Elastic moduli calculation and instability in structure I methane clathrate hydrate

The thermal expansion of structure I clathrate hydrates with empty cages and with enclathrated methane molecules has been calculated from 5 to 270 K using the lattice dynamics approach within the quasiharmonic approximation. The temperature dependence of several elastic properties, namely the dynamical, adiabatic and isothermal elastic moduli, are calculated. The dynamical and thermodynamical stability of the crystals are investigated according to the Born stability criteria. Methane hydrate is unstable against small homogeneous deformations near the melting transition at normal pressure. For the empty hydrate lattice, a thermodynamical instability was found to occur at significantly higher temperature. The theoretical results are compared with new thermal expansion data on methane hydrate and results from a previous molecular dynamics study.