def hardness_XX(self, initial_cutoff_radius=0.8, use_laplacian=True):
bonds, coordination, cutoff_radius = self.bonds_coordination(
initial_cutoff_radius=initial_cutoff_radius,
use_laplacian=use_laplacian)
sigma = 3.0
c_hard = 1300.0
xprod = 1.
tot = 0.0
f_d = 0.0
f_n = 1.0
atomicnumbers = atomic_number(self.structure.species)
pcm_log.debug('Atomic numbers in the structure : %s' %
str(atomicnumbers))
for i in atomicnumbers:
f_d += valence(i) / covalent_radius(i)
f_n *= valence(i) / covalent_radius(i)
if f_d == 0:
pcm_log.debug('Returning zero as hardness. f_d= %10.3f' % f_d)
return 0.0
f = 1.0 - (self.structure.nspecies *
f_n**(1.0 / self.structure.nspecies) / f_d)**2
diff_bonds = [x for x in bonds if len(bonds[x]) > 0]
for pair in diff_bonds:
i1 = pair[0]
i2 = pair[1]
ei = valence(self.structure.symbols[i1]) / covalent_radius(
self.structure.symbols[i1])
ej = valence(self.structure.symbols[i2]) / covalent_radius(
self.structure.symbols[i2])
for dij in bonds[pair]:
sij = math.sqrt(
ei * ej) / (coordination[i1] * coordination[i2]) / dij
xprod *= sij
num_i_j_bonds = len(bonds[pair])
pcm_log.debug('Number of bonds for pair %s = %d' %
(str(pair), num_i_j_bonds))
tot += num_i_j_bonds
vol = self.structure.volume
pcm_log.debug("Structure volume: %7.3f" % vol)
pcm_log.debug("Total number of bonds: %d" % tot)
pcm_log.debug("Bonds: %s" % str(bonds))
hardness_value = (c_hard / vol) * tot * (xprod**(1. / tot)) * math.exp(
-sigma * f)
return round(hardness_value, 3), cutoff_radius, coordination
def hardness_XX(self, initial_cutoff_radius=0.8, use_laplacian=True):
"""
Implementation of Hardness algorithm:
First-principles structural design of superhard materials
J. Chem. Phys. 138, 114101 (2013); https://doi.org/10.1063/1.4794424
Xinxin Zhang, et al.
"""
bonds, coordination, cutoff_radius = self.bonds_coordination(initial_cutoff_radius=initial_cutoff_radius,
use_laplacian=use_laplacian)
sigma = 3.0
c_hard = 1300.0
xprod = 1.
tot = 0.0
f_d = 0.0
f_n = 1.0
atomicnumbers = atomic_number(self.structure.species)
pcm_log.debug('Atomic numbers in the structure : %s' % str(atomicnumbers))
for i in atomicnumbers:
f_d += valence(i) / covalent_radius(i)
f_n *= valence(i) / covalent_radius(i)
if f_d == 0:
pcm_log.debug('Returning zero as hardness. f_d= %10.3f' % f_d)
return 0.0
f = 1.0 - (self.structure.nspecies * f_n ** (1.0 / self.structure.nspecies) / f_d) ** 2
diff_bonds = [x for x in bonds if len(bonds[x]) > 0]
for pair in diff_bonds:
i1 = pair[0]
i2 = pair[1]
ei = valence(self.structure.symbols[i1]) / covalent_radius(self.structure.symbols[i1])
ej = valence(self.structure.symbols[i2]) / covalent_radius(self.structure.symbols[i2])
for dij in bonds[pair]:
sij = math.sqrt(ei * ej) / (coordination[i1] * coordination[i2]) / dij
xprod *= sij
num_i_j_bonds = len(bonds[pair])
pcm_log.debug('Number of bonds for pair %s = %d' % (str(pair), num_i_j_bonds))
tot += num_i_j_bonds
vol = self.structure.volume
pcm_log.debug("Structure volume: %7.3f" % vol)
pcm_log.debug("Total number of bonds: %d" % tot)
pcm_log.debug("Bonds: %s" % str(bonds))
hardness_value = (c_hard / vol) * tot * (xprod ** (1. / tot)) * math.exp(-sigma * f)
return round(hardness_value, 3), cutoff_radius, coordination
def hardness_XX(self, initial_cutoff_radius=0.8, use_laplacian=True):
bonds, coordination, cutoff_radius = self.bonds_coordination(initial_cutoff_radius=initial_cutoff_radius,
use_laplacian=use_laplacian, verbose=True)
sigma = 3.0
c_hard = 1300.0
xprod = 1.
tot = 0.0
f_d = 0.0
f_n = 1.0
atomicnumbers = atomic_number(self.structure.species)
pcm_log.debug('Atomic numbers in the structure : %s' % str(atomicnumbers))
for i in atomicnumbers:
f_d += valence(i) / covalent_radius(i)
f_n *= valence(i) / covalent_radius(i)
if f_d == 0:
pcm_log.debug('Returning zero as hardness. f_d= %10.3f' % f_d)
return 0.0
f = 1.0 - (self.structure.nspecies * f_n ** (1.0 / self.structure.nspecies) / f_d) ** 2
diff_bonds = [x for x in bonds if len(bonds[x]) > 0]
for pair in diff_bonds:
i1 = pair[0]
i2 = pair[1]
ei = valence(self.structure.symbols[i1]) / covalent_radius(self.structure.symbols[i1])
ej = valence(self.structure.symbols[i2]) / covalent_radius(self.structure.symbols[i2])
for dij in bonds[pair]:
sij = math.sqrt(ei * ej) / (coordination[i1] * coordination[i2]) / dij
xprod *= sij
num_i_j_bonds = len(bonds[pair])
pcm_log.debug('Number of bonds for pair %s = %d' % (str(pair), num_i_j_bonds))
tot += num_i_j_bonds
vol = self.structure.volume
pcm_log.debug("Structure volume: %7.3f" % vol)
pcm_log.debug("Total number of bonds: %d" % tot)
pcm_log.debug("Bonds: %s" % str(bonds))
hardness_value = (c_hard / vol) * tot * (xprod ** (1. / tot)) * math.exp(-sigma * f)
return round(hardness_value, 3), cutoff_radius, coordination
def hardness_old(self, noupdate=False, verbose=False, tolerance=0.05):
"""
Calculates the hardness of a structure based in the model of XX
We use the covalent radii from pychemia.utils.periodic.
If noupdate=False
the Laplacian matrix method is not used and rcut is 2*max(cov_radii)
:param noupdate: (bool) If True, the Laplacian method is used
:param verbose: (bool) To print some debug info
:param tolerance: (float)
:rtype : (float)
"""
superc = self.structure.copy()
superc.supercell(2, 2, 2)
structure_analisys = StructureAnalysis(superc)
natom = superc.natom
volume = superc.volume
max_covalent_radius = max(covalent_radius(superc.symbols))
if verbose:
print('Number of atoms', natom)
print('Volume ', volume)
print('Covalent rad max', max_covalent_radius)
rcut, coord, dis_dic = structure_analisys.get_bonds(2.0 * max_covalent_radius, noupdate, verbose, tolerance)
sigma = 3.0
c_hard = 1300.0
x = 1.
tot = 0.0
f_d = 0.0
f_n = 1.0
dic_atms = {}
for i in superc.symbols:
dic_atms[i] = atomic_number(i)
for i in dic_atms.keys():
f_d += valence(i) / covalent_radius(i)
f_n *= valence(i) / covalent_radius(i)
f = 1.0 - (len(dic_atms) * f_n ** (1.0 / len(dic_atms)) / f_d) ** 2
if verbose:
print('BONDS')
print(dis_dic)
print('COORDINATION')
print(coord)
for i in dis_dic.keys():
i1 = dis_dic[i][2][0]
i2 = dis_dic[i][2][1]
ei = valence(superc.symbols[i1]) / covalent_radius(superc.symbols[i1])
ej = valence(superc.symbols[i2]) / covalent_radius(superc.symbols[i2])
sij = math.sqrt(ei * ej) / (coord[i1] * coord[i2]) / dis_dic[i][0]
tot += dis_dic[i][1]
x *= sij * dis_dic[i][1]
if verbose:
print("V:", volume)
print("f:", f)
print("x:", x)
hardness_value = c_hard / volume * (len(dis_dic) * x ** (1. / (len(dis_dic)))) * math.exp(-sigma * f)
if verbose:
print(hardness_value)
return round(hardness_value, 3)
def hardness(self, verbose=False, initial_cutoff_radius=0.8, ensure_conectivity=False, use_laplacian=True,
use_jump=True):
"""
Calculates the hardness of a structure based in the model of XX
We use the covalent radii from pychemia.utils.periodic.
If noupdate=False
the Laplacian matrix method is not used and rcut is 2*max(cov_radii)
:param use_jump:
:param ensure_conectivity:
:param verbose: (bool) To print some debug info
:param initial_cutoff_radius: (float)
:param use_laplacian: (bool) If True, the Laplacian method is used
:rtype : (float)
"""
if self._supercell == (1, 1, 1) and verbose:
print('''Only internal connectivity can be ensure, for complete connectivity in the crystal you must use a
supercell at of (2,2,2)''')
bonds, coordination, all_distances, tolerances, cutoff_radius = \
self.get_bonds_coordination(initial_cutoff_radius=initial_cutoff_radius,
ensure_conectivity=ensure_conectivity,
use_laplacian=use_laplacian, verbose=verbose, use_jump=use_jump)
if verbose:
print('Structure coordination : ', coordination)
sigma = 3.0
c_hard = 1300.0
x = 1.
tot = 0.0
f_d = 0.0
f_n = 1.0
atomicnumbers = atomic_number(self.structure.species)
if verbose:
print('Atomic numbers in the structure :', atomicnumbers)
for i in atomicnumbers:
f_d += valence(i) / covalent_radius(i)
f_n *= valence(i) / covalent_radius(i)
# if verbose:
# print 'fd', f_d
# print 'fn', f_n
# print atomicnumbers
if f_d == 0:
return 0.0
f = 1.0 - (len(atomicnumbers) * f_n ** (1.0 / len(atomicnumbers)) / f_d) ** 2
# Selection of different bonds
diff_bonds = np.unique(np.array(reduce(lambda xx, y: xx + y, bonds)))
if verbose:
print('Number of different bonds : ', len(diff_bonds))
for i in diff_bonds:
i1 = all_distances[i]['pair'][0]
i2 = all_distances[i]['pair'][1]
ei = valence(self.structure.symbols[i1]) / covalent_radius(self.structure.symbols[i1])
ej = valence(self.structure.symbols[i2]) / covalent_radius(self.structure.symbols[i2])
# print 'bond ->', sqrt(ei * ej), (coordination[i1] * coordination[i2]), all_distances[i]['distance']
sij = math.sqrt(ei * ej) / (coordination[i1] * coordination[i2]) / all_distances[i]['distance']
num_i_j_bonds = len([j for j in diff_bonds if i1 in all_distances[j]['pair'] and
i2 in all_distances[j]['pair']])
# print 'sij', sij
# print 'num_i_j_bonds', num_i_j_bonds
tot += num_i_j_bonds
x *= sij
# print 'x', x
vol = self.structure.volume
if verbose:
print("Structure volume:", vol)
# print("f:", f)
# print("x:", x)
# print 'len_bonds', len(diff_bonds
hardness_value = c_hard / vol * (len(diff_bonds) * x ** (1. / (len(diff_bonds)))) * math.exp(-sigma * f)
return round(hardness_value, 3), cutoff_radius, coordination
def valence_electrons(self):
ret = 0
for key, value in self.composition.items():
ret += value * valence(key)
return ret
def hardness_old(self, noupdate=False, verbose=False, tolerance=0.05):
"""
Calculates the hardness of a structure based in the model of XX
We use the covalent radii from pychemia.utils.periodic.
If noupdate=False
the Laplacian matrix method is not used and rcut is 2*max(cov_radii)
:param noupdate: (bool) If True, the Laplacian method is used
:param verbose: (bool) To print some debug info
:param tolerance: (float)
:rtype : (float)
"""
superc = self.structure.copy()
superc.supercell(2, 2, 2)
structure_analisys = StructureAnalysis(superc)
natom = superc.natom
volume = superc.volume
max_covalent_radius = max(covalent_radius(superc.symbols))
if verbose:
print('Number of atoms', natom)
print('Volume ', volume)
print('Covalent rad max', max_covalent_radius)
rcut, coord, dis_dic = structure_analisys.get_bonds(
2.0 * max_covalent_radius, noupdate, verbose, tolerance)
sigma = 3.0
c_hard = 1300.0
x = 1.
tot = 0.0
f_d = 0.0
f_n = 1.0
dic_atms = {}
for i in superc.symbols:
dic_atms[i] = atomic_number(i)
for i in dic_atms.keys():
f_d += valence(i) / covalent_radius(i)
f_n *= valence(i) / covalent_radius(i)
f = 1.0 - (len(dic_atms) * f_n**(1.0 / len(dic_atms)) / f_d)**2
if verbose:
print('BONDS')
print(dis_dic)
print('COORDINATION')
print(coord)
for i in dis_dic.keys():
i1 = dis_dic[i][2][0]
i2 = dis_dic[i][2][1]
ei = valence(superc.symbols[i1]) / covalent_radius(
superc.symbols[i1])
ej = valence(superc.symbols[i2]) / covalent_radius(
superc.symbols[i2])
sij = math.sqrt(ei * ej) / (coord[i1] * coord[i2]) / dis_dic[i][0]
tot += dis_dic[i][1]
x *= sij * dis_dic[i][1]
if verbose:
print("V:", volume)
print("f:", f)
print("x:", x)
hardness_value = c_hard / volume * (
len(dis_dic) * x**(1. / (len(dis_dic)))) * math.exp(-sigma * f)
if verbose:
print(hardness_value)
return round(hardness_value, 3)
def hardness(self,
verbose=True,
initial_cutoff_radius=0.8,
ensure_conectivity=False,
use_laplacian=True,
use_jump=True,
tol=1E-15):
"""
Calculates the hardness of a structure based in the model of XX
We use the covalent radii from pychemia.utils.periodic.
If noupdate=False
the Laplacian matrix method is not used and rcut is 2*max(cov_radii)
:param use_jump:
:param ensure_conectivity:
:param verbose: (bool) To print some debug info
:param initial_cutoff_radius: (float)
:param use_laplacian: (bool) If True, the Laplacian method is used
:param tol: (float) Tolerance for considering two atoms bonded
:rtype : (float)
"""
if self._supercell == (1, 1, 1) and verbose:
print(
'''Only internal connectivity can be ensure, for complete connectivity in the crystal you must use a
supercell at of (2,2,2)''')
bonds, coordination, all_distances, tolerances, cutoff_radius = \
self.get_bonds_coordination(initial_cutoff_radius=initial_cutoff_radius,
ensure_conectivity=ensure_conectivity,
use_laplacian=use_laplacian, verbose=verbose, use_jump=use_jump, tol=tol)
if verbose:
print('Structure coordination : ', coordination)
sigma = 3.0
c_hard = 1300.0
x = 1.
tot = 0.0
f_d = 0.0
f_n = 1.0
atomicnumbers = atomic_number(self.structure.species)
if verbose:
print('Atomic numbers in the structure :', atomicnumbers)
for i in atomicnumbers:
f_d += valence(i) / covalent_radius(i)
f_n *= valence(i) / covalent_radius(i)
# if verbose:
# print 'fd', f_d
# print 'fn', f_n
# print atomicnumbers
if f_d == 0:
return 0.0
f = 1.0 - (len(atomicnumbers) * f_n**(1.0 / len(atomicnumbers)) /
f_d)**2
# Selection of different bonds
diff_bonds = np.unique(
np.array(functools.reduce(lambda xx, y: xx + y, bonds)))
if verbose:
print('Number of different bonds : ', len(diff_bonds))
for i in diff_bonds:
i1 = all_distances[i]['pair'][0]
i2 = all_distances[i]['pair'][1]
ei = valence(self.structure.symbols[i1]) / covalent_radius(
self.structure.symbols[i1])
ej = valence(self.structure.symbols[i2]) / covalent_radius(
self.structure.symbols[i2])
# print 'bond ->', sqrt(ei * ej), (coordination[i1] * coordination[i2]), all_distances[i]['distance']
sij = math.sqrt(ei * ej) / (coordination[i1] * coordination[i2]
) / all_distances[i]['distance']
num_i_j_bonds = len([
j for j in diff_bonds if i1 in all_distances[j]['pair']
and i2 in all_distances[j]['pair']
])
# print 'sij', sij
# print 'num_i_j_bonds', num_i_j_bonds
tot += num_i_j_bonds
x *= sij
# print 'x', x
vol = self.structure.volume
if verbose:
print("Structure volume:", vol)
# print("f:", f)
# print("x:", x)
# print 'len_bonds', len(diff_bonds
hardness_value = c_hard / vol * (
len(diff_bonds) * x**(1. /
(len(diff_bonds)))) * math.exp(-sigma * f)
return round(hardness_value, 3), cutoff_radius, coordination
def hardness_OLD(self, noupdate=False, verbose=False, tolerance=0.05):
"""
Calculates the hardness of a structure based in the model of XX
We use the covalent radii from pychemia.utils.periodic.
If noupdate=False
the Laplacian matrix method is not used and rcut is 2*max(cov_radii)
:param noupdate: (bool) If True, the Laplacian method is used
:param verbose: (bool) To print some debug info
:param tolerance: (float)
:rtype : (float)
"""
#from ase.data import covalent_radii
#atms=atms.repeat([2,2,2])
spc = self.copy()
spc.supercell(2, 2, 2)
natom = spc.natom
volume = spc.volume
#max_covalent_radius = max([covalent_radii[i.number] for i in atms])
max_covalent_radius = max(covalent_radius(spc.symbols))
if verbose:
print('Number of atoms', natom)
print('Volume ', volume)
print('Covalent rad max', max_covalent_radius)
#rcut, coord, dis_dic = get_bonds(atms,2.0*max_covalent_radius, noupdate,verbose,tolerance)
rcut, coord, dis_dic = spc.get_bonds(2.0 * max_covalent_radius, noupdate, verbose, tolerance)
sigma = 3.0
c_hard = 1300.0
x = 1.
tot = 0.0
f_d = 0.0
f_n = 1.0
dic_atms = {}
#for i in atms:
# dic_atms[i.symbol] = i.number
for i in spc.symbols:
dic_atms[i] = atomic_number(i)
#for i in dic_atms.keys():
# f_d += Z[i] / covalent_radii[dic_atms[i]]
# f_n *= Z[i] / covalent_radii[dic_atms[i]]
#f = 1.0 - (len(dic_atms)*f_n**(1.0/len(dic_atms)) / f_d)**2
for i in dic_atms.keys():
f_d += valence(i) / covalent_radius(i)
f_n *= valence(i) / covalent_radius(i)
f = 1.0 - (len(dic_atms) * f_n ** (1.0 / len(dic_atms)) / f_d) ** 2
if verbose:
print 'BONDS'
print dis_dic
print 'COORDINATION'
print coord
for i in dis_dic.keys():
i1 = dis_dic[i][2][0]
i2 = dis_dic[i][2][1]
#ei = Z[atms[i1].symbol] / covalent_radii[atms[i1].number]
#ej = Z[atms[i2].symbol] / covalent_radii[atms[i2].number]
ei = valence(spc.symbols[i1]) / covalent_radius(spc.symbols[i1])
ej = valence(spc.symbols[i2]) / covalent_radius(spc.symbols[i2])
#print 'bond ->', sqrt(ei * ej), (coord[i1] * coord[i2]), dis_dic[i][0]
# print atms[i1].symbol, ei, atms[i2].symbol, ej
sij = sqrt(ei * ej) / (coord[i1] * coord[i2]) / dis_dic[i][0]
#print 'sij', sij
#print 'num_i_j_bonds', dis_dic[i][1]
tot += dis_dic[i][1]
x *= sij * dis_dic[i][1]
#print 'x', x
if verbose:
print("V:", volume)
print("f:", f)
print("x:", x)
#print 'len_bonds', len(dis_dic)
#print 'hardness_value =', c_hard, volume, (len(dis_dic)), ( x ** (1. / (len(dis_dic)))), exp(-sigma * f)
hardness_value = c_hard / volume * (len(dis_dic) * x ** (1. / (len(dis_dic)))) * exp(-sigma * f)
if verbose:
print hardness_value
return round(hardness_value, 3)
def hardness(self, noupdate=False, verbose=False, tolerance=1):
"""
Calculates the hardness of a structure based in the model of XX
We use the covalent radii from pychemia.utils.periodic.
If noupdate=False
the Laplacian matrix method is not used and rcut is 2*max(cov_radii)
:param noupdate: (bool) If True, the Laplacian method is used
:param verbose: (bool) To print some debug info
:param tolerance: (float)
:rtype : (float)
"""
bonds, coordination, all_distances, tolerances = self.get_bonds_coordination(tolerance=tolerance, ensure_conectivity=True)
if verbose:
print 'BONDS'
print bonds
print 'COORDINATION'
print coordination
sigma = 3.0
c_hard = 1300.0
x = 1.
tot = 0.0
f_d = 0.0
f_n = 1.0
atomicnumbers = atomic_number(self.get_composition().species)
if verbose:
print atomicnumbers
for i in atomicnumbers:
f_d += valence(i) / covalent_radius(i)
f_n *= valence(i) / covalent_radius(i)
f = 1.0 - (len(atomicnumbers) * f_n ** (1.0 / len(atomicnumbers)) / f_d) ** 2
# Selection of different bonds
diff_bonds = _np.unique(_np.array(reduce(lambda x, y: x+y, bonds)))
for i in diff_bonds:
i1 = all_distances[i]['pair'][0]
i2 = all_distances[i]['pair'][1]
ei = valence(self.symbols[i1]) / covalent_radius(self.symbols[i1])
ej = valence(self.symbols[i2]) / covalent_radius(self.symbols[i2])
#print 'bond ->', sqrt(ei * ej), (coordination[i1] * coordination[i2]), all_distances[i]['distance']
sij = sqrt(ei * ej) / (coordination[i1] * coordination[i2]) / all_distances[i]['distance']
num_i_j_bonds = len([j for j in diff_bonds if i1 in all_distances[j]['pair'] and i2 in all_distances[j]['pair']])
#print 'sij', sij
#print 'num_i_j_bonds', num_i_j_bonds
tot += num_i_j_bonds
x *= sij
#print 'x', x
if verbose:
print("V:", self.volume)
print("f:", f)
print("x:", x)
#print 'len_bonds', len(diff_bonds)
#print 'hardness_value =', c_hard, self.volume, (len(diff_bonds)), ( x ** (1. / (len(diff_bonds)))), exp(-sigma * f)
hardness_value = c_hard / self.volume * (len(diff_bonds) * x ** (1. / (len(diff_bonds)))) * exp(-sigma * f)
if verbose:
print hardness_value
return round(hardness_value, 3)
def valence_electrons(self):
ret = 0
for key, value in self.composition.items():
ret += value * valence(key)
return ret