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

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.