Abstract

When nonstoichiometric impurities enter a crystal lattice substitutionally, they are charge compensated by defects such as vacancies or interstitials which associate with the impurity at nearby sites or are unassociated at distant sites. These impurity-defect complexes have characteristic parameters such as diffusion coefficients and binding energies which may be studied with electron paramagnetic resonance (EPR) spectroscopy. If <i>c</i> is the ion fraction impurity concentration for a particular defect, <i>p</i> the degree of association, <i>cp</i> the fraction of associated, and <i>c</i> (1–<i>p)</i> the fraction of unassociated impurity-defect complexes, application of the mass action law gives <i>cp/[c</i> (1–<i>p</i>)]²=<i>K(T)</i>, where <i>K(T)</i> may be expressed such that <i>p</i>/(1–<i>p</i>)²=<i>zce^E/kT,</i> (1) where <i>z</i>=6 is the number of distinct orientations of the complex and <i>E</i> is the Gibbs free energy of binding. A semilog plot against 1/<i>kT</i> of Eq. 1 would give <i>E</i> and <i>c</i> from the slope and intercept, respectively, of the resulting straight line.

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