Recent Works in the Field of High Pressures\*

P. W. Bridgman

Submitted 1947 | SovietRxiv: ru-194701.01990 | Translated from Russian

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Recent Works in the Field of High Pressures*

P. W. Bridgman

Mechanical effects of high pressure. 4. Phase transformations under pressure in one-component systems. 5. Phase changes under pressure in multicomponent systems. 6. Effect of pressure on viscosity. 7. Effect of pressure on elastic constants. 8. Effect of pressure on plastic flow and similar phenomena. 9. Various mechanical effects of hydrostatic pressure.

Mechanical Effects of High Pressure

4. Phase Transformations under Pressure in One-Component Systems

A. Evaporation

We shall not consider ordinary evaporation or critical phenomena, but shall dwell on one paper because of the considerable interest it presents and the magnitude of the pressures. Basse^198 found that the triple point for graphite is at 4000°K and 105 kg/cm². The pressure was transmitted by argon, and the observations were made visually through a window. Above the triple point the method was not sufficiently accurate for a quantitative determination of the value

$$ \frac{dt}{dp} $$

for the solidification of graphite from its amorphous phase, but it gave sufficiently accurate values to establish the fact that the sign of the derivative was positive. This made it possible to correct Basse’s earlier conclusions that the crystallization curve of graphite falls with increasing pressure. In these experiments the pressure reached 11,500 kg/cm², and in all cases the graphite phase separated out from the amorphous phase.

B. Melting

It is not possible to draw an absolute boundary between the discussion of questions of melting, which are the main subject of this section, and polymorphic transformations, which will be discussed in the following section, since in a number of cases one polymorphic form passes

* Continuation. See Uspekhi Fizicheskikh Nauk, vol. XXXI, no. 1, p. 53 (1947), P. W. Bridgman, Reviews of Modern Physics 18, no. 1, 1 (1946). Translated by D. Gamburg and D. Tsiklis, edited by Prof. I. Krichevsky.

into the other along the melting curve. Many of the works devoted to melting have as their aim the resolution of the question of the character of the melting curve, with respect to which even now there is no unanimous opinion.

The disagreements concern whether the melting curve ends at a critical point, whether it has a maximum, whether it rises to some asymptotic temperature with increasing pressure, or rises without bound with increasing temperature and pressure.

At the end of the period covered in my book, Simon and his collaborators^199 carried out an important study of the melting curves of certain permanent gases at pressures up to 6000 atm.

Simon and Glatzel^200 proposed an analytical expression for the melting curve, namely $\log(a+p)=c\log \tau+b$, which reproduced the melting curve over a wide interval and acquired great importance. The form of the equation requires an infinite growth of pressure and temperature. Simon’s point of view was that, nevertheless, the melting curve probably ends at a critical point.

To clarify this question, it is not enough to know the form of the melting curve; it is necessary to determine other thermodynamic parameters. For this purpose Simon and Stekly^201, at the beginning of the period under discussion, undertook direct measurements of the latent heat of melting of helium along the melting curve. The experimental difficulties were very serious, and only preliminary results were obtained. They showed that the latent heat of melting at first increases, and then decreases slightly, which, as Simon notes, is compatible with the final fall that should be expected if a critical point exists. The experiment, however, was not convincing, and Simon did not return to this question.

There is a series of works from Leiden^202–207 by Keesom and his collaborators, in which the melting of certain permanent gases was determined over a considerably smaller pressure interval than in Simon’s work, but with greater accuracy. These measurements concerned the melting of hydrogen up to a pressure of 610 kg/cm², neon up to 200 kg/cm², oxygen up to 170 kg/cm², and nitrogen up to 200 kg/cm².

The Simon–Glatzel equation proved applicable, and its constants were determined. In comparison with the results of Simon, Ruhemann, and Edwards, the temperatures obtained by Keesom were higher. This could be explained by the insufficient purity of the substances used by Simon; however, there is another, more probable source of errors, which I noted when comparing Simon’s results for nitrogen with my own data. Both Simon and Keesom used the capillary-blockage method. In this method the substance under investigation was placed in two vessels connected by a capillary, the temperature of which was lowered until the increase of pressure in one vessel was no longer transmitted to the other vessel, owing to the solidification of the substance in the capillary. The plug formed in the capillary is evidently subjected to a certain shear stress, and it is known that na-

shear stress lowers the melting point, forcing one to suppose the presence of impurities. If the possibility of an error has been ascertained, it can be reduced by appropriate measures; however, Simon evidently did not notice this cause, and it may have introduced a noticeable error into his measurements. In the last paper by Keesom in this series, devoted to oxygen and published in 1935, my criticism was mentioned, and the author promised to investigate in the following work the question of whether this error would be significant under the conditions in which Keesom worked; apparently, this investigation was not carried out.

Later, Michels^208 and his collaborators in Amsterdam applied the same method to the investigation of the melting curve of CO₂ under pressures up to 2800 kg/cm² and of mercury^209 up to 3000 kg/cm². They were fully aware of the possibility of error and, by suitable changes in temperature, were able to reduce the difference in pressure on the two sides of the plug, at the moment of its formation, to a value less than one atmosphere, so that the error should have been very small. Michels’s results agreed with mine within the errors of my experiments. He was able to represent his results over the whole pressure interval by the Simon and Glatzel equation. Neither Keesom’s nor Michels’s measurements are sufficient to determine the distinction between a critical point and infinite growth, since the other necessary parameters were not determined.

Here the data of Keesom and Clusius^202 should be mentioned; although they do not pertain to melting proper, the results they obtained are unique and do not fit into the general classification scheme. Helium is the only substance with two liquid amorphous phases. The transition temperature is a function of pressure. Keesom and Clusius determined the coordinates of the transition line. It is very short and terminates on the degassing line. This line is directed downward from 2.19° and 0.050 atm to 1.86° and 23.6 atm.

Returning to the melting curve, it should be pointed out that much activity on this problem was shown in Tammann’s laboratory^210–214, with most of the work being carried out by Deffet. These works are limited to a pressure interval of 1000 kg/cm²; their special feature is the careful purification of the substances.

Deffet’s original method^210 was a modification of the well-known temperature-arrest-point method, widely used at atmospheric pressure. In Deffet’s method the high-pressure vessel was maintained at constant temperature, and the pressure was lowered from a value sufficient for complete solidification of the substance. On crossing the melting line, melting occurred with automatic restoration of the pressure.

A drawback of this method is the circumstance that it gives no change in volume and, in the case of appreciable impurities in the substance, requires careful work in order to introduce the appropriate corrections.

With this apparatus, a study was made of the melting curves of forty substances up to a pressure of $1000\ \mathrm{kg}/\mathrm{cm}^2$. These substances were as follows: carbon tetrachloride, nitromethane, pentachloroethane, ethylene bromide, tertiary butyl alcohol, tertiary amyl alcohol, formic acid, acetic acid, propionic acid, butyric acid, valeric acid, caproic acid, enanthic acid, caprylic acid, formamide, cyclohexane, benzene, nitrobenzene, $p$-nitrotoluene, $o$-xylene, $p$-xylene, phenol, $m$-cresol, benzophenone, methyl benzoate, benzonitrile, aniline, dimethylaniline, $p$-toluidine, piperidine, cetyl alcohol (melting and transition), dotriacontane (m.p. and transition), methylcyclopentanol (m.p. and transition), acetophenone (m.p. and transition), cetyl iodide (stable and unstable modifications), $o$-nitrotoluene (stable and unstable forms), orthotoluidine (stable and unstable modifications), salol (one stable and two unstable modifications), and methylene iodide. The last has a new stable modification under pressure and also an entirely unstable modification, the existence of which had not previously been known. This entirely unstable modification can reversibly transform into the new stable modification. This is precisely the phenomenon that explains many strange features of the phase diagram obtained by Tammann for this substance. In comparison with the work of other authors, Deffet’s melting curves generally have somewhat smaller curvature. Deffet combined the slope of the melting curves with known values of the latent heat of fusion in order to calculate the change in volume on melting. The pressure interval he used is hardly sufficient to give a complete picture of the final character of the melting curve. He inclines to the opinion that an infinite rise is just as possible as anything else.

Timmermans and Deffet $^{211}$ traced the melting curve of heavy water up to $1051\ \mathrm{kg}/\mathrm{cm}^2$ and $-5.00^\circ$; they found that it runs almost parallel to the melting curve of ordinary water. In 1940 Deffet $^{213}$ modified his method so as to measure the changes in volume on melting in the same pressure interval up to $1000\ \mathrm{atm}$. He published data for the freezing temperature as a function of pressure, the change in volume, the latent heat, and the slope of the melting curves for the following substances: gallium, succinic acid, bromobenzene, $m$-cresol, benzyl alcohol, alpha-bromonaphthalene, dibenzyl, ethyl stearate (stable and unstable), cyclohexanol (also the transition), $p$-dibromobenzene (with transition), $p$-dichlorobenzene (with transition), $o$-cresol (with transition), and veratrol (stable and unstable modifications). Deffet and Vlerick $^{214}$ in 1942 published analogous data for benzene, $p$-xylene, and naphthalene. In 1938 Robberechts $^{212}$, using the same apparatus, traced the ordinary melting line and the transition line of an isotropic liquid into an anisotropic one (liquid crystals) for the following substances: formate, acetate, propionate, $n$-butyrate, $n$-caproate, and $n$-valerate, and cholesteryl chlo-

of chloride, methyl-, ethyl-, and propylcarbonates of cholesterol and p-azoxyanisole, and ethyl carbonates of azoxyphenol, p-azophenol, p-azoxybenzoate. It was found that the transition line for all these substances rises approximately in the same way: by $50^\circ$ per $1000\ \mathrm{kg}/\mathrm{cm}^2$. This is in all cases greater than for the melting of the anisotropic phase, so that the region of existence of liquid crystals becomes more extensive with increasing pressure.

Basset $^{215-218}$ published several papers on the melting of graphite, already mentioned, and also traced the melting curve of tetrahydronaphthalene $^{219,220}$ up to $11000\ \mathrm{kg}/\mathrm{cm}^2$ and drew the conclusion that a critical point exists, evidently without full knowledge of the literature.

Svalow and Gibson $^{221}$ determined by a visual method the effect of pressure up to $2000\ \mathrm{kg}/\mathrm{cm}^2$ on the melting point of o-, m-, and p-xylene. Their results are in satisfactory agreement with Tammann’s and my own results. Dow and Gibson $^{222}$ investigated, up to $4000\ \mathrm{kg}/\mathrm{cm}^2$, the melting of o-, m-, and p-mononitrophenol. They compared two methods: the usual method of a moving piston with another method in which the high-pressure vessel was kept in a thermostat at constant temperature, the pressure was lowered until it intersected the melting curve, and the onset of melting was detected with the aid of a thermocouple placed in the substance under investigation. Good agreement was obtained between the two methods.

Clusius and Weigand $^{223}$ traced the melting curves from the triple point to 200 atmospheres for the following gases: A, Kr, Xe, CH$_4$, CH$_3$D, CD$_4$, C$_2$H$_4$, C$_2$H$_6$, COS, and PH$_3$. The results were represented by a second-degree equation in pressure.

Several theoretical papers appeared on the question of the character of the melting curve. In 1932 van Laar $^{224}$ abandoned his former view that the melting curve has some temperature as an asymptote, and adopted the view that the rise of the curve is unlimited. He derived theoretically an equation for the melting curve:

\[ p+a=Bt+Ct^{1+\varepsilon}, \]

where the coefficients depend on the properties of the pure phases. This equation is very reminiscent of the empirical formula of Simon and Glatzel, which, for purposes of comparison, may be written in the form: $p+a=Ct^b$.

Ieneke, at about the same time, published two papers $^{225}$. The first paper showed what equation should be written for a melting curve that, according to van Laar, possesses an asymptote; in the other paper this equation was rejected when van Laar changed his point of view. In 1934 Tammann and Moritz $^{226}$ published a paper on the character of the melting curve. Tammann was still not inclined to abandon his maximum temperature, although the temperature of any possible maximum rose continuously with every widening of the experimental interval. In this paper he notes that my experi-

experimental data for the change in volume upon melting up to $12\,000\ \mathrm{kg/cm^2}$ can be represented, within the limits of experimental error, by the equation: $\Delta v = a - b \log(C + p)$. According to this equation $\Delta v$ must become zero at some finite pressure, which is the pressure of the maximum. For $\mathrm{CO_2}$ this should occur at $40\,000\ \mathrm{kg/cm^2}$ and for nitrobenzene at $67\,000\ \mathrm{kg/cm^2}$. The Simon and Glatzel equation for the melting curve was rejected, since it does not allow for a maximum. Rice ${}^{227,228}$ published two theoretical papers on the liquid—solid variety for argon. As a result of theoretical reasoning he gives expressions for some thermodynamic parameters separately for the solid and liquid phases, from which an equation for the melting line can be derived. His equations reproduce my experimental data up to $10\,000\ \mathrm{kg/cm^2}$. Rice evidently adheres to the opinion that the critical point can in no way be excluded.

Several papers on this question came from my laboratory. In 1934 ${}^{111}$ I traced the melting curves of nitrogen and argon up to $5000\ \mathrm{kg/cm^2}$ and pointed out that from these new data, obtained over a considerably larger interval of the given parameters than any previous data for liquids up to $12\,000\ \mathrm{kg/cm^2}$, one can draw the same conclusion as from my earlier works, namely that there is an unlimited rise of the melting curve with pressure. My melting temperatures were higher than Simon’s, and I indicated the possible source of the error, which has already been discussed. Later Benedict ${}^{110}$ improved my apparatus and obtained more accurate data for the melting curve. In particular, he could not confirm the existence of the anomaly that I had found at the end of the curve at low pressure, and attributed it to the possible formation of a new modification of nitrogen.

In 1935 ${}^{131}$ I determined the melting curves of $\mathrm{D_2O}$ up to $9000\ \mathrm{kg/cm^2}$ and $20^\circ$; they included the melting curves of four different modifications. In general, the melting curves for heavy water run parallel to the melting curves of ordinary water. At the same time the complete phase diagram was determined, and this question will be discussed below. In 1937 ${}^{229}$ the melting curve of a new modification of ice, existing at high pressure (ice VII), was traced up to $190^\circ\mathrm{C}$ and $40\,000\ \mathrm{kg/cm^2}$. The difference in densities between the liquid and solid phases proved to be surprisingly large, if one takes into account the formation of four other modifications of ice at lower pressures. At the triple point liquid—ice VI—ice VII, the change in volume is $0.09\ \mathrm{cm^3/g}$. The change in volume and the curvature of the new melting curve had the usual character. On the other hand, a new peculiarity was found for the latent heat. Usually it remains approximately constant along the melting line. In this case the latent heat increases with increasing pressure and temperature, and at a rate more than sufficient to compensate for the increase in temperature, so that the difference in entropy between the liquid and solid

with the phase increases with the rise of temperature and pressure along the melting line. This is the first clearly expressed example of such a regularity. It must be particularly emphasized that this is incompatible with either a maximum or a critical point.

Finally, there are my measurements, up to 50,000 kg/cm², of the volumes of both the liquid and the solid phases, which have already been discussed¹³² in connection with the compressibility of liquids and solids. The melting of the following substances was studied: ethyl alcohol, n-butyl alcohol, ethyl bromide, n-propyl bromide, chloroform, carbon disulfide, chlorobenzene, methylene chloride, and water. The pressure interval covered 40,000 kg/cm², and the temperature reached 200°.

It is usually very difficult to trace melting phenomena up to the highest pressures, 50,000 kg/cm², owing to the phenomenon of supercooling, and also often because at such pressures a considerably higher temperature is required.

The measurements were carried out by the method of the moving piston, which made it possible to determine all the necessary parameters. The general character of the results remained the same as for lower pressures, and not one of the parameters, either by itself or in combination with the others, changed in such a way as not to confirm the previous opinion that the melting curve rises continuously with temperature and pressure. The curve rises with diminishing curvature, the curve of the difference of volumes becomes convex toward the pressure (or temperature) axis, and the latent heat does not decrease. In fact, the latent heat shows a new tendency in this pressure interval; in general it formerly remained constant, whereas now it shows a tendency to increase. In all cases there is at least a slight increase, and there are three cases of so noticeable an increase that the entropy difference of the liquid and the solid increases along the curve. These substances are: the already mentioned water, ethyl alcohol, and n-butyl alcohol. The last two substances show a less noticeable increase in entropy. In general, in my opinion, these results, obtained over a considerably extended pressure interval, only confirm the conclusion that I drew from all my previous experiments, namely, that there is no basis whatever for expecting anything other than an infinite rise of the melting curve. This need not necessarily mean, however, that any substance, regardless of the magnitude of the temperature, can be made to solidify by applying a sufficiently high pressure.

At high pressure a new phenomenon appears, namely a large increase in viscosity, which retards the course of all internal changes and may lead to infinitely great supercooling.

The notion compatible with other experimental data is that the tendency toward the formation of nuclei of a new phase passes through a maximum when the pressure is shifted at constant temperature beyond

point of equilibrium. Thus, if a liquid has not yet been brought to freezing at pressures within the limits of the given interval, there is a possibility that no pressure will be sufficient for this. In the above-mentioned work four substances were found which could not be brought to freezing, although the thermodynamic conditions were favorable.

The significance of this phenomenon for geophysics is clear.

Other regularities in this pressure interval, connected with the phenomenon of melting, were also discovered. The absolute values of the volumes of liquids and solids decrease along the melting line, and the influence of pressure predominates over the influence of temperature. The compressibility of the solid phase at the melting point is never greater than that of the liquid phase at the melting point, and is usually smaller, though not by much, of the order of 25%. The internal energy of both the liquid and the solid phase, in general, probably increases along the melting curve. Finally, the fact that the entropy difference between the liquid and solid phases increases means that high pressure favors the specific heat capacity of the liquid phase being greater than the specific heat capacity of the solid phase.

CITED LITERATURE

J. Basset, J. de phys. et rad. 10, 217 (1939). Melting of graphite in argon. The triple point and preliminary diagram of the solid, liquid, and gaseous states of carbon. Part I.
F. Simon, M. Ruhemann and W. A. M. Edwards, Zschr. f. phys. Chem. B 6, 331 (1930). Melting curves of hydrogen, neon, nitrogen, and argon.
F. Simon und G. Glatzel, Zschr. f. anorg. allgem. Chemie, 178, 309 (1929). Remarks on melting curves under pressure.
F. Simon u. K. Steckel, Zschr. f. phys. Chem., Bodenstein Festband, 737 (1931). Latent heat of melting and density of helium between 15 and 20°K.
W. H. Keesom a. K. Clusius, Proc. Amst. Acad. Sci. 34, 605 (1931). Transition of liquid helium I into liquid helium II under pressure.
W. H. Keesom a. J. H. C. Lisman, Kon. Akad. van Wetens. Amst. Proc. 34, 598 (1931). Melting curve of hydrogen up to 450 kg/cm².
W. H. Keesom a. J. H. C. Lisman, Kon. Akad. van Wetens. Amst. Proc. 35, 605 (1932). Melting curve of hydrogen up to 610 kg/cm².
W. H. Keesom a. J. H. C. Lisman, Kon. Akad. van Wetens. Amst. Proc. 36, 378 (1933). Melting curve of neon up to 200 kg/cm².
J. H. C. Lisman (N. V. Boeken Steendrukkerij Eduard Ljdo, Leiden, 1934). Dissertation, melting curves of condensed gases.
J. H. C. Lisman a. W. H. Keesom, Physica 2, 901 (1935). Melting curve of oxygen up to 170 kg/cm².
A. Michels, B. Biaisse a. J. Hoohschagen, Physica 9, 565 (1942). Melting curve of CO₂ up to 2800 atm.
A. Michels, T. Wassenaar a. B. Blaisse, Physica 9, 574 (1942). Melting curve of Hg up to 3000 atm.
Lois Deffet, Bull. Soc. Chim. Belg. 44, 41 (1935). Piezometric investigations. I. Influence of high pressures on the melting temperature and the transformation temperature of organic substances.

Jean Timmermans et L. Deffet, Comptes rendus 200, 1661 (1935). Physical constants of the melting point of heavy water as a function of pressure.
Jean Robberecht, Bull. Soc. Chim. Belg. 47, 597 (1938). Piezometric studies. V. Anisotropic liquids under pressure.
L. Deffet, Bull. Soc. Chim. Belg. 49, 223 (1940). Piezometric studies. VI. Melting and transition temperatures.
L. Deffet et G. Vlerick, Bull. Soc. Chim. Belg. 51, 237 (1942). Piezometric studies. VII. Measurements of volume changes by piezometric analysis.
J. Basset, Comptes rendus 199, 144 (1934). Attempts to obtain crystalline carbon dioxide at very high pressures.
J. Basset, Soc. Fran. Phys. 434, 90 (1939). Phase diagram of carbon dioxide—new investigations of the triple point and the melting temperature of carbon dioxide under pressure.
J. Basset, Comptes rendus 208, 267 (1939). Melting of graphite under very high argon pressure.
J. Basset, Chim. et Ind. 46, 7 (1941). Experimental realization of the melting of graphite under argon pressure up to 11,500 kg/cm². Establishment of the triple point and sketch of a preliminary diagram of the solid, liquid, and gaseous states of carbon.
J. Basset, Soc. Fran. Phys. 434, 91 (1939). Solidification isotherms of tetralin at high pressures up to 11,000 kg/cm² and the possibility of a critical point in the solid—liquid system.
J. Basset, Comptes rendus 208, 169 (1939). Liquid—solid isotherm for tetrahydronaphthalene under pressure.
J. C. Swallow a. R. O. Gibson, J. Chem. Soc. 440 (1934). Effect of pressure on the melting point of o-, m-, and p-xylene.
R. B. Dow a. F. B. Hibbsham, J. Chem. Phys. 5, 960 (1937). Study of the melting of monotropic ice under high pressure.
K. Clusius u. K. Weigand, Zschr. f. phys. Chem. 46, 1 (1940). Melting curves of gases: A, Kr, Xe, CH₄, CH₃D, CD₄, C₂H₄, C₂H₆, COS, and PH₃ up to 200 atm.
J. J. van Laar, Kon. Acad. van Wetens. Amst. Proc. 35, 624 (1932), Equation of the melting curve.
Ernst Jänecke, Zschr. f. phys. Chem. A. 156, 161 (1931). On melting under pressure. I—Report on the significance of interpolation formulas; II, ibid, 162, 286 (1932).
G. Tammann u. G. Moritz, Zschr. f. anorg. allgem. Chemie 218, 60 (1934). On the course of melting curves.
O. K. Rice, J. Chem. Phys. 6, 472 (1938). Solid—liquid equilibrium for argon.
O. K. Rice, J. Chem. Phys. 7, 136 (1939). Some further comments on the solid—liquid equilibrium for argon.
P. W. Bridgman, J. Chem. Phys. 5, 964 (1937). Phase diagram of water up to 45,000 kg/cm².

C. Polymorphic Transformations

Two papers by Goranson and Kracek from the geophysical laboratory were published on the transformations of K₂Si₄O₉ ²³⁰ and sodium tungstate ²³¹. The measurements were carried out in an apparatus in which an electric furnace was mounted inside a high-pressure vessel; for cooling, water was passed intensively through the channels between the layers of the high-pressure vessel.

The closure of the vessel was effected by two lids pressed by the plates of a hydraulic press, the pressure of which could be increased in accordance with the rise of the internal pressure in the vessel. The polymorphic transformation was detected by the method of a temperature arrest, detected by a thermocouple introduced into the high-pressure vessel. Measurements with $K_2Si_4O_9$ were carried out up to a maximum pressure of $3000\ \text{kg}/\text{cm}^2$ and a temperature of $775^\circ$, just above the melting temperature. The melting curve of modification I falls with increasing pressure from $765^\circ$ (this is an example of ice-type melting, which has practically never been cited), and the transformation curve of modification I into modification II rises from $592^\circ$ to the triple point, close to $650^\circ$ and 2250 bar. Above 140 bar the substance decomposes into quartz and water, so that the transformation mentioned above belongs to the continuation of the curves into the region of thermodynamic instability. The melting curve of sodium tungstate was followed up to 1000 bar, starting from $695^\circ$. There are three solid modifications—the modification II has a very limited region of stability and almost immediately gives way to modification III, whose transformation curve into modification I was followed up to 1000 bar. The transition between modifications I and II is anomalous in that it proceeds without a change in volume, which means that the transformation temperature is independent of pressure.

The unstable continuation of the transformation line was followed up to 600 bar.

In 1931 Tammann and Kölgas $^{232}$ described a method which, independently of them, I later applied in some of my preliminary investigations. The substance, in the form of a cylindrical button with a thickness smaller than its diameter, is placed, in order to reduce friction, in a massive steel sleeve and is compressed simultaneously from both sides by two pistons set in motion by a hydraulic press. The chief advantage of the method consists in the enlargement of the pressure interval. With this apparatus they redetermined some transformation parameters for phenol and $AgJ$. The values obtained for the decreases in volume agreed with the data published by me better than with their own former values, obtained earlier by another method. They studied transformations in $FeS$. The transformation temperature changes from $130^\circ$ at atmospheric pressure to $10^\circ$ at $3000\ \text{kg}/\text{cm}^2$. This substance exhibits irreversible phenomena, and the density depends on the nature of the preliminary pressure treatment. They also investigated the transformations of borneol and of white tin into gray. The main purpose of applying the new apparatus was nevertheless the attempt to discover a modification of bismuth under high pressure analogous to the modifications of ice at high pressures. The investigators had no success in this: it later became clear that their maximum pressure of $19000\ \text{kg}/\text{cm}^2$ was not sufficient for this purpose.

Jacobs[^233] in my laboratory published several papers. His first investigation concerned the transformation of black phosphorus. The chief aim of this work was to find an explanation for the anomalous reaction rates that I had discovered. The range of his measurements extended to $230^\circ$ and $15{,}000\ \mathrm{kg/cm^2}$. He used the moving-piston method, together with quenching and investigation at atmospheric pressure. Jacobs found a new modification of black phosphorus, which is formed in the region of the pressure–temperature diagram lying below the line running from $17{,}000$ and $180^\circ$ to $11{,}000$ and $230^\circ$. Above this line, in the temperature–pressure plane, there is a region and, if the initial compression begins in this region, the anomalous rates of transition that I discovered occur, with possible transformation into the old, denser form. Still higher there is a region such that compression begun in it leads to an immediate and complete transition into the old form. The explanation of the anomalous phenomena I observed was that the less dense form was formed first under my conditions, and that, as the transformation developed, enough heat was liberated to raise the temperature inside the apparatus to that of a possible transition into the denser form. Calorimetric measurements lead to the following order of stability: black crystalline (the old dense form), red phosphorus, black amorphous (the new, less dense form), and yellow. The amorphous, less dense black modification of phosphorus found by Jacobs is probably the same as the second modification of black phosphorus found by Gulbransen, Gingrich, and Warren[^234] in an X-ray analysis of a sample of black phosphorus with which I had supplied them.

Jacobs[^235–^237] further developed the method, already cited by me,[^158] for taking X-ray photographs of substances under pressure, and applied this method to determine certain unknown crystal systems of such new modifications as can be obtained at a pressure of $5000\ \mathrm{kg/cm^2}$. He showed for the first time that AgJ at high pressure has the NaCl structure. From the spacings between the lines he calculated that the change in volume on transition is $0.0288\ \mathrm{cm^3/g}$, which is considerably greater than the value $0.0239$ found by me. He expressed the opinion that this discrepancy might be attributed to incomplete transformation of my sample. The latter had been pressed from powder, and suppression of such a transition in small grains is not something unnatural. Later I checked his explanation: with preliminary compression above $20{,}000\ \mathrm{kg/cm^2}$, which considerably exceeds the pressure of my first measurements, and subsequent lowering of the pressure, the change in volume exactly confirms Jacobs’s X-ray measurements. In the same article Jacobs gives X-ray photographs for the modification of $\mathrm{CsClO_4}$ existing at high pressure; however, the X-ray pattern was too complex, and it was not possible to establish the crystal system.

In the second paper he was able to investigate the transition of RbI. This substance proved to be especially sensitive to supercooling and to suppression of the transformation; to eliminate these effects it was necessary to use preparations of high purity. The modification existing at high pressure turned out to be a body-centered cubic lattice. One may suppose that other alkali halides, whose transition pressures lie outside the range of pressures attainable in this apparatus, have the same lattice. These experiments provide a firmer basis for various theoretical considerations concerning the structure of matter at high pressure. Jacobs found the change in volume at the transition to be 30% greater than mine; the explanation of this circumstance is probably the same as that already given. In the same paper a theory of these transformations is given. The energy relations in this case work out in such a way that the sodium halides will probably not be stable, at arbitrarily high pressure, in a body-centered lattice. This agrees with my recent observations up to 100,000 kg/cm². On the other hand, although the theory indicates that AgI, built on the NaCl type, may undergo a transition to a body-centered lattice near 50,000 kg/cm², this transition was not detected even at 100,000 kg/cm².

In this connection it is necessary to mention MacFarlane’s²³⁸ determination of the crystalline structure of high-pressure ice, although these measurements were not made under pressure. At the temperature of liquid air the transformation of this ice is so slow that it does not proceed at any appreciable rate at atmospheric pressure. Thus, if the ice has already formed at a higher temperature under pressure, the apparatus can be cooled and opened, the ice removed, and its structure determined roentgenographically in a chamber maintained at the temperature of liquid air. By this method MacFarlane found that ice II has a face-centered orthorhombic structure; at the same time all its crystallographic parameters were determined. Subsequently, less complete data were obtained for ices III, V, and VI, but not all of them were published.

Clusius and Weigand²³⁹ determined the effect of pressure up to 250 kg/cm² at low temperature on the I—III transition of solid H₂S and D₂S. The changes in volume for the deuterium compound were approximately 20% smaller than for the compound of ordinary hydrogen.

Wilson²⁴⁰ studied the influence of pressure up to 10,000 kg/cm², at temperatures up to 426°, on the transformations ordered phase—disordered phase in the alloys CuAu, Cu₃Au, CuZn, and Cu₃Zn. The work was carried out at Yale University under the direction of MacKinnon.

The method was based on determining the break in the curve of electrical resistance as a function of pressure. The general high-pressure technique was very similar to that used by me, and part of the apparatus was lent by me. The entire vessel containing the specimen was heated to the required temperature, and leads for measuring the resistance...

passed through a connecting tube. The critical points for the alloys CuAu and Cu$_3$Au increased with pressure, the overall effect of which apparently somewhat increased the degree of ordering of the components. Among the results obtained were detailed data on the effect of pressure and temperature on resistance over an unusually wide temperature range. As regards the general questions concerning transformations of the ordered phase—disordered phase type, one may again refer to my data on anomalous changes of volume for this class of substances.

Bars$^{241}$ determined by the X-ray method the structure of the high-pressure modification KNO$_3$ III. The method is in principle similar to Mac Farlane’s method, although quite different from it in its details. With appropriate manipulations it is possible to obtain the high-pressure modification at atmospheric pressure and to investigate its structure. It was found that the structure of the substance belongs to the ditrigonal pyramidal class according to Groth (space group $C^5_{3v}$).

Dow$^{242}$ studied the effect of pressure on the internal change in rubber which corresponds to solidification. At 8000 kg/cm$^2$ there is an enormous delay in the transformation, which under these conditions did not occur even over fourteen days. At a lower pressure, 1270 kg/cm$^2$, and a temperature of 77° it proceeds completely; the coordinates of the transformation point coincide with those calculated from the Clapeyron equation.

Prosvirin$^{243}$ found that a uniaxial pressure of 12,000 kg/cm$^2$ (nonhydrostatic pressure) has a considerable stabilizing effect on the internal transformations that often occur spontaneously in tool steel.

Günther, Geselle, and Rebentisch$^{244}$ made a serious, though unsuccessful, attempt to effect the transformation of graphite into diamond, applying at sufficiently high temperatures a pressure exceeding the pressure of the thermodynamically reversible transition, so that an appreciable rate of this transformation was to be expected.

In estimating the necessary conditions they used Simon’s calculations, according to which at 2000° the pressure of the reversible transition is 45,000 kg/cm$^2$. Their apparatus was multilayered in order to give it greater strength.

The pressure was obtained by means of air pressure on a hydraulic press that drove a large piston. Air was admitted until sufficient pressure was created to break the two rods by which the press plate was supported. When they broke, the plate received a jolt and moved the piston, and the latter forced into the high-pressure vessel a piece of graphite heated by an electric current inside the vessel. The initial pressure was impulsive in character and was calculated from the deformation of calibrated steel plates. The final pressure was determined from the air pressure on the press plate. The graphite was initially heated to 3000°.

It was assumed that the initial pressure was approximately $120\,000\ \mathrm{kg}/\mathrm{cm}^2$, and the final pressure $100\,000\ \mathrm{kg}/\mathrm{cm}^2$. The transformation was not effected, and the authors regard their results as negative, explaining them by the short duration of the experiment, insufficient for an appreciable course of the transformation. It seems to me, however, more probable that their estimate of both the temperature and the pressure was too high. The piece of graphite was small and had to pass several centimeters before finally reaching the receiver; in this process there must have been a considerable drop in temperature.

It is difficult to believe that the steel in the construction of their apparatus could withstand so high a stress; this almost certainly could not have been the case at their final static pressure, estimated at $100\,000\ \mathrm{kg}/\mathrm{cm}^2$. No account was taken of the friction of the steel piston against the walls of the vessel, which under the conditions of the experiment must have been extremely large. They reported that under their conditions graphite with a density of 2.355 was obtained instead of 2.25, characteristic of a normal single crystal of graphite, with a contraction of the normal atomic spacing along the C-axis by $0.07\ \text{\AA}$.

The same authors$^{245}$ used the same apparatus to study the conditions for the formation of black phosphorus. Holding yellow phosphorus for five minutes at $60\,000\ \mathrm{kg}/\mathrm{cm}^2$ leads to the formation of a grayish-black mass, for the most part soluble in $\mathrm{CS}_2$. With an impact of $1\,000\,000\ \mathrm{kg}/\mathrm{cm}^2$, a black product is formed, insoluble in $\mathrm{CS}_2$. It conducts electric current and has practically the same density as my black crystalline phosphorus. They observed a partial reverse transformation into yellow phosphorus after a specimen of black phosphorus had been kept for six months in a sealed glass tube; the origin of the sample of black phosphorus was not indicated. The conclusion was drawn that black phosphorus is unstable in comparison with yellow and, all the more, in comparison with red phosphorus. They also noted that they obtained black phosphorus directly from modification I of yellow phosphorus at room temperature, instead of from modification II of yellow phosphorus, as I had done. They overlooked, however, the fact that their modification I had passed through region II before the conditions for transformation into black phosphorus were reached. It seems to me probable that, under the conditions of their experiments, they obtained both Jacobs’s black amorphous phosphorus and my crystalline modification of black phosphorus. They were acquainted neither with the works of Jacobs$^{233}$ nor with my own work of 1935,$^{246}$ in which violet phosphorus was transformed into black.

My own investigations of polymorphic transformations in this period began in 1931 with the study, at a pressure of $12\,000\ \mathrm{kg}/\mathrm{cm}^2$, of the already reported$^{178}$ volume anomalies in $\mathrm{NH}_4\mathrm{Cl}$ and $\mathrm{NH}_4\mathrm{Br}$. At atmospheric pressure these anomalies are usually described as transformations of the second order. With increasing pressure, the temperature of the anomalies in $\mathrm{NH}_4\mathrm{Cl}$ rises, and the abruptness of the discontinuity in thermal expansion

becomes smeared out. In $NH_4Br$, on the other hand, the temperature of the anomaly decreases with increasing pressure, and the discontinuity becomes sharper, so that it cannot be distinguished experimentally from a discontinuity of the volume itself, i.e., the transformation of the second order passes over into a transformation of the first order with increasing pressure. In reality, of course, no true discontinuity of continuity can be established experimentally, and the description of the data in terms of a discontinuity of one kind or another is only a matter of approximation and convenience.

In 1932 investigations up to $12000\ \mathrm{kg}/\mathrm{cm}^2$ were carried out for the considerably more smeared-out transition in $Ag_2O$, already referred to$^{179}$.

In 1934 I made my first measurements in a new, much wider pressure range$^{247}$. In an apparatus with two pistons, already used by Tammann, I found the expected transition of bismuth at $25000\ \mathrm{kg}/\mathrm{cm}^2$ and transformed white phosphorus into black at room temperature and $35000\ \mathrm{kg}/\mathrm{cm}^2$. It is very probable that this black phosphorus contains a noticeable fraction of amorphous black phosphorus of Jacobs; there were indications that I had not obtained the former crystalline modification.

In 1935$^{181}$ a complete phase diagram was compiled for heavy water up to $9000\ \mathrm{kg}/\mathrm{cm}^2$. The transition lines between the various modifications ran almost parallel to the corresponding lines of the diagram for ordinary water: the temperatures were approximately from $2.5^\circ$ to $4^\circ$ and higher. During the investigation an absolutely unstable modification of ice was discovered; the latter usually forms instead of the stable modification V in the region of stability of this modification. The thermodynamic parameters of the reversible melting of ice IV were determined, the new modification of ice was named, and the reversible transformation of ice IV into ice VI was established. After the existence of this modification of ice had been established for heavy water, I again reviewed my original data for ordinary water and found that the existence of the same unstable modification of ice had already then been discovered and some parameters measured. Earlier this result had been rejected as due to experimental errors. In detail there is an absence of complete parallelism between the phase diagrams for the two forms of water, which must be taken into account in the final and complete theory. This discrepancy shows that the phenomenon is not fully explicable from the standpoint of the difference in zero-point energy alone.

In 1935$^{4(a)}$ I published my first results obtained with the new technique of external reinforcement of conical vessels. The first measurements were made with elements, in the pressure range up to $50000\ \mathrm{kg}/\mathrm{cm}^2$ at temperatures from $-80^\circ$ to $200^\circ$. The method used was that of the moving piston at constant temperature, permitting the determination of all thermodynamic parameters of the transformation. Three high-pressure modifications were found

for bismuth, one for mercury, and one for thallium, two for tellurium, one of which was probably the same as had been known as a high-temperature modification at atmospheric pressure. Two new modifications were found for gallium, one of them being quite unstable, and one new modification was found for iodine.

New modifications were found for three potassium halides in the pressure interval from 18,000 to 20,000 kg/cm², which had been expected by analogy with rubidium salts but had not been found in previous investigations. In 1937, I4 (b) and (c) applied the same technique in the same pressure and temperature intervals to determine the phase diagram and thermodynamic parameters at the transitions of the following thirty-five substances (hereafter, the number after the substance will indicate the number of high-pressure forms in excess of 1): Cu₂J₂, AgCl, AgBr, Ag₂S, ZnBr₂, HgCl₂, HgBr₂ (3), HgJ₂ (2), GeJ₂, PbJ₂ (2), Cr₂O₃, KCN (3), AgCN, NaNO₂, AgNO₃, RbNO₃, CsNO₃, AgNO₃ (3), NaClO₃ (3), NaBrO₃, NaClO₄ (2), NaJO₄, KClO₃, KJO₄, RbClO₄, AgJO₃, AgClO₄, CsClO₄, CsJO₄, TiClO₄, NH₄ClO₄, Na₂SO₄ (2), KMnO₄, CsMnO₄ (2), and Pb(C₂H₃O₂)₂ (3). A statistical study of these new transitions, in comparison with those previously studied in the pressure range up to 12,000 kg/cm², shows a noticeable relative increase in the number of so-called abnormal transitions of the ice type with a negative value of $d\tau/dp$, when the volume of the high-temperature phase is smaller than that of the low-temperature phase. In the previous interval up to 12,000 kg/cm², 24% of the transitions were of the ice type; in the new interval, 43% of the transitions belonged to this type. The abnormal type of ice melting disappears at high pressures in all known cases. The same type of polymorphic transformations apparently does not acquire substantial instability, and here there is no tendency for this type to disappear at high pressures, but rather the opposite. At such high pressures, changes in thermal energy upon increments lose their significance, and the difference in phase energies is determined mainly by the difference in mechanical energy caused by the action of pressure when the volume changes. Study of the relationship between the phase diagram and chemical composition confirms the conclusion drawn for a lower pressure interval, namely that chemical similarity does not in general predispose to similarity in the phase diagram, and there are even some contrary examples.

In 1937229 new apparatus was used to determine the phase diagram of water from 22,000 to 40,000 kg/cm². Just beyond the pressure interval of the preceding works, a new modification of ice was found—ice VII. In 1938184, transformations of barium near 17,000 and of CO₂ near 25,000 kg/cm² were discovered incidentally during volumetric measurements. In 1938248 a study was published on the transformations of 25 organic compounds, carried out—

...in the apparatus to $50\,000\ \mathrm{kg/cm^2}$ between the previous temperature limits. These substances were: carbon tetrabromide (3), iodoform (3), cyanamide, urea (5), thiourea, ammonium rhodanide, nitroguanidine, ammonium formate (2), urea nitrate, methylamine hydrochloride (4), semicarbazide hydrochloride, dichloroacetamide, iodoacetic acid (2), oxamide (2), acetamide (3), guanidine sulfate (4), quinone, $p$-dichlorobenzene, dichlorophenol, hydroquinone, $p$-toluidine (2), naphthalene, $d$-camphor (10), menthol (3), and aniline sulfate.

In comparison with inorganic substances, polymorphism must apparently be a more general phenomenon among organic compounds. On the other hand, the transformations are less sharply expressed, the changes in volume are less large, and the phenomena of supercooling or of complete suppression of the transformation are more frequent. In general, all the phenomena are more difficult to study. This should probably be attributed to the greater complexity of organic molecules.

One paradoxical phenomenon, discovered in $\mathrm{CBr_4}$, must be noted specially. Below $160^\circ$ the transformation of this substance combines, in an unusual way, the phenomena of delay and retardation with the phenomenon of preliminary initiation. At low temperatures the transformation, thermodynamically possible at a pressure of approximately $13\,000\ \mathrm{kg/cm^2}$, does not occur at pressures up to $50\,000\ \mathrm{kg/cm^2}$, regardless of the holding time. Certain initiation processes evidently proceed at this pressure, since after some holding at $50\,000\ \mathrm{kg/cm^2}$ and a subsequent lowering of the pressure to a value at which the viscosity is lower, the transformation may occur, for example, at $20\,000\ \mathrm{kg/cm^2}$, as a result of a decrease in pressure, with a decrease in volume. The phenomenon is thermodynamically impossible if the transition is reversible, and is often mistakenly regarded as also physically impossible under any conditions.

It should be noted that there are eleven different modifications of $d$-camphor, whereas the largest number of modifications in other substances is relatively small.

In 1939,^249 in the study of certain minerals, two new high-pressure forms were found for calcite in the pressure interval from $15\,000$ to $25\,000\ \mathrm{kg/cm^2}$, and its phase diagram was established. The second-order transition for quartz glass was also investigated. At low pressures the compressibility of quartz glass increases anomalously with increasing pressure. This phenomenon is observed at room temperature up to a pressure of 35,000 bar, when it ceases so abruptly that an angular point is formed on the volume isotherm, i.e., a second-order transition is observed.

In studying the compressibility of a series of new compounds at pressures up to $50\,000\ \mathrm{kg/cm^2}$ in 1940, already reported in 4(c), new modifications were found for the following substances: BaTe, PbS, PbSe, PbTe, ZnSe, ZnTe, HgSe, and HgTe, and changes in volume were measured from $-80^\circ$ to room temperature. In addition to the reversible transition...

for HgTe there occurs the phenomenon (observed for the first time) of decomposition under pressure. HgTe is one of the few compounds that forms from the elements with an increase in volume. At pressures above $15\,000\ \mathrm{kg/cm^2}$ it slowly decomposes into the elements at room temperature; the decomposition proceeds so slowly that it is possible approximately to study the superposition upon it of the reverse transition.

In the course of measurements of the volume of liquids$^{132(b)}$, a new modification of $\mathrm{CS_2}$ was found, in appearance very similar to black phosphorus. At pressures above $40\,000\ \mathrm{kg/cm^2}$ and temperatures above $175^\circ$, $\mathrm{CS_2}$ changes slowly and irreversibly into a black solid, quite stable in air at room temperature. The density of the new modification of $\mathrm{CS_2}$ is 4% greater than the density of its constituent elements. It can be heated in air to $\sim 175^\circ$ without decomposition; above this temperature the new modification of $\mathrm{CS_2}$ calmly decomposes into sulfur and carbon. The structure of the substance is too fine to carry out an X-ray analysis; other physical properties of the substance were likewise not determined. It is natural to suppose that the structure of this substance may be similar to the structure of $\mathrm{SiO_2}$.

Finally, when the pressure interval was extended from $50\,000$ to $100\,000\ \mathrm{kg/cm^2}$, a number of new high-pressure forms were found for a series of substances$^{187,188}$. Measurements at a pressure of $100\,000\ \mathrm{kg/cm^2}$ were carried out only at room temperature, so that for these transitions it was not possible to determine phase diagrams or obtain the thermal parameters of the transitions. It was possible, however, to determine the change in volume at this temperature.

New transitions in the interval from $50\,000$ to $100\,000\ \mathrm{kg/cm^2}$ were found for Ca, Sr, Ba, Sn (probably analogous to the lower transition of bismuth) and two for bismuth (thus, a total of 6 modifications for bismuth), Te, AgCl, AgBr, and $\mathrm{NaNO_3}$.

A new transition was also discovered in an apparatus of carboloy for rapid measurements up to $40\,000\ \mathrm{kg/cm^2}$, for lithium perchlorate at a pressure of $16\,000\ \mathrm{kg/cm^2}$ and room temperature.

CITED LITERATURE

R. W. Goranson a. F. C. Kracek, J. Phys. Chem. 36, 913 (1932). Experimental study of the phase diagram for $\mathrm{K_2Si_4O_9}$ under pressure.
R. W. Goranson a. F. C. Kracek, J. Chem. Phys. 3, 87, (1935). Effect of pressure on the phase equilibria of sodium tungstate and related thermodynamic properties.
G. Tammann u. R. Kohlhaas, Zschr. f. anorg. allgem. Chemie 199, 209 (1931). On a method for investigating transformations of crystalline substances at high pressures.
R. B. Jacobs, J. Chem. Phys. 5, 945 (1937). Phosphorus at high temperatures and pressures.
R. Hultgren, N. S. Gingrich a. B. E. Warren. J. Chem. Phys. 3, 351 (1935). Atomic distribution in red and black phosphorus and the crystalline structure of black phosphorus.

Robert B. Jacobs, Phys. Rev. 51, 999 (1937). Diffraction of X-rays in crystalline substances under very high hydrostatic pressure.
R. B. Jacobs, Phys. Rev. 54, 325 (1938). Diffraction of X-rays in substances under high pressure.
R. B. Jacobs, Phys. Rev. 54, 438 (1938). Polymorphic transformations in halide metals.
R. L. McFarlan, Rev. Sci. Inst. 7, 82 (1936). Apparatus for the study, by X-rays, of modifications of ice under high pressure; J. Chem. Phys. 4, 60 (1936). Structure of ice II.
Klaus Clusius and Karl Weigand, Zschr. f. Electrochemie 44, 674 (1938). Transformation I—III of solid H₂S and solid D₂S at 225 kg/cm².
T. C. Wilson, Phys. Rev. 56, 598 (1939). Effect of high pressure on transformations: ordered phase—disordered phase in alloys.
T. E. W. Barth, Zschr. f. phys. Chem. 43, 448 (1939). Structure of the high-pressure modification of selenium.
R. B. Dow, J. Chem. Phys. 7, 201 (1939). Retardation of the crystallization of rubber under high pressure.
V. I. Prosvirin, Vestnik metalloprom. 20, 55 (1940). Effect of pressure on transformations in high-speed steel.
Paul L. Günter, Paul Geselle and W. Rebentisch, Zschr. f. anorg. allgem. Chem. 250, 357 (1943). Studies connected with the problem of diamond.
P. L. Günter, P. Geselle and W. Rebentisch, Zschr. f. anorg. allgem. Chemie 250, 373 (1943). Preparation and stability of black phosphorus.
P. W. Bridgman, Phys. Rev. 48, 825 (1935). Effect of high shear stress in combination with high hydrostatic pressure.
P. W. Bridgman, Phys. Rev. 45, 844 (1934). Two new phenomena at very high pressures.
P. W. Bridgman, Proc. Am. Acad. Arts Sci. 72, 227 (1938). Polymorphic transformations up to 50,000 kg/cm² of several organic compounds.
P. W. Bridgman, Am. J. Sci. 237, 7 (1939). Behavior of various minerals under high pressure.

5. PHASE CHANGES UNDER PRESSURE IN MULTICOMPONENT SYSTEMS

The complete phenomena of phase changes in multicomponent systems are very complex, and they cannot be fitted into any unambiguous classification scheme.

The phenomena that have attracted the principal attention are the solubility limit or the separation of a dissolved substance from a solution upon an increase in concentration. We shall first discuss the phenomena of solubility, and then other phenomena, such as, for example, the displacement of the eutectic point with pressure.

A. Solubility of Gases in Liquids

The simplest case of solubility is the solubility of a gas in a liquid. We shall give only a brief survey of these phenomena, since the pressures applied are below those of interest to us. At low pressures Henry’s law is approximately obeyed, which states that

the amount of dissolved gas is directly proportional to the pressure of the gas. The chief interest of most works on the solubility of gases consists in finding quantitative deviations from Henry’s law for solubilities. Because of the industrial importance of this question, there are many works on it. The works reviewed are cited below, chiefly in chronological order.

Frolich, Tauch, Hogan, and Peer $^{250}$ measured the solubilities at $200\ atm$ of the following gases: $\mathrm{H_2}$, $\mathrm{N_2}$, $\mathrm{O_2}$, and $\mathrm{CH_4}$ in sixteen organic solvents and in water. Henry’s law is fulfilled if the deviations of the gases from the ideal-gas law are taken into account. For these gases Henry’s law apparently holds up to $2/3$ of the saturation point. Goodman and Krase $^{251}$ measured the solubility of nitrogen in water up to $300\ atm$ at temperatures from 0 to $169^\circ$. Wiebe, Gaddy, and Heins $^{252}$ measured the solubility of nitrogen in water at $25^\circ$ up to $1000\ atm$. Wiebe and Tremearne $^{253}$ determined the solubility of hydrogen in liquid ammonia between $25^\circ$ and $100^\circ$ up to $1000\ atm$. The dependences were linear over the greater part of the interval. In the initial region there are intersections of the solubility curves. Krichevsky and Kazarnovsky $^{254}$ gave a theory of the solubility of nitrogen and hydrogen in water up to $1000\ atm$, obtaining approximate agreement with experiment and clarifying certain erroneous notions that had existed in earlier theoretical works.

Krichevsky, Zhavoronkov, and Epelbaum $^{255}$ determined the solubility of various gas mixtures in water up to a pressure of $30\ atm$. Wiebe and Gaddy $^{256}$ measured the solubility of a $1:3$ nitrogen–hydrogen mixture in water at $25^\circ$ and pressures up to $1000\ atm$. The solubility of the mixture can be calculated, with an error of a few percent, from the solubilities of its pure components. The same authors $^{257}$ determined the solubility of helium in water between $0^\circ$ and $75^\circ$ at a pressure of $1000\ atm$. The solubility passes through a minimum at $30^\circ$, and the solubility at high pressure could not be calculated from the solubility at low pressure. Ipatiev and Levina $^{258}$ measured the solubility of hydrogen in hydrocarbons of the aromatic and naphthene series. Henry’s law proved applicable up to $100^\circ$ and $100\ atm$. Above this interval deviations occurred; the solubility coefficient increased with increasing pressure. The solubility proved to be smaller in aromatic compounds. Michels, Gerver, and Bijl $^{259}$ determined the solubility of methane in water and in aqueous solutions of six halide salts, sugar, glucose, and formaldehyde up to $450\ atm$ at a temperature which sometimes rose to $150^\circ$. A somewhat complicated equation represented the results obtained. Basset and Dodge $^{250}$ determined the solubility of nitrogen in water at room temperature and pressures up to $4500\ kg/cm^2$. At higher pressures we are dealing here almost with two liquids. A striking phenomenon was discovered: the solubility, measured in $\mathrm{cm^3}$ of nitrogen in $1\ \mathrm{cm^3}$ of water, passed through a maximum at approximately $3000\ atm$. They found that

the nitrogen—water system shows no tendency toward complete miscibility at higher pressure, and water always remains the denser phase up to a pressure of 15,000 kg/cm².

Krichevskii and Kazarnovskii261 published another theoretical paper in which they successfully calculated the solubility of a 1:3 nitrogen–hydrogen mixture in water up to 1000 atm. Krichevskii, Zhavoronkov, and Tsiklis262 determined the solubility of hydrogen and carbon monoxide and their mixtures in methanol up to 300 atm and 140°. The solubility increases with increasing temperature, and the CO solubility isotherms intersect. Krichevskii263 gave a theoretical explanation of the maximum in the solubility of nitrogen in water found by Basse and Dode. Wiebe and Gaddy264 determined the solubility of hydrogen and nitrogen in liquid ammonia up to 100° and 1000 atm and investigated critical phenomena in the ammonia—nitrogen system. They found that the critical pressure is 600 atm at 90° and 400 atm at 100°. Ipatiev and Levina265 determined, in the range up to 200° and 200 atm, the solubility of hydrogen, nitrogen, carbon monoxide, carbon dioxide, and methane in kerosene and gasoline. Bykov266 determined the solubility, within the limits up to 240° and 100 atm, of air, oxygen, nitrogen, and hydrogen in three aqueous KCl solutions. The solubility passed through a sharp minimum with increasing temperature. Hydrogen followed Henry’s law better than nitrogen and oxygen.

Zelvenskii267 determined the solubility of carbon dioxide in water up to 100 atm and between 0° and 100°; it obeyed Henry’s law. Gonikberg, Fastovskii, and Gurvich268 measured the solubility of hydrogen in liquid nitrogen at temperatures from 79° to 109° K and up to 190 atm, and found good agreement between calculations and experiments. Gonikberg and Fastovskii269 determined the solubility of helium in liquid nitrogen in the same temperature range and at pressures up to 295 atm. The system obeyed the laws of ideal solutions.

Gerver270 published a review article on the question of the solubility of gases. Dodge and Newton271 published a theoretical paper on liquid—gas equilibrium in binary systems, in which they calculated the solubility of nitrogen in water up to a pressure of 1000 atm from experimental solubility data up to a pressure of 300 atm. Levina and Sibarovskaya272 determined the solubility of air, oxygen, and nitrogen in aqueous NaOH solutions of three concentrations up to 100 atm between 0° and 240°. They found a solubility minimum for nitrogen and oxygen in pure water at 75°. The minimum shifted to lower temperatures with increasing NaOH concentration.

Zelvenskii273 studied the solubility of the gas mixtures CO₂ + N₂ and CO₂ + H₂ up to 300 atm. In general, the presence of one of the gases decreases the solubility of the other. Wiebe and Gaddy274 determined the solubility of carbon dioxide in water between 50° and 100° and up to a pressure of 70 atm. Their results are in agreement with the theory of dilute solutions. A critical review of one of the propositions

of this work, Wiebe and Gaddy was made by Katz;[^275] Fastovsky and Gonikberg[^276] determined the solubility of hydrogen in liquid methane at temperatures between 90° and 127° K up to 230 atm. The results agree with Krichevsky’s theoretical equation. Krichevsky, in an article entitled “Limited mutual solubility of gases at high pressures,”[^277] found that at 140° and 5000 kg/cm² a mixture of 67.6% NH$_3$ and 32.4% N$_2$ separates into two gas phases containing 76.6% and 33.1% NH$_3$, respectively. This is an interesting result obtained in a pressure range much higher than that of most of the works presented in this section of the review. The pressure is far beyond the critical pressure, but the densities are probably approximately the same as those of ordinary liquid phases, and in this case the designation “liquid” would be more appropriate than the designation “gas.”*)

The phenomenon of limited miscibility of liquid phases, as is known, is frequently encountered. Wiebe and Gaddy[^278] measured the solubility of carbon dioxide in water in the temperature interval from 12° to 40° and up to 500 atm. The existence of the solid cryohydrate CO$_2$·6H$_2$O was established at high pressure. Zattler[^279] found that the solubility of hydrogen in hexane, cyclohexane, benzene, and m-xylene is a linear function of pressure up to 150 atm. Shoch, Hoffmann, and Mayfield[^280] determined the solubility of methane in cyclohexane up to the critical pressure and at temperatures from 100 to 220° F. They also give data for the volumes and compressibility of the liquid phase. In a second article,[^281] the same authors determined the solubility of methane in hexane in the same interval. Gonikberg and Fastovsky[^282] determined the solubility of helium in liquid methane between 90° and 106° K up to 160 atm.

This article, apparently, has not yet reached us in full. Krichevsky and Tsiklis[^283] extended the pressure interval of Krichevsky’s first work from 4500 to 9500 atm and found the phenomenon of limited mutual solubility in the systems methane—ammonia, methane—nitrogen—ammonia, and hydrogen—nitrogen—ammonia. Again they call this phenomenon limited mutual solubility in gases.

CITED LITERATURE

K. Frolich, E. J. Tauch, J. J. Hogan and A. A. Peer, Ind. Eng. Chem. 23, 548 (1931). Solubility of gases in liquids at high pressures.
J. B. Goodman and N. W. Krase, Ind. Eng. Chem. 23, 401 (1931). Solubility of nitrogen in water at high pressures and temperatures.

*) The classification of phase equilibria is made not according to the criterion of phase density, but according to the origin of the equilibrium. Since the equilibrium under consideration is not connected with the liquid–vapor equilibrium curve for a pure component, it has therefore received the name gas–gas equilibrium. (I. K.)

R. Wiebe, V. L. Gaddy and Conrad Heins, Jr., Ind. Eng. Chem. 24, 927 (1932). Solubility of nitrogen in water at 25° from 25 to 1000 atm.
R. Wiebe and Th. Tremearne, J. Am. Chem. Soc. 56, 2357 (1934). Solubility of hydrogen in liquid ammonia at 25, 50, 75 and 100° C and pressures up to 1000 atm.
I. R. Krichevskii and Ya. S. Kazarnovskii, Zhurn. fiz. khim. 6, 1320 (1935). Solubility of nitrogen and hydrogen in water at high pressures.
I. R. Krichevskii, N. M. Zhavoronkov and V. A. Apel’baum, Zhurn. khim. prom. 16, 975 (1936). Solubility of gaseous mixtures in water under pressure.
R. Wiebe and V. L. Gaddy, J. Am. Chem. Soc. 57, 1487 (1935). Solubility of a mixture of nitrogen and hydrogen in water at 25° in the pressure range from 50 to 1000 atm.
R. Wiebe and V. L. Gaddy, J. Am. Chem. Soc. 57, 847 (1935). Solubility of helium in water at 0.25, 50 and 75° and pressures up to 1000 atm.
V. V. Ipatiev and M. I. Levina, Zhurn. fiz. khim. 6, 632 (1935). Equilibrium between the liquid and gas phases at high pressures and temperatures. I. Solubility of hydrogen in individual hydrocarbons of the aromatic and naphthene series.
A. Michels, J. Gerver and A. Bijl, Physica 3, 797 (1936). Effect of pressure on the solubility of gases.
J. Basset and M. Dodé, Comptes rendus 203, 775 (1936). Solubility of nitrogen in water at high pressures up to 4500 kg/cm².
I. R. Krichevskii and Ya. S. Kazarnovskii, Zhurn. fiz. khimii 7, 659 (1936). Thermodynamic calculation of the solubility of a nitrogen–hydrogen mixture in water under pressure.
I. R. Krichevskii, N. M. Zhavoronkov and D. S. Tsiklis, Zhurn. khim. prom. 14, 170 (1937). Solubility of hydrogen, carbon monoxide, and their mixtures in methanol under pressure.
I. R. Krichevskii, J. Am. Chem. Soc. 59, 596 (1937). On the existence of a maximum on the curve: solubility of a gas in a liquid—pressure.
R. Wiebe and V. L. Gaddy, J. Am. Chem. Soc. 59, 1984 (1937). Solubility in liquid ammonia of hydrogen at 0° and nitrogen at 0°, 50, 75, 90 and 100° under pressure up to 1000 atm. Critical phenomena in ammonia–nitrogen mixtures.
V. V. Ipatiev and M. I. Levina, Khimiya tverdogo topliva 8, 866 (1937). Equilibrium between the liquid and gas phases at high pressures and temperatures. II. Solubility of gases in petroleum products.
M. M. Vukov, Acta Univ. Vor. 9, 29 (1937). Solubility of gases in salt solutions under pressure at high temperatures.
Ya. D. Zel’venskii, Zhurn. khim. prom. 14, 1250 (1937). Solubility of carbon dioxide in water under pressure.
M. G. Gonikberg, V. G. Fastovskii and I. G. Gurvich, Acta URSS, 11, 865 (1939). Solubility of gases in liquids at low temperatures and high pressures. I. Solubility of hydrogen in liquid nitrogen at temperatures from 79.0 to 109°.0 K and pressures up to 190 atm.
M. G. Gonikberg and V. G. Fastovskii, Acta URSS 12, 67 (1940). Solubility of gases in liquids at low temperatures and high pressures. II. Solubility of helium in liquid nitrogen at temperatures from 78.0 to 109°.0 K and pressures up to 295 atm.
J. Gerver, Chem. Weekblad 35, 913 (1938). Solubility of gases in liquids under pressure.
V. G. Dodge and R. H. Newton, Ind. Eng. Chem. 29, 718 (1937). Effect of pressure on liquid–vapor equilibrium in binary systems.
M. I. Levina and N. P. Stsiblarovskaya, Zhurn. Fiz. khim. 12, 653 (1939). Liquid–gas equilibrium at high pressures and temperatu-

Fig. IV. Solubility of air in water and in caustic soda solutions of various concentrations.

Ya. D. Zel’venskii, Zhurn. fiz. khim. 13, 514 (1939). Solubility of gaseous mixtures under pressure.
R. Wiebe and V. L. Gaddy, J. Am. Chem. Soc. 61, 315 (1939). Solubility of CO₂ in water at 50, 75, and 100° and at pressures up to 700 atm.
D. L. Katz, J. Am. Chem. Soc. 62, 1629 (1940). Mutual solubility of carbon dioxide and water at high pressures.
V. G. Fastovskii and M. G. Gonikberg, Acta URSS 12, 485 (1940). Solubility of gases in liquids at low temperatures and high pressures. III. Solubility of hydrogen in liquid methane.
I. A. Krichevskii, Acta URSS 12, 480 (1940). Mutual limited solubility at high pressures.
R. Wiebe and V. L. Gaddy, J. Am. Chem. Soc. 62, 815 (1940). Solubility of carbon dioxide in water at various temperatures from 12 to 40° and pressures up to 500 atm. Critical phenomena.
Hermann Sattler, Zschr. f. tech. Physik 21, 410 (1940). Solubility of hydrogen in liquid hydrocarbons.
E. P. Schoch, A. E. Hoffmann and F. D. Mayfield, Ind. Eng. Chem. 32, 1351 (1940). Solubility of methane in cyclohexane.
E. P. Schoch, A. E. Hoffmann and F. D. Mayfield, Ind. Eng. Chem. 33, 688 (1941). Solubility of methane in hexane.
M. G. Gonikberg and V. G. Fastovskii, Foreign Petroleum Tech. 9, 214 (1941). Solubility of gases in liquids at low temperatures and high pressures. IV. Solubility of helium in liquid methane at temperatures from 90.3 to 106° K and pressures up to 160 atm.
I. R. Krichevskii and D. S. Tsiklis, Zhurn. fiz. khim. 15, 1059 (1941). Mutual limited solubility of gases at high pressures.

B. Solubility of Solids in Liquids and Related Phenomena

Our knowledge of the phenomena in this field expanded noticeably during the period covered by this report, to a considerable extent thanks to the work of the Geophysical Laboratory. The pressure interval in investigations carried out at ordinary temperatures was 12,000 kg/cm². Goranson made measurements at a temperature of 1000° and above, with pressures in this case up to 4000 kg/cm².

In the earlier part of this period there appeared three papers by Adams and Gibson²⁸⁴, Adams and Hall²⁸⁵, and Adams²⁸⁶ on the NaCl—water system. In this work both direct and indirect methods were used. In general, the indirect methods proved more convenient, while the direct methods were for the most part used for control. The indirect methods are based on the fact that the solubility limit is established when the chemical potentials of a component in different phases are equal. Chemical potentials under pressure can be obtained from the known chemical potentials at atmospheric pressure and their pressure derivatives. The pressure derivatives depend on the partial volumes. Experimentally, the method reduces to determining partial volumes, which requires accurate determination

compressibilities of solutions at various concentrations, as functions of pressure. Fortunately, the methods of measuring compressibility are now sufficiently accurate to give the required precision in the calculation of chemical potentials. At low pressures up to 1000 atm the method of measuring compressibility was the modified mercury-injection method already cited^135; between 1000 and 12,000 atm, the piston-displacement method.

The first paper of Adams and Gibson was devoted to the melting of the little-known dihydrate $ \mathrm{NaCl}\cdot 2\mathrm{H}_2\mathrm{O} $. At atmospheric pressure this hydrate melts incongruently, forming solid $ \mathrm{NaCl} $ and a saturated aqueous solution of $ \mathrm{NaCl} $. The temperature of incongruent melting rises with increasing pressure. The incongruent-melting curve passes through a maximum at $25.8^\circ$ and a pressure of 9500 bars; this is the second example of such a phenomenon, the first being $ \mathrm{Na}_2\mathrm{SO}_4\cdot 10\mathrm{H}_2\mathrm{O} $, discovered by Tammann. Thermodynamically, the existence of a maximum means that the change in volume during the transformation passes through zero. This means that on an isotherm below

Fig. 4. Adams’ equilibrium diagram for the system $ \mathrm{NaCl}—\mathrm{H}_2\mathrm{O} $ under pressure at $25^\circ\mathrm{C}$. The freezing curve under pressure intersects the solubility curve at the eutectic pressure. On the right the solubility curve is shown on a larger scale.

the temperature of the maximum, with increasing pressure, saturated solution plus $ \mathrm{NaCl} $ can be brought to crystallization of solid $ \mathrm{NaCl}\cdot 2\mathrm{H}_2\mathrm{O} $ with a decrease in volume. With a further increase of pressure, solid $ \mathrm{NaCl}\cdot 2\mathrm{H}_2\mathrm{O} $ can be brought to melting with a further decrease in volume. This was verified experimentally. It was also found that, near the maximum, a rapid increase of pressure is accom-

...an anomalous secondary reaction would be expected with a further increase in pressure. This can be only for finite changes of pressure. For an infinitely small change of pressure thermodynamics requires the opposite sign.

In the work of Adams and Hall the electrical-conductivity method was applied to determine the solubility of NaCl in water at $30^\circ$ up to 4000 bar, and the results obtained by them agreed with results found by other methods. Finally, Adams gave a complete phase diagram for the system NaCl—water at $25^\circ$ up to $12\,000\ \text{kg}/\text{cm}^2$ from experimental data and up to $16\,000\ \text{kg}/\text{cm}^2$ from calculated data; the diagram is reproduced in Fig. 4. At this temperature the phase diagram breaks up into eight regions. Two isolated regions of existence of NaCl solution must be noted. This is the result of the existence of a temperature maximum on the curve of incongruent melting of the dihydrate. There must also be a eutectic under pressure for NaCl solution, ice VI + solution, and ice VI + NaCl. This means that, on compression, any mixture of NaCl and water at $25^\circ$ and 16,700 bar undergoes a pressure arrest until the solution has completely solidified into NaCl + ice VI.

Adams$^{287}$ applied the same technique to the study of the $K_2SO_4$ system at $25^\circ$ and found a complex phase diagram. Again a eutectic under pressure was found, involving ice VI, this time at 10,750 bar and $25^\circ$. As in the case of NaCl, it was found that the fictive*) volume of the salt in solution increases with increasing pressure; this means that the solution approaches the ideal one more closely.

Adams and Gibson$^{288}$ investigated the solubility of ammonium nitrate in water at $25^\circ$ up to 10,000 bar. The partial volume of $NH_4NO_3$ in the total decreases with increasing pressure. Above 15% it is independent of concentration, and the partial compressibility differs only very slightly from the compressibility of solid $NH_4NO_3$. The solubility curves of ice VI and $NH_4NO_3$ were calculated, and a eutectic under pressure was found at 12,100 bar at 25.3 weight percent nitrate.

Later, Adams$^{289}$ published an article, mainly theoretical in character, in which he developed the details of an indirect thermodynamic method for determining the phase diagram of hydrates and systematized the various types of phase diagrams that could be expected.

Gibson$^{290}$ considers methods of calculating solubility under pressure and shows that, by applying Tait’s equation and Tammann’s hypothesis (already considered), one can calculate solubilities up to $10\,000\ \text{kg}/\text{cm}^2$ from experimental data obtained only up to $1000\ \text{kg}/\text{cm}^2$. He compared the results obtained with experimental data for the already known cases NaCl, $K_2SO_4$, and $NH_4NO_3$, and published new experimental material for KI, which was also subjected to verification. These four salts give solubility curves—

) Fictive volume—the partial molar volume. (I. K.*)

of different types, so that it may be assumed that any other salt can be treated by the same method. In a later paper Gibson^291 gave an interpretation of the effect of pressure on the solubility of solids in liquids. Only in exceptional cases does the solubility of a solid in a liquid increase with increasing pressure. These exceptional cases include aqueous solutions of carbonates, sulfates, sulfides, fluorides, and hydrides of some alkalis, alkaline earths, and heavy metals. In his opinion, it is unlikely that in the geophysical field there are important cases of increased solubility caused by pressure. New experimental material is given for the solubility of CsBr in water up to 1500 and the partial volumes of NaCl up to 1000 bar at temperatures up to 95°. Previous investigations had been carried out at temperatures no higher than 30°. In 1938^292 he published a popular review article entitled “The Nature of Solutions and Their Behavior under High Pressure.” In this connection mention should be made of Gibson’s review^293 in the handbook of physical constants issued by the Geological Society of America.

Goranson’s work in the Geophysical Laboratory in this field was concentrated mainly around high temperatures of the order of 1000°, with the use of the high-pressure apparatus already described by us. In 1936^294 he determined the solubility of water in albite melt between 900° and 1200° and up to 3000 or 4000 bar. At any constant temperature the amount of dissolved water can be expressed by the equation

\[ x=\frac{p}{a+bp}. \]

Both constants $a$ and $b$ in this equation increase with increasing temperature. The dissolution of water is accompanied by the liberation of heat. The amount of heat increases with temperature and decreases with pressure. In 1938^295 Goranson published a paper on phase equilibrium in the systems NaAlSi$_3$O$_8$—water and KAlSi$_3$O$_8$—water in the same range of pressures and temperatures. A full discussion of some of these results will be possible only when the constants for pure water in this region have been determined. It was established that during the process of crystallization in these systems a sufficient pressure develops, which may serve as an explanation of volcanic phenomena.

Let us now turn to individual works in this field. Svodau and R. O. Gibson^221, in the course of their already cited measurements of the effect of pressure on the melting point of oxygen, investigated a binary system consisting of 30% para and 70% orthooxygen. The triple point of crystallization was −16.3° at 445 kg/cm$^2$ and 11.6° at 1605 kg/cm$^2$. The eutectic temperature was shifted from −11.5° at 1135 kg/cm$^2$ to 10.0° at 2180 kg/cm$^2$. In both cases the relation between temperature and pressure was linear. Their results were in agreement with the results obtained by Nakatsuchi in 1929.

May, Key, and Higman^296 carried out a theoretical thermodynamic discussion of the relations at the eutectic point. Dissatisfied with previous work in this direction, they derived equations that are not contradicted by the experimental data of Pushin and Grebenshchikov, cited in my book, on the displacement of the eutectic point with pressure.

Popp^297 studied in Timmermans’ laboratory, up to 1030 kg/cm², the phenomena of solubility in thirty binary systems, where both components of each system were liquids, chiefly organic ones, including three systems with ordinary water as one of the components and four systems with heavy water. Of particular interest was the delineation of the limits of the regions of complete immiscibility, and the systems were chosen precisely from this point of view. In general, the results confirmed Timmermans’ initial work. Heavy water, in comparison with ordinary water, in all cases had a noticeably expanded region in all directions with respect to immiscibility.

Deffet^298,299 studied various binary systems up to 1000 kg/cm², in the apparatus already described in connection with the determination of the melting of simple substances. In the benzene—naphthalene system the composition of the eutectic point does not depend on pressure. The eutectic temperature rises by 23° at 1000 atm. In the benzene—urethane system the eutectic becomes richer in urethane with increasing pressure. In the system Na₂CO₃·10H₂O a break in the slope of the melting curve was found at 51 kg/cm². It was found that pressure has only a small influence on the shape of the melting curve (i.e., the entire curve shifts with pressure) for the following systems: p-dichlorobenzene, p-dibromobenzene, aniline—phenol, and o-cresol—m-cresol. In the cyclohexane—aniline and hexane—nitrobenzene systems there is a composition region in which two liquid phases are in equilibrium with a solid phase. The size of this region decreases with increasing pressure.

Kean^300 in my laboratory investigated the phase diagram of sodium and potassium alloys up to 10,000 kg/cm² and 165°. The method of investigation was electrical. The resistance of alloy specimens of a number of compositions was measured as a function of pressure and temperature. Breaks in the resistance curves indicated the onset of formation of new phases. The phase diagram had two eutectics: liquid with Na₂K and K, and liquid with Na₂K and Na. The effect of pressure was not linear. In addition, the method furnished material on the influence of pressure on resistance, which will be cited later.

CITED LITERATURE

L. H. Adams and R. E. Gibson, J. Am. Chem. Soc. 52, 4252 (1930). Curves of melting and liquidus for sodium chloride up to 12,000 atm.
L. H. Adams and R. E. Hall, J. Wash. Acad. Sci. 21, 183 (1931). The effect of pressure on the solubility of sodium chloride in water—a new method for measuring the solubility of electrolytes under pressure.

L. H. Adams, J. Am. Chem. Soc. 57, 3769 (1931). Equilibrium in binary systems under pressure. I. Experimental and thermodynamic investigation in the NaCl—H₂O system at 25°.
L. H. Adams, J. Am. Chem. Soc. 54, 2229 (1932). Equilibrium in binary systems under pressure. II. The K₂SO₄—H₂O system at 25°.
L. H. Adams and R. E. Gibson, J. Am. Chem. Soc. 54, 4520 (1932). Equilibrium in binary systems under pressure. III. The effect of pressure on the solubility of ammonium nitrate in water at 25°.
L. H. Adams, Am. J. Sci. 5, 35—A, 1 (1932). Temperature curves of freezing—solubility of hydrates and other compounds under pressure.
R. E. Gibson, J. Am. Chem. Soc. 56, 865 (1934). Calculated solubilities of salts at high pressures.
R. E. Gibson, Am. J. Sci. 35, A, 49 (1938). The effect of pressure on the solubility of solids in liquids.
R. E. Gibson, Sci. Mo. 46, 103 (1938). The nature of solutions and their behavior at high pressures.
R. E. Gibson, Section B of special papers No. 36, Geological Society of America, Handbook of Physical Constants (edited by Francis Birch, 1942), pp. 187—202. The effect of pressure on phase equilibria in binary condensed systems.
R. W. Goranson, Trans. Am. Geophys. Union, 17th Annual Meeting, 257 and 259 (1936). Silicate—water systems: solubility of water in albite melts.
R. W. Goranson, Am. J. Sci. 35, A, 71 (1938). Silicate—water systems: phase equilibria in the systems NaAlSi₃O₈H₂O and KAlSi₃O₈H₂O at high temperatures and pressures.
H. A. C. McKay and B. Higman, Phil. Mag. 19, 367 (1935). The effect of pressure on eutectic mixtures.
G. Poppe, Bull. Soc. Chim. Belg. 44, 640 (1935). Piezometric investigations. II. New experiments on the mutual solubility of liquids.
L. Deffet, Bull. Soc. Chim. Belg. 45, 213 (1936). Piezometric investigations. III. The effect of pressure on the melting point of binary mixtures.
L. Deffet, Bull. Soc. Chim. Belg. 47, 461 (1938). Piezometric investigations. IV. The effect of high pressure on the melting curves of binary mixtures.
C. H. Kean, Phys. Rev. 55, 750 (1939). The $P—T$ phase diagram of Na—K alloys and the effect of pressure on the resistance of the liquid phase.

6. THE EFFECT OF PRESSURE ON VISCOSITY

A. Viscosity of gases

Boyd[^301] determined the viscosity of nitrogen, hydrogen, and their mixtures at temperatures of 30°, 50°, and 70° and pressures up to 240 atm. The method consisted in the flow of gas at a small pressure difference. A theory was proposed, based on the analogy between kinetic pressure and viscosity. Applying an equation of state of the Lorentz type, he obtained agreement with experiment. It is indicated that this theory gives, for the first time, direct proof of the validity of treating the kinetic and cohesive pressures separately in the equation of state.

Michels and Gibson[^302] measured the viscosity of nitrogen up to 1000 atm at 25°, 50°, and 75° by the same flow method, with a pressure difference of 1 atm. The viscosity isotherms, as functions of pressure, intersect near 400 atm.

Below this pressure the viscosity is lower at low temperature, and above it the viscosity is lower at high temperature. A minimum was found in the ratio of viscosity to density, as predicted by Enskog’s theory, and in general there is good agreement with the theory.

Nasini and Pastonesi measured the viscosity of air at $14^\circ$ and $200\ \mathit{atm}$ by the efflux method. The viscosity increased by $26\%$ over this pressure interval in comparison with the value at atmospheric pressure.

Gibson in 1933${}^{304}$ published his doctoral dissertation, carried out in Michels’ laboratory, on the viscosity of gases at high pressure. Along with measurements of the viscosity of nitrogen, already published jointly with Michels, data were presented for hydrogen at $25^\circ$ up to 300 atmospheres. They were, in general, in agreement with Enskog’s theory.

Sage and Lacey${}^{305}$ made measurements up to $200^\circ$ and $200\ \mathit{atm}$ of the viscosity of air, methane, and lean and rich natural gas. The viscosity always increases with increasing pressure. The degree of increase with pressure is greater at lower temperatures. The viscosity isotherms intersect near $35\ \mathit{atm}$. Golubev${}^{306}$ described a new type of capillary viscometer adapted for measuring the viscosity of gases up to $5000\ \mathit{atm}$, and applied it to measurements of the viscosity of air up to $300\ \mathit{atm}$ between $0^\circ$ and $100^\circ$.

Sage, Yale, and Lacey${}^{307}$ measured the viscosity of butane and isobutane in the gaseous and liquid regions between $100^\circ$ and $200^\circ\mathrm{F}$ up to $150\ \mathrm{kg}/\mathrm{cm}^2$. Cummings, Mayland, and Egly${}^{308}$, and Cummings and Egly${}^{309}$, measured the viscosity of $\mathrm{CO_2}$, $\mathrm{C_2H_4}$, $\mathrm{CH_4}$, and $\mathrm{C_3H_6}$ by the falling mercury drop method up to $105^\circ\mathrm{C}$ and $170\ \mathit{atm}$.

CITED LITERATURE

James H. Boyd, Jr., Phys. Rev. 35, 1284 (1930). Viscosity of compressed gases.
A. Michels and R. O. Gibson, Proc. Roy. Soc. A, 134, 288 (1931). Measurement of the viscosity of gases at high pressures—viscosity of nitrogen up to $1000\ \mathit{atm}$.
A. G. Nasini and G. Pastonesi, Gazz. Chim. Ital. 63, 821 (1933). Viscosity of air up to $200\ \mathit{atm}$.
R. O. Gibson (Amsterdam, 1933). Viscosity of gases at high pressures.
B. H. Sage and W. N. Lacey, Am. Inst. Min. Met. Eng. Tech. Publ. No. 845 (1937). Effect of pressure on the viscosity of air, methane, and two kinds of natural gas.
I. F. Golubev, Zhurn. tekhn. fiz. 8, 1932 (1938). Viscosity of gases and gas mixtures at high pressures.
B. H. Sage, W. D. Yale, and W. N. Lacey, Ind. Eng. Chem. 31, 223 (1939). Effect of pressure on the viscosity of butane and isobutane.
E. W. Comings, B. J. Mayland, and R. S. Egly, Univ. Ill. Bull. 42, 15 (Nov. 28, 1944). Viscosity of gases at high pressures.
E. W. Comings and R. S. Egly, Ind. Eng. Chem. 33, 1224 (1941). Viscosity of ethylene and carbon dioxide under pressure.

B. Viscosity of Liquids

A considerable part of the work with liquids was connected with the study of lubricating oils, since for determining lubricating properties, especially under heavy load, it is important to know the variation of the coefficient of viscosity with pressure. The most systematic work in this direction was carried out either by Dow himself or by Dow with his various collaborators. The work was begun at Harvard with my apparatus and continued at Penn State. Dow’s dissertation ^310, published in 1935, contains a study of the viscosity of six pairs of liquids over the entire concentration range at 30° and 75° up to pressures of 12,000 kg/cm². The falling-weight method served as the method, and the apparatus used was the same as that already described in my book. The pairs of liquids were: n-hexane—CS₂, n-hexane—diethyl ether, n-hexane—n-decane, n-hexane—chlorobenzene, n-pentane—benzene, and ethanol—CS₂. Pure n-decane was also measured. Mixtures of n-hexane with CS₂ and with normal decane followed Arrhenius’ rule for mixtures: the logarithm of the viscosity was a linear function of the composition. For the other mixtures, rather complex deviations from Arrhenius’ rule were found. These anomalies were sometimes observed at the edges of the concentration curve and sometimes occurred in its middle. The effect was attributed to the close interlocking of molecules because of their complex shape. In 1935 Dow ^311 published theoretical studies of the data of Kleinschmidt and Dow on the viscosity of lard, spermaceti, and Pennsylvania petroleum, in which they showed that in this case Batchinsky’s theory is not applicable, since the viscosity is far from being a function solely of volume. In 1936 ^312 they published results obtained by the ball-viscometer method up to 4000 kg/cm² on the viscosity of Pennsylvania, California, and Oklahoma petroleums. These were “corresponding” petroleums, i.e., they had been mixed in such a way that the initial viscosity of all of them was the same. However, the effect of pressure was entirely different: at 2000 kg/cm² the increase in viscosity of the California petroleum was four times greater than that of the Pennsylvania petroleum. In 1937 ^313 these investigations were continued for the same petroleums with the inclusion of temperatures from 100° to 210° F. In 1937 Dow, Fenske, and Morgan ^314 studied viscosity by the same method, over the same pressure and temperature ranges, for three petroleums and two chlorinated diphenyls, Aroclors. They observed the greatest pressure effect ever found on one of the latter specimens, which showed a fifteenfold increase in viscosity at a pressure of only 250 kg/cm².

Morgan and Dow ^315 measured, by the same method up to 100° C and 4000 kg/cm², the viscosity of ortho-, meta-, and para-toluidine and of their bromo-, iodo-, and nitro-monosubstituted derivatives. The coefficient of viscosity with pressure may systematically either increase or decrease with a change in the position of the substituent group. If the molecular weight of the substituent group increases, the coefficient of viscosity with pressure in ortho-

...and meta positions, but decreases in the para position. In 1939, Diber, Dow, and Fink $^{316}$ measured, in this same range of pressures and temperatures, the viscosity of six different grades of Pennsylvania oil. The coefficient of viscosity as a function of pressure tends to increase with increasing molecular weight, but this correlation is precise only within a narrow boiling range for homogeneous oil. The temperature coefficient of viscosity at constant pressure increases with increasing molecular weight at all pressures for all oils.

In 1939, Dow $^{317}$ gave a review of some of his earlier works and reported new data for the viscosity of six mixtures of $\mathrm{CS_2}$ and $\mathrm{CCl_4}$ at $30^\circ$ and $75^\circ$ up to $10\,000\ \mathrm{kg/cm^2}$. In 1939, Thomas, Hamm, and Dow $^{318}$ described a new apparatus with which it was possible to determine absolute viscosity under pressure. This apparatus consists of a cylinder rotating at a known speed inside another concentric cylinder elastically fastened to it. The displacement from the equilibrium position gives a measure of the viscous retardation and, consequently, of the viscosity itself. The entire apparatus, motor, and everything else are mounted inside a high-pressure vessel. This method is not as suitable for determining the pressure coefficient as the falling-ball method, which is relative rather than absolute. Within the errors of experiment, the pressure coefficients obtained by both methods for different oils agree. In 1941, Dow, McCartney, and Fink $^{319}$ measured the viscosity of Russian and Romanian oils over ordinary ranges of pressure and temperature. The effect of pressure in these oils is greater than in American ones, which is associated with the chemical structure of naphthenic or aromatic hydrocarbons instead of paraffins. The change in viscosity depends exponentially on density.

Let us now touch on episodic works. Suga $^{320}$ measured twenty oils up to $1000\ \mathrm{kg/cm^2}$ and compared the effect of pressure on mineral, vegetable, and animal oils. A linear dependence was found between pressure and the logarithm of viscosity. Hersey and Snyder $^{321}$ gave a thorough theoretical analysis of the general outflow from a viscometer and showed how to calculate the coefficient of viscosity at any pressure from the dependence of the general outflow on pressure. Measurements by this method were made on heavy and light oils and on castor oil up to $3000\ \mathrm{kg/cm^2}$. For castor oil, satisfactory agreement was obtained with previous investigations carried out by other methods. Talbott, in connection with his volumetric measurements of liquids already noted by us $^{115}$, measured the viscosity of oil by the falling-load method up to $400\ \mathrm{atm}$ and $210^\circ\mathrm{F}$, and found typical effects.

Ebbeke and Haubrich $^{322}$ investigated the effect of pressure up to $800\ \mathrm{atm}$ on the viscosity of various organic liquids. It was found that pressure has a small effect on protein solutions, a “weak” effect on carbohydrates, a “noticeable” effect on egg yolk, starch, and honey, and a very large effect on various oils. Versluys, Michels

and Gerver[^323] applied the falling-load method to measure the viscosity of oil saturated with methane up to 218 atm and between 25° and 100°. The solubility of methane increases with pressure so rapidly that it more than compensates for the normal increase of viscosity with pressure, leaving as the net effect a sevenfold decrease of viscosity over the entire pressure range. Sage, Inman, and Lacey[^324] determined, up to 200 atm, the viscosity of the liquid phase of eighteen mixtures of methane and propane with crystal oil.

Bradford and Vandergrift[^325] carried out a theoretical investigation concerning the significance of the pressure coefficient of viscosity in ensuring satisfactory performance of oil in bearings, and indicated the desirable dependence between the temperature coefficient and the pressure coefficient. Hersey and Hopkins[^326] summarized the work carried out on fatty oils by Hyde, Kussolt, and Sudge in connection with the study of lubricating action under the A.S.M.E. program1. Apparatus of various types was used, and complete agreement was obtained.

Dunn and Birch[^327] published a paper on the influence of pressure, under various experimental conditions, on the viscosity of boric anhydride glass. The investigation was prompted by the need in geophysics to know the influence of pressure on the viscosity of glass, which, as some considerations show, should be very large. Boric anhydride is the only glass for which, with the present experimental technique, measurements can be made at temperatures sufficiently close to geological conditions for the results obtained to be significant. The method of complete efflux was used; the pressure interval was 2000 kg/cm² and the temperature—between 359° and 516°C. At constant temperature the relationship between viscosity and pressure is exponential: $\eta=\eta_0 e^{aP}$. At higher temperatures $a=4.64\cdot10^{-4}\ \text{cm}^2/\text{kg}$, and at lower temperatures $a=15\cdot10^{-4}\ \text{cm}^2/\text{kg}$. The variation of the pressure coefficient with temperature is considerably greater than that given by Andrade’s theory of viscosity.

Needs[^328] discussed phenomena occurring in bearings that are associated with the pressure coefficient of viscosity of castor oil, paraffin mineral oils, and glycerin up to a pressure of 1500 atm. The effective coefficient of friction passes through a minimum at high pressure. Eibbecke and Gaubrich[^329] studied the influence of pressure up to 300 atm on solutions containing spherical molecules (glycogen) and long-chain molecules (starch). The influence of pressure is considerably greater for starch solutions, which is attributed to the form of the molecules. Volarovich[^330] described a modified falling-ball method with a controlled magnetic counterweight. By this method he determined the viscosity up to 1000 kg/cm² and 100° of various aviation and machine oils, rosin—

foli and solutions of sugar in glycerine. The least effect of pressure was found for sugar solutions (threefold), and the greatest for caniphene (22.3-fold). From a later paper by Volarovich331 it follows that the oil in the work cited above was saturated with nitrogen, which corresponds to the conditions in the cylinders of compressors or internal-combustion engines. Swearingen and Redding332 investigated the effect of pressures up to 250 atm on saturated solutions of natural gas in various petroleums. Under these conditions the viscosity decreased with increasing pressure.

There are a number of theoretical papers devoted to the theory of the viscosity of liquids in general and to the effect of pressure on the viscosity of a liquid in particular. The weakness of most early theories of the viscosity of liquids was that they required viscosity to be only a function of volume. This is definitely not true for liquids that I measured up to 12,000 kg/cm². Van Wijk and Sider, in two papers333, 334, propose a theory in which liquids are divided into two classes—configurational and non-configurational liquids. For the first class there is a temperature effect on viscosity in addition to the purely volume effect. An exponential formula has been derived for the dependence on temperature with a coefficient that includes the covolume. By means of this formula one can reproduce my data for organic liquids and mercury, for which the effect is very small, up to a pressure of about 7000 atm. Above this pressure deviations appear: viscosity increases with pressure more rapidly than the theory requires. Bingham, Adams, and MacCauslin335 developed a theory based on my measurements of viscosity up to 12,000 kg/cm². They introduced the concept of the minimum molecular volume for fluidity.

The Princeton school of physical chemists also published several theoretical papers. The basic idea of these works is that there is an analogy between the molecular process in which momentum is transferred from one layer to another during the viscous flow of a liquid, and an ordinary chemical reaction. A molecule moving along the velocity gradient receives or gives up energy. In passing from one layer to another, it must cross a potential barrier before it can find itself in its new position, just as a molecule taking part in a chemical reaction must cross a potential barrier before it occupies a position of greater stability. An exponential equation of one and the same type describes the rate of any process possessing an activation energy. The activation energy for viscous flow can be calculated from the kinetic theory of liquids and, in general, it is considerably smaller than the energy of evaporation. Ewell and Eyring336 and Ewell333, 338 developed this point of view in three papers, and among other results they derived an expression for the effect of pressure on viscosity which, in the first paper, agrees with my data up to 2000 kg/cm² and which was then improved and gave agreement up to 7000 kg/cm². For

These works were followed by two papers by Eyring and his collaborators—Frisch, Kincaid, and Stern339, 340, in which the concept was introduced of a free volume available to a molecule, in its viscous flow around neighboring molecules, for occupying the most stable position. This free volume is connected with various thermodynamic parameters. The authors found that their theory makes it possible to reproduce, with small error, the viscosity of any liquid up to 10,000 kg/cm². Auluck and Kothari341 applied the “hole” theory in liquids, in which physical reality is ascribed to vacant sites in liquids, and were able to give a qualitatively correct picture of the variation of viscosity with pressure.

REFERENCES CITED

R. B. Dow, Physics 6, 71 (1935). Viscosity of liquid mixtures at high pressure.
R. B. Dow, Physics 6, 270 (1935). Note on the viscosity of oils as a function of volume and temperature.
R. B. Dow, Paper read at New York meeting of Soc. of Rheol (October 31, 1936). Influence of pressure and temperature on the viscosity of lubricating oils.
R. B. Dow, J. Appl. Phys. 8, 367 (1937). Influence of pressure and temperature on the viscosity of lubricating oils.
R. B. Dow, M. R. Fenske a. H. E. Morgan, Ind. Eng. Chem. 29, 1078 (1937). Influence of pressure on the viscosity of oils and chlorinated diphenyls.
H. E. Morgan a. R. B. Dow, Phys. Rev. 54, 312 (1938). Influence of pressure and temperature on the viscosity of monosubstituted toluenes.
R. M. Dibert, R. B. Dow a. C. E. Fink, J. Appl. Phys. 10, 113 (1939). Viscosity of Pennsylvania petroleum at high pressures.
R. B. Dow, Phil. Mag. 28, 403 (1939). Viscosity of liquids at high hydrostatic pressures.
B. W. Thomas, W. R. Ham a. R. B. Dow, Ind. Eng. Chem. 31, 1267 (1939). Dependence of the viscosity of lubricating oils on high pressure.
R. B. Dow, J. S. McCartney a. C. E. Fink, J. Inst. Petroleum 13, 301 (1941). Viscosity of Russian and Romanian lubricating oils at high pressure.
Yoshio Suga, Bull. Inst. Phys. Chem. Research., Tokyo 11, 877 (1932). Viscosity of oil under pressure, 1.
M. D. Hersey a. G. H. C. Snyder, J. Rheol. 3, 298 (1932). Flow in capillaries at high pressure.
U. Ebbecke u. R. Haubrich, Arch. Ges. Phys. 238, 429 (1936). Influence of compression on the viscosity of various organic liquids.
J. Versluys, A. Michels a. J. Gerver, Physica 3, 1093 (1936). Method for measuring the viscosity of methane-saturated petroleum solutions under pressure.
B. H. Sage, B. N. Inman a. W. N. Lacey, Ind. Eng. Chem. 29, 888 (1937). Viscosity of hydrocarbon solutions, methane–propane system: “crystal oil.”
L. Y. Bradford a. C. G. Vandergrift, Inst. Mech. Eng. Lub. Disc., Group I, 23–29. October (1937). Relation between the effect of pressure on viscosity and the operation of bearings.
M. D. Hersey a. R. F. Hopkins, J. Appl. Phys. 8, 560 (1937). Viscosity of lubricating oils under pressure. Part I. Fatty oils.

E. W. Dane and F. Birch, J. Appl. Phys. 9, 669 (1938). Effect of pressure on the viscosity of amorphous boron anhydride.
S. J. Needs, Inst. Mech. Eng. Lub. Disc., Group I, 198—204 (October 1937). Effect of pressure on the viscosity of a film in heavily loaded bearings.
U. Ebbecke and R. Haubrich, Biochem. Zschr. 303, 242 (1939). Viscosity of double and spherical molecules, especially glycogen and starch in compressed liquids.
M. P. Volarovich, Acta Physicochim. USSR, 13, 69 (1940). Effect of pressures up to 1000 kg/cm² on the viscosity of liquids similar to lubricating oils.
M. P. Volarovich, Acta Physicochim. USSR, 14, 564 (1941). Remarks on the article “Effect of pressures up to 1000 kg/cm² on the viscosity of liquids similar to lubricating oils.”
J. S. Swearingen and E. D. Redding, Ind. Eng. Chem. 34, 1496 (1942). Viscosity of lubricating oils saturated with natural gas at high pressures.
W. R. van Wijk and W. A. Seeder, Physica 4, 1073 (1937). Effect of temperature and specific volume on the viscosity of liquids. I.
W. R. van Wijk and W. A. Seeder, Physica 6, 129 (1939). Effect of temperature and specific volume on the viscosity of liquids. II.
E. C. Bingham, H. E. Adams and G. R. McCauslin, J. Am. Chem. Soc. 63, 466 (1941). Dependence between fluidity, volume, pressure, and temperature in liquids.
R. H. Ewell and H. Eyring, J. Chem. Phys. 5, 726 (1937). Theory of the viscosity of liquids as a function of temperature and pressure.
R. H. Ewell, J. Chem. Phys. 5, 571 (1937). Temperature coefficient, pressure coefficient, and volume coefficient of the viscosity of liquids.
R. H. Ewell, J. Appl. Phys. 9, 257 (1938). Reaction rate as a theory of viscosity and some of its applications.
D. Frisch, H. Eyring and J. F. Kincaid, J. Appl. Phys. 11, 75 (1940). Effect of pressure and temperature on the viscosity of liquids.
J. F. Kincaid, H. Eyring and A. E. Stearn, Chem. Rev. 28, 301 (1941). Theory of absolute reaction rates and its application to viscosity and diffusion in the liquid state.
F. C. Auluck and D. S. Kothari, Nature 153, 777 (1944). Hole theory of liquids.

7. EFFECT OF PRESSURE ON ELASTIC CONSTANTS

This question is of great interest to geophysicists, since the velocity of propagation of seismic waves in the deep layers of the earth’s crust must depend on the effect of pressure on the elastic constants.

Experimental work in this field has recently been carried out only by Birch and Bancroft342—346 in connection with the program of geophysical investigations at Harvard. There are also several theoretical works. Some of the earlier works, in particular those of Green and, much later, Brillouin, led to the improbable conclusion that the velocity of propagation of deformation should decrease with increasing pressure. In 1932 Genky347 proposed a theory of finite deformations, which was formally plausible and gave the correct expression for the velocity of a compression wave.

Murnaghan^348 in 1937 proposed the theory of finite deformations, which was the most natural both physically and mathematically. In his investigations Murnaghan applied this theory specifically to my experimental measurements of the change of compressibility with pressure and achieved considerable success.

Birch^344 continued the discussion of the question and obtained expressions for the influence of pressure on the elastic constants of isotropic solids which, in general, agreed well with experiment.

There is a difference of opinion as to whether the success of Murnaghan’s formula is to a considerable extent formal and empirical, or whether there is a deeper meaning here. In my opinion, the theory is formal and owes its success chiefly to the use of a mathematical expression for volume as a function of pressure which automatically leads to zero volume at infinite pressure. With our present knowledge of atomic structure such a limiting volume must be assumed; most earlier theories accepted a finite limiting volume, and these theories broke down when the pressure of the original experiments was exceeded.

I think that the formal character of Murnaghan’s investigations is most clearly revealed in his very latest work,^349 in which he modifies some of his earlier propositions in the light of my measurements up to 100,000 atm. He now considers the conditional elastic constant $\lambda + 2/3\mu$ as a linear function of pressure and derives a formula for the change of volume as a function of pressure. The formula contains two empirical constants, and my data can be brought into agreement with it.

In Birch’s first paper^342 a dynamic method is described, in which torsional vibrations were excited by means of an electromagnet in a cylindrical specimen subjected to pressure.

In connection with this method it was necessary to investigate various questions, such as, for example, the influence of the viscosity of the transmitting medium, which was nitrogen. It was found that the influence of the transmitting medium on the torsional vibrations could be neglected, but that this influence would prevent an attempt to determine Young’s modulus by excitation of longitudinal waves.

The method was tested on a large number of homogeneous substances, metals and glasses. It was found that the elastic modulus increases with pressure for metals and decreases for quartz and Pyrex glasses. The agreement with my previous investigations, obtained by the static method, was very good.

In this first paper Birch reached $4000 \text{ kg}/\text{cm}^2$ at room temperature. Birch and Bancroft, in two subsequent papers,^343, ^345 and later Birch in the concluding article,^346 report that they reached a temperature of $600^\circ$ and a pressure of $9000 \text{ kg}/\text{cm}^2$; they determined the elastic constants of many rocks. Differences in the behavior of so-called “covered” and “uncovered” rocks were accurately studied, and achieved

proper understanding of the complex phenomena taking place. In general, at first the influence of hydrostatic pressure consists in a large increase in the elastic constant, which subsequently asymptotically considerably diminishes its rate of growth, when the influence of the initial porosity of the rocks is eliminated.

These results were applied in geophysics to the discussion of such questions as the structure of the depths of the earth’s crust, by comparing measured velocities of seismic waves with velocities calculated with the aid of coefficients of change of elasticity with pressure.

CITED LITERATURE

F. Birch, J. Appl. Phys. 8, 129 (1937). The effect of pressure on the modulus of rigidity of metals and glasses.
F. Birch and D. Bancroft, J. Geol. 46, 59; 113 (1938). The effect of pressure on the rigidity of rocks.
F. Birch, J. Appl. Phys. 9, 279 (1938). The effect of pressure on the elastic parameters of isotropic solids, according to Murnaghan’s finite-strain theory.
F. Birch and D. Bancroft, J. Geolog. 48, 752 (1940). New measurements of the rigidity of rocks at high pressures.
F. Birch, Bull. Geol. Soc. Am. 54, 263 (1943). Elasticity of igneous rocks at high pressures and temperatures.
H. Hensky, Phil. Mag. 14, 254 (1932). On the propagation of elastic waves in substances at high hydrostatic pressures.
F. D. Murnaghan, Am. J. Math. 59, 235 (1937). Finite deformations in an elastic solid.
F. D. Murnaghan, Proc. Nat. Acad. Sci. 30, 244 (1944). Compressibility of matter at ultrahigh pressures.

8. THE INFLUENCE OF PRESSURE ON PLASTIC FLOW AND SIMILAR PHENOMENA

Most of the work in this field during the period under consideration was carried out at Harvard, first by me and then by Griggs. The question does not lend itself so easily to exact investigation, and therefore many results are qualitative in character.

The apparatus in which my investigations were carried out was described in 1937.350 Two cylindrical steel blocks $B$ (Fig. 5) have very short enlargements. These blocks, by means of a hydraulic press, are forced with their enlargements into a rectangular steel block $C$. In the region of contact between the enlargements and block $C$, large stress concentrations arise. Since this region of large stresses is isolated at the center of the surrounding mass of comparatively slightly stressed steel, considerably greater stresses can be attained at this point without fracture than if the stresses were uniformly distributed. With suitably treated tool steel, stresses up to $50\,000\ \mathrm{kg/cm^2}$ can be attained without frac-

failure, whereas under ordinary conditions pistons made of this steel cannot withstand compressive stresses above $30\,000\ \text{kg}/\text{cm}^2$.

If some plastic material is placed at $A$ between the thickening and block $C$, and pressure is applied, this material will be extruded until there remains a certain limiting thin layer, whose thickness depends on the pressure and on the plasticity. Complete extrusion would be impossible because of friction on the contacting surfaces; it is obvious that friction can sustain any pressure, however great, provided only that the disk of material becomes sufficiently thin. In practice, deformations appear in the steel parts, and the disk assumes a lens-like shape, with thinning toward the edges.

Fig. 5. Diagram of an apparatus for combining hydrostatic pressure with shear stresses.

The effective friction preventing extrusion is confined to a narrow ring at the boundaries of the lens, while the greater part of the plastic material inside the lens experiences an almost hydrostatic pressure. The experiment consists in rotating the steel block about the axis of the two thickenings, while the thin disk is subjected to pressure. A photograph of the apparatus is given in Fig. 6. At low pressure, surface slip is observed between the steel and the substance; when the pressure is raised to such a degree that the frictional force becomes equal to the internal stress of plastic flow, slipping ceases and, from this point on, regions of internal flow appear in the disk, their planes being arranged as a single whole, perpendicular to the shear axis above and below it.

By measuring the torque required to rotate the block, one can calculate the shear stresses necessary to produce internal plastic flow.

The experiment, briefly described above, consists in measuring the torque as a function of the pressure applied perpendicular to the thickenings, and in calculating from this value the shear stresses as a function of pressure.

At ordinary stresses and under ordinary conditions, the influence of pressure on the flow stress is small, and in ordinary engineering practice it may be neglected.

In this apparatus a range of pressures can be attained sufficient to produce a noticeable effect on the flow stress. Possibly the most important application of this method consists in determining the influence of pressure on the flow stress; in practically every case the flow stress increases with pressure, sometimes to a considerable degree. A typical example is shown in

Fig. 7. A substantial difference between plastic flow in a solid and viscous flow in a liquid is immediately manifested when this apparatus is used: for a liquid the viscous retardation of motion is proportional to the velocity, whereas the resistance to plastic flow in a solid substance is almost independent of velocity, and the twisting moment correspondingly also does not depend on velocity.

Fig. 6. General view of the torsion apparatus, mounted in a hydraulic press together with the handle for rotation.

Initially this apparatus was used for an entirely different purpose. When a substance undergoes a polymorphic transformation as the pressure is increased, the flow stress of the new modification will in general differ from that of the old one, from which it is obtained, and this will be expressed in the break of the curve of twisting moment as a function of pressure at the point corresponding to the transition pressure. Fig. 8 shows this phenomenon for bismuth. The simplicity of handling this apparatus made it possible to carry out uncomplicated experi-

Fig. 7. Relation between shear force and pressure for magnesium. Approximately in the interval with coordinates $10\,000$—$20\,000\ \mathrm{kg/cm^2}$, surface sliding ceases and internal plastic flow begins.

experiments for detecting polymorphic transitions in new substances. The method was initially applied exclusively for this purpose, and in this way a large number of new transformations were discovered, for which thermodynamic parameters were subsequently determined in an apparatus with a moving piston.

Transitions in which the change in volume is too small for it to be detected from the displacement of the piston, under favorable conditions, can be detected by this method.

Furthermore, a transformation that would be suppressed as a result of viscous resistance to the formation of new nuclei will proceed when shear is combined with pressure, even at temperatures sometimes 100 and 200° lower than the temperature at which these transformations cease to take place under purely hydrostatic pressure.

It may also be assumed that certain reversible transformations occur only under shear stresses and do not take place at all under purely hydrostatic pressure; lithium is possibly one such example.

Fig. 8. Dependence between shear force and pressure for bismuth. Breaks in the curves are the result of polymorphic transformations.

Fig. 8. Dependence between shear force and pressure for bismuth. Breaks in the curves are the result of polymorphic transformations.

By this method up to three hundred substances of the most varied material were investigated. Fifty-seven elements, about two hundred and fifty inorganic compounds, and a certain number of organic compounds were studied.[^248] The rate of increase of the plastic-flow stress with pressure is a characteristic of a substance; usually the curve of plastic stress as a function of pressure is concave toward the pressure axis, and the total increase in the rate for most elements and inorganic substances up to a pressure of $50\,000\ \mathrm{kg/cm^2}$ is no more than a factor of two, while some substances show a very small increase. With organic substances, on the contrary, the increase in shear stress has an exponential character, with a thousandfold increase at maximum pressure (for example, paraffin).

With continuous rotation of the steel block between the projections, it is evidently possible to produce infinitely large shear deformations. At the beginning of rotation various short-term effects occur, depending on the nature of the substance, but after a rotation of 20 or 30° a stationary state is usually reached. The total rota-

deformation is often carried out by more than $60^\circ$; this corresponds to a shear deformation in the outer layers of the disk of the order of 120 radians. Such very large deformations are difficult to achieve under ordinary conditions, because the experiment ends owing to destruction of the specimen; here, however, the geometry is such that destruction does not terminate the experiment. Under these extreme conditions, for most substances a great change in the initial structure of the lattice is observed; in many cases X-ray analysis shows barely noticeable traces of the original lines.

The nature of the flow, when a stationary state has been reached, varies depending on the substance; many substances flow smoothly under a constant shear force. For others, the flow continually undergoes jumps, i.e., internal fracture occurs, with self-restoration under high stresses and renewal of the cycle of limited flow and fracture. It is possible that the mechanism of deep-focus earthquakes is connected with this effect.

As a rule, flow is smooth in those substances which usually crystallize in the cubic system and have many slip planes, and it proceeds spasmodically, with internal fractures, if the crystal has no or few slip planes.

Flow under such exceptional conditions may be accompanied by various irreversible phenomena. Thermodynamically unstable forms of some minerals are transformed into stable ones; for example, wurtzite passes into sphalerite, or red phosphorus into crystalline black phosphorus—transformations which do not proceed under other conditions.

Chemical changes may also occur, including syntheses from the elements, such as $\mathrm{Cu}_2\mathrm{S}$, decompositions, such as $\mathrm{Bi}_2\mathrm{O}_3$ into metallic bismuth and oxygen, or a change in valence when, for example, $\mathrm{SnO}_2$ passes into $\mathrm{SnO}$. In the cases just mentioned, the chemical transformation occurs completely throughout the whole mass of the substance and can be confirmed by X-ray analysis.

There are also cases of a partial transition, observed by a change in color at the surface, when the amount of substance formed is too small for analysis. It is evident that, if the shear stress of the new substance is less than that of the initial one, the reaction may cease, since the plastic flow occurring in the thin film of the substance formed will not allow the shear stress inside the substance to reach the value necessary for the transition to take place.

Organic substances may undergo strong changes, the nature of which is not easy to explain; thus, for example, rubber changes into a horn-like mass. In my earlier works I cited a number of examples in which, under these conditions, an explosion occurred.

The question is not sufficiently clear, but it is possible that in most cases of explosion the matter was not only a pure pressure effect,

but also under the action of high temperature. In several cases, at the highest pressures, steel wedges are cut off from the edges of the ram, the extrusion of which is accompanied by intense local overheating. In other cases, if the initial thickness of the disk is too great, then, as the pressure is increased, an unstable state sets in and the test material is squeezed out from the sides at high speed, as a result of which local overheating also occurs.

There is the possibility of direct application of many results to geophysics; the conditions of deformation of rocks in the depths of the earth’s crust are very similar to the experimental conditions, with the exception of temperature. Larsen and Bridgman^351 studied the effect of shear deformations together with hydrostatic pressure on a number of minerals, either pure or in their combinations. They were unable to synthesize a single so-called stress mineral (stress minerals), but they did observe other kinds of permanent changes. Many cases were noted of the transition of crystalline substances into glass; opal was transformed into quartz. In many cases a definite reorientation occurred, often coinciding with Sander’s geological observations.

There still remains an enormous amount of work to be done in this field, especially in establishing the nature of the chemical changes.

The accuracy of measurements of flow stress and the magnitude of the stress can be considerably increased by replacing the steel in the apparatus with carburized steel. I have built such an apparatus and made preliminary tests, in a number of cases confirming the results obtained with the steel apparatus. With the new apparatus I reached pressures above $100\,000\ \mathrm{kg/cm^2}$ in combination with shear stresses sufficient to cause flow, and this apparatus proved to be much more durable than the steel one.

Boyd and Robertson^352 recently, copying this apparatus and providing an automatic device for drawing the torque–shear curve, investigated the lubricating properties of many lubricating substances at high pressure from the standpoint of their practical application; they qualitatively reproduced some of my results and found that stearic acid, tungsten disulfide, and molybdenum disulfide are the best lubricants at high pressures under the experimental conditions.

Griggs’s experiments^353–354 in this field were directed chiefly toward clarifying geophysical problems. The experiments of F. D. Adams and von Karman in this field are well known; according to these works, substances such as, for example, marble and limestone can undergo large compressive deformations if they have lateral support. Griggs considerably extended the pressure range and improved the experimental technique.

He built an improved apparatus in which the specimen under test is subjected to true hydrostatic pressure, exerting

with a liquid, and to the action of a simple compressive force independent of the hydrostatic pressure.

The work was usually carried out in the region up to $10\,000\ \mathrm{kg/cm^2}$, but sometimes a pressure of $13\,000\ \mathrm{kg/cm^2}$ was reached. They observed 30% shortening without failure under uniaxial compression of marble and limestone.

Beginning with a hydrostatic pressure of about $6000\ \mathrm{kg/cm^2}$, the temporary resistance to compression increases at a high rate. It was found that the increase in the temporary resistance to compression was considerably greater if the specimen was protected from penetration into its pores by the pressure-transmitting liquid.

A modification of this apparatus made it possible to apply tensile forces to a limestone specimen under hydrostatic pressure; to their surprise, the authors found that the phenomenon of increased plasticity, characteristic of compressive deformations, does not extend to tension, and the specimen breaks under tension under hydrostatic pressure just as brittly as at atmospheric pressure. This effect was later attributed to the shape of the tensile specimen, which caused a concentration of stresses at its shoulders.

Griggs $^{354}$ also studied the flow of a calcite single crystal under a hydrostatic supporting pressure and found that the effect differs qualitatively from that for limestone, which is a random conglomerate of crystals.

The plasticity of single crystals under compressive stresses also increases with hydrostatic pressure, but does not show an accelerating growth at very high pressure, remaining linear up to $10\,000\ \mathrm{kg/cm^2}$. At low pressures the plasticity of the single crystal is greater than that of the conglomerate, and, conversely, at higher pressures it is less.

The mechanism of flow was studied $^{355,356}$. Griggs could not produce plastic flow in quartz under these conditions. He therefore studied this problem on my apparatus at pressures up to $50\,000\ \mathrm{kg/cm^2}$. He could not produce any measurable flow up to the region of failure under simple compression, but observed a large increase in the temporary resistance, of exponential character, in the region above $10\,000\ \mathrm{kg/cm^2}$ supporting pressure.

The conditions of this experiment were, however, exceptionally difficult to control; the pressure was transmitted through lead, and the compressive force was determined from the leakage of lead through the free space around a freely mounted piston.

In his later work I repeated the measurements of the temporary resistance to compression of quartz under better conditions, with a true liquid as the pressure-transmitting medium, and was able to find only a linear increase in the temporary resistance to compression with increasing pressure. Griggs also observed the failure of quartz at high temperature and lower pressures in the presence of water and obtained results agreeing with field geological observations.

As regards plastic slips in quartz at low temperatures and high stresses, mention may be made of some of my unpublished earlier experiments.

In connection with experiments on squeezing out cavities in rocks under external hydrostatic pressure, I subjected quartz crystals containing well-known cavities, partly filled with liquid $CO_2$, the so-called “negative crystals,” to an external pressure of up to $30\,000\ \mathrm{kg}/\mathrm{cm}^2$, without any effect.

The crystals were put away and were accidentally examined after ten or fifteen years. Fine cracks were then found, radiating in all directions from all the cavities. Apparently, under the action of the applied pressure, permanent deformations had formed, too small to be noticed at the time; with time they slowly increased and finally produced cracks.

In 1940, Griggs$^{355}$ discussed his work in the light of geological problems and came to the conclusion that, besides hydrostatic pressure, other factors are necessary in order to bring about such deformation of rocks as is observed in nature; possibly the most important is the presence of water in combination with temperature.

Goranson$^{357}$, basing himself on Griggs’s experiments, gave an analysis of the process of plastic flow from the standpoint of thermodynamics and, among other things, considered the influence of hydrostatic confining pressure on flow.

The basic point of view is that a large part of plastic flow in the presence of water is caused by the phenomena of solubility and recrystallization, whose dependence on hydrostatic pressure can be determined from thermodynamic considerations.

Goranson calculated that the rate of flow of alabaster under compressive stresses at a hydrostatic confining pressure of $1000\ \mathrm{kg}/\mathrm{cm}^2$ is one and a half times greater than at atmospheric pressure. Griggs determined this quantity and found it to be 1.6.

Griggs later reconstructed and improved his apparatus for the study of tension under pressure. The specimens to be stretched were made in the form of simple cylinders, so that the stresses were uniformly distributed and not concentrated at particular points. The specimen was in contact with a hardened steel piston of the same diameter, passing into the high-pressure vessel through a gland, and was surrounded by a thin copper tube soldered to the steel piston. By pressing on the outward-projecting end of the piston, it is possible to produce in the specimen various compressive stresses equivalent to an all-round hydrostatic pressure plus a superposed simple tension along the axis, equal in intensity to the hydrostatic pressure.

The apparatus was used in only one case; Basley$^{357a}$ studied the deformation of marble in tension under pressure up to $10\,000\ \mathrm{kg}/\mathrm{cm}^2$.

In these conditions marble exhibits appreciable plasticity in tension, elongations of up to $25\%$ being observed without rupture. At lower pressures the appearance of a neck is observed, as in metals. The tensile strength increases to $5000\ \mathrm{kg/cm^2}$, i.e., it is approximately twenty times greater than under simple compression at atmospheric pressure.

The geometrical interpretation of flow processes still has to be developed either as twinning or as shear—sliding.

At the beginning of the period described there were certain little-known qualitative experiments by Heide$^{358}$ on plastic flow. He enclosed single crystals of barite, celestine, and anglesite in clay, which he placed in a thick-walled steel vessel and compressed with a piston up to $20\,000\ \mathrm{kg/cm^2}$. Owing to the friction of the clay against the walls of the vessel, the deformations were nonuniform, and planes perpendicular to the axis were deformed.

This deformation under high supporting pressure occurred without destruction. Heide studied the sliding of planes that accompanies bending. He found that deformation at high temperatures ($400^\circ\mathrm{C}$) is accompanied by sliding along a larger number of crystallographic planes than at room temperature. It is necessary to mention the review article by Volarovich$^{359}$, in which the results of many of the works just noted are discussed from the standpoint of their application to geology and geophysics. Some of the results of Volarovich’s experiments on the dissolution of water in basalt at high pressures and temperature are also given there.

Over the last several years I have carried out extensive investigations of the influence of hydrostatic pressure on the plastic flow of metals.

The experiments were carried out$^{360–364}$ in an apparatus for $30\,000\ \mathrm{kg/cm^2}$; the supporting pressure was transmitted by a true liquid, the pressure in which could be brought to $30\,000\ \mathrm{kg/cm^2}$, and it was possible accurately to measure the deforming forces acting on the specimen by means of the same electrical device that had been used for measuring compressions up to $100\,000\ \mathrm{kg/cm^2}$, using the change in resistance caused by the stress.

The experiments were conducted mainly with various steels, but it was found that copper, aluminum, bronze, and brass give, from the qualitative point of view, the same effect.

In Fig. 9 the specimen on the left is shown ruptured at atmospheric pressure, in which the reduction of the cross-sectional area is small; on the right is the same specimen, subjected to pressure and stretched without rupture, with a very large reduction of area.

The degree of increase of plasticity with pressure depends on the quality of the steel and, in general, is the smaller the harder the steel or the higher its carbon content.

A typical example is steel with a carbon content of $0.45\%$, which at atmospheric pressure ruptures with a two- or threefold—

…elongation, while under a confining pressure of $25\,000\ \mathrm{kg/cm^2}$ it undergoes a 300-fold elongation without rupture.

The quantitative relationships are simple. If, for measuring deformation, one takes “natural” strains, i.e. the natural logarithm of the ratio of the initial cross-sectional area to its final area—which, owing to constancy of volume, is the same as the ratio of the final length to the initial length (taken in the neck of the stretched specimen,

Fig. 9

Fig. 9. Illustration of the effect of hydrostatic pressure on ductility in tension. On the left is a stretched specimen which ruptured at atmospheric pressure with a reduction in area of approximately $60\%$. On the right is a specimen of the same steel which, at a pressure of $25\,000\ \mathrm{kg/cm^2}$, was stretched to a much greater reduction in area (cross section) and did not rupture.

where the deformations are maximal), it turns out that the natural stress at rupture is, almost exactly, a linear function of the hydrostatic confining pressure. The slope of the line is greater the softer the steel.

This relationship holds for natural strains equal to 5, i.e. up to 100-fold elongations. At larger elongations the geometry is no longer maintained, since the influence of individual crystalline grains begins to predominate, and the measurements cannot be carried out so simply. With such an abnormal increase in stress, a noticeable increase in hardness is observed; the tensile stress required to attain plastic flow increases together with the stress. Here again the dependence is simple: the stress required to attain plastic flow is a linear function of the natural stress up to the point of rupture.

If a specimen is stretched under pressure, but not to the breaking point, and then the supporting pressure is removed, and if the specimen is then stretched a second time at atmospheric pressure, then, although the elongation under pressure considerably exceeds the elongation required for rupture in ordinary tension at atmospheric pressure, nevertheless some degree of further increase in plasticity appears, and the stress required for rupture may considerably exceed the rupture stress at atmospheric pressure. If the specimen fails under supporting pressure, the nature of the rupture depends strongly on that pressure.

As the pressure is increased, the phenomenon of rupture across the fibers, parallel to the direction of tension, becomes less pronounced and finally disappears; the rupture acquires entirely the character of shear. The large increase in plasticity in tension of steel also extends to other kinds of deformation; thus, through a sheet of low-carbon steel immersed in a liquid and subjected to a large hydrostatic pressure, a punch may be forced, with no chipping out observed.

The experiments just described have not yet been fully published in any scientific journal; however, they have been described in several reports to the Watertown Arsenal.

REFERENCES CITED

P. W. Bridgman, Proc. Am. Acad. Arts Sci. 71, 387 (1937). Shear phenomena at high pressure, especially in inorganic substances.
E. S. Larsen and P. W. Bridgman, Am. J. Sci. 36, 81 (1938). Experiments on the study of shear in certain selected minerals and their combinations.
John Boyd and B. P. Robertson, Trans. A.S.M.E. 67, 51 (1945). Frictional properties of various lubricants at high pressures.
D. T. Griggs, J. Geol. 44, 544 (1936). Deformation of rocks under high supporting pressures.
D. Griggs, Am. Min. 23, 28 (1938). Deformation of calcite single crystals under high supporting pressures.
D. Griggs, Bull. Geol. Soc. Am. 51, 1002 (1940). Artificial flow of rocks under conditions favorable for recrystallization.
D. Griggs, J. Geol. 47, 225 (1939). Creep of rocks.
R. W. Goranson, Bull. Geol. Am. 51, 1023 (1940). Flow in stressed solids; explanation.
357a. J. R. Baisley, Trans. Am. Geophys. Union, Part II, 519 (1941). Deformation of marble in tension under high pressure.
F. Heide, Zschr f. Krist. 78, 257 (1931). Deformation of crystals at high pressures and temperatures.
M. P. Volarovich, Izv. Akad. Nauk SSSR, 985 (1940). On the application of high pressure to geology and geophysics.
P. W. Bridgman, Am. Scientist 31, 1 (1943). Recent work in the field of high pressures.
P. W. Bridgman, Metals Tech. 32–39 (December 1944). Flow and fracture.
P. W. Bridgman, Metals Tech. (April 1945). Symposium on cohesive forces—discussion.

P. W. Bridgman, Eight reports to the Watertown Arsenal from March 1943 to December 1945 under the numbers WAL 111/7, WAL 111/7—1, etc. through WAL 111/7—7.
P. W. Bridgman, Rev. Mod. Phys. 17, 3 (1945). The influence of high hydrostatic pressure on the plasticity of metals.

9. VARIOUS MECHANICAL EFFECTS OF HYDROSTATIC PRESSURE

There are a number of papers on the penetration of gases and liquids into metals under pressure. Eilender[^365] observed that steel, palladium, and silver can be activated by heating in a gaseous medium in such a way that they acquire the ability reversibly to absorb or desorb hydrogen or nitrogen when subjected to the pressure of these gases. The pressure interval was 30 atm. The method consisted in determining the electrical resistance, which was a function of the amount of gas absorbed. Ipatiev and Tikhomirov[^366] studied the diffusion of hydrogen into water at pressures of 100 kg/cm²; they found no appreciable difference in comparison with diffusion at atmospheric pressure.

Poulter and Wilson[^367] studied the permeability of glass and fused quartz with respect to various liquids up to a pressure of 15,000 kg/cm². Water, alcohol, and ether diffuse under high pressure into quartz or glass and, when the pressure is released, are given off again. This manifests itself in various kinds of destruction. If glass is subjected to the pressure of water for some time, a certain noticeable amount of water is absorbed in the outer layers of the glass. If the pressure is rapidly reduced, the water has no time to diffuse back, and the glass cracks because of the expansion of the water enclosed in the pores. With a slow reduction of pressure, no cracking is observed, since the water has time to escape. For the same reason, a rapid rise and fall of pressure also does not cause cracks, since the water does not have time to penetrate into the glass. Paraffin, oil, and glycerin apparently do not penetrate into glass.

I may add that I made similar observations, but did not publish them. A thick-walled glass capillary, sealed at both ends and subjected to the hydrostatic pressure of water, can, after the pressure is released, peel like an onion. The effect depends strongly on the kind of glass.

Poulter and Uffelman[^368] observed, in a special apparatus, the penetration of hydrogen through steel under a pressure of 4000 atm—a phenomenon that greatly hindered me in my attempts to determine the compressibility of hydrogen. Poulter and Uffelman found that the degree of penetration depends on the kind of steel.

Inglis and Andrews[^369] studied the effect of hydrogen on steel as a function of pressure (up to 250 atm) and temperature (500°C) with holding times of up to 5000 hours. Above all, for low-carbon

For steels there exists a period of absorption accompanied by deterioration of physical properties, which are restored by heating. If the action of hydrogen continues, the disturbances become permanent and are accompanied by decarburization. The influence of hydrogen depends noticeably on grain size and decreases in some alloy steels containing Ni, Cr, or Mo.

Alekseev and Ostroumov$^{370}$ studied the influence of hydrogen on steel up to 780 atm and 530°. The change in mechanical properties is the greater, the more carbon the steel contains, and proceeds in parallel with decarburization. Steels containing up to 0.3% carbon cannot safely withstand pressures above 50 atm at 500°.

Maxwell$^{371}$ studied the action of hydrogen on various iron-containing alloys up to 400° and 250 atm. A decrease in elongation and a reduction in cross-sectional area are noted, as well as a slight decrease in the ultimate tensile strength; the cause of the increase in brittleness is the effect on grain cohesion. The addition of from 2.25 to 3% Cr reduces the rate of the effect.

Smizels and Ransley$^{371}$ studied the diffusion of oxygen through nickel up to 900° at low pressures. The rate increases rapidly up to a pressure of 0.25 mm Hg, and thereafter remains constant. The explanation is that a surface film is formed, which becomes saturated at this pressure. They also studied the diffusion of hydrogen through nickel up to 400° and 112 atm. In this interval the diffusion rate is proportional to the pressure. It may be assumed that hydrogen molecules striking the surface, in contrast to oxygen, penetrate through the surface film into the metal.

Perminov and Vyunov$^{373}$ studied the diffusion of hydrogen through Armco iron up to 360° and 1750 atm. Over almost the entire pressure range the diffusion rate is proportional to the square root of the pressure. Diffusion proceeds both through the grains and between them; it is greater in the latter case. At high pressures the influence of grain size is relatively small.

Welter and Mikołajczyk$^{374}$ determined the influence of casting conditions on the permeability of castings to liquid pressure up to 1000 atm and gas pressure up to 150 atm. Most castings were impermeable under these conditions.

Smizels$^{375}$ studied the diffusion of hydrogen through iron, nickel, molybdenum, platinum, copper, and aluminum up to 1000°. Large differences were observed depending on the metal: at room temperature diffusion is most significant for iron. The total quantity of gas that has diffused does not depend strongly on the wall thickness.

Several articles are devoted to the question of the influence of pressure on adsorption. Frolich and White$^{376}$ studied the adsorption of methane and hydrogen on charcoal up to 180 atm and 100°C. The amount of adsorbed gas at first increases rapidly with pressure, reaching saturation at about 100 atm. At 25° almost three times more methane than hydrogen is adsorbed. In mixtures, me—

methane, while hydrogen is practically almost not adsorbed. The amount of methane adsorbed is approximately the same as if it alone were present at its partial pressure.

Antropov^377 measured the adsorption of nitrogen on charcoal up to 200 kg/cm² between 160° and 150°. The saturation pressure was reached at lower temperatures, and saturation was a function of temperature. The results fit into the Langmuir adsorption isotherm.

Coolidge^376,379 devoted two papers to adsorption at high pressure. In the first paper he applies Polanyi’s theory, and in the second paper he checks it against experimental data for the adsorption of CO₂, N₂O, and SiF₄ on charcoal up to 100 atm.

Krichevsky and Kalvarskaya^380 investigated, between −10° and 50° and up to 600 atm, the adsorption of benzene and carbon tetrachloride from nitrogen and hydrogen on sugar charcoal. A maximum of adsorption was found.

Bozen^381 measured the adsorption of acetic acid from its solutions by activated charcoal at 25° and 1, 1000, and 2000 atm. At all three pressures the adsorption isotherms had the same character and did not fit the Freundlich equation. The dependence of adsorption on pressure is expressed by a straight line for concentrations from 0.01 to 0.15 M. The remaining questions cannot be divided into definite groups, and they will be set forth chronologically.

Welter^382 studied the influence of pressure on the casting of many low-melting metals, such as aluminum and zinc, their alloys with one another and with copper, up to pressures of 12,000 atm. It was found that under pressure the metal solidifies with better mechanical properties, having a higher temporary resistance (up to 25%), greater elongation, and greater hardness. The structure is finer-grained and the density higher. The effect is attributed chiefly to the removal of microscopic cracks and voids. Annealing of solid castings under normal conditions at atmospheric pressure and at a pressure of 20,000 atm in lead did not lead to any noticeable improvement in properties.

Trzebiatowski^383 compressed gold and copper powder in an oxygen-free atmosphere at temperatures up to 600° and pressures up to 15,000 atm. The density and hardness increase as the temperature is raised to 200°. Between 200° and 400° the hardness decreases, probably owing to annealing. The density, electrical resistivity, and temperature coefficient of electrical resistivity reach the values of these quantities for massive metal when compressed at 400° C. Above 400° softening occurs because of recrystallization.

Van Wert^384 studied in my laboratory the influence of pressure on the period of hardening of alloys. Duralumin, various other aluminum alloys, and lead–calcium alloys were investigated at room temperature up to pressures of 12,000 kg/cm². In all cases pressure slowed the rate of solidification, but the final equilibrium hardness did not change. An exception was iron with 0.07% nitrogen, for which, even at a pressure of 20,000 kg/cm², no observable ...

LATEST WORK IN THE FIELD OF HIGH PRESSURES

it was possible to change the rate of solidification. In general this effect is the greater, the more compressible the substance; Van Wert attributed it to the effect of an increase in viscosity.

In 1935,^385 when measuring the linear compressibility of exceptionally pure single crystals of zinc up to 12,000 kg/cm², I established that the volume compressibility is insensitive to small amounts of impurities. This work was prompted by Hanson’s measurements, who obtained some of the elastic constants, calculated the volume compressibility, and drew the conclusion that it could probably be affected by small impurities. Hanson’s results were probably connected with the high sensitivity of the elastic constants measured by him to internal stresses. Incidentally, this article^385 contains better values for the compressibility of zinc than my earlier data.

Selissky and Kuznetsov^386 found that at 150° the aging of duralumin proceeds more slowly at 10,000 kg/cm² than at atmospheric pressure. Tammann and Hartmann^387 studied the period of solidification of duralumin at room temperature and at pressures of 1,150 and 3000 atm. The rate decreased with pressure; at 3000 atm it was more than half as small as at 1500 atm.

Tissen and Kirsch^388 found that a pressure of 100 atm between 0° and 15° causes crystallization of rubber if this pressure acts for three months. The crystallization was permanent and was determined by X-ray photography.

Poulter^389 discussed the importance of the application of superhigh pressures in engineering. This is largely a review of his own work. In this article Poulter asserts that he reached 100,000 kg/cm² in apparatus apparently made of steel. However, he gives no details either here or in later published works; it is quite possible that the true pressure was distorted by friction. In his opinion, one of the most important areas of application of pressure is the study of the properties of lubricants at high pressures. In a previous article^390 he pointed out the fact that if there is moisture in lubricating oil, then under the conditions of stresses in a bearing, ice VI may form, which may have abrasive properties.

Jones^391 discussed the possibility of attaining very high pressures in compacting powders in metallurgy by applying to dies the same principle of external conical support which I used to obtain 50,000 kg/cm².

I also discussed this article and pointed out the possibility of strengthening during drawing or extrusion when such a design is used.

Efremov, Selissky, and Georgievsky^392 studied the effect of quenching eutectoid steel from 1000° under simple compression (nonhydrostatic pressure) of 20,000 kg/cm². The hardened steel had a martensitic structure; the authors explain this by saying that the stress lowered point A below the martensite point.

Bochvar, I. Velichko, and Yu. Velichko $^{393}$ found that the mechanical properties of bronzes containing Si and Sn are improved when cast under pressure up to 10 atm. After 7 atm there are no major improvements, and the authors attributed this improvement to the destruction of gas bubbles. Bochvar $^{394}$, in a subsequent article, reports that improvement of properties during pressure casting is observed for those alloys which normally crystallize over a certain temperature interval; under these conditions the alloy remains plastic during part of the solidification process, and cracks cannot form. If, however, the alloy solidifies at a single temperature, then exceptionally high pressures are required in order to eliminate cracks.

Goranson $^{395}$, in a review article, describes various effects produced by pressure, as well as his method for attaining the highest pressures by means of the “cascade” apparatus already mentioned by us. Gilpin $^{396}$ gives a preliminary account of work carried out in my laboratory on the influence of pressure on surface tension. The differential rise of mercury in two capillaries of different diameters was observed through glass windows. Measurements up to $2500\ \text{kg}/\text{cm}^2$ showed a decrease in the surface tension at the mercury—water interface. The complete work has not yet been published, but it is available in the form of a dissertation.

Leipunsky and Frank $^{397}$ found that the rate of setting of thixotropic colloids of ferric oxide hydrate decreases under a pressure of 2000 atm. The effect is especially noticeable in fresh gels at low electrolyte concentration and is attributed to a change in the adsorption conditions on the surfaces of the micelles.

CITED LITERATURE

H. Jellinek, Zschr. f. Phys. 66, 543 (1930). Penetration of gas into metal at high pressure.
V. V. Ignat’ev and V. I. Tikhomirov, Zhurn. Obshch. Khimii 1, 736 (1931). Diffusion of gases under pressure.
T. C. Poulter a. R. O. Wilson, Phys. Rev. 40, 877 (1932). Permeability of glass and fused quartz with respect to ether, alcohol, and water at high pressure.
T. C. Poulter a. L. Uffelman, Physics 3, 147 (1932). Penetration of hydrogen into steel at high temperatures and pressures.
N. P. Inglis a. W. Andrews, Engineering 136, 613 (1933). Influence of hydrogen on various steels at high pressures and temperatures.
D. V. Alekseev and V. V. Ostroumov, Zhurn. Prikl. Khim. 6, 621 (1933). Influence of hydrogen on steel at elevated temperatures and pressures.
H. L. Maxwell, Penn. State Coll. Bull. No. 18, 128 (1935). Influence of gases on iron-containing materials at high temperatures and pressures.
C. J. Smithells and C. E. Ransley, Proc. Roy. Soc. 157, 292 (1936). Diffusion of gases through metal. IV. Diffusion of oxygen and hydrogen through nickel at very high pressures.

P. S. Perminov and B. F. Vyunov, Korrozija 4, 229 (1938). Diffusion of hydrogen through iron at high pressures.
G. Welter and J. Mikolajczyk, Wiad. Inst. Metall. Metal. 5, 105 (1938). Impermeability of metals and alloys at high pressures and its dependence on casting conditions.
C. J. Smithells, Nature 139, 1113 (1937). Penetration of hydrogen into metals.
P. K. Frölich and A. White, Ind. Eng. Chem. 22, 1058 (1930). Adsorption of methane and hydrogen on coal at high pressure.
A. V. Antropoff, Zschr. f. Elektrochemie 39, 616 (1933). Adsorption of nitrogen by coal at high pressures.
A. S. Coolidge, J. Am. Chem. Soc. 56, 554 (1934). Adsorption at high pressures. I.
A. S. Coolidge, J. Am. Chem. Soc. 56, 561 (1934). Adsorption at high pressures. II.
I. R. Krichevskii and R. S. Kalvarskaya, Acta URSS 13, 49 (1940). Adsorption of gases under pressure.
A. M. Rosen, D.A.N. 41, 296 (1943). Adsorption from solutions at high pressure.
G. Welter, Metallwirtschaft 10, 475 (1931). Experiments on crystallization under pressures up to 20,000 atm.
W. Trzebiatowski, Zschr. f. phys. Chemie 169, 91 (1934). Pressing of finely ground metallic powders. III.
L. R. Van Wert, Preprint of Am. Soc. for Metals, New York City (1934). Effect of high hydrostatic pressure on aging.
P. W. Bridgman, Phys. Rev. 47, 393 (1935). On the influence of small impurities on elastic constants, especially the compressibility of zinc.
Ya. P. Selisskii and V. G. Kuznetsov, Metallurg 12, 130 (1937). Aging of duralumin under high pressure.
G. Tammann and H. Hartmann, Zschr. Metallkunde 29, 88 (1937). Effect of hydrostatic pressure on the hardening of duralumin.
P. A. Thiessen and W. Kirsch, Naturwiss 26, 387 (1938). Crystallization of rubber under pressure.
T. C. Poulter, J. Appl. Phys. 9, 307 (1938). Ultra-high pressures and their importance in the study of engineering problems.
T. C. Poulter, Oil Gas. J. 36, 47 (1937). Some investigations of liquids and solids under pressure.
W. D. Jones, Metals and Alloys 9, 125 (1938). Possibilities of applying high pressures in powder metallurgy.
I. N. Efremov, Ya. P. Selisskii, and P. I. Georgievskii, Metallurg 13, 20 (1938). Influence of high pressure on the transformation of carbon steel.
A. A. Bochar, I. P. Velichko, and Ya. A. Velichko, Izv. Akad. N. SSSR No. 5, 13 (1940). Influence of high pressures on the properties of copper alloys during crystallization.
A. A. Bochar, Izv. Ak. Nauk SSSR No. 7, 27 (1940). Crystallization of alloys under pressure as a function of alloy composition.
R. W. Goranson, Sci. Mo. 51, 524 (1940). Effect of ultra-high pressures on physical properties.
L. B. Heilprin, Phys. Rev. 59, 921 (1941). Apparatus for studying surface tension at high pressures.
O. I. Leipunskii and P. E. Frank, ZhFKh 15, 504 (1941). Behavior of thixotropic colloids under pressure. I. Gelatinization of iron oxide hydrates under pressure.

(To be concluded in the next issue.)

A.S.M.E. — American Society of Mechanical Engineers — the American Society of Mechanical Engineers. ↩

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Recent Works in the Field of High Pressures*

Mechanical Effects of High Pressure

4. Phase Transformations under Pressure in One-Component Systems

A. Evaporation

B. Melting

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C. Polymorphic Transformations

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5. PHASE CHANGES UNDER PRESSURE IN MULTICOMPONENT SYSTEMS

A. Solubility of Gases in Liquids

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B. Solubility of Solids in Liquids and Related Phenomena

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6. THE EFFECT OF PRESSURE ON VISCOSITY

A. Viscosity of gases

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B. Viscosity of Liquids

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7. EFFECT OF PRESSURE ON ELASTIC CONSTANTS

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8. THE INFLUENCE OF PRESSURE ON PLASTIC FLOW AND SIMILAR PHENOMENA

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9. VARIOUS MECHANICAL EFFECTS OF HYDROSTATIC PRESSURE

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Recent Works in the Field of High Pressures\*