Faseveld

Faseveld, or phase-field, is a computational modeling framework used to simulate how microstructures evolve in materials. It represents different phases, components, or orderings with continuous field variables rather than tracking sharp interfaces, allowing complex morphologies to develop without explicit interface tracking. The central idea is to describe the state of a material with an order parameter, often denoted phi, which varies smoothly across space and time.

The phase-field approach derives evolution equations from thermodynamic principles. A free-energy functional F[phi, ...] encodes bulk phase preferences, interfacial energy, and other physical effects. The interface between phases becomes a diffuse region whose thickness is controlled by model parameters. Two common classes of equations are the Allen-Cahn equation for non-conserved order parameters and the Cahn-Hilliard equation for conserved quantities such as composition. Realistic models may couple phi to other fields, including temperature, stress, and fluid flow, leading to multi-field phase-field systems.

Extensions of the method cover multiple phases, anisotropy in interfacial energies, elasticity, plasticity, and hydrodynamics. This makes phase-field suitable for simulating solidification and dendritic growth, spinodal decomposition, grain growth, recrystallization, and polymer or alloy blends. It is widely used in materials science and engineering to study microstructural mechanisms that influence properties like strength, toughness, and diffusivity.

Numerical implementation typically relies on finite-difference, finite-element, or spectral methods, often with adaptive meshing and stabilization techniques to handle stiff equations. While powerful, phase-field simulations can be computationally intensive and require careful calibration of parameters to reflect real materials. The approach originates from diffuse-interface theory developed in the mid-20th century and gained prominence in phase-field modeling during the 1990s and beyond.