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The necessary heat treatment of single-crystal semi-insulating gallium arsenide (GaAs), which is deployed in micro-and optoelectronic devices, generates undesirable liquid precipitates in the solid phase. The appearance of precipitates is influenced by surface tension at the liquid-solid interface and deviatoric stresses in the solid.The central quantity for the description of the various aspects of phase transitions is the chemical potential, which can be additively decomposed into a chemical and a mechanical part. In particular, the calculation of the mechanical part of the chemical potential is of crucial importance. We determine the chemical potential in the framework of the St. Venant-Kirchhoff law, which gives an appropriate stress-strain relation for many solids in the small-strain regime. We establish criteria that allow the correct replacement of the St. Venant-Kirchhoff law by the simpler Hooke law.The main objectives of this study are the following: (i) we develop a thermomechanical model that describes diffusion and interface motions, which are both strongly influenced by surface tension effects and deviatoric stresses, (ii) we give an overview and outlook on problems that can be posed and solved within the framework of the model, and (iii) we calculate non-standard phase diagrams for GaAs above 1059 K, i.e. those that take into account surface tension and deviatoric stresses, and we compare the results with classical phase diagrams without these phenomena.

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SUMMARYWe present a mathematical model of impulse resistance welding. It accounts for electrical, thermal and mechanical e ects, which are non-linearly coupled by the balance laws, constitutive equations and boundary conditions. The electrical e ects of the weld machine are incorporated by a discrete oscillator circuit which is coupled to the ÿeld equations by a boundary condition. We prove the existence of weak solutions for a slightly simpliÿed model which however still covers most of its essential features, e.g. the quadratic Joule heat term and a quadratic term due to non-elastic energy dissipation. We discuss the numerical implementation in a 2D setting, present some numerical results and conclude with some remarks on future research.