Phase diagram and deuteration contribution to the phonon analysis of the normal-to-incommensurate phase transition of 4-4′ dichlorobiphenyl sulfone determined using Raman and neutron scattering

4-4\ensuremath{'}dichlorobiphenyl sulfone (BCPS) presents a phase transition from a high-symmetry monoclinic phase $I2/a$ to an incommensurate phase $I2/a$ (0\ensuremath{\beta}0) at ${T}_{\mathrm{i}}=150$ K without any lock-in phase transition observed down to the lowest temperatures at atmospheric pressure. Such examples which remain incommensurate close to 0 K are quite rare and are prototype materials for the study of the competitive terms between internal energy and residual entropic contributions defining their stable phases. The present study reports an experimental determination of the temperature versus pressure phase diagram for BCPS. A Raman study of the amplitudon mode in the incommensurate phase reveals that the transition temperature diminishes under pressure and vanishes at about 320 MPa for the hydrogenated compound. It also sheds light on the properties of the low-frequency phonons and their assignments by a hydrogen isotopes comparison. In particular, it shows that the chlorophenyl torsion modes have frequencies in the 100 $\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ range and cannot be a primary order parameter. A neutron-diffraction experiment reveals that there is no tendency for a lock-in phase transition at any pressure, with the critical wave vector remaining always far away from any simple rational value. Inelastic neutron-scattering experiments on the deuterated compound versus pressure at 50 K report, as expected, much lower damping of the critical excitations around ${T}_{\mathrm{i}}$ compared to the ones at atmospheric pressure (${T}_{\mathrm{i}}=150$ K). It reveals the complexity of the spectral function when both soft mode and central peak are present and allows the observation of both the phason and the amplitudon modes at lower pressure within the incommensurate phase. High-resolution neutron diffraction carried out at the same temperature reveals very different pressure responses of the crystallographic parameters inducing deviatoric strains.