The relationship between vibrational entropy and ratio of cationic radii in fluorite-type solid solutions

Abstract

Solid solutions of fluorite-type fluorides have been studied with respect to a structural defect cluster model and/or high anionic conductors [1]. When trivalent compounds dissolve in fluorite-type fluorides, the resulting solid solutions have an excess of anions. A Willis cluster model is generally used to represent defect structures with such excess anions. Recently, this model has been confirmed by neutron diffraction by many researchers (e.g. [2]). The model pays most attention to the excess anions. In fluoritetype solid solutions of the systems (Ca, Sr, Ba)FzLnF3 (Ln: lanthanide), alkali-earth ions are also substituted by lanthanide ions, therefore, the effects of substituted cations must also be considered. Lanthanide ions are convenient for investigating the heterosize effect which is caused by the misfit and the strain energy [3, 4]. The strain energy is also considered to be associated with a vibrational entropy which could be calculated from the solvus line in the phase diagram. We calculated an enthalpy change and vibrational entropy change for solution from pure (Ln) to the fluorite-type solid solution from the solubility limits in systematic phase diagrams for the systems (Ca, Sr)F 2LnF~ reported by Sobolev's group [5, 6]. In this letter we discuss the relationship between solute cation heterosize/heterovalence and enthalpy change/vibrational entropy change which is associated with a strain energy contribution/neutralizing electivity. The theory of calculation of thermodynamic quantities from a simple phase diagram is explained in detail by Swalin [7]. Let us consider, in the case of a eutectic binary system indicating limited mutual solubility of A and B,