#! /usr/bin/env python
# ============================================================
# Copyright (c) 2012, Lawrence Livermore National Security, LLC.
# Produced at the Lawrence Livermore National Laboratory.
# Written by Joel Bernier <bernier2@llnl.gov> and others.
# LLNL-CODE-529294.
# All rights reserved.
#
# This file is part of HEXRD. For details on dowloading the source,
# see the file COPYING.
#
# Please also see the file LICENSE.
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License (as published
# by the Free Software
# Foundation) version 2.1 dated February 1999.
#
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the IMPLIED WARRANTY OF MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the terms and conditions of the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with this program (see file LICENSE); if not, write to
# the Free Software Foundation, Inc., 59 Temple Place, Suite 330,
# Boston, MA 02111-1307 USA or visit <http://www.gnu.org/licenses/>.
# ============================================================
#
"""This module contains mappings from space group number to either
Hall or Hermann-Mauguin notation, as well as the inverse notations.
Space groups can be mapped to crystal class (one of 32 point groups)
and then to crystal system .
NOTES:
* Laue group is the cyrstal class if you add a center of symmetry.
There are 11 Laue groups, determined directly from the point group.
* This module avoids the use of numpy and uses math module instead.
That means the hkl lists are not numpy arrays, but simple lists of
tuples.
* Rhombohedral lattices:
REFERENCES
1. Mappings among space group number, Hall symbols and Hermann-Mauguin symbols.
http://cci.lbl.gov/sginfo/hall_symbols.html
2. For mapping space group number to point group (crystal class in Schonflies
notation)
http://en.wikipedia.org/wiki/Space_group
3. Crystallography and crystal defects By Anthony Kelly, G. W. Groves, P. Kidd
4. Contains point group from sgnum.
http://en.wikipedia.org/wiki/Space_group#Classification_systems_for_space_groups
5. Point group to laue group
http://www.ruppweb.org/Xray/tutorial/32point.htm
6. For discussion of rhombohedral lattice and "obverse"
and "reverse" settings for lattice parameters.
Crystal structure determination (book) By Werner Massa
TESTING
Run this module as main to generate all space groups and test
the HKL evaluation.
"""
from collections import OrderedDict
from math import sqrt, floor
from hexrd import constants
from hexrd.material import symbols, symmetry
import numpy as np
#
__all__ = ['SpaceGroup']
#
# ---------------------------------------------------CLASS: SpaceGroup
#
[docs]class SpaceGroup:
def __init__(self, sgnum):
"""Constructor for SpaceGroup
INPUTS
sgnum -- (int) space group number (between 1 and 230)
"""
self.sgnum = sgnum
def __str__(self):
"""Print information about the space group"""
s = 'space group number: %d\n' % self.sgnum
s += ' Hall Symbol: %s\n' % self.HallSymbol
s += ' Hermann-Mauguin: %s\n' % self.hermannMauguin
s += ' Point Group: %s\n' % self.pointGroup
s += ' Laue Group: %s\n' % self.laueGroup
s += ' Lattice Type: %s\n' % self.latticeType
return s
#
# ============================== API
#
# ========== Properties
#
# property: sgnum
def _get_sgnum(self):
"""Get method for sgnum"""
return self._sgnum
def _set_sgnum(self, v):
"""Set method for sgnum"""
self._sgnum = v
self._Hall = lookupHall[v]
#
# Set point group and laue group
#
# * Point group dictionary maps a range of space group numbers
# to a Schoenflies string for the point group
#
for k in list(_pgDict.keys()):
if v in k:
pglg = _pgDict[k]
self._pointGroup = pglg[0]
self._laueGroup = pglg[1]
pass
pass
return
sgnum = property(_get_sgnum, _set_sgnum, None,
"Space group number")
@property
def laueGroup(self):
"""Schonflies symbol for Laue group (read only)"""
return self._laueGroup
@property
def laueGroup_international(self):
"""Internationl symbol for Laue group (read only)"""
return _laue_international[self._laueGroup]
@property
def pointGroup(self):
"""Schonflies symbol for point group (read only)"""
return self._pointGroup
@property
def latticeType(self):
"""Lattice type
Possible values are 'cubic', 'hexagonal', 'trigonal',
'tetragonal', 'orthorhombic', 'monoclinic' and 'triclinic'
Rhombohedral lattices are treated as trigonal using the
"obverse" setting.
"""
return _ltDict[self.laueGroup]
@property
def reqParams(self):
"""(read only) Zero-based indices of required lattice parameters"""
return _rqpDict[self.latticeType][0]
@property
def hermannMauguin(self):
"""(read only) Hermann-Mauguin symbol"""
return lookupHM[self.sgnum]
@property
def HallSymbol(self):
"""(read only) Hall symbol"""
return self._Hall
# ========== Public Methods
#
[docs] def sixLatticeParams(self, lparams):
"""
Return the complete set of six lattice parameters from
the abbreviated set
INPUTS
lparams -- (tuple) the abbreviated set of lattice parameters
OUTPUTS
sparams -- (tuple) the complete set of lattice parameters;
(a, b, c, alpha, beta, gamma)
DESCRIPTION
* Output angles are in degrees
"""
return _rqpDict[self.latticeType][1](lparams)
#
# -----------------------------------------------END CLASS: SpaceGroup
#
#
# Hall Symbols copied from:
#
_hallStr = r"""
1 P 1
2 -P 1
3:b P 2y
3:c P 2
3:a P 2x
4:b P 2yb
4:c P 2c
4:a P 2xa
5:b1 C 2y
5:b2 A 2y
5:b3 I 2y
5:c1 A 2
5:c2 B 2
5:c3 I 2
5:a1 B 2x
5:a2 C 2x
5:a3 I 2x
6:b P -2y
6:c P -2
6:a P -2x
7:b1 P -2yc
7:b2 P -2yac
7:b3 P -2ya
7:c1 P -2a
7:c2 P -2ab
7:c3 P -2b
7:a1 P -2xb
7:a2 P -2xbc
7:a3 P -2xc
8:b1 C -2y
8:b2 A -2y
8:b3 I -2y
8:c1 A -2
8:c2 B -2
8:c3 I -2
8:a1 B -2x
8:a2 C -2x
8:a3 I -2x
9:b1 C -2yc
9:b2 A -2yac
9:b3 I -2ya
9:-b1 A -2ya
9:-b2 C -2ybc
9:-b3 I -2yc
9:c1 A -2a
9:c2 B -2bc
9:c3 I -2b
9:-c1 B -2b
9:-c2 A -2ac
9:-c3 I -2a
9:a1 B -2xb
9:a2 C -2xbc
9:a3 I -2xc
9:-a1 C -2xc
9:-a2 B -2xbc
9:-a3 I -2xb
10:b -P 2y
10:c -P 2
10:a -P 2x
11:b -P 2yb
11:c -P 2c
11:a -P 2xa
12:b1 -C 2y
12:b2 -A 2y
12:b3 -I 2y
12:c1 -A 2
12:c2 -B 2
12:c3 -I 2
12:a1 -B 2x
12:a2 -C 2x
12:a3 -I 2x
13:b1 -P 2yc
13:b2 -P 2yac
13:b3 -P 2ya
13:c1 -P 2a
13:c2 -P 2ab
13:c3 -P 2b
13:a1 -P 2xb
13:a2 -P 2xbc
13:a3 -P 2xc
14:b1 -P 2ybc
14:b2 -P 2yn
14:b3 -P 2yab
14:c1 -P 2ac
14:c2 -P 2n
14:c3 -P 2bc
14:a1 -P 2xab
14:a2 -P 2xn
14:a3 -P 2xac
15:b1 -C 2yc
15:b2 -A 2yac
15:b3 -I 2ya
15:-b1 -A 2ya
15:-b2 -C 2ybc
15:-b3 -I 2yc
15:c1 -A 2a
15:c2 -B 2bc
15:c3 -I 2b
15:-c1 -B 2b
15:-c2 -A 2ac
15:-c3 -I 2a
15:a1 -B 2xb
15:a2 -C 2xbc
15:a3 -I 2xc
15:-a1 -C 2xc
15:-a2 -B 2xbc
15:-a3 -I 2xb
16 P 2 2
17 P 2c 2
17:cab P 2a 2a
17:bca P 2 2b
18 P 2 2ab
18:cab P 2bc 2
18:bca P 2ac 2ac
19 P 2ac 2ab
20 C 2c 2
20:cab A 2a 2a
20:bca B 2 2b
21 C 2 2
21:cab A 2 2
21:bca B 2 2
22 F 2 2
23 I 2 2
24 I 2b 2c
25 P 2 -2
25:cab P -2 2
25:bca P -2 -2
26 P 2c -2
26:ba-c P 2c -2c
26:cab P -2a 2a
26:-cba P -2 2a
26:bca P -2 -2b
26:a-cb P -2b -2
27 P 2 -2c
27:cab P -2a 2
27:bca P -2b -2b
28 P 2 -2a
28:ba-c P 2 -2b
28:cab P -2b 2
28:-cba P -2c 2
28:bca P -2c -2c
28:a-cb P -2a -2a
29 P 2c -2ac
29:ba-c P 2c -2b
29:cab P -2b 2a
29:-cba P -2ac 2a
29:bca P -2bc -2c
29:a-cb P -2a -2ab
30 P 2 -2bc
30:ba-c P 2 -2ac
30:cab P -2ac 2
30:-cba P -2ab 2
30:bca P -2ab -2ab
30:a-cb P -2bc -2bc
31 P 2ac -2
31:ba-c P 2bc -2bc
31:cab P -2ab 2ab
31:-cba P -2 2ac
31:bca P -2 -2bc
31:a-cb P -2ab -2
32 P 2 -2ab
32:cab P -2bc 2
32:bca P -2ac -2ac
33 P 2c -2n
33:ba-c P 2c -2ab
33:cab P -2bc 2a
33:-cba P -2n 2a
33:bca P -2n -2ac
33:a-cb P -2ac -2n
34 P 2 -2n
34:cab P -2n 2
34:bca P -2n -2n
35 C 2 -2
35:cab A -2 2
35:bca B -2 -2
36 C 2c -2
36:ba-c C 2c -2c
36:cab A -2a 2a
36:-cba A -2 2a
36:bca B -2 -2b
36:a-cb B -2b -2
37 C 2 -2c
37:cab A -2a 2
37:bca B -2b -2b
38 A 2 -2
38:ba-c B 2 -2
38:cab B -2 2
38:-cba C -2 2
38:bca C -2 -2
38:a-cb A -2 -2
39 A 2 -2c
39:ba-c B 2 -2c
39:cab B -2c 2
39:-cba C -2b 2
39:bca C -2b -2b
39:a-cb A -2c -2c
40 A 2 -2a
40:ba-c B 2 -2b
40:cab B -2b 2
40:-cba C -2c 2
40:bca C -2c -2c
40:a-cb A -2a -2a
41 A 2 -2ac
41:ba-c B 2 -2bc
41:cab B -2bc 2
41:-cba C -2bc 2
41:bca C -2bc -2bc
41:a-cb A -2ac -2ac
42 F 2 -2
42:cab F -2 2
42:bca F -2 -2
43 F 2 -2d
43:cab F -2d 2
43:bca F -2d -2d
44 I 2 -2
44:cab I -2 2
44:bca I -2 -2
45 I 2 -2c
45:cab I -2a 2
45:bca I -2b -2b
46 I 2 -2a
46:ba-c I 2 -2b
46:cab I -2b 2
46:-cba I -2c 2
46:bca I -2c -2c
46:a-cb I -2a -2a
47 -P 2 2
48:1 P 2 2 -1n
48:2 -P 2ab 2bc
49 -P 2 2c
49:cab -P 2a 2
49:bca -P 2b 2b
50:1 P 2 2 -1ab
50:2 -P 2ab 2b
50:1cab P 2 2 -1bc
50:2cab -P 2b 2bc
50:1bca P 2 2 -1ac
50:2bca -P 2a 2c
51 -P 2a 2a
51:ba-c -P 2b 2
51:cab -P 2 2b
51:-cba -P 2c 2c
51:bca -P 2c 2
51:a-cb -P 2 2a
52 -P 2a 2bc
52:ba-c -P 2b 2n
52:cab -P 2n 2b
52:-cba -P 2ab 2c
52:bca -P 2ab 2n
52:a-cb -P 2n 2bc
53 -P 2ac 2
53:ba-c -P 2bc 2bc
53:cab -P 2ab 2ab
53:-cba -P 2 2ac
53:bca -P 2 2bc
53:a-cb -P 2ab 2
54 -P 2a 2ac
54:ba-c -P 2b 2c
54:cab -P 2a 2b
54:-cba -P 2ac 2c
54:bca -P 2bc 2b
54:a-cb -P 2b 2ab
55 -P 2 2ab
55:cab -P 2bc 2
55:bca -P 2ac 2ac
56 -P 2ab 2ac
56:cab -P 2ac 2bc
56:bca -P 2bc 2ab
57 -P 2c 2b
57:ba-c -P 2c 2ac
57:cab -P 2ac 2a
57:-cba -P 2b 2a
57:bca -P 2a 2ab
57:a-cb -P 2bc 2c
58 -P 2 2n
58:cab -P 2n 2
58:bca -P 2n 2n
59:1 P 2 2ab -1ab
59:2 -P 2ab 2a
59:1cab P 2bc 2 -1bc
59:2cab -P 2c 2bc
59:1bca P 2ac 2ac -1ac
59:2bca -P 2c 2a
60 -P 2n 2ab
60:ba-c -P 2n 2c
60:cab -P 2a 2n
60:-cba -P 2bc 2n
60:bca -P 2ac 2b
60:a-cb -P 2b 2ac
61 -P 2ac 2ab
61:ba-c -P 2bc 2ac
62 -P 2ac 2n
62:ba-c -P 2bc 2a
62:cab -P 2c 2ab
62:-cba -P 2n 2ac
62:bca -P 2n 2a
62:a-cb -P 2c 2n
63 -C 2c 2
63:ba-c -C 2c 2c
63:cab -A 2a 2a
63:-cba -A 2 2a
63:bca -B 2 2b
63:a-cb -B 2b 2
64 -C 2bc 2
64:ba-c -C 2bc 2bc
64:cab -A 2ac 2ac
64:-cba -A 2 2ac
64:bca -B 2 2bc
64:a-cb -B 2bc 2
65 -C 2 2
65:cab -A 2 2
65:bca -B 2 2
66 -C 2 2c
66:cab -A 2a 2
66:bca -B 2b 2b
67 -C 2b 2
67:ba-c -C 2b 2b
67:cab -A 2c 2c
67:-cba -A 2 2c
67:bca -B 2 2c
67:a-cb -B 2c 2
68:1 C 2 2 -1bc
68:2 -C 2b 2bc
68:1ba-c C 2 2 -1bc
68:2ba-c -C 2b 2c
68:1cab A 2 2 -1ac
68:2cab -A 2a 2c
68:1-cba A 2 2 -1ac
68:2-cba -A 2ac 2c
68:1bca B 2 2 -1bc
68:2bca -B 2bc 2b
68:1a-cb B 2 2 -1bc
68:2a-cb -B 2b 2bc
69 -F 2 2
70:1 F 2 2 -1d
70:2 -F 2uv 2vw
71 -I 2 2
72 -I 2 2c
72:cab -I 2a 2
72:bca -I 2b 2b
73 -I 2b 2c
73:ba-c -I 2a 2b
74 -I 2b 2
74:ba-c -I 2a 2a
74:cab -I 2c 2c
74:-cba -I 2 2b
74:bca -I 2 2a
74:a-cb -I 2c 2
75 P 4
76 P 4w
77 P 4c
78 P 4cw
79 I 4
80 I 4bw
81 P -4
82 I -4
83 -P 4
84 -P 4c
85:1 P 4ab -1ab
85:2 -P 4a
86:1 P 4n -1n
86:2 -P 4bc
87 -I 4
88:1 I 4bw -1bw
88:2 -I 4ad
89 P 4 2
90 P 4ab 2ab
91 P 4w 2c
92 P 4abw 2nw
93 P 4c 2
94 P 4n 2n
95 P 4cw 2c
96 P 4nw 2abw
97 I 4 2
98 I 4bw 2bw
99 P 4 -2
100 P 4 -2ab
101 P 4c -2c
102 P 4n -2n
103 P 4 -2c
104 P 4 -2n
105 P 4c -2
106 P 4c -2ab
107 I 4 -2
108 I 4 -2c
109 I 4bw -2
110 I 4bw -2c
111 P -4 2
112 P -4 2c
113 P -4 2ab
114 P -4 2n
115 P -4 -2
116 P -4 -2c
117 P -4 -2ab
118 P -4 -2n
119 I -4 -2
120 I -4 -2c
121 I -4 2
122 I -4 2bw
123 -P 4 2
124 -P 4 2c
125:1 P 4 2 -1ab
125:2 -P 4a 2b
126:1 P 4 2 -1n
126:2 -P 4a 2bc
127 -P 4 2ab
128 -P 4 2n
129:1 P 4ab 2ab -1ab
129:2 -P 4a 2a
130:1 P 4ab 2n -1ab
130:2 -P 4a 2ac
131 -P 4c 2
132 -P 4c 2c
133:1 P 4n 2c -1n
133:2 -P 4ac 2b
134:1 P 4n 2 -1n
134:2 -P 4ac 2bc
135 -P 4c 2ab
136 -P 4n 2n
137:1 P 4n 2n -1n
137:2 -P 4ac 2a
138:1 P 4n 2ab -1n
138:2 -P 4ac 2ac
139 -I 4 2
140 -I 4 2c
141:1 I 4bw 2bw -1bw
141:2 -I 4bd 2
142:1 I 4bw 2aw -1bw
142:2 -I 4bd 2c
143 P 3
144 P 31
145 P 32
146:H R 3
146:R P 3*
147 -P 3
148:H -R 3
148:R -P 3*
149 P 3 2
150 P 3 2"
151 P 31 2c (0 0 1)
152 P 31 2"
153 P 32 2c (0 0 -1)
154 P 32 2"
155:H R 3 2"
155:R P 3* 2
156 P 3 -2"
157 P 3 -2
158 P 3 -2"c
159 P 3 -2c
160:H R 3 -2"
160:R P 3* -2
161:H R 3 -2"c
161:R P 3* -2n
162 -P 3 2
163 -P 3 2c
164 -P 3 2"
165 -P 3 2"c
166:H -R 3 2"
166:R -P 3* 2
167:H -R 3 2"c
167:R -P 3* 2n
168 P 6
169 P 61
170 P 65
171 P 62
172 P 64
173 P 6c
174 P -6
175 -P 6
176 -P 6c
177 P 6 2
178 P 61 2 (0 0 -1)
179 P 65 2 (0 0 1)
180 P 62 2c (0 0 1)
181 P 64 2c (0 0 -1)
182 P 6c 2c
183 P 6 -2
184 P 6 -2c
185 P 6c -2
186 P 6c -2c
187 P -6 2
188 P -6c 2
189 P -6 -2
190 P -6c -2c
191 -P 6 2
192 -P 6 2c
193 -P 6c 2
194 -P 6c 2c
195 P 2 2 3
196 F 2 2 3
197 I 2 2 3
198 P 2ac 2ab 3
199 I 2b 2c 3
200 -P 2 2 3
201:1 P 2 2 3 -1n
201:2 -P 2ab 2bc 3
202 -F 2 2 3
203:1 F 2 2 3 -1d
203:2 -F 2uv 2vw 3
204 -I 2 2 3
205 -P 2ac 2ab 3
206 -I 2b 2c 3
207 P 4 2 3
208 P 4n 2 3
209 F 4 2 3
210 F 4d 2 3
211 I 4 2 3
212 P 4acd 2ab 3
213 P 4bd 2ab 3
214 I 4bd 2c 3
215 P -4 2 3
216 F -4 2 3
217 I -4 2 3
218 P -4n 2 3
219 F -4c 2 3
220 I -4bd 2c 3
221 -P 4 2 3
222:1 P 4 2 3 -1n
222:2 -P 4a 2bc 3
223 -P 4n 2 3
224:1 P 4n 2 3 -1n
224:2 -P 4bc 2bc 3
225 -F 4 2 3
226 -F 4c 2 3
227:1 F 4d 2 3 -1d
227:2 -F 4vw 2vw 3
228:1 F 4d 2 3 -1cd
228:2 -F 4cvw 2vw 3
229 -I 4 2 3
230 -I 4bd 2c 3
"""
# Hermann-Mauguin notation
_hmStr = r"""
1 P 1
2 P -1
3:b P 1 2 1
3:c P 1 1 2
3:a P 2 1 1
4:b P 1 21 1
4:c P 1 1 21
4:a P 21 1 1
5:b1 C 1 2 1
5:b2 A 1 2 1
5:b3 I 1 2 1
5:c1 A 1 1 2
5:c2 B 1 1 2
5:c3 I 1 1 2
5:a1 B 2 1 1
5:a2 C 2 1 1
5:a3 I 2 1 1
6:b P 1 m 1
6:c P 1 1 m
6:a P m 1 1
7:b1 P 1 c 1
7:b2 P 1 n 1
7:b3 P 1 a 1
7:c1 P 1 1 a
7:c2 P 1 1 n
7:c3 P 1 1 b
7:a1 P b 1 1
7:a2 P n 1 1
7:a3 P c 1 1
8:b1 C 1 m 1
8:b2 A 1 m 1
8:b3 I 1 m 1
8:c1 A 1 1 m
8:c2 B 1 1 m
8:c3 I 1 1 m
8:a1 B m 1 1
8:a2 C m 1 1
8:a3 I m 1 1
9:b1 C 1 c 1
9:b2 A 1 n 1
9:b3 I 1 a 1
9:-b1 A 1 a 1
9:-b2 C 1 n 1
9:-b3 I 1 c 1
9:c1 A 1 1 a
9:c2 B 1 1 n
9:c3 I 1 1 b
9:-c1 B 1 1 b
9:-c2 A 1 1 n
9:-c3 I 1 1 a
9:a1 B b 1 1
9:a2 C n 1 1
9:a3 I c 1 1
9:-a1 C c 1 1
9:-a2 B n 1 1
9:-a3 I b 1 1
10:b P 1 2/m 1
10:c P 1 1 2/m
10:a P 2/m 1 1
11:b P 1 21/m 1
11:c P 1 1 21/m
11:a P 21/m 1 1
12:b1 C 1 2/m 1
12:b2 A 1 2/m 1
12:b3 I 1 2/m 1
12:c1 A 1 1 2/m
12:c2 B 1 1 2/m
12:c3 I 1 1 2/m
12:a1 B 2/m 1 1
12:a2 C 2/m 1 1
12:a3 I 2/m 1 1
13:b1 P 1 2/c 1
13:b2 P 1 2/n 1
13:b3 P 1 2/a 1
13:c1 P 1 1 2/a
13:c2 P 1 1 2/n
13:c3 P 1 1 2/b
13:a1 P 2/b 1 1
13:a2 P 2/n 1 1
13:a3 P 2/c 1 1
14:b1 P 1 21/c 1
14:b2 P 1 21/n 1
14:b3 P 1 21/a 1
14:c1 P 1 1 21/a
14:c2 P 1 1 21/n
14:c3 P 1 1 21/b
14:a1 P 21/b 1 1
14:a2 P 21/n 1 1
14:a3 P 21/c 1 1
15:b1 C 1 2/c 1
15:b2 A 1 2/n 1
15:b3 I 1 2/a 1
15:-b1 A 1 2/a 1
15:-b2 C 1 2/n 1
15:-b3 I 1 2/c 1
15:c1 A 1 1 2/a
15:c2 B 1 1 2/n
15:c3 I 1 1 2/b
15:-c1 B 1 1 2/b
15:-c2 A 1 1 2/n
15:-c3 I 1 1 2/a
15:a1 B 2/b 1 1
15:a2 C 2/n 1 1
15:a3 I 2/c 1 1
15:-a1 C 2/c 1 1
15:-a2 B 2/n 1 1
15:-a3 I 2/b 1 1
16 P 2 2 2
17 P 2 2 21
17:cab P 21 2 2
17:bca P 2 21 2
18 P 21 21 2
18:cab P 2 21 21
18:bca P 21 2 21
19 P 21 21 21
20 C 2 2 21
20:cab A 21 2 2
20:bca B 2 21 2
21 C 2 2 2
21:cab A 2 2 2
21:bca B 2 2 2
22 F 2 2 2
23 I 2 2 2
24 I 21 21 21
25 P m m 2
25:cab P 2 m m
25:bca P m 2 m
26 P m c 21
26:ba-c P c m 21
26:cab P 21 m a
26:-cba P 21 a m
26:bca P b 21 m
26:a-cb P m 21 b
27 P c c 2
27:cab P 2 a a
27:bca P b 2 b
28 P m a 2
28:ba-c P b m 2
28:cab P 2 m b
28:-cba P 2 c m
28:bca P c 2 m
28:a-cb P m 2 a
29 P c a 21
29:ba-c P b c 21
29:cab P 21 a b
29:-cba P 21 c a
29:bca P c 21 b
29:a-cb P b 21 a
30 P n c 2
30:ba-c P c n 2
30:cab P 2 n a
30:-cba P 2 a n
30:bca P b 2 n
30:a-cb P n 2 b
31 P m n 21
31:ba-c P n m 21
31:cab P 21 m n
31:-cba P 21 n m
31:bca P n 21 m
31:a-cb P m 21 n
32 P b a 2
32:cab P 2 c b
32:bca P c 2 a
33 P n a 21
33:ba-c P b n 21
33:cab P 21 n b
33:-cba P 21 c n
33:bca P c 21 n
33:a-cb P n 21 a
34 P n n 2
34:cab P 2 n n
34:bca P n 2 n
35 C m m 2
35:cab A 2 m m
35:bca B m 2 m
36 C m c 21
36:ba-c C c m 21
36:cab A 21 m a
36:-cba A 21 a m
36:bca B b 21 m
36:a-cb B m 21 b
37 C c c 2
37:cab A 2 a a
37:bca B b 2 b
38 A m m 2
38:ba-c B m m 2
38:cab B 2 m m
38:-cba C 2 m m
38:bca C m 2 m
38:a-cb A m 2 m
39 A b m 2
39:ba-c B m a 2
39:cab B 2 c m
39:-cba C 2 m b
39:bca C m 2 a
39:a-cb A c 2 m
40 A m a 2
40:ba-c B b m 2
40:cab B 2 m b
40:-cba C 2 c m
40:bca C c 2 m
40:a-cb A m 2 a
41 A b a 2
41:ba-c B b a 2
41:cab B 2 c b
41:-cba C 2 c b
41:bca C c 2 a
41:a-cb A c 2 a
42 F m m 2
42:cab F 2 m m
42:bca F m 2 m
43 F d d 2
43:cab F 2 d d
43:bca F d 2 d
44 I m m 2
44:cab I 2 m m
44:bca I m 2 m
45 I b a 2
45:cab I 2 c b
45:bca I c 2 a
46 I m a 2
46:ba-c I b m 2
46:cab I 2 m b
46:-cba I 2 c m
46:bca I c 2 m
46:a-cb I m 2 a
47 P m m m
48:1 P n n n:1
48:2 P n n n:2
49 P c c m
49:cab P m a a
49:bca P b m b
50:1 P b a n:1
50:2 P b a n:2
50:1cab P n c b:1
50:2cab P n c b:2
50:1bca P c n a:1
50:2bca P c n a:2
51 P m m a
51:ba-c P m m b
51:cab P b m m
51:-cba P c m m
51:bca P m c m
51:a-cb P m a m
52 P n n a
52:ba-c P n n b
52:cab P b n n
52:-cba P c n n
52:bca P n c n
52:a-cb P n a n
53 P m n a
53:ba-c P n m b
53:cab P b m n
53:-cba P c n m
53:bca P n c m
53:a-cb P m a n
54 P c c a
54:ba-c P c c b
54:cab P b a a
54:-cba P c a a
54:bca P b c b
54:a-cb P b a b
55 P b a m
55:cab P m c b
55:bca P c m a
56 P c c n
56:cab P n a a
56:bca P b n b
57 P b c m
57:ba-c P c a m
57:cab P m c a
57:-cba P m a b
57:bca P b m a
57:a-cb P c m b
58 P n n m
58:cab P m n n
58:bca P n m n
59:1 P m m n:1
59:2 P m m n:2
59:1cab P n m m:1
59:2cab P n m m:2
59:1bca P m n m:1
59:2bca P m n m:2
60 P b c n
60:ba-c P c a n
60:cab P n c a
60:-cba P n a b
60:bca P b n a
60:a-cb P c n b
61 P b c a
61:ba-c P c a b
62 P n m a
62:ba-c P m n b
62:cab P b n m
62:-cba P c m n
62:bca P m c n
62:a-cb P n a m
63 C m c m
63:ba-c C c m m
63:cab A m m a
63:-cba A m a m
63:bca B b m m
63:a-cb B m m b
64 C m c a
64:ba-c C c m b
64:cab A b m a
64:-cba A c a m
64:bca B b c m
64:a-cb B m a b
65 C m m m
65:cab A m m m
65:bca B m m m
66 C c c m
66:cab A m a a
66:bca B b m b
67 C m m a
67:ba-c C m m b
67:cab A b m m
67:-cba A c m m
67:bca B m c m
67:a-cb B m a m
68:1 C c c a:1
68:2 C c c a:2
68:1ba-c C c c b:1
68:2ba-c C c c b:2
68:1cab A b a a:1
68:2cab A b a a:2
68:1-cba A c a a:1
68:2-cba A c a a:2
68:1bca B b c b:1
68:2bca B b c b:2
68:1a-cb B b a b:1
68:2a-cb B b a b:2
69 F m m m
70:1 F d d d:1
70:2 F d d d:2
71 I m m m
72 I b a m
72:cab I m c b
72:bca I c m a
73 I b c a
73:ba-c I c a b
74 I m m a
74:ba-c I m m b
74:cab I b m m
74:-cba I c m m
74:bca I m c m
74:a-cb I m a m
75 P 4
76 P 41
77 P 42
78 P 43
79 I 4
80 I 41
81 P -4
82 I -4
83 P 4/m
84 P 42/m
85:1 P 4/n:1
85:2 P 4/n:2
86:1 P 42/n:1
86:2 P 42/n:2
87 I 4/m
88:1 I 41/a:1
88:2 I 41/a:2
89 P 4 2 2
90 P 42 1 2
91 P 41 2 2
92 P 41 21 2
93 P 42 2 2
94 P 42 21 2
95 P 43 2 2
96 P 43 21 2
97 I 4 2 2
98 I 41 2 2
99 P 4 m m
100 P 4 b m
101 P 42 c m
102 P 42 n m
103 P 4 c c
104 P 4 n c
105 P 42 m c
106 P 42 b c
107 I 4 m m
108 I 4 c m
109 I 41 m d
110 I 41 c d
111 P -4 2 m
112 P -4 2 c
113 P -4 21 m
114 P -4 21 c
115 P -4 m 2
116 P -4 c 2
117 P -4 b 2
118 P -4 n 2
119 I -4 m 2
120 I -4 c 2
121 I -4 2 m
122 I -4 2 d
123 P 4/m m m
124 P 4/m c c
125:1 P 4/n b m:1
125:2 P 4/n b m:2
126:1 P 4/n n c:1
126:2 P 4/n n c:2
127 P 4/m b m
128 P 4/m n c
129:1 P 4/n m m:1
129:2 P 4/n m m:2
130:1 P 4/n c c:1
130:2 P 4/n c c:2
131 P 42/m m c
132 P 42/m c m
133:1 P 42/n b c:1
133:2 P 42/n b c:2
134:1 P 42/n n m:1
134:2 P 42/n n m:2
135 P 42/m b c
136 P 42/m n m
137:1 P 42/n m c:1
137:2 P 42/n m c:2
138:1 P 42/n c m:1
138:2 P 42/n c m:2
139 I 4/m m m
140 I 4/m c m
141:1 I 41/a m d:1
141:2 I 41/a m d:2
142:1 I 41/a c d:1
142:2 I 41/a c d:2
143 P 3
144 P 31
145 P 32
146:H R 3
146:R R 3
147 P -3
148:H R -3
148:R R -3
149 P 3 1 2
150 P 3 2 1
151 P 31 1 2
152 P 31 2 1
153 P 32 1 2
154 P 32 2 1
155:H R 32
155:R R 32
156 P 3 m 1
157 P 3 1 m
158 P 3 c 1
159 P 3 1 c
160:H R 3 m
160:R R 3 m
161:H R 3 c
161:R R 3 c
162 P -3 1 m
163 P -3 1 c
164 P -3 m 1
165 P -3 c 1
166:H R -3 m
166:R R -3 m
167:H R -3 c
167:R R -3 c
168 P 6
169 P 61
170 P 65
171 P 62
172 P 64
173 P 63
174 P -6
175 P 6/m
176 P 63/m
177 P 6 2 2
178 P 61 2 2
179 P 65 2 2
180 P 62 2 2
181 P 64 2 2
182 P 63 2 2
183 P 6 m m
184 P 6 c c
185 P 63 c m
186 P 63 m c
187 P -6 m 2
188 P -6 c 2
189 P -6 2 m
190 P -6 2 c
191 P 6/m m m
192 P 6/m c c
193 P 63/m c m
194 P 63/m m c
195 P 2 3
196 F 2 3
197 I 2 3
198 P 21 3
199 I 21 3
200 P m -3
201:1 P n -3:1
201:2 P n -3:2
202 F m -3
203:1 F d -3:1
203:2 F d -3:2
204 I m -3
205 P a -3
206 I a -3
207 P 4 3 2
208 P 42 3 2
209 F 4 3 2
210 F 41 3 2
211 I 4 3 2
212 P 43 3 2
213 P 41 3 2
214 I 41 3 2
215 P -4 3 m
216 F -4 3 m
217 I -4 3 m
218 P -4 3 n
219 F -4 3 c
220 I -4 3 d
221 P m -3 m
222:1 P n -3 n:1
222:2 P n -3 n:2
223 P m -3 n
224:1 P n -3 m:1
224:2 P n -3 m:2
225 F m -3 m
226 F m -3 c
227:1 F d -3 m:1
227:2 F d -3 m:2
228:1 F d -3 c:1
228:2 F d -3 c:2
229 I m -3 m
230 I a -3 d
"""
def _buildDict(hstr):
"""build the dictionaries from the notation string
Returns two dictionaries: one taking sg number to string
and the inverse
Takes the first Hall symbol it finds. This is desired
for the rhombohedral lattices so that they use the hexagonal
convention.
"""
d = dict()
di = dict()
hs = hstr.split('\n')
for l in hs:
li = l.strip()
if li:
nstr, hstr = li.split(None, 1)
nstr = nstr.split(':', 1)[0]
n = int(nstr)
if n not in d:
d[n] = hstr
pass
di[hstr] = n
pass
pass
return d, di
lookupHall, Hall_to_sgnum = _buildDict(_hallStr)
lookupHM, HM_to_sgnum = _buildDict(_hmStr)
def _map_sg_info(hstr):
"""build the dictionaries from the notation string
Returns two dictionaries: one taking sg id to string
and the inverse.
"""
d = OrderedDict()
di = OrderedDict()
hs = hstr.split('\n')
for l in hs:
li = l.strip()
if li:
sgid, altid = li.split(None, 1)
d[sgid] = altid
di[altid] = sgid
return d, di
sgid_to_hall, hall_to_sgid = _map_sg_info(_hallStr)
sgid_to_hm, hm_to_sgid = _map_sg_info(_hmStr)
# ==================== Point Groups/Laue Groups
# TODO: make sane mappings
laue_1 = 'ci'
laue_2 = 'c2h'
laue_3 = 'd2h'
laue_4 = 'c4h'
laue_5 = 'd4h'
laue_6 = 's6'
laue_7 = 'd3d'
laue_8 = 'c6h'
laue_9 = 'd6h'
laue_10 = 'th'
laue_11 = 'oh'
_laue_international = {laue_1:"-1",
laue_2:"2/m",
laue_3:"mmm",
laue_4:"4/m",
laue_5:"4/mmm",
laue_6:"-3",
laue_7:"-3m",
laue_8:"6/m",
laue_9:"6/mmm",
laue_10:"m3",
laue_11:"m3m"}
def _sgrange(min, max): return tuple(range(min, max + 1)) # inclusive range
_pgDict = {
_sgrange(1, 1): ('c1', laue_1), # Triclinic
_sgrange(2, 2): ('ci', laue_1), # laue 1
_sgrange(3, 5): ('c2', laue_2), # Monoclinic
_sgrange(6, 9): ('cs', laue_2),
_sgrange(10, 15): ('c2h', laue_2), # laue 2
_sgrange(16, 24): ('d2', laue_3), # Orthorhombic
_sgrange(25, 46): ('c2v', laue_3),
_sgrange(47, 74): ('d2h', laue_3), # laue 3
_sgrange(75, 80): ('c4', laue_4), # Tetragonal
_sgrange(81, 82): ('s4', laue_4),
_sgrange(83, 88): ('c4h', laue_4), # laue 4
_sgrange(89, 98): ('d4', laue_5),
_sgrange(99, 110): ('c4v', laue_5),
_sgrange(111, 122): ('d2d', laue_5),
_sgrange(123, 142): ('d4h', laue_5), # laue 5
_sgrange(143, 146): ('c3', laue_6), # Trigonal
_sgrange(147, 148): ('s6', laue_6), # laue 6 [also c3i]
_sgrange(149, 155): ('d3', laue_7),
_sgrange(156, 161): ('c3v', laue_7),
_sgrange(162, 167): ('d3d', laue_7), # laue 7
_sgrange(168, 173): ('c6', laue_8), # Hexagonal
_sgrange(174, 174): ('c3h', laue_8),
_sgrange(175, 176): ('c6h', laue_8), # laue 8
_sgrange(177, 182): ('d6', laue_9),
_sgrange(183, 186): ('c6v', laue_9),
_sgrange(187, 190): ('d3h', laue_9),
_sgrange(191, 194): ('d6h', laue_9), # laue 9
_sgrange(195, 199): ('t', laue_10), # Cubic
_sgrange(200, 206): ('th', laue_10), # laue 10
_sgrange(207, 214): ('o', laue_11),
_sgrange(215, 220): ('td', laue_11),
_sgrange(221, 230): ('oh', laue_11), # laue 11
}
#
# Lattice type dictionary on Laue Group
# . to replace Symmetry.ltypeOfLaueGroup()
# . see also lparm.latticeVectors()
#
ltype_1 = 'triclinic'
ltype_2 = 'monoclinic'
ltype_3 = 'orthorhombic'
ltype_4 = 'tetragonal'
ltype_5 = 'trigonal'
ltype_6 = 'hexagonal'
ltype_7 = 'cubic'
_ltDict = {
laue_1: ltype_1,
laue_2: ltype_2,
laue_3: ltype_3,
laue_4: ltype_4,
laue_5: ltype_4,
laue_6: ltype_5,
laue_7: ltype_5,
laue_8: ltype_6,
laue_9: ltype_6,
laue_10: ltype_7,
laue_11: ltype_7
}
# Required parameters by lattice type
# * dictionary provides list of required indices with
# a function that takes the reduced set of lattice parameters
# to the full set
# * consistent with lparm.latticeVectors
#
_rqpDict = {
ltype_1: (tuple(range(6)), lambda p: p), # all 6
# note beta
ltype_2: ((0, 1, 2, 4), lambda p: (p[0], p[1], p[2], 90, p[3], 90)),
ltype_3: ((0, 1, 2), lambda p: (p[0], p[1], p[2], 90, 90, 90)),
ltype_4: ((0, 2), lambda p: (p[0], p[0], p[1], 90, 90, 90)),
ltype_5: ((0, 2), lambda p: (p[0], p[0], p[1], 90, 90, 120)),
ltype_6: ((0, 2), lambda p: (p[0], p[0], p[1], 90, 90, 120)),
ltype_7: ((0,), lambda p: (p[0], p[0], p[0], 90, 90, 90)),
}
def Allowed_HKLs(sgnum, hkllist):
"""
this function checks if a particular g vector is allowed
by lattice centering, screw axis or glide plane
"""
sg_hmsymbol = symbols.pstr_spacegroup[sgnum-1].strip()
symmorphic = False
if(sgnum in constants.sgnum_symmorphic):
symmorphic = True
hkllist = np.atleast_2d(hkllist)
centering = sg_hmsymbol[0]
if(centering == 'P'):
# all reflections are allowed
mask = np.ones([hkllist.shape[0], ], dtype=bool)
elif(centering == 'F'):
# same parity
seo = np.sum(np.mod(hkllist+100, 2), axis=1)
mask = np.logical_not(np.logical_or(seo == 1, seo == 2))
elif(centering == 'I'):
# sum is even
seo = np.mod(np.sum(hkllist, axis=1)+100, 2)
mask = (seo == 0)
elif(centering == 'A'):
# k+l is even
seo = np.mod(np.sum(hkllist[:, 1:3], axis=1)+100, 2)
mask = seo == 0
elif(centering == 'B'):
# h+l is even
seo = np.mod(hkllist[:, 0]+hkllist[:, 2]+100, 2)
mask = seo == 0
elif(centering == 'C'):
# h+k is even
seo = np.mod(hkllist[:, 0]+hkllist[:, 1]+100, 2)
mask = seo == 0
elif(centering == 'R'):
# -h+k+l is divisible by 3
seo = np.mod(-hkllist[:, 0]+hkllist[:, 1]+hkllist[:, 2]+90, 3)
mask = seo == 0
else:
raise RuntimeError(
'IsGAllowed: unknown lattice centering encountered.')
hkls = hkllist[mask, :]
if(not symmorphic):
hkls = NonSymmorphicAbsences(sgnum, hkls)
return hkls.astype(np.int32)
def omitscrewaxisabsences(sgnum, hkllist, ax, iax):
"""
this function encodes the table on pg 48 of
international table of crystallography vol A
the systematic absences due to different screw
axis is encoded here.
iax encodes the primary, secondary or tertiary axis
iax == 0 : primary
iax == 1 : secondary
iax == 2 : tertiary
@NOTE: only unique b axis in monoclinic systems
implemented as thats the standard setting
"""
latticeType = symmetry.latticeType(sgnum)
if(latticeType == 'triclinic'):
"""
no systematic absences for the triclinic crystals
"""
pass
elif(latticeType == 'monoclinic'):
if(ax != '2_1'):
raise RuntimeError(
'omitscrewaxisabsences: monoclinic systems\
can only have 2_1 screw axis')
"""
only unique b-axis will be encoded
it is the users responsibility to input
lattice parameters in the standard setting
with b-axis having the 2-fold symmetry
"""
if(iax == 1):
mask1 = np.logical_and(hkllist[:, 0] == 0, hkllist[:, 2] == 0)
mask2 = np.mod(hkllist[:, 1]+100, 2) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
else:
raise RuntimeError(
'omitscrewaxisabsences: only b-axis\
can have 2_1 screw axis')
elif(latticeType == 'orthorhombic'):
if(ax != '2_1'):
raise RuntimeError(
'omitscrewaxisabsences: orthorhombic systems\
can only have 2_1 screw axis')
"""
2_1 screw on primary axis
h00 ; h = 2n
"""
if(iax == 0):
mask1 = np.logical_and(hkllist[:, 1] == 0, hkllist[:, 2] == 0)
mask2 = np.mod(hkllist[:, 0]+100, 2) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(iax == 1):
mask1 = np.logical_and(hkllist[:, 0] == 0, hkllist[:, 2] == 0)
mask2 = np.mod(hkllist[:, 1]+100, 2) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(iax == 2):
mask1 = np.logical_and(hkllist[:, 0] == 0, hkllist[:, 1] == 0)
mask2 = np.mod(hkllist[:, 2]+100, 2) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(latticeType == 'tetragonal'):
if(iax == 0):
mask1 = np.logical_and(hkllist[:, 0] == 0, hkllist[:, 1] == 0)
if(ax == '4_2'):
mask2 = np.mod(hkllist[:, 2]+100, 2) != 0
elif(ax in ['4_1', '4_3']):
mask2 = np.mod(hkllist[:, 2]+100, 4) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(iax == 1):
mask1 = np.logical_and(hkllist[:, 1] == 0, hkllist[:, 2] == 0)
mask2 = np.logical_and(hkllist[:, 0] == 0, hkllist[:, 2] == 0)
if(ax == '2_1'):
mask3 = np.mod(hkllist[:, 0]+100, 2) != 0
mask4 = np.mod(hkllist[:, 1]+100, 2) != 0
mask1 = np.logical_not(np.logical_and(mask1, mask3))
mask2 = np.logical_not(np.logical_and(mask2, mask4))
mask = ~np.logical_or(~mask1, ~mask2)
hkllist = hkllist[mask, :]
elif(latticeType == 'trigonal'):
mask1 = np.logical_and(hkllist[:, 0] == 0, hkllist[:, 1] == 0)
if(iax == 0):
if(ax in ['3_1', '3_2']):
mask2 = np.mod(hkllist[:, 2]+90, 3) != 0
else:
raise RuntimeError(
'omitscrewaxisabsences: trigonal \
systems can only have screw axis')
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(latticeType == 'hexagonal'):
mask1 = np.logical_and(hkllist[:, 0] == 0, hkllist[:, 1] == 0)
if(iax == 0):
if(ax == '6_3'):
mask2 = np.mod(hkllist[:, 2]+100, 2) != 0
elif(ax in ['3_1', '3_2', '6_2', '6_4']):
mask2 = np.mod(hkllist[:, 2]+90, 3) != 0
elif(ax in ['6_1', '6_5']):
mask2 = np.mod(hkllist[:, 2]+120, 6) != 0
else:
raise RuntimeError(
'omitscrewaxisabsences: hexagonal \
systems can only have screw axis')
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(latticeType == 'cubic'):
mask1 = np.logical_and(hkllist[:, 0] == 0, hkllist[:, 1] == 0)
mask2 = np.logical_and(hkllist[:, 0] == 0, hkllist[:, 2] == 0)
mask3 = np.logical_and(hkllist[:, 1] == 0, hkllist[:, 2] == 0)
if(ax in ['2_1', '4_2']):
mask4 = np.mod(hkllist[:, 2]+100, 2) != 0
mask5 = np.mod(hkllist[:, 1]+100, 2) != 0
mask6 = np.mod(hkllist[:, 0]+100, 2) != 0
elif(ax in ['4_1', '4_3']):
mask4 = np.mod(hkllist[:, 2]+100, 4) != 0
mask5 = np.mod(hkllist[:, 1]+100, 4) != 0
mask6 = np.mod(hkllist[:, 0]+100, 4) != 0
mask1 = np.logical_not(np.logical_and(mask1, mask4))
mask2 = np.logical_not(np.logical_and(mask2, mask5))
mask3 = np.logical_not(np.logical_and(mask3, mask6))
mask = ~np.logical_or(~mask1, np.logical_or(~mask2, ~mask3))
hkllist = hkllist[mask, :]
return hkllist.astype(np.int32)
def omitglideplaneabsences(sgnum, hkllist, plane, ip):
"""
this function encodes the table on pg 47 of
international table of crystallography vol A
the systematic absences due to different glide
planes is encoded here.
ip encodes the primary, secondary or tertiary plane normal
ip == 0 : primary
ip == 1 : secondary
ip == 2 : tertiary
@NOTE: only unique b axis in monoclinic systems
implemented as thats the standard setting
"""
latticeType = symmetry.latticeType(sgnum)
if(latticeType == 'triclinic'):
pass
elif(latticeType == 'monoclinic'):
if(ip == 1):
mask1 = hkllist[:, 1] == 0
if(plane == 'c'):
mask2 = np.mod(hkllist[:, 2]+100, 2) != 0
elif(plane == 'a'):
mask2 = np.mod(hkllist[:, 0]+100, 2) != 0
elif(plane == 'n'):
mask2 = np.mod(hkllist[:, 0]+hkllist[:, 2]+100, 2) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(latticeType == 'orthorhombic'):
if(ip == 0):
mask1 = hkllist[:, 0] == 0
if(plane == 'b'):
mask2 = np.mod(hkllist[:, 1]+100, 2) != 0
elif(plane == 'c'):
mask2 = np.mod(hkllist[:, 2]+100, 2) != 0
elif(plane == 'n'):
mask2 = np.mod(hkllist[:, 1]+hkllist[:, 2]+100, 2) != 0
elif(plane == 'd'):
mask2 = np.mod(hkllist[:, 1]+hkllist[:, 2]+100, 4) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(ip == 1):
mask1 = hkllist[:, 1] == 0
if(plane == 'c'):
mask2 = np.mod(hkllist[:, 2]+100, 2) != 0
elif(plane == 'a'):
mask2 = np.mod(hkllist[:, 0]+100, 2) != 0
elif(plane == 'n'):
mask2 = np.mod(hkllist[:, 0]+hkllist[:, 2]+100, 2) != 0
elif(plane == 'd'):
mask2 = np.mod(hkllist[:, 0]+hkllist[:, 2]+100, 4) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(ip == 2):
mask1 = hkllist[:, 2] == 0
if(plane == 'a'):
mask2 = np.mod(hkllist[:, 0]+100, 2) != 0
elif(plane == 'b'):
mask2 = np.mod(hkllist[:, 1]+100, 2) != 0
elif(plane == 'n'):
mask2 = np.mod(hkllist[:, 0]+hkllist[:, 1]+100, 2) != 0
elif(plane == 'd'):
mask2 = np.mod(hkllist[:, 0]+hkllist[:, 1]+100, 4) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(latticeType == 'tetragonal'):
if(ip == 0):
mask1 = hkllist[:, 2] == 0
if(plane == 'a'):
mask2 = np.mod(hkllist[:, 0]+100, 2) != 0
elif(plane == 'b'):
mask2 = np.mod(hkllist[:, 1]+100, 2) != 0
elif(plane == 'n'):
mask2 = np.mod(hkllist[:, 0]+hkllist[:, 1]+100, 2) != 0
elif(plane == 'd'):
mask2 = np.mod(hkllist[:, 0]+hkllist[:, 1]+100, 4) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(ip == 1):
mask1 = hkllist[:, 0] == 0
mask2 = hkllist[:, 1] == 0
if(plane in ['a', 'b']):
mask3 = np.mod(hkllist[:, 1]+100, 2) != 0
mask4 = np.mod(hkllist[:, 0]+100, 2) != 0
elif(plane == 'c'):
mask3 = np.mod(hkllist[:, 2]+100, 2) != 0
mask4 = mask3
elif(plane == 'n'):
mask3 = np.mod(hkllist[:, 1]+hkllist[:, 2]+100, 2) != 0
mask4 = np.mod(hkllist[:, 0]+hkllist[:, 2]+100, 2) != 0
elif(plane == 'd'):
mask3 = np.mod(hkllist[:, 1]+hkllist[:, 2]+100, 4) != 0
mask4 = np.mod(hkllist[:, 0]+hkllist[:, 2]+100, 4) != 0
mask1 = np.logical_not(np.logical_and(mask1, mask3))
mask2 = np.logical_not(np.logical_and(mask2, mask4))
mask = ~np.logical_or(~mask1, ~mask2)
hkllist = hkllist[mask, :]
elif(ip == 2):
mask1 = np.abs(hkllist[:, 0]) == np.abs(hkllist[:, 1])
if(plane in ['c', 'n']):
mask2 = np.mod(hkllist[:, 2]+100, 2) != 0
elif(plane == 'd'):
mask2 = np.mod(2*hkllist[:, 0]+hkllist[:, 2]+100, 4) != 0
mask = np.logical_not(np.logical_and(mask1, mask2))
hkllist = hkllist[mask, :]
elif(latticeType == 'trigonal'):
if(plane != 'c'):
raise RuntimeError(
'omitglideplaneabsences: only c-glide \
allowed for trigonal systems')
if(ip == 1):
mask1 = hkllist[:, 0] == 0
mask2 = hkllist[:, 1] == 0
mask3 = hkllist[:, 0] == -hkllist[:, 1]
if(plane == 'c'):
mask4 = np.mod(hkllist[:, 2]+100, 2) != 0
else:
raise RuntimeError(
'omitglideplaneabsences: only c-glide \
allowed for trigonal systems')
elif(ip == 2):
mask1 = hkllist[:, 1] == hkllist[:, 0]
mask2 = hkllist[:, 0] == -2*hkllist[:, 1]
mask3 = -2*hkllist[:, 0] == hkllist[:, 1]
if(plane == 'c'):
mask4 = np.mod(hkllist[:, 2]+100, 2) != 0
else:
raise RuntimeError(
'omitglideplaneabsences: only c-glide \
allowed for trigonal systems')
mask1 = np.logical_and(mask1, mask4)
mask2 = np.logical_and(mask2, mask4)
mask3 = np.logical_and(mask3, mask4)
mask = np.logical_not(np.logical_or(
mask1, np.logical_or(mask2, mask3)))
hkllist = hkllist[mask, :]
elif(latticeType == 'hexagonal'):
if(plane != 'c'):
raise RuntimeError(
'omitglideplaneabsences: only c-glide \
allowed for hexagonal systems')
if(ip == 2):
mask1 = hkllist[:, 0] == hkllist[:, 1]
mask2 = hkllist[:, 0] == -2*hkllist[:, 1]
mask3 = -2*hkllist[:, 0] == hkllist[:, 1]
mask4 = np.mod(hkllist[:, 2]+100, 2) != 0
mask1 = np.logical_and(mask1, mask4)
mask2 = np.logical_and(mask2, mask4)
mask3 = np.logical_and(mask3, mask4)
mask = np.logical_not(np.logical_or(
mask1, np.logical_or(mask2, mask3)))
elif(ip == 1):
mask1 = hkllist[:, 1] == 0
mask2 = hkllist[:, 0] == 0
mask3 = hkllist[:, 1] == -hkllist[:, 0]
mask4 = np.mod(hkllist[:, 2]+100, 2) != 0
mask1 = np.logical_and(mask1, mask4)
mask2 = np.logical_and(mask2, mask4)
mask3 = np.logical_and(mask3, mask4)
mask = np.logical_not(np.logical_or(
mask1, np.logical_or(mask2, mask3)))
hkllist = hkllist[mask, :]
elif(latticeType == 'cubic'):
if(ip == 0):
mask1 = hkllist[:, 0] == 0
mask2 = hkllist[:, 1] == 0
mask3 = hkllist[:, 2] == 0
mask4 = np.mod(hkllist[:, 0]+100, 2) != 0
mask5 = np.mod(hkllist[:, 1]+100, 2) != 0
mask6 = np.mod(hkllist[:, 2]+100, 2) != 0
if(plane == 'a'):
mask1 = np.logical_or(np.logical_and(
mask1, mask5), np.logical_and(mask1, mask6))
mask2 = np.logical_or(np.logical_and(
mask2, mask4), np.logical_and(mask2, mask6))
mask3 = np.logical_and(mask3, mask4)
mask = np.logical_not(np.logical_or(
mask1, np.logical_or(mask2, mask3)))
elif(plane == 'b'):
mask1 = np.logical_and(mask1, mask5)
mask3 = np.logical_and(mask3, mask5)
mask = np.logical_not(np.logical_or(mask1, mask3))
elif(plane == 'c'):
mask1 = np.logical_and(mask1, mask6)
mask2 = np.logical_and(mask2, mask6)
mask = np.logical_not(np.logical_or(mask1, mask2))
elif(plane == 'n'):
mask4 = np.mod(hkllist[:, 1]+hkllist[:, 2]+100, 2) != 0
mask5 = np.mod(hkllist[:, 0]+hkllist[:, 2]+100, 2) != 0
mask6 = np.mod(hkllist[:, 0]+hkllist[:, 1]+100, 2) != 0
mask1 = np.logical_not(np.logical_and(mask1, mask4))
mask2 = np.logical_not(np.logical_and(mask2, mask5))
mask3 = np.logical_not(np.logical_and(mask3, mask6))
mask = ~np.logical_or(
~mask1, np.logical_or(~mask2, ~mask3))
elif(plane == 'd'):
mask4 = np.mod(hkllist[:, 1]+hkllist[:, 2]+100, 4) != 0
mask5 = np.mod(hkllist[:, 0]+hkllist[:, 2]+100, 4) != 0
mask6 = np.mod(hkllist[:, 0]+hkllist[:, 1]+100, 4) != 0
mask1 = np.logical_not(np.logical_and(mask1, mask4))
mask2 = np.logical_not(np.logical_and(mask2, mask5))
mask3 = np.logical_not(np.logical_and(mask3, mask6))
mask = ~np.logical_or(
~mask1, np.logical_or(~mask2, ~mask3))
else:
raise RuntimeError(
'omitglideplaneabsences: unknown glide \
plane encountered.')
hkllist = hkllist[mask, :]
if(ip == 2):
mask1 = np.abs(hkllist[:, 0]) == np.abs(hkllist[:, 1])
mask2 = np.abs(hkllist[:, 1]) == np.abs(hkllist[:, 2])
mask3 = np.abs(hkllist[:, 0]) == np.abs(hkllist[:, 2])
if(plane in ['a', 'b', 'c', 'n']):
mask4 = np.mod(hkllist[:, 2]+100, 2) != 0
mask5 = np.mod(hkllist[:, 0]+100, 2) != 0
mask6 = np.mod(hkllist[:, 1]+100, 2) != 0
elif(plane == 'd'):
mask4 = np.mod(2*hkllist[:, 0]+hkllist[:, 2]+100, 4) != 0
mask5 = np.mod(hkllist[:, 0]+2*hkllist[:, 1]+100, 4) != 0
mask6 = np.mod(2*hkllist[:, 0]+hkllist[:, 1]+100, 4) != 0
else:
raise RuntimeError(
'omitglideplaneabsences: unknown glide \
plane encountered.')
mask1 = np.logical_not(np.logical_and(mask1, mask4))
mask2 = np.logical_not(np.logical_and(mask2, mask5))
mask3 = np.logical_not(np.logical_and(mask3, mask6))
mask = ~np.logical_or(~mask1, np.logical_or(~mask2, ~mask3))
hkllist = hkllist[mask, :]
return hkllist
def NonSymmorphicAbsences(sgnum, hkllist):
"""
this function prunes hkl list for the screw axis and glide
plane absences
"""
planes = constants.SYS_AB[sgnum][0]
for ip, p in enumerate(planes):
if(p != ''):
hkllist = omitglideplaneabsences(sgnum, hkllist, p, ip)
axes = constants.SYS_AB[sgnum][1]
for iax, ax in enumerate(axes):
if(ax != ''):
hkllist = omitscrewaxisabsences(sgnum, hkllist, ax, iax)
return hkllist
#
# ================================================== HKL Enumeration
#
def _getHKLsBySS(ss):
"""Return a list of HKLs with a given sum of squares'
ss - (int) sum of squares
"""
#
# NOTE: the loop below could be speeded up by requiring
# h >= k > = l, and then applying all permutations
# and sign changes. Could possibly save up to
# a factor of 48.
#
def pmrange(n): return list(range(n, -(n+1), -1)) # plus/minus range
def iroot(n): return int(floor(sqrt(n))) # integer square root
hkls = []
hmax = iroot(ss)
for h in pmrange(hmax):
ss2 = ss - h*h
kmax = iroot(ss2)
for k in pmrange(kmax):
rem = ss2 - k*k
if rem == 0:
hkls.append((h, k, 0))
else:
l = iroot(rem)
if l*l == rem:
hkls += [(h, k, l), (h, k, -l)]
pass
pass
pass
pass
return hkls
#
# ================================================== Test Functions
#
def testHKLs():
#
# Check reduced HKLs
#
# 1. Titanium (sg 194)
#
sg = SpaceGroup(194)
print('==================== Titanium (194)')
ssmax = 20
myHKLs = sg.getHKLs(ssmax)
print('Number of HKLs with sum of square %d or less: %d'
% (ssmax, len(myHKLs)))
for hkl in myHKLs:
ss = hkl[0]**2 + hkl[1]**2 + hkl[2]**2
print((hkl, ss))
pass
#
# 2. Ruby (sg 167)
#
sg = SpaceGroup(167)
print('==================== Ruby (167)')
ssmax = 10
myHKLs = sg.getHKLs(ssmax)
print('Number of HKLs with sum of square %d or less: %d'
% (ssmax, len(myHKLs)))
for hkl in myHKLs:
ss = hkl[0]**2 + hkl[1]**2 + hkl[2]**2
print((hkl, ss))
pass
#
# Test Generic HKLs
#
for ss in range(1, 10):
print('==================== ss = %d' % ss)
hkls = _getHKLsBySS(ss)
print(' number of hkls: ', len(hkls))
print(hkls)
pass
return
if __name__ == '__main__':
#
import sys
#
if 'testHKLs' in sys.argv:
testHKLs()
sys.exit()
#
# Test Space groups:
#
for n in range(1, 231):
try:
sg = SpaceGroup(n)
sg.getHKLs(10)
print(sg)
print('\n')
except:
print(('failed for space group number: ', n))
print(('Hall symbol: ', lookupHall[n]))
pass
pass
#
pass