Phase Field Model (Cahn-Hilliard)¶

Optional dependency

Phase Field Model requires calphad. Plotting/visualization support additionally requires plots.

uvpip

uv add "materialsframework[calphad]"

# For plotting/visualization support
uv add "materialsframework[calphad,plots]"

pip install "materialsframework[calphad]"

# For plotting/visualization support
pip install "materialsframework[calphad,plots]"

PhaseFieldModel ¶

PhaseFieldModel(
    material_properties: MaterialParameters,
    simulation_grid: SimulationGrid | None = None,
    wrt_cycle: int = 5000,
    stop_iter: int = 50000,
    seed: int = 42,
)

Implements the Cahn-Hilliard solver with output visualization.

Initializes the phase field model with simulation grid and material properties.

Parameters:

Name	Type	Description	Default
`material_properties`	`MaterialParameters`	Material properties for the simulation.	required
`simulation_grid`	`SimulationGrid \| None`	The grid for the simulation. Defaults to None, meaning a new `SimulationGrid` with default parameters is created.	`None`
`wrt_cycle`	`int`	Frequency of writing output files. Defaults to 5000.	`5000`
`stop_iter`	`int`	Number of iterations to run the simulation. Defaults to 50000.	`50000`
`seed`	`int`	Seed for the random number generator. Defaults to 42.	`42`

laplacian ¶

laplacian(field: ndarray) -> np.ndarray

Computes the discrete Laplacian using a 9-point stencil.

Parameters:

Name	Type	Description	Default
`field`	`ndarray`	The field for which to compute the Laplacian.	required

Returns:

Type	Description
`ndarray`	np.ndarray: The computed Laplacian of the field.

free_energy ¶

free_energy(phi: ndarray) -> np.ndarray

Computes the free energy derivative based on the polynomial coefficients.

Parameters:

Name	Type	Description	Default
`phi`	`ndarray`	The phase field variable.	required

Returns:

Type	Description
`ndarray`	np.ndarray: The computed free energy derivative.

evolve ¶

evolve() -> None

Evolves the phase field using the Cahn-Hilliard equation.

save_plot ¶

save_plot(iteration: int) -> None

Saves the current phase field as an image.

Parameters:

Name	Type	Description	Default
`iteration`	`int`	The current iteration number.	required

run_simulation ¶

run_simulation(plot: bool = False) -> None

Runs the simulation for a specified number of iterations.

Parameters:

Name	Type	Description	Default
`plot`	`bool`	Whether to save plots of the phase field. Default is False.	`False`

SimulationGrid ¶

SimulationGrid(
    nx: int = 128,
    ny: int = 128,
    lx: float = 2e-06,
    ly: float = 2e-06,
    dt: float = 1e-12,
)

Handles the simulation grid and phase field variables.

Initializes the simulation grid with given parameters.

Parameters:

Name	Type	Description	Default
`nx`	`int`	Number of grid points in x-direction. Defaults to 128.	`128`
`ny`	`int`	Number of grid points in y-direction. Defaults to 128.	`128`
`lx`	`float`	Length of the grid in x-direction. Defaults to 2e-6.	`2e-06`
`ly`	`float`	Length of the grid in y-direction. Defaults to 2e-6.	`2e-06`
`dt`	`float`	Time step for the simulation. Defaults to 1e-12.	`1e-12`

MaterialParameters ¶

MaterialParameters(
    db: Database | str,
    temperature: float,
    component: str,
    composition: float,
    elements: list[str] | None = None,
    phase: str | None = None,
)

Stores material parameters such as energy and kinetic properties.

Initializes material parameters with given composition and potential values.

Parameters:

Name	Type	Description	Default
`db`	`Database \| str`	pycalphad Database object or path to the database file.	required
`temperature`	`float`	Temperature in Kelvin.	required
`component`	`str`	Component name.	required
`composition`	`float`	Composition value.	required
`elements`	`list[str] \| None`	List of elements. Defaults to None.	`None`
`phase`	`str \| None`	Phase name. Defaults to None.	`None`

Raises:

Type	Description
`ValueError`	If multiple phases are found in the database and no phase is specified.