No description available.

The problem solved in this thesis is one of transient linear heat conduction in a two layer, three-dimensional slab subjected to an arbitrary heat flux on one surface, where each layer is thermally orthotropic. The sides and bottom of the slab are either insulated (Bi = 0) or held at a constant temperature (Bi = infinity). The Biot number of the top surface varies from zero to infinity. The solution is developed by decomposing the problem into a number of simpler problems, each of which is solved using eigenfunction expansions. In the vertical direction, the eigenvalue problem is solved using the Krawczyk algorithm, and an orthogonality relationship is found by Vodicka's method.

No description available.

Decompositions of solids are typically of the form: A(s) ----> B(s) + gases. Symmetry-controlled routes (based on known and hypothetical crystal structures) for transforming the solid reactant into the solid product were devised as possible decomposition pathways. Lattice energies of the reactants, of the postulated transient intermediate structures and of the final solid products were then estimated by crystal modelling procedures. Profiles of lattice energy changes during the proposed decomposition routes were constructed and any energy barriers were compared with experimental activation energies reported for the thermal decompositions. The crystal modelling was performed with the computer program WMIN. Calculation of the lattice energies involved the development of a model potential for the perfect lattice and the evaluation of the interatomic parameters. The potential was based on the Born model of ionic solids using the Buckingham potential (Ø(r)= Ae⁻r/p - C/r⁶) to describe the short-range energy contribution. Empirical fitting was used to establish reliable interatomic energy parameters. The reliability of the interatomic potentials was assessed by calculating crystal structures and lattice energies (which were not included in the fitting). The particular reactions selected for modelling were the decompositions of the alkaline-earth metal (Ca, Sr, Ba) peroxides and carbonates: M0₂(s) ---> MO(s) + ¹/₂0₂(g) MC0₃(s) ---> MO(s) + CO₂(g)The lattice energies calculated for the known structures were in good agreement with reported values, (except for Ba0₂ and BaC0₃) which provided support for the adequacy of the potential model used. Activation energies calculated for the decomposition of the carbonates were in the correct order but hlgher than experimental values, i. e., 422, 422, 465 and 499 kJ mol̄̄⁻¹ compared to the experimental values of 205, 87(?), 222 and 283 kJ mol̄̄⁻¹ for CaC0₃ (calcite), CaC0₃(aragonite), SrC0₃ and BaC0₃. The values calculated for the peroxides (91 and 100 kJ mol⁻¹ compared to the experimental values of 119 and 185 kJ mol⁻¹ for Sr0₂ and Ba0₂ respectively) were less satisfactory but could be a reflection of the poor structural data used for the peroxides. The significance of this approach to the modelling of solid decompositions is discussed.

The isothermal, endothermic, stepwise decomposition of ammonium metavanadate (AMV) in inert (argon or nitrogen), oxidising (air or oxygen) and reducing (ammonia) atmospheres as well as under high vacuum (pressure < IOn bar) conditions has been investigated. The reverse reaction, the isothermal recombination of V₂ 0₅ with ammonia and water vapour has also been investigated. The decomposition and recombination reactions were followed by continuously recording the mass loss of the sample with time using a Cahn R.G. Automatic Electrobalance. This enabled small samples ( ~ lOmg) to be used and consequently any self cooling of the sample during the decomposition was minimized. The intermediates and final products formed have been characterized by chemical analysis, X-ray powder diffraction studies, infrared spectroscopy and the mass loss involved in their formation. The changes in the physical properties of the samples during decomposition and recombination have been investigated by surface area measurements (using the BET method and krypton adsorption) and eIectron microscopy. Values for the enthalpy changes involved in the decomposition have been obtained by differential scanning calorimetry. The stoichiometry of the isothermal decomposition of ammonium metavanadate, under the various conditions of surrounding atmosphere has been discussed. Except for the later stages of the decomposition in ammonia, the results correspond well to the gradual reduction of the ratio of "(NH₄)₂ 0" to "V₂0₅" units from the original 1:1 ratio in ammonium metavanadate to pure "V₂0₅" with ammonia and water being evolved throughout the decomposition in the mole ratio of 2:1. The final product of the decomposition in vacuum, argon and air is "V₂0₅" and in ammonia, below 360°, V0₂. The kinetic parameters for each of the stages of the decomposition of AMV in each of the atmospheres studied have been determined. The mechanism of the first stage of the decomposition under the different conditions of surrounding atmosphere has been discussed from both the kinetic and the thermodynamic points of view. The absolute reaction rate theory has been applied to the decomposition in inert atmospheres enabling the formulae of the activated complexes formed during each stage to be calculated. It has also been shown that the detailed atomic movements occurring during the first stage of the decomposition in ammonia can be predicted from a knowledge of the stoichiometry of the reaction and of the detailed crystal structures of the starting and product materials. The kinetics and mechanism of the recombination of "V₂0₅" with ammonia and water vapour to form AMV have also been discussed in detail.

[From Introduction] The first step in the study of the thermal decompositions of solids is an examination of the kinetics, since this casts much light on the mechanism of the reaction. It must be borne in mind, however, that a theoretical expression, derived on the basis of a particular mechanism, even if it fits the observed experimental results, is not conclusive proof of the validity of the mechanism when applied to the decomposition under examination.

At the high-temperature conditions of the Earth's interior, lattice anharmonic effects in crystalline mineral phases can become pronounced. Anharmonicity, i.e., deviations of vibrations from harmonic oscillations, is caused by phonon-phonon interactions. Knowledge of lattice anharmonicity is essential to elucidate distinctive thermal properties in solids. Yet, accurate investigations of anharmonicity encounter difficulties owing to cumbersome computations. Here we present anharmonic property calculations with the phonon quasiparticle approach for various solids. The phonon quasiparticle approach efficiently and reliably addresses lattice anharmonicity by combining molecular dynamics and lattice dynamics calculations. It characterizes anharmonic phonons by extracting renormalized frequency and phonon lifetime from the mode-projected velocity autocorrelation function without explicitly computing higher-order interatomic force constants. In principle, it accounts for full anharmonic effects and overcomes finite-size effects typical of molecular dynamics. The validity and effectiveness of the current approach are demonstrated in computations of temperature-induced frequency shifts, anharmonic thermodynamics, phase boundaries, and lattice thermal conductivities of both weakly and strongly anharmonic, both insulating and metallic, and both simple and complex systems. These materials include a simple model crystal, Si with diamond structure, minerals of geophysical significance, MgSiO₃ perovskite and postperovskite, cubic CaSiO₃ perovskite, and B8 and B2 phases of FeO. Accurate anharmonic thermodynamic properties, phase boundaries, and lattice thermal conductivities presented in this thesis are important for geodynamic modeling. The theoretical framework validated in this thesis also enables predictive studies of various anharmonic materials which could not be previously addressed by conventional approaches, such as quasiharmonic approximation for thermodynamics calculations and finite displacement method for anharmonic lattice dynamics calculations.