Lattice dynamics of crystals havingR2MX6structure

Abstract

The theory of lattice dynamics in the harmonic approximation using a rigid-ion model due to Born and Huang ͓Dynamical Theory of Crystal Lattices ͑Oxford University Press, New York, 1954͔͒, is applied to ionic crystals of the R 2 M X 6 type with antifluorite structure namely, K 2 SnCl 6 , K 2 PtBr 6 , Cs 2 SnBr 6 , and Rb 2 SnBr 6 in the cubic phase. The model expresses the potential energy as the sum of long-range Coulomb interactions and repulsive short-range interactions between ions in the primitive cell. A function of axially symmetric type is used to approximate the short-range part, and the number of force constant parameters were reduced utilizing stability conditions in the manner described by Katiyar ͓J. Phys. C 3, 1087 ͑1970͔͒. The remaining constants were determined by a nonlinear least-squares analysis of some experimental frequencies at the critical point ⌫. The long-range contributions were calculated using the Ewald transformation as described by Cowley ͓Acta Crystallogr. 15, 687 ͑1962͔͒. Phonon frequencies and the normal modes of vibrations at the zone center were obtained; of particular interest is the resulting lowest librational frequency for each crystal. We obtained excellent agreement between the calculated and the observed frequencies. The resulting effective charge parameters indicated that these crystals are partially ionic. In general, the results offered a better vision of the structural phase transition mechanism involving the rotational mode T 1g .

Acid‐ and Base‐Stable Cs2Pt(Cl,Br)6 Vacancy‐Ordered Double Perovskites and Their Core–Shell Heterostructures for Solar Water Oxidation

“…[ 39 ] Due to the alternate vacant octahedra in A 2 BX 6 , the whole octahedra can vibrate as a rigid body resulting in a third IR active mode of vibration. Three IR active mode of vibration for the R 2 MX 6 crystal structure was also reported by Torres et al [ 40 ] The highest, intermediate, and lowest wavenumber vibrational peaks were assigned to X‐Sn asymmetric stretching, X‐Sn‐X asymmetric bending and vibration of [SnX 6 ] 2− octahedra as a rigid body against Cs + cation respectively. [ 41 ] The Cs 2 PtCl 6 showed three IR active peaks at 328, 184, and 67 cm −1 (Figure 1b) and the peaks are assigned to Pt–Cl asymmetric stretching, Cl–Pt–Cl asymmetric bending and vibration of [PtCl 6 ] 2− octahedra as a rigid body, respectively.…”

OPTOELECTRONIC STUDY OF DOUBLE PEROVSKITE Rb2SnBr6: A FIRST PRINCIPLES CALCULATIONS

“…Structural PropertiesRb2SnBr6 crystallized in face-centered cubic crystal with space group Fm-3m (#225) is shown in Figure1. The optimized lattice parameter is 10.75 Å which is near to the investigational (Å[25].…”

The Fabrication of Lead‐Free Cs2SnI6 Perovskite Films Using Iodine‐Rich Strategy for Optoelectronic Applications

“…Room-temperature Raman analysis of the fabricated films was performed using 633 nm excitation wavelength to complement the XRD results and probe the vibration property of the I 2 -rich Cs 2 SnI 6 film. Theoretical studies [42,43] have suggested that the ten normal modes are present in the vibrational spectrum, including one IR active, one acoustic, two silent, and four Raman active. Among the active Raman modes in Cs 2 SnI 6 perovskite, three are associated with [SnI 6 ] 2À octahedral and one is related to the vibration of Cs atoms in the rigid [SnI 6 ] 2À lattice.…”