Katarzyna Tkacz-Śmiech

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.

Interdiffusion: compatibility of Darken and Onsager formalisms

Abstract A unified treatment of interdiffusion in various reference frames is presented in view of the consistency between Nernst–Planck, Onsager and Darken formalisms. A present discussion involves (i) material, (ii) laboratory and (iii) Rth component reference frames. It is shown that when the fluxes and forces are linearly interrelated, one can define a symmetric matrix of phenomenological coefficients. Its explicit form is derived. Problem is generalised to the case of different molar volumes that satisfy Vegard law, which presents entirely new result. An evidence is given that the Onsager fluxes can be equivalently treated as the fluxes due to the material drift and diffusion, as accounted in Darken treatment. The entropy production is the same within both formalisms.

Stability of a-C:N:H Layers Deposited by RF Plasma Enhanced CVD

A series of amorphous hydrogenated carbon layers doped with nitrogen (a-C:N:H) was deposited on Si (001). The synthesis was performed from gaseous N2/CH4 mixture using PE CVD (RF CVD technique; 13,56 MHz). An influence of the processing conditions on layer-growth rate was analysed. Thickness of the layers deposited during 1 hour at various temperatures, pressures and RF powers were taken as a basis. It has been proved that the substrate temperature is a key parameter for the layer formation. Temperature rise results in the deposition rate decrease. This unfavourable effect may be reduced by application of increased gas pressure and/or higher plasma RF generator power. At optimal conditions (46 oC; 0,8 Tr; 60 W) the deposition rate reaches up to 600 nm/hour. FT-IR spectra of the layers were measured within 1250 - 4000 cm-1 and discussed with regard to the atomic structure. The intensities of the characteristic absorption bands were compared. The results show that the layers have various N/C ratios according to the applied processing conditions.

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.

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.

A Morphology of Diffusion Zone from Entropy Production Calculations

Interdiffusion plays a significant role in the formation and stability of metallic joints and coatings. It is also of critical importance in designing advanced materials. Because commercial alloys are usually multicomponent, the key target is prediction of a complex morphology of the diffusion zone which grows between the alloys, alloy-coating, etc. In a two-component system, the diffusion zone can be composed of single-phase layers of the intermetallic compounds and solid solutions. The evolution of the composition and thicknesses of such layers are fairly well understood and consistent with the phase diagrams. The situation is qualitatively different in multicomponent systems. For example, the diffusion zone in a ternary system can be composed of single-and two-phase sublayers. Their number and thicknesses depend on the initial conditions, i.e. composition, component diffusivities and geometry of the system. The usual way of presenting the sequence of the layers and their compositions is by drawing adiffusion path which is, by definition, a mapping of the stationary concentrations onto the isothermal section of the equilibrium phase diagram. The diffusion path connects initial compositions of the diffusion couple and can go across the single-, two-and three-phase fields. It starts at the composition of one alloy and ends at the other. The possibility of mapping the concentration profiles onto the ternary isotherm has been postulated in one from the seventeen theorems by Kirkaldy and Brown [] for the diffusion path. The detailed presentation of all theorems was recently done by Morral []. Here we remind the reader only of the chosen ones (shown in italics).

Bi-velocity model of mass transport in two-phase zone of ternary system

Bi-velocity (Darken) method, which includes material drift and diffusion fluxes, is for the first time applied to describe mass transport in multiphase materials. The respective model is formulated in details and then applied for a ternary diffusion couple in which a two-phase zone can grow during isothermal diffusion. Thanks to the use of a phase-field order parameter, identified here with volume fraction of a chosen phase, the mass transport throughout both phases within a two-phase zone can be considered. The model allows smooth crossing of the type 1 boundary, which makes the mass transport equations valid in both single- and two-phase regions. The solution obtained for 1D geometry provides: (1) a diffusion path in the concentration triangle, (2) element-concentration profiles, (3) volume fractions of the phases in the two-phase zone and (4) drift-velocity distribution along x axis parallel to the mass transport. As an example, the interdiffusion in the diffusion couple of Type 0 boundary is modelled. The zigzag diffusion path is predicted and the profiles of the element concentrations are simulated. For the first time, the drift velocity for the diffusion in two-phase system is determined and correlated with the changes in volume fractions of the phases.

Dielectric and electric properties of synthetic melanin: the effect of europium ions

Detailed studies on dielectric and electric properties of synthetic pirocatechol and indolederived melanin, pure and doped with Eu3+, have been performed, D.C. and a.c. electrical conductivity as well as dielectric permittivity and loss angle tg have been investigated. Activation energy of d.c. conductivity for the investigated temperature range (0°C<T<50°C equals 0.63 eV for pirocatechol and 0.62 eV for indolemelanin. Europium ions Eu3+ doped to the samples do not influence the values of activation energy, but the addition of Eu3+ ions decreases the conductivity values. On the basis of depolarization current curves the energy of trap level referred to Eu3+ has been calculated. It equals 0.58 eV for pirocatechol and 0.60 eV for indolemelanin.