Theoretical study of the phonon states and thermodynamic properties on surfaces of energetic material

We develop a method to calculate the local phonon states on crystal surfaces, and use it to investigate a high energy explosive, beta-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (beta-HMX). The required force constants are obtained by first principles calculations under the GGA + vdW functional. By using them, the phonon density of states (PDOSs) for thirteen kinds of surfaces are calculated, including the (100), (010), (001), (110), (1 - 10), (101), (10 - 1), (011), (01 - 1), (111), (11 - 1), (1 - 11) and (111) faces. We find that there are five representative phonon states on beta-HMX surfaces, and obtain the corresponding vibrational modes and atomic displacement fields. Based on the PDOSs, a set of surface properties are evaluated, such as the vibrational degree of freedom, surface free energy and surface heat capacity. The particle morphology of beta-HMX in vacuum is predicted by using the surface free energies. We prove that at fixed temperature, the particle morphology is independent of the particle size. The evolution of particle morphology with respect to temperature is obtained.