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.

In this paper we present second harmonic generation (SHG) experiments designed to confirm the mechanism and quantify the transformation kinetics 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 β phase adopts a centrosymmetric crystallographic configuration (P21/c) while the δ phase adopts a noncentrosymmetric one (P61(P65)). As expected, this results in a very poor generation of SHG intensity from the β phase, while the δ phase is very efficient, rivaling KH2PO4 in absolute efficiency. SHG thus provides a very high sensitivity zero background probe of the δ phase. We discuss the use of this signal as a quantitative measure of the δ phase mole fraction in ensembles of free HMX crystals and crystals embedded in a visco–elastic polymer matrix. We report imaging experiments where the spatial characteristics of the transformation are shown to be consistent with nucleation from a low density of initial sites, followed by rapid growth. We also report experiments where the total integrated SHG is measured and used to infer the transition progress as a function of time in a series of isothermal experiments on both β–δ conversion and δ–β reversion. Additionally, reversibility experiments are reported which are used to verify both the volumetric mechanism of SHG generation in this system and the independence of these results to the internal stress state of the polycrystalline samples. We compare the measured SHG intensity as a function of time for a range of temperatures with predictions of the two state kinetic model presented in the accompanying paper [B. F. Henson et al., J. Chem. Phys. 117, 3780 (2002)]. We perform a set of parameter optimization calculations based on agreement with the predictions of the model. Optimization does not significantly change the kinetic parameters that are thermodynamically constrained by the model, but there is a distribution of parameters necessary to reproduce the nucleation kinetics observed. In particular, a striking difference in nucleation kinetics is observed between samples of free crystals and crystals embedded in a visco–elastic polymer matrix.

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In our previous work on the mechanism for the β-δ solid-solid phase transition in octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX), we used an empirical mechanism for the nucleation step and hypothesized a defect mechanism that was greatly affected by the presence of a nitroplasticizer/estane binder in the HMX formulation. Since then, we have acquired further evidence for this and have separated out the components of the binder to confirm that it is the nitroplasticizer that controls the nucleation energy in HMX formulations containing a nitroplasticizer/estane binder. While the exact distribution of nucleation energies as a function of synthesis route/defect type has not been worked out, it is likely that the solubility of the HMX in the nitroplasticizer is responsible for lowering the nucleation energy at the crystal surface, and therefore determines the nucleation rate for the formulation.