-
Notifications
You must be signed in to change notification settings - Fork 9
/
latt.py
258 lines (208 loc) · 9.13 KB
/
latt.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
# this file is part of gosam (generator of simple atomistic models)
# Licence: GNU General Public License version 2
"""\
CrystalLattice, UnitCell, etc.
"""
from math import cos, sin, acos, sqrt, radians, degrees
from numpy import linalg
from numpy import array, dot, transpose
class UnitCell:
"""basic unit cell - triclinic
"""
def __init__(self, a, b, c, alpha, beta, gamma,
system="triclinic", rad=False, reciprocal=None):
self.abc = self.a, self.b, self.c = a, b, c
if not rad: #degrees
self.alpha, self.beta, self.gamma = alpha, beta, gamma
self.alpha_rad, self.beta_rad, self.gamma_rad = radians(alpha), \
radians(beta), radians(gamma)
else: #radians
self.alpha, self.beta, self.gamma = degrees(alpha), \
degrees(beta), degrees(gamma)
self.alpha_rad, self.beta_rad, self.gamma_rad = alpha, beta, gamma
self._compute_sin_cos_V()
if not reciprocal: #lattice in direct space
self.is_reciprocal = False
self.reciprocal = self.get_reciprocal_unit_cell()
else: #lattice in reciprocal space
self.is_reciprocal = not reciprocal.is_reciprocal
self.reciprocal = reciprocal
self.system = system
self.system_name = self.system.title() + " system " \
+ (self.is_reciprocal and "(reciprocal)" or "(direct)")
self.compute_transformation_matrix()
def __str__(self):
return self.system_name \
+ " a=%s, b=%s, c=%s, alpha=%s, beta=%s, gamma=%s" % (self.a,
self.b, self.c, self.alpha, self.beta, self.gamma)
# overloaded for hexagonal lattice
def get_orthorhombic_supercell(self):
if self.alpha == 90 and self.beta == 90 and self.gamma == 90:
return self.a, self.b, self.c
else:
assert "Not implemented."
def _compute_sin_cos_V(self):
"precomputations of some values (eg. sin(alpha)) -- for optimization"
a, b, c = self.a, self.b, self.c
alpha, beta, gamma = self.alpha_rad, self.beta_rad, self.gamma_rad
self.sines = array([sin(alpha), sin(beta), sin(gamma)])
self.cosines = array([cos(alpha), cos(beta), cos(gamma)])
#Giacovazzo p.62
G = (a*b*c)**2 * (1 - cos(alpha)**2 - cos(beta)**2 - cos(gamma)**2
+ 2*cos(alpha)*cos(beta)*cos(gamma))
self.V = sqrt(G)
def get_reciprocal_unit_cell(self):
""" returns instance of UnitCell, that is reciprocal to self
self.reciprocal.(a|b|c|alpha|...)
a* = self.reciprocal.a, etc.
(Giacovazzo, p. 64)
"""
a, b, c, V = self.a, self.b, self.c, self.V
alpha, beta, gamma = self.alpha_rad, self.beta_rad, self.gamma_rad
ar = b*c*sin(alpha)/V
br = a*c*sin(beta)/V
cr = a*b*sin(gamma)/V
cos_alphar = (cos(beta)*cos(gamma)-cos(alpha)) / (sin(beta)*sin(gamma))
cos_betar = (cos(alpha)*cos(gamma)-cos(beta)) / (sin(alpha)*sin(gamma))
cos_gammar = (cos(alpha)*cos(beta)-cos(gamma)) / (sin(alpha)*sin(beta))
return UnitCell(ar, br, cr, acos(cos_alphar), acos(cos_betar),
acos(cos_gammar), rad=True, reciprocal=self)
def compute_transformation_matrix(self):
""" sets self.M and self.M_1 (M^-1)
[ 1/a 0 0 ]
M = [ -cosG/(a sinG) 1/(b sinG) 0 ]
[ a*cosB* b*cosA* c* ]
where A is alpha, B is beta, G is gamma, * means reciprocal space.
E=MA
(Giacovazzo, p.68)
"""
a, b, c = self.a, self.b, self.c
alpha, beta, gamma = self.alpha_rad, self.beta_rad, self.gamma_rad
r = self.reciprocal
self.M = array([
(1/a, 0, 0),
(-cos(gamma)/(a * sin(gamma)), 1/(b*sin(gamma)), 0),
(r.a * cos(r.beta_rad), r.b * cos(r.alpha_rad), r.c)
])
self.M_1 = array([
(a, 0, 0),
(b*cos(gamma), b*sin(gamma), 0),
(c*cos(beta), -c*sin(beta)*cos(r.alpha_rad), 1/r.c)
])
def rotate(self, rot_mat):
assert (abs(transpose(rot_mat) - linalg.inv(rot_mat)) < 1e-6).all(), \
"not orthogonal"
assert abs(linalg.det(rot_mat) - 1) < 1e-6, "not a pure rotation matrix"
self.M_1 = dot(self.M_1, rot_mat)
self.M = dot(transpose(rot_mat), self.M)
#print "1=", dot(self.M_1, self.M)
def get_unit_shift(self, i):
return self.M_1[i]
class CubicUnitCell(UnitCell):
def __init__(self, a):
UnitCell.__init__(self, a, a, a, 90, 90, 90, system="cubic")
def __str__(self):
return self.system_name + " a=%s" % self.a
class TetragonalUnitCell(UnitCell):
def __init__(self, a, c):
UnitCell.__init__(self, a, a, c, 90, 90, 90, system="tetragonal")
def __str__(self):
return self.system_name + " a=%s, c=%s" % (self.a, self.c)
class OrthorhombicUnitCell(UnitCell):
def __init__(self, a, b, c):
UnitCell.__init__(self, a, b, c, 90, 90, 90, system="orthorhombic")
def __str__(self):
return self.system_name + " a=%s, b=%s, c=%s"%(self.a, self.b, self.c)
class HexagonalUnitCell(UnitCell):
def __init__(self, a, c):
UnitCell.__init__(self, a, a, c, 90, 90, 120, system="hexagonal")
def __str__(self):
return self.system_name + " a=%s, c=%s" % (self.a, self.c)
def get_orthorhombic_supercell(self):
return self.a, self.a * 3**0.5, self.c
class AtomInNode:
"""atom with its coordinates (as fraction of unit cell parameters) in node
(atoms in one node can't be separated; node is in unit cell) """
def __init__(self, name, xa=0, yb=0, zc=0):
self.name = name
self.pos = array((xa, yb, zc), float)
self.non_zero = (xa != 0 or yb != 0 or zc != 0)
def __str__(self):
return "%s at %s in node"% (self.name, tuple(self.pos))
class Node:
""" Node in unit cell consists of a few (eg. 1 or 2) atoms, which should
be kept together when cutting grains
"""
def __init__(self, pos_in_cell, atoms_in_node):
self.pos_in_cell = array(pos_in_cell, float)
self.atoms_in_node = [isinstance(i, AtomInNode) and i or AtomInNode(*i)
for i in atoms_in_node]
def __str__(self):
return "Node at %s in cell with: %s" % (tuple(self.pos_in_cell),
", ".join([str(i) for i in self.atoms_in_node]))
def shift(self, v):
self.pos_in_cell = (self.pos_in_cell + array(v)) % 1.0
def is_normalized(self):
"""Are positions of all the atoms in this node in the <0,1) range.
(i.e. checking self.pos_in_cell+atom.pos)
"""
for atom in self.atoms_in_node:
p = self.pos_in_cell + atom.pos
if (p >= 1).any() or (p < 0).any():
return False
return True
class CrystalLattice:
"Unfinite crystal lattice = unit cell + nodes in cell"
def __init__(self, unit_cell, nodes, name="Mol"):
self.unit_cell = unit_cell
self.nodes = nodes
assert isinstance(name, basestring)
self.name = name
def __str__(self):
return str(self.unit_cell) + " Nodes:\n" \
+ "\n".join([str(i) for i in self.nodes])
def count_species(self):
names = set()
for i in self.nodes:
for j in i.atoms_in_node:
names.add(j.name)
return len(names)
def swap_node_atoms_names(self):
"works only if there are two atoms in every node"
for i in self.nodes:
ain = i.atoms_in_node
assert len(ain) == 2
ain[0].name, ain[1].name = ain[1].name, ain[0].name
def shift_nodes(self, v):
for i in self.nodes:
i.shift(v)
def export_powdercell(self, f):
cell = self.unit_cell
print >>f, "CELL %f %f %f %f %f %f" % (cell.a, cell.b, cell.c,
cell.alpha, cell.beta, cell.gamma)
names = []
for node in self.nodes:
for atom in node.atoms_in_node:
pos = node.pos_in_cell + atom.pos
names.append(atom.name)
xname = "%s%i" % (atom.name, names.count(atom.name))
print >>f, "%-4s %-4s %-8s %-8s %-8s" % (atom.name, atom.name,
pos[0], pos[1], pos[2])
def generate_polytype(a, h, polytype):
"""utility for dealing with various polytypes. a is a from hexagonal
structure, h is a distance between layers.
Usage:
cell, nodes = generate_polytype(a=3.073, h=2.51, polytype="ABABABC")
"""
pos = { "A" : (0.0, 0.0),
"B" : (1/3., 2/3.),
"C" : (2/3., 1/3.)
}
polytype = polytype.upper()
N = len(polytype)
cell = HexagonalUnitCell(a=a, c=h*N)
nodes = []
for n, i in enumerate(polytype):
t = pos[i]
nodes.append((t[0], t[1], float(n)/N))
return cell, nodes