First-principles characterisation of the pressure-dependent elastic anisotropy of SnO₂ polymorphs

Abstract

Using DFT calculations, this study investigates the pressure-dependent variations of elastic anisotropy in the following SnO₂ phases: rutile-type (tetragonal; P4₂/mnm), CaCl₂-type (orthorhombic; Pnnm)-, α-PbO₂-type (orthorhombic; Pbcn)- and fluorite-type (cubic; Fm-3m). Experimentally, these polymorphs undergo sequential structural transitions from rutile-type → CaCl₂-type → α-PbO₂-type → fluorite-type with increasing pressure at 11.35, 14.69 and 58.22 GPa, respectively. We estimate the shear anisotropy (A₁ and A₃) on {1 0 0} and {0 0 1} crystallographic planes of the tetragonal phase and (A₁, A₂ and A₃) on {1 0 0}, {0 1 0} and {0 0 1} crystallographic planes of the orthorhombic phases. The rutile-type phase shows strongest shear anisotropy on the {0 0 1} planes (A₂ > 4.8), and the degree of anisotropy increases nonlinearly with pressure. In contrast, the anisotropy is almost absent on the {1 0 0} planes (ie A₁ ~ 1) irrespective of the pressure. The CaCl₂-type phase exhibits similar shear anisotropy behaviour preferentially on {0 0 1} (A₃ > 5), while A₁ and A₂ remain close to 1. The α-PbO₂-type phase shows strikingly different elastic anisotropy characterised by a reversal in anisotropy (A₃ > 1 to < 1) with increasing pressure at a threshold value of 38 GPa. We provide electronic density of states and atomic configuration to account for this pressure-dependent reversal in shear anisotropy. Our study also analyses the directional Young’s moduli for the tetragonal and orthorhombic phases as a function of pressure. Finally, we estimate the band gaps of these four SnO₂ phases as a function of pressure which are in agreement with the previous results.

Keywords:

• DFT calculations
• structural transitions
• elastic constants
• shear anisotropy
• band gaps

Acknowledgements

PKD and AC are grateful to the Department of Science and Technology, Government of India for providing the INSPIRE Fellowships to them. NM acknowledges the J.C. Bose Fellowship, awarded to him by DST, Government of India.