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$δ$-Bi$_2$O$_3$ is one of the fastest known solid oxide ion conductors owing to its intrinsically defective fluorite-like structure with 25\% vacant sites in the O sub-lattice. Numerous diffraction measurements and molecular dynamics simulations indicate that the Bi ions construct a cubic, fcc lattice, and the O ions are %distributing and migrating through it. Nonetheless, in this study we present Raman scattering measurements that clearly show that the Bi sub-lattice preserves the monoclinic symmetry of the low temperature phase ($α$-Bi$_2$O$_3$) up to the melting temperature of the crystal. The apparent contradiction between our observations and previous findings suggests that Bi ions oscillate between local minima of the effective potential energy surface. These minima represent the monoclinic phase while the time-averaged structure is the cubic phase. We discuss the implication of these low-frequency oscillations on ion conduction., 4 pages, 4 figures

The anharmonic lattice dynamics of oxide and halide perovskites play a crucial role in their mechanical and optical properties. Raman spectroscopy is one of the key methods used to study these structural dynamics. However, despite decades of research, existing interpretations cannot explain the temperature dependence of the observed Raman spectra. We demonstrate the non-monotonic evolution with temperature of the scattering intensity and present a model for 2nd-order Raman scattering that accounts for this unique trend. By invoking a low-frequency anharmonic feature, we are able to reproduce the Raman spectral line-shapes and integrated intensity temperature dependence. Numerical simulations support our interpretation of this low-frequency mode as a transition between two minima of a double-well potential surface. The model can be applied to other dynamically disordered crystal phases, providing a better understanding of the structural dynamics, leading to favorable electronic, optical, and mechanical properties in functional materials.

We report a strongly temperature dependent luminescence Stokes shift in the electronic spectra of both hybrid and inorganic lead-bromide perovskite single crystals. This behavior stands in stark contrast to that exhibited by more conventional crystalline semiconductors. We correlate the electronic spectra with the anti-Stokes and Stokes Raman vibrational spectra. Dielectric solvation theories, originally developed for excited molecules dissolved in polar liquids, reproduce our experimental observations. Our approach, which invokes a classical Debye-like relaxation process, captures the dielectric response originating from an anharmonic LO phonon at about 20 meV (160 cm-1) in the lead-bromide framework. We reconcile the liquid-like picture with more standard solid-state theories of the Stokes shift in crystalline semiconductors.

In a large variety of applications the data for a variable we wish to explain is ordered and categorical. In this paper we present a new similarity-based model for the scenario and investigate its properties. We establish that the process is ψ-mixing and strictly stationary and derive the explicit form of the autocorrelation function (ACF) in some special cases. Consistency and asymptotic normality of the maximum likelihood estimator (MLE) of the model’s parameters are proven. A simulation study supports our findings. The results are applied to the Netflix data set, comprised of a survey on users’ grading of movies.