Understanding the Phase Behaviour of Pyrochlore Bi₂Sn₂O₇

Bi₂Sn₂O₇ exists in a number of polymorphic forms, with an α to β transition occurring at ≈400 K and β to γ transition occurring above 900 K.¹ The structural model for γ is undisputed (Fd-3m) but there has been a controversy over the structural models of α and β, with two models existing for α, one with 352 atoms per cell (P1C1)² and other with 88 atoms per cell (C1c1),³ and recently β belonging to space group Aba2 has been reported.³ We perform DFT lattice dynamics calculations using Phonopy⁴ starting from γ, and map out the potential energy surfaces⁵ spanned by imaginary mode eigenvectors, with the aim of elucidating the lowest energy structure. This approach successfully takes us from γ to the new structural model suggested for α, and also shows that β is a thermal average of a lower symmetry structure. The success of the method highlights the strength of ab-intio lattice dynamics in predicting the dynamically stable structural model of a compound and can speed up the exploration of different structures for solid-state applications.

¹Shannon et al., J. Phys. Chem. Solids, 1980, 41, 117
²Evans et al., J. Mater. Chem., 2003, 13, 2098
³Lewis et al., J. Am. Chem. Soc., 2016, 138, 8031
⁴Togo et al., Phys. Rev. B, 2008, 78, 134106
⁵Skelton et al., Phys. Rev. Lett., 2016, 117, 075502