ELASTIC INSTABILITIES IN CRYSTALS FROM AB-INITIO STRESS-STRAIN RELATIONS

Pressure-induced elastic instabilities are investigated in the prototy pic ionic and covalent solids (MgO, CaO, SiO2 and Si) using generalize d elastic stability criteria based on the elastic stiffness coefficien ts (c(ij)) which are determined directly from stress-strain relations. From first-principles computer simulations of the instabilities, we d emonstrate the validity and importance of the generalized criteria rel ative to the conventional criteria in describing the crystal stability under hydrostatic pressure in relation to the real structural transfo rmations. We examine systems for which the two phases can be related b y 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) boun ds the first-order B1-B2 phase transition pressure from above and belo w 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-CaCl2 transition in S iO2. The high-pressure elastic behaviour of diamond structure Si is st udied in detail. A tetragonal shear instability corresponding to its t ransformation to the beta-Sn structure should occur in diamond structu re Si at a pressure of 101 GPa, compared to the experimental value of 9 to 13 GPa for the transition pressure.