Solid-to-solid phase transition in crystalline benzil: A Raman scattering study

Benzil, which crystallizes at $T=368\mathrm{}$ K in the trigonal space group $P{3}_{1}21 (D_3^4$), undergoes a solid-to-solid phase transition at $T_c=84\mathrm{}$ K with monoclinic $C2\mathrm{}\left(C_2^3\right)$ symmetry below $T_c$; the primitive unit cell below $T_c$ shows a fourfold expansion. Raman spectra associated with modes in which benzil molecules execute rigid translatory and rotatory (librational) oscillations—the external modes—show the consequences of the lowered symmetry and the unit-cell enlargement below $T_c$. The doubly degenerate zone-center $E$ modes in the high-temperature phase show splittings, one of which manifests a pronounced softening and a discontinuity in its frequency at $T_c$ characteristic of a first-order transition. The zone-boundary external modes associated with the $M$ points of the Brillouin zone for $T>\mathrm{}{T}_c$ transform into Raman-active zone-center phonons below $T_c$. The Raman spectra at $T\le T_c$ show a large number of new lines which can be attributed to these zone-boundary $M$ modes; one of these is a second soft mode related to the unit-cell enlargement. The experimental results are discussed in terms of a model in which the $M$-point instability is triggered by the one at the zone center.