Response of the mode Grüneisen parameters with anisotropic compression: A pressure and temperature dependent Raman study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math>-Sn

Abstract

The lattice dynamic response of body-centered tetragonal $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Sn}$ $(I{4}_{1}/amd)$ under high-pressure and -temperature conditions is determined using experimental optical vibration modes. Raman scattering is used to map the phase stability region of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Sn}$ to perform mode Gr\"uneisen analysis, and we demonstrate the necessity of an optical intensity calibration for Raman thermometry. The Gr\"uneisen tensor is evaluated along a set of isotherms to address shortcomings of single-mode Gr\"uneisen parameters with respect to anisotropic deformations of this tetragonal structured soft metal. The changes observed here in the Gr\"uneisen tensor as a function of temperature are related to anharmonicity and denote potential criteria for the onset of premelting.