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For a further understanding of the phase transitions mechanism in type-I silicon clathrates K₈Si 46 , ab initio self-consistent electronic calculations combined with linear-response method have been performed to investigate the vibrational properties of alkali metal K atoms encapsulated type-I silicon-clathrate under pressure within the framework of density functional perturbation theory. Our lattice dynamics simulation results showed that the pressure induced phase transition of K₈Si 46 was believed to be driven by the phonon instability of the calthrate lattice. Analysis of the evolution of the partial phonon density of state with pressure, a legible dynamic picture for both guest K atoms and host lattice, was given. In addition, based on phonon calculations and combined with quasi-harmonic approximation, the specific heat of K₈Si 46 was derived, which agreed very well with experimental results. Also, other important thermal properties including the thermal expansion coefficients and Grüneisen parameters of K₈Si 46 under different temperature and pressure were also predicted.

Lattice Dynamics Study of Phonon Instability and Thermal Properties of Type-I Clathrate K8Si46 under High Pressure