GitHub

Getting Started

This guide covers the basic concepts of PhaseFields.jl.

Phase Field Method Overview

The phase field method represents interfaces using a continuous order parameter φ:

  • φ = 1: Solid phase
  • φ = 0: Liquid phase
  • 0 < φ < 1: Diffuse interface region

This approach avoids explicit interface tracking and naturally handles topological changes like merging and splitting.

Available Models

PhaseFields.jl provides several phase field models for different applications:

ModelApplicationOrder Parameter
Allen-CahnSolidification, grain growthNon-conserved
Cahn-HilliardSpinodal decompositionConserved
KKSMulti-component alloysLocal equilibrium
WBMDilute alloysMixture rule
ThermalSolidification with heatCoupled φ-T

Quick Example

using PhaseFields
using OrdinaryDiffEq

# 1. Create model
model = AllenCahnModel(τ=1.0, W=0.05)

# 2. Set up spatial grid
grid = UniformGrid1D(N=101, L=1.0)
bc = NeumannBC()

# 3. Initial condition
φ0 = [0.5 * (1 - tanh((x - 0.3) / 0.1)) for x in grid.x]

# 4. Create ODE problem
prob = create_allen_cahn_problem(model, grid, bc, φ0, (0.0, 2.0))

# 5. Solve
sol = solve(prob, Tsit5())

Key Concepts

Interpolation and Double-Well Functions

All models use:

  • h(φ): Interpolation function (0→1 transition)
  • g(φ): Double-well potential (energy barrier)
# Standard choices
h = h_polynomial(φ)  # 3φ² - 2φ³
g = g_standard(φ)    # φ²(1-φ)²

See Common API Reference for details.

DifferentialEquations.jl Integration

PhaseFields.jl uses Method of Lines for time integration:

using OrdinaryDiffEq

# Explicit solver (fast, non-stiff)
sol = solve(prob, Tsit5())

# Implicit solver (stiff problems)
sol = solve(prob, QNDF(autodiff=false))

See DifferentialEquations.jl Integration for details.

CALPHAD Coupling (Optional)

For realistic thermodynamics:

using PhaseFields
using OpenCALPHAD  # Activates extension

db = read_tdb("AgCu.TDB")
ΔG = calphad_driving_force(db, 1000.0, 0.3, "FCC_A1", "LIQUID")

See CALPHAD Coupling for details.

Next Steps