lattice

Parameters and functions describing the evolution of the crystal lattice.

class lattice.Lattice(params, work_dir, logger)[source]

Bases: object

Store parameters relative to vacancy annihilation/creation.

Variables:

  • k_dislo (float) – Sink strength related to dislocations (s-1).

  • k_pores (float) – Sink strength related to pores (s-1).

  • rho_dislo (float) – Line density used to compute k_dislo from local DVa (m-2).

  • rho_pores (float) – Line density used to compute k_pores from local DVa (m-2).

  • ideal (bool) – Whether lattice is ideal, in the sense that vacancies are maintained at equilibrium.

__init__(params, work_dir, logger)[source]

Class constructor.

Parameters:

  • params (dict) – Input parameters related to sink strength.

  • work_dir (pathlib.Path) – Work directory.

  • logger (log_utils.CustomLogger) – Logger.

is_ideal(logger)[source]

Check whether lattice is ideal and print info messages.

If the input files contains no value for k_dislo, k_pores, rho_dislo or rho_pores, the lattice is ideal. If either parameter is given, the lattice is non-ideal.

process_sink_terms(params, work_dir, logger)[source]

Process user input for non-ideal lattice parameters.

Parameters of interest: k_dislo, k_pores, rho_dislo, rho_pores. Input can be a float or a string indicating a file name. If neither k_dislo or rho_dislo is given, k_dislo defaults to 0. Same for k_pores and rho_pores. (This will occur if k_dislo is specified but k_pores is not, or vice versa.)

lattice.compute_alpha_nonideal(dt, yVa, yVa_eq, V, Vp, fm, k_dislo, k_pores)[source]

Compute lattice sink rate in non-ideal case.

Parameters:

  • dt (float) – Time step.

  • yVa (1D array) – Vacancy site fraction, shape (nz - 1,).

  • yVa_eq (1D array) – Equilibrium vacancy site fraction, shape (nz - 1,).

  • V (1D array) – System average molar volume, shape (nz - 1,).

  • Vp (dict of floats) – Partial molar volumes.

  • fm (1D array) – Metal volume fraction, shape (nz - 1,).

  • k_dislo (1D array) – Sink strength associated with dislocation climb, shape (nz - 1,).

  • k_pores (1D array) – Sink strength associated with pore growth, shape (nz - 1,).

Returns:

  • alpha_d (1D array) – Sink term associated with dislocation climb, shape (nz - 1,).

  • alpha_p (1D array) – Sink term associated with pore growth, shape (nz - 1,).

lattice.compute_gamma(Jlat, z, Vk, V0, Vp, V, alpha_d, alpha_p, y_Va, geometry)[source]

Compute relative volume variation rate.

Parameters:

  • Jlat (1D array) – Fluxes in the lattice frame, shape (ninds + 1, nz).

  • z (1D array) – Node positions, shape (nz,).

  • Vk (1D array) – Partial molar volumes.

  • V0 (float or 1D array) – Partial molar volume of the vacancy.

  • Vp (float or 1D array) – Partial molar volume of the pore.

  • V (1D array) – System average molar volume, shape (nz - 1,).

  • alpha_d (1D array) – Sink term associated with dislocation climb, shape (nz - 1,).

  • alpha_p (1D array) – Sink term associated with pore growth, shape (nz - 1,).

  • y_Va (1D array) – Vacancy site fraction, shape (nz - 1,).

  • geometry (str) – Domain geometry (planar, cylindrical or spherical).

Returns:

gamma – Relative volume variation rate, shape (nz - 1,).

Return type:

1D array

lattice.compute_gamma_V(Jlat, z, Vk, V0, Vm, V, y_Va, alpha, geometry)[source]

Compute relative volume variation rate due to molar volume variation.

Parameters:

  • Jlat (1D array) – Fluxes in the lattice frame, shape (ninds + 1, nz).

  • z (1D array) – Node positions, shape (nz,).

  • Vk (1D array) – Partial molar volumes.

  • V0 (float or 1D array) – Partial molar volume of the vacancy.

  • Vm (1D array) – Average molar volume of the metal phase, shape (nz - 1,).

  • V (1D array) – System average molar volume, shape (nz - 1,).

  • y_Va (1D array) – Vacancy site fraction, shape (nz - 1,).

  • alpha (1D array) – Sink term, shape (nz - 1,).

  • geometry (str) – Domain geometry (planar, cylindrical or spherical).

Returns:

gamma_V – Relative volume variation rate due to molar volume variation, shape (nz - 1,).

Return type:

1D array

lattice.compute_velocity(gamma, z, Vk, V0, Jlat, yVa, geometry)[source]

Compute velocity field of the lattice in the laboratory frame.

v is calculated via an integral from 0 to z -> need to add value at 0. v_left is obtained assuming ideal lattice activity on left boundary (and neglecting the gradient of Vm/(1 - yVa) in getting the primitive).

Parameters:

  • gamma (1D array) – Relative volume variation rate, shape (nz - 1,).

  • z (1D array) – Node positions, shape (nz,).

  • Vk (1D array) – Partial molar volumes.

  • V0 (float or 1D array) – Partial molar volume of the vacancy.

  • Jlat (1D array) – Fluxes in the lattice frame, shape (ninds + 1, nz).

  • yVa (1D array) – Vacancy site fraction, shape (nz - 1,).

  • geometry (str) – Domain geometry (planar, cylindrical or spherical).

Returns:

v – Lattice velocity, shape (nz,)

Return type:

1D array