Low-pressure ferroelastic phase transition in rutile-type AX₂ minerals: cassiterite (SnO₂), pyrolusite (MnO₂) and sellaite (MgF₂)

Abstract

The structural behaviour of cassiterite (SnO₂), pyrolusite (MnO₂) and sellaite (MgF₂), i.e. AX₂-minerals, has been investigated at room temperature by in situ high-pressure single-crystal diffraction, up to 14 GPa, using a diamond anvil cell. Such minerals undergo a ferroelastic phase transition, from rutile-like structure (SG: P4₂/mnm) to CaCl₂-like structure (SG: Pnnm), at ≈ 10.25, 4.05 and 4.80 GPa, respectively. The structural evolution under pressure has been described by the trends of some structure parameters that are other than zero in the region of the low-symmetry phase’s stability. In particular, three tilting-angles (ω, ω′, ABS) and the metric distortion of the cation-centred octahedron (quantified via the difference between apical-anion and equatorial-anion distances Δ|X_ax−X_eq|) are used to express the atoms’ readjustment, i.e. relaxation, taking place in the CaCl₂-like structures under pressure. The crystallographic investigation presented is complemented with an analysis of the energy involved in the phase transition using the Landau formalism and adopting the following definition for the order parameter: Q = η₁₁–η₂₂, η_ij being the spontaneous strain tensor. The dependence of ω, ω′, ABS and Δ|X_ax−X_eq| on Q allows determination of a correlation between geometrical deformation parameter and energy. Lastly, the relaxation mechanisms that exploits ω, ω′, ABS and Δ|X_ax−X_eq| may be related to the ionic degree of bonding, the latter modelled via quantum mechanics and Bader theory. Sellaite, the mineral exhibiting the highest degree of ionic bonding among those investigated, tends to accomplish relaxation through pure rotation of the octahedron, rather than a metric distortion (Δ|X_ax−X_eq|), which would shorten inter-atomic distances thus increasing repulsion between anions.

Appendix 1

Quantum mechanics modelling

Static calculations were performed at a given pressure and 0 K by the HF/DFT-CRYSTAL14 program (Dovesi et al. 2014), which implements “Ab initio Linear-Combination-of-Atomic-Orbitals” for periodic systems. Neither zero-point-energy nor thermal pressure were taken into account, as in the present case we pay attention only to the trend, at room temperature. Exchange and correlation functionals were chosen on the basis of the capacity to reproduce experimental cell parameters and energy gaps. For sellaite, a combination of the Exchange Second Order GGA functional (SOGGA) with the PBE correlation functional (Zhao and Truhlar 2008) was chosen, using 5% of HF exchange hybridization. For cassiterite and pyrolusite the one-parameter B1WC hybrid functional (Bilc et al. 2008), which combines WC exchange and PWGGA correlation functionals, was employed, with 18 and 8% of HF exchange hybridization, respectively. The following tolerance values were chosen to govern the accuracy of the integrals of the self-consistent-field-cycles: 10⁻⁸ for coulomb overlap, 10⁻⁸ for coulomb penetration, 10⁻⁸ for exchange overlap, 10⁻⁸ for exchange pseudo-overlap in direct space, 10⁻¹⁶ for exchange pseudo-overlap in reciprocal space and 10⁻⁸ Ha threshold for SCF-cycles’ convergence.

For all the structures under investigation, the Peintinger–Oliveira–Bredow (POB) basis sets (Peintinger et al. 2013), constituted by triple-ζ valence plus polarization functions, were used, with the exception of Sn (Sn_9763111-631 basis set available at http://www.tcm.phy.cam.ac.uk/~mdt26/basis_sets/Sn_basis.txt).