Anomalous Isotopic Effect on the Lattice Parameter of Silicon

Abstract

The difference $\ensuremath{\Delta}a={a}_{(30)}\ensuremath{-}{a}_{(28)}$ of the lattice parameter of $^{\mathrm{30}}\mathrm{S}\mathrm{i}$ and $^{\mathrm{28}}\mathrm{S}\mathrm{i}$ crystals is measured over a temperature range from 4.7 to 700 K. In disagreement with existing knowledge, the strongest isotopic effect is not detected at the lowest achieved temperature $T=4.7\text{ }\text{ }\mathrm{K}$. An anomalous behavior is observed: The relative difference $|\ensuremath{\Delta}a/a|$ attains its maximum value of 56.8(5) ppm at $T=75(10)\text{ }\text{ }\mathrm{K}$. The anomalous behavior is attributed to the influence of phonon modes with negative Gr\"uneisen parameters. At $T=700\text{ }\text{ }\mathrm{K}$ the effect still amounts to 30% of the maximal value. The experimental data are consistent with an approach based on the density-functional perturbation theory.