Andrzej Koleżyński

Crystal-chemical aspects of phase transitions in barium titanate

Abstract Structural aspects of phase transitions in barium titanate are analysed from a crystal-chemical point of view. The respective discussion is focused on two possible sources of ferroelectric deformation of TiO 6 8− octahedron. First, gradual changes of π-electron localisation are considered. Under an assumption of a mean field related to actual crystal symmetry, an adequate model is proposed. The values of bond orders are evaluated from resonance structures. They are compared with respective bond lengths. Another source of the ferroelectric deformation, which is taken into consideration, relates to the Ti-ion movements between eight potential minima on the cube diagonals. The analysis of the problem is grounded within adiabatic (local field) approximation and follows ideas of an eight-site model. The crystal structure is treated as a result of averaging of atomic positions according to the postulated disorder. Comparison of the X-ray interatomic distances with the values calculated from the disorder model is made. The collected data generally prove that the ferroelectric deformation of the TiO 6 8− octahedron, which is observed in barium titanate, contains two components. One is related to the changes of structural disorder degree and should be considered as a main factor. The other includes the effects attributed to the changes of π-electron localisation.

From the Molecular Picture to the Band Structure of Cubic and Tetragonal Barium Titanate

A band structure of barium titanate crystal has been calculated with the WIEN2k program, using FP LAPW method. A broad dispersion of the valence band (about 5 eV) and a narrow forbidden energy gap (about 2 eV) confirm the crucial role of covalent interactions in this compound. The calculations have been performed for cubic and tetragonal structures of the crystal, which have allowed to determine the changes in the electronic structure due to the ferroelectric phase transition. It is found that the transition between cubic and tetragonal structures does not change significantly either the bands widths or their positions in relation to the Fermi level. The main difference concerns the character of the bands and is clearly related to the oxygen electronic states. This indicates that the ferroelectric behavior of the material may be explained by the crucial role of the π bonds formed by the oxygen ions. The band structure obtained remains in direct relation to the molecular picture thus confirming ligand field theory.

The influence of the long-range order on the vibrational spectra of structures based on sodalite cage

Zeolites are a group of tecto-aluminosilicates with numerous practical applications, e.g. gas separators, molecular sieves and sorbents. The unique properties result from porous structure of channels and cages which are built from smaller units - the so-called Secondary Building Units (SBU), and sometimes also larger groups (Breck, 1974; Ciciszwili et al., 1974; Mozgawa, 2008; Čejka and van Bekkum, 2005). The aim of this study was the examination of the influence of long-range order on vibrational spectra of sodalite and zeolite A. Ab initio calculations (geometry optimizations and vibrational spectra calculations) of sodalite cage and selected SBU were carried out by means of Gaussian09 (Frisch et al., 2009) (in the case of isolated clusters) and Crystal09 (Dovesi et al., 2005, 2009) (for periodic structures). The obtained results were compared with the experimental spectra of sodalite and zeolite A crystal structures, synthesized under hydrothermal conditions. These results allowed analyzing of the long-range ordering influence on the vibrational spectra, as well as the identification of the characteristic vibrations in β cage based frameworks. It has been found, that based on small structural fragment (SBU) models a characteristic vibrations can be identify. However, full spectra analysis and especially the interpretation of far-infrared region of the spectra require using periodic models under the influence of translational crystal lattice.

Chemical bond in ferroelectric perovskites

Abstract The chemical bond in ferroelectric ABO3 perovskites has been considered as a mixed ionic-covalent one. The effect of covalency on the structure has been analyzed using valence bond theory. A particular attention has been paid to the π bond formation and resulting distortion of the lattice. A role of two ferroelectricity-driving parameters, ionic effective charges and oxygen octahedron volume, has been underlined in the light of overlapping of the orbitals forming (d←p)π bond. The phase transitions, which may occur in perovskite crystals, have been discussed from the point of view of electron charge localization.

Model potentials in studies of atomic electron density distribution

In density functional theory (DFT), a many-electron problem for the electron density in atoms may be reduced, according to the Kohn-Sham scheme, to a one-electron problem. In the present work, a variational model is proposed which leads, within some assumptions, to the set of equations describing the change of the electron density ρ and energy ϵ during the ionization process. It is shown that the one-electron density contributions are not necessarily spherically symmetric, but assume the symmetry which depends upon the symmetry of the positive field. A few nonspherically symmetric potentials are studied in the present article. The nonlinear differential equation for density r is formulated and solved for Coulombic, Fues-Kratzer, and Hartmann potentials. The solutions and some particular examples are presented.

Phase Transitions in BaTiO3 from IR Autocorrelation Spectrum

Temperature dependence of infrared spectrum from BaTiO 3 micro-crystals has been analysed. The measurements have been made within temperature range from 140 to 330 K in the IR region between 380 and 4000 cm−1 . The low temperature spectrum shows two clear bands at about 498 and 550 cm−1 that are in agreement with expectations for trigonal symmetry. The spectra at higher temperatures have the profiles that are difficult to be interpreted using a conventional peak fitting procedure. To explain the obtained results an autocorrelation method has been used for the frequency region between 480 and 700 cm−1 (where IR active vibrations occur). A special attention has been paid to the effects following the phase transitions. It has been possible to formulate some additional arguments concerning a complex character of the phase transitions in barium titanate with indication of an increasing role of order-disorder mechanism.

Pauling's electrostatic rule for partially covalent/partially ionic crystals

Abstract Second Paulings rule, known as the electrostatic rule, has been reformulated with regard to partial net charges in covalent–ionic crystals. For more uniform treatment, an idea of atomic ionicity coefficients (AIC) related to the respective bond ionicities (BI) is introduced. The proposed definitions are consistent with crystal-chemistry principles. Examples are presented, showing how the reformulated Paulings rule works for chosen compounds. Some other possibilities of applications of the model are also discussed. In particular, for the chosen crystals, the net charges of the ions have been calculated from a knowledge of the ionicities of the respective bonds and the BIs have been estimated from the ionic charges. A case concerning structures with non-equivalent anions is also discussed.

The structure, electrical properties and chemical stability of porous Nb-doped SrTiO3 – experimental and theoretical studies

A series of porous SrTi1−xNbxO3 samples (with x = 0, 1, 2 and 3 mol%) were prepared by wet synthesis and sintered at 1573 K. Single phase samples were obtained for each composition, as confirmed by XRD measurements. For all samples, aging tests in CO2/H2O atmosphere and electrochemical impedance spectroscopy measurements in air and hydrogen (reduced) atmosphere were carried out. Simultaneously, for model superstructures corresponding to 2 and 3 mol% experimental compositions, FP-LAPW DFT calculations of electronic structure and bonding properties (using QTAiM approach) were performed. Both experimental and theoretical results show an increase of cell parameters with increasing niobium amount. The influence of the amount of niobium on the microstructure of the synthesized samples as well as on their chemical stability was also observed. Electrical properties measurements showed different conduction mechanism for synthetic air and reduced atmosphere, i.e. mixed ionic-electron conduction and dominating electron conduction, respectively.

New approach for determination of the influence of long-range order and selected ring oscillations on IR spectra in zeolites

Vibrational spectroscopy can be considered as one of the most important methods used for structural characterization of various porous aluminosilicate materials, including zeolites. On the other hand, vibrational spectra of zeolites are still difficult to interpret, particularly in the pseudolattice region, where bands related to ring oscillations can be observed. Using combination of theoretical and computational approach, a detailed analysis of these regions of spectra is possible; such analysis should be, however, carried out employing models with different level of complexity and simultaneously the same theory level. In this work, an attempt was made to identify ring oscillations in vibrational spectra of selected zeolite structures. A series of ab initio calculations focused on S4R, S6R, and as a novelty, 5-1 isolated clusters, as well as periodic siliceous frameworks built from those building units (ferrierite (FER), mordenite (MOR) and heulandite (HEU) type) have been carried out. Due to the hierarchical structure of zeolite frameworks it can be expected that the total envelope of the zeolite spectra should be with good accuracy a sum of the spectra of structural elements that build each zeolite framework. Based on the results of HF calculations, normal vibrations have been visualized and detailed analysis of pseudolattice range of resulting theoretical spectra have been carried out. Obtained results have been applied for interpretation of experimental spectra of selected zeolites.

Periodic model of LTA framework containing various non-tetrahedral cations.

A simplified periodic model of Linde Type A zeolite (LTA) structure with various selected mono- and di-valent extra-framework cations was formulated. Ab initio calculations (geometry optimization and vibrational spectra calculations) using the proposed model were carried out by means of Crystal09 program. The resulting structures and simulated spectra were analyzed in detail and compared with the experimental ones. The presented results show that in most cases the proposed model agrees well with experimental results. Individual bands were assigned to respective normal modes of vibration and the changes resulting from the selective substitution of extra framework cations were described and explained.