Formation Free Energies and Vacancy-Divalent-Ion Binding Energy from Internal-Friction Experiments on NaCl

Abstract

The properties of charged dislocations are exploited to obtain the formation free energies for positive and negative ion vacancies and the cation-vacancy-divalent-impurity binding energy for calcium-doped NaCl. An internal-friction technique was used to determine the temperatures for which the dislocations were uncharged, for four calcium concentrations. These critical temperatures were then related to the defect parameters of the system in various ways involving different treatments of the defect interactions. The importance of including defect interactions in such analyses is demonstrated. In the temperature range $400°\mathrm{C}<T<\mathrm{}700\mathrm{}°\mathrm{C}$, we find the cation-vacancy free formation energy to be $F^{+}=0.635\mathrm{}\pm 0.011 \mathrm{eV}-(6.1\mathrm{}\pm 0.5)k(T-823°\mathrm{K})$, while the binding energy of a calcium ion and a nearest-neighbor cation vacancy is $B=0.49\mathrm{}\pm 0.10$ eV.