dislocation_SDVPN.py

Calculation functions

sdvpn(ucell: System, C: ElasticConstants, burgers: list | ndarray, ξ_uvw: list | ndarray, slip_hkl: list | ndarray, gamma: GammaSurface, m: list | ndarray = [0, 1, 0], n: list | ndarray = [0, 0, 1], cutofflongrange: float = 1000.0, tau: ndarray = array([[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]), alpha: list = [0.0], beta: ndarray = array([[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]), cdiffelastic: bool = False, cdiffsurface: bool = True, cdiffstress: bool = False, fullstress: bool = True, halfwidth: float = 1.0, normalizedisreg: bool = True, xnum: int | None = None, xmax: float | None = None, xstep: float | None = None, xscale: bool = False, min_method: str = 'Powell', min_options: dict = {}, min_cycles: int = 10) → dict

Solves a Peierls-Nabarro dislocation model.

Parameters:

  • ucell (atomman.System) – The unit cell to use as the seed for the dislocation system. Note that only box information is used and not atomic positions.

  • C (atomman.ElasticConstants) – The elastic constants associated with the bulk crystal structure for ucell.

  • burgers (array-like object) – The dislocation’s Burgers vector given as a Miller or Miller-Bravais vector relative to ucell.

  • ξ_uvw (array-like object) – The dislocation’s line direction given as a Miller or Miller-Bravais vector relative to ucell.

  • slip_hkl (array-like object) – The dislocation’s slip plane given as a Miller or Miller-Bravais plane relative to ucell.

  • m (array-like object, optional) – The m unit vector for the dislocation solution. m, n, and ξ (dislocation line) should be right-hand orthogonal. Default value is [0,1,0] (y-axis).

  • n (array-like object, optional) – The n unit vector for the dislocation solution. m, n, and ξ (dislocation line) should be right-hand orthogonal. Default value is [0,0,1] (z-axis). n is normal to the dislocation slip plane.

  • cutofflongrange (float, optional) – The cutoff distance to use for computing the long-range energy. Default value is 1000 angstroms.

  • tau (numpy.ndarray, optional) – A (3,3) array giving the stress tensor to apply to the system using the stress energy term. Only the xy, yy, and yz components are used. Default value is all zeros.

  • alpha (list of float, optional) – The alpha coefficient(s) used by the nonlocal energy term. Default value is [0.0].

  • beta (numpy.ndarray, optional) – The (3,3) array of beta coefficient(s) used by the surface energy term. Default value is all zeros.

  • cdiffelastic (bool, optional) – Flag indicating if the dislocation density for the elastic energy component is computed with central difference (True) or simply neighboring values (False). Default value is False.

  • cdiffsurface (bool, optional) – Flag indicating if the dislocation density for the surface energy component is computed with central difference (True) or simply neighboring values (False). Default value is True.

  • cdiffstress (bool, optional) – Flag indicating if the dislocation density for the stress energy component is computed with central difference (True) or simply neighboring values (False). Only matters if fullstress is True. Default value is False.

  • fullstress (bool, optional) – Flag indicating which stress energy algorithm to use. Default value is True.

  • halfwidth (float, optional) – A dislocation halfwidth guess to use for generating the initial disregistry guess. Does not have to be accurate, but the better the guess the fewer minimization steps will likely be needed. Default value is 1 Angstrom.

  • normalizedisreg (bool, optional) – If True, the initial disregistry guess will be scaled such that it will have a value of 0 at the minimum x and a value of burgers at the maximum x. Default value is True. Note: the disregistry of end points are fixed, thus True is usually preferential.

  • xnum (int, optional) – The number of x value points to use for the solution. Two of xnum, xmax, and xstep must be given.

  • xmax (float, optional) – The maximum value of x to use. Note that the minimum x value will be -xmax, thus the range of x will be twice xmax. Two of xnum, xmax, and xstep must be given.

  • xstep (float, optional) – The delta x value to use, i.e. the step size between the x values used. Two of xnum, xmax, and xstep must be given.

  • xscale (bool, optional) – Flag indicating if xmax and/or xstep values are to be taken as absolute or relative to ucell’s a lattice parameter. Default value is False, i.e. the x parameters are absolute and not scaled.

  • min_method (str, optional) – The scipy.optimize.minimize method to use. Default value is ‘Powell’.

  • min_options (dict, optional) – Any options to pass on to scipy.optimize.minimize. Default value is {}.

  • min_cycles (int, optional) – The number of minimization runs to perform on the system. Restarting after obtaining a solution can help further refine to the best pathway. Default value is 10.

Returns:

Dictionary of results consisting of keys:

  • ’SDVPN_solution’ (atomman.defect.SDVPN) - The SDVPN solution object at the end of the run.

  • ’minimization_energies’ (list) - The total energy values measured after each minimization cycle.

  • ’disregistry_profiles’ (list) - The disregistry profiles obtained after each minimization cycle.

Return type:

dict