Diffusion of Kr Isotopes in Solid Ar

The diffusion coefficient $D=D^0{e}^{-\frac{Q^0}{\mathrm{RT}}}$ and isotope effect for ${\mathrm{Kr}}^{78}$ and ${\mathrm{Kr}}^{86}$ in solid Ar have been measured using a tracer technique. The activation energy $Q_{\mathrm{Kr}}^{}{}_{}{}^0$ depends on the interchange parameter $w$, but is estimated to lie in the range 3500-3900 cal ${\mathrm{mole}}^{-1\mathrm{}}$, with the most reliable $w$ giving the lower value. Thus, the two calculated $Q_{\mathrm{Kr}}^{}{}_{}{}^0$ (3853 and 4050 cal ${\mathrm{mole}}^{-1\mathrm{}}$) for the vacancy mechanism using a two-body (12, 6) potential appear somewhat high, but in reasonable agreement with experiment. The isotope effect gives $f\Delta K\equiv \frac{(\frac{D_{78}}{D_{86}}-1)}{[{\left(\frac{86}{78}\right)}^{\frac{1}{2}}-1]}=0.48\mathrm{}\pm 0.25$ which, since $Q_{\mathrm{Kr}}^{}{}_{}{}^0Q_{\mathrm{Ar}}^{}{}_{}{}^0$, suggests that $\Delta K\sim 0.6$ for a single-vacancy mechanism. {Here $f$ is the correlation factor and $\Delta K\equiv \frac{(\frac{\omega _2^{}{}_{}{}^{78}}{\omega _2^{}{}_{}{}^{86}}-1)}{[{\left(\frac{86}{78}\right)}^{\frac{1}{2}}-1]}$, where ${\omega }_2$ is the tracer jump rate.}