Class pypfc_pre

Bases: setup_base

Functions

__init__

__init__(
    domain_size: Union[List[float], ndarray],
    ndiv: Union[List[int], ndarray],
    config: Dict[str, Any],
) -> None

Initialize the class.

Parameters:

Name	Type	Description	Default
domain_size	array_like of int, shape (3,)	Number of grid divisions along each coordinate axis [nx, ny, nz].	required
ndiv	array_like of int, shape (3,)	Number of grid divisions along each coordinate axis [nx, ny, nz].	required
config	dict	Configuration parameters as key-value pairs. See the pyPFC overview for a complete list of the configuration parameters.	required

do_bicrystal

do_bicrystal(
    xtal_rot: ndarray,
    params: Optional[List[float]] = None,
    liq_width: float = 0.0,
    model: int = 0,
) -> np.ndarray

Define a bicrystal with two different crystal orientations.

Parameters:

Name	Type	Description	Default
xtal_rot	ndarray of float, shape (3,3,2)	Crystal orientations (rotation matrices) for the two grains.	required
params	list	List containing parameters for the bicrystal model. model=0: [r] - cylindrical crystal radius model=1: [r] - spherical crystal radius model=2: [gb_x1, gb_x2] - grain boundary positions along x	None
liq_width	float	Width of the liquid band along the grain boundary.	0.0
model	int	Density field layout. 0: Cylindrical crystal, extending through z 1: Spherical crystal 2: Bicrystal with two planar grain boundaries, normal to x	0

Returns:

Name	Type	Description
density	ndarray of float, shape (nx,ny,nz)	Density field.

Raises:

Type	Description
ValueError	If the value of model is not supported (should be 0, 1 or 2).

do_polycrystal

do_polycrystal(
    xtal_rot: ndarray,
    params: Optional[List[float]] = None,
    liq_width: float = 0.0,
    model: int = 0,
) -> np.ndarray

Define a polycrystal in a periodic 3D domain.

Parameters:

Name	Type	Description	Default
xtal_rot	ndarray of float, shape (3,3,n_xtal)	Crystal orientations (rotation matrices) for n_xtal crystals.	required
params	list	List containing parameters for the polycrystal model. model=0: No parameter needed. The number of crystal seeds is determined from the number of provided orientations.	None
liq_width	float	Width of the liquid band along the grain boundaries.	0.0
model	int	Density field layout. 0: A row of cylindrical seeds along y, with cylinders extending through z	0

Returns:

Name	Type	Description
density	ndarray of float, shape (nx,ny,nz)	Polycrystal density field.

Raises:

Type	Description
ValueError	If the value of model is not supported (should be 0).

do_single_crystal

do_single_crystal(
    xtal_rot: Optional[ndarray] = None,
    params: Optional[List[float]] = None,
    model: int = 0,
) -> np.ndarray

Define a single crystal in a periodic 3D domain.

Parameters:

Name	Type	Description	Default
xtal_rot	ndarray of float, shape (3,3)	Crystal orientation (rotation matrix). Default is an identity matrix.	None
params	list	List containing parameters for the single crystal model: model=0: [r] - spherical crystal radius model=1: [x1, x2] - crystal extent in x direction model=2: [r] - cylindrical crystal radius	None
model	(int, optional)	Density field layout. 0: Spherical crystal 1: Crystal extending throughout y and z, covering interval in x 2: Cylindrical crystal, extending through z	0

Returns:

Name	Type	Description
density	ndarray of float, shape (nx,ny,nz)	Density field.

Raises:

Type	Description
ValueError	If the value of model is not supported (should be 0 or 1).

evaluate_ampl_dens

evaluate_ampl_dens() -> Tuple[np.ndarray, np.ndarray]

Get density field amplitudes and phase densities for PFC simulations.

Returns:

Name	Type	Description
ampl	ndarray of float, shape (npeaks,)	Density field amplitudes for the specified crystal structure and number of peaks.
nLnS	ndarray of float, shape (2,)	Densities in the liquid (nL) and solid (nS) phases.

Raises:

Type	Description
ValueError	If npeaks is not supported for the current crystal structure.
ValueError	If sigma value is not supported for the current configuration.
ValueError	If struct is not 'SC', 'BCC' or 'FCC' or if amplitudes and densities are not available for the specified structure.

Notes

This method provides pre-calculated density field amplitudes and phase densities for different crystal structures (SC, BCC, FCC) and numbers of Fourier peaks in the two-point correlation function. The values depend on the temperature-like parameter sigma.

Fore efficiency, the method uses lookup tables of pre-computed values.

Supported configurations:

struct	npeaks	sigma range
SC	1	[0.0, 0.25]
	2	[0.0, 0.22]
	3	[0.0, 0.22]
BCC	1	[0.0, 0.33]
	2	[0.0, 0.30]
	3	[0.0, 0.25]
FCC	1	[0.0, 0.25]
	2	[0.0, 0.25]
	3	[0.0, 0.25]

generate_density_field

generate_density_field(
    crd: ndarray, g: ndarray
) -> np.ndarray

Define a 3D density field for (X)PFC modeling.

Parameters:

Name	Type	Description	Default
crd	ndarray of float, shape (3,...)	Grid point coordinates [x,y,z].	required
g	ndarray of float, shape (3,3)	Rotation matrix for crystal orientation.	required

Returns:

Name	Type	Description
density	ndarray of float	Density field for the specified crystal structure with appropriate Fourier modes and amplitudes.

Raises:

Type	Description
ValueError	If struct is not one of the supported crystal structures ('SC', 'BCC', 'FCC', 'DC').

Notes

The density field is generated based on the current crystal structure (struct) and density field amplitudes (ampl) settings.

get_ampl

get_ampl() -> np.ndarray

Get the amplitudes in the density approximation.

Returns:

Name	Type	Description
ampl	ndarray of float, shape (N,)	Amplitudes.

get_density

get_density() -> np.ndarray

Get the density field.

Returns:

Name	Type	Description
den	ndarray of float, shape (nx,ny,nz)	Density field.

get_nlns

get_nlns() -> np.ndarray

Get the liquid and solid phase densities.

Returns:

Name	Type	Description
nlns	ndarray of float, shape (2,)	\([n_{l},n_{s}]\) where \(n_{l}\) is liquid phase density and \(n_{s}\) is solid phase density.

get_npeaks

get_npeaks() -> int

Get the number of peaks in the density field approximation.

Returns:

Name	Type	Description
npeaks	int	Number of peaks in the density field approximation.

get_sigma

get_sigma() -> float

Get the temperature-like parameter sigma.

Returns:

Name	Type	Description
sigma	float	Temperature-like parameter sigma

get_struct

get_struct() -> str

Get the crystal structure.

Returns:

Name	Type	Description
struct	str	Crystal structure type: 'FCC', 'BCC'.

set_ampl

set_ampl(ampl: Union[List[float], ndarray]) -> None

Set the amplitudes in the density approximation.

Parameters:

Name	Type	Description	Default
ampl	array_like of float, shape (N,)	Amplitudes.	required

set_density

set_density(den: ndarray) -> None

Set the density field.

Parameters:

Name	Type	Description	Default
den	ndarray of float, shape (nx,ny,nz)	Density field.	required

set_energy

set_energy(ene: ndarray) -> None

Set the PFC energy field.

Parameters:

Name	Type	Description	Default
ene	ndarray of float, shape (nx,ny,nz)	PFC energy field.	required

set_nlns

set_nlns(nlns: Union[List[float], ndarray]) -> None

Set the liquid and solid phase densities.

Parameters:

Name	Type	Description	Default
nlns	array_like of float, shape (2,)	\([n_{l},n_{s}]\) where \(n_{l}\) is liquid phase density and \(n_{s}\) is solid phase density.	required

set_npeaks

set_npeaks(npeaks: int) -> None

Set the number of peaks in the density field approximation.

Parameters:

Name	Type	Description	Default
npeaks	int	Number of peaks in the density field approximation.	required

set_sigma

set_sigma(sigma: float) -> None

Set the temperature-like parameter sigma.

Parameters:

Name	Type	Description	Default
sigma	float	Temperature-like parameter sigma.	required

set_struct

set_struct(struct: str) -> None

Set the crystal structure.

Parameters:

Name	Type	Description	Default
struct	(FCC, BCC)	Crystal structure type: 'FCC', 'BCC'.	'FCC'