Thermal properties of 2:1 bismuth borate: Temperature-dependent characterizations of lone electron pairs

Abstract

Applications of bismuth borate ceramics require understanding of the microscopic features, leading to macroscopic behaviors such as thermal expansion. We report the structural and spectroscopic features of Bi4B2O9 between 4 K and 900 K using a combination of temperature-dependent neutron and X-ray powder diffractions and Raman spectroscopy. Lattice thermal expansion was modeled using the Debye-Einstein-Anharmonicity (DEA) fit. The model also follows four independent thermal expansion tensors of the monoclinic system. Phonon density of states obtained from the density functional theory (DFT) calculations helps to understand the low Debye temperature calculated from the metric expansion as well as from the isotropic atomic displacement parameters. Both Wang-Liebau eccentricity (WLE) parameter and Liebau density vector (LDV) are calculated from the structural data and from the DFT calculation, respectively. Whereas, the dimensionless absolute value of WLE measures the degree of deformation of the electronic deformation density of the 6s2 lone electron pairs (LEPs) of the Bi3+ cations, LDV additionally shows the changes of the orientation of the LEP-lobes as function of temperature. Analyses of the temperature-dependent frequencies of some selected Raman modes support the choice of the elastic model of the Debye approach.