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
|
/*
* cell.c
*
* Unit Cell Calculations
*
* (c) 2007-2009 Thomas White <thomas.white@desy.de>
*
* pattern_sim - Simulate diffraction patterns from small crystals
*
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
#include "cell.h"
#include "utils.h"
/* Update the cartesian representation from the crystallographic one */
static void cell_update_cartesian(UnitCell *cell)
{
double tmp, V, cosalphastar, cstar;
if ( !cell ) return;
/* a in terms of x, y and z
* +a (cryst) is defined to lie along +x (cart) */
cell->ax = cell->a;
cell->ay = 0.0;
cell->az = 0.0;
/* b in terms of x, y and z
* b (cryst) is defined to lie in the xy (cart) plane */
cell->bx = cell->b*cos(cell->gamma);
cell->by = cell->b*sin(cell->gamma);
cell->bz = 0.0;
tmp = cos(cell->alpha)*cos(cell->alpha)
- cos(cell->beta)*cos(cell->beta)
- cos(cell->gamma)*cos(cell->gamma)
+ 2.0*cos(cell->alpha)*cos(cell->beta)*cos(cell->gamma);
V = cell->a * cell->b * cell->c * sqrt(1.0 - tmp);
cosalphastar = cos(cell->beta)*cos(cell->gamma) - cos(cell->alpha);
cosalphastar /= sin(cell->beta)*sin(cell->gamma);
cstar = (cell->a * cell->b * sin(cell->gamma))/V;
/* c in terms of x, y and z */
cell->cx = cell->c*cos(cell->beta);
cell->cy = -cell->c*sin(cell->beta)*cosalphastar;
cell->cz = 1.0/cstar;
}
/* Update the crystallographic representation from the cartesian one */
static void cell_update_crystallographic(UnitCell *cell)
{
if ( !cell ) return;
cell->a = modulus(cell->ax, cell->ay, cell->az);
cell->b = modulus(cell->bx, cell->by, cell->bz);
cell->c = modulus(cell->cx, cell->cy, cell->cz);
cell->alpha = angle_between(cell->bx, cell->by, cell->bz,
cell->cx, cell->cy, cell->cz);
cell->beta = angle_between(cell->ax, cell->ay, cell->az,
cell->cx, cell->cy, cell->cz);
cell->gamma = angle_between(cell->ax, cell->ay, cell->az,
cell->bx, cell->by, cell->bz);
}
UnitCell *cell_new()
{
UnitCell *cell;
cell = malloc(sizeof(UnitCell));
if ( !cell ) return NULL;
cell->a = 1.0;
cell->b = 1.0;
cell->c = 1.0;
cell->alpha = M_PI_2;
cell->beta = M_PI_2;
cell->gamma = M_PI_2;
cell_update_cartesian(cell);
return cell;
}
void cell_set_parameters(UnitCell *cell, double a, double b, double c,
double alpha, double beta, double gamma)
{
if ( !cell ) return;
cell->a = a;
cell->b = b;
cell->c = c;
cell->alpha = alpha;
cell->beta = beta;
cell->gamma = gamma;
cell_update_cartesian(cell);
}
void cell_set_cartesian(UnitCell *cell,
double ax, double ay, double az,
double bx, double by, double bz,
double cx, double cy, double cz)
{
if ( !cell ) return;
cell->ax = ax; cell->ay = ay; cell->az = az;
cell->bx = bx; cell->by = by; cell->bz = bz;
cell->cx = cx; cell->cy = cy; cell->cz = cz;
cell_update_crystallographic(cell);
}
UnitCell *cell_new_from_parameters(double a, double b, double c,
double alpha, double beta, double gamma)
{
UnitCell *cell;
cell = cell_new();
if ( !cell ) return NULL;
cell_set_parameters(cell, a, b, c, alpha, beta, gamma);
return cell;
}
void cell_get_cartesian(UnitCell *cell,
double *ax, double *ay, double *az,
double *bx, double *by, double *bz,
double *cx, double *cy, double *cz)
{
if ( !cell ) return;
*ax = cell->ax; *ay = cell->ay; *az = cell->az;
*bx = cell->bx; *by = cell->by; *bz = cell->bz;
*cx = cell->cx; *cy = cell->cy; *cz = cell->cz;
}
void cell_get_reciprocal(UnitCell *cell,
double *asx, double *asy, double *asz,
double *bsx, double *bsy, double *bsz,
double *csx, double *csy, double *csz)
{
int s;
gsl_matrix *m;
gsl_matrix *inv;
gsl_permutation *perm;
m = gsl_matrix_alloc(3, 3);
gsl_matrix_set(m, 0, 0, cell->ax);
gsl_matrix_set(m, 0, 1, cell->bx);
gsl_matrix_set(m, 0, 2, cell->cx);
gsl_matrix_set(m, 1, 0, cell->ay);
gsl_matrix_set(m, 1, 1, cell->by);
gsl_matrix_set(m, 1, 2, cell->cy);
gsl_matrix_set(m, 2, 0, cell->az);
gsl_matrix_set(m, 2, 1, cell->bz);
gsl_matrix_set(m, 2, 2, cell->cz);
/* Invert */
perm = gsl_permutation_alloc(m->size1);
inv = gsl_matrix_alloc(m->size1, m->size2);
gsl_linalg_LU_decomp(m, perm, &s);
gsl_linalg_LU_invert(m, perm, inv);
gsl_permutation_free(perm);
gsl_matrix_free(m);
/* Transpose */
gsl_matrix_transpose(inv);
*asx = gsl_matrix_get(inv, 0, 0);
*bsx = gsl_matrix_get(inv, 0, 1);
*csx = gsl_matrix_get(inv, 0, 2);
*asy = gsl_matrix_get(inv, 1, 0);
*bsy = gsl_matrix_get(inv, 1, 1);
*csy = gsl_matrix_get(inv, 1, 2);
*asz = gsl_matrix_get(inv, 2, 0);
*bsz = gsl_matrix_get(inv, 2, 1);
*csz = gsl_matrix_get(inv, 2, 2);
}
double resolution(UnitCell *cell, signed int h, signed int k, signed int l)
{
const double a = cell->a;
const double b = cell->b;
const double c = cell->c;
const double alpha = cell->alpha;
const double beta = cell->beta;
const double gamma = cell->gamma;
const double Vsq = a*a*b*b*c*c*(1 - cos(alpha)*cos(alpha)
- cos(beta)*cos(beta)
- cos(gamma)*cos(gamma)
+ 2*cos(alpha)*cos(beta)*cos(gamma) );
const double S11 = b*b*c*c*sin(alpha)*sin(alpha);
const double S22 = a*a*c*c*sin(beta)*sin(beta);
const double S33 = a*a*b*b*sin(gamma)*sin(gamma);
const double S12 = a*b*c*c*(cos(alpha)*cos(beta) - cos(gamma));
const double S23 = a*a*b*c*(cos(beta)*cos(gamma) - cos(alpha));
const double S13 = a*b*b*c*(cos(gamma)*cos(alpha) - cos(beta));
const double brackets = S11*h*h + S22*k*k + S33*l*l
+ 2*S12*h*k + 2*S23*k*l + 2*S13*h*l;
const double oneoverdsq = brackets / Vsq;
const double oneoverd = sqrt(oneoverdsq);
return oneoverd / 2;
}
|
