Bruce R. Patton

Grain growth in anisotropic systems: comparison of effects of energy and mobility

Grain growth in systems of anisotropic grain boundary energy and mobility is investigated by computer simulations in a two-dimensional textured polycrystalline system. The energy and mobility are allowed to depend on both grain boundary inclination and misorientation. Mobility anisotropy alone does not significantly change the growth kinetics or statistical distributions of misorientation, grain size and number of grain edges, even though grain shapes evolve in a self-dissimilar fashion where the aspect ratio of grains and inclination distribution of grain boundaries are time dependent. Energy anisotropy, however, causes significant deviation of grain growth kinetics, misorientation and edge-distributions from the ones observed in isotropic systems. Moreover, misorientation distribution is skewed towards low energy (special) boundaries. Size distributions are similar in all cases. Mobility anisotropy influences grain growth kinetics only when energy is also anisotropic. Variation of misorientation distribution with time plays the key role in determining the grain growth behavior.

Generalized phase-field model for computer simulation of grain growth in anisotropic systems

We study the dynamics and morphology of grain growth with anisotropic energy and mobility of grain boundaries using a generalized phase field model. In contrast to previous studies, both inclination and misorientation of the boundaries are considered. The model is first validated against exact analytical solutions for the classical problem of an island grain embedded in an infinite matrix. It is found that grain boundary energy anisotropy has a much stronger effect on grain shape than that of mobility anisotropy. In a polycrystalline system with mobility anisotropy, we find that the system evolves in a non-self-similar manner and grain shape anisotropy develops. However, the average area of the grains grows linearly with time, as in an isotropic system.

Conduction and Gas–Surface Reaction Modeling in Metal Oxide Gas Sensors

A phenomenological approach to the operation of metal oxide gas sensors, the Integrated Reaction Conduction (IRC) model, is proposed which integrates the gas-surface reactions with the electrical conduction process in a weakly sintered, porous metal oxide. An effective medium approximation is employed to relate the mesoscopic microstructure and the carrier depletion at the granular surface to the macroscopic electrical conduction. For a given ambient gas concentration and temperature, the electron concentration in the depletion layer is calculated from the gas-surface reaction kinetics. The adsorption and oxidation reaction energies of the gas sensing reactions are extracted for a TiO2-x CO sensor by comparing experimental data with three-dimensional plots of IRC model resistance as a function of the ambient [CO(g)] and temperature. The IRC model predicts novel properties of the gas sensor, including the sensitivity and the response range, which depend on the doping of the sensor material, the temperature, the grain size, and the geometry of the necks between grains.

On the theory of grain growth in systems with anisotropic boundary mobility

Abstract We analyze grain growth kinetics in systems with anisotropic grain boundary mobility. In contrast to most previous studies of grain growth dynamics, we relax self-similarity assumptions that strongly constrain the dynamics and statistics during microstructural evolution in polycrystalline materials. We derive analytical expressions for the average growth rate within each topological class of n -sided grains as well as for the growth rate of the average grain area; we explain the results using underlying symmetries. Although anisotropic grain growth may in general be non-linear in time, we show, even in the absence of the self-similarity constraint, that the evolution kinetics obeys the von Neumann–Mullins relationship in the two limiting cases of textured and fully random microstructure with a time dependence solely determined by changes in the misorientation distribution. Our analytical results agree well with recent computer simulations using a generalized phase field approach.

Numerical Calculation of Electrical Conductivity of Porous Electroceramics

A numerical method for the calculation of the electrical conductivity of porous ceramics for gas sensing applications is developed, which takes into account detailed microstructural features by mapping a mesoscopic irregular resistor network onto the microstructure. The overall conductance of the ceramic sample is obtained by solving the Kirchhoff equations for the irregular network using an efficient iterative algorithm. The method is designed to handle the widely varying conductivities of different microstructural components present in ceramic gas sensors. The evolution of the macroscopic conductance of the model systems during a phase field simulation of sintering is obtained and several characteristic stages are distinguished. The potential applications of the method in computer aided microstructural optimization for ceramic gas sensors is discussed.

Anomalous magnetic properties of Y1−xScxBa2Cu3O7−δ

Abstract We report here anomalous magnetic behavior in the Y 1− x Sc x Ba 2 Cu 3 O 7− δ series where x varies from x = 0 to x = 0.5. With increasing Sc concentration, there is a decrease in the density of states. The occurrence of a large paramagnetic spin equivalent to 2.7 μ B per Sc and an increase in the residual resistivity as well as the temperature dependence of the resistivity. It is suggested that these effects may be caused by antisite disorder and increased tendency of Sc toward covalent bonding. Changes in the density of states and possible localization by doping with Sc are discussed.

Magnetic behavior of the high Tc composite compound of Y1Ba2Cu3O7-δ in the superconducting phase

Abstract Detailed measurements of the magnetic properties in the superconducting state of a composite sample with approximately 35% Y1Ba2Cu3O7-δ and a Tc of 87K are compared with results on a corresponding single phase sample. The susceptibility is approximately linear in temperature below and near Tc indicating large magnetic field penetration near the transition. At low temperatures, a volume flux expulsion of 5% is found in lowest magnetic field, with Hc1 indicated to be 1.5kG. Magnetization loops are presented, showing hysteretic behavior even at 4.2K and 100G. At higher temperatures, the magnetization curves bear a striking resemblance to those for a large κ type II superconductor. The Curie susceptibility associated with spin in the non-superconducting phase remains unscreened below Tc in sharp contrast to the behavior of the rare earth 1-2-3 compounds, indicating that the magnetic flux percolates easily through the composite.

Measurement of Fluctuation-Enhanced Conductivity Above Tc in Y-Ba-Cu-O

We have made careful measurements of the resistivity vs. temperature in a sample of polycrystalline YBa2Cu3O7-δ and have fit the data to a theoretical expression for the fluctuation-enhanced conductivity in the normal state. From this fit, we infer a value for the zero-temperature Ginzberg-Landau coherence length ξ(0) of 21±5A.

Second Critical Point in First Order Metal-Insulator Transitions

For first order metal-insulator transitions we show that, together with the dc conductance zero, there is a second critical point where the dielectric constant becomes zero and further turns negative. At this point the metallic reflectivity sharply increases. The two points can be separated by a phase separation state in a 3D disordered system but may tend to merge in 2D. For illustration we evaluate the dielectric function in a simple effective medium approximation and show that at the second point it turns negative. We reproduce the experimental data on a typical Mott insulator such as MnO, demonstrating the presence of the two points clearly. We discuss other experiments for studies of the phase separation state and a similar phase separation in superconductors with insulating inclusions.

Monte Carlo study of a bond-diluted q -state clock model: A simple representation for the glass transition

We consider the idea of bond ordering as a model for glass transition: a generic covalently bonded liquid may substantially reduce its energy through bond ordering, without undergoing significant structural order. This concept is developed for a model system using quantities such as a bond order parameter and susceptibility which provide new identification for calorimetric glass transition temperature. Monte Carlo simulation results exhibit bond ordering at intermediate temperatures uncorrelated with any long-range structural ordering. Also discussed are various other implications of bond-ordering model for glass transition.