Molecular dynamics study of diffusionless phase transformations in HMX: $\beta$-HMX twinning and $\beta$-$\epsilon$ phase transition

We use molecular dynamics to study mechanism of deformation twinning of $\beta$-1,3,5,7-tetranitro-1,3,5,7-tetrazocane ($\beta$-HMX) in the $P2_1/n$ space group setting for the twin system specified by $K_1=(101)$, $\eta_1=[10\overline{1}]$, $K_2=(10\overline{1})$, and $\eta_2=[101]$ at $T=1$ K and 300 K. Twinning of a single perfect crystal was induced by imposing increasing stress. The following three forms of stress were considered: uniaxial compression along $[001]$, shear stress in $K_1$ plane along $\eta_1$ direction, and shear stress in $K_2$ plane along $\eta_2$ direction. In all cases the crystal transforms to its twin by the same mechanism: as the stress increases, the $a$ and $c$ lattice parameters become, respectively, longer and shorter; soon after the magnitude of $a$ exceeds that of $c$ the system undergoes a quick phase-transition-like transformation. This transformation can be approximately separated into two stages: glide of the essentially intact $\{101\}$ crystal planes along $\langle10\overline{1}\rangle$ crystal directions followed by rotations of all HMX molecules accompanied by N-NO$_2$ and CH$_2$ group rearrangements. The overall process corresponds to a military transformation. If uniaxial compression along $[001]$ is applied to a $\beta$-HMX crystal which is already subject to a hydrostatic pressure $\gtrsim 10$ GPa, the transformation described above proceeds through the crystal-plane gliding stage but only minor molecular rearrangements occurs. This results in a high-pressure phase of HMX which belongs to the $P2_1/n$ space group. The coexistence curve for this high-pressure phase and $\beta$-HMX is constructed using the harmonic approximation for the crystal Hamiltonians.