Valence isostructural transition

When the itinerant state is formed, a volume collapse AV/V is always encountered, as predicted by the theory of the preceding sections. In one of the lanthanides, cerium, this volume collapse is particularly accentuated for its isostructural transition from the y to the a form, possibly associated with a change in metallic valence from three to four (both oxidation numbers are stable in cerium chemistry) (see Fig. 1 of Chap. A),... 

Cerium metal is discussed in ch. 4 and only a brief mention of its high pressure behavior will be made here (for references see the list in ch. 4). Cerium can exist at atmospheric pressure in the fee (y) or dhep (iS) form and undergoes an isostructural transition near 100 K to another fcc-form referred to as o-Ce. The y-a Ce transition occurs at 7 kbar at room temperature and this transition is accompanied by about 8% volume decrease. This is one of the most widely studied transitions as a function of pressure and temperature and is believed to involve a valence change from 3 towards a higher valence state (3.7 ). The y to a transition line terminates at a critical point the very first example in which a solid - solid transition was shown to exhibit a liquid-vapor-like critical point. A pressure-induced phase transition near 50 kbar, initially reported to be yet another isostructural transition has been shown to be from fee (a-Ce) to an orthorhombic phase with the a-U structure. Stager and Drickamer (1964) have reported a pronounced resistance anomaly near 120 kbar indicative of a phase transition, but the nature of this transition is unknown. The fusion behavior of Ce is again unique in that it exhibits a minimum. 

In CeAl2, Croft and Jayaraman (1979) and Bartholin etal. (1980) observed an isostructural transition around 7 GPa, accompanied by a volume collapse of about 4%. This observation was interpreted, like in the case of the lanthanide chalcogenides, as a valence change from - - 3 to -I- 4 of the Ce ion. This interpretation was supported by the fact that the corresponding compound of the non-4f metal La, LaAl2, did not show any phase transition up to 3 GPa, the highest pressure reached for both... 

Most transition metals of the three d-series in all their valency states exhibit ionic radii within the limits of 0.55 and 0.86 A, favourable to octahedral coordination. In fact higher coordination numbers are observed only in fluorides of the largest transition ions, above all in compounds of the lanthanide and actinide series. Therefore fluorides of those elements, though sometimes isostructural with compounds of the d-series, will not be discussed here. For information the books and reviews written by Spedding and Daane (291), Katz and Seaborg (181) and Kaiz and Sheft (182) may be consulted. 

For TmSe and TmTe, one observes continuous isostructural (B1 Bl) valence transitions over a wide volume range, for TmSe already starting at ambient conditions. The calculated discontinuous volume changes are in good agreement with the experimental volumes. 

In Table 5, the calculated and available experimental data are collected for the isostructural pressure transitions in Yb chalcogenides. The general trends are reproduced by the calculations. Only for the case of YbO, the calculated transition pressure seems to be significantly too high. In the intermetallic YbAls compound, pressure induces a continuous increase of valence (Kumar et al., 2008), which is in good agreement with the calculated rate of depletion of the 14th f-band in the SIC-LSD calculations. 

In isostructural Pr70i2 (von Dreele et al. 1975) and Tb70 2 (Zhang et al. 1993a,b), the rhombohedral cell contains one Pr(l) or Tb(l) atom coordinated by six O atoms. There are six Pr(2) or Tb(2) atoms each coordinated by seven O atoms. This gives a total of 6-1-6x7=48, the number of R-O bonds in the cell. The Pr(l) or Tb(l) atoms are each surrounded by six equidistant O atoms whereas the Pr(2) or Tb(2) atoms are each surrounded by seven O atoms with variable R-O distances. In these oxides, the O atom, being more electronegative than the central R atom induces an attractive interaction on an f electron of the R atom. This interaction is proportional to /df, where a is the R-O separation. As a decreases, at a critical value uo, the interaction becomes sufficient to pull out a 4f electron and to drive a trivalent to tetravalent transition. This process implies an increase in the population of the valence electron by transfer of a 4f electron to the oxy n band. 

Fig. 20.9. Lattice parameter change with temperature (upper figure) and composition (lower figure) in the Sm., Yi compounds. The abrupt changes are due to first order isostructural phase transition. In the bottom of lower figure the valence calculated from the lattice parameter is shown (from Tao and Holzberg, 1975).

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