Free itinerant electron system

From a thermodynamic viewpoint, we may imagine that, in an actinide metal, the model of the solid in which completely itinerant and bonding 5 f electrons exist and that in which the same electrons are localized, constitute the descriptions of two thermodynamic phases. The 5f-itinerant and the 5 f-localized phases may therefore have different crystal properties a different metallic volume, a different crystal structure. The system will choose that phase which, at a particular T and p (since we are dealing with metals, the system will have only one component) has the lower Gibbs free-energy. A phase transition will occur then the fugacity in the two possible phases is equal e.g. the pressure. To treat the transition, therefore, the free energies and the pressures of the two phases have to be compared. We recall that ... 

All the above transitions are accompanied by changes in Seebeck coefficient, structural parameters, heat capacity and other characteristics. The V2O3 system has been explained in terms of a thermodynamic model which uses different free energy expressions for electrons in the itinerant and localized regimes (Honig Spalek, 1986). 

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