia-nitrogen-hydrogen mixtures up to a pressure of \(1640\ \mathrm{kg}/\mathrm{cm}^{2}\) and \(300^\circ\mathrm{C}\), and Bolshakov and Eterman \(^{104}\) investigated hydrogen—nitrogen—methane mixtures from \(-30^\circ\) to \(250^\circ\) and up to a pressure of \(800\ \mathrm{kg}/\mathrm{cm}^{2}\).

Buchmann \(^{105}\), in Simon’s laboratory, investigated the isotherms of helium at \(13.5^\circ\) and \(20.4^\circ\mathrm{K}\) up to the freezing pressure, approximately \(2000\ \mathrm{kg}/\mathrm{cm}^{2}\). Three communications by Maron and Turnbull \(^{105-108}\) should be mentioned on an equation of state expressed in terms of the critical constants, which can reproduce the data cited above up to \(1000\ \mathrm{kg}/\mathrm{cm}^{2}\).

Finally, there are two works at somewhat higher pressure. Basse and Doping \(^{109}\) measured the volumes of hydrogen and nitrogen at \(0^\circ\mathrm{C}\) up to \(5000\ \mathrm{kg}/\mathrm{cm}^{2}\). Benedict \(^{110}\), in my laboratory, determined the volumes of nitrogen from \(-175^\circ\) to \(200^\circ\) and up to \(5800\ \mathrm{kg}/\mathrm{cm}^{2}\). Benedict’s data are undoubtedly more accurate than my own data, published earlier in my book. The difference in the values of the volume is of the order of \(1\%\). Benedict proposed an equation of state which represents his data with an error of \(0.14\%\). With the exception of this work by Benedict, there are no further additions to or repetitions of my measurements made in 1923 for five permanent gases up to a pressure of \(15000\ \mathrm{kg}/\mathrm{cm}^{2}\), apart from some of my own \(^{111}\). In determining the melting parameters of nitrogen and argon I made repeated measurements, as well as some new determinations of the initial data which had previously been adopted and which now made it possible to obtain the volumes of gaseous nitrogen up to pressures of \(6000\ \mathrm{kg}/\mathrm{cm}^{2}\) and at temperatures between \(-140^\circ\mathrm{C}\) and \(23.5^\circ\mathrm{C}\), and also to combine these data with the earlier data for argon in order to obtain absolute values of the volumes up to \(15000\ \mathrm{kg}/\mathrm{cm}^{2}\), whereas previously only differences of volumes had been known.

REFERENCES

1. J. Otto, A. Michels and H. Wouters, Phys. Zeits. 35, 97 (1934). Isotherms of nitrogen between \(0^\circ\) and \(150^\circ\) up to a pressure of \(400\ \mathrm{atm}\).

2. A. Michels, G. P. Nijhoff and A. J. J. Gerver, Ann. d. Phys. 12, 562 (1932). Isothermal measurements with hydrogen between \(0^\circ\) and \(100^\circ\mathrm{C}\) and up to a pressure of \(1000\ \mathrm{atm}\).

3. A. Michels, H. Wouters and J. de Boer, Physica [7] 1, 587 (1934). Isotherms of nitrogen between \(0^\circ\) and \(150^\circ\) and at pressures from 20 to \(80\ \mathrm{atm}\).

4. A. Michels and G. W. Nederbragt, Physica 2, 1000 (1935). Isotherms of methane between \(0^\circ\) and \(150^\circ\) and at densities between 19 and 53 amagat (pressure between 20 and \(80\ \mathrm{atm}\)).

1. A. Michels, C. Michels and H. Wouters, Proc. Roy. Soc. 153, 214 (1935). Isotherms of CO₂ between 70 and 3000 atm.

2. A. Michels and C. Michels, Proc. Roy. Soc. 153, 201 (1935). Isotherms of CO₂ between 0° and 150° and at pressures from 16 to 250 atm.

3. A. Michels and G. W. Nederbragt, Physica 3, 569 (1936). Isotherms of methane between 0° and 150 for densities up to 225 amagat; calculation of heat capacity, energy, and entropy in this same region. Isotherms of ethylene between 0° and 150° at pressures from 20 to 270 atm.

4. A. Michels, J. de Groot and F. Niesen, Physica 3, 346 (1936). Isotherms of ethylene between 0° and 150° at pressures from 20 to 270 atm.

5. A. Michels, H. Wouters and J. de Boer, Physica 3, 597 (1936). Calculation of the thermodynamic properties of nitrogen up to 3000 atm between 0° and 150°.

6. A. Michels, H. Wouters and J. de Boer, Physica 3, 585 (1936). Isotherms of nitrogen between 200 and 3000 atm and 0° and 150°.

7. A. Michels, A. Bijl and Mrs. C. Michels, Proc. Roy. Soc. 160, 376 (1937). Thermodynamic properties of CO₂ up to 3000 atm between 25° and 150°.

8. A. Michels and Mrs. C. Michels, Proc. Roy. Soc. 160, 348 (1937). Series for calculating the isotherms of carbon dioxide between 0° and 150° up to 3000 atm.

9. C. A. M. Michels-Veraart, Thesis, Amsterdam (1937). Some physical properties of compressed carbon dioxide.

10. A. Michels and M. Goudeket, Physica 8, 353 (1941). Compressibility of deuterium between 0° and 150° up to 3000 atm.

11. A. Michels and M. Goudeket, Physica 8, 347 (1941). Compressibility of hydrogen between 0° and 150° up to 3000 atm.

12. A. Michels and M. Goudeket, Physica 8, 387 (1941). Thermodynamic properties of hydrogen and deuterium up to 700 amagat between 0° and 150°.

13. A. Michels and M. Geldermans, Physica 9, 967 (1942). Isotherms of ethylene up to 3000 atm between 0° and 150°.

14. A. Michels and G. W. Nederbragt, Physica 6, 656 (1939). Isotherms of a mixture of methane—ethane at 0°, 25° and 50° up to 60 atm.

15. Frederick G. Keyes, J. Am. Chem. Soc. 53, 965 (1931). P—V—T data for ammonia up to 1000 atm at temperatures from 30 to 200°.

16. F. G. Keyes and S. C. Collins, Proc. Nat. Acad. Sci. 18, 328 (1932). Change of heat content with pressure, as a method of directly measuring van der Waals forces.

17. J. A. Beattie, C. Hadlock and N. Poffenberger, J. Chem. Phys. 3, 93 (1935). Compressibility and equation of state for gaseous ethane.

18. W. B. Kay, Ind. Eng. Chem. 28, 1014 (1936). Density of hydrocarbon gases and vapors at high temperatures and pressures.

19. J. A. Beattie, W. C. Kay and Joseph Kaminsky, J. Am. Chem. Soc. 59, 1589 (1937). Compressibility and equation of state for gaseous propane.

20. L. B. Smith, J. A. Beattie and W. C. Kay, J. Am. Chem. Soc. 59, 1587 (1937). Compressibility of liquid and gaseous normal heptane and equation of state for gaseous heptane.

21. J. A. Beattie, Su Gouq-Jen and G. L. Simard, J. Am. Chem. Soc. 61, 926 (1939). Compressibility of gaseous ethane in the high-density region.

22. J. A. Beattie, G. L. Simard and Su Gouq-Jen, J. Am. Chem. Soc. 61, 26 (1939). Compressibility and equation of state for gaseous normal butane.

23. J. A. Beattie, H. G. Ingersoll and W. H. Stockmayer, J. Am. Chem. Soc. 64, 548 (1942). Compressibility and equation of state for gaseous isobutane.

24. E. P. Bartlett, H. C. Hetherington, H. M. Kvalnes and T. H. Tremearne, J. Am. Chem. Soc. 52, 1374 (1930). Isotherms of carbon monoxide compressibility at temperatures from −70° to 200° and pressures up to 1000 atm.

1. H. M. Kvalnes and V. L. Gaddy, J. Am. Chem. Soc. 53, 394 (1931). Isotherms of compressibility of methane.

2. R. Wiebe, V. L. Gaddy and C. Heins, Jr., J. Am. Chem. Soc. 53, 1721 (1931). Isotherms of compressibility of helium for temperatures from −70° to 200° C and pressures up to 1000 atm.

3. W. E. Deming and Lola Shupe, Some physical properties of compressed gases. Phys. Rev. 37, 638 (1931). I — nitrogen; Phys. Rev. 38, 2245 (1931); II — carbon dioxide; Phys. Rev. 40, 848 (1932); III — hydrogen.

4. R. Wiebe and V. L. Gaddy, J. Am. Chem. Soc. 60, 2300 (1938). Compressibility of hydrogen and four mixtures of H₂ + N₂.

5. R. H. Olds, N. H. Reamer, B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 36, 282 (1944). Phase equilibrium in hydrocarbon systems: volumes of n-butane.

6. H. H. Reamer, R. H. Olds, B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 36, 956 (1944). Phase equilibrium in hydrocarbon systems: XLIV. Volumes of ethane.

7. H. H. Reamer, R. H. Olds, B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 36, 381 (1944). Phase equilibria in hydrocarbon systems: compositions of coexisting phases of the system n-butane—water in the three-phase region.

8. H. H. Reamer, R. H. Olds, B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 36, 88 (1944). Phase equilibria in hydrocarbon systems: methane—carbon dioxide in the gas region.

9. H. H. Reamer, R. H. Olds, B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 35, 790 (1943). Phase equilibria in hydrocarbon systems: composition of the dew point of the water—ethane system.

10. H. H. Reamer, R. H. Olds, B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 34, 1526 (1942). Phase equilibria in hydrocarbon systems: methane—decane system.

11. B. H. Sage, R. H. Olds and W. N. Lacey, Reprint Am. Pet. Inst. Chicago Meeting, November (1942). Enthalpy of gaseous hydrocarbon mixtures.

12. Ya. S. Kazarnovskii, Acta USSR 12, 513 (1940). Compressibility of ammonia at high temperatures and pressures.

13. I. R. Krychevskii and V. P. Markov, Acta USSR 12, 59 (1940).

14. P. E. Bolshakov and E. S. Lebedeva, Acta USSR 12, 501 (1940).

15. Ya. S. Kazarnovskii, G. B. Simonov and G. E. Aristov, ZhFKh 14, 774 (1940).

16. P. E. Bolshakov and A. Eterman, Acta USSR 14, 365 (1941).

17. Ernst Buchmann, Zeits. f. Phys. Chem., Abt. A., 163, 461 (1933). Isotherms of helium at low temperatures and high pressures.

18. S. H. Maron and D. Turnbull, J. Am. Chem. Soc. 64, 44 (1942). Thermodynamic properties of nitrogen at high pressures as analytical functions of temperature and pressure.

19. S. H. Maron and D. Turnbull, J. Am. Chem. Soc. 64, 2195 (1942). Equations of state for gases at high pressures, containing only critical constants.

20. S. H. Maron and D. Turnbull, Ind. Eng. Chem. 34, 544 (1942). Generalized thermodynamic properties of gases at high pressures.

21. J. Basset and R. Dupinay, Comptes Rendus 191, 1295 (1930). Compressibility of nitrogen and hydrogen up to a pressure of 5000 atm.

22. Manson Benedict, J. Am. Chem. Soc. 59, 2224 and 2233 (1937). P—V—T data for nitrogen at high densities. I. Results obtained with a balance piezometer. II. Results obtained by the moving-piston method.

23. P. W. Bridgman, Phys. Rev. 46, 330 (1934). Melting parameters of nitrogen and argon under pressure and the nature of the melting curve; Proc. Am. Acad. Arts Sci. 70, 1 (1935). Melting curves and compressibility of nitrogen and argon.

2. VOLUME CHANGES IN LIQUIDS

A. Pure Liquids

In this field comparatively little new work has been done, with the exception of some of my own. There are a certain number of acoustic measurements of the velocity of sound which make it possible to calculate compressibility; however, since in general they are applicable only at atmospheric pressure, we shall not consider them, although this is a good method for obtaining the initial adiabatic compressibility.

In the further account of the work, except for my own, chronological order is observed. Jessup[^112] measured the volume of fourteen petroleum oils between \(0^\circ\) and \(300^\circ\)C up to \(50\ \mathrm{kg/cm^2}\). The compressibility of different oils of the same initial density may vary within \(30\%\); however, compressibility is an almost single-valued function of the initial viscosity and density taken together. Tammann and Ruenbeck[^113] measured the volume of water between \(20^\circ\) and \(650^\circ\), and of ethyl ether and ethyl alcohol up to \(400^\circ\) and up to \(2500\ \mathrm{kg/cm^2}\), by the piston-displacement method. They confirmed the existence of a temperature maximum of thermal expansion (at constant pressure) at high pressures, which I had found. Růžička[^114], with his collaborators, determined the compressibility of four polynuclear cyclic compounds.

Smith and Keyes[^115] measured the compressibility of liquid mercury from \(30^\circ\) to \(300^\circ\) between 50 and \(350\ \mathrm{kg/cm^2}\). Dow[^116] measured in my laboratory, by my siphon method, which will be described later, the volume of six oils up to \(4000\ \mathrm{kg/cm^2}\) in the range from \(25^\circ\) to \(75^\circ\)C. The same method was applied by Dow and Fenske[^117] to the study of the compressibility of separate petroleum fractions.

Talbott[^118] applied the acoustic method for measuring adiabatic compressibility and used a Richards piezometer for determining the isothermal compressibility of a whole series of oils between \(0^\circ\) and \(80^\circ\)C up to a pressure of \(400\ \mathrm{kg/cm^2}\). MacLeod[^119] theoretically treated my measurements of the compressibility of liquids up to a pressure of \(12\,000\ \mathrm{atm}\) and, applying the van der Waals equation of state to the molecules themselves, reported that he had obtained an equation with three constants which reproduces my data. Tammann[^120] theoretically explained the anomalous behavior of liquid water by the presence of two different molecules of water. Russell and Gottell[^121] measured the volumes of liquid naphthalene up to its critical temperature, \(425^\circ\), and a pressure of \(400\ \mathrm{kg/cm^2}\). Under these conditions no decomposition of naphthalene is observed.

Bicar[^122][^123] carried out a careful investigation of the propagation of acoustic waves under pressures up to \(1000\ \mathrm{kg/cm^2}\) in an apparatus designed by Basse, with fourteen windows which made it possible to observe the system of standing waves. He investigated water and four

organic liquids. The acoustic absorption at 500 kg/cm² was twice as great as could have been expected from theoretical considerations taking into account the influence of pressure on viscosity. Kelsö and Felsing \(^{124}\) carried out studies of \(n\)-hexane and 2-methylpentane up to the critical point.

Dow and Fink \(^{125}\) summarized the above-mentioned measurements with petroleum and presented the result in analytical form. Felsing and Watson \(^{126}\) give values for the compressibility of liquid \(n\)-octane up to 300 kg/cm² at intervals of 25° between 100°C and 275°C. In a subsequent communication \(^{127}\) these authors gave the same data for 2,2,4-trimethylpentane.

From the following section on the compressibility of solutions, mention should be made of Gibson’s episodic work on determining the compressibility of a series of pure liquids, carried out up to a pressure of 1000 kg/cm².

My own work on the compressibility of liquids falls into two parts. First come the works on improving the new measurement technique up to 12,000 kg/cm², and second, the extension of the pressure range to 50,000 kg/cm².

The siphon or metal-bellows method was improved for measuring compressibility up to 12,000 atm. It had already been described in my book; however, its improvement came at the end of the period, and it had not been published anywhere at that time, so that its description may legitimately be included in this review \(^{128}\). My previous method of measuring compressibility was a simple piston-displacement method, whose advantage lay in its simplicity; however, this method suffered from certain shortcomings. Corrections for the transmitting medium could be larger than the entire measured effect. A correction for the change in volume of the transmitting medium when it passed from a vessel having one temperature into a vessel with another temperature was especially necessary in measurements of thermal expansion. In the new method the corrections are very small; the apparatus in which the measurements are made is at one temperature, and (a very important circumstance) the manometer can always be kept at room temperature, which eliminates the influence of temperature changes on the manometer constant and on the zero point. In addition, this method is more convenient and faster. In my opinion, this method is just as good as the moving-piston method; however, Goranson, in his review of the properties of water for the Handbook of Physical Constants of the Geological Society of America, prefers to use my earlier data for water, suspecting some deformation of the siphon. In the most unfavorable case, different determinations of the volume for one and the same liquid by both methods differed by 0.003. With this apparatus I determined the volumes of forty-five liquids between 0° and 95° and up to 12,000 kg/cm² (or up to the freezing pressure) \(^{128–131}\). These liquids were: normal and iso-pentane, \(n\)-hexane, 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane, 2,3-di-

methylbutane, n-octane, n-decane, benzene, monochlorobenzene, monobromobenzene, carbon tetrachloride, bromoform, i-propyl alcohol, n-butyl alcohol, n-hexyl alcohol, ether, water, mixtures of glycerin with water, ethylene glycol, trimethylene glycol, propylene glycol, dimethylene glycol, glycerin, tricresyl phosphate, triacetin, ethyl benzylmalonate, methyloleate, tricaproin, n-butyl phthalate, eigenol, i-octane, isoprene, triethanolamine, chlorides, bromides and iodides of normal propyl, butyl and amyl, octane-3,2-methylheptanol, 3,2-methylheptanol, 5,3-methylheptanol-1, and heavy water. These new measurements confirmed the two most important results of the earlier measurements, namely the change of sign of \((\partial^2 V/\partial T^2)_p\) with increasing temperature at constant pressure at pressures of several thousand kg/cm², and the fact that \((\partial P/\partial T)_v\) is not only a function of volume.

The experimental material makes it possible to study rather fully the effect of molecular substitutions. For discussion it is necessary to turn to the original papers. Here we shall mention the following most important points.

The difference in volumes between isomers tends to be erased at a pressure of 12,000 atm; however, the tendency is not universal, and there are even examples where the difference in volumes becomes more noticeable, showing that the peculiarities of molecular structure remain important even at such high pressures.

Glycerin stands out by having the smallest compressibility of all the organic compounds studied. Its small compressibility may be attributed to the three OH groups. In general, the greater the number of OH groups in the molecule, the smaller the compressibility. Oxygen in the molecule produces a similar, though somewhat smaller, effect of reducing the compressibility. Replacement of hydrogen by a halogen, as, for example, in monochlorobenzene or monobromobenzene, is accompanied by a noticeable decrease in compressibility. The molecular volume of heavy water is greater than that of ordinary water at all pressures and temperatures; the difference in volumes tends to become smaller at high temperature and high pressure. There are small differences which apparently lie outside the experimental errors. In general, all these liquids showed small differences characteristic of the individual liquid, as my earlier measurements had already shown. In the most recent measurements less attention was paid to this question. The temperature intervals were chosen wider, and often small deviations lying outside the limits of experimental error were deliberately smoothed out in processing the measurement results. When the theory of the liquid state is more developed, it will be necessary to return to this question anew and obtain exact data for the dependence of volume on structural features. This will evidently require considerably greater experimental effort than hitherto.

Let us now turn to my measurements¹³² up to 50,000 kg/cm². I carried them out by the method of the moving piston in a conical reinforced

from the outside in a vessel already described in the section on technique. Measurements were made at intervals of \(25^\circ\)—from \(25^\circ\) to \(175^\circ\)—with the following twenty-one substances: methyl, ethyl, \(n\)-propyl, \(i\)-propyl, \(n\)-butyl, and \(n\)-amyl alcohols; ethyl, \(n\)-propyl, and \(n\)-butyl bromides; ethyl acetate; \(n\)-amyl ether; chloroform; carbon disulfide; benzene; chlorobenzene; methylene chloride; ethylene bromide; cyclohexane; methylcyclohexane; \(p\)-xylene; and water. Owing to the experimental conditions, the usual piston packing was unsuitable, and these liquids were placed in lead capsules. In almost all cases freezing occurred within the portion of the temperature–pressure field, and both phases—the liquid and the solid—as well as the melting parameters were fully studied. Data including the solid phase and melting will be reported later. The most striking result for the liquid phase is the approach to an almost complete uniformity in the behavior observed for all liquids at the highest pressure. The maximum difference in the decrease of volume between 25,000 and 50,000 \(\mathrm{kg}/\mathrm{cm}^2\) was from 0.054 for methyl alcohol to 0.070 for \(n\)-butyl bromide, the volume under standard conditions being taken as unity. Differences of up to \(10\%\) in compressibility at the upper pressure limit were rare. Roughly speaking, compressibility varied inversely with pressure, and the volume may be expressed approximately by the formula \(V_0 - V = C \log(P/P_0)\), where \(P_0\) is approximately equal to 10,000. It should be noted that this formula is very similar to Tait’s formula, which Gibson found so satisfactory. However, neither this formula nor Tait’s formula can be applied at all pressures, since both require negative volumes at sufficiently high pressures. According to my formula, the pressure at which the volume changes sign is of the order of \(10^7\ \mathrm{kg}/\mathrm{cm}^2\), so that no substantial limitations are imposed on the practical use of the formula.

The accuracy of measurements at 50,000 atm is naturally not as great as at lower pressure, so that a number of very interesting questions cannot receive satisfactory answers. It appears definite that thermal expansion decreases continuously with increasing pressure, but to a noticeably lesser extent than does compressibility. The same qualitative relations were found over narrower pressure intervals. The course of thermal expansion has an obvious connection with the entropy at infinite pressure.

Finally, it is necessary to note a recent improvement in the technique for measuring the compressibility of liquids, which I have not yet published and which ensures rapid measurements at pressures of the order of 5000 \(\mathrm{kg}/\mathrm{cm}^2\), with an accuracy sufficient for many purposes. Compressibility is measured by a moving piston; the piston is packed only minimally and is mounted so that it can be rotated in order to reduce friction. The piston is moved by a large pis—

...with a similar reduced friction. The latter, in turn, is connected directly to a free-piston manometer. The high-pressure vessel is entirely filled with the liquid on which the measurements are to be made, and the corrections are small.

LITERATURE

1. R. S. Jessup, Bur. Stand. Research Pap. 244 (1930). Compressibility and thermal expansion of petroleum oils between 0° and 300° C.

2. G. Tammann and A. Ruhenbeck, Ann. d. Physik 13, 63 (1932). Specific volumes of water between 20° and 650°, of ethyl ether and ethyl alcohol between 20° and 400° at pressures from 1 to 2500 kg/cm².

3. L. Ruzicka, H. A. Boekenoogen and H. J. Eedman, Helv. Chim. Acta 16, 487 (1933). Hydrocarbons of ring XIII. Paraffin and the compressibility of compounds with mult-membered rings.

4. Leighton B. Smith and Fred. G. Keyes, Proc. Am. Acad. 69, 313 (1934). An investigation of water vapor. III. A. Compressibility of liquid mercury from 30 to 300°.

5. Richard B. Dow, J. Wash. Acad. Sci. 24, 516 (1934). \(P—V—T\) relation for six oils.

6. R. B. Dow and M. R. Fenske, Ind. Eng. Chem. 27, 165 (1935). \(P—V—T\) relation for fractions of one oil.

7. A. C. Talbott, Phil. Mag. 19, 1126 (1935). Velocity of propagation of waves in oil under pressure.

8. D. B. Macleod, Trans. Faraday Soc. 33, 694 (1937). Compressibility of liquids and a method for determining the compressibility of molecules.

9. G. Tammann, Zeits. f. anorg. allgem. Chemie, 235, 49 (1937). Anomalous dependence of the properties of water on temperature and pressure.

10. F. R. Russell and H. C. Hottel, Ind. Eng. Chem. 30, 372 (1938). Compressibility of liquid naphthalene.

11. P. Biquard, Comptes Rendus, 206, 897 (1938). Supersonic waves in liquids under pressure.

12. P. Biquard, Rev. d’acoustique 8, 130 (1939). Study of the velocity of propagation and absorption of sound in liquids under pressure.

13. E. A. Kelso and W. A. Felsing, J. Am. Chem. Soc. 62, 3132 (1940). \(P—V—T\) relation for \(n\)-hexane and 2-methylpentane.

14. R. B. Dow and C. E. Fink, J. Appl. Phys. 11, 353 (1940). Calculation of the physical properties of lubricating oils at high pressures. Part I. Density.

15. W. A. Felsing and G. M. Watson, J. Am. Chem. Soc. 64, 1822 (1942). Compressibility of liquid \(n\)-octane.

16. W. A. Felsing and G. M. Watson, J. Am. Chem. Soc. 65, 780 (1943). \(P—V—T\) relation for 2,2,4-trimethylpentane.

17. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 66, 185 (1931). Volume phase transitions as a function of pressure and temperature.

18. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 67, 1 (1932). \(P—V—T\) relation for several nonvolatile liquids.

19. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 68, 1 (1933). \(P—V—T\) relation for 15 liquids.

20. P. W. Bridgman, J. Chem. Phys. 3, 597 (1935). \(P—V—T\) relation for liquids and the phase diagram of heavy water.

21. P. W. Bridgman, J. Chem. Phys. 9, 794 (1941):
    a) Freezing and compression to 50,000 kg/cm²;
    Proc. Am. Acad. Arts Sci. 74, 399 (1942);
    b) Freezing parameters and compression of 21 substances to 50,000 kg/cm².

B. Mixtures of Liquids and Solutions

It is not easy to give a fully satisfactory scheme for the classification of systems with more than one component. In multicomponent systems we have a complex picture of separation into individual phases, which may be liquid or solid. If the separated phase is solid, the phenomenon may be described as solubility for one component or as melting for another component. The scheme of classification will be dictated to some extent by the interests and inclinations of the experimenter. If the chief interest lies in the homogeneous liquid phase, the question will be treated in this section; if, however, the interest lies in the separation of various phases, the question will be discussed later, after the phenomena of melting and polymorphic transformations in one-component systems.

The most extensive investigations of volume relations in homogeneous solutions, including solutions of solid substances, including salts, in liquids and of liquids in other liquids, were carried out at the Washington Geophysical Laboratory, chiefly by Gibson and Gibson and by Lefler[^133-142]. The pressure interval in most of these works is \(1000\ \mathrm{kg/cm^2}\). Until 1938 almost all measurements were made at \(25^\circ\); later the temperature interval was extended to \(100^\circ\mathrm{C}\). The experimental technique was considerably improved. The method is essentially Richards’ mercury injection piezometer. The piezometer was made of fused quartz, which eliminated inaccuracies caused by stresses in glass. The injection device was moved to the bottom, eliminating the necessity of a strictly monotonic increase of pressure. The injecting capillary was of small diameter, and the final stage of the injection process was controlled visually through suitably mounted windows. In this way inaccuracies caused by random changes in the size of the hanging mercury droplets were eliminated.

With this apparatus a decrease in volume could be determined with an accuracy of up to one thousandth. In connection with replacing glass by quartz in the manufacture of the piezometer, Gibson reported that the volume compressibility of glass is a function of its thermal treatment. The experimental material is very extensive. In 1938 Gibson indicated that 250 solutions had been measured, chiefly aqueous electrolyte solutions. Since then a considerable amount of data has been accumulated for various organic solvents. Along the way, the compressibility was determined for a series of pure liquids: water, carbon tetrachloride, ethylene glycol, methanol, aniline, nitrobenzene, bromobenzene, and chlorobenzene. The original articles give a detailed discussion of the theoretical significance of the results obtained. Two results of theoretical significance were obtained.

The first result is the broad applicability of Tait’s equation for the volumes of liquids as a function of pressure:

\[ V=V_0-C\log[(B+P)/B]. \]

This equation reproduces not only Gibson’s results for solutions up to a pressure of \(1000\ \mathrm{kg/cm^2}\), but also data for pure liquids up to a pressure of \(10\,000\ \mathrm{kg/cm^2}\). It is shown that the constants in the equation have a theoretical meaning. They are connected with internal repulsive and attractive pressures. It is shown that the internal attractive pressure is a function only of volume.

Further, there is a simple relation between the constants of the Tait equation for solutions and for pure components. The second result is the confirmation of Tammann’s thesis, practically without changes for aqueous solutions and with simple changes for nonaqueous solutions. This thesis consists in the fact that, in a solution, the solvent behaves like a pure solvent which, however, under the same conditions would be at a greater external pressure than the pressure on the solution.

The difference between these two pressures is the so-called internal pressure (Binnendruck) of the solution.

The further exposition of the works, except for the works of the geophysical laboratory, is essentially chronological.

Permann and Urry \(^{143}\) investigated, up to \(200\ \mathrm{kg/cm^2}\) and up to \(80^\circ\mathrm{C}\), solutions of sucrose, urea, KCl, and \(\mathrm{CaCl_2}\) in water up to concentrations close to saturation. The Hildebrand formula was used, and the Debye–Hückel theory was confirmed. Gucker \(^{144,145}\) published two papers on the compressibility of solutions which are often cited. These are review articles that contain no new experimental material: the discussion is limited to the influence of pressures below \(200\ \mathrm{kg/cm^2}\). It was found that the apparent molar compressibility is a linear function of the square root of the concentration and also an approximately linear function of the molarity. Thomas and Permann \(^{146}\) investigated, at \(30^\circ\), up to \(100\ \mathrm{kg/cm^2}\), aqueous solutions of KCl, KBr, KI, \(\mathrm{CaBr_2}\), \(\mathrm{SrBr_2}\), \(\mathrm{BaBr_2}\), ACOH, and HCOH. Debye published a theoretical paper in which the decrease in the compressibility of solutions is connected with an increase in the concentration of water adjacent to the ions, caused by electrostatic forces. The effective pressure in water near an ion was estimated at approximately \(50\,000\ \mathrm{kg/cm^2}\). Scott, Obenhaus, and Wilson \(^{148}\) carried out, by Richards’ method, measurements up to \(300\ \mathrm{kg/cm^2}\) of aqueous solutions of the chlorides and bromides of lithium, Na, and K, and of the iodides of Na and K, for half the concentration range of each solution. Scott and Wilson \(^{149}\) discussed the theoretical significance of the measurement results. In the measurements, deviations from linearity were found for lithium in the opposite direction from that observed for the other alkalis. They found their results compatible with the idea that the solubility limit is reached when the compressibility of the dissolved substance becomes equal to

compressibility of crystalline salt. Lannman and Meier^150 measured, at 25°, by Richards’ method, up to 300 kg/cm², three concentrations of each solution of the following substances: LiCl, NaCl, KCl, LiOH, NaOH, KOH, HCl, acetic acid, and potassium acetate. They also determined the compressibility of glacial acetic acid. They confirmed Gucker’s conclusions concerning the linear dependence between the apparent molar compressibility and the square root of the concentration. Bridgman and Dow^151 measured, by the siphon method, up to 8000 kg/cm², the compressibility of aqueous solutions of three amino acids: glycine, α-aminobutyric acid, and δ-aminocaproic acid, at five concentrations up to 2.5 N at 25° and 75°. The pressure limit of 8000 atm was determined by the solubility limit. These measurements are apparently the only ones for this type of substance. Noticeable deviations from linearity were found. The most important result was that at low pressures the apparent compressibility of the acid in solution is positive, whereas in all other known cases the apparent compressibility is negative. In the light of Tammann’s hypothesis this should mean that in solutions of these acids water behaves like pure water under negative pressure. Brander^152,153 published two theoretical investigations, using for this purpose mainly the old Tammann data up to 3000 kg/cm². A relation was found between the coefficients in the equations for solutions and for pure water, and Tammann’s hypothesis was confirmed. Scott and Bridger^154,155 published two papers on aqueous solutions of LiCl, LiBr, and Ca(NO₃)₂, up to supersaturated concentrations, at 35° and up to 300 kg/cm². The lithium salts showed some anomalies. Certain propositions put forward by Masson, as well as by Redlich and Rosenfeld, are inapplicable. Sage and Lacey^156, in carrying out part of the program of the American Petroleum Institute, made measurements on liquid mixtures of butane and “crystal oil” up to 200 kg/cm², and also calculated from volumetric data a number of thermodynamic parameters. Krichevsky^157 carried out a theoretical investigation as a result of which, on the basis of Born’s data, a formula was derived for the dependence of the partial molar volume on pressure, and its application was given for infinitely dilute aqueous solutions of NaCl and K₂SO₄ up to 3000 kg/cm².

LITERATURE

1. R. E. Gibson, J. Am. Chem. Soc. 56, 4 (1934). Concentration and compressibility of aqueous solutions.

2. R. E. Gibson, J. Am. Chem. Soc. 57, 284 (1935). Influence of the concentration and nature of the dissolved substance on the compressibility of certain aqueous solutions.

3. R. E. Gibson, J. Am. Chem. Soc. 57, 1551 (1935). Compressibility and specific volume of aqueous solutions of resorcinol and methanol at 25° and the behavior of water in these solutions.

4. R. E. Gibson, J. Am. Chem. Soc. 59, 1521 (1937). Compressibility of solutions of salts in water, glycol, and methanol.

1. R. E. Gibson, Sci. Mo. 46, 103 (1938). The nature of solutions and their behavior under high pressures.

2. R. E. Gibson and O. H. Loeffler, J. Phys. Chem. 43, 207 (1939). Dependence of \(P\)-\(V\)-\(T\) in solutions.
   I. Observations on the behavior of solutions in benzene and some of its derivatives.

3. R. E. Gibson and O. H. Loeffler, J. Am. Chem. Soc. 61, 2515 (1939). Dependence of \(P\)-\(V\)-\(T\) in solutions.
   II. Energy–volume coefficients for aniline, nitrobenzene, bromobenzene, and chlorobenzene.

4. R. E. Gibson and O. H. Loeffler, J. Am. Chem. Soc. 61, 2877 (1939). Dependence of \(P\)-\(V\)-\(T\) in solutions.
   III. Some thermodynamic properties of mixtures of aniline and nitrobenzene.

5. R. E. Gibson and O. H. Loeffler, J. Am. Chem. Soc. 63, 898 (1941). Dependence of \(P\)-\(V\)-\(T\) in solutions.
   V. Energy–volume coefficients for carbon tetrachloride, water, and ethylene glycol.

6. R. E. Gibson and O. H. Loeffler, J. Am. Chem. Soc. 63, 2287 (1941). Dependence of \(P\)-\(V\)-\(T\) in solutions.
   VI. Apparent and partial volumes of sodium bromide dissolved in glycol, and energy–volume coefficients of solutions at various pressures and temperatures.

7. E. P. Perman and W. D. Urry, Proc. Roy. Soc. 126, 44 (1929). Compressibility of aqueous solutions.

8. Frank T. Gucker, Jr., J. Am. Chem. Soc. 55, 2809 (1933). Compressibility of solutions. I. Apparent molar compressibility of strong electrolytes.

9. Frank T. Gucker, Jr., Chem. Rev. 13, 111 (1933). Apparent molar heat capacity, volume, and compressibility of electrolytes.

10. W. G. Thomas and E. P. Perman, Proc. Roy. Soc. 146, 641 (1934). Compressibility of aqueous solutions. Part III.

11. P. Debye, Zanger-Festschrift (Rascher a. Cie, 1934), p. 877. Compressibility of ionic solutions.

12. A. F. Scott, V. M. Obenhaus and R. W. Wilson, J. Phys. Chem. 38, 931 (1934). Compressibility coefficients of solutions of nine alkali halides.

13. A. F. Scott and R. W. Wilson, J. Phys. Chem. 38, 951 (1934). Compressibility and apparent volumes of salts in solutions.

14. E. H. Lanman and B. J. Mair, J. Am. Chem. Soc. 56, 390 (1934). Compressibility of aqueous solutions.

15. P. W. Bridgman and R. B. Dow, J. Chem. Phys. 3, 35 (1935). Compressibility of three amino-acid solutions.

16. E. Brander, Soc. Sci. Fenn. Comm. Phys. Math. 8, 17 (1935). Influence of pressure and temperature on the volume change accompanying electrolytic dissociation.

17. E. Brander, Soc. Sci. Fenn. Comm. Phys. Math. 9, 1 (1936). Compressibility of aqueous solutions.

18. A. F. Scott and G. L. Bridger, J. Phys. Chem. 39, 1031 (1935). Compressibility and apparent volume of salts in solution. II.

19. A. F. Scott and G. L. Bridger, J. Phys. Chem. 41, 461 (1936). Apparent volumes and compressibilities of dissolved substances in solutions. Part III.

20. B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 28, 106 (1936). Phase equilibria in hydrocarbon systems. X. Thermodynamics of mixtures of butane and “crystal-oil.”

21. I. R. Krychevskii, Acta USSR 8, 181 (1938). Partial molar volumes of strong electrolytes at high pressures.

3. VOLUME CHANGES IN SOLIDS

Systematic investigations devoted to this question, represented by more than one or two papers, belong to the geophysical laboratory in Washington, at Harvard—at first to Zisman, and during the greater part of the period described—to Birch, and also to me. In general it must be said that only the use of pressures of the order of thousands of atmospheres can give here acceptable accuracy, instead of the hundreds of atmospheres that are suitable for obtaining the same accuracy in the case of gases and liquids. In what follows, individual works will be described first. Only one radical innovation appeared in measurement technique. In 1939 Jacobs\(^{158}\) measured the lattice constant of copper and aluminum by X-rays when the metals were under a hydrostatic pressure of \(4500\ \mathrm{kg}/\mathrm{cm}^2\), and was able to obtain the cubic compressibility of the substance. The measurements were carried out by the Debye–Scherrer method. A miniature camera was mounted entirely in a vessel filled with a pressure-transmitting medium. Gaseous helium served as such a medium; its absorption of X-rays, even at such high pressure, did not constitute an obstacle.

The X-rays passed into the camera through beryllium windows. For the mean compressibility of copper in this pressure interval Jacobs obtained a value lower by \(0.26 \times 10^{-7}\) than my data, obtained by the volumetric method for a polycrystalline substance, and for aluminum lower by \(0.46 \times 10^{-7}\). The first of the results mentioned lies within the errors of the method, the second does not. Jacobs thought that the discrepancy is real in both cases and that it can probably be explained by a difference in compressibility between the grains of the crystal and the intercrystalline cement, the compressibility of the latter being greater. Jacobs also developed and first applied the X-ray technique for investigations of polymorphic transformations under pressure. This question will be discussed later. Müller\(^{159}\) in 1941 carried out X-ray measurements on a series of normal hydrocarbons subjected to a pressure of \(1500\ \mathrm{kg}/\mathrm{cm}^2\). The substance was placed in a thin-walled steel or beryllium vessel, made by pressing powders, and the X-rays passed through the walls of the vessel. By this method it was possible to obtain the linear compressibility parallel and perpendicular to the hydrocarbon chains. In the direction perpendicular to the chain, the linear compressibility varied within the limits from \(3\) to \(12 \cdot 10^{-12}\ \mathrm{cm}^2/\mathrm{dyn}\), but in the direction of the chains it was less than \(3 \cdot 10^{-13}\). In 1935 Frevel\(^{160}\) described a technique for investigating substances under pressure by X-rays. According to this method, the substance together with a liquid is placed in a thick-walled capillary, and the pressure is developed upon heating. Frevel did not measure compressibilities by this method, but solved the inverse problem, estimating the pressure developed from the displacement of the lines and known compressibilities. He obtained a pressure somewhat less than \(1000\ \mathrm{kg}/\mathrm{cm}^2\). The X-ray method in his

in its present state of development does not make it possible to use it at very high pressures or to obtain sufficiently accurate data for answering such questions as the change of compressibility with pressure; however, apparently it contains possibilities within it, and work in this direction should be continued.

Let us now turn to other individual works. Tammann and Elinghaus^161 measured the volumes of glasslike selenium, salol, and rosin in the region of their softening from \(10^\circ\) to \(70^\circ\) and up to \(2000 \text{ kg}/\text{cm}^2\). At pressures somewhat above \(1000 \text{ kg}/\text{cm}^2\) the isotherms intersect. This means that above this pressure the volume at first decreases with increasing temperature, passing through a flat minimum. In discussing these results the conclusion was drawn that the volume of a glass may depend on the pressure under which its solidification takes place. One should recall the result obtained by Gibson, that the compressibility of the glass of his piezometer depended on the heat treatment. Scott^162 at the Bureau of Standards measured the compressibility and the increase of volume between \(10^\circ\) and \(85^\circ\) up to \(800 \text{ kg}/\text{cm}^2\) for a series of rubbers containing from 3 to 31% sulfur. The method consisted in visual observation of the change in length through Poulter windows. The compressibility decreases with increasing sulfur content; the range is from \(21 \cdot 10^{-6}\) to \(66 \cdot 10^{-6}\) (the pressure is expressed in \(\text{kg}/\text{cm}^2\)). A large change of compressibility with pressure was found, considerably larger than had previously been found by Adams.

The most important of the episodic works is that of Ebert^163 on the absolute determination of the linear compressibility of a number of metals up to \(3000 \text{ kg}/\text{cm}^2\). The change in length was observed in a microscope through windows. As preliminary preparation for this work an investigation was carried out with a free-piston manometer, already described in the section on technique. The accuracy was sufficient to give the term with the second power in the change of volume as a function of pressure. Determination of this term was one of the principal aims of the investigation. The measurements were made on single crystals of metals of the cubic system: iron, aluminum, gold, lead, and silver; on hexagonal magnesium in three orientations; and on polycrystalline copper, manganin, and steel. In general, the absolute compressibility which he obtained for single crystals was slightly less than mine, as was also the second-degree term obtained by him. For polycrystalline copper exact agreement was observed for both terms. Ebert, like Jacobs, is inclined to see a real difference between single-crystal and polycrystalline materials and believes that, if this factor is taken into account, there is complete agreement between his work and mine in both the first- and second-degree terms. It should be pointed out, however, that I have recently changed my second-degree term, so that the agreement has proved not to be as close as it might have seemed.

Megaw and Simon^164 determined the compressibility of solid hydrogen and deuterium at \(4.2^\circ\text{K}\) up to \(100 \text{ kg}/\text{cm}^2\). The mean compressibility of the first

is \((5.0 \pm 0.3)\cdot 10^{-4}\) and for the latter \((3.3 \pm 0.7)\cdot 10^{-4}\) (pressure in kg/cm²). A very rapid change of compressibility with pressure was found, the initial values being twice as high as the mean ones. Bartolomé\(^{165}\) determined the compressibility of solid hydrogen and deuterium at their triple point; for the former it is 2.3 times greater than for the latter. Lyman and Parks\(^{166}\) determined the compressibility of glassy glucose at 24° to 25 atm. It was equal to \(18.8\cdot 10^{-4}\) (pressure in atmospheres). Basset\(^{167}\) measured the compressibility of graphite up to 20,000 kg/cm² at intervals of 5000 and obtained an average compressibility of \(4.41\cdot 10^{-6}\) in the interval 1—5000 kg/cm² and \(1.90\cdot 10^{-6}\) between 15,000 and 20,000 kg/cm². Comparing these data with my measurements, one may say that the absolute compressibilities obtained by him are considerably higher and their decrease with increasing pressure is much more rapid.

In the geophysical laboratory in Washington, Adams and Gibson\(^{168}\) measured, by means of a moving piston, the compressibility of one specimen of hard rubber and two specimens of soft rubber up to 12,000 kg/cm². They found that the total decrease in volume amounted to from 16 to 20%. The change of compressibility with pressure was very large, with a rapid fall of compressibility being observed in the first part of the pressure interval. On the whole it was found that the volume relations in rubber are in many respects similar to those for a liquid. Adams\(^{169}\) discussed the application to geophysical questions of the most probable values of the compressibility of phenolite and its change with pressure up to 15,000 kg/cm². Adams and Gibson\(^{170}\) measured, up to 12,000 kg/cm², the compressibility of Pyrex, quartz glass, obsidian, duralumin, \(NH_4NO_3\), \(K_2SO_4\), \(Na_2SO_4\), and n-butyl ether. Garanson\(^{171}\) discussed the elastic properties of rocks under pressure, dealing chiefly with Zisman’s results. He came to the conclusion that the method of linear compressibility for materials such as rocks is not as good as the measurement of volume compressibility by the moving-piston method, which is used almost exclusively in the geophysical laboratory.

The work at Harvard in connection with the geophysical program was carried out mainly by the method of linear compressibility. In this case a sliding contact was used, and the change in the resistance of a wire was determined with a potentiometer, as I had done in my earlier work. The first measurements were made by Zisman\(^{172—174}\) for fifteen representatives of rocks at room temperature and pressures up to 1000 kg/cm². A large initial compressibility was discovered, which rapidly decreases and approaches an asymptotic value. Very great differences were found, especially for the more porous rocks, depending on whether the pressure-transmitting medium penetrated into the pores or acted only on the surface, i.e., whether the specimen was “covered” or “uncovered.”

Later Birch clarified the question of the correct method of measuring the compressibility of rocks for geophysical purposes (they must be “covered”), and the linear method gives satisfactory results,

if the rock is sufficiently fine-grained) and considerably improved the measurement technique. He constructed apparatus for attaining a pressure of \(10\,000\ \mathrm{kg/cm^2}\), maintaining the entire cylinder at a temperature of \(500^\circ\mathrm{C}\). If the heating furnace is mounted inside the high-pressure vessel, measurements can be carried out at higher temperatures at the same pressures, as had already been done in the geophysical laboratory some time earlier.

Birch improved the method for measuring linear compressibility under the conditions just mentioned, the specimen being mounted in the heated cylinder. The change in length under pressure was transmitted by means of a rigid connection passing through a connecting tube into another vessel, at room temperature, where the displacement was measured. Nitrogen served as the transmitting medium for the high temperature at which the experiments were performed. Birch and Dow\(^{175}\) determined the mean compressibility up to \(10\,000\ \mathrm{kg/cm^2}\) of lead at temperatures up to \(200^\circ\mathrm{C}\), of aluminum up to \(435^\circ\), of silica glass up to \(283^\circ\), and of diabase glass up to \(300^\circ\). My data for metals were approximately confirmed both as to the absolute value and as to the temperature coefficient for my narrower range of measurements. For silica glass they found the same anomalous sign for the second-degree term that I had found. Diabase glass had a maximum of compressibility at a temperature close to \(150^\circ\). Birch and Dow\(^{176}\) investigated six artificial glasses, lithographic stone, and diabase from Vinal Haven up to \(10\,000\ \mathrm{kg/cm^2}\) at temperatures up to \(300^\circ\) or \(400^\circ\). The anomalous decrease in the compressibility of glasses with increasing temperature ceases near \(200^\circ\), so that above this temperature the compressibility increases with temperature, with the exception of silicate glass, whose behavior remains anomalous over the entire temperature interval up to \(400^\circ\). There are indications that silicate glass also will become normal at a still higher temperature.

Of interest for geophysics are calculations of the probable velocity of seismic waves at depths down to \(40\ \mathrm{km}\) in the earth’s crust. My work on this question had several phases. In the first part of the period up to 1935, measurements up to \(12\,000\ \mathrm{kg/cm^2}\) at temperatures of \(30^\circ\) and \(75^\circ\), by the method of linear compressibility described in my book, were extended to a number of new substances and new types of materials. In 1931 such measurements were carried out for: NaF, BaF\(_2\), CdF, AlSb, CdTe, HgTe, TiNi, TiC, and single-crystal magnesia. The compressibility of NaF is in agreement with the compressibility of the other alkali halides, for which the data are thus now complete. In the series of halides of Ca, Sr, and Ba, however, the same regular increase was not observed. The compressibility of the other compounds is generally low, considerably less than could have been calculated from the rule of mixtures. In 1931\(^{178}\) I studied the effect of pressure on the well-known volume anomalies of NH\(_4\)Cl and NH\(_4\)Br and, incidentally, determined the volume of the first

to a pressure of \(12\,000\ \mathrm{kg/cm^2}\) at temperatures from \(0^\circ\) to \(75^\circ\), and the volume of the latter at temperatures from \(-72^\circ\) to \(75^\circ\). In 1932,\(^{179}\) I measured the volume of \(\mathrm{Ag_2O}\) within the usual limits of temperature and pressure. Here a very slow polymorphic transformation is observed, spread out over the whole pressure interval.

In 1932,\(^{180}\) results were published for eighteen compounds of the cubic system: \(\mathrm{CaS}\), \(\mathrm{SrS}\), \(\mathrm{BaS}\), \(\mathrm{MgO}\), \(\mathrm{CaO}\), \(\mathrm{Cu_2O}\), \(\mathrm{Al_2O_3}\), \(\mathrm{Sr(NO_3)_2}\), \(\mathrm{CuCl}\), \(\mathrm{CuBr}\), \(\mathrm{CuJ}\), \(\mathrm{LiJ}\), \(\mathrm{NaJ}\), \(\mathrm{RbCl}\), \(\mathrm{CsCl}\), \(\mathrm{CsBr}\), \(\mathrm{CsF}\), and \(\mathrm{CsJ}\). The specimens for a number of such measurements were prepared from pressed powders, owing to the difficulty of obtaining these substances in another form. The powders were pressed under a pressure of \(20\,000\ \mathrm{kg/cm^2}\) at a temperature of \(450^\circ\mathrm{C}\) and, after this operation, appeared at first sight to be compact and homogeneous. I subsequently found, however, that it is practically impossible to press a powder in such a way as to obtain the same compressibility as in a perfectly homogeneous substance (a single crystal). The magnitude of the effect depends on the substance; for a substance such as \(\mathrm{NaJ}\), it is impossible to detect any difference between the compressibility of the pressed powder and that of the single crystal, but for \(\mathrm{MgO}\), which was later obtained in the form of a single crystal, the best pressed powder I could obtain gave a compressibility, roughly speaking, twice as great as that of the single crystal. I found this effect important even for so seemingly innocent a substance as lead.

In 1933,\(^{181}\) I published results in the same pressure range for the elements \(\mathrm{Cb}\), \(\mathrm{Rh}\), \(\mathrm{Ru}\), \(\mathrm{Cr}\), \(\mathrm{As}\), and \(\mathrm{Be}\), and for the compounds: gulonolactose (single crystal, along three axes), rhamnose (single crystal, three axes), sucrose (single crystal, four axes), \(\mathrm{MnCl_2}\), \(\mathrm{ZnCl_2}\), \(\mathrm{Al_2O_3}\), and \(\mathrm{Cu_5Cd_8}\), three gold—silver alloys, three iron—tungsten alloys, three tungsten—cobalt alloys, and a ternary alloy of iron, tungsten, and cobalt. It is known that a number of these substances, especially the alloys, exhibit various phenomena connected with a shift of internal equilibrium when the temperature changes, and it could be expected that pressure would cause similar changes. Indeed, a number of the substances listed showed anomalies of various types; some of them were reversible and belonged to transitions of the second kind or of higher order, and some possessed hysteresis. Thus an enormous field has been opened to investigation, and, when theory makes progress, it will be necessary to obtain more systematic data. I myself have not found occasion to return to this question. Among the other substances described in this article, the element chromium deserves special mention. It has noticeable volume anomalies; below \(0^\circ\mathrm{C}\) its compressibility increases with increasing pressure—an unusual effect, which among other substances is most sharply manifested in quartz glass. The anomaly is manifested in chromium of high purity.

My last work in the range of \(12\,000\ \mathrm{kg/cm^2}\) was published in 1935,\(^{182}\) and dealt mainly with intermetallic compou-

...of which the following were measured: Ag₅Cd₈, Ag₅Zn₈, Cu₅Cd₈, Cu₅Zn₈, Cu₃₁Zn₈, CuZn, AgCd, AuZn, AgZn, Cu₅Sn, Ag₂Al, Mg₃Al, Mg₂Al, Mg₂Pb, MgZn₂, SbSn, AuSb₂, Sb₂Tl. In addition, germanium, LiF₂, Ag₂S, PbSe, PbTe, Ag₂SO₄, 4NH₃, and basalt glass were investigated. In intermetallic compounds, in many cases pressure hysteresis was found, as well as other small anomalies, discontinuities, and sometimes creep. The compressibility in almost all cases is noticeably less than could have been calculated by the rule of mixture according to the components. This indicates a large internal pressure caused by chemical affinity. In this article some compressibility values published before 1925 have been corrected, since we discovered an error in calculating the old power term in the transition from linear compressibility to volume compressibility.

In 1935[^183] the results of my first serious attempts to extend the pressure range considerably beyond the usual 12,000 kg/cm² were published. These first attempts did not include radical changes in technique; the best grades of steel that had appeared on the market were used, and the apparatus was simplified, made as a single piece, with only one hole running along the axis of the cylinder. After numerous experiments with apparatus of this kind, it became evident that it would not permit a sufficient expansion of the pressure range, as a result of which there was no point in putting up with frequent and unexpected ruptures and the inevitable destruction of the inner part of the apparatus. Some results, however, were obtained with this apparatus as well. The electrical resistance of certain materials was measured, which seemed especially interesting to measure at high pressure (this will be indicated later); furthermore, the volumes of three alkali metals, Li, Na, and K, were measured as functions of pressure and temperature in the range from 0° to 95° and up to 20,000 kg/cm². Of special interest was the dependence of thermal expansion on pressure. Two important deviations from the usual relations for thermal expansion were found in the case of these three alkali metals. First, the decrease of thermal expansion with increasing pressure is greater than the decrease of compressibility, contrary to the usual behavior. Second, the expansion curves intersect with increasing pressure, so that at high pressure K is the least, and Li the most, expansible. This reversal of expansibility is similar to the reversal of the order of melting points already described in my book, and probably is connected with it. The decrease of thermal expansion for these metals is so great that the approach of the entropy to zero at infinite pressure, which has often been suspected on thermodynamic grounds, seems very improbable. If one assumes that the rate of decrease of entropy with increasing pressure remains constant at ever-increasing pressures and equal to the value it has at 20,000 kg/cm², then the entropy of potassium, for example, will not become zero before 450,000 kg/cm². In fact...

same matter, the rate of decrease of entropy at a pressure of \(20\,000\ \mathrm{kg/cm^2}\) itself falls rapidly with increasing pressure.

My subsequent attempts to attain higher pressures were connected with fundamental changes in technique—with the use of such external strengthening of the cylinder as increases with the growth of pressure. This strengthening could be effected in two ways: by partial strengthening of the external cylindrical surface, most simply carried out by making the vessel of a somewhat conical form instead of a strictly cylindrical one, and by complete external strengthening by immersing the vessel in a liquid under hydrostatic pressure. Both of these methods make it possible to extend the former range of \(12\,000\ \mathrm{kg/cm^2}\). One type of apparatus makes it possible to carry out precise and delicate measurements up to \(30\,000\ \mathrm{kg/cm^2}\) instead of the former \(12\,000\ \mathrm{kg/cm^2}\); with the other type of apparatus, measurements are possible which are less precise, but over a broader range; at present these measurements are almost exclusively volumometric.

The first measurements of compressibility by the new method were published in 1938[^184]. The compressibility of a number of the most compressible solids was measured up to a pressure of \(45\,000\ \mathrm{kg/cm^2}\) at room temperature. These substances were: Li, Na, K, Rb, Cs, Ca, Sr, Ba, In, Sn, Pb, S, NaCl, and \(\mathrm{CO_2}\) (at \(-80^\circ\) and \(0^\circ\) up to \(35\,000\ \mathrm{kg/cm^2}\)). The measurements were made by the moving-piston method in a conical vessel with one stage of external strengthening. The compressibility of the alkali metals proved to be in good agreement with the values derived theoretically on the basis of wave mechanics, as will be reported later, and in all cases an entirely acceptable extrapolation from \(20\,000\) to \(45\,000\ \mathrm{kg/cm^2}\) could be carried out by means of the semiempirical formula just derived by Murnaghan.

Subsequent volume measurements were published in 1940[^185]; their purpose was to bring precise measurements up to pressures of \(30\,000\ \mathrm{kg/cm^2}\). An important question here is the change of compressibility with pressure. The accuracy of experimental measurements, other things being equal, is proportional to the square of the pressure interval. Theory was able to give the change of compressibility with pressure, and theoretical physicists were not satisfied with my quantitative measurements, which, in their opinion, were too high, especially for the less compressible substances. For substances of the iron type, my second-order term, as was thought, was 10 to 100 times too large. The compressibility of most substances was measured in comparison with iron, so that the first step in checking this question was to determine the compressibility of iron in the range up to \(30\,000\ \mathrm{kg/cm^2}\). This involved, first of all, establishing fixed pressure points and determining the deviations of the manganin manometer from exact linearity, which has already been described. In determining the absolute compressibility of iron it was necessary to measure the shortening of an iron rod relative to the high-pressure vessel and the absolute deformation of this vessel,

The first problem was solved with my standard apparatus with a sliding contact; the second problem was solved by means of probing rods inserted into narrow drilled holes and reaching the main parts of the high-pressure vessel. The result of about four hundred measurements, smoothed by the method of least squares, was a formula for the volume compression of iron, in which the value of the first-degree term was almost the same as before; however, the value of the second-degree term was three times smaller. There was no possibility of reducing the value of the second-degree term by a factor of 10 or 100. Recently it has been shown that an error had been made in the theoretical calculations, and experiment and theory apparently now agree even for weakly compressible substances. I give here the equation (it may find wide application) for the change in volume of pure iron at \(24^\circ\) up to a pressure of \(30000\ \mathrm{kg}/\mathrm{cm}^2\):

\[ -\frac{\Delta V}{V_0}=5.826\cdot 10^{-7}P-0.80\cdot 10^{-12}P^2, \]

\[ (P\ \text{in}\ \mathrm{kg}/\mathrm{cm}^2). \]

At \(75^\circ\) the best value for the temperature coefficient is given by increasing the value of the first-degree term by \(0.066\cdot 10^{-7}\). The second-degree term does not change in any appreciable way.

The new value for iron affects all determinations of compressibility carried out with respect to iron. I give here formulas, not previously published, for correcting my earlier data according to the new values for iron.

The decrease in volume is given by the second-degree expression

\[ \frac{\Delta V}{V_0}=a_{\text{new}}\cdot P-b_{\text{new}}P^2. \]

Then

\[ a_{\text{new}}=a_{\text{old}}-0.033\cdot 10^{-7}, \]

\[ b_{\text{new}}=b_{\text{old}}-1.56\cdot 10^{-12}-a_{\text{old}}\cdot 0.022\cdot 10^{-7}. \]

The pressure is measured in \(\mathrm{kg}/\mathrm{cm}^2\). The corrections are the same for \(30^\circ\) and \(75^\circ\). Such measurements of compressibility relative to iron up to \(30000\ \mathrm{kg}/\mathrm{cm}^2\) have only just begun. I already have, but have not yet published, results for copper, aluminum, and lead.

In 1940 measurements\(^{186}\) were published of the compressibility of forty-six substances up to \(50000\ \mathrm{kg}/\mathrm{cm}^2\) at \(-80^\circ\) and at room temperature. These measurements were carried out in an apparatus improved in comparison with that in which the original measurements up to \(45000\ \mathrm{kg}/\mathrm{cm}^2\) had been obtained.

The principal improvement consisted in the use of two-stage external reinforcement, which considerably reduced the deformation of the working vessel and increased its service life, and also reduced the magnitude of the corrections. These forty-six substances include twenty-one halide compounds of Na, K, Rb, Cs, NH\(_4\), Ag, and Tl, eighteen

sulfides, selenides, and tellurides of Ca, Sr, Ba, Pb, Zn and Hg, In, S, Se, Te, Sb, Bi, and rubber. The principal results consisted in the fact that the compressibility at \(50\,000\ \mathrm{kg/cm^2}\) is on average 30 to 50% less than the initial value, and that the thermal expansion is roughly equal to half the initial value. A relatively smaller decrease in compressibility with pressure is accompanied by a smaller absolute compressibility, as was already generally known.

The measurement of the compressibility of twenty-one liquids up to \(50\,000\ \mathrm{kg/cm^2}\), carried out in 1942 and already reported\({}^{132}\), included the measurement of the compressibility of the solid phases of these substances above the melting pressure. All these were organic substances, with the exception of water; at high pressure in the solid state they resembled one another even more than in the liquid state.

The decrease in volume between 25,000 and \(50\,000\ \mathrm{kg/cm^2}\) varied from a minimum of 0.045 to a maximum of 0.059.

In 1941\({}^{187}\), the first data were published on compressibility up to a pressure of \(100\,000\ \mathrm{kg/cm^2}\) for seventeen elements: Li, Na, K, Rb, Ca, Sr, Ba, Zn, Cd, In, Tl, Sn, As, Sb, Bi, Se, and Te, all at room temperature. Some of these results are shown in Fig. 3.

Fig. 3. Decrease in volume of several elements up to \(100\,000\ \mathrm{kg/cm^2}\). Breaks in some curves indicate the presence of polymorphic transformations.

In 1945\({}^{188}\) (many of the measurements had been performed before December 1941), measurement was undertaken of the compressibility up to \(100\,000\ \mathrm{kg/cm^2}\) of the same 21 halide compounds previously investigated up to a pressure of \(50\,000\ \mathrm{kg/cm^2}\), of the nitrates of Na, K, Rb, Cs, Ag, Tl, \(\mathrm{NH_4}\), and \(\mathrm{AgBrO_3}\), Pb, In, and S.

For the elements, the relative decrease in compressibility upon doubling the pressure interval from 25,000 to 50,000 kg/cm² is greater than the decrease in compressibility upon the subsequent doubling of the pressure from 50,000 to 100,000 kg/cm². Such behavior could have been expected as a geometrical consequence of the fact that volume cannot have a negative value at any pressure. On the whole, however, compressibility did not decrease as rapidly in the new pressure interval as might have been expected, or, in other words, these elements proved to be more compressible than had been assumed. Various compounds showed the same qualitative picture as the elements. In general, the substances retained their original order of volumes, and there were only a small number of cases in which the volume curves intersected above 50,000 kg/cm². In general, substances with a larger number of atoms in the molecule have the greatest relative decrease in compressibility with increasing pressure. The accuracy of measurements up to 100,000 kg/cm² is, in general, not as high as at smaller pressure intervals, and the apparatus is not yet sufficiently perfected to make it possible to carry out volume measurements of substances having a compressibility smaller than that of the least compressible of the substances listed above. The chief source of errors lies in the fact that the displacement of the piston is measured outside the vessel for securing the piston. A number of corrections must be introduced, in particular for friction and hysteresis. In the new apparatus, which is now being constructed, the displacement of the piston is measured inside the vessel for securing the piston, and there is hope that measurements of the compressibility of less compressible substances will be possible within the range up to 100,000 kg/cm².

In 1945[^89] another method was also published for measuring the compressibility of solids at high pressures, which at present is limited to room temperature, but has the advantage of great convenience and speed in carrying out the experiment and of greater accuracy in determining the value of the second finite difference than any other method applicable up to 30,000 kg/cm². A substance in the form of a thin disk, with a thickness equal to half its diameter in order to reduce friction, is compressed between two carboloy pistons in a carboloy cylinder placed in the conical recess of a steel reinforcing cylinder, having such dimensions that no change in cross section occurs under internal pressure, which reduces corrections.

Measurements by this method were published only up to a pressure of 25,000 kg/cm²; however, later they were continued to a pressure of 40,000 kg/cm². With this apparatus the compressibility was determined for sixty-one substances: the elements Tl, As, Cd, In, Pb and graphite; NaCl; the nitrates Na, K, Rb, Cs, Ag, Tb and NH₄; the chlorates Na, K and NH₄; the bromates Na and Ag; the iodates Na, K and NH₄; the perchlorates Li, Na, K, Rb, Cs, NH₄; the periodates Na, K, Rb and NH₄; levulose, dextrose, dextrin, starch, menthol, naphthalene; anthracene, triphenylmethane; thymol, succinic acid, anthraquinone, benzophenone, o-, m-, p-amino-

benzoic acids and fourteen synthetic and natural rubbers. For the above-mentioned organic solids, the compressibility at high pressure, plotted as a function of the initial density, lies very close to a single curve. The volume compressibility of rubbers at \(25\,000\ \mathrm{kg/cm^2}\) varies from 0.146 to 0.212. A certain number of these rubbers exhibit a more or less pronounced second-order transition near \(4000\ \mathrm{kg/cm^2}\), which may be regarded as diffuse freezing. Because of this, rubbers have a tendency toward volume hysteresis at higher pressures.

It is beyond the scope of this review to summarize the various theoretical works connected with the change of volume under the action of pressure. It will be appropriate, however, to mention a small number of works in which new experimental data were examined. Bardeen\(^{190}\), developing the method of Wigner and Seitz, gave two formulas for the volumes of Na and Li as functions of pressure. One of them is semi-empirical, since it contains one arbitrary constant, and agrees almost completely with my data obtained up to a pressure of \(45\,000\ \mathrm{kg/cm^2}\) (later data up to \(100\,000\ \mathrm{kg/cm^2}\) had not yet been published at that time). The other formula has no arbitrary constants and reproduces the volume of sodium; for lithium, however, there is a discrepancy of \(15\%\). Herring\(^{191}\) discussed this question and pointed to an assumption to which the discrepancy for lithium may be attributed. Fuchs published papers in 1941\(^{192}\) and in 1944\(^{193}\), in which he applied formulas originating from Born’s theory of the crystal lattice (Born and his students developed their theory as applied to lattices of various types). In his work Fuchs obtained approximate agreement with my experimental data for salts up to \(50\,000\ \mathrm{kg/cm^2}\) and for metals up to \(100\,000\ \mathrm{kg/cm^2}\).

Of a different order are theoretical discussions of the volume–pressure relation at astronomical and superastronomical pressures, sufficient for the destruction of the atom. Among such works are those of Hund\(^{194}\), Cernuschi\(^{195}\), and Auluck\(^{196}\). Hund carries the calculations up to a pressure of \(10^{23}\ \mathrm{kg/cm^2}\), at which matter disintegrates into a neutron gas, which is degenerate at temperatures below \(10^{10}\) degrees. More directly related to the experimental material is the work of Jensen\(^{197}\), in which calculations were made on the basis of the Thomas–Fermi model and the Pauli exclusion principle up to pressures of \(10^{15}\ \mathrm{kg/cm^2}\), when all substances disintegrate into an ideal electron gas. Under these conditions the curves of volume as a function of pressure differ completely from the curves for ordinary substances. The form of these latter curves in the usual range gives no hint whatever that, upon extrapolation to high pressures, they can turn into the theoretical curves. Jensen\(^{197}\), using my new data for Cs and Ba up to \(50\,000\ \mathrm{kg/cm^2}\), plotted the logarithm of volume as a function of the logarithm of pressure and found that near \(20\,000\ \mathrm{kg/cm^2}\) the curves give the rise required by the theory.

LITERATURE

1. R. B. Jacobs, Phys. Rev. 56, 211 (1939). Measurement of compressibility by means of X-rays.

2. A. Müller, Proc. Roy. Soc. 178, 227 (1941). Further investigations of solid n-paraffins (repulsion potential and compressibility).

3. K. L. Frevel, Rev. Sci. Inst. 6, 214 (1935). Technique for studying matter under high pressure by means of X-rays.

4. G. Tammann and W. Jellinghaus, Ann. d. Physik 2, 264 (1929). Change in the volume of glass above the softening region.

5. A. H. Scott, Rubber Chem. Techn. 8, 401 (1935). Specific volume, compressibility, and thermal expansion of vulcanized rubber.

6. H. Ebert, Physik. Zeits. 36, 385 and 388 (1935). Studies up to pressures of 5000 kg/cm².

7. H. D. Megaw and F. Simon, Nature 138, 244 (1936). Density and compressibility of solid hydrogen and deuterium at 4.2° K.

8. E. Bartholomé, Zeits. f. Phys. Chemie, 33, 387 (1936). Equation of state of solid isotopes of hydrogen. I. Experimental determination of the parameters of state.

9. J. C. Lyman and G. S. Parks, J. Chem. Phys. 4, 218 (1936). Compressibility of glassy glucose.

10. J. Basset, Comptes Rendus 213, 829 (1941). Density of graphite and determination of the mean compressibility coefficient between 1 and 20,000 kg/cm².

11. L. H. Adams and R. E. Gibson, J. Wash. Acad. Sci. 20, 213 (1930). Compressibility of rubber.

12. L. H. Adams, Gerl. Beitr. z. Geophys. 31, 315 (1931). Compressibility of fayalite and the velocity of elastic waves in peridotite with different iron–magnesium ratios.

13. L. H. Adams and R. E. Gibson, J. Wash. Acad. Sci. 21, 381 (1931). Volume compressibility of certain substances.

14. R. W. Goranson, J. Wash. Acad. Sci. 24, 419 (1934). Elastic properties of rocks.

15. W. A. Zisman, Proc. Nat. Acad. Sci. 19, 666 (1933). Compressibility and anisotropy of rocks at and near the earth’s surface.

16. W. A. Zisman, Proc. Nat. Acad. Sci. 19, 680 (1933). Comparison of static and seismological determinations of elastic constants of rocks.

17. W. A. Zisman, Gerl. Beitr. z. Geophys. 39, 408 (1933). Elastic properties of rocks at and near the earth’s surface and their relation to seismology.

18. F. Birch and R. R. Law, Bull. Geol. Soc. Am. 46, 1219 (1935). Measurement of compressibility at high pressures and high temperatures.

19. F. Birch and R. B. Dow, Bull. Geol. Soc. Am. 47, 1235 (1936). Compressibility of glasses and rocks at high temperatures and pressures; application to seismology.

20. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 66, 255 (1931). Compressibility and pressure coefficient of resistance, including single crystals of magnesium.

21. P. W. Bridgman, Phys. Rev. 38, 182 (1931). The P-V-T relation for ammonium chloride and bromide, and especially the effect of pressure on volume anomalies.

22. P. W. Bridgman, Rec. Trav. Chim. Pays-Bas 51, 627 (1932). Transformation of silver oxide under pressure.

23. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 67, 345 (1932). Compressibility of eighteen cubic substances.

24. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 68, 27 (1933). Compressibility and pressure coefficient of resistance of elements, compounds, and alloys, many of them anomalous.

1. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 70, 285 (1935). Compressibility and electrical resistance under pressure, with special consideration of intermetallic compounds.

2. P. W. Bridgman, Proc. Nat. Acad. Sci. 21, 109 (1935). Electrical resistance and volume changes up to a pressure of 20,000 kg/cm²; Proc. Nat. Acad. Arts Sci. 70, 71 (1935). Changes in resistance, compressibility, and thermal expansion up to a pressure of 20,000 kg/cm².

3. P. W. Bridgman, fourth quotation in reference 4.

4. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 74, 11 (1940). Linear compression of iron up to 30,000 kg/cm²; first quotation in reference 6.

5. P. W. Bridgman, see both quotations in reference 6.

6. P. W. Bridgman, second and third quotations under reference 7.

7. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 76, 1 (1945). Compressibility of twenty-one halogen compounds and eleven other simple substances up to 100,000 kg/cm².

8. P. W. Bridgman, Proc. Am. Acad. Arts Sci. 76, 9 (1945). Compressibility of sixty-one solid substances up to 250,000 kg/cm², determined by a new accelerated method.

9. J. Bardeen, J. Chem. Phys. 6, 372 (1938). Compressibility of the alkali metals.

10. C. Herring, Phys. Rev. 55, 598 (1938). Compressibility of lithium.

11. R. Fürth, Proc. Camb. Phil. Soc. 37, 177 (1941). Stability of crystal lattices. VI. Properties of matter under high pressure and the theory of crystal lattices.

12. R. Fürth, Proc. Roy. Soc. 183, 87 (1944). On the equation of state for solids.

13. F. Hund, Ergebn. d. exact. Naturwiss. 15, 189 (1936).

14. F. Gernuschi, Phys. Rev. 56, 450 (1939). On the behavior of matter at extremely high pressures and temperatures.

15. F. C. Auluck, M. N. R. A. S. 99, 239 (1939). Theory of pressure-induced ionization and the structure of white dwarf stars.

16. H. Jensen, Zeits. f. techn. Physik 19, 563 (1938). Density–pressure dependence for elements at high pressure and a temperature of absolute zero.

(To be continued in the next issue.)