CRYSTALLOGRAPHY

E. G. PONYATOVSKII

ON THE CRITICAL POINT ON THE CURVE OF THE POLYMORPHIC TRANSFORMATION OF CERIUM

(Presented by Academician N. V. Belov, March 22, 1958)

The polymorphic transformation of cerium is at present the only known first-order phase transformation in which a sharp decrease in the crystal-lattice constant occurs, while the symmetry of the lattice does not change.

The polymorphic transformation of cerium at ultrahigh pressures was first discovered by Bridgman (^1). Lawson and Yuan (^2) carried out an x-ray study of the modification of cerium formed at high pressure. A powder specimen was placed in a beryllium bomb and subjected to a pressure of 15,000 kg·cm\(^{-2}\). At this pressure a Debye diagram was taken from it. It turned out that cerium at 15,000 kg·cm\(^{-2}\), just as at atmospheric pressure, has a face-centered cubic lattice. The lattice constants at pressures of 1 and 15,000 kg·cm\(^{-2}\) are, respectively, 5.14 and 4.84 Å. The total change in volume upon compression of cerium to 15,000 kg·cm\(^{-2}\) is 16.6%. Lawson and Yuan suggested that the transformation occurring at high pressures is identical with the transformation discovered somewhat earlier by Trombe and Foex (^3) at atmospheric pressure and low temperatures, and that this transformation is associated with the transition of an electron from the \(4f\)-state to the \(5d\)-state. Schuch and Sturdivant (^4) investigated the crystal structure of cerium at low temperatures. They showed that at a temperature of \(-179^\circ\) the cerium specimen is a mixture of the high-temperature and low-temperature modifications (we shall denote them below by \(\alpha\)-Ce and \(\alpha'\)-Ce). Both modifications have a face-centered cubic lattice. The lattice constants are: \(\alpha\)-Ce \(a = 5.14\) Å, \(\alpha'\)-Ce \(a = 4.82\) Å. The volume effect amounts to 16.5% of the \(\alpha\)-modification.

Likhter, Ryabinin, and Vereshchagin (^5) investigated part of the \(P\)—\(T\) diagram of cerium in the temperature interval from \(-71\) to \(+94.5^\circ\). The pressure of the \(\alpha \to \alpha'\) transformation was determined from the jump in compressibility. It was shown that the pressure of the \(\alpha \to \alpha'\) transformation of cerium increases with increasing temperature, while the volume effect decreases noticeably as the transformation temperature increases. The magnitude of the volume effect at room temperature was estimated at 8%.

The preservation of lattice symmetry and the decrease in the difference between the specific volumes of the \(\alpha\)- and \(\alpha'\)-phases along the curve make it possible to assume the existence of a critical point on the curve of the polymorphic transformation of cerium. To verify this assumption, a further investigation of the \(P\)—\(T\) diagram of cerium was carried out using the method of thermographic analysis (^6), which permits investigation of phase transformations of a substance at pressures up to 35,000 kg·cm\(^{-2}\) and temperatures up to \(>650^\circ\). The study was carried out on cerium containing (in %) \(<0.75\) Nd, \(<0.75\) Pr, 0.01 Fe, \(<1 \cdot 10^{-4}\) Pb. Hydrostatic pressure was produced by compressing a mixture of isopentane with normal pentane in an ultrahigh-pressure multiplier. The pressure was measured with a manganin manometer with an accuracy of \(\pm 100\) kg·cm\(^{-2}\), and the temperature—with an iron—nichrome thermocouple with an accuracy of \(\pm 1.5^\circ\).

The points of the \(\alpha \to \alpha'\) transformation were determined by two different methods. In the first method the pressure was raised to a definite value and, at constant pressure, the specimen was heated and cooled at different rates. The readings of the absolute and differential thermocouples were recorded by means of a Kurnakov pyrometer. From the thermograms the temperatures of the \(\alpha \to \alpha'\) and \(\alpha' \to \alpha\) transformations were determined. In the second method the temperature of the specimen was kept constant, while the pressure was smoothly raised and lowered within the required limits. In processing the thermograms, the necessary corrections were introduced for a certain increase of pressure during heating of the specimen and for the change in specimen temperature when the pressure was changed. From the data obtained a \(P\)—\(T\) diagram of cerium was constructed, shown in Fig. 1. The equilibrium line was conventionally taken to be the line equidistant from the branches \(\alpha \to \alpha'\) and \(\alpha' \to \alpha\) (shown by the dotted line).

Fig. 1. \(a\) — Bridgman’s data \((1,7,8)\); \(b\) — data of Lichter, Ryabinin, and Vereshchagin; \(v\) — our data

As is seen from the diagram, the transformation of cerium at temperatures close to room temperature proceeds with a large hysteresis. The hysteresis of the transformation with increasing temperature decreases from \(6000\ \mathrm{kg}\cdot\mathrm{cm}^{-2}\) at \(20^\circ\) to zero at \(\sim 280^\circ\). With increasing temperature the thermal effect of the \(\alpha \to \alpha'\) transformation also decreases, and at temperatures above \(280^\circ\), and correspondingly at pressures above \(18\,500\ \mathrm{kg}\cdot\mathrm{cm}^{-2}\), it becomes so small that on thermograms taken at higher pressures no special points are noticeable. Both the \(\alpha \to \alpha'\) and the \(\alpha' \to \alpha\) transformations proceed at constant temperature over a considerable pressure interval.

Fig. 2

To determine the amount of \(\alpha'\)-phase formed as a function of pressure, the following experiments were carried out. At room temperature the pressure, beginning with \(5000\ \mathrm{kg}\cdot\mathrm{cm}^{-2}\), was increased in steps of \(\sim 300\ \mathrm{kg}\cdot\mathrm{cm}^{-2}\), with a pause of 5 min after each increase. In the pressure interval in which the transformation had not yet begun, the light spot of the differential thermocouple remained in place as the pressure was raised. In the pressure interval corresponding to the pressures of the \(\alpha \to \alpha'\) transformation, at each pressure increase a deflection of the light spot of the differential thermocouple occurred. One of the thermograms obtained in this way is shown in Fig. 2. The areas of the individual peaks in the thermogram are proportional to the amount of heat evolved during the transformation and, consequently, to the amount of \(\alpha'\)-phase formed at each pressure increase.

From the thermograms, a curve has been constructed for the amount of the \(\alpha'\)-phase versus pressure at a temperature of \(20^\circ\) (see Fig. 3). The transformation \(\alpha \to \alpha'\) begins at a pressure close to \(7000\ \mathrm{kg\cdot cm^{-2}}\) and ends at \(10000\ \mathrm{kg\cdot cm^{-2}}\). In the pressure interval \(7700\text{–}8350\ \mathrm{kg\cdot cm^{-2}}\), \(70\%\) \(\alpha'\)-Ce is formed. The end of the transformation is more diffuse. Increasing the holding time after each increase in pressure (up to several hours) does not substantially affect the subsequent course of the transformation. The pressure corresponding to the maximum intensity of the transformation was taken as the transformation pressure. The transformation temperature upon heating and cooling of the specimens was determined analogously.

Fig. 3

As is seen from Fig. 1, with increasing pressure the equilibrium temperature of \(\alpha\)- and \(\alpha'\)-Ce increases linearly. The tangent of the angle of inclination of the \(\alpha\)—\(\alpha'\) equilibrium line to the pressure axis is \(0.0225\ \mathrm{deg}/\mathrm{kg\cdot cm^{-2}}\). Along the equilibrium curve, as pressure increases, the magnitude of the thermal effect and, consequently, of the volume effect of the transformation decreases. The constancy of the angle of inclination of the equilibrium curve to the pressure axis indicates that the thermal and volume effects decrease according to a common law.

The parameters indicated above, \(280^\circ\) and \(18\,500\ \mathrm{kg\cdot cm^{-2}}\), are not yet parameters determining the position of the point on the curve of the polymorphic transformation of cerium. For a more accurate determination of the position of the point at which the volume and thermal effects become zero, further investigation of the \(P\)—\(T\) diagram of cerium by means of a more sensitive method is necessary.

Assuming that the thermal and volume effects of the transformation of cerium with increasing pressure do indeed tend to zero, the following assumptions may be made about the further course of the equilibrium curve of \(\alpha\)-Ce and \(\alpha'\)-Ce:

1. The curve of the first-order phase transformation passes into a curve of a second-order phase transformation, the difference in symmetry between \(\alpha\)-Ce and \(\alpha'\)-Ce arising not from a difference in the symmetry of the crystal lattices, as is usually the case, but from a difference in the symmetry of the electron shells.

2. The curve of the first-order phase transformation ends at a critical point. Above the critical point there is neither a first-order phase transformation nor a second-order phase transformation.

Received
10 III 1958

CITED LITERATURE

1. P. W. Bridgman, Proc. Am. Acad. Arts and Sci., 62, 207 (1927).
2. A. W. Lawson, Ting Yuan Tang, Phys. Rev., 76, 301 (1949).
3. F. Trombe, M. Foex, Ann. Chim., 19, 416 (1944).
4. A. F. Schuch, J. H. Sturdivant, J. Chem. Phys., 18, 145 (1950).
5. А. И. Лихтер, Ю. Н. Рябинин, Л. Ф. Верещагин, ЖЭТФ, 33, 610 (1957).
6. В. П. Бутузов, С. С. Бокша, М. Т. Гоникберг, ДАН, 108, No. 5 (1956).
7. P. W. Bridgman, Proc. Am. Acad. Arts and Sci., 79, 164 (1951).
8. P. W. Bridgman, Proc. Am. Acad. Arts and Sci., 81, 213 (1952).