Elasticity of (K,Na)AlSi3O8 hollandite from lattice dynamics calculations

We compute the elastic constants tensor and the seismic properties of KAlSi3O8 and K0.8Na0.2AlSi3O8 up to the ferroelastic transition using density-functional theory and density-functional perturbation theory in the ABINIT implementation. We observe a softening of the tetragonal shear with pressure that precedes the ferroelastic transition. The Reuss shear moduli become negative at respectively 23 GPa and 13 GPa for the two compositions considered in here. The ferroelastic transition is associated with a strong decrease of the horizontal shear wave velocities and a corresponding increase of the seismic anisotropy. The presence of Na enhances these features.