Critical point cerium

Cerium metal has unique soHd-state properties and is the only material known to have a soHd—soHd critical point. Three aHotropes, a, P, y, are stable at or close to ambient conditions and have complex stmctural interrelationships. 

Cerium is a rare earth metal and the most abundant member of the lanthanide series discovered in 1803. It is the only material known to have a solid-state critical point. 

Fig. 11. The pressure-temperature diagrams (schematic representation) of (a) cerium and (b) ytterbium. In the cerium diagram (a) the ietters C.P. means critical point, and tbc means tetragonal body-centered.

The eccentric ones cerium and ytterbium Cerium as we had noted previously exhibited some anomalous behaviors (sections 3.3.4 and 3.4.1), and thus one might expect its high-pressure properties to be different. A quick glance at fig. 11 reveals that we will not be disappointed. The existence of a critical point (a point where the two phases in co-existence are indistinguishable) in the solid state at 2.5 GPa and 695 K (422 C) is unique - the only one known to exist between two solids. This critical point arises from the 4f valenee fluctuation behavior in the fee phases of a- and y-Ce. As the critical point is approached with increasing temperature and pressure the properties of the two phases become more and more alike — the valence in y increases from 3.06 to 3.26 at the critical point while that of a decreases from 3.67 to 3.26, and the volume of... 

Fig. 4.1. Pseudo-equilibrium pressure-temperature phase diagram of cerium. The phase boundaries involving 5-Ce and liquid are true equilibrium boundaries. The letters C.P. mean critical point. The question mark for the ala phase boundary indicates that there is considerable doubt about the slope of this boundary, see text for further discussion.

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. 

Johansson (1978) and Brooks etal. (1984) utilized the energy difference (f d transitions) between trivalent (f"ds ) and tetravalent (f" M s ) cerium and other f-element metals to estimate thermochemical data for compounds. A similar approach has been used by Mikheev et al. (1986) and Spitsyn et al. (1985) to include the divalent as well as the tetravalent state. Again, a critical issue has been the behavior of the heavy actinides with respect to f- d transitions, and the need to utilize and to interpret the few experimental measurements on these actinides, which are discussed below (e.g., section 2.4.1.3). Johansson and Munck (1984) defined a function P (M) that removes the intershell multiplet coupling energy from the atomic reference state (A ,.,up,i j is the energy difference between the baricenter and the lowest level of a multiplet). For the lanthanides P (M) is significantly smoother than P(M),-except for an anomaly at Yb that may be due to an error in experimental data. Unfortunately, Johansson and Munck (1984) point out that spectroscopic data on the heavy actinides are inadequate to correct P(M) to P (M) for the actinides. 

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