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.
Highlights
Direct measurement of warm, dense metals to probe their lattice dynamical properties has only recently been possible [1,2,3,4,5,6]
Discontinuous responses are to be expected for these soft metals as the melt is approached and their elastic properties respond to increases in bond anharmonicity
Using the same Raman scattering data, we explore the effects of anisotropy in the calculation of the Grüneisen parameter and discuss the importance of reframing this parameter as a tensor
Summary
Dense metals to probe their lattice dynamical properties has only recently been possible [1,2,3,4,5,6]. Main group metals straddle the boundary with nonmetals and exhibit a large variation in orbital hybridization under high-pressure and -temperature conditions. This diversity in metallic bonding permits structural motifs more complicated than the simple metals [7]. Discontinuous responses are to be expected for these soft metals as the melt is approached and their elastic properties respond to increases in bond anharmonicity. The sp hybridization of α-Sn is similar to lighter group 14 elements that adopt the diamond structure, whereas the sp hybridization of β-Sn behaves more like heavier, metallic Pb due to relativistic effects
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