Thermodynamic Estimations of Defect Equilibria and Vacancy Concentrations in ZnS

With the equilibrium constants for atomic vacancies, K S , for electronic charge carriers, K i , and for the vaporization of ZnS, K p , the densities of atomic point defects and of electronic charge carriers were obtained as a function of temperature. The computed metal vacancy concentrations of ZnS are in close agreement with independently reported experimental data. Combining K S and K i values with vacancy formation reactions and with equilibrium partial pressures of the constituent species yielded the relative concentrations of doubly ionized metal and noñmetal vacancies and of electronic carriers as a function of pressure. The point of material stoichiometry is given by the expression Log(K 8 p M ) stoich. = Log K i + 1/2 Log K S , which is generally true, but different from that for singly ionized vacancies. With the stoichiometry relationship, derived in this work, and partial pressures of the relevant species, equilibrium constants for individual vacancy formation reactions are computed as a function of temperature. The resulting Zn vacancy densities are in close agreement with those based on the Schottky constant alone and with those of independent experimental data. In addition, the predominant vacancy type (conductivity) can be predicted from the individual reactions. These results are useful for the optimization of synthesis conditions, and for the characterization of materials.