X-ray diffraction study of the atomic interactions, anharmonic displacements and inner-crystal field in orthorhombic KNbO₃

Abstract

An X-ray diffraction study aimed at establishing the subtle details of the electron density and anharmonicity of the atomic vibrations in a stoichiometric monodomain single crystal of potassium niobate, KNbO3, has been conducted at room temperature (orthorhombic ferroelectric phase Amm2). The cation and anion displacements obtained from the experiment are weakly anharmonic without any manifestation of structural disorder. The chemical bond and interatomic interactions inside and between crystal substructures at the balance of intracrystalline forces are characterized in detail. The role of each of the ions in the formation of the ferroelectric phase was studied and the features of the electron-density deformation in the niobium and oxygen substructures, and the role of each of them in the occurrence of spontaneous polarization are established. The position-space distribution of electrostatic and quantum forces in KNbO3 is restored. It is emphasized that for the completeness of the analysis of the nature of the ferroelectric properties it is necessary to consider both static and kinetic electronic factors, which are of a quantum origin. The experimental results and theoretical estimations by the Kohn–Sham calculation with periodic boundary conditions are in reasonable agreement, thus indicating the physical significance of the findings of this study.

Real‐Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields**

“…[15] However, although f k -basins (pseudoatoms) and corresponding kinetic force field have a robust physical definition, it is not clear for now how they can be exploited to retrieve chemical information. [15,20,64,72] In this work, we generalize the described methodology to different kinds of chemical bonds present in a diverse set of selected crystals, including polar and nonpolar covalent bonds, ionic ones, and classical and nonclassical hydrogen bonds, as well as several weak to moderate intermolecular interactions. By combining the approach of superposing 1-and f-basins with the study of the behaviour of electronic potentials and corresponding forces, [15] we arrived at a phenomenological partitioning scheme of many-nuclear many-electron systems, which enables us to further understand the complex atomic structure of electron occupier revealed by different basin boundaries and phenomena of charge transfer and subsequent exchange, electron sharing, and chemical bonding.…”

“…Further, the gap between ‐ and ‐basins is attributed to phenomena of interatomic charge (electron) transfer and can be used to estimate it [15] . However, although ‐basins (pseudoatoms) and corresponding kinetic force field have a robust physical definition, it is not clear for now how they can be exploited to retrieve chemical information [15,20,64,72] …”

Unified Picture of Interatomic Interactions, Structures, and Chemical Reactions by Means of Electrostatic and Kinetic Force Density Fields: Appel’s Salt and Its Ion Pairs

“…It is worth noting that the FAEM scriptF ( r ) and Ehrenfest force density frakturH ( r ) exhibit similar behavior, topology, and physical meaning, , but scriptF ( r ) , as well as the other abovementioned force fields F i ( r ), is accessible from experimental ED distributions in crystals applying the ideas of the orbital-free density functional theory (OF DFT). , In particular, the behavior of FAEM scriptF ( r ) and kinetic force F k ( r ) in crystals obtained from experimental data has recently been described in detail on the several examples. − ,,, The behavior of frakturH ( r ) in calculated systems has also been the subject of fruitful research. − …”

WinXPRO, 3DPlot and TrajPlot computer software: new options for orbital-free quantum crystallography studies

“…This approach arose recently from studies of electron density in crystals (Tsirelson & Ozerov, 1996;Gatti & Macchi, 2012;Stalke, 2012) within the framework of the orbital-free density functional theory (Wesolowski & Wang, 2013), information theory (Nalewajski, 2006), and an extension of Bader's quantum theory (Bader, 1990) of atoms in molecules and crystals Tsirelson, 2007). Early work has demonstrated the effectiveness of this approach (Shteingolts et al, 2021;Stash et al, 2021;Bartashevich et al, 2021). We report here the release of a software package consisting of the WinXPRO (version 3.4.51), 3DPlot (version 2.5.26) and TrajPlot (version 1.4.0.2) programs.…”