Modern Research in the Field of High Pressures*)

P. W. Bridgman

Since 1905 I have been engaged in measuring various physical effects observed at high pressures1. During these years the magnitude of the pressure attainable in our apparatus has increased considerably, and the number of phenomena investigated has become so large that it seems of interest to consider, in a general survey, all the stages in the development of this subject, both from the factual side—the description of newly discovered phenomena—and with the aim of determining the paths and methods for conquering new regions of physics. From this point of view, it is a very favorable circumstance that the field of high pressures does not enjoy wide popularity. As a result, it lacks the competition characteristic of such a subject as, for example, nuclear physics, and, consequently, the study of high-pressure physics has been able to develop on strictly scientific foundations and to be stimulated only by the requirements of scientific inquiry, without any external motives.

Historical Survey

The range of high pressures attained at the present time is naturally divided into several parts. Each part is defined by a number of phenomena of especially great importance within it, or by the technique necessary for its investigation. The first of these may include the region of critical states in all gases. Characteristic of it are pressures of 200–300 atmospheres. The research technique here is simple, since thick-walled glass capillaries can always be made to hold the gas under pressure and the phenomena themselves can be observed visually. In addition, all ground joints and connections can easily withstand the pressures with the aid of so simple a means as a good sealant. The study of this region began with the discovery of critical phenomena, made by Andrews in the middle of the last century, and developed very intensively until approximately 1890. By that time this region had been almost exhausted, since critical and

other phenomena relating to it were studied. Other effects, however (for example, the effect of pressure on the electrical resistance of metals), were for the most part so slight and so difficult to measure that the numerical results of the measurements differed greatly. As a result, measurements of this kind themselves were made comparatively rarely.

At the second stage in the investigation of the field of high pressures, pressures of about \(3000\ \mathrm{kg}/\mathrm{cm}^2\) were attained—pressures with which, for the most part, one has to deal in modern artillery. Investigations in this region were carried out very intensively between 1890 and 1905, and two outstanding scientists were engaged in them—Amagat \(^{2}\) and Tammann \(^{3}\). Amagat’s work is a natural continuation of the earlier work in the critical region. The pressures with which he worked greatly exceeded the critical pressures for ordinary gases; at the highest of them, gases, in their properties, were already becoming liquids, although they did not pass through a state of condensation. The most important results of Amagat’s work are measurements of the pressure, volume, and temperature and their interrelations for a number of liquids or gases in this pressure region. Tammann’s investigations, on the other hand, connected the liquid and solid states of matter. He was especially interested in determining the effect of pressure on the temperatures of melting and solidification. The experimental technique in the pressure range up to \(3000\ \mathrm{kg}/\mathrm{cm}^2\) was developed chiefly by Amagat. He designed a shell that was quite closed. It was tightened with strong screws and began to leak only at the highest pressures. It was precisely leakage that set the limit to investigations in this region and restricted the possible manipulations. Amagat also proposed a very precise method of measuring pressure, which required extremely accurate operation of the mechanisms and, perhaps, could not have been carried out at an earlier stage in the development of experimental technique.

PRESSURE RANGE UP TO \(20\,000\ \mathrm{kg}/\mathrm{cm}^2\)

Beginning my work in 1905, I intended to study certain optical effects associated with pressure. I did not plan to obtain pressures at all close to the limit established by Amagat, since for my purposes it was necessary to use glass as a transparent medium. After my apparatus had been constructed and preliminary experiments had been carried out, an explosion occurred. Something happened to the glass, which is a very capricious substance. The explosion destroyed the main part of the apparatus, and it had to be ordered again from Europe. At that time the United States of America had not yet attained its present degree of independence in this respect. While waiting for the new apparatus, I tried to use my apparatus for obtaining pressure in another way. In constructing the shell of the high-pressure chamber so that it

could be rapidly disassembled and assembled, I saw that the principle underlying this construction could yield more than had been expected, because, as the pressure increased, the chamber automatically became stronger, and there could be no grounds for expecting leakage.

Figure 1 shows the diagram of such a construction*). This at once opened up an entirely new region of high pressures, limited only by the strength of the chamber and not by the onset of leakage. My proposed optical investigations were abandoned. The laboratory wrote off the expense of making the new parts of the apparatus. The development of a new stage in the field of high pressures began. I never returned to the original subject. This was a case in which persistence in one’s former intentions would have been a bad line of conduct.

The first task in this new field was to find the limit determined by the strength of the chamber. One might have thought that the information needed to solve this question could be drawn from textbooks on the strength of materials. It turned out, however, that very little of the necessary data could be found in them. The practice of construction work proceeded under conditions quite different from those with which we had to deal in solving our problems. The strength limits accepted in engineering theories had hardly been tested, owing to the wide allowances in the safety margin. Under our new conditions, the ordinary technical criteria of tensile strength often gave entirely erroneous results. Therefore, before beginning investigations in the new pressure region, it was necessary to turn aside and undertake a systematic study of the strength of chambers for high pressures and of other parts of the apparatus, for example, pistons. These investigations were necessarily very extensive and included the search for the strongest grades of steel.

Fig. 1. Diagram of a gasket of soft material, automatically maintaining a pressure somewhat greater than that in the liquid inside the apparatus.

As a result of these experiments, new points of view arose, and new facts were obtained concerning the rupture of ordinary engineering materials⁴. Thus, for example, it turned out that thick cylinders subjected to internal hydrostatic pressure failed beginning from the outside, and not from the inside, as might have been expected. Two such cylinders are shown in Figs. 2 and 3. Fortunately, the maximum press—

*) The gasket construction shown in Fig. 1, preventing leakage, is based on the so-called principle of “uncompensated area” (1). Ed. note.

phenomenon, which could withstand such a thick cylinder, proved considerably higher than the limit indicated by the theory. These investigations very often were accompanied by rupture of the apparatus, and the experimenters were not infrequently exposed to serious danger. Experiments showed that rupture of a special kind is possible, one that had not previously been suspected and whose existence not even all experts recognize even now. This rupture occurs in a direction in which there is apparently no corresponding component of the stress, and is observed, moreover, when the specimen is lengthened in a given direction, whereas in that direction there are apparently no tensile forces. I have called this type of failure the “pinch effect”; the corresponding specimen is shown in Fig. 4*).

Fig. 2. External appearance of the ruptured cylinder. The rupture began at the outer surface; pressure was applied from within.

The pressures that were reached in these preliminary experiments sometimes amounted to \(40\,000\ \text{kg}/\text{cm}^2\). Such pressures could be obtained only in a soft solid body such as lead. They could not be used for studying physical phenomena, except perhaps rupture itself. Pressures at which interesting physical measurements could be made had to be reduced considerably, approximately by half.

Over a number of years my experiments were aimed at finding the most important physical phenomena in this region. A characteristic feature of the formulation of the problem in this case is that the strength of the chamber limits the magnitude of the pressure. In this case the chamber is, if possible, simply a vessel made from a solid piece of well-tempered steel of the proper grade. The upper limit of pressure that can be reached in this way is determined by the following considerations. If the phenomenon itself is of interest, one may content oneself with obtaining pressures higher than the usual ones. Thus, for example, at the beginning—

*) For details concerning the “pinch effect,” see P. W. Bridgman’s book, p. 95. Editor’s note.

work in this area, in order to construct the melting curve of water, pressures of up to 21,000 kg/cm² were obtained. This experiment was of interest at the time, and I considered it worth the effort, but the apparatus withstood such a pressure only once. The cylinder stretched so much that it became unfit for further work. Obviously, it was necessary, for reasons of economy, to confine oneself to less destructive pressure values.

Fig. 3. Half of a cylinder made of tool steel, ruptured by an internal pressure of 31,500 kg/cm². The inner cavity expanded from 1.25 to 3.0 cm.

Fig. 4. Specimen ruptured by the “pinch effect.”

Lowering the pressure greatly increases the service life of the apparatus. Most of the work was therefore carried out at a maximum pressure of 12,000 kg/cm². If the apparatus had no defects from the very beginning, it withstood high pressures within the stated limits several hundred times without failure.

Having thus established the limiting pressure, I had to choose the phenomena that were to be studied in this region, and to outline the order of their investigation. One of the most important questions

of research tactics, like any other tactics, is the order in which experiments are carried out. Obviously, first on the list had to be the measurement of pressure. The manometers used in the two preceding regions were unsuitable here; new ones had to be constructed. Usually two series of manometers were prepared. The manometers of the second series were calibrated against those of the first, and with their aid pressure measurements were made during the experiments. Calibration was greatly facilitated by establishing fixed points on the pressure scale, analogous to the fixed points of a thermometer. Such fixed points are determined by the pressure of melting or of polymorphic transformation of standard substances at definite temperatures. We established them for this new region.

The accuracy of measurements is always a very important question, one that must be discussed. How much time should be spent on preparatory work in order to ensure sufficient accuracy of the results? It is unpleasant to think that your work will be redone someday later, and therefore there arises a desire to dwell on improvements. There can be no general basis for choosing the degree of accuracy under such circumstances, because the accuracy of measurements is determined by the nature of the phenomena being investigated. And, on the other hand, how can one foresee what phenomena may arise in a new field of research, or predict what direction physical theory will take, in order to decide the question of the importance of an investigation and of the necessity of refining the measurements? The compromise at which the investigator arrives in this matter depends on temperament and on his personal ideas of what is actually important*). In my particular case the decision was left to the natural course of events. A certain degree of accuracy could be obtained without too much effort with the new manometers, and I stopped at it, hoping that it would be sufficient. It turned out that up to \(12\,000\ \mathrm{kg/cm^2}\) pressures could easily be measured with an accuracy of up to \(0.1\%\). In justification of my having limited myself to this degree of accuracy, one may point out that at that time theory did not require even such accuracy in the study of phenomena that were of interest to investigate at high pressures. The theory of the liquid state, for example, was by no means so developed as to require such accuracy of measurement.

COMPRESSIBILITY OF LIQUIDS

In the absence of other motivating reasons, the order of investigations in a new pressure region is dictated by the ease and simplicity of the question under investigation itself. The solution of any problem may encounter

) Often the question of the accuracy of measurements is determined by the nature of the practical applications of the phenomenon under study, which the investigator must have in mind. Editor’s note.*

on technical difficulties, but success in overcoming them should increase as practical skills are acquired and as the ability to manage simpler operations is developed. On this basis, measurements of the compressibility of liquids were chosen as the first investigations. The volume changes of liquids are very large and reach \(30^{0}/_{0}\), and therefore it is easy to measure them with the required degree of accuracy. Here a great advantage is obtained in comparison with the first measurements of the compressibility of liquids, when it was only with difficulty possible to establish the very existence of volume compression by means of sensitive piezometers constructed on the model of thermometers.

Another advantage in measurements of the volume compression of liquids is that Amagat also measured it. In addition to the direct interest of continuing his experiment, comparison of my results with Amagat’s data at the lower limit of my pressure range was to serve as a check on the new methods. Furthermore, the compressibility of liquids is of enormous importance in the design of apparatus for high pressures, whose dimensions are determined by the need to obtain the maximum pressure at each individual stroke of the piston; and this, in turn, depends on the compressibility of the liquid transmitting the pressure. Thus measurements were made of the compressibility of liquids previously investigated by Amagat; in particular, the results of pressure measurements were checked. In the process, new phenomena in the liquid state were discovered, phenomena whose existence Amagat did not even suspect, such as, for example, the reversal of the course of thermal expansion as a function of temperature at high pressures.

After the experiments with Amagat’s liquids, the next task, interesting from the point of view of ease of experimentation and of obtaining results, was the continuation of Tammann’s investigations of melting in the region of higher pressures. These experiments also yielded important new results, since it turned out that the course of the melting curve did not coincide with that predicted by Tammann on the basis of extrapolation of his results. He expected that the curve would have a temperature maximum at pressures of the order of those obtained by me in the new pressure range. It turned out, however, that this was not the case. On the other hand, the melting curve did not end at a critical point of the solid and liquid phases, as many theorists expected, by analogy with the critical point gas—liquid. At the same time it became evident that the curve increases monotonically with pressure and temperature.

POLYMORPHISM AT HIGH PRESSURES

Closely connected with the phase transition on melting, both thermodynamically in essence and in the technique of the experiment, are phase transitions in polymorphic transformations of solids. The thermodynamic relations for transitions in the solid state are expressed by the same equation as for melting, and the parameters of the transformation may be

determined with the very same instruments and on the same installations. A small number of polymorphic transformations had been investigated by Tammann at lower pressures. His most important result was the transition of ordinary ice, at a pressure of \(2000 \text{ kg}/\text{cm}^2\), into a new modification, denser than water, as a consequence of which the anomalous expansion of water on freezing disappears at high pressures. Tammann also found a third modification of ice at temperatures below the melting curve.

The first result of my investigations in this area was the discovery of other varieties of ice. Tammann’s ice is stable only at pressures of about \(2000 \text{ kg}/\text{cm}^2\) and already at a pressure of \(3500 \text{ kg}/\text{cm}^2\) passes into another form. This latter, in turn, undergoes a transformation at a pressure of \(6400 \text{ kg}/\text{cm}^2\). I have found recently that at a pressure of \(22000 \text{ kg}/\text{cm}^2\) still another modification of ice is formed. Altogether there are seven different modifications of ice, stable in definite pressure regions. The melting point of one of them reaches \(175^\circ\text{C}\) at the pressures I have recently obtained. In the new pressure region polymorphism proved to be a much more usual phenomenon than could have been expected from its manifestations at low pressures. My investigations revealed many instances of this phenomenon. In the course of work in this direction another type of transition was discovered\(^{5}\): the transformation of yellow phosphorus into black phosphorus at pressures of \(12000 \text{ kg}/\text{cm}^2\) and \(200^\circ\text{C}\). This type of transformation is irreversible, and the product obtained as a result is stable at atmospheric pressure. Black phosphorus differs essentially from yellow phosphorus. Thus, for example, it is stable in air and conducts electric current. Somewhat later, Jacobs\(^{6}\) made a more careful study of this transformation.

The experimental technique in investigating the compressibility of liquids and the melting of substances is almost the same. It is based on determining the displacement of a piston as a function of pressure, and therefore requires the complete absence of leakage. The experience and skills developed over a number of years in measuring piston displacements enabled me to feel ready to investigate other physical phenomena. The next step was again determined by the requirement of the greatest simplicity and ease of experimental technique. This time the measurement chosen was the effect of pressure on the electrical resistance of metals. Experiments at lower pressures had given contradictory results because the effect being measured was very small. Thus, for example, under a pressure of \(1000 \text{ kg}/\text{cm}^2\) the resistance of copper decreases by only \(0.2\%\). In a wider pressure range, where larger effects could be expected, it would not be difficult to attain a more satisfactory accuracy of measurement. This proved to be true. However, in order to ensure the desired accuracy of the results, temperature measurements had to be made with an accuracy of up to \(0.01^\circ\text{C}\), almost the limiting accuracy in our investigations. Another technical

A complication in measuring resistance was the introduction of current into the pressure chamber. This problem, however, had already been solved fairly well earlier in connection with the design of manometers, where the principle of the change in the resistance of manganin under pressure was also used.

PRESSURE AND THERMOELECTRIC PHENOMENA

After the measurement of electrical resistance, simple technical improvements made it possible to determine the influence of pressure on the thermoelectric properties of metals, and this was done for a number of metallic conductors. New experimental data on resistance and thermoelectric properties were bound to be of significance for the electron theory of metals, in which at that time a certain revival was being observed. I spent much time trying to explain the influence of pressure on the mechanism of electrical conductivity and arrived at a new view of this process. These considerations were of some interest, but at present they have become obsolete in connection with the development of wave mechanics. The theoretical considerations naturally suggested the idea that it would be desirable to establish the influence of pressure on the thermal conductivity of metals, since there is a simple relation between the electrical and thermal conductivity of metals in the form of the well-known Wiedemann–Franz law. Such measurements were indeed carried out for a number of metals, but their results deviated strongly from those predicted by the simple theory. This case, however, turned out to be one in which the desire to meet the requirements of theory was a poor line of conduct, because these experiments involved great experimental difficulties, and the accuracy of the results obtained was insufficient. Tactically, it would have been more correct to postpone the study of this effect until the experimental technique in this field had been sufficiently improved. Later Starr7 in my laboratory repeated these measurements under more refined conditions, so that these effects are now quite well studied, at least for several metals. The thermal conductivity of liquids proved much easier to measure, because for them all the effects are larger than for solids. For ordinary liquids such measurements were made, making it possible to establish a simple relation between the thermal conductivity of amorphous bodies and their mechanical properties. This relation holds even outside the pressure range described here8.

COMPRESSIBILITY OF SOLIDS

Only after all these problems had been solved did I attempt to carry out such measurements as, from the modern point of view, may be considered the simplest and are the most readily treated theoretically—namely, measurements of the compressibility of solids, in particular metals and simple salts. One of the reasons why

that this was not done earlier lies in the fact that only relatively recently did the formulation of such experiments receive stimulus from theory. At the beginning of our century it was customary to think that the theoretical study of matter should proceed from the gaseous to the liquid state, and then to the solid state. However, the development of the theory of the solid state of matter by Born^9 and other authors around 1920 showed that solids, like gases, are simple bodies, and that the study of liquids should be placed last.

Furthermore, from the technical point of view, experiments on the compressibility of solids are much easier to describe than to carry out. The effects in this case are small and are confused by the distortion of the apparatus itself under the influence of pressure. This is connected with corrections of the same order as the phenomenon being studied, whereas in experiments on the compressibility of liquids the distortions of the apparatus are of a lower order of magnitude in comparison with the quantity measured. However, in the present field the advantage is, after all, the very magnitude of the pressure, since these effects are proportional to the pressure and are considerably larger for higher pressures. Thus there was much hope of success here. This problem did indeed prove possible to solve satisfactorily. A method was found for eliminating the distortions of the apparatus, and results were obtained for many substances.

There remained one more important phenomenon still uninvestigated: the effect of pressure on the viscosity of a liquid. There were indications concerning it that very large effects might be observed in this region, so that the necessary accuracy of measurement could easily be attained. On the other hand, radical changes had to be made in the apparatus so that, for example, the entire instrument could be turned over quickly and often. Owing to all these complications, investigations in this field were postponed almost to the end of the program. It turned out that such measurements were quite feasible, and the influence of pressure on the viscosity of many liquids was successfully determined for pressures up to \(12\,000\ \mathrm{kg/cm^2}\). Typical results are presented in Fig. 5. The viscosity almost always increases with pressure. The pressure effect is large, reaching \(10^7\). It may be said that the influence of pressure on viscosity is greater than on any other physical property. The results of these measurements proved to be extremely important for the theory of liquid viscosity^10.

The experimental technique in the field of high pressures was thus well developed, and the objects of research in this field reached a high stage of development and perfection; no striking qualitative effects are now being discovered, but a very large number of essentially important determinations still remain to be made. Possibly, of special interest in connection with the development of the technique of growing single crystals of metals was the study of their properties, in particular the pressure effect, as a function of the orientation of the crystal. The question

of studying single crystals arose because the compressibility of a single crystal with a non-cubic lattice depends very strongly on its orientation. Thus, measurements of the Young’s modulus of non-cubic crystals are of far less significance than measurements of the linear compressibility along a definite crystallographic direction.

Several years, during which the successes achieved were being consolidated, were occupied with the production of analogous measurements with new elements as they became available in the form of very pure substances, with liquids of another type, with substances of special interest, such as various minerals of the earth’s crust; experiments were also made at other temperatures, for example, at the temperature of liquid air. And yet much work of great importance still remained; but the law of diminishing returns began to operate, and the work began to slow down somewhat. There was one direction in these investigations that could develop continuously—namely, increasing the accuracy of the measurements. In physics it has often happened that a new, as yet undiscovered fact is hidden behind the next decimal place. Such facts may have great, even revolutionary, significance, as was the case, for example, in the field of quantum phenomena. The situation in the field of high pressures is very similar. I had long since found that in liquids there are phenomena, so to speak, of small scale, characteristic of each individual liquid. Later I discovered many such small-scale phenomena in solids of complex structure, for example, in alloys, in which a transition from an ordered to a disordered state is observed[^11]. Nevertheless, despite the probable success in this direction, I personally, by temperament, could not be enthusiastic about investigating phenomena of “the next decimal place,” especially if this could be done by improving techniques already in use.

Fig. 5. Effect of pressure on the viscosity of isobutyl alcohol.

In this respect, I think, I do not differ too much from most of my fellow physicists. One recalls the dissatisfaction with which many physicists in the nineties of the last century ...

decades looked upon the prospect of gray and tedious monotony in determining the “next decimal place.” However, the “next decimal place,” as a rule, could rarely be determined without developing an entirely new technique.

PRESSURE RANGE FROM 20,000 TO 50,000 kg/cm²*)

It was obvious that a more satisfactory continuation of the work, at least from my point of view, would be the attainment of still higher pressures. For several years I worked in this direction, making measurements between 12,000 and 20,000 kg/cm². These phenomena, as I knew, were quite accessible, since I had made my first measurements with water at pressures of 21,000 kg/cm². For testing within these extended pressure limits, only those phenomena were chosen which, in experiments at lower pressures, had proved especially significant. In this way I discovered several new pressure effects, such as, for example, a minimum in the resistance of rubidium at a certain pressure and the reversal of thermal expansion in the alkali metals. The work, however, was very discouraging, because the pressure chambers often burst, and the entire apparatus was destroyed as well.

Fig. 6. Simplified apparatus for obtaining a pressure somewhat above 25,000 kg/cm².

The frequent ruptures of the vessels were difficult to explain, in view of my success in obtaining this limiting pressure almost twenty years earlier, especially since I was now using some new grades of steel with an ultimate strength 50% greater than before. I learned, however, that steelmakers are well aware that the new high-strength steels are “temperamental.” This means that articles of complex shape are difficult to harden without cracks appearing. In order to make full use of the possibilities associated with the use of the new steels, I tried to achieve the greatest simplicity in the design and finally arrived at the ultimate simplification, using only one vessel, as shown in Fig. 6, in the form of a simple cylinder drilled through, without any connections by screws of any kind whatsoever.^12 In such a vessel, naturally, only simple experiments can be carried out—for example, the study of polymorphic transformations, which are revealed by disturbance of the regular motion of the piston.

*) Some experiments with pressures up to 50,000 kg/cm² are described in P. W. Bridgman’s article “On the Nature of Metals in Connection with the Study of Their Properties at High Pressures,” Uspekhi Fizicheskikh Nauk, 20, no. 4, 513, 1938. Ed. note.

This instrument made it possible to solve one problem in this field which had long attracted general attention. Bismuth at its melting point exhibits the same anomaly as water, since the volume of its solid phase is greater than that of its liquid phase. The anomaly of water, as has already been said, is only a temporary phenomenon and disappears at a pressure of 2000 kg/cm². One might have expected, by analogy, that solid bismuth under pressure would likewise undergo a polymorphic transformation into a new form, denser than the liquid. Searches for such a transformation were made, and there was a report in the literature of its discovery. Later, however, it turned out that this was incorrect. With the new simple high-pressure apparatus this long-awaited transformation was found at a pressure of about 25,000 kg/cm². Thus in the earlier experiments a sufficiently high pressure had not been reached. The same apparatus proved capable of withstanding a number of analogous tests at pressures up to almost 30,000 kg/cm². This limit is determined by the strength of the cylinder and piston. The prospects for work with this apparatus, however, are not very attractive, owing to the difficulty of the experiment. The steel of the cylinder and piston begins to show creep at the limiting pressures, as a result of which the entire apparatus is very short-lived; usually the cylinder bursts, or the piston expands and becomes jammed in it. In addition, because of the slow shortening of the piston, measurements of its displacement do not give exact values of the change in volume.

Because of such unfavorable features I began to look for ways of obtaining higher pressures by another method. Theoretically, obviously—and also in conversations I often had occasion to hear it said—that one can obtain any pressure by placing a series of pressure apparatuses one inside another. The pressure in one vessel uniformly supports the inner vessel placed in it, as a result of which the latter is capable of withstanding an internal pressure exceeding its normal value by the amount of the external pressure. The difficulties lay in designing the details without excessive complication. There was nothing especially attractive in this work, but since I had to do it, I designed an apparatus and built it. I never once tested it, because in the meantime I had found a better solution to the problem, which I shall now describe. In this case, once again, excessive persistence would have been poor tactics.

Simultaneously with changing the methods of obtaining higher pressures, I was occupied with another problem connected with this one, namely, obtaining diamonds from graphite. Previous investigations¹³ had shown that thermodynamic equilibrium between diamond and graphite can be attained at a pressure of 30,000 kg/cm², and this was precisely the pressure with which I was working. However, pressures of 30,000 and 40,000 kg/cm² proved insufficient to carry out this transition. This failure can, in all probability, be explained by the influ-

by the phenomena of viscosity; which, presumably, could be overcome by still higher pressure. It was obvious that the pressure necessary for this transformation could be obtained only in a very small volume. It is further known that very high local stresses can be created in steel if it is properly reinforced from other parts of the apparatus. Thus, for example, the stresses at the contact of two crossed knife blades, or under the ball in a Brinell hardness test apparatus, are very high. A very small piece of graphite placed under the ball in the Brinell apparatus will therefore experience considerably higher pressures than those applied in my earlier experiments. I designed and tested various constructions of a shell capable of withstanding very high pressures in a working space of small volume, and with one such scheme I succeeded in keeping a small piece of graphite under a pressure of \(100\,000\ \mathrm{kg}/\mathrm{cm}^2\) for several hours. However, no transformation of graphite into diamond occurred*). This attempt was abandoned, and the failure was ascribed to the extremely high internal friction hindering the reaction. Fortunately, these experiments were successful from another point of view, because solving the problem of designing the shell and the “support” of the pressure chamber yielded new ideas in the design of vessels for high pressures.

Fig. 7. Schematic diagram of the construction of the external shell (“support”) of a pressure chamber, making it possible to increase the resistance of the shell as the internal pressure increases.

The scheme of the support for the pressure chamber, developed as a result of all these attempts, is shown in Fig. 7. The outer surface of the chamber is a truncated cone. When pressure is developed inside the vessel by means of a piston, the whole vessel is forced into the conical seat, like a stopper into the neck of a bottle. In this way an external pressure is exerted on the vessel, increasing in proportion to the increase of the internal pressure. With the aid of such a construction it proved possible easily to obtain pressures up to \(50\,000\ \mathrm{kg}/\mathrm{cm}^2\). This pressure was considerably greater than the limiting pressure previously obtained, and this fully justified the accumulation of systematic data, which I then undertook, although it even accom—

) For a survey of attempts at the artificial production of diamonds, see O. I. Leipunsky, Uspekhi Khimii, 8, issue 10, 1519, 1939. Ed. note.*

was accompanied in the lower part of this pressure range by a duplication of the results. This duplication was not, however, a complete repetition of the data obtained earlier, because previously the degree of accuracy of measurements at the lower pressure limit had been very restricted by friction of the piston. Moreover, whenever the pressure range is newly extended it is always desirable to overlap the results obtained earlier, since in this way one can check the accuracy of the methods developed for the new range.

The conical form of the pressure chamber still did not provide the possibility of extending this range to \(50\,000\ \text{kg}/\text{cm}^2\). No steel can withstand such compressive stress, and therefore steel pistons could not be used. Fortunately, however, at just this time a new material appeared—carboloy—which at first came into use for cutting tools. It proved to be much harder and stronger in compression than steel. Carboloy, tungsten carbide cemented with cobalt, proved to be an excellent material for making pistons. I was fortunate enough to obtain it in sufficient quantity, thanks to the kindness of the General Electric Company, and to make use of carboloy at a time when its cost was so high that its use, in general, was not accessible.

The choice of experiments that could be performed at pressures up to \(50\,000\ \text{kg}/\text{cm}^2\) is still more limited than at lower pressures. First of all, the apparatus has considerably smaller dimensions. To most people it seems very strange that with increasing pressure the apparatus should become smaller. The first reason for this surprising fact is that steel can be hardened throughout its entire volume only in the form of small pieces. In addition, it must be borne in mind that safety, expense, and time are less for small apparatuses, because the ruptures of a bomb become more frequent as the pressure increases. The working space in the apparatus for obtaining a pressure of \(50\,000\ \text{kg}/\text{cm}^2\) has only about \(6\ \text{mm}\) in diameter and \(10\ \text{mm}\) in length, whereas an apparatus for pressures of \(12\,000\ \text{kg}/\text{cm}^2\) consisted of two or more chambers connected by a tube, each chamber having a capacity of \(20\)—\(30\ \text{cm}^3\). The dimensions of the apparatus not only narrowed the field of experimentation at \(50\,000\ \text{kg}/\text{cm}^2\), but also limited it almost exclusively to the study of solids. One of the reasons for the latter circumstance is that nearly all bodies, with the exception of some permanent gases, solidify at such a pressure at room temperature. Even if a substance, inclined to supercooling, having a complex arrangement of molecules, characteristic of liquids, and requiring a large free volume, cannot exist under these conditions.

The simplicity of the construction of the apparatus described necessarily limited the investigation of solids to the study of volume compres-

...as a function of the stroke of the piston. Fortunately, however, much can be done in this field; polymorphic transformations, experienced by many substances, are the easiest to study. The thermodynamic parameters of the transitions for 75 substances were determined in this pressure range[^14]. Fig. 8 shows transformation curves for some metallic elements, and Fig. 9 the same for \(d\)-camphor, the most complex of the substances investigated. Polymorphism proves to be an ever more general phenomenon as the pressure is increased, so that almost any arbitrarily chosen substance may reveal it. It seems paradoxical that this phenomenon, which is most easily observed and is connected, one may think, with the most fundamental properties of a substance—in particular with its space lattice—is theoretically the most difficult to predict or calculate. This is because modern methods of calculation make the existence of this phenomenon depend on small differences of large quantities. As a result, the enormous number of experimental facts on polymorphism—which, as is easy to see, depends on the fundamental properties of a substance—is at present accumulating like a collection in a museum, awaiting its interpretation in the future, just as spectroscopic data accumulated for years until later theoretical investigations generalized them.

Fig. 8. “Phase diagrams” (equilibrium diagrams) for pure metals.

The compressibility of solids could be measured over the entire pressure range up to \(50\,000\ \mathrm{kg/cm^2}\), although with considerable difficulties. Corresponding data were obtained for a large number of materials. Liquids could also be investigated in that part of the new pressure range in which they did not solidify under pressure. In doing so, they had to be enclosed in the mass of some easily deformable solid, for example lead, and the total compressibility measured. Thus it became possible to study the change of compressibility upon solidification over a wide pressure range[^15]. The accuracy of the measurements is, of course, not as great as at lower pressures,

Fig. 9. Phase diagram for \(d\)-camphor.

because of complications associated with the rapid increase of friction and the distortion of the apparatus.

Some effects sometimes change sign; therefore the accuracy can, if necessary, be increased by increasing the number of measurements. In these measurements the old problem again arises of how best to reconcile breadth in the formulation of the problem with the desire for the greatest accuracy of measurement. Its solution depends to a certain extent on the personal inclinations of the experimenter and, moreover, changes with the development of theory and the interest of theoretical physicists in the results obtained. It is a very favorable circumstance that the error in determining compressibility (one of the most difficult effects to measure accurately at low pressures because of its smallness) becomes smaller at high pressures owing to the increase in the absolute magnitude of this effect.

The experimental arrangements that were used to determine the compressibility of the liquid and solid phases of a substance can also be used to determine the effect of pressure on tempera-

the melting temperature at a pressure of almost \(50\,000\ \mathrm{kg/cm^2}\). Earlier I had investigated this effect for 30 or 40 substances at pressures up to \(12\,000\ \mathrm{kg/cm^2}\). In doing so I came to the conclusion that the melting curves behave alike in the sense that they rise indefinitely with increasing temperature and pressure, do not end in a critical point, and do not have a maximum at a definite temperature, as was at one time assumed. Theoretical physicists have recently again put forward the possibility of the existence of a critical point,

Fig. 10. Dependence of the melting temperature on pressure for various substances. At a pressure of \(15\,000\ \mathrm{kg/cm^2}\) the order of the substances, beginning from the top, is as follows: chloroform, chlorobenzene, chlorobenzene (second modification), water (ice VI), butyl alcohol, normal carbon disulfide, methylene chloride, normal propyl bromide, ethyl bromide, and ethyl alcohol.

and therefore it was highly desirable to reexamine this question experimentally over a broader range of pressures. A number of newly determined melting curves are shown in Fig. 10. They appear to break off in our diagram, but this is not connected with any indications of the existence of a critical point. It simply means that, owing to experimental difficulties, the curve could not be followed further. By combining these curves with other thermodynamic melting parameters—the latent heat and the change in volume—one can extrapolate the course of the curve into the region of pressures higher than those that were obtained experimentally. The conclusion from these investi-

studies confirms the conclusion, made earlier from measurements in a narrower pressure range, that there are no experimental indications of the existence of a critical point or of a maximum on the curves—all of them indicate that the melting curves increase monotonically with pressure and temperature. This conclusion is obviously of very great importance for geology.

If one is satisfied with pressures below \(50\,000\ \mathrm{kg}/\mathrm{cm}^2\), it is possible to construct more complicated instruments on the same principle as the conical support. With such an instrument it is possible to investigate a much greater variety of phenomena and to obtain a considerably greater degree of accuracy. I built an instrument of this type, in which a pressure of \(30\,000\ \mathrm{kg}/\mathrm{cm}^2\) can be obtained very easily, as a quite ordinary matter.^16 In this instrument the volume of the vessel is about \(15\ \mathrm{cm}^3\), and the transmission of pressure is effected by means of a liquid. The latter circumstance makes it possible to introduce electrically insulated leads into the apparatus, and this opens the possibility of carrying out many varied experiments. A pressure up to \(30\,000\ \mathrm{kg}/\mathrm{cm}^2\) is sufficiently high to justify a broad program of investigations in this field, especially since, with the aid of the new design, the frequency of accidents was reduced to the smallest proportions.

Some interesting questions at pressures up to \(30\,000\ \mathrm{kg}/\mathrm{cm}^2\) require especially accurate measurements. For example, the study of changes in the compressibility of salts, in particular sodium chloride, when it is a question of determining the curvature of the curve of the dependence of volume on pressure, gives unsatisfactory results. For metals the curvature is so small that it was difficult to measure. But at the present time the theory has been developed not only for salts but also for metals, and therefore it was desirable to obtain for them, too, measurement results as accurate as possible. The accuracy of determining the curvature increases, other conditions being equal, as the square of the limiting pressure. Consequently, this effect at \(30\,000\ \mathrm{kg}/\mathrm{cm}^2\) can be established with an accuracy six times greater than at \(12\,000\ \mathrm{kg}/\mathrm{cm}^2\). The “other conditions being equal” include the accuracy of pressure measurement. Thus, as before, the preliminary experiments had to consist in developing a method of measuring pressure with a sufficient degree of accuracy and in determining fixed points for graduating the measuring instruments. Having established a pressure scale and obtained reproducibility of measurements with an accuracy of up to \(0.2\%\), it was necessary to carry out analogous work for measuring compressibility. The most convenient method for measuring compressibility appears to be the differential method, in which the difference in compressibility of the substance under test and of some standard substance is measured. To obtain absolute values of compressibility in such a case, knowledge of the absolute compressibility of the standard substance is required. To determine this latter quantity it was necessary to develop special methods. Such methods were indeed developed, and the absolute compressibility of the standard

substance, namely iron, was determined up to 30,000 kg/cm². The final result obtained for the deviation from the linear dependence of the compressibility of ordinary metals was a value considerably smaller than that found in previous measurements at lower pressures. This new value was more acceptable to theoretical physicists, who by that time had brought the theory to such a degree of perfection that it gave them confidence in the higher-order terms.

Fig. 11. Insulation of conductors withstanding pressure up to 30,000 kg/cm²; A—a thin coupling of foam golly 0.0002 dm thick; B—a wire from a piano string 0.0005 dm in diameter.

Just at this time there occurred a significant change in the relationship between theory and experiment. When I made my measurements of the effect of pressure up to 12,000 kg/cm² on the electrical resistance of metals and on the compressibility of solids, the theory of both these phenomena was still so simple that an attempt to introduce some changes into it on the basis of new experimental material did not seem hopeless. By the time I began to make measurements of compressibility up to 50,000 kg/cm², wave mechanics had already been developed, and in such a complex form that I could have introduced anything into the theory on the basis of my new data only by abandoning experimental work and setting out to swim along a very problematic course, in order to acquire sufficient ease in handling wave mechanics. The difficulty of combining theorist and experimenter in one person has greatly increased in recent times. For the experimenter this means that he must be especially on guard lest his work be reduced to the mere accumulation of facts for their own sake.

The task of maintaining pressure without rupture of the vessel or the appearance of leakage was not the only one in carrying out my investigations in the new pressure range. The question of insulating the conductors presented many difficulties, since the methods of insulating them at lower pressures were not suitable for the high-pressure range. At first the very best insulation I could devise usually became unusable after a twofold application of pressure, being destroyed either mechanically or electrically. Under these conditions the accumulation of results proceeded very slowly, owing to the necessity of almost continuously dismantling and reassembling the apparatus.

I had to choose and decide whether to engage systematically in developing a new and more perfect method of insulation, or to continue the measurements, carrying out from time to time such...

changes in the method of insulation which seemed to me necessary. The latter line of conduct, which I followed, proved, I think, tactically more correct, because now, after several years, I not only possess a considerable number of measurements of compressibility and of the influence of pressure on electrical resistance, but also a well-developed and improved method of insulation, which makes it possible to carry out a series of measurements before it becomes necessary to reassemble the apparatus anew[^17]. The scheme of insulation of the leads is shown in Fig. 11.

PRESSURE RANGE ABOVE 50,000 kg/cm²

Work with instruments of two types—one up to 50,000 kg/cm², with somewhat lower accuracy of results and measurements only of volume changes, and the other up to 30,000 kg/cm², with a higher degree of accuracy and with a greater variety of effects studied—continued simultaneously for several years. Throughout this time the problem of obtaining still higher pressures was constantly kept in view. It was obvious that 50,000 kg/cm² was almost the limiting pressure that could be obtained in an apparatus of conical form and with a piston of carboloy. The pressure chamber was operating at the limit of its strength and was ready to fly to pieces. Not infrequently the vessel ruptured along three mutually perpendicular planes at once. In exactly the same way the carboloy piston was close to the limit of its strength and broke more often than was desirable. It was becoming clear that the design of the bomb in this form could not be retained. With the aid of the experience accumulated over several years, a new extension of the pressure range accessible to investigation did not seem hopeless. I again took up the solution of this problem with great optimism and with great hopes for a substantial increase in the limiting pressure, because now it was possible to use, as a preliminary, i.e. supporting, pressure 30,000 or 50,000 kg/cm² instead of 12,000 kg/cm².

The first attempts were made with the shell (support) used in the apparatus for pressures of 50,000 kg/cm², and were very successful. They showed the possibility of obtaining a pressure of 200,000 kg/cm² and even higher[^18]. Such a high limiting pressure is considerably greater than it seemed the apparatus itself could withstand. It exceeded, perhaps, all calculations, but this agreed with my earlier experiments, which showed that the theory of rupture of vessels by internal pressure gives too low limits of strength. These results coincided with the data of Griggs[^19], who was carrying out geophysical investigations in my laboratory and observed an increase in strength, as well as in the plasticity of rocks and minerals under hydrostatic pressure. He found a large increase in strength, and the rate of its increase itself increa-

...increased with increasing pressure, so that an exponential relation between them could be assumed. My observations agreed with these results, and I regarded them as confirmation of my experiments. However, the accuracy of the measurements at such high pressures was so low that it seemed doubtful whether such an extension of the high-pressure range would have scientific significance, and whether valuable results could be obtained by a simple extrapolation of the data for lower pressures. The reason for such a considerable decrease in the degree of accuracy was that the “liquid” which withstood the external supporting “hydrostatic” pressure was a soft metal—lead, indium, or bismuth—and the friction in it was so great that it confused the whole matter. It soon became clear that, in order to ensure satisfactory accuracy in the operation of the apparatus, the first stage of the external hydrostatic pressure had to be obtained in the device up to 30,000 kg/cm² with a true liquid, since in that case it was possible to make accurate measurements by means of electrically insulated leads.

MEASUREMENT OF PRESSURE

First of all it was necessary to construct a “compressometer” for measuring the pressure on a piston immersed in a liquid under high pressure. This was done satisfactorily, and an installation was built consisting of a piston, a cylinder, and a manometer, all of which was entirely immersed in the liquid of the external pressure apparatus. Such instruments are shown in Figs. 12 and 13. The internal piston had a diameter of 1.55 mm, which again shows how greatly the dimensions of the instruments decrease with increasing pressure.

Fig. 12. Small-size instrument for obtaining a pressure of 100,000 kg/cm², mounted in an external pressure vessel. The pressure on the piston is measured by electrical resistance, as shown in Fig. 13.

Almost immediately, when more accurate apparatus was used, it turned out that the preliminary estimate of the possible limiting pressure with a single-stage support had been too high. The upper limit is not sharp, because rupture is always peculiar. However, apparently it is impossible under any circumstances and with any materials to obtain more than 150,000 kg/cm² in the inner cylinder with the piston; it would even be more correct to take 125,000 kg/cm² as the upper pressure limit in such instruments.

On the basis of more accurate measurements, the previous data obtained in an instrument in which the pressure was 50,000 kg/cm² were revised, and it proved possible to preserve the previous interpretation of the results and to reconcile

with them this new limit of 150,000 kg/cm². In light of the results obtained by means of more accurate measurements, it turned out that the previously assumed exponential dependence between the increase of external pressure and the strength of the substance being tested in fact does not hold. It became clear that this dependence is at least approximately linear. This fact, I think, any physicist will intuitively consider more correct and more consistent with the real state of affairs. Be that as it may, there is an increase in strength with increasing external pressure, and it is advantageous to apply the external supporting pressure in the form of hydrostatic pressure. As the specimens in Fig. 14 show, under these conditions there is a noticeable increase in the plasticity of steel.

The pressure limit mentioned above, 125,000 kg/cm², must be reduced still further when more accurate measurements are required, since the carboloy piston exhibits the phenomenon of slow creep. Under the influence of high external supporting pressure, carboloy loses its usual brittleness and becomes capable of appreciable plastic deformations. At the same time, no strengthening after deformation (work hardening), as in steel, is observed in it; the phenomenon taking place in it is rather close to viscous flow, which is characterized by an arbitrarily large deformation under a sufficiently prolonged action of pressure. For accurate measurements it is desirable to reduce the pressure on the piston to 110,000 kg/cm². This corresponds to a pressure of 100,000 kg/cm² inside the vessel, if the influence of friction is taken into account.

Fig. 13. Small-size apparatus immersed in the fluid of a large apparatus for pressures of 25,000 kg/cm² and higher, making it possible to obtain a pressure of 100,000 kg/cm². The substance under test is compressed on two sides by two carboloy pistons. The cylinder of the small apparatus is made of carboloy and is embraced by a steel ring.

APPLICATION OF CARBOLOY

Thus, the possibility opened up of making simple measurements of volume at pressures up to 100,000 kg/cm², and of studying polymorphic transformations and compressibility in this pressure range. When I began to work on this program, it soon became clear that yet another circumstance hindered the obtaining of accurate results, namely, a strong distortion (increase) of the transverse section of the steel vessel, exceeding 10%; moreover, there were absolutely no data for introducing a correction for this error. Obviously, the only way to eliminate this error was to make the vessel from a material,

Fig. 14. Increase in the plasticity of steel under pressure. At the top is shown steel of two grades, fractured at atmospheric pressure. At the bottom are specimens of the same grades of steel, fractured under a hydrostatic pressure of 25,000 kg/cm²; the almost complete reduction in the diameter of the specimens on the right is striking.

possessing higher elastic constants and, consequently, deforming less. The only material suitable for this purpose in terms of elastic constants was carboloy, but at first it seemed to me that it would have to be rejected for two reasons: the impossibility of making cylinders from it, and the fact that carboloy, as one might think, should tear more easily under tensile stress than steel, since its excess strength is manifested in compression. However, after some search for data on the relative properties of carboloy, it turned out that neither of these reasons was decisive. Basset[^20] published the results of work on obtaining high pressures in carboloy cylinders with outer shells of stressed steel. It also turned out that by just this time the technique of drilling carboloy had been developed in America, and it became possible to make cylinders from it. As for rupture of carboloy by internal pressure, my conditions were more favorable than Basset’s, since the external pressure of the support, owing to the difference in compressibility of carboloy and the steel shell, had to be greater. I hoped that this additional pressure would be sufficient to give the vessel the strength necessary to exceed the pressure obtained in Basset’s experiments to the desired value.

The first test was successful, which is very rare. The expansion of the cylinder was three times smaller than with steel, and it could be calculated with less uncertainty than before. The total accuracy of the measurements was approximately \(2^0/_0\). Often, when expanding the field of investigation, one has to work with lower accuracy; however, in the present case the accuracy was sufficiently high for the results obtained to be of interest. This accuracy probably falls within the limits required by modern theory.

With the new apparatus I began to carry out a program of measurements at pressures up to \(100\,000\ \mathrm{kg}/\mathrm{cm}^2\). I obtained values of volume compression and established polymorphic transformations of seventeen elements[^21] and several simple compounds in this new region. Compressibility curves for some of them are given in Fig. 15. In this pressure range there are a number of new polymorphic forms. For example, bismuth has a new transformation, and its state diagram proves to be extraordinarily similar to the state diagram of water. Antimony also revealed a new form, which had been sought unsuccessfully at lower pressures on the basis of the similarity of the crystal lattices of the ordinary forms of bismuth and antimony.

Generally speaking, still higher pressures are attainable, but here the experimenter must already reconcile himself to the increasing uncertainty of the pressure values themselves and to the lesser scientific significance of the useful results obtained. In the literature one can find groundless values of pressures that can be obtained

in very short intervals of time when a steel projectile is fired into a conical recess in a massive block. No other results were obtained in these experiments, apart from expansion or rupture of the steel itself. The study of rupture under such conditions may be of interest, but it is unlikely that, apart from this, anything can be obtained in this way. Even the very study of rupture loses significance, owing to the impossibility of indicating the magnitude of the stress. All our ever-expanding knowledge of the properties of matter under pressures up to \(100\,000\ \mathrm{kg/cm^2}\) shows that the stresses attainable under the indicated conditions have been greatly exaggerated. In reality they are no greater than those which can be attained by other, more refined methods.

[In the graph: vertical axis \(\Delta V/V_0\); horizontal axis “Pressure in \(\mathrm{kg/cm^2}\)”; curves labeled \(Rb\), \(K\), \(Ba\), \(Li\), \(Se\), \(Bi\), \(Sb\).]

Fig. 15. Volumetric compressibility of the elements under pressures up to \(100\,000\ \mathrm{kg/cm^2}\). The jumps in the curves correspond to polymorphic transformations.

It seems to me that some very limited investigations can be carried out at a constant and measured pressure even above \(100\,000\ \mathrm{kg/cm^2}\). I shall recall that I kept small pieces of graphite under a pressure of \(100\,000\ \mathrm{kg/cm^2}\) in an apparatus made entirely of steel. It is quite obvious that higher pressures can be obtained if a very small apparatus of this kind is subjected to an external hydrostatic pressure, developed in the apparatus up to \(30\,000\ \mathrm{kg/cm^2}\), and that still higher pressures can be reached in small apparatuses made of Carboloy. This, in essence, is what I did, with only a few changes. Fig. 16 shows two pieces of Carboloy after such experiments. In thin layers of various materials pressures up to \(400\,000\ \mathrm{kg/cm^2}\) and even more can readily be obtained.^22

These specimens are nevertheless large enough that, after holding them under pressure, they could be examined radiographically and it could be determined whether any irreversible changes had occurred in them, such as the transformation of yellow phosphorus into black at \(12000\ \mathrm{kg}/\mathrm{cm}^2\). For these experiments seven or eight elements were chosen, whose positions in Mendeleev’s periodic table suggested that analogous transformations might be expected, but the result of these experiments proved negative. Even at such high pressures

Fig. 16. Two pieces of carboloy, compressed over the contact area by a pressure of \(400000\ \mathrm{kg}/\mathrm{cm}^2\). After release of the pressure, radial cracks formed.

graphite does not transform into diamond. It is very likely that Tammann is right, and if a certain transformation does not appear with a moderate excess of pressure compared with the pressure for the thermodynamically reversible transition, then it will not take place under any pressure, however high, since the tendency toward transformation passes through a maximum with increasing pressure.

Extremely interesting cases of ruptures are observed at these very high pressures. It would be very important to carry out their systematic investigation, because they can be measured with some degree of accuracy; but so far I have not had the opportunity to take up this question. Another problem that arises in connection with obtaining very high pressures is the search for irreversible transformations. In view of the negative results obtained so far

by me in this direction, I shall in all likelihood cease to occupy myself with this question until more well-founded theoretical considerations appear concerning the most probable places in the periodic system in which such effects may be sought.

The next stage in the development of the technique for obtaining still higher pressures evidently consists in the construction of a two-stage external support, but this for the present appears to be a task of the very distant future.

REFERENCES

1. A general survey of work on high pressures up to 1931 may be found in my book: The Physics of High Pressure, McMillan, 1931*).
2. Amagat, E. H., Ann. Chem. Phys., 29, 68, 1893.
3. Tamman, G., Kristallisieren und Schmelzen, Barth, Leipzig, 1903.
4. Bridgman, P. W., Phil. Mag., July, 1912, p. 63; Journ. Appl. Phys., 9, 1938, 517; Mech. Eng., Feb., 1919.
5. Bridgman, P. W., Journ. Am. Chem. Soc., 36, 1914, 1344; 38, 1916, 609.
6. Jacobs, R. B., Journ. Chem. Phys., 5, 1937, 945.
7. Starr, Chauncey, Phys. Rev., 54, 1938, 210.
8. Bridgman, P. W., Proc. Am. Acad., 59, 1923, 165.
9. Born, Max, Atomtheorie des festen Zustandes, Teubner, Leipzig, 1923.
10. Ewell, R. H. and Eyring, H., Journ. Chem. Phys., 1937, 726.
11. Bridgman, P. W., Proc. Am. Acad., 68, 1933, 27.
12. Bridgman, P. W., Phys. Rev., 48, 1933, 825.
13. Rossini, F. D. and Jessup, R. S., Nat. Bur. Stds., Research Paper RP1141, 1938.
14. Bridgman, P. W., Proc. Am. Acad., 72, 1937; 72, 1938, 222.
15. Bridgman, P. W., Journ. Chem. Phys., 9, 1941, 794.
16. Bridgman, P. W., Proc. Am. Acad., 74, 1940, 1.
17. Bridgman, P. W., Proc. Am. Acad., 74, 1940, 11.
18. Bridgman, P. W., Phys. Rev., 57, 1940, 342.
19. Griggs, D. T., Journ. Geol., 44, 1936, 541.
20. Basset, J., Journ. de Phys. et de Rad., 1, 1940, 121.
21. Bridgman, P. W., Phys. Rev., 60, 1941, 351.
22. Bridgman, P. W., Journ. Appl. Phys., 12, 1941, 461.

*) P. W. Bridgman, The Physics of High Pressures, translated from English by M. P. Volarovich, ONTI, Moscow—Leningrad, 1935.

1. American Scientist, 31, No. 1, 1, 1943; translated from the English by A. A. Leont’eva under the editorship of Prof. M. P. Volarovich. ↩