About the Strain-Coupled Molecular Dynamics in the Ferroelastic Phase Transition of TMACd(N$_3$)$_3$
Tetramethylammonium (TMA) cadmium azide, is a new perovskite-like compound which undergoes a series of first-order phase transitions, including a ferroelastic transition above room temperature. Understanding the order-disorder structural phase transition (SPT) mechanism in hybrid organic--inorganic perovskites (HOIPs) is crucial for designing new compounds with enhanced barocaloric efficiency, as well as unlocking other multifunctional properties. In this paper, we employed the energy fluctuation (EF) model to investigate the experimental linewidth of Raman modes in TMACd(N$_3$)$_3$ near the critical phase transition temperature ($T_C = {322}{K}$), aiming to gain insights into the molecular dynamics around the SPT. The temperature dependence of the strain, used as an order parameter, was obtained using the appropriate thermodynamic potential for the first-order phase transition in TMACd(N$_3$)$_3$, expressed through a Landau expansion, which can be successfully employed to model first-order ferroelastic phase transitions. We show that the EF model suitably captures the behavior of the Raman linewidths in the vicinity of the structural phase transition in TMACd(N$_3$)$_3$. The activation energies obtained for TMACd(N$_3$)$_3$ are comparable to those of DMACd(N$_3$)$_3$, as well as to $k_B T_C$. Additionally, the temperature dependence of the relaxation reveals that the torsional and librational modes require longer to renormalize after the phase transition in TMACd(N$_3$)$_3$ when compared with DMACd(N$_3$)$_3$. The discussion based on these new parameters provides a new perspective for understanding molecular dynamics in systems undergoing order-disorder phase transitions, particularly in ferroelastic transitions, where order-disorder mechanisms are coupled to symmetry-breaking lattice distortions.