Statistical Thermodynamics of Mixed Valence at Low Temperatures

Abstract

In these lectures we discuss an expression for the free enthalpy of Rare Earth (RE) mixed valence compounds designed to describe the experimental data (in particular the temperature and pressure dependent fractional valence) as far as possible by well known or by easily measurable properties of the two integral valence states involved in the mixture. These properties are the volumes, bulk moduli, thermal expansion and linear specific heat coefficients of the unit cell of the crystal with the RE atom in the two adjacent integral valence states and the Hund’s rule ground states and excited spin orbit (SO) multiplets with their crystal field (CF) splittings and degeneracies in the corresponding configurations of the 4f shell, 4fⁿ⁺¹ and 4fⁿ. In this way the number of bona fide mixed valence (adjustable) energy parameters can be reduced to two, namely to E_xc, the difference between the free enthalpies of the two integral valence states at some fixed temperature and pressure, i.e. a constant, and to Δ, the effective configurational mixing matrix element.