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

Abstract

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 the comparatively lower boson peak in the VDOS. The proposed framework brings together all the key aspects of glassy physics (VDOS with the boson peak, dynamical heterogeneity, dissipation, and anharmonicity) into a single model.

Low-energy optical phonons induce glassy-like vibrational and thermal anomalies in ordered crystals

“…It will be very interesting, in future work, to study how these soft optical modes relate to motions involved in the β relaxation of glasses (a connection that has been recently studied in [43]), since those are responsible for the jump from one local minimum in the energy landscape to another one nearby, which defines the β relaxation process.…”

Fluctuation–dissipation relations far from equilibrium: a case study

“…For equilibrium systems, the FDTs can be rigorously derived within linear response theory [3,13], their validity in non-equilibrium situations has, however, been extensively and controversially discussed in the literature [9][10][11][14][15][16][17][18][19][20][21][22][23][24]. Outside the linear response regime, these theorems should therefore be rather seen as unproven "relations" [25].…”

Secondary relaxation in the terahertz range in 2-adamantanone from theory and experiments

“…Despite the Kohlrausch stretched-exponential function and its Fourier transform analog Havriliak-Negami function provide still the most popular empirical functions to describe the slow α relaxation in any type of supercooled systems (SGs, OGs, etc), a different approach, which starts from first principles, was recently proposed 33 . This simple approach (see next section) was successfully applied to two orientational glasses, Freon 112 and Freon 113 34 , for which the appearance of the secondary β relaxation for Freon 112 was rationalized on the basis of lower and intermediate-energy excitations in the VDOS.…”

“…a system with well-defined occupational disorder (M phase) and for which the fully ordered (O) phase is known. By using the modified theoretical model previously developed 34 we are able to account for the secondary relaxation appearing in the disordered M phase of 2O=A as well as the dynamical coupling of molecular disorder as a function of the eigenfrequencies, in particular, those concerning low-energy localized (optical) modes. Even more, we will demonstrate that the small differences in the VDOS between disordered M and ordered O phases are so subtle (just some optical modes shifted to lower energy for the disordered phase) that the dielectric susceptibility can be reproduced by using either of the two VDOS, despite the glassy features emerge due to the piling up of those optical modes (see also Ref.…”