ELASTIC-MODULI AND INSTABILITY IN MOLECULAR-CRYSTALS

The phenomenon of instability in pressurized molecular crystals is stu died using the lattice-dynamics approach. General expressions for the elastic moduli are obtained taking into account both short-range and l ong-range (electrostatic) interactions within the framework of the qua si-harmonic approximation. The behaviour of a system under changing pr essure and temperature conditions and the born stability criteria are investigated. Two types of instabilities, dynamical and thermodynamica l, associated with the elastic moduli are presented. The dynamical ins tability occurs when the instability of acoustic modes of the phonon H amiltonian occurs in the q = 0 region. The nature of thermodynamical s tability implies that the equilibrium state of the crystal becomes the rmodynamically unstable with respect to a small homogeneous deformatio n 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 poten tial for water's interactions. The results show that one of the stabil ity conditions for the isothermal (adiabatic) moduli (C-11 - \C-12\ > 0) is violated at P similar or equal to 3-7 kbar and, as a consequence , thermodynamical instability occurs. In contrast, the dynamical insta bility of the phonon spectrum occurs at a significantly higher pressur e, about 20 kbar.