Kondo volume collapse

Fig. 38. Isothermal sections at 25°C of (a) intra-lanthanide and (b) intra-actinide generalized binary phase diagrams, showing equilibrium phase boundaries [with estimated hysteresis for (a)] as full hnes (Benedict et al. 1986). The broken line in (a) indicates the interpolated boundary for the volume collapse transition of the lanthanides. The atomic radius of Ce at room temperature as a function of pressure is shown in (c) (Franceschi and Olcese 1969), with the Kondo-volume collapse transition at about 7 kbar. This transition can be traced to negative pressures by alloying (Lawrence et al. 1984), as seen in (d) via the temperature dependence of the resistance.

In reality both forms of coupling to the lattice are doubtless present. Under these circumstances nonlinear effects can occur. As the temperature increases, the concomitant increase in ti will cause AV to increase which will decrease Vm and hence decrease Ta. This will lead to a further increase of f = f(7 /7 K(F)) and will cause the thermal expansion to be more rapid than for fixed Tk- It is the basis of the Kondo volume collapse treatment of the y a phase transition in cerium (Allen and Martin 1982). 

Another, and widely held, view of the electronic structure of a-cerium is contained in the so-called Kondo volume collapse model (Allen and Martin 1982, Lavagna et al. 1982, 1983, Martin and Allen 1985), where the 4f electrons are localized but strongly coupled to the spd conduction electrons. The strong volume dependence of this coupling drives y-cerium to a-cerium. A detailed analysis of this model has been performed by Allen and Liu (1992). 

Thompson et al. 1983, Martin and AUen 1985). In general, such volume-collapse transitions occur in a variety of lanthamde and actinide materials (Benedict et al. 1986, Franceschi and Olcese 1969), see figs. 38a and b, with IV SmS as a different characteristic case, where real charge fluctuations play a more important role (Grewe et al. 1980). In CeCug (Thompson and Fisk 1985) the f-occupation in the Kondo-lattice state is mildly reduced by pressure. Here, as in a number of other cases (Lawrence et al. 1984), external or lattice pressure can also cause continuous transitions with considerable volume changes as is, e.g., apparent from fig. 38d. 

CeAl2 is trivalent, orders magnetically at low temperatures, and is Kondo-like at higher temperatures. It has a collapsed-volume phase at higher pressures similar to that of a-Ce. Several photoemission studies of CeAl2 have been reported. 

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