An Ising theory of the plastic phase-transition in diazabicyclo[2,2,2]octane

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Abstract
To elucidate the behaviour of molecules through a plastic-phase transition we have calculated the zero pressure thermodynamic and structural properties of ‘model DABCO’ as a function of temperature. ‘Model DABCO’ interacts with an ‘atom-atom intermolecular potential’ and is a rigid molecule of the same geometry as diazabicyclo[2,2,2]octane (DABCO). The crystal has behaviour approximated by Ising models for the orientational disordering. There is a first-order transition from a P63/m ‘h.c.p.’ lattice to a rotationally disordered f.c.c. lattice in which there is still angular correlation of molecules. This transition is initiated by a two-dimensional disordering of molecular rotation angle about the N-N axis which is parallel to the hexagonal c axis of P63/m. The extra driving force needed for the change in centre-of-mass topology from h.c.p. to f.c.c. is a further three-dimensional disordering, which tilts the molecular N-N axis 70° away from the crystal c axis. Only in the f.c.c. lattice is this tilting disorder coupled strongly enough to the two-dimensional rotational disorder to occur at the same critical temperature. We thus observe a transition from the two-dimensionally disordered P63/m ‘h.c.p.’ structure to the two and three-dimensionally disordered f.c.c. structure. The numerical values for thermodynamic, structural and kinetic properties of ‘model DABCO’ calculated with no variable parameters compare well with experimental observables for DABCO, including our powder neutron diffraction results. This demonstrates the applicability of the microscopic molecular model to DABCO, and possibly other molecular crystals with plastic phases. The disordering and correlation in molecular angular motion is shown to have a strong effect in diffraction experiments. The entropy change in the transition is calculated to be 60 per cent due to entropy of expansion and only 40 per cent due to configurational entropy change.