Bridgman’s Investigations in the Region of High Pressures

A. V. Rakovskii.

PART III.

MUTUAL TRANSFORMATIONS OF LIQUID AND SOLID PHASES.

1.

The most interesting and effective group of Bridgman’s works is that which concerns the phenomena of melting, freezing, and mutual transformations of solid phases. The number of substances already studied in this respect exceeds one hundred; in many cases Bridgman succeeded in discovering entirely new facts and phenomena.

To study melting and, in general, the transition of one phase into another, Bridgman used three kinds of apparatus. In all the instruments the common parts were a manganin manometer, a piston, and a bomb—glass, copper, or steel—containing the substance under investigation. The piston, which allowed absolutely no leakage, was provided with a micrometer that made it possible to take precise account of changes in the volume \(\Delta v\) of the system. The arrangement of these important parts in the instruments varied depending on the range of temperatures and pressures in which it was intended to work.

For medium temperatures and pressures Bridgman used two cylinders: in the upper cylinder there was the piston, in the lower one the manganin manometer and the bomb with the substance. In his first experiments Bridgman left the upper cylinder in the air and placed the lower one in a thermostat. In the event of a temperature difference, he introduced the corresponding correction, determined experimentally. With a similar arrangement of instruments Tammann, who worked up to 3000–4000 atmospheres, did not introduce the indicated correction. In his subsequent experiments Bridgman also placed the upper cylinder in the thermostat.

The apparatus for low pressures and temperatures (up to 80°) consisted of three cylinders: the upper one with the piston, the middle one with the manometer, and a small lower cylinder with the bomb; this latter

the cylinder was placed in a cooling mixture of ether and solid carbon dioxide in a Dewar vessel. In both apparatuses the cylinders were connected by tubes, and the pressure was transmitted by means of kerosene or gasoline.

For high pressures and temperatures considerably above room temperature, the apparatus consisted of a single cylinder, since pressures above \(12000\) kg/sq. cm, especially at high temperatures, could not be withstood by any tubes.

The details of the apparatuses and the methods of testing, fitting, and assembling them are set forth in the first article of the present essay.

The study of the phenomena of melting and of the mutual transitions of solid phases is substantially facilitated, in comparison with the study of the properties of liquids, by the fact that here the process of transformation is accompanied by a change of volume \(\Delta v\) at constant pressure and temperature. Consequently, all the experimentally found \(\Delta v\) refers to the transformation of phases under study; a whole series of corrections, or the parallel experiment with steel replacing them,¹ is unnecessary here. The experiment is conducted as follows. After the apparatus has been assembled, the piston is gradually driven into the cylinder by a hydraulic press. With the aid of a microscrew the change in volume of the system is determined (from the magnitude of the piston’s depression and its cross-section; here a correction is introduced in the final result for the elastic deformation of the piston under the influence of pressure and temperature). After 15–20 minutes of waiting for the heat of compression to dissipate, the manometer is read. On the axis of abscissae the pressure is plotted, and on the axis of ordinates—the positions of the piston. Suppose that the substance under investigation is liquid water. So long as only compression of the liquid water occurs at the given temperature, every displacement of the piston corresponds to an increase of pressure (curve \(ab\)). When the water begins to freeze, then, in order to maintain constant pressure, the piston must be driven deeper. We obtain a sharp change in the volume of the system (straight line \(bc\)) at constant pressure and temperature. When all the water has frozen, every further inward motion of the piston will again correspond to an increase of pressure (curve \(cd\)). Upon decreasing the pressure, i.e. with gradual upward motion of the piston, we shall describe the same curve \(dcba\) in the reverse order. By this method we simultaneously obtain all the data necessary for studying the process of phase transformation: pressure, temperature, and change of volume.

Fig. 1.

¹ See the second article on the properties of liquids.

The results are considered good if the transition from \(ab\) to \(cd\) is indeed sharp and not small. If one starts from the liquid phase, the picture is very often somewhat obscured by the fact that the liquid phase is easy to supercool; the curve \(ab\) does not break off at \(b\), but continues somewhat farther (sometimes to 1000 and more atmospheres), then, when the freezing process begins, there occurs a sharp and sudden jump in the pressure (a return to point \(b\)). Such a jump in pressure, especially in the region of high pressures, has an extremely harmful effect on the strength of the apparatus and the accuracy of its readings. The harmful phenomena described do not occur at all if we move in the opposite direction, i.e. study melting. Since a solid phase cannot be superheated with respect to the liquid, the jump always occurs at \(c\); the curve \(cd\) cannot be prolonged to the left. Moreover, the instruments work much better when we go from higher pressures to lower ones (the effect of habituation of the metal to high pressures).

In view of what has been said, Bridgman, as a rule, made the readings of the necessary quantities during melting, and not during freezing of the substance.

From the pressures \(p\), temperatures \(t\), and volume changes \(\Delta v\) found experimentally in the phase transformations, Bridgman calculated: 1) the latent heat of melting (or of transition of one solid phase into another) \(\Delta H\), according to Clapeyron’s equation,

\[ \Delta H = T \Delta v \frac{dp}{dt}, \]

where \(T\) is the absolute temperature of the phase transformation at the given pressure, while \(\frac{dp}{dt}\) is determined from the transformation \((p,t)\) curves (for example, melting curves);

2) the mechanical work of transformation

\[ \Delta R = p \Delta v, \]

3) the change in the internal energy of the substance upon transition from one phase to another

\[ \Delta E = \Delta H - p\Delta v; \]

Let us now consider a number of the most interesting results obtained by Bridgman.

2.

Mercury.

For mercury only one solid phase has been found, and accordingly we have only one melting curve for mercury.

The change in volume upon freezing of mercury is insignificant, only 3% of its entire volume. The value of \(\left(\dfrac{dp}{dt}\right)_v\) at ordinary pressure is 196.4, and at 12000 kg/cm² is 199.3. These figures show by how many kg the pressure must be increased in order that the freezing temperature should rise by \(1^\circ\). In Table I are given some data obtained for mercury.

TABLE I.

In Figure 2 are shown the melting curve \((p,t)\) and the curve of change of volume upon freezing of mercury for various pressures1. Attention should be paid to the latter curve: toward the pressure axis it is turned with its concavity. Figure 3 is also very important, showing the isotherms of liquid and solid mercury. The curves \(AB\) and \(A'B'\) are the boundary curves of the region where mercury cannot exist in the form of a single phase, but immediately separates into liquid and solid phases. We shall return to these Figures 2 and 3 at the end of the article, when we discuss the theories of the solid and liquid states.

Fig. 2.

The melting temperatures of mercury at various pressures were deter-

are still determined by measuring the electrical resistance of a mercury capillary. The details of this method are described in the article on Bridgman’s experimental technique. The electrical method of determining the \(p\) and \(t^\circ\) melting curve is more accurate than the “piston” method, but, unfortunately, it is suitable

Fig. 3.

only for mercury, and not for water or a number of other substances; moreover, it does not give the third important quantity—the change of volume on melting. When mercury freezes there is a sharp drop (to 1.3) in its electrical resistance: thus, at \(-15.1^\circ\) and \(5450\) kg/sq. cm, the electrical resistance of liquid mercury is \(0.863\), that of solid mercury \(0.258\); as the unit is taken the electrical resistance of the same column of mercury at \(-15.1^\circ\) and atmospheric pressure1.

3.

Water.

The first substance studied by Bridgman—mercury—gave a very simple picture of the phenomena of melting; the second substance—water—on the contrary, gave an exceedingly complex and interesting picture.

For the first time, water was studied in greater detail by Tammann up to 3000 atmospheres. Tammann found two new modifications of ice. Calling our ordinary ice ice I, he designated the new modifications as ices II and III. Figure 4 shows the results of Tammann’s first experiments. \(Ac\) is the melting curve of ice I, \(dfc\) is the curve of transition of ice I into ice II, \(afb\) is the curve of transition of ice I into ice III. The difference between the curves \(af\) and \(cf\) is very small (20–30 kg/cm²), in view of which, at one time, Roozeboom, interpreting the facts obtained by Tammann, assumed that \(af\) and \(cf\), within the limits of experimental error, form a single curve and that \(f\) is a triple point, from which there should also issue the curve \(fg\), the curve of mutual transformations of ices II and III. Tammann did not agree with Roozeboom; his later views, fully defined during his polemic with Bridgman, will be briefly set forth at the end of the article. Repeating his experiments with water, Tammann once obtained several new points in the region of ice I and allowed that there was still another new form of ice—ice IV. He did not succeed in causing the formation of this new form of ice in subsequent experiments.

Fig. 4.

Bridgman, in his experiments carried out up to 20,500 kg/cm², confirmed Roozeboom’s views regarding the mutual relations of ices II and III; he could not obtain ice IV, but instead discovered two new forms—ices V and VI. He left aside the numeral IV in order to avoid confusion in the terminology. The general picture for water obtained by Bridgman is shown in Fig. 5, which we shall consider in somewhat greater detail.

Fig. 5.

Curve I–L (\(AB\) in Fig. 5)—the melting curve of ice I—shows how the melting temperature of ice changes with pres-

This curve is remarkable in that it runs from top to bottom, which is closely connected with the fact that the specific volume of ice I is greater than the specific volume of liquid water. With an increase, consequently, of pressure, the freezing temperature of water decreases according to a complicated law: at atmospheric pressure \(dp/dt = 138.5\), while at 2000 atmospheres \(dp/dt = 74\). These figures show by how many atmospheres the pressure must be raised near \(0^\circ\) and \(-20^\circ\) in order to lower the freezing temperature by \(1^\circ\). The change of volume \(\Delta v\) upon melting of ice I is greater the higher the pressure (at \(1\) kg/cm\(^2\), \(\Delta v = 0.900\) cubic cm; at \(1970\) kg/cm\(^2\), \(\Delta v = 0.1313\) cubic cm for \(1\) gram of water), which is explained by the greater compressibility of water than of ice. The stable part of the curve I—\(L\) ends at \(B\), but it can be continued into the region of ice III (water and ice I are unstable along the segment \(Bd\)¹).

The curve of mutual transformation of ices I and III (curve I—III, \(BC\) in Fig. 5). Tammann obtained ice III by increasing the pressure on ice I to \(2500\) kg/cm\(^2\) at low temperatures down to \(-60^\circ\) and by subsequently raising the temperature. Bridgman applied high pressure to water at \(22^\circ\) and then, releasing the pressure, arrived at the equilibrium curve I—III. The curve I—III is interesting because it can readily be continued into the region of ice II that is unstable for it (segment \(Cc\)) to the triple point \(C\); the temperature there is \(-34.7^\circ\), the pressure \(2170\) kg/cm\(^2\), while the point \(c\) lies at about \(-70^\circ\); consequently, ice III can be supercooled to \(35^\circ\). The rate of the reaction of transformation of ices I and III is very peculiar. Acting with pressure on ice I, we must considerably exceed the equilibrium pressure in order to force ice I to transform into ice III. At higher temperatures ice I meets the continuation of the curve \(AB\) and here melts into liquid water, obeying the general law according to which a solid phase cannot be superheated with respect to a liquid phase. If ice III has formed, then on releasing the pressure the reaction \( \mathrm{I} \rightleftarrows \mathrm{III} \) above \(-30^\circ\) proceeds very rapidly; sometimes a sharp sound can be heard in the apparatus, caused by the sudden change of volume. But at temperatures below \(-30^\circ\) the reaction proceeds very slowly, and it is practically impossible to measure directly the difference of volumes \(\Delta v\) of ices I and III at low temperatures. To determine the values of \(\Delta v\) along the curve \(BCc\), Bridgman described the following cycle (Fig. 6).

The middle line is the equilibrium curve I—III (curve \(BC\) of Fig. 5); to the left of it is the region of ice I, to the right the region of ice III. We start from ice I at point 1. Keeping the temperature constant, we drive the piston inward, each time accurately noting its position—

¹ The coordinates of the triple point \(B\): \(t = -22.0\), \(p = 2115\) kg/cm\(^2\); point \(b\) lies at \(t^\circ\) about \(-28^\circ\).

temperature and pressure in the chamber (points 2—6). At point 6 ice III has already formed from ice I. Without moving the piston, we lower the temperature and record the pressure. Having reached point \(A\), we advance the piston at constant temperature until we arrive at point \(B\). Then in the same way we describe the paths \(BC\), \(CD\), \(DE\), \(EF\), and \(FG\). In the final result, if the work is done correctly, point \(G\) should coincide with point 1, which indeed occurred in Bridgman’s experiments.

The most important paths are \(BC\) and \(DE\). Each of them lies in the region of only one ice and runs very close to the equilibrium curve I—III. Knowing \(p\), \(t\), and the position of the piston at the various points of these paths, it is not difficult to calculate \(\Delta v\) along the equilibrium curve I—III. The cycle described here is rather simple; in other cases Bridgman had to carry out considerably more complicated cycles in order to determine \(\Delta v\).

Fig. 6.

The curve I—III is also of interest because to the eye it is almost vertical; in reality it is slightly curved, as can be seen from Table II.

TABLE II.
(Curve I—III).

The slight curvature of the curve I—III in the vertical direction is reflected in the very small latent heat \((\Delta H)\) of transformation of the ices; moreover, above \(-40^\circ\) ice I, on passing into ice III, absorbs heat, while below \(-40^\circ\) it gives it off. The internal energy \((\Delta E)\) of ice III, throughout, is greater than that of ice I.

Ice III is denser than water and, consequently, than ice I; upon the transformation of ice I into ice III the volume decreases by \(20\%\)¹).

¹) Tables analogous to II were given by Bridgman for each curve; we present here the most interesting of them.

The melting curve of ice III (curve III—$L$, $BE$ in Fig. 5) belongs to curves that are very difficult to determine, owing to the great slowness of the reaction, the small values of $\Delta v$2, and the large latent heat of transition. At $-22^\circ$ and 2115 kg/sq. cm (point $B$), $\Delta v = 0.0466$ cc, $\Delta H = 50.9$; at $-17.0^\circ$ and 3530 kg/sq. cm (point $E$), $\Delta v = 0.0231$ and $\Delta H = 61.4$. Thus, when water freezes into ice III, the volume of the water decreases by 2–4%.

The curve of transformation of ices I and II (curve I—II, $CD$ in Fig. 5).

Ice II is of interest because its region of stability is surrounded on all sides by regions of ices, and consequently it does not melt directly. Ice II is obtained from ice I by a strong increase of pressure at low temperatures. In order to cause the formation of ice II, it is necessary the first time to exceed the equilibrium pressure by 1000 kg. The curve I—II cannot be continued into the region of ice III. Here we have a rare case in which one solid phase (ice II) cannot be superheated with respect to another (ice III), just as in general a solid phase cannot be superheated with respect to a liquid one. At point $C$ ice II immediately transforms into ice III, and with an increase of temperature we pass from the curve I—II to the curve I—III. The curve I—II has been traced to $80^\circ$. On extrapolation this curve meets the absolute zero of temperature at zero pressure. Ice II is denser than ice I; in the transformation of ice I into II the volume decreases by 22 percent, with heat being evolved ($\Delta H = 8—10$ cal.). The internal energy of ice II is greater than the energy of ice I.

The curve of transformation of ices II and III (curve II—III $CF$ in Fig. 5) is extremely difficult to study. The discovery of this curve (subsequently confirmed by Tammann) resolves the dispute between Tammann and Roozeboom in favor of the latter: point $C$ is undoubtedly a triple point. The reason for the great difficulty in studying this curve lies in the very small difference of the specific volumes of ices II and III (about 1.5—2%). It is impossible to find it by using a discontinuity in the continuity of the curve $(\Delta v, p)$ (Fig. 1). In studying this curve, Bridgman held the piston in a fixed position, varied the temperature of the system, and looked for a discontinuity (jump) in the curve $(p, t)$. The determination of the values of $\Delta v$ for this curve was made by means of complicated cycles in the regions of ices II, III, and V. The specific volume of ice II is smaller than that of ice III, as is also its internal energy. Heat is absorbed when ice II transforms into ice III.

The curve of transformation of ices III and V (curve III—V $FF'$ in Fig. 5). Ice III can exist in the region of ice V and

back, near the curve III—V separating these regions. In order to bring about the transformation \(\mathrm{III}\rightleftarrows \mathrm{V}\), it is necessary to exceed the pressure for the reaction \(\mathrm{III}\to \mathrm{V}\) and to lower it more strongly for the reaction \(\mathrm{V}\to \mathrm{III}\) than the equilibrium pressure. But if, in a given apparatus, both ices have already once existed, then the reaction \(\mathrm{III}\rightleftarrows \mathrm{V}\) proceeds without difficulty. This reaction is very remarkable in its rate. At \(-20^\circ\) it is instantaneous, explosive; at \(-35^\circ\), other conditions being equal, the reaction is completed after several hours. The reaction of transformation of ices \(\mathrm{III}\rightleftarrows \mathrm{V}\) has an enormous temperature coefficient.

The difference in the specific volumes of these ices reaches up to \(5.5\%\); the latent heat of transformation is very small—less than one calorie.

The transformation curve of ices II and V (curve II—V, \(FG\) in Fig. 5).

Ice II cannot be superheated with respect to ice V; upon an increase of temperature or of pressure corresponding to the curve \(FG\), ice II at once transforms into ice V. The rate of the transformation \(\mathrm{II}\to \mathrm{V}\) also changes rapidly with temperature. The coordinates of point \(F\): \(t=-24.3^\circ\), \(p=3510\) kg/sq. cm; of point \(G\): \(t=-34^\circ\), \(p=4200\) kg/sq. cm.

The melting curve of ice V (curve V—I, \(EH\) in Fig. 5).

The history of the discovery of ice V is very interesting. Ice VI was discovered earlier than ice V. Bridgman, studying the melting curve of ice VI, reached a temperature of \(-8^\circ\). The usual picture of the motion of the piston and of the pressure is shown in Fig. 7. As the piston is driven in, the pressure rises regularly (\(AB\)); at \(B\) the liquid water freezes into ice VI, the pressure drops slightly to \(b\) and remains constant as the piston is driven in as far as \(C\); at \(C\) all the water has already frozen into ice VI, and further driving in of the piston causes a rapid and regular rise of the pressure (curve \(C\)).

Fig. 7.

With gradual release of the pressure (withdrawal of the piston), the same curves are obtained in the reverse order. The pressure corresponding to \(UC\) is the equilibrium pressure of water and ice VI at \(-8^\circ\). In one of the experiments, during the reverse motion of the piston, at point \(E\) there occurred a sudden increase of pressure up to \(F\), and then a new path \(FGH\) was described. Along the path \(EF\) a new ice V formed from ice VI; along the path \(GH\) ice V melted into liquid water. The same picture was also obtained at \(-6^\circ\). In both cases, after the apparatus was opened it turned out that the glass bomb in which the water had been placed had burst owing to the sudden increase of pressure at \(F\). For repeated

a copper bomb had been used in the experiments; but ice V was not obtained at all, and the melting curve of ice VI could be studied without hindrance down to −20° (curve HL₁, Fig. 5). Two months later Bridgman returned to the experiments on obtaining ice V; it turned out that a necessary condition for its formation was the use of a glass bomb. Subsequently Bridgman obtained ice V by throwing a piece of glass into a copper bomb. Under these conditions ice V is always formed from ice VI; from liquid water it is never formed the first time. But if, in a given apparatus, ice V has once already been present, then it is obtained considerably more easily and can even be obtained from liquid water.

After ice V had been obtained and the curve V—L studied, Bridgman had to seek out and study the curves III—V and II—V, and then it turned out that the easiest path for obtaining ice V was via ice II; true, for this one must work at low temperatures (−60°).

The melting curve V—L was traced within the limits from 0° to −21° and from 6380 to 3000 kg/cm². Its stable portion extends from H to E (coordinates of E: 3530 kg/cm² and −17°.0). This curve can be continued into the region of ice III, where, consequently, ice V, being unstable, melts into water that is also unstable here. It is interesting to note that extrapolation of the curves ABb and HEe leads to the labile triple point L—I—V, in the region of ice III, but it was not possible to realize this point experimentally.

The specific volume of ice V is less than the specific volume of water at 0° by 5.27%, at −20° by 8.28%; its latent heat of fusion is 60–70 calories.

The transformation curve of ices V and VI (curve V—VI HM in Fig. 5) is remarkable for its almost vertical character; its upper end H corresponds to 0° and 6380 kg/cm², while the lower end has been traced down to −25° and 6365 kg/cm². In view of its verticality, the latent heat of the transformation V ⇄ VI is negligible (less than 0.2 cal.). The difference in the specific volumes of these ices reaches 3.8%. Here we also have a sharp decrease in the rate of transformation with decreasing temperature: near H the reaction proceeds very rapidly; at −25° there is no possibility of following the reaction to completion.

The melting curve of ice VI (curve VI—L HK in Fig. 5) was traced over a range of 16000 kg/cm². Its limits are: about −20° and 4500 kg/cm² (point L′) and +76.35° and 20670 kg/cm². Ice VI was discovered in studying the compressibility of water and mercury. At temperatures above 0° irregularities were obtained, so large that they could not be explained by the phenomena of freezing of mercury. The assumption that above 0° under the influence of high pressures water freezes was confirmed by subsequent experiments.

TABLE II.

Melting of ice VI.

Above $60^\circ$ and 16690 kg/sq. cm the errors of the experiment, owing to phenomena of aftereffects and hysteresis, made an exact determination of $\Delta v$ impossible1.

Thus, at 20670 kg/sq. cm water freezes at $+76,35^\circ$; undoubtedly, such ice may be called hot ice.

In the doctrine of phases, triple points play a very important role (for systems with one component). At a triple point three curves must meet, and at this point three phases are in equilibrium. The coordinates of five triple points were determined very accurately by Bridgman. We shall give them here in full in view of their importance. In the first column of Table III are indicated the phases that are in equilibrium at the given triple point.

Concerning the reliability of the results obtained by Bridgman, it must be said that these results were subjected to various checks. First of all, a rare curve was studied in one and the same apparatus. At high pressures individual parts of the apparatus very often break and have to be replaced by new ones, not—

TABLE III.

the entire apparatus is sharply spoiled. If changing the instruments is not reflected in the course of the figures obtained, then this serves as a great guarantee that the investigator has fully mastered the method. The principal control, however, is provided by the triple points. At the triple point three curves must intersect within the limits of experimental error; furthermore, at the triple point the following relations between \(\Delta v\) and \(\Delta H\) must hold for each pair of phases:

\[ \Delta v_{\mathrm{I-II}}+\Delta v_{\mathrm{II-III}}=\Delta v_{\mathrm{I-III}}, \]

\[ \Delta v_{\mathrm{I-II}}+\Delta v_{\mathrm{II-III}}=\Delta v_{\mathrm{I-III}}. \]

This control is especially difficult for \(\Delta H\), since in calculating \(\Delta H\) we use the derivative \(\frac{dp}{dt}\), where any error in the experimental data has an amplified effect. Of course, the results obtained differ, but this difference is small and lies entirely within the limits of experimental error. Besides the very existence of a triple point, the fact that it is possible to continue a number of curves on the other side of the triple point is very important. This fact undoubtedly proves that the given point is indeed a point of intersection of curves, and not an accidental point of sharp bend of a single analytical curve; the presence of different curves proves the existence of different phases of the substance1.

It should be noted that it is never possible to continue all three curves on the other side of the triple point. At every triple point, at least one curve cannot be continued; for example, curve II—III into region V, curve II—V into region III, etc.

To the question whether the phases of water newly discovered by Tammann and Bridgman are in fact solid, i.e. are ices, we must answer in the affirmative. The strongest proof was given by Tammann: he cooled ice III in liquid air and quickly opened the apparatus. The ice III ejected outward (being denser) changed into ice I with a sharp increase in volume. For ice VI, Bridgman proved its solid nature by determining its electrical conductivity. When ordinary tap water froze into ice VI, the current ceased.

Bridgman’s investigations called forth objections from Tammann. Tammann continues to insist that the divergence of the curves \(af\) and \(cf\) (Fig. 4) does indeed exist and that \(f\) is not a triple point. Repeating his experiments, Tammann found the curve II—III, but places it above the curve \(fg\). The existence of the curves \(af\) and \(cf\), the accidental formation of ice IV, and certain other experimental facts lead Tammann to a very original and risky idea. According to Tammann, alongside the principal phases of water—ices I, II, III, etc.—there also exist varieties of these phases. Thus, in the final reckoning, besides ordinary ice I, he counts 6 further varieties of it. They exist in the same region as ice I, differ from it very little in their specific volume, and melt \(0^\circ,10\)—\(5^\circ,2\) lower. Ice IV belongs to the same group and, perhaps, is identical with ice I. Ice III has variety III: at 2512—2513 kg/sq. cm, ice III melts at \(-17^\circ,4\), ice III at \(-19^\circ,9\).

Bridgman resolutely and, one thinks, quite rationally, does not agree with Tammann. Subjecting Tammann’s method to criticism, Bridgman shows that the differences between the varieties of ice lie wholly within the limits of experimental error. There is as yet not a single figure for the varieties that would fall outside these limits.

Besides mercury and water, Bridgman also studied a whole series of inorganic substances, of which about 100 substances gave only one solid phase, like mercury, and about 30 substances proved to be polymorphic. Detailed information has so far been reported only for 11 substances (not counting mercury and water); for the rest there is a preliminary communication.

Carbon dioxide has been traced within the limits from \(-56^\circ,6\) to \(+93^\circ,5\) and up to 12000 kg/sq. cm. Tammann’s experimental data, according to Bridgman, are incorrect. Carbon dioxide gives only one solid phase. The coordinates of the curve of phase transition of \(CO_2\) are curious in that up to 6000

kg/sq. cm we have melting of solid carbon dioxide; above 6000 kg/sq. cm, its evaporation (sublimation, since the transition temperature is above the critical value, 31°):

\[ \begin{aligned} p&= \quad 1.6\quad 1000\quad 3000\quad 5000\quad 6000\quad 8000\quad 10000\quad 12000\ \text{kg/sq. cm},\\ t^\circ&= -56.6\quad -37.3\quad -5.5\quad +21.4\quad +33.1\quad +55.2\quad +75.4\quad +93.5 . \end{aligned} \]

Ortho-cresol is dimorphic, and it is of interest that all its transformations are very slow; liquid ortho-cresol can be supercooled by 50° and the equilibrium pressure can be exceeded by 4500 kg/sq. cm without causing crystallization. The transformation of solid phases I and II proceeds extremely slowly (Fig. 8). At a pressure of 6100 kg/sq. cm and 103°.2 we have a triple point. At a temperature 2°.4 below the triple point, equilibrium between I and II is established after an hour. At 95°.4 it was no longer possible to determine the equilibrium pressure. In Fig. 8 the broken curves show how \(\Delta v\) (the difference of the specific volumes of two phases) changes with pressure. The scale for \(\Delta v\) is shown on the right.

Fig. 8.

Phosphorus gives several solid phases with complicated and not yet fully studied relations among them. In Fig. 9 are shown the results of Bridgman’s experiments. Form II cannot be red phosphorus (I is yellow phosphorus), since it is obtained at low temperatures and \(\Delta v\) for I—II is too small for II to be red phosphorus. The transformation I—II proceeds very slowly; in this respect phosphorus occupies second place after ortho-cresol.

Fig. 9.

Sometimes, at temperatures above 175°, the melting of yellow phosphorus (I) is made abrupt and irregular; in these cases, as shown by opening the apparatus, a certain quantity of red phosphorus is formed.

Bridgman was unable to establish the conditions for the formation of red phosphorus. During these investigations a new modification of phosphorus was discovered, which is formed at 200° and 12000—13000 kg/sq. cm. At the moment of formation of this modification the pressure suddenly falls to 4000 kg/sq. cm, a pressure considerably lower than the melting pressure of yellow phosphorus at 200°. The new form of phosphorus is a grayish-black, graphite-like mass; it is stable in air, ignites with difficulty, and does not explode upon

struck with a hammer (red phosphorus explodes) and conducts electric current well. The density of the new gray phosphorus is 2.69, the density of red is 2.34, of yellow—1.9. When heated in a sealed tube, gray phosphorus evaporates, while yellow and red phosphorus are deposited in the cold parts of the tube.

Judging by density, the stable form of phosphorus should be considered gray phosphorus; the other forms are unstable. If this is so, then here we observe for the first time reversible processes between unstable forms (I and II) and irreversible ones—between stable and unstable forms (gray and yellow phosphorus).

With this we shall conclude the survey of individual substances studied by Bridgman; for a number of other substances we shall confine ourselves to a small table IV, showing the melting temperatures at 1 and 12000 kg/sq. cm, and to the composite figure 10.

...with an almost vertical curve I—II, \(KHSO_4\), \(NH_4HSO_4\), urethane, and camphor, with their abundance of solid forms.

Fig. 10.

From the results already obtained, Bridgman draws a number of more or less general conclusions, of which we shall dwell on the most interesting and on those having the character of completeness.

With regard to melting under ordinary pressure, it was known that the solid phase cannot be superheated: at a strictly determined temperature the solid phase immediately melts. At higher pressures one might have expected cases of superheating of the solid phase, in...

in view of the enormous viscosity of the substance and the large external work which must be expended if the solid phase melts with an increase of volume (sometimes a considerable one) under high pressure. However, no exceptions have been found here either; apparently, in the impossibility of superheating a solid phase we have a general law of nature, which cannot be foreseen or explained from the theoretical point of view. The opposite phenomenon—supercooling of a liquid—seems always to be possible. A liquid can exist as an unstable phase in the regions of solid phases. The magnitude of the supercooling, i.e. the depth of penetration of the liquid into a region of solid phases foreign to it, is very different and depends on a number of causes.

As regards the mutual relations between solid phases, in the vast majority of cases they may be both superheated and supercooled, i.e. they may penetrate to various depths into regions of neighboring solid phases foreign to them. But there are several examples where a solid phase cannot exist at all above its equilibrium curve and immediately transforms into another solid phase. Thus, ice II cannot be superheated with respect to ices III and V; carbon tetrachloride II and III cannot be drawn out into region I. Here too the depth to which a phase passes into a foreign region is different and depends on a number of causes: the nature of the substance and of the vessel, the size and shape of the latter, but chiefly, as Bridgman puts it, on whim (i.e. on unknown causes).

As a general rule, one may also note the ease with which a given phase arises if it has already once occurred in the given apparatus (see ice V), as though from each phase a trace of its structure remains in the substance. There is no explanation of this fact.

The rate of transformation of phases is very varied and peculiar. As a rule, it must be noted that the rate of transformation: liquid phase $\rightleftarrows$ solid phase is always less (at high pressures) than the rate of transformation of two solid phases. The process of melting of ices I and II under the conditions of Bridgman’s experiments lasted 2 hours; under the same conditions the melting of III practically did not reach completion in the course of an entire day. The rate of mutual transitions of solid phases into one another has in some cases an extremely high temperature coefficient (see the transformation of o-cresol, ices III $\rightleftarrows$ V, etc.). The enormous rate is apparently due to proximity to a triple point; thus, the transformation of ices:

\[ \begin{aligned} \mathrm{I} &\rightleftarrows \mathrm{II} &&\text{at } -35^\circ \text{ (triple point) is instantaneous,}\\ \mathrm{III} &\rightleftarrows \mathrm{V} &&\text{at } -35^\circ \text{ is very slow,}\\ \mathrm{III} &\rightleftarrows \mathrm{V} &&\text{at } -17^\circ \text{ (triple point) is instantaneous,}\\ \mathrm{V} &\rightleftarrows \mathrm{VI} &&\text{at } -17^\circ \text{ takes 2 hours.} \end{aligned} \]

But the triple point has such an influence only in the case when, at the given point, the third phase is a liquid. If the triple point contains only solid phases, then the rate of transformation of the phases is substantially different; thus, in the case of tetrachloromethane this rate is almost independent of temperature throughout the entire region.

We now turn to Bridgman’s conclusions in the domain of theories of the liquid and solid states. On the question of the relations between the liquid and solid states there exist two theories. According to the first theory (Planck, Poynting, Ostwald, and others), for both states there exists a critical point, above which the general liquid–solid isotherm has no discontinuities of continuity; consequently, a continuous transition from the liquid to the solid state is possible. In a word, the general character of the isotherms for the liquid and solid states is the same as for the liquid and gaseous states. Fig. 11 shows isotherms for all three states from the point of view of the indicated theory. \(BC\) and \(ED\) are experimentally observed discontinuities of continuity of properties in the transformations of gas into liquid and of liquid into the solid state. Theoretically, here we have continuous transitions along the dotted curves (van der Waals). It has been proved experimentally that, with increasing temperature, the discontinuity \(BC\) becomes smaller and smaller and, at a certain temperature, called the critical temperature, disappears: one obtains a single continuous isotherm. The first theory assumes an entirely analogous picture also for \(ED\), i.e. for the liquid and solid states.

Fig. 11.

The second theory, first expressed by Damien and developed in detail by Tammann, does not recognize the existence of a critical point for the liquid and solid states. Tammann proceeds from the position that liquid and gas differ only quantitatively, by the magnitude of the distance between molecules, whereas the solid state differs from the first two states qualitatively, by the presence of a crystalline lattice, i.e. by a definite order in the distribution of molecules. Together with Tammann we must call only the crystalline state solid; the noncrystalline solid state is amorphous. An amorphous substance (e.g., glass) is strongly

supercooled liquid of great viscosity. In Fig. 11 the curve \(DC\) is the isotherm of the amorphous state. There is no critical point for the crystalline and liquid states; the discontinuity \(DE\) is absolute.

Instead of the critical theory, Tammann, following Damien, develops the theory of a maximum in the melting curves. According to Tammann, our conception of the structure of a crystal makes unthinkable a continuous transition from chaos (in the liquid) to order (in the solid phase). According to the theory of a maximum, the equilibrium curve: liquid \(\rightleftarrows\) solid state (the melting curve) is a closed curve (Fig. 12)\(^1\). Let us divide this curve into 4 quadrants. \(AB\) is the ordinary experimental melting curve of most substances; \(BC\) is the melting curve of such substances as ice I (the solid phase is less dense than the liquid); the curves in the lower quadrants are not realizable. To confirm this theory means to obtain an experimental curve encompassing both upper quadrants and, consequently, passing through a maximum (point \(B\)). But it has not been possible to find such a curve, and Tammann had to seek indirect proofs. As a first proof, Tammann points out that the experimental melting curves have the form of curves which can pass through a maximum (the curves are turned with their concavity toward the pressure axis). Tammann investigated melting curves up to 3000 kg/sq. cm; the results obtained were fitted by the equation of a parabola, and from this equation the coordinates of the maximum of the melting curve (point \(B\)) were calculated. The maxima calculated in this way lie between 4000 and 12000 kg/sq. cm.

Fig. 12.

Further indirect methods for proving or refuting both theories relate to the course, with pressure, of the changes in volume \(\Delta v\) upon melting and of the latent heat \(\Delta H\) of melting. Namely, at the

Both at the critical point and at the maximum, the specific volumes of both phases are equal, but in the former there is at the same time also latent

\(^1\) Consequently, the crystalline (solid) state on the diagram is surrounded on all sides by the liquid state.

the heat and the difference of energies are equal to zero; at the very maximum point, even if the specific volumes are equal, in the solid phase there is a crystalline lattice; consequently, the energies of the two phases in the general case cannot be equal; nor is the latent heat of fusion equal to zero.

Tammann’s experiments are not very accurate, since leakage was not eliminated in his apparatus, and since he did not introduce certain necessary corrections and, finally, used a Bourdon manometer. The values of $\Delta v$ obtained by him at different pressures $p$ form, in a first approximation, a straight line $(p,\Delta v)$ intersecting the pressure axis; consequently, $\Delta v$ becomes equal to zero at high pressures. The calculated values of the latent heat of fusion $\Delta H$ either do not change with pressure or increase. It is clear that, when $\Delta v$ tends to zero, $\Delta H$ remains finite, which is the strongest argument against the critical theory.

Let us also note that Tammann attempted, by thermodynamic means, to prove that the melting curves must pass through a maximum.

In his first work on the properties of mercury, Bridgman’s sympathies inclined toward the critical theory. Further investigations forced him finally to reject both theories.

The experimental curves up to 12000, and for water up to 20500 kg/sq. cm, showed neither a tendency toward a critical point nor passed through a maximum. In Fig. 3 it is seen that the region of discontinuity in the properties of liquid and solid mercury is bounded by almost parallel curves (dotted); if a broad extrapolation is admitted, then the critical point for mercury would lie at about 50000 kg/sq. cm. Similar data were obtained for other substances as well. The melting curves do not pass through a maximum. Their form, however, cannot serve as proof of the existence of a maximum beyond the limits of attainable pressures1. Bridgman showed that Tammann’s attempt to prove thermodynamically a maximum in the melting curves is erroneous. The method consisting in fitting empirical equations to experimental curves and calculating (with extrapolation) maxima cannot serve as an argument in favor of the existence of a maximum; this method gives only a probable position of the maximum, if such a maximum exists.

Tammann’s calculations gave, for a number of substances, maximum pressures of 4000–11000 kg/sq. cm. Not one of the substances investigated by Bridgman up to 12999 kg/sq. cm gave a melting curve with a maximum. The curves studied tend to infinity according to an unknown law.

The course of the curves \((\Delta v,p)\) and \((\Delta H,p)\) for all substances speaks against the critical theory: the change in volume on melting decreases with pressure, whereas the latent heat increases. At first glance these curves speak in favor of Tammann’s theory, but closer examination leads to the opposite conclusion. In most cases \(\Delta v\) does not tend to zero, but tends asymptotically to some finite value. Finally, for long curves (copper VI–L) the curve \((p,\Delta v)\) and \((p,\Delta H)\) have an inflection, which shows the complexity of the relations, not foreseen by any theory. It is interesting to note that all substances, including potassium and sodium, but with the exception of mercury, gave a curve \((p,\Delta v)\) convex toward the axis of abscissas (Figs. 8 and 2). Mercury occupies a special position among liquids, as we have already seen earlier from its properties as a liquid1.

The investigations of Bridgman published up to now give us the right to reject both theories of melting, but as yet they give nothing in exchange for them. Only an idea is taking shape which may become the starting point of a new theory, namely: Bridgman often points to facts indicating that already in the liquid, at high pressures, the molecules can acquire a definite orientation, i.e., that part of the molecules of the liquid (changing with time) forms a definite structure, while another part of the molecules still moves quite chaotically.

At this point we break off our survey of Bridgman’s investigations. So far as one may judge from Bridgman’s papers, in the near future we should expect from him not only new experimental investigations, but also a series of theoretical inquiries in the field he is studying. It remains for us to wait patiently and warmly to wish the young2 American scientist further successes.

Principal Literature¹

G. Tammann. Kristallisieren und Schmelzen, 1903; Zeit. physik. Chem. 72, 609 (1910). Part IV.

E. H. Amagat. Ann. chim. phys. (6), 22, 68 (1893). Description of the manometer.

P. W. Bridgman. Proceedings of the American Academy of Arts and Sciences, 44, 201, 221, 255; 46, 325; 47, 321; 49, 627. Methodology.

P. W. Bridgman. ib. 47, 347 (1911), (mercury), 441 (1912), (water and ice); 48, 309 (1912), (liquid water); 49, 1 (1913), (12 liquids).

P. W. Bridgman. Phys. Review Vol. III, Ser. II, 126 (1914). Solids.
This article contains a detailed index of the literature on theories of melting.

Controversy:

G. Tammann. Zeit. physik. Chem. 84, 257 (1913); 88, 57 (1914).

P. W. Bridgman. ib. 86, 513 (1914).

A. Rakovsky.

¹ Only those articles are indicated which I had in my hands. Offprints of Bridgman’s articles from Proc. of Amer. Acad. are available for separate sale.

1. It is interesting to note that mercury gives a sharp deviation from all other liquids also in its fluidity (a quantity reciprocal to viscosity). According to Batschinski’s law, fluidity varies linearly with the specific volume for normal liquids; for associated liquids the experimental curves deviate to the right from a straight line; mercury alone gives a curve deviating to the left. ↩↩↩↩↩↩

2. Percy Williams Bridgman (Research Fellow in Physics at Harvard University) was born in 1882. ↩↩