Interpretation of the ${}^{119}\mathrm{Sn}$ Mössbauer isomer shifts in complex tin chalcogenides

The main observed trends in the variations of the ${}^{119}\mathrm{Sn}$ Mössbauer isomer shift δ for tin chalcogenides are interpreted in terms of the valence electronic populations, and are related to changes in the Sn local environment. First, the values of the valence electron charge density at the nucleus ${\rho }_v\mathrm{}\left(0\right)\mathrm{}$ have been evaluated from a tight-binding calculation for a number of binary compounds in order to check the accuracy of the theoretical approach. A linear correlation between the experimental values of δ and the calculated values of ${\rho }_v\mathrm{}\left(0\right)\mathrm{}$ is obtained, providing a mean square radius of the nucleus in the Mössbauer transition $\Delta 〈r^2〉$ in correct agreement with the previously published values. The same approach is applied to tin chalcogenides with complex structures, and a correct linear correlation between ${\rho }_v\mathrm{}\left(0\right)\mathrm{}$ and δ is obtained. Different series of chalcogenides have been distinguished considering the Sn oxidation state, the type of chalcogen, and the Sn site symmetry. These series correspond to different ranges of experimental values for δ which have been correlated to the calculated values of ${\rho }_v\mathrm{}\left(0\right)\mathrm{}$ and the Sn valence electron populations. Finally, a molecular model is proposed which gives simple analytical expressions of the numbers of Sn $5s$ and Sn $5p$ electrons as a function of the Sn site symmetry, the type of chalcogen, and the tin-chalcogen interatomic distance. This model provides a rather simple interpretation of the changes in the values of δ for the different series of chalcogenides.