Numerical Methods in Alloy Design
Matrix and Phase-Field Approaches to the Cahn-Hilliard Equation
Rahul Basu
Modern alloy design depends on predicting how microstructure evolves—not only on equilibrium phase diagrams. This book develops the numerical tools needed to solve the Cahn-Hilliard equation and related phase-field models, and shows how to use them for real materials problems.
What you will learn
• Finite-difference and Fourier spectral methods for Cahn-Hilliard dynamics
• Matrix formulations, mixed (concentration-chemical potential) systems, and conjugate-gradient solvers
• Quasi-steady and slowly varying reductions for ageing and coarsening
• Putzer and Apostol matrix-exponential methods for linearised blocks
• One-dimensional solvers, verification tests, and MATLAB/Python implementations
Materials applications
• Order-disorder transformations
• Nickel-base superalloys (? / ?')
• High-entropy alloys
• Steels and Fe-Cr-type spinodals
• Amorphous alloys and bulk metallic glasses
• Ceramics and functional oxides
• Miscibility gaps and nanoalloys
Each major method is illustrated with non-dimensional spinodal benchmarks (mass conservation, free-energy decay, interfacial width). Appendices collect runnable Python and MATLAB codes, matrix derivations, display-form equations, and a consolidated reference list.
Who it is for
Graduate students, PhD researchers and materials engineers who need working numerical methods—not only formal PDE theory—for phase separation and alloy design.
Formats
Ebook (EPUB) and print editions via StreetLib.
