Lattice dynamics of substitutionalSn119min silicon, germanium, andα-tin

An experimental and theoretical study has been undertaken on the lattice dynamics of ${}_{}{}^{119m}{}_{}{}^{}\mathrm{Sn}$ atoms on substitutional sites in the diamond lattices of the group-IV elements silicon, germanium, and $\alpha$-tin. Experimentally, the temperature dependences of the Debye-Waller factors for the 24-keV $\gamma$ transition of ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$ have been determined by Mössbauer-emission spectroscopy in the temperature interval between 77 and 297 K. The ${}_{}{}^{119m}{}_{}{}^{}\mathrm{Sn}$ was implanted on substitutional sites in the host lattices with an isotope separator. Polycrystalline $\alpha$-tin material was also grown from metallic $\beta$-tin containing small amounts of radioactive ${}_{}{}^{119m}{}_{}{}^{}\mathrm{Sn}$. Relative Debye-Waller factors for different materials or for different temperatures have been determined with an accuracy of ≲2% by a resonance counting technique for the emitted 24-keV $\gamma$ radiation. The measured temperature dependences of the Debye-Waller factors may be compared to theoretical results obtained from various models. A critical review on the applicability and the relevance of various dynamical models for substitutional impurity atoms in a diamond lattice is given. New calculations are presented in the framework of an extension of Mannheim's model to the diamond and zinc-blende lattices. The calculations are based on the phonon densities of states from an adiabatic bond-charge model for the group-IV elements. Unexpected large changes of the impurity-host force constants as compared to the host-host force constants are found for substitutional Sn in silicon and germanium, whereas the result from the model for the perfect lattice agree reasonably well with the experimental values for $\alpha$-tin. Possible reasons for the force-constant changes are discussed.