Elastic instabilities in crystals fromab initiostress - strain relations
Journal of Physics: Condensed Matter
Pressure-induced elastic instabilities are investigated in the prototypic ionic and covalent solids (MgO, CaO, SiO 2 and Si) using generalized elastic stability criteria based on the elastic stiffness coefficients (c ij ) which are determined directly from stress-strain relations. From first-principles computer simulations of the instabilities, we demonstrate the validity and importance of the generalized criteria relative to the conventional criteria in describing the crystal stability under
... l stability under hydrostatic pressure in relation to the real structural transformations. We examine systems for which the two phases can be related by a simple deformation, and in all cases we show that the generalized elastic stiffness coefficient associated with that deformation softens toward the transition. The shear stability criterion (c 44 > 0) bounds the first-order B1-B2 phase transition pressure from above and below in MgO and CaO, suggesting a wide pressure regime of metastability, whereas the tetragonal shear stability criterion ((c 11 − c 12 )/2 > 0) predicts precisely the second-order rutile-to-CaCl 2 transition in SiO 2 . The high-pressure elastic behaviour of diamond structure Si is studied in detail. A tetragonal shear instability corresponding to its transformation to the β-Sn structure should occur in diamond structure Si at a pressure of 101 GPa, compared to the experimental value of 9 to 13 GPa for the transition pressure.