The resistivity of ?[Beta]-alumina-based solid electrolytes is partially determined by the relative concentration of the phases present in the electrolyte. in order to determine the concentrations of the phases within such electrolytes, several methods of quantitative phase analysis using X-ray powder diffraction data were investigated. Several analytical equations found in the literature specifically addressing the assay of phases in these systems have been found to be inconsistent. New equations, extended to accommodate the often present sodium aluminate phase, were derived and applied successfully in the calculation of the relative abundance of each phase in calcined electrolyte powders. Verification of the accuracy of these equations was obtained by comparing the results to those obtained from a Rietveld whole-pattern fitting algorithm.
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