Phenomenological model for the structural transition in benzil

We reconcile apparently contradictory crystallographical and optical results relative to the 83.5 K transition in ${({\mathrm{C}}_6{\mathrm{H}}_5-\mathrm{C}\mathrm{O})}_2$ crystals. X-ray data are reinterpreted and shown to be compatible with a monoclinic low-symmetry phase, thus lifting the present uncertainty on the crystal's system below the transition. The spontaneous strain components are deduced from the crystallographical data. From their values, it is pointed out that the orientation of a certain type of boundary between domains is determined by the combined influence of elastic and electrostatic compatibility conditions. On the other hand, the high values at $T_c$ of the strain components disclose the pronounced first-order character of the transition. On this basis, the mechanism of the transition is assumed to proceed through the triggering of an $M$ point instability by a $\Gamma$ point one. The consequences of this model are analyzed by a discussion of the Landau free energy corresponding to its symmetry characteristics. It accounts for the observed simultaneous occurence of the softening of a Brillouin-zone-center optic mode and of a fourfold expansion of the crystal's primitive unit cell. The qualitative temperature dependences of the soft-mode frequency, the spontaneous strain, and the dielectric constant are also satisfactorily reproduced.