lattice

Compute variables describing the evolution of the crystal lattice.

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