Phase-Field Methods in Materials Science and Engineering

This comprehensive and self-contained, one-stop source discusses phase-field methodology in a fundamental way, explaining advanced numerical techniques for solving phase-field and related continuum-field models. It also presents numerical techniques used to simulate various phenomena in a detailed, step-by-step way, such that readers can carry out their own code developments.

Features many examples of how the methods explained can be used in materials science and engineering applications.

PART I: Phase Transformation in Materials Science
1. Introduction to Phase transformations and microstructure formation in materials science
2. An example: Solidification of pure materials
3. Phase Transformations and Phenomenology of Landau
4. Phase field model for solidification in pure materials
5. Phase Transformations in binary alloys
6. Phase-field models of phase transformations in binary alloys
7. Applications to microstructure growth in binary alloys
8. Connection between phase-field and sharp-interface parameters
 
PART II: Elastic and Plastic Effects in Phase Transformations
1. Review of Mechanics of Materials
2. Overview of Modeling and Simulation Techniques in Mechanics
3. Phase-field Models
4. Applications: Effects of Elastic Stress on Thin Film Growth and Phase Transformations
 
PART III: Modeling Atomic Scale Systems using the Phase-Field Method
1. Phase field Modeling of Periodic Systems
2. Modeling Crystals with Phase Fields
3. Applications
 
PART IV: Numerical Solution Methods for simulating Phase-Field Models
1. Introduction to Numerical Methods for PDEs - Space Discretization
2. Iterative Methods for sparse Linear Systems
3. Numerical Methods for PDEs - Time Marching Schemes
4. Discretization of the Diffusion Equation
5. Discretization of Advection Diffusion Equations
6. Introduction to the Message Passing Interface (MPI)
7. Solved MPI Examples

• By (author) Nikolas Provatas
• By (author) Ken Elder