Elastic moduli and instability in molecular crystals

The phenomenon of instability in pressurized molecular crystals is studied using the lattice-dynamics approach. General expressions for the elastic moduli are obtained taking into account both short-range and long-range (electrostatic) interactions within the framework of the quasi-harmonic approximation. The behaviour of a system under changing pressure and temperature conditions and the Born stability criteria are investigated. Two types of instabilities, dynamical and thermodynamical, associated with the elastic moduli are presented. The dynamical instability occurs when the instability of acoustic modes of the phonon Hamiltonian occurs in the q = 0 region. The nature of thermodynamical stability implies that the equilibrium state of the crystal becomes thermodynamically unstable with respect to a small homogeneous deformation of the crystal lattice when the Born stability criteria are violated for isothermal or adiabatic moduli. These types of instabilities are illustrated in a series of calculations for ice Ic using the SPC potential for water's interactions. The results show that one of the stability conditions for the isothermal (adiabatic) moduli (C₁₁ - |C₁₂| > 0) is violated at P ≃ 3-7 kbar and, as a consequence, thermodynamical instability occurs. In contrast, the dynamical instability of the phonon spectrum occurs at a significantly higher pressure, about 20 kbar.