Statistical Thermodynamics of Mixed Valence at High Temperatures

  • Dieter Wohlleben
Part of the NATO ASI Series book series (NSSB, volume 117)


In these lectures we present an expression for the free enthalpy of Rare Earth (RE) mixed valence compounds for thermal energies large compared to the energy gain associated with quantum mixing between the two integral valence states “4fn+1” and “4fn” involved in the mixture. This expression uses only well known or at least measurable properties of the two integral valence states, such as Hund’s rule ground states and excited spin orbit (SO) multiplets and crystal field (CF) splittings of the 4f shell with their degeneracies, and volumes, thermal expansion coefficients and bulk moduli of the unit cell of the crystal in 4fn+1 and 4fn. The only bona fide mixed valence parameter entering the formalism is the temperature and pressure dependent fractional valence or the interconfigurational excitation energy, Ex, associated with it. We show that the experimental data available at high temperatures, such as the susceptibility, lattice constant anomaly, thermal expansion anomaly, LIII valence etc., can be explained on the basis of such a simple, semi-classical Ansatz. The high temperature behavior of mixed valence compounds turns out to be a good starting point to understand the more complicated anomalies which one observes at thermal energies comparable to or smaller than the energy gain due to quantum mixing, as we try to show in another set of lectures 1.


Bulk Modulus Spin Orbit Mixed Valence Entropy Force Mixed Valence State 
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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • Dieter Wohlleben
    • 1
  1. 1.II. Physikalisches InstitutUniversität zu KölnKöln 41Germany

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