Mathematics of Microstructure Evolution

Materials science is a growth area for applied mathematics in the United States. This is the fourth in a series of monographs sponsored by the Electronic, Magnetic and Photonic Materials Division of TMS, and it contains modern mathematical methods presented in a tutorial way through the joint efforts of both mathematicians and materials scientists. Coverage includes: surface evolver as a tool for materials science research; edge-energy minimizing surfaces; the thermal stability of alloys having a periodic minimal surface microstructures; real-space lattice statics description of a random lattice; computer simulations of phase decomposition in real-alloy systems based on a discrete-type diffusion equation; on the physics of self-organizing microstructual evolution; the mathematics of processing for material microstructuring; and modelling and control of advanced chemical vapour deposition processes.

Table of Contents:
Surface evolver as a tool for materials science research, W.C. Carter; the simulation of two-dimensional grain growth by the surface evolver, K. Marthinsen; edge-energy minimizing surfaces, M.J. Kelley; zener pinning of normal grain growth, J. Gao; the thermal stability of alloys having periodic minimal surface microstructures, B. Fultz and L. Anthony; modelling magnetostrictive microstructure under loading, R. James et al; Ma microlocal forces and precursor oscillations, D. Brandon and R.C. Rogers; real-space lattice statics description of a random lattice, J.R. Willis and T.J. Gosling; modulated patterns and pinning effect in phase-separating alloys, A. Onuki; discrete atom method for morphological evolution of coherent particles, J.H. Choy; computer simulations of phase decomposition in real alloy systems based on a discrete-type diffusion equation, T. Miyazaki and T. Koyama; equilibrium particle morphologies in elastically stressed solids, M.E. Thompson and P.W. Voorhees; anisotropic interface motion, J.E. Taylor; thermodynamic driving forces and equilibrium in multicomponent systems with anisotropic surfaces, J.W. Cahn and J.E. Taylor; analysis of anisotropic characteristics of dislocation loop morphology, D. Schwendeman and K. Rajan; on the physics of self-organizing microstructural evolution, J.S. Kirkaldy; the geometrical phase transformations during evolution in finite media, V.Ya. Shur et al; phase-field modelling of crystal growth - new asymptotics and computational limits, A. Karma and W.-J. Rappel; phase field instabilities and adaptive mesh refinement, R.F. Almgren and A.S. Almgren; microstructural evolution and grain growth kinetics in a two-phase solid with quadrijunctions, D. Fan and L.Q. Chen; anisotropic interfaces and ordering in fcc alloys - a multiple-order-parameter continuum theory, R.J. Braun et al; diffusional phase transformations on the atomic scale - experiment and modelling, J.M. Hyde et al; non-classical nucleation and growth of ordered domains in a disordered matrix, R. Poduri and L.Q. Chen.