Disentangling $α$ and $β$ relaxation in orientationally disordered crystals with theory and experiments

We use a microscopically motivated Generalized Langevin Equation (GLE) approach to link the vibrational density of states (VDOS) to the dielectric response of orientational glasses (OGs). The dielectric function calculated based on the GLE is compared with experimental data for the paradigmatic case of two OGs: Freon 112 and Freon 113, around and just above $T_g$. The memory function is related to the integral of the VDOS times a spectral coupling function $γ(ω_p)$, which tells the degree of dynamical coupling between molecular degrees of freedom at different eigenfrequencies. The comparative analysis of the two Freons reveals that the appearance of a secondary $β$ relaxation in Freon 112 is due to cooperative dynamical coupling in the regime of mesoscopic motions caused by stronger anharmonicity (absent in Freon 113), and is associated with comparatively lower boson peak in the VDOS. The proposed framework brings together all the key aspects of glassy physics (VDOS with boson peak, dynamical heterogeneity, dissipation, anharmonicity) into a single model.