Phase-field method
What ? Why ? How ?
Embedded Files
What ?
What ?
The phase-field method is an advanced computational technique for modeling and simulating the complex physical processes that drive microstructure evolution in materials. It helps study phenomena such as solidification, grain growth, spinodal decomposition, precipitation and fracture mechanics and is widely applied in materials science, physics, and engineering.
Essentially, the phase-field method uses one or more continuous field variables (= the phase-field), which are a function of space and time, to represent different states or phases within a material. These variables transition smoothly across interfaces (= diffuse interface approach), eliminating the need to explicitly track the moving domain boundaries. This makes it possible to mathematically handle the evolution of complex domain shapes. The evolution of phase-fields is governed by partial differential equations derived from thermodynamic principles and physical theories.
Left: Diffuse interface representation of a grain boundary using 2 phase-fields.
Right: Diffuse interface representation of a ternary 2-phase microstructure using 1 phase-field and 2 concentration fields.
Why ?
Why ?
The phase-field method offers several key advantages
The phase-field method offers several key advantages
Naturally handles complex grain shapes, morphological evolution, and interface conditions.
Captures a wide range of microstructure phenomena, including multi-phase and multi-component evolution, and accounting for various competing driving forces and transport processes.
Adaptable to various numerical frameworks, such as finite differences, finite elements and spectral techniques.
Integrates seamlessly with multi-physics and multi-scale approaches making it a key method of Integrated Computational Materials Engineering (ICME).
The phase-field method has become an indispensable tool for tailoring material properties, enabling researchers and engineers to design advanced materials more efficiently and in less time.
Inputs, outputs and usage
Inputs, outputs and usage
The phase-field method requires the following inputs
The thermodynamic and kinetic properties of the phases and interfaces present in the system, which may depend on temperature, composition and grain orientation.
The initial microstructure, either obtained from a digitized experimental micrograph or generated synthetically.
The externally applied conditions, such as temperature, pressure, mechanical loading, external magnetic end electric fields, and oxygen or hydrogen activity.
Using this information, the phase-field method simulates the evolution of grain structures and spatial variations in composition over time. As output, it generates a time series of microstructures, providing information on the size, shape and spatial distribution of grains and phases, as well as spatial variations in composition.
This output can be used for various purposes :
Model validation by comparing simulated microstructures with experimental micrographs to refine input parameters or verify hypothesized mechanisms
Gaining insights into how composition and environmental conditions influence grain structure evolution
Train surrogate models, which can be integrated into macroscopic finite element simulations and used to predict and optimize macroscopic material properties
Further reading
Further reading
An introduction to phase-field modeling of microstructure evolution : Basic introduction to the different aspects of phase-field modeling.
Phase field modeling in extractive metallurgy : This review discusses the basics and some more advanced aspects of phase-field modeling. It has a focus on extractive metallurgy applications, however, the principles described are generally applicable.
Phase-field method of materials microstructures and properties: recent success stories of applying the phase-field method to understanding, discovering, and designing mesoscale structures and materials.
(c) 2025, Nele Moelans. Last update Oct 2025.
Page updated
Google Sites
Report abuse