"""
"""
import os
import numpy as np
import warnings
import itertools
from ase.io import write
import uuid
import gzip
import io
from scipy.special import sph_harm
import copy
from pyscal.atoms import Atoms, AttrSetter
import pyscal.csystem as pc
import pyscal.traj_process as ptp
from pyscal.formats.ase import convert_snap
import pyscal.structure_creator as pcs
import pyscal.operations.operations as po
#import pyscal.routines as routines
#import pyscal.visualization as pv
[docs]class System:
"""
Python class for holding the properties of an atomic configuration
"""
[docs] def __init__(self, filename=None, format="lammps-dump",
compressed = False, customkeys=None):
self.initialized = True
self.neighbors_found = False
self.neighbor_method = None
self.ghosts_created = False
self.actual_box = None
#box parameters
self.rot = [[0,0,0], [0,0,0], [0,0,0]]
self.rotinv = [[0,0,0], [0,0,0], [0,0,0]]
self.boxdims = [0,0,0]
self.triclinic = 0
self._structure_dict = None
self._atoms = Atoms()
if filename is not None:
self.read_inputfile(filename, format=format,
compressed = compressed, customkeys=customkeys)
[docs] @classmethod
def from_structure(cls, structure, lattice_constant = 1.00, repetitions = None, ca_ratio = 1.633, noise = 0, element=None, chemical_symbol=None):
atoms, box, sdict = pcs.make_crystal(structure, lattice_constant=lattice_constant,
repetitions=repetitions, ca_ratio=ca_ratio,
noise=noise, element=element, return_structure_dict=True)
obj = cls()
obj.box = box
obj.atoms = atoms
obj.atoms._lattice = structure
obj.atoms._lattice_constant = lattice_constant
obj._structure_dict = sdict
return obj
[docs] def iter_atoms(self):
return self.atoms.iter_atoms()
@property
def natoms(self):
return self.atoms.natoms
@property
def concentration(self):
return self.atoms.composition
@property
def composition(self):
return self.atoms.composition
@property
def box(self):
"""
Wrap for inbuilt box
"""
if self.actual_box is not None:
return self.actual_box
else:
return self._box
@box.setter
def box(self, userbox):
"""
Box setter
"""
#we should automatically check for triclinic cells here
summ = 0
for i in range(3):
box1 = np.array(userbox[i-1])
box2 = np.array(userbox[i])
summ += np.dot(box1, box2)/(np.linalg.norm(box1)*np.linalg.norm(box2))
#check if the summ is zero
if (np.abs(summ) > 1E-6):
#this is a triclinic box
rot = np.array(userbox).T
rotinv = np.linalg.inv(rot)
self.triclinic = 1
self.rot = rot
self.rotinv = rotinv
self.boxdims[0] = np.sum(np.array(userbox[0])**2)**0.5
self.boxdims[1] = np.sum(np.array(userbox[1])**2)**0.5
self.boxdims[2] = np.sum(np.array(userbox[2])**2)**0.5
self._box = userbox
@property
def box_dimensions(self):
return [np.linalg.norm(self.box[x]) for x in range(3)]
@property
def direct_coordinates(self):
dims = self.box_dimensions
xfrac = np.array(self.atoms.positions)[:,0]/dims[0]
yfrac = np.array(self.atoms.positions)[:,1]/dims[1]
zfrac = np.array(self.atoms.positions)[:,2]/dims[2]
coords = np.column_stack((xfrac, yfrac, zfrac))
return coords
@property
def volume(self):
"""
Volume of box
"""
vol = np.dot(np.cross(self._box[0], self._box[1]), self._box[2])
return vol
@property
def atoms(self):
return self._atoms
@atoms.setter
def atoms(self, atoms):
"""
Set atoms
"""
if(len(atoms['positions']) < 200):
#we need to estimate a rough idea
needed_atoms = 200 - len(atoms)
#get a rough cell
needed_cells = np.ceil(needed_atoms/len(atoms))
nx = int(needed_cells**(1/3))
nx = int(np.ceil(nx/2))
if np.sum(self.box) == 0:
raise ValueError("Simulation box should be initialized before atoms")
atoms, box = self.repeat((nx, nx, nx), atoms=atoms, ghost=True, scale_box=True, assign=False, return_atoms=True)
self.actual_box = self.box.copy()
self.box = box
self._atoms = atoms
[docs] def add_atoms(self, atoms):
"""
Cleanly add a given list of atoms
Parameters
----------
atoms : dict
Returns
-------
None
"""
## MOVE TO ATOMS
self._atoms.add_atoms(atoms)
[docs] def repeat(self, repetitions, atoms=None, ghost=False, scale_box=True, assign=False, return_atoms=False):
"""
"""
return po.repeat(self, repetitions,
atoms=atoms, ghost=ghost,
scale_box=scale_box,
return_atoms=return_atoms)
[docs] def remap_atoms_into_box(self):
"""
Go through atoms in the list and remap them into the bix
"""
rot = np.array(self.box).T
rotinv = np.linalg.inv(rot)
for x in range(self.natoms):
pos = pc.remap_atom_into_box(self.atoms["positions"][x],
self.triclinic,
rot,
rotinv,
self.box_dimensions)
self.atoms["positions"][x] = pos
[docs] def apply_mask(self, mask_type="primary", ids=None, indices=None, condition=None, selection=False):
"""
Notes
-----
Masks can be used to exclude atoms from neighbor calculations. An atom for which
mask is set to True is excluded from the calculation. There are two types of masks,
`primary` or `secondary`. For example, neighbors are being calculated for a central
atom `i`. The neighbor atom is denoted as `j`. If `primary` mask of `i` is True, no neighbor
calculation is carried out for `i`. If it is False, `i` is considered. Now if `secondary`
mask of `j` is True, it will not included in the list of neighbors of `i` even if it is within
the cutoff distance. The `primary` mask of `j` has no effect in this situation.
An example situation can be to calculate the local concentration around Ni atoms in a NiAl
structure. In this case, the `primary` mask of all Al atoms can be set to True so that
only `Ni` atoms are considered. Now, in a second case, the task is to count the number of Al
atoms around each Ni atom. For this case, the `primary` mask of all Al atoms can be set to True,
and the `secondary` mask of all Ni atoms can be set to True.
The masks for ghost atoms are copied from the corresponding mask for real atoms.
"""
#check if length of mask is equal to length of real atoms
self.atoms.apply_mask(mask_type=mask_type, ids=ids,
indices=indices, condition=condition, selection=selection)
[docs] def remove_mask(self, mask_type="primary", ids=None, indices=None, condition=None, selection=False):
"""
Remove applied masks
Parameters
----------
mask_type: string, optional
type of mask to be applied, either `primary`, `secondary` or `all`
Returns
-------
None
"""
self._atoms.remove_mask(mask_type=mask_type, ids=ids,
indices=indices, condition=condition, selection=selection)
[docs] def apply_selection(self, ids=None, indices=None, condition=None):
self._atoms.apply_selection(ids=ids, indices=indices, condition=condition)
[docs] def remove_selection(self, ids=None, indices=None, condition=None):
self._atoms.remove_selection(ids=ids, indices=indices, condition=condition)
[docs] def delete(self, ids=None, indices=None, condition=None, selection=False):
self._atoms.delete(ids=ids, indices=indices, condition=condition, selection=selection)
[docs] def embed_in_cubic_box(self, input_box=None, return_box=False):
"""
Embedded the triclinic box in a cubic box
"""
return po.embed_in_cubic_box(self, input_box=input_box,
return_box=return_box)
[docs] def get_distance(self, pos1, pos2, vector=False):
"""
Get the distance between two atoms.
Parameters
----------
pos1 : list
first atom position
pos2 : list
second atom position
vector: bool, optional
If True, return the vector between two atoms
Returns
-------
distance : double
distance between the first and second atom.
Notes
-----
Periodic boundary conditions are assumed by default.
"""
if vector:
return dist, diff
else:
return dist
[docs] def get_concentration(self):
"""
Return a dict containing the concentration of the system
Parameters
----------
None
Returns
-------
condict : dict
dict of concentration values
"""
return self.concentration
[docs] def to_file(self, outfile, format='lammps-dump', customkeys=None, customvals=None,
compressed=False, timestep=0, species=None):
"""
Save the system instance to a trajectory file.
Parameters
----------
outfile : string
name of the output file
format : string, {'lammps-dump', 'lammps-data', 'poscar'}
format of the output file, default `lammps-dump`
Currently only `lammps-dump` format is supported.
customkeys : list of strings, optional
a list of extra atom wise values to be written in the output file.
customvals : list or list of lists, optional
If `customkey` is specified, `customvals` take an array of the same length
as number of atoms, which contains the values to be written out.
compressed : bool, optional
If true, the output is written as a compressed file.
timestep : int, optional
timestep to be written to file. default 0
species : None, optional
species of the atoms. Required if any format other than 'lammps-dump' is used. Required
for convertion to ase object.
Returns
-------
None
Notes
-----
`to_file` method can handle a number of file formats. The most customizable format is the
`lammps-dump` which can take a custom options using customkeys and customvals. customkeys
will be the header written to the dump file. It can be any Atom attribute, any property
stored in custom variable of the Atom, or calculated q values which can be given by `q4`,
`aq4` etc. External values can also be provided using `customvals` option. `customvals` array
should be of the same length as the number of atoms in the system.
For all other formats, ASE is used to write out the file, and hence the `species` keyword
needs to be specified. If initially, an ASE object was used to create the System, `species`
keyword will already be saved, and need not be specified. In other cases, `species` should
be a list of atomic species in the System. For example `["Cu"]` or `["Cu", "Al"]`, depending
on the number of species in the System. In the above case, atoms of type 1 will be mapped to
Cu and of type 2 will be mapped to Al. For a complete list of formats that ASE can handle,
see `here <https://wiki.fysik.dtu.dk/ase/ase/io/io.html>`_ .
"""
ptp.write_file(self, outfile, format = format,
compressed = compressed, customkeys = customkeys, customvals = customvals,
timestep = timestep, species = species)
[docs] def to_ase(self, species=None):
"""
Convert system to an ASE Atoms object
Parameters
----------
species : list of string
The chemical species
Returns
-------
None
"""
return convert_snap(self, species=species)
[docs] def reset_neighbors(self):
"""
Reset the neighbors of all atoms in the system.
Parameters
----------
None
Returns
-------
None
Notes
-----
It is used automatically when neighbors are recalculated.
"""
self.atoms["neighbors"] = []
self.atoms["neighbordist"] = []
self.atoms["temp_neighbors"] = []
self.atoms["temp_neighbordist"] = []
self.atoms["neighborweight"] = []
self.atoms["diff"] = []
self.atoms["r"] = []
self.atoms["theta"] = []
self.atoms["phi"] = []
self.atoms["cutoff"] = []
self.neighbors_found = False
mapdict = {}
mapdict["neighbors"] = {}
mapdict["neighbors"]["index"] = "neighbors"
mapdict["neighbors"]["distance"] = "neighbordist"
mapdict["neighbors"]["weight"] = "neighborweight"
mapdict["neighbors"]["displacement"] = "diff"
mapdict["neighbors"]["cutoff"] = "cutoff"
mapdict["neighbors"]["angle"] = {}
mapdict["neighbors"]["angle"]["polar"] = "theta"
mapdict["neighbors"]["angle"]["azimuthal"] = "phi"
mapdict["neighbors"]["temporary"] = {}
mapdict["neighbors"]["temporary"]["index"] = "temp_neighbors"
mapdict["neighbors"]["temporary"]["distance"] = "temp_neighbordist"
self.atoms._add_attribute(mapdict)
def _check_neighbors(self):
"""
Check if neighbors are calculated
"""
if not self.neighbors_found:
raise ValueError("This calculation needs neighbors to be calculated")
[docs] def average_over_neighbors(self, key, include_self=True):
"""
Perform a simple average over neighbor atoms
Parameters
----------
key: string
atom property
include_self: bool, optional
If True, include the host atom in the calculation
Returns
-------
"""
print(key)
self._check_neighbors()
if not key in self.atoms.keys():
raise KeyError("required property not found!")
test = self.atoms[key][0]
if isinstance(test, list):
raise TypeError("Averaging can only be done over 1D quantities")
avgarr = []
for i in range(len(self.atoms["positions"])):
arr = []
if include_self:
arr.append(self.atoms[key][i])
for j in self.atoms["neighbors"][i]:
arr.append(self.atoms[key][j])
avgarr.append(np.mean(arr))
return avgarr
[docs] def find_neighbors(self, method='cutoff', cutoff=0, threshold=2,
voroexp=1, padding=1.2, nlimit=6,
cells=None, nmax=12, assign_neighbor=True):
"""
Find neighbors of all atoms in the :class:`~pyscal.core.System`.
Parameters
----------
method : {'cutoff', 'voronoi', 'number'}
`cutoff` method finds neighbors of an atom within a specified or adaptive cutoff distance from the atom.
`voronoi` method finds atoms that share a Voronoi polyhedra face with the atom. Default, `cutoff`
`number` method finds a specified number of closest neighbors to the given atom. Number only populates
cutoff : { float, 'sann', 'adaptive'}
the cutoff distance to be used for the `cutoff` based neighbor calculation method described above.
If the value is specified as 0 or `adaptive`, adaptive method is used.
If the value is specified as `sann`, sann algorithm is used.
threshold : float, optional
only used if ``cutoff=adaptive``. A threshold which is used as safe limit for calculation of cutoff.
voroexp : int, optional
only used if ``method=voronoi``. Power of the neighbor weight used to weight the contribution of each atom towards
Steinhardt parameter values. Default 1.
padding : double, optional
only used if ``cutoff=adaptive`` or ``cutoff=number``. A safe padding value used after an adaptive cutoff is found. Default 1.2.
nlimit : int, optional
only used if ``cutoff=adaptive``. The number of particles to be considered for the calculation of adaptive cutoff.
Default 6.
cells : bool, optional
If True, always use cell lists. Default None.
nmax : int, optional
only used if ``cutoff=number``. The number of closest neighbors to be found for each atom. Default 12
Returns
-------
None
Raises
------
RuntimeWarning
raised when `threshold` value is too low. A low threshold value will lead to 'sann' algorithm not converging
when finding a neighbor. This function will try to automatically increase `threshold` and check again.
RuntimeError
raised when neighbor search was unsuccessful. This is due to a low `threshold` value.
Notes
-----
This function calculates the neighbors of each particle. There are several ways to do this. A complete description of
the methods can be `found here <https://pyscal.readthedocs.io/en/latest/nearestneighbormethods.html>`_.
Method cutoff and specifying a cutoff radius uses the traditional approach being the one in which the neighbors of an atom
are the ones that lie in the cutoff distance around it.
In order to reduce time during the distance sorting during thefind_neighbors adaptive methods, pyscal sets an initial guess for a cutoff distance.
This is calculated as,
.. math:: r_{initial} = threshold * (simulation~box~volume/ number~of~particles)^{(1/3)}
threshold is a safe multiplier used for the guess value and can be set using the `threshold` keyword.
In Method cutoff, if ``cutoff='adaptive'``, an adaptive cutoff is found during runtime for each atom [1].
Setting the cutoff radius to 0 also uses this algorithm. The cutoff for an atom i is found using,
.. math:: r_c(i) = padding * ((1/nlimit) * \sum_{j=1}^{nlimit}(r_{ij}))
padding is a safe multiplier to the cutoff distance that can be set through the keyword `padding`. `nlimit` keyword sets the
limit for the top nlimit atoms to be taken into account to calculate the cutoff radius.
In Method cutoff, if ``cutoff='sann'``, sann algorithm is used [2]. There are no parameters to tune sann algorithm.
The second approach is using Voronoi polyhedra which also assigns a weight to each neighbor in the ratio of the face area between the two atoms.
Higher powers of this weight can also be used [3]. The keyword `voroexp`
can be used to set this weight.
If method is `number`, instead of using a cutoff value for finding neighbors, a specified number of closest atoms are
found. This number can be set through the argument `nmax`.
If `cells` is None, cell lists are used if number of atoms are higher than 2500. If True, cell lists are always used.
.. warning::
Adaptive and number cutoff uses a padding over the intial guessed "neighbor distance". By default it is 2. In case
of a warning that ``threshold`` is inadequate, this parameter should be further increased. High/low value
of this parameter will correspond to the time taken for finding neighbors.
References
----------
.. [1] Stukowski, A, Model Simul Mater SC 20, 2012
.. [2] van Meel, JA, Filion, L, Valeriani, C, Frenkel, D, J Chem Phys 234107, 2012
.. [3] Haeberle, J, Sperl, M, Born, P, arxiv 2019
"""
#first reset all neighbors
self.reset_neighbors()
self.filter = 0
if threshold < 1:
raise ValueError("value of threshold should be at least 1.00")
if cells is None:
cells = (self.natoms > 250)
if method == 'cutoff':
if cutoff=='sann':
finished = False
for i in range(1, 10):
finished = pc.get_all_neighbors_sann(self.atoms, 0.0,
self.triclinic, self.rot, self.rotinv,
self.boxdims, threshold*i, cells)
if finished:
if i>1:
warnings.warn("found neighbors with higher threshold than default/user input")
break
warnings.warn("Could not find sann cutoff. trying with a higher threshold", RuntimeWarning)
else:
raise RuntimeError("sann cutoff could not be converged. This is most likely, \
due to a low threshold value. Try increasing it.")
elif cutoff=='adaptive' or cutoff==0:
finished = pc.get_all_neighbors_adaptive(self.atoms, 0.0,
self.triclinic, self.rot, self.rotinv,
self.boxdims, threshold, nlimit, padding, cells)
if not finished:
raise RuntimeError("Could not find adaptive cutoff")
else:
if cells:
pc.get_all_neighbors_cells(self.atoms, cutoff,
self.triclinic, self.rot, self.rotinv, self.boxdims)
else:
pc.get_all_neighbors_normal(self.atoms, cutoff,
self.triclinic, self.rot, self.rotinv, self.boxdims)
elif method == 'number':
finished = pc.get_all_neighbors_bynumber(self.atoms, 0.0,
self.triclinic, self.rot, self.rotinv,
self.boxdims, threshold, nmax, cells, assign_neighbor)
if not finished:
raise RuntimeError("Could not find enough neighbors - try increasing threshold")
elif method == 'voronoi':
clean_vertices = (cutoff>0)
#CLEANING is TURNED OFF
#if not clean_vertices:
#copy the simulation cell
backupbox = self._box.copy()
if self.triclinic:
if not self.ghosts_created:
atoms, box = self.repeat((1, 1, 1), ghost=True, scale_box=True, assign=False, return_atoms=True)
self._atoms = atoms
self = self.embed_in_cubic_box()
pc.get_all_neighbors_voronoi(self.atoms, 0.0,
self.triclinic, self.rot, self.rotinv,
self.boxdims, voroexp)
if self.triclinic:
self._box = backupbox
#now clean up
#else:
# real_atomdict = {"positions":copy.copy(self.atoms.positions_for_all),
# "ghost":copy.copy(self.atoms.positions_for_ghost)}
#we need to call the method
#this means alles good
# if self.actual_box is None:
# if self.triclinic:
# new_box = self.embed_in_cubic_box(inputbox=self._box, return_box=True)
# rot = np.array(new_box).T
# rotinv = np.linalg.inv(rot)
# else:
# new_box = self._box
# rot = [[0,0,0], [0,0,0], [0,0,0]]
# rotinv = [[0,0,0], [0,0,0], [0,0,0]]
# #ghosts are present
# else:
# if self.triclinic:
# new_box = self.embed_in_cubic_box(inputbox=self.actual_box, return_box=True)
# rot = np.array(new_box).T
# rotinv = np.linalg.inv(rot)
# else:
# new_box = self.actual_box
# rot = [[0,0,0], [0,0,0], [0,0,0]]
# rotinv = [[0,0,0], [0,0,0], [0,0,0]]
# boxdims = [0,0,0]
# boxdims[0] = np.sum(np.array(new_box[0])**2)**0.5
# boxdims[1] = np.sum(np.array(new_box[1])**2)**0.5
# boxdims[2] = np.sum(np.array(new_box[2])**2)**0.5
# pc.get_all_neighbors_voronoi(real_atomdict, 0.0,
# self.triclinic, rot, rotinv,
# boxdims, 1)
# pc.clean_voronoi_vertices(real_atomdict,
# self.atoms, 0.0,
# self.triclinic, rot, rotinv,
# boxdims, cutoff)
#unique_vertices = []
#for i in range(len(self.vertex_is_unique)):
# for j in range(len(self.vertex_is_unique[i])):
# if self.vertex_is_unique[i][j]:
# unique_vertices.append(self.vertex_positions[i][j])
#self.atoms["vertex_positions_unique_skipcheck"] = unique_vertices
#assign extra options
mapdict = {}
mapdict["voronoi"] = {}
mapdict["voronoi"]["volume"] = "voronoi_volume"
mapdict["voronoi"]["face"] = {}
mapdict["voronoi"]["face"]["vertices"] = "face_vertices"
mapdict["voronoi"]["face"]["perimeters"] = "face_perimeters"
mapdict["voronoi"]["vertex"] = {}
mapdict["voronoi"]["vertex"]["vectors"] = "vertex_vectors"
mapdict["voronoi"]["vertex"]["numbers"] = "vertex_numbers"
mapdict["voronoi"]["vertex"]["positions"] = "vertex_positions"
#mapdict["voronoi"]["vertex"]["unique_positions"] = "vertex_positions_unique_nofilter"
self.atoms._add_attribute(mapdict)
self.neighbors_found = True
[docs] def calculate_q(self, q, averaged=False, continuous_algorithm=False):
"""
Find the Steinhardt parameter q_l for all atoms.
Parameters
----------
q : int or list of ints
A list of all Steinhardt parameters to be found.
averaged : bool, optional
If True, return the averaged q values, default False
continuous_algorithm: bool, optional
See Notes for description.
Returns
-------
q : list of floats
calculated q values
Notes
-----
Enables calculation of the Steinhardt parameters [1] q. The type of
q values depend on the method used to calculate neighbors. See the description
:func:`~pyscal.core.System.find_neighbors` for more details.
The option `continuous_algorithm` specifies which algorithm to use for calculations. If False,
an algorithm [3] is used. The C++ algorithm is faster is a large, consecutive number of q values (> 200)
are to be calculated.
This function creates three new attributes for this class: `qx`, `qx_real` and `qx_imag`,
where `stands` for the q number.
References
----------
.. [1] Steinhardt, PJ, Nelson, DR, Ronchetti, M. Phys Rev B 28, 1983
.. [2] Lechner, W, Dellago, C, J Chem Phys, 2013
"""
if isinstance(q, int):
qq = [q]
else:
qq = q
self._check_neighbors()
if averaged:
self._calculate_aq(qq)
qvals = [self.atoms["avg_q%d"%x] for x in qq]
else:
if continuous_algorithm:
lm = max(qq)
pc.calculate_q(self.atoms, lm)
else:
self._calculate_q(qq)
qvals = [self.atoms["q%d"%x] for x in qq]
return qvals
def _calculate_q(self, qq):
"""
Private method for calculation of qvals
"""
for val in qq:
pc.calculate_q_single(self.atoms, val)
mapdict = {}
mapdict["steinhardt"] = {}
mapdict["steinhardt"]["generic"] = {}
for val in qq:
key1a = "q%d_norm"%val
key1b = "q%d"%val
key2 = "q%d_real"%val
key3 = "q%d_imag"%val
mapdict["steinhardt"]["generic"][key1a] = key1b
mapdict["steinhardt"]["generic"][key2] = key2
mapdict["steinhardt"]["generic"][key3] = key3
self.atoms._add_attribute(mapdict)
def _calculate_aq(self, qq):
"""
Private method for calculation of avged qvals
"""
todo_q = []
for q in qq:
keys = ["q%d"%q, "q%d_real"%q, "q%d_imag"%q]
prod = []
for key in keys:
if key in self.atoms.keys():
prod.append(True)
else:
prod.append(False)
prod = np.prod(prod)
if not prod:
todo_q.append(q)
_ = self._calculate_q(todo_q)
#loop over atoms
for val in qq:
pc.calculate_aq_single(self.atoms, val)
mapdict = {}
mapdict["steinhardt"] = {}
mapdict["steinhardt"]["average"] = {}
for val in qq:
key1a = "q%d_norm"%val
key1b = "q%d"%val
key2 = "q%d_real"%val
key3 = "q%d_imag"%val
mapdict["steinhardt"]["average"][key1a] = key1b
mapdict["steinhardt"]["average"][key2] = key2
mapdict["steinhardt"]["average"][key3] = key3
self.atoms._add_attribute(mapdict)
[docs] def calculate_disorder(self, averaged=False, q=6):
"""
Calculate the disorder criteria for each atom
Parameters
----------
averaged : bool, optional
If True, calculate the averaged disorder. Default False.
q : int, optional
The Steinhardt parameter value over which the bonds have to be calculated.
Default 6.
Returns
-------
None
Notes
-----
Calculate the disorder criteria as introduced in [1]. The disorder criteria value for each atom is defined by,
.. math::
D_j = \\frac{1}{N_b^j} \sum_{i=1}^{N_b} [ S_{jj} + S_{kk} -2S_{jk}]
where .. math:: S_{ij} = \sum_{m=-6}^6 q_{6m}(i) q_{6m}^*(i)
Any q value other than six can also be used. This can be specified using the `q` argument.
The keyword `averaged` is True, the disorder value is averaged over the atom and its neighbors.
For ordered systems, the value of disorder would be zero which would increase
and reach one for disordered systems.
This function creates two new attributes for this class: `disorder` and `avg_disorder`.
References
----------
.. [1] Kawasaki, T, Onuki, A, J. Chem. Phys. 135, 2011
"""
#now routine for calculation of disorder
keys = ["q%d_real"%q, "q%d_imag"%q]
prod = []
for key in keys:
if key in self.atoms.keys():
prod.append(True)
else:
prod.append(False)
prod = np.prod(prod)
if not prod:
self.calculate_q(q)
pc.calculate_disorder(self.atoms, q)
mapdict = {}
mapdict["steinhardt"] = {}
mapdict["steinhardt"]["disorder"] = {}
mapdict["steinhardt"]["disorder"]["norm"] = "disorder"
if averaged:
#average the disorder
avg_arr = self.average_over_neighbors("disorder")
self.atoms["avg_disorder"] = avg_arr
mapdict["steinhardt"]["disorder"]["average"] = "avg_disorder"
self.atoms._add_attribute(mapdict)
[docs] def find_solids(self, bonds=0.5, threshold=0.5, avgthreshold=0.6,
cluster=True, q=6, cutoff=0, right=True):
"""
Distinguish solid and liquid atoms in the system.
Parameters
----------
bonds : int or float, optional
Minimum number of solid bonds for an atom to be identified as
a solid if the value is an integer. Minimum fraction of neighbors
of an atom that should be solid for an atom to be solid if the
value is float between 0-1. Default 0.5.
threshold : double, optional
Solid bond cutoff value. Default 0.5.
avgthreshold : double, optional
Value required for Averaged solid bond cutoff for an atom to be identified
as solid. Default 0.6.
cluster : bool, optional
If True, cluster the solid atoms and return the number of atoms in the largest
cluster.
q : int, optional
The Steinhardt parameter value over which the bonds have to be calculated.
Default 6.
cutoff : double, optional
Separate value used for cluster classification. If not specified, cutoff used
for finding neighbors is used.
right: bool, optional
If true, greater than comparison is to be used for finding solid particles.
default True.
Returns
-------
solid : int
Size of the largest solid cluster. Returned only if `cluster=True`.
Notes
-----
The neighbors should be calculated before running this function.
Check :func:`~pyscal.core.System.find_neighbors` method.
`bonds` define the number of solid bonds of an atom to be identified as solid.
Two particles are said to be 'bonded' if [1],
.. math:: s_{ij} = \sum_{m=-6}^6 q_{6m}(i) q_{6m}^*(i) \geq threshold
where `threshold` values is also an optional parameter.
If the value of `bonds` is a fraction between 0 and 1, at least that much of an atom's neighbors
should be solid for the atom to be solid.
An additional parameter `avgthreshold` is an additional parameter to improve solid-liquid distinction.
In addition to having a the specified number of `bonds`,
.. math:: \langle s_{ij} \\rangle > avgthreshold
also needs to be satisfied. In case another q value has to be used for calculation of S_ij, it can be
set used the `q` attribute. In the above formulations, `>` comparison for `threshold` and `avgthreshold`
can be changed to `<` by setting the keyword `right` to False.
If `cluster` is True, a clustering is done for all solid particles. See :func:`~pyscal.csystem.find_clusters`
for more details.
References
----------
.. [1] Auer, S, Frenkel, D. Adv Polym Sci 173, 2005
"""
#check if neighbors are found
self._check_neighbors()
if not isinstance(q, int):
raise TypeError("q should be interger value")
if not isinstance(threshold, (int, float)):
raise TypeError("threshold should be a float value")
else:
if not ((threshold >= 0 ) and (threshold <= 1 )):
raise ValueError("Value of threshold should be between 0 and 1")
if not isinstance(avgthreshold, (int, float)):
raise TypeError("avgthreshold should be a float value")
else:
if not ((avgthreshold >= 0 ) and (avgthreshold <= 1 )):
raise ValueError("Value of avgthreshold should be between 0 and 1")
#start identification routine
#check the value of bonds and set criteria depending on that
if isinstance(bonds, int):
criteria = 0
elif isinstance(bonds, float):
if ((bonds>=0) and (bonds<=1.0)):
criteria = 1
else:
raise TypeError("bonds if float should have value between 0-1")
else:
raise TypeError("bonds should be interger/float value")
if right:
compare_criteria = 0
else:
compare_criteria = 1
self.calculate_q(q)
#calculate solid neighs
pc.calculate_bonds(self.atoms, q,
threshold, avgthreshold, bonds,
compare_criteria, criteria)
mapdict = {}
mapdict["steinhardt"] = {}
mapdict["steinhardt"]["order"] = {}
mapdict["steinhardt"]["order"]["bonds"] = "bonds"
mapdict["steinhardt"]["order"]["sij"] = {}
mapdict["steinhardt"]["order"]["sij"]["norm"] = "sij"
mapdict["steinhardt"]["order"]["sij"]["average"] = "avg_sij"
mapdict["steinhardt"]["order"]["sij"]["solid"] = "solid"
self.atoms._add_attribute(mapdict)
if cluster:
lc = self.cluster_atoms(self.atoms.steinhardt.order.sij.solid, largest=True)
return lc
[docs] def find_largest_cluster(self):
"""
Find largest cluster among given clusters
Parameters
----------
None
Returns
-------
lc : int
Size of the largest cluster.
"""
if not "cluster" in self.atoms.keys():
raise RuntimeError("cluster_atoms needs to be called first")
clusterlist = [x for x in self.atoms["cluster"] if x != -1]
xx, xxcounts = np.unique(clusterlist, return_counts=True)
arg = np.argsort(xxcounts)[-1]
largest_cluster_size = xxcounts[arg]
largest_cluster_id = xx[arg]
self.atoms["largest_cluster"] = [True if self.atoms["cluster"][x]==largest_cluster_id else False for x in range(len(self.atoms["cluster"]))]
mapdict = {}
mapdict["cluster"] = {}
mapdict["cluster"]["largest"] = "largest_cluster"
self.atoms._add_attribute(mapdict)
return largest_cluster_size
[docs] def cluster_atoms(self, condition, largest = True, cutoff=0):
"""
Cluster atoms based on a property
Parameters
----------
condition : callable or atom property
Either function which should take an :class:`~Atom` object, and give a True/False output
or an attribute of atom class which has value or 1 or 0.
largest : bool, optional
If True returns the size of the largest cluster. Default False.
cutoff : float, optional
If specified, use this cutoff for calculation of clusters. By default uses the cutoff
used for neighbor calculation.
Returns
-------
lc : int
Size of the largest cluster. Returned only if `largest` is True.
Notes
-----
This function helps to cluster atoms based on a defined property. This property
is defined by the user through the argument `condition` which is passed as a parameter.
`condition` should be a boolean array the same length as number of atoms in the system.
"""
self.apply_selection(condition=condition)
pc.find_clusters(self.atoms, cutoff)
mapdict = {}
mapdict["cluster"] = {}
mapdict["cluster"]["id"] = "cluster"
self.atoms._add_attribute(mapdict)
#done!
lc = self.find_largest_cluster()
#pcs.System.get_largest_cluster_atoms(self)
self.remove_selection()
if largest:
return lc
[docs] def calculate_rdf(self, rmin=0, rmax=5.00, bins=100):
"""
Calculate the radial distribution function.
Parameters
----------
rmin : float, optional
minimum value of the distance histogram. Default 0.0.
rmax : float, optional
maximum value of the distance histogram. Default 5.0
bins : int
number of bins in the histogram
Returns
-------
rdf : array of ints
Radial distribution function
r : array of floats
radius in distance units
"""
self.find_neighbors(method="cutoff", cutoff=rmax)
distances = list(itertools.chain(*self.atoms["neighbordist"]))
hist, bin_edges = np.histogram(distances, bins=bins,
range=(rmin, rmax), density=True)
edgewidth = np.abs(bin_edges[1]-bin_edges[0])
hist = hist.astype(float)
r = bin_edges[:-1]
#get box density
rho = self.natoms/self.volume
shell_vols = (4./3.)*np.pi*((r+edgewidth)**3 - r**3)
shell_rho = hist/shell_vols
#now divide to get final value
rdf = shell_rho/rho
return rdf, r
[docs] def calculate_angularcriteria(self):
"""
Calculate the angular criteria for each atom
Parameters
----------
None
Returns
-------
None
Notes
-----
Calculates the angular criteria for each atom as defined in [1]_. Angular criteria is
useful for identification of diamond cubic structures. Angular criteria is defined by,
.. math::
A = \sum_{i=1}^6 (\cos(\\theta_i) + \\frac{1}{3})^2
where cos(theta) is the angle size suspended by each pair of neighbors of the central
atom. A will have a value close to 0 for structures if the angles are close to 109 degrees.
The calculated A parameter for each atom can be accessed by system.angular
References
----------
.. [1] Uttormark, MJ, Thompson, MO, Clancy, P, Phys. Rev. B 47, 1993
"""
self._check_neighbors()
angulars = []
for count, pos1 in enumerate(self.atoms["positions"]):
dists = []
distneighs = []
distvectors = []
for count2, neigh in enumerate(self.atoms["neighbors"][count]):
pos2 = self.atoms["positions"][neigh]
dist = self.atoms["neighbordist"][count][count2]
vectors = self.atoms["diff"][count][count2]
dists.append(dist)
distneighs.append(neigh)
distvectors.append(vectors)
args = np.argsort(dists)
#find top four
topfourargs = np.array(args)[:4]
combos = list(itertools.combinations(topfourargs, 2))
costhetasum = 0
for combo in combos:
vec1 = distvectors[combo[0]]
vec2 = distvectors[combo[1]]
modvec1 = np.sqrt(np.sum([x**2 for x in vec1]))
modvec2 = np.sqrt(np.sum([x**2 for x in vec2]))
costheta = np.dot(vec1, vec2)/(modvec1*modvec2)
costhetasum += (costheta +(1./3.))**2
angulars.append(costhetasum)
self.atoms["angular"] = angulars
mapdict = {}
mapdict["angular_parameters"] = {}
mapdict["angular_parameters"]["diamond_angle"] = "angular"
self.atoms._add_attribute(mapdict)
[docs] def calculate_chiparams(self, angles=False):
"""
Calculate the chi param vector for each atom
Parameters
----------
angles : bool, optional
If True, return the list of cosines of all neighbor pairs
Returns
-------
angles : array of floats
list of all cosine values, returned only if `angles` is True.
Notes
-----
This method tries to distinguish between crystal structures by finding the cosines of angles
formed by an atom with its neighbors. These cosines are then historgrammed with bins
`[-1.0, -0.945, -0.915, -0.755, -0.705, -0.195, 0.195, 0.245, 0.795, 1.0]` to find a vector for
each atom that is indicative of its local coordination. Compared to chi parameters from chi_0 to
chi_7 in the associated publication, the vector here is from chi_0 to chi_8. This is due to an additional
chi parameter which measures the number of neighbors between cosines -0.705 to -0.195.
Parameter `nlimit` specifies the number of nearest neighbors to be included in the analysis to find the cutoff.
If parameter `angles` is true, an array of all cosine values is returned. The publication further provides
combinations of chi parameters for structural identification which is not implemented here. The calculated
chi params can be accessed using :attr:`~pyscal.catom.chiparams`.
References
----------
.. [1] Ackland, Jones, Phys. Rev. B 73, 2006
"""
self._check_neighbors()
bins = [-1.0, -0.945, -0.915, -0.755, -0.705, -0.195, 0.195, 0.245, 0.795, 1.0]
chiparams = []
cosines = []
for count, pos in enumerate(self.atoms["positions"]):
dists = self.atoms["neighbordist"][count]
neighs = self.atoms["neighbors"][count]
args = range(len(dists))
combos = list(itertools.combinations(args, 2))
costhetas = []
for combo in combos:
vec1 = self.atoms["diff"][count][combo[0]]
vec2 = self.atoms["diff"][count][combo[1]]
modvec1 = np.linalg.norm(vec1)
modvec2 = np.linalg.norm(vec2)
costheta = np.dot(vec1, vec2)/(modvec1*modvec2)
#found costheta
costhetas.append(costheta)
#now add according to classification in paper
chivector = np.histogram(costhetas, bins=bins)
chiparams.append(chivector[0])
if angles:
cosines.append(costhetas)
self.atoms["chiparams"] = chiparams
mapdict = {}
mapdict["angular_parameters"] = {}
mapdict["angular_parameters"]["chi_params"] = "chiparams"
if angles:
self.atoms["cosines"] = cosines
mapdict["angular_parameters"]["cosines"] = "cosines"
self.atoms._add_attribute(mapdict)