def test_grid_instance_is_initialised( self, mock_Grid_Point, mock_index ):
#volumes = [ 0.025, 0.025, 0.025, 0.025, 0.025 ]
#mock_volumes.return_value = volumes
mock_index.side_effect = [ 1, 3 ]
mock_grid_points = [ Mock( spec=Grid_Point ), Mock( spec=Grid_Point ), Mock( spec=Grid_Point ), Mock( spec=Grid_Point ), Mock( spec=Grid_Point ) ]
for g in mock_grid_points:
g.sites = []
mock_Grid_Point.side_effect = mock_grid_points
x_coordinates = np.array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] )
b = 0.25
c = 0.1
limits = [ 1.0, 1.0 ]
limits_for_laplacian = [1.0, 1.0]
set_of_sites = MagicMock( spec=Set_of_Sites )
sites = [ Mock( spec=Site ), Mock( spec=Site ) ]
sites[0].x = 1.0
sites[1].x = 3.0
sites[0].defect_species = [ Mock( spec=DefectSpecies ) ]
sites[1].defect_species = [ Mock( spec=DefectSpecies ) ]
set_of_sites.__iter__.return_value = iter( sites )
grid = Grid( x_coordinates=x_coordinates, b=b, c=c, limits=limits, limits_for_laplacian=limits_for_laplacian, set_of_sites=set_of_sites )
self.assertEqual( grid.points, mock_grid_points )
self.x = x_coordinates
self.limits = limits
self.limits_for_laplacian = limits_for_laplacian
expected_sites_at_grid_points = [ [], [ sites[0] ], [], [ sites[1] ], [] ]
for p, e in zip( grid.points, expected_sites_at_grid_points ):
self.assertEqual( p.sites, e )
for defect_species_list in [ sites[0].defect_species, sites[1].defect_species ]:
for defect_species in defect_species_list:
self.assertEqual( defect_species in grid.defect_species, True )
def form_continuum_sites( all_sites, x_min, x_max, n_points, b, c, defect_species, limits_for_laplacian, site_labels, defect_labels ):
"""
Creates a Set_of_Sites object for sites interpolated onto a regular grid, this is equivalent to assuming a continuum approximation.
Args:
all_sites (object): Orginal Set_of_Sites object from full data.
x_min (float): Minimum x coordinate value defining the calculation region.
x_max (float): Maximum x coordinate value defining the calculation region.
n_points (int): Number of points that the data should be interpolated on to.
b (float): b dimension for every grid point.
c (float): c dimension for every grid point.
defect_species (object): Class object containing information about the defect species present in the system.
limits for laplacian (list): distance between the endmost sites and the midpoint of the next site outside of the calculation region for the first and last sites respectively.
site_labels( list ): List of strings for the different site species.
defect_labels (list): List of strings for the different defect species.
Returns:
:obj:`Set_of_Sites`: Sites interpolated onto a regular grid.
"""
grid = np.linspace( x_min, x_max, n_points )
limits = [grid[1] - grid[0], grid[1] - grid[0]]
sites = []
for label, d_label in zip(site_labels, defect_labels):
scaling = len( all_sites.subset( label ) ) / len( grid )
continuum_grid = Grid( grid, b, c, limits, limits_for_laplacian, all_sites.subset( label ) )
average_energies = np.array( [ site.average_local_energy( method = 'mean' )[0] for site in all_sites.subset( label ) ] )
new_energies = griddata( ( [ site.x for site in all_sites.subset( label ) ] ), average_energies, grid, method = 'nearest' )
for x, e in zip( grid, new_energies):
sites.append( Site( label, x, [ defect_species[ d_label ] ], [e], scaling = np.array( scaling ) ) )
return Set_of_Sites( sites ), limits
def form_continuum_sites_new(all_sites, x_min, x_max, n_points, b, c,
defect_species, limits_for_laplacian,
site_labels, defect_labels):
limits = [x_min, x_max]
grid = np.linspace(x_min, x_max, n_points)
sites = []
for label, d_label in zip(site_labels, defect_labels):
scaling = len(all_sites.subset(label)) / len(grid)
continuum_grid = Grid(grid, b, c, limits, limits_for_laplacian,
all_sites.subset(label))
average_energies = np.array([
site.average_local_energy(method='mean')[0]
for site in all_sites.subset(label)
])
new_energies = griddata(
([site.x for site in all_sites.subset(label)]),
Vo.average_energies,
grid,
method='nearest')
for x, e in zip(grid, new_energies):
sites.append(
Site(label,
x, [defect_species[d_label]], [e],
scaling=np.array(scaling)))
return Set_of_Sites(sites)
def calculate_mobile_defect_conductivities(self,
pos_or_neg_scr,
scr_limit,
species,
mobility_scaling=False):
"""Calculate the conductivity ratio between the space charge region and the bulk both perpendicular and parallel to the grain boundary.
A `Set_of_Sites` object is created for the sites in the space charge region, and the defect distributions calculated. The width of the space charge region is calculated and a bulk region of the same width is defined. A Set_of_Sites object for the bulk region is created and the defect distributions calculated. Taking each site as a resistor in series or parallel respectively, the conductivity is calculated and the ratio between the space charge region and the bulk is taken.
Args:
pos_or_neg_scr (str): 'positive' - for a positive space charge potential.
'negative' - for a negative space charge potential.
scr_limit (float): The minimum electrostatic potential that the electrostatic potential must exceed to be included in the space charge region.
species (str): The species for which the conductivity is being calculated.
mobility_scaling (bool): For particles on a lattice which only interact through volume exclusion, the mobility exhibits a blocking term. True if the blocking term is to be included, False if the blocking term is not to be included. Default = False.
Returns:
float: The perpendicular conductivity ratio. The conductivity ratio between the bulk and the space charge region perpendicular to the grain boundary.
float: The parallel conductivity ratio. The conductivity ratio between the bulk and the space charge region parallel to the grain boundary.
"""
space_charge_region = self.create_space_charge_region(
self.subgrids[species], pos_or_neg_scr, scr_limit)
space_charge_region_limits = self.calculate_offset(
self.subgrids[species], np.min(space_charge_region),
np.max(space_charge_region))
space_charge_region_sites = self.create_subregion_sites(
self.subgrids[species], np.min(space_charge_region),
np.max(space_charge_region))
for site in space_charge_region_sites:
charge = site.defects[0].valence
mobilities = site.defects[0].mobility
space_charge_region_grid = Grid.grid_from_set_of_sites(
space_charge_region_sites, space_charge_region_limits,
space_charge_region_limits, self.grid.b, self.grid.c)
space_charge_region_width = space_charge_region_grid.x[
-1] - space_charge_region_grid.x[0]
mobile_defect_density = Set_of_Sites(
self.subgrids[species].set_of_sites
).subgrid_calculate_defect_density(self.subgrids[species], self.grid,
self.phi, self.temp)
space_charge_region_mobile_defect_mf = space_charge_region_sites.calculate_probabilities(
space_charge_region_grid, self.phi, self.temp)
space_charge_region_mobile_defect_density = space_charge_region_sites.subgrid_calculate_defect_density(
space_charge_region_grid, self.grid, self.phi, self.temp)
if mobility_scaling:
mobile_defect_conductivity = space_charge_region_mobile_defect_density * (
1 - space_charge_region_mobile_defect_mf) * charge * mobilities
else:
mobile_defect_conductivity = space_charge_region_mobile_defect_density * charge * mobilities
bulk_x_max = self.bulk_x_min + space_charge_region_width
min_bulk_index, max_bulk_index = self.find_index(
self.subgrids[species], self.bulk_x_min, bulk_x_max)
self.bulk_limits = self.calculate_offset(self.subgrids[species],
self.bulk_x_min, bulk_x_max)
bulk_mobile_defect_sites = self.create_subregion_sites(
self.subgrids[species], self.bulk_x_min, bulk_x_max)
bulk_mobile_defect_grid = Grid.grid_from_set_of_sites(
bulk_mobile_defect_sites, self.bulk_limits, self.bulk_limits,
self.grid.b, self.grid.c)
bulk_mobile_defect_density = Set_of_Sites(
bulk_mobile_defect_grid.set_of_sites
).subgrid_calculate_defect_density(bulk_mobile_defect_grid, self.grid,
self.phi, self.temp)
bulk_region_mobile_defect_mf = bulk_mobile_defect_sites.calculate_probabilities(
bulk_mobile_defect_grid, self.phi, self.temp)
if mobility_scaling:
bulk_mobile_defect_conductivity = bulk_mobile_defect_density * charge * mobilities
else:
bulk_mobile_defect_conductivity = bulk_mobile_defect_density * charge * mobilities * (
1 - bulk_region_mobile_defect_mf)
space_charge_array = np.column_stack(
(mobile_defect_conductivity, space_charge_region_grid.x))
bulk_array = np.column_stack(
(bulk_mobile_defect_conductivity, bulk_mobile_defect_grid.x))
if mobilities != 0.0:
space_charge_perpendicular = sum(space_charge_region_grid.delta_x /
mobile_defect_conductivity)
self.average_bulk_mobile_defect_density = sum(
bulk_mobile_defect_grid.delta_x *
bulk_mobile_defect_density) / sum(
bulk_mobile_defect_grid.delta_x)
bulk_perpendicular = sum(bulk_mobile_defect_conductivity /
bulk_mobile_defect_grid.delta_x)
space_charge_parallel = sum(mobile_defect_conductivity /
space_charge_region_grid.delta_x)
bulk_parallel = sum(bulk_mobile_defect_grid.delta_x /
bulk_mobile_defect_conductivity)
perpendicular_conductivity_ratio = 1 / (
space_charge_perpendicular * bulk_perpendicular)
parallel_conductivity_ratio = space_charge_parallel * bulk_parallel
else:
perpendicular_conductivity_ratio = 0.0
parallel_conductivity_ratio = 0.0
# self.depletion_factor = 1 - ( mobile_defect_density / average_bulk )
return perpendicular_conductivity_ratio, parallel_conductivity_ratio
def calculate_mobile_defect_conductivities(
self,
pos_or_neg_scr: str,
scr_limit: float,
species: str,
mobility_scaling: bool = False) -> Tuple[float, float]:
"""Calculate the conductivity ratio between the space charge region and the bulk both perpendicular and parallel to the grain boundary.
A `SetOfSites` object is created for the sites in the space charge region, and the defect distributions calculated. The width of the space charge region is calculated and a bulk region of the same width is defined. A SetOfSites object for the bulk region is created and the defect distributions calculated. Taking each site as a resistor in series or parallel respectively, the conductivity is calculated and the ratio between the space charge region and the bulk is taken.
Args:
pos_or_neg_scr (str): 'positive' - for a positive space charge potential.
'negative' - for a negative space charge potential.
scr_limit (float): The minimum electrostatic potential that the electrostatic potential must exceed to be included in the space charge region.
species (str): The species for which the conductivity is being calculated.
mobility_scaling (bool): For particles on a lattice which only interact through volume exclusion, the mobility exhibits a blocking term. True if the blocking term is to be included, False if the blocking term is not to be included. Default = False.
Returns:
float: The perpendicular conductivity ratio. The conductivity ratio between the bulk and the space charge region perpendicular to the grain boundary.
float: The parallel conductivity ratio. The conductivity ratio between the bulk and the space charge region parallel to the grain boundary.
"""
# TODO: Needs refactoring.
# TODO: Updated copy of this function from Jacob.
space_charge_region = self.create_space_charge_region(
self.subgrids[species], pos_or_neg_scr, scr_limit)
space_charge_region_limits = self.calculate_offset(
self.subgrids[species], np.min(space_charge_region),
np.max(space_charge_region))
space_charge_region_sites = self.create_subregion_sites(
self.subgrids[species], np.min(space_charge_region),
np.max(space_charge_region))
for site in space_charge_region_sites:
charge = site.defects[0].valence
mobilities = site.defects[0].mobility
space_charge_region_grid = Grid.from_set_of_sites(
space_charge_region_sites, space_charge_region_limits,
space_charge_region_limits, self.grid.b, self.grid.c)
space_charge_region_width = space_charge_region_grid.x[
-1] - space_charge_region_grid.x[0]
mobile_defect_density = self.subgrids[
species].set_of_sites.subgrid_calculate_defect_density(
self.subgrids[species], self.grid, self.phi, self.temp)
space_charge_region_mobile_defect_mf = space_charge_region_sites.calculate_probabilities(
space_charge_region_grid, self.phi, self.temp)
space_charge_region_mobile_defect_density = space_charge_region_sites.subgrid_calculate_defect_density(
space_charge_region_grid, self.grid, self.phi, self.temp)
# TODO: According to Jacob this only scales the mobility of space-charge region but not the
# TODO: bulk region, or vice-versa depending on whether it is switched on or not?
if mobility_scaling:
mobile_defect_conductivity = space_charge_region_mobile_defect_density * (
1 - space_charge_region_mobile_defect_mf) * charge * mobilities
else:
mobile_defect_conductivity = space_charge_region_mobile_defect_density * charge * mobilities
# TODO: This example bulk region can overlap with the space-charge region for cells that are similar lengths to the space-charge width, and will give spurious results.
# TODO: Possible solution: We can directly compute the bulk resistivity from the bulk site density, without having to query the space-charge model.
# TODO: Jacob to share his working code for this from his solver.
bulk_x_max = self.bulk_x_min + space_charge_region_width
min_bulk_index, max_bulk_index = self.find_index(
self.subgrids[species], self.bulk_x_min, bulk_x_max)
self.bulk_limits = self.calculate_offset(self.subgrids[species],
self.bulk_x_min, bulk_x_max)
bulk_mobile_defect_sites = self.create_subregion_sites(
self.subgrids[species], self.bulk_x_min, bulk_x_max)
bulk_mobile_defect_grid = Grid.from_set_of_sites(
bulk_mobile_defect_sites, self.bulk_limits, self.bulk_limits,
self.grid.b, self.grid.c)
bulk_mobile_defect_density = bulk_mobile_defect_grid.set_of_sites.subgrid_calculate_defect_density(
bulk_mobile_defect_grid, self.grid, self.phi, self.temp)
bulk_region_mobile_defect_mf = bulk_mobile_defect_sites.calculate_probabilities(
bulk_mobile_defect_grid, self.phi, self.temp)
# TODO: According to Jacob this only scales the mobility of space-charge region but not the
# TODO: bulk region, or vice-versa depending on whether it is switched on or not?
if mobility_scaling:
bulk_mobile_defect_conductivity = bulk_mobile_defect_density * charge * mobilities
else:
bulk_mobile_defect_conductivity = bulk_mobile_defect_density * charge * mobilities * (
1 - bulk_region_mobile_defect_mf)
space_charge_array = np.column_stack(
(mobile_defect_conductivity, space_charge_region_grid.x))
bulk_array = np.column_stack(
(bulk_mobile_defect_conductivity, bulk_mobile_defect_grid.x))
# TODO: This uses an incorrect definition of the perpendicular resistivity!!!
# TODO: Jacob has fixed this!!
# TODO: Should be refactored into its own function.
if mobilities != 0.0:
space_charge_perpendicular = sum(space_charge_region_grid.delta_x /
mobile_defect_conductivity)
self.average_bulk_mobile_defect_density = sum(
bulk_mobile_defect_grid.delta_x *
bulk_mobile_defect_density) / sum(
bulk_mobile_defect_grid.delta_x)
bulk_perpendicular = sum(bulk_mobile_defect_conductivity /
bulk_mobile_defect_grid.delta_x)
space_charge_parallel = sum(mobile_defect_conductivity /
space_charge_region_grid.delta_x)
bulk_parallel = sum(bulk_mobile_defect_grid.delta_x /
bulk_mobile_defect_conductivity)
perpendicular_conductivity_ratio = 1 / (
space_charge_perpendicular * bulk_perpendicular)
parallel_conductivity_ratio = space_charge_parallel * bulk_parallel
else:
perpendicular_conductivity_ratio = 0.0
parallel_conductivity_ratio = 0.0
# self.depletion_factor = 1 - (mobile_defect_density / average_bulk)
return perpendicular_conductivity_ratio, parallel_conductivity_ratio