Modules

Pad Dump File

gbpy.pad_dump_file.p_arr(non_p)

Function creates an array for the periodic direction.

Parameters

non_pbcint

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

Returns

arr0numpy array

A 1*2 array having the periodic directions.

gbpy.pad_dump_file.pad_dump_file(data, l1, rCut, non_p, str_alg, csc_tol)

Function to take as input the dump data (from OVITO),find the GB atoms and add padding to the GB atoms (including images) within rCut. These atoms (with padding) will be triangulated to compute Voronoi vertices and their radii.

Parameters

dataclass

Data object computed using OVITO I/O

rCutfloat

Cut-off radius for computing Delaunay triangulations

non_pbcint

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

Returns

pts_w_imgsnumpy.ndarray

Points of interest (GB atoms and neighbors) on which Delaunay triangulation is called.

gb1_indsnumpy.ndarray

Indices of the GB atoms

inds_arrnumpy.ndarray

The atom indices of the initial unit cell with no replicates.

gbpy.pad_dump_file.GB_finder(data, l1, non_pbc, str_alg, csc_tol)

The function finds the GB region usning Polyhedral Template Matching.

Parameters

filename0string

The lammps dump file

lat_par: float

The lattice parameter

non_pbcint

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

Returns

GbRegion: list

The maximum and Minimum value of postion of atoms in Z direction in the GB region.

GbWidthlist

GbRegion[1] - GbRegion[0]

GbIndexnumpy.ndarray

The index of atoms in GB

w_bottom_SClist

The width of the region on the bottom side of GB which have single crystal structure

w_top_SClist

The width of the region on the top side of GB which have single crystal structure

gbpy.pad_dump_file.num_rep_2d(xvec, yvec, rCut)

Function finds the number of replications necessary such that thecircle of radius rCut at the center of the primitive-cell lies completely inside the super-cell.

Parameters

xvecnumpy array

The basis vector in x direction in x-z plane

yvecnumpy array

The basis vector in z direction in x-z plane

rCutfloat

Cut-off radius for computing Delaunay triangulations

Returns

[int(m_x), int(m_y)]list

int(m_x) is the number of replications in x direction, int(m_y) is the number of replication in z direction.

gbpy.pad_dump_file.pad_gb_perp(data, GbRegion, GbIndex, rCut, non_p)

Function to take as input the dump data (from OVITO), find the GB atoms and add padding to the GB atoms within rCut in Z direction.

Parameters

dataclass

Data object computed using OVITO I/O

GbRegionlist

Indices of atoms in GB area

GbIndexnumpy array

Indices of atoms in GB area

rCutfloat

Cut-off radius for computing Delaunay triangulations

non_pbcint

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

Returns

pts1numpy array

Indices of the atoms which Z value is in range [GBRegion[0] - rCut, GBRegion[1] + rCut].

gb1_indsnumpy array

Indices of the GB atoms

gbpy.pad_dump_file.create_imgs(pts1, n1, n2, sim_1vec, sim_2vec, non_p)

Creates the replicates of the main cell in X and Z direction.

Parameters

pts1numpy array

Indices of the atoms which Y value is in range [GBRegion[0] - rCut, GBRegion[1] + rCut].

n1int

Number of replications in 1st periodic direction

n2int

Number of replications in 2nd periodic direction

sim_1vecnumpy array

The simulation cell basis vector in 1st periodic direction

sim_2vecnumpy array

The simulation cell basis vector in 2nd periodic direction

non_pbcint

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

Returns

pts_w_imgsnumpy array

The position of atoms after replicating the box n_x and n_z times in X and Z direction.

inds_arraynumpy array

The atom indices of the initial unit cell with no replicates.

gbpy.pad_dump_file.slice_along_planes(orig, sim_1vec, sim_2vec, sim_nonp_vec, rCut, pts_w_imgs, gb1_inds, non_p, inds_arr)

Function cuts the pts_w_imgs within an rCut from the GB.

Parameters

orignumpy array

The origin of the main cell.

sim_1vecnumpy array

The simulation cell basis vector in a direction

sim_2vecnumpy array

The simulation cell basis vector in b direction

sim_nonp_vecnumpy array

The simulation cell basis vector in c direction

rCutfloat

Cut-off radius for computing Delaunay triangulations

pts_w_imgsnumpy array

The position of atoms after replicating the box n_x and n_z times in X and Z direction.

gb1_indsnumpy array

Indices of the GB atoms

non_pbcint

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

inds_arrnumpy array

The atom indices of the initial unit cell with no replicates.

Returns

pts_w_imgsnumpy array

The position of atoms after replicating the box, n_x and n_z times in x and z direction.

gb1_indsnumpy array

Indices of the GB atoms

inds_arrnumpy array

The atom indices of the initial unit cell with no replicates.

gbpy.pad_dump_file.del_inds(ind1, pts1, gb1_inds, inds_arr)

Function deletes the indices of atoms outside of the main box plus rCut margin around it

Parameters

ind1numpy array

The indices of atoms we want to keep

pts1numpy array

The position of atoms after replicating the box n_x and n_z times in x and z direction.

gb1_indnumpy array

Indices of the GB atoms

inds_arrnumpy array

The atom indices of the initial unit cell with no replicates.

Returns

pts1numpy array

The position of atoms we want to keep

gb1_indsnumpy array

Indices of the GB atoms

inds_arrnumpy array

The atom indices of the initial unit cell with no replicates.

gbpy.pad_dump_file.inds_to_keep(norm_vec, pl_pt, orig, pts)

Function identifies the indices of atoms which are in inside the main box plus a rCut margin around it

Parameters

norm_vecnumpy array

Plane normal within rCut distance from the considered box face

pl_ptnumpy array

A point on a plane within rCut distance from the considered box face

orignumpy array

The origin of the main cell.

ptsnumpy array

The position of atoms after replicating the box, n_x and n_z times in x and z direction.

Returns

inds_keepnumpy array

The indices of atoms within the replicates which are within rCut distance of the main cell

vv props

gbpy.vv_props.Circum_O_R(vertex_pos, tol)

Function finds the center and the radius of the circumsphere of the every tetrahedron. Reference: Fiedler, Miroslav. Matrices and graphs in geometry. No. 139. Cambridge University Press, 2011.

Parameters

vertex_posnumpy array

The position of vertices of a tetrahedron

tolfloat

Tolerance defined to identify co-planar tetrahedrons

Returns

circum_centernumpy array

The center of the circum-sphere

circum_radfloat

The radius of the circum-sphere

gbpy.vv_props.triang_inds(pts_w_imgs, gb1_inds, inds_arr)

Function finds the indices of atoms which make tetrahedrons with at least one GB atom.

Parameters

pts_w_imgsnumpy array

The position of atoms which are inside the main box and within rCut to the main box.

gb1_indsnumpy array

Indices of the GB atoms

inds_arrnumpy array

The atom indices of the initial unit cell with no replicates.

Returns

tri_verticesnumpy array

Tetrahedrons with at least one corner in the GB region.

gb_tri_inds1numpy array

The indices of atoms which make tri_vertices tetrahedrons.

gbpy.vv_props.vv_props(pts_w_imgs, tri_vertices, gb_tri, l1)

Function finds the circum-center/sphere of tetrahedrons containing at least one GB atom.

Parameters

pts_w_imgsnumpy array

The position of atoms which are inside the main box and within rCut to the main box.

tri_verticesnumpy array

Tetrahedrons with at least one corner in the GB region.

gb_trinumpy array

The indices of atoms which make tri_vertices tetrahedrons.

lat_parfloat

Lattice parameter for the crystal being simulated.

Returns

cc_coors1numpy array

The coordinates of the circum-center of the tetrahedrons

cc_rad1numpy array

The circum-radius of the tetrahedrons.

gbpy.vv_props.wrap_cc(cell1, pts)

Function finds the indices of atoms making tetrahedrons

Parameters

cell1numpy array

The simulation cell ( a 3*4 numpy array where the first 3 columns are the cell vectors and the last column is the box origin)

ptsnumpy array

Position of atoms in initial cell, the atoms within an rCut of the initial cell.

Returns

pts1numpy array

Position of atoms in initial cell, the atoms within an rCut of the initial cell, and the Voronoi coordinates as the new set of atoms.

Utility Function

gbpy.util_funcs.compute_ovito_data(filename0)

Computes the attributes of ovito

Parameters

filename0string

The name of the input file.

Returns

dataclass

all the attributes of data

gbpy.util_funcs.identify_pbc(data)

Function finds the non-periodic direction

Parameters

dataclass

all the attributes of data

Returns

non_pbcint

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

gbpy.util_funcs.box_size_reader(dump_name)

Function reads the box_bound from lammps dump file.

Parameters

dump_namestring

The name of the lammps input file.

Returns

box_boundnp.array

The box bound read from lammps dump file which is 9 parameters: xlo, xhi, ylo, yhi, zlo, zhi, xy, xz, yz

gbpy.util_funcs.define_bounds(box_bound)

Function to find the untilted, tilt, and box type.

Parameters

box_boundnp.array

The box bound read from lammps dump file which is 9 parameters: xlo, xhi, ylo, yhi, zlo, zhi, xy, xz, yz

Returns

untiltednp.array

values of xlo, xhi, ylo, yhi, zlo, zhi.

tiltnp.array

For box type “block” this values id []. For box type “prism” this value is [xy, yz, xz].

box_typestring

type of box which is eaither “block” or “prism”.

gbpy.util_funcs.RemProb(data, CohEng, GbIndex)

The function finds The atomic removal probabilty.

Parameters

filename0string

The lammps dump file

CohEngfloat

The cohesive energy

GbIndexnumpy.ndarray

The index of atoms in GB

gbpy.util_funcs.RemIns_decision(p_rm)

The function finds The atomic removal probabilty.

Parameters

p_rmnumpy.ndarray

The probability of removing an atom

gbpy.util_funcs.radi_normaliz(cc_rad)

The function finds the atomic insertion probabilty.

Parameters

cc_rad :

The circum-radius of the tetrahedrons.

gbpy.util_funcs.choos_rem_ins()

The function makes the decision whether the trail operation is insertion or removal.

gbpy.util_funcs.atom_insertion(filename0, path2dump, cc_coors1, atom_id)

The function adds the inserted atom to the lammps dump file.

Parameters

filename0string

The initial lammps dump file

path2dumpstring

The path to dump the lammps dump file

cc_coors1numpy.ndarray

The coordinates of the circum-center of the tetrahedrons.

atom_idnumpy.ndarray

The atom ID of the inserted atom which is the ID of last atom + 1

gbpy.util_funcs.atom_removal(filename0, path2dump, ID2change, var)

The function removes the chosen atom from the lammps dump file.

Parameters

filename0string

The lammps dump file

path2dumpstring

The path to dump the lammps dump file

ID2changeint

The ID of the atom which will be removed

varnumpy.ndarray

The indices of the atom which will be removed. This is just to check.

gbpy.util_funcs.cal_area(data, non_p)

The function finds the area of the GB plane.

Parameters

dataclass

all the attributes of data

non_pinteger

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

gbpy.util_funcs.cal_GB_E(data, weight_1, non_p, l1, CohEng, str_alg, csc_tol)

The function finds the energy of the GB.

Parameters

dataclass

all the attributes of data

non_p :

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

lat_par :

Lattice parameter for the crystal being simulated.

CohEngfloat

The cohesive energy

str_algstring

The algorithm used to find the atoms in the GB and the surfaces. str_alg=”csc” which uses centrosymmetry parameter str_alg=”ptm” which uses polyhedral template matching

csc_tolfloat

The tolerance for identifing the atoms in the GB and surfaces using the str_alg=”csc”

Return

—————-

E_GBfloat

The enrgy of GB plane

gbpy.util_funcs.p_boltz_func(dE, area, Tm)

The function finds the botzman probability of acceptance.

Parameters

dEfloat

The energy difference the initial structure and the structure after the trial operation.

areafloat

The surface area of the GB plane.

Tmfloat

The melting temperature of the material

gbpy.util_funcs.decide(p_boltz)

The function decides whether the new structure is accepted or not.

Parameters

p_boltzfloat

The boltzman probaility

gbpy.util_funcs.check_SC_reg(data, l1, rCut, non_p, tol_fix_reg, SC_tol, str_alg, csc_tol)

Function to identify whether single crystal region on eaither side of the GB is bigger than a tolerance (SC_tol)

Parameters

data :

Data object computed using OVITO I/O

lat_par :

Lattice parameter for the crystal being simulated

rCut :

Cut-off radius for computing Delaunay triangulations

non_pbcint

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

tol_fix_regfloat

The user defined tolerance for the size of rigid translation region in lammps simulation.

SC_tolfloat

The user defined tolerance for the minimum size of single crystal region.

str_algstring

The algorithm used to find the atoms in the GB and the surfaces. str_alg=”csc” which uses centrosymmetry parameter str_alg=”ptm” which uses polyhedral template matching

csc_tolfloat

The tolerance for identifing the atoms in the GB and surfaces using the str_alg=”csc”

Returns

SC_boolean :

A boolean list for low/top or left/right single crytal region. True means the width > SC_tol.

gbpy.util_funcs.add_sc(pkl_file, data_0, l1, rCut, non_p, tol_fix_reg, SC_tol, str_alg, csc_tol, box_bound)

Function adds single crystal region to the simulation case the GB get close to the edges

Parameters

pkl_file :

data_0 :

lat_par :

Lattice parameter for the crystal being simulated.

rCut :

Cut-off radius for computing Delaunay triangulations

non_pbcint

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

tol_fix_regfloat

The user defined tolerance for the size of rigid translation region in lammps simulation.

SC_tolfloat

The user defined tolerance for the minimum size of single crystal region.

str_algstring

The algorithm used to find the atoms in the GB and the surfaces. str_alg=”csc” which uses centrosymmetry parameter str_alg=”ptm” which uses polyhedral template matching

csc_tolfloat

The tolerance for identifing the atoms in the GB and surfaces using the str_alg=”csc”

box_boundnp.array

The box bound read from lammps dump file which is 9 parameters: xlo, xhi, ylo, yhi, zlo, zhi, xy, xz, yz

Returns

uniq_atomsnumpy.ndarray

The ID, atom type and position of the atoms in the single crystal region which will be added to the lammps dump file.

Lammps Dump Writer

gbpy.lammps_dump_writer.lammps_box(pkl_name)

Function calculates the box bound and the atom coordinates of the GB simulation. Ref: https://lammps.sandia.gov/doc/Howto_triclinic.html

Parameters

pkl_name :

The name of the pkl file which contains the simulation cell ( a 3*4 numpy array where the first 3 columns are the cell vectors and the last column is the box origin), the cordinates of the upper and lower grain.

Returns

box_bound :

The box bound needed to write lammps dump file which is 9 parameters: xlo, xhi, ylo, yhi, zlo, zhi, xy, xz, yz

dump_lamp :

A numpy nd.array having atom ID, atom type( 1 for upper grain and 2 for lower grain), x, y, z

box_type :

The type of simulation box which is eaither “prism” or “block”

gbpy.lammps_dump_writer.box_bound_func(sim_cell)

This function finds the simulation cell type and the bounds of the simulation cell.

Parameters

sim_cell: numpy.ndarray

A 3x4 matrix (with column-major ordering). The first

three columns of the matrix represent the three cell

vectors and the last column is the position of the cell’s origin.

Returns

box_bound :

The box bound needed to write lammps dump file which is 9 parameters: xlo, xhi, ylo, yhi, zlo, zhi, xy, xz, yz

box_type :

The type of simulation box which is eaither “prism” or “block”

gbpy.lammps_dump_writer.write_lammps_dump(filename0, box_bound, dump_lamp, box_type)

Function writes the lammps dump file.

Parameters

filename0 :

Name of the lammps dump file

box_bound :

The box bound needed to write lammps dump file which is 9 parameters: xlo, xhi, ylo, yhi, zlo, zhi, xy, xz, yz

dump_lamp :

A numpy nd.array having atom ID, atom type( 1 for upper grain and 2 for lower grain), x, y, z

Lammps Script Writer

gbpy.lammps_script_writer.file_gen(fil_name)

Function opens the input file.

Parameters

fil_namestr

name of the input lammps dump file

Returns

———-

fiw:

the opened lammps dump file

fil_name: str

name of the input lammps dump file

gbpy.lammps_script_writer.run_lammps_anneal(filename0, fil_name, pot_path, l1, tol_fix_reg, lammps_exe_path, output, Tm, check, step=2, Etol=1e-25, Ftol=1e-25, MaxIter=5000, MaxEval=10000, Iter_heat=1000, Iter_equil=10000, Iter_cool=12000)

Function runs the lammps script

Parameters

filename0str

the opened lammps dump file

fil_name: str

name of the input lammps dump file

pot_path: str

The directory of the interatomic potential

lat_par: int

The lattice parameter

tol_fix_reg: int

The thickness of the fix rigid part in the simulation cell

lammps_exe_path: str

The path of the lammps .exe file

output: str

The name of the lammps output file

Tm: int

The melting point of the material of interest

Etol: int

stopping tolerance for energy (unitless)

Ftol: int

stopping tolerance for force (force units)

MaxIter: int

max iterations of minimizer

MaxEval: int

max number of force/energy evaluations

Iter_heat: int

number of iteration for the heating process

Iter_equil: int

number of iteration for the equilibration process

Iter_cool: int

number of iteration for the cooling process

gbpy.lammps_script_writer.run_lmp(non_p, fil_name, Etol, Ftol, MaxIter, MaxEval, Iter_heat, Iter_equil, Iter_cool, l1, dump_name, pot_path, output, check)

Function writes the lammps script for heating/equil/cooling process

Parameters

non_p: int

The non-periodic direction. 0 , 1 or 2 which corresponds to x, y and z direction, respectively.

fil_name: str

name of the input lammps dump file

Etol: int

stopping tolerance for energy (unitless)

Ftol: int

stopping tolerance for force (force units)

MaxIter: int

max iterations of minimizer

MaxEval: int

max number of force/energy evaluations

Iter_heat: int

number of iteration for the heating procedure

Iter_equil: int

number of iteration for the equilibration procedure

Iter_cool: int

number of iteration for the cooling procedure

lat_par :

Lattice parameter for the crystal being simulated

dump_name: str

Name of the lammps dump file

pot_path: str

The directory of the interatomic potential

output: str

Name of the lammps script

check: str

If check=”SC” it means the gb gets very close to the GB.