Calcium Tungstate—IV: The Theory of Coupled Substitution

A theory is developed for the coupled substitution e.g., of Nd³⁺ and Na⁺ in Ca²⁺ sites in the scheelite (CaWO₄) lattice. Allowance is made for Schottky defect formation.

The results fit the CaWO₄: Nd system up to 2 % Nd, the CaWO₄: Nd: Na system up to 15 % Na and 5 % Nd, and the CaWO₄: Nd: K system up to 8 % K and 2% Nd.

Equilibrium constants resulting from the theory give the vacancy concentrations in O and Ca sites as 0.054 % each and the free energy of formation of a pair of vacancies as 55 kcal or 2.4 eV, all in pure CaWO₄ in air at the melting point.

Energies are also obtained for the various other substitution arrangements. For exactly balanced substitution of one Na⁺ for each Nd³⁺ in the crystal, it is necessary to use 4.05 Na for each Nd in the melt. This also results in the minimum number of vacancies in the crystal.

 

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