Dilatometric and X-Ray Thermal Expansion in Non cubic Crystals. II. Experiments on Cadmium

Abstract

Precision measurements of macroscopic thermal expansion $\frac{\delta l}{l_0}$ and microscopic (x-ray) thermal expansion $\frac{\delta d}{d_0}$ have been carried out for cadmium single crystals in both the $a$ and $c$ directions, between room temperature and the melting point. In accordance with the prediction of the previous paper (paper I) it was found that the difference $\Delta =\left(\frac{\delta L}{L_0}\right)-\left(\frac{\delta d}{d_0}\right)$ in a given direction is sample dependent. Accordingly, information on the equilibrium defect concentration was obtained from samples cut from the same large crystal. The mole fraction of vacancies in equilibrium, given by $2{\Delta }_a+{\Delta }_c$, has the value 5.6×${10}^{-4\mathrm{}}$ at the melting point. The results as a function of temperature are consistent with an interpretation in terms of monovacancies only, with enthalpy and entropy of formation, respectively, of (0.40±0.02) eV and $(0.3\mathrm{}\pm 0.4)k$.. With the aid of self-diffusion data, appropriate vacancy-migration parameters are also obtained. In addition, the ratio $\frac{{\Delta }_c}{{\Delta }_a}$ is found to be independent of temperature, and is interpreted in accordance with the theory of paper I. In particular, it is found that nonbasal dislocations play a large role as sources and sinks for vacancies.