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CALPHAD Coupling

Overview

PhaseFields.jl provides optional integration with OpenCALPHAD.jl for realistic thermodynamic calculations. This coupling is implemented as a Julia package extension that loads automatically when OpenCALPHAD is imported.

Installation

using Pkg
Pkg.add(url="https://github.com/hsugawa8651/OpenCALPHAD.jl")

Basic Usage

using PhaseFields
using OpenCALPHAD  # Activates extension automatically

# Load thermodynamic database
db = read_tdb("AgCu.TDB")

# Calculate driving force
T = 1000.0  # Temperature [K]
x = 0.3     # Composition (Cu mole fraction)
ΔG = calphad_driving_force(db, T, x, "FCC_A1", "LIQUID")

CALPHAD-Coupled Models

Allen-Cahn with CALPHAD

using PhaseFields
using OpenCALPHAD

db = read_tdb("AgCu.TDB")
T = 1000.0
x = 0.3

# Create coupled model
model = create_calphad_allen_cahn(db, T, x, "FCC_A1", "LIQUID";
    τ = 1.0,
    W = 1.0,
    m = 1e-4  # Scaling factor for ΔG
)

# The model caches the driving force from CALPHAD

KKS with CALPHAD

db = read_tdb("AgCu.TDB")
T = 1000.0

# Create model with CALPHAD free energies
model, f_s, f_l = create_calphad_kks_model(db, T, "FCC_A1", "LIQUID";
    τ = 1.0,
    W = 1.0,
    m = 1.0,
    M_s = 1.0,
    M_l = 10.0
)

# Partition with real thermodynamics
c_avg = 0.3
φ = 0.5
c_s, c_l, μ, converged = kks_partition(c_avg, φ, f_s, f_l)

WBM with CALPHAD

db = read_tdb("AgCu.TDB")
T = 1000.0

model, f_s, f_l = create_calphad_wbm_model(db, T, "FCC_A1", "LIQUID";
    M_φ = 1.0,
    κ = 1.0,
    W = 1.0,
    D_s = 1e-13,
    D_l = 1e-9
)

Thermodynamic Functions

Driving Force

# Gibbs energy difference: ΔG = G_solid - G_liquid
# Negative ΔG means solid is stable
ΔG = calphad_driving_force(db, T, x, "FCC_A1", "LIQUID")

Chemical Potential

# Get chemical potentials for a phase
μ = calphad_chemical_potential(db, "FCC_A1", T, x)

Diffusion Potential

# Second derivative d²G/dx² (thermodynamic factor)
d2G = calphad_diffusion_potential(db, "FCC_A1", T, x)

API Reference

PhaseFields.calphad_driving_force — Function
calphad_driving_force(db, T, x, solid_phase, liquid_phase)

Calculate the thermodynamic driving force for solidification using CALPHAD data.

Requires OpenCALPHAD.jl: Load with using OpenCALPHAD to enable this function.

Arguments

  • db: OpenCALPHAD Database object
  • T: Temperature [K]
  • x: Composition (mole fraction of solute)
  • solid_phase: Name of solid phase (e.g., "FCC_A1")
  • liquid_phase: Name of liquid phase (e.g., "LIQUID")

Returns

  • Driving force ΔG [J/mol] (negative = solid stable)
source
PhaseFields.calphad_chemical_potential — Function
calphad_chemical_potential(db, phase, T, x)

Get chemical potentials from CALPHAD database.

Requires OpenCALPHAD.jl: Load with using OpenCALPHAD to enable this function.

Returns

  • Tuple of chemical potentials (μ₁, μ₂, ...) [J/mol]
source
PhaseFields.calphad_diffusion_potential — Function
calphad_diffusion_potential(db, phase, T, x)

Get second derivative of Gibbs energy d²G/dx² from CALPHAD.

Requires OpenCALPHAD.jl: Load with using OpenCALPHAD to enable this function.

Returns

  • d²G/dx² [J/mol]
source
PhaseFields.create_calphad_allen_cahn — Function
create_calphad_allen_cahn(db, T, x, solid_phase, liquid_phase; kwargs...)

Create an Allen-Cahn model coupled with CALPHAD thermodynamics.

Requires OpenCALPHAD.jl: Load with using OpenCALPHAD to enable this function.

Arguments

  • db: OpenCALPHAD Database object
  • T: Temperature [K]
  • x: Composition (mole fraction)
  • solid_phase: Name of solid phase
  • liquid_phase: Name of liquid phase

Keyword Arguments

  • τ: Relaxation time [s] (default: 1.0)
  • W: Interface width parameter (default: 1.0)
  • m: Scaling factor for ΔG (default: 1e-4)

Returns

  • CALPHADAllenCahnModel with cached driving force
source
PhaseFields.create_calphad_kks_model — Function
create_calphad_kks_model(db, T, solid_phase, liquid_phase; kwargs...)

Create a KKS model setup with CALPHAD free energies.

Requires OpenCALPHAD.jl: Load with using OpenCALPHAD to enable this function.

Arguments

  • db: OpenCALPHAD Database object
  • T: Temperature [K]
  • solid_phase: Name of solid phase
  • liquid_phase: Name of liquid phase

Keyword Arguments

  • τ: Relaxation time [s] (default: 1.0)
  • W: Interface width parameter (default: 1.0)
  • m: Driving force scale (default: 1.0)
  • M_s: Solid mobility (default: 1.0)
  • M_l: Liquid mobility (default: 10.0)

Returns

  • Tuple of (KKSModel, CALPHADFreeEnergysolid, CALPHADFreeEnergyliquid)
source
PhaseFields.create_calphad_wbm_model — Function
create_calphad_wbm_model(db, T, solid_phase, liquid_phase; kwargs...)

Create a WBM model setup with CALPHAD free energies.

Requires OpenCALPHAD.jl: Load with using OpenCALPHAD to enable this function.

Arguments

  • db: OpenCALPHAD Database object
  • T: Temperature [K]
  • solid_phase: Name of solid phase
  • liquid_phase: Name of liquid phase

Keyword Arguments

  • M_φ: Phase field mobility (default: 1.0)
  • κ: Gradient energy coefficient (default: 1.0)
  • W: Barrier height (default: 1.0)
  • D_s: Solid diffusivity (default: 1e-13)
  • D_l: Liquid diffusivity (default: 1e-9)

Returns

  • Tuple of (WBMModel, CALPHADFreeEnergysolid, CALPHADFreeEnergyliquid)
source

See Also