Numerical Methods in Alloy Design

The book develops matrix methods, finite-difference and Fourier spectral schemes, quasi-steady reductions and classical matrix exponential techniques (Putzer and Apostol formulas) side by side. Each is tested on spinodal-alloy benchmarks with worked numerical examples. You will see how to check mass conservation and free-energy decay, compare Newton–conjugate-gradient steady-state solvers, study interface width and parameter effects, and verify numerical results against analytical solutions (tanh interfaces, travelling waves, Laplace-transform and series solutions).

The second half applies these methods to real alloy design problems:

order–disorder transformations and the Allen–Cahn equation superalloys and gamma/gamma-prime microstructures high-entropy alloys steels and Fe–Cr spinodal systems amorphous alloys and bulk metallic glasses ceramics, oxides and battery-electrode particles nanoalloys and size-dependent phase separation miscibility gaps and CALPHAD-style free-energy inputs What you get

26 chapters moving from theory to implementation, plus a model spinodal alloy used as a running example ready-to-run Python and MATLAB programs, with the complete source printed in the appendices symbolic solutions using Wolfram Language literature reviews, annotated references and a consolidated bibliography a subject index and an index of numerical examples Whether you are building a phase-field simulation, choosing a time-stepping scheme, checking a code against analytical results, or screening composition and temperature in a miscibility-gap design, this book gives you the methods and the code to start.

Keywords: Cahn–Hilliard equation, spinodal decomposition, phase-field modelling, alloy design, microstructure simulation, coarsening, matrix exponential, spectral methods, Python, MATLAB, computational materials science.