:orphan: .. status publishable .. product PhaseField .. sectionauthor Leonid .. SME Leonid .. PR Kyle .. TW Katherine .. date 2026 .. keywords: phase field, finite elements, microstructure, simulation, elasticity .. _phasefieldDTS: |medea| *PhaseField* - Simulate years of microstructure evolution—in minutes -------------------------------------------------------------------------------- .. admonition:: **At-a-Glance** The |medea|\ :sup:`®`\ [#TM]_ *PhaseField* module employs the phase field method to predict grain growth, phase separation, other microstructural evolution phenomena, and stress response in metal alloys, organic materials, and ceramics at length and time scales inaccessible to atomistic simulation methods. **Key Benefits** * *Models Realistically the microstructural evolution in diverse materials* * *Accesses time and length scales of days and micrometers, unreachable with atomistic simulations* * *Accepts material property input available from first principles and atomistic |medea| modules* * *Flexible and scalable finite element-based simulations* Phase field modeling is the method of choice for simulating material microstructures, enabling prediction of properties like mechanical strength, phase transitions, and environmental degradation behavior. By simulating the evolution of material phases under different conditions, |medea| *PhaseField* can predict behaviors like grain growth, phase separation, corrosion and hydriding behavior, stress evolution, crack initiation and propagation, nucleation, and much more. |medea| *PhaseField* is a versatile finite element based solver [#Anderson]_ for coupled phase field, mass transport, and linear elasticity equations. This coupling enables detailed simulations of microstructure evolution in metals, ceramics, and other materials in which mechanical properties are influenced by phase changes. *PhaseField* supports diverse boundary conditions and initial conditions, making it applicable to a wide range of real world scenarios. The user defines an initial microstructure and phase properties such as free energies, bulk diffusion coefficients, and interfacial properties such as interface energies and grain boundary diffusivities. Also the temperature dependence of these properties can be specified, if known, to simulate thermal treatment of materials. If unknown, many such properties can be calculated directly from first principles or atomistics using |medea|’s powerful tool suite. Once a simulation is initialized, the finite element grid evolves adaptively, even to complex geometries, as the simulation progresses, enabling optimal trades between fidelity and speed. .. figure:: /Datasheets/images/PhaseField.png :align: center :width: 3.2in Examples of phase-field modeling applications for microstructure evolution with |medea| *PhaseField*. (a) Martensitic transformation showing variant selection and plate morphology, (b) pore network evolution with intergranular crack propagation, (c) cuboidal precipitate formation in a matrix phase, (d) columnar microstructure oxide growth, (e) spinodal decomposition resulting in interconnected bicontinuous morphology, (f) polycrystalline grain growth, and (g) thin film heterostructure growth on a substrate. |medea| *PhaseField* empowers users to simulate many, and varied phenomena of engineering importance. For example, the figure shows snapshots of a 2D simulation of an oxidation process, and a 3D simulation of phase separation in an Ag-Cu binary eutectic alloy. In both cases, elastic effects are critical for predicting the formation of microstructural features. Elastic anisotropy, phase transformation kinetics, and the coupling between phase and mechanical fields are key features that can be adjusted to match experimental data or theoretical models. Advanced users can modify the finite element mesh, refine the phase field equations, or introduce custom boundary conditions to further enhance the realism and accuracy of simulations. Integration of the phase field and elasticity equations enables self-consistent calculations of stress and strain, making *PhaseField* suitable for studying deformation-induced phase transformations and the interaction between microstructure and mechanical properties. If nucleation of new grains is important, users can specify nucleation rates and seed sizes for both homogeneous and heterogeneous nucleation, enabling simulations of phenomena like precipitation hardening. *PhaseField* simulation results are exportable to post-processing tools for further analysis, including visualization and data extraction for validation against experimental findings. .. add for a column break, adjust where needed .. raw:: latex \newpage Key Features ^^^^^^^^^^^^ * Finite element-based simulation of microstructure evolution * Supports multiple phases and diffusing species * Coupled phase field, mass transport, and linear elasticity equations * Phase-field fracture model for crack initiation and propagation (coupled with elasticity) * Nucleation of new phases, both homogeneous (in bulk) and heterogeneous (at interfaces), with user-defined rates and nucleus sizes * Temperature evolution coupled with temperature-dependent free energies, diffusion, and thermal expansion * Grain-boundary diffusion with per-interface grain boundary diffusivity * Access to first-principles and atomistic material property values inside |medea| * Adaptive mesh refinement and adaptive timestepping for optimal convergence * Easily exportable results for post-processing and visualization Required Modules ^^^^^^^^^^^^^^^^ * |medea| |menvironment| * |medea| |mphasefield| Recommended Modules ^^^^^^^^^^^^^^^^^^^^ * |medea| |mvasp| * |medea| |diffusion| * |medea| |munclefull| * |medea| |interfacebuilder| .. [#TM] |regTMinfo| .. [#Anderson] R. Anderson *et al.*, *Comput. Math. Appl.* **81**, 42 (2021) (`DOI `__) .. only:: html :download: :download:`pdf `