The β–δ phase transition in the energetic nitramine octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine: Thermodynamics

In this and the accompanying paper [L. Smilowitz et al., J. Chem. Phys. 117, 3789, 2002] we present a theoretical treatment and experimental study, respectively, of the β–δ solid state phase transition in the organic nitramine molecule octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). The transition is thermodynamically first order with a measured latent heat, occurs via nucleation and growth, and exhibits a thermally activated rate of transformation. We construct a two state kinetic model of the system consisting of equilibrium terms first order in the β or δ mole fraction simulating nucleation, and second order in β and δ simulating growth. The model has four rate constants, the temperature dependence of which is described by eight parameters. We use the transition state formulation of the rate constants and apply a thermodynamic model of the activated state that associates the difference in activated state free energy in forward and reverse directions with the equilibrium transition free energy, and identifies the activated state of the growth process with a metastable melt. By associating components of the activated state free energy with independently measured thermodynamic energies we reduce the degrees of freedom to three, which we fix initially by comparison with previously published kinetic data. We apply the model to both the β–δ and δ–β transformations over a temperature range from 300 to 700 K in order to assess the theoretical validity of the model. The model reproduces the half time of the transition over this entire range, spanning conversion times from 106 to 10−4 s. In the accompanying paper we present an experimental study of the kinetics and mechanism of the phase transition based on second harmonic generation spectroscopy. We use second harmonic generation to verify the nucleation and growth mechanism of the transition and measure the mole fraction change with time over a wide range of temperatures. We use the set of parameters established by theoretical considerations in this paper as an initial parameter set and determine an optimized set by comparison with these data.