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
|
/*
* diffraction.c
*
* Calculate diffraction patterns by Fourier methods
*
* (c) 2007-2009 Thomas White <thomas.white@desy.de>
*
* pattern_sim - Simulate diffraction patterns from small crystals
*
*/
#include <stdlib.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <complex.h>
#include "image.h"
#include "utils.h"
#include "cell.h"
#include "ewald.h"
#include "diffraction.h"
#include "sfac.h"
static double lattice_factor(struct threevec q, double ax, double ay, double az,
double bx, double by, double bz,
double cx, double cy, double cz)
{
struct threevec Udotq;
double f1, f2, f3;
int na = 4;
int nb = 4;
int nc = 30;
Udotq.u = ax*q.u + ay*q.v + az*q.w;
Udotq.v = bx*q.u + by*q.v + bz*q.w;
Udotq.w = cx*q.u + cy*q.v + cz*q.w;
/* At exact Bragg condition, f1 = na */
if ( na > 1 ) {
f1 = sin(M_PI*(double)na*Udotq.u) / sin(M_PI*Udotq.u);
} else {
f1 = 1.0;
}
/* At exact Bragg condition, f2 = nb */
if ( nb > 1 ) {
f2 = sin(M_PI*(double)nb*Udotq.v) / sin(M_PI*Udotq.v);
} else {
f2 = 1.0;
}
/* At exact Bragg condition, f3 = nc */
if ( nc > 1 ) {
f3 = sin(M_PI*(double)nc*Udotq.w) / sin(M_PI*Udotq.w);
} else {
f3 = 1.0;
}
/* At exact Bragg condition, this will multiply the molecular
* part of the structure factor by the number of unit cells,
* as desired (more scattering from bigger crystal!) */
return f1 * f2 * f3;
}
/* Look up the structure factor for the nearest Bragg condition */
static double complex molecule_factor(struct molecule *mol, struct threevec q,
double ax, double ay, double az,
double bx, double by, double bz,
double cx, double cy, double cz)
{
double hd, kd, ld;
signed int h, k, l;
double complex r;
hd = q.u * ax + q.v * ay + q.w * az;
kd = q.u * bx + q.v * by + q.w * bz;
ld = q.u * cx + q.v * cy + q.w * cz;
h = (signed int)rint(hd);
k = (signed int)rint(kd);
l = (signed int)rint(ld);
r = lookup_sfac(mol->reflections, h, k, l);
return r;
}
double water_intensity(struct threevec q, double en,
double beam_r, double water_r)
{
double complex fH, fO;
double s, modq;
double width;
double complex ifac;
/* Interatomic distances in water molecule */
const double rOH = 0.09584e-9;
const double rHH = 0.1515e-9;
/* Volume of water column, approximated as:
* (2water_r) * (2beam_r) * smallest(2beam_r, 2water_r)
* neglecting the curvature of the faces of the volume */
if ( beam_r > water_r ) {
width = 2.0 * water_r;
} else {
width = 2.0 * beam_r;
}
const double water_v = 2.0*beam_r * 2.0*water_r * width;
/* Number of water molecules */
const double n_water = water_v * WATER_DENSITY
* (AVOGADRO / WATER_MOLAR_MASS);
/* s = sin(theta)/lambda = 1/2d = |q|/2 */
modq = modulus(q.u, q.v, q.w);
s = modq / 2.0;
fH = get_sfac("H", s, en);
fO = get_sfac("O", s, en);
/* Four O-H cross terms */
ifac = 4.0*fH*fO * sin(2.0*M_PI*modq*rOH)/(2.0*M_PI*modq*rOH);
/* Three H-H cross terms */
ifac += 3.0*fH*fH * sin(2.0*M_PI*modq*rHH)/(2.0*M_PI*modq*rHH);
/* Three diagonal terms */
ifac += 2.0*fH*fH + fO*fO;
return cabs(ifac) * n_water;
}
void get_diffraction(struct image *image)
{
int x, y;
double ax, ay, az;
double bx, by, bz;
double cx, cy, cz;
/* Generate the array of reciprocal space vectors in image->qvecs */
get_ewald(image);
if ( image->molecule == NULL ) {
image->molecule = load_molecule();
if ( image->molecule == NULL ) return;
}
cell_get_cartesian(image->molecule->cell, &ax, &ay, &az,
&bx, &by, &bz,
&cx, &cy, &cz);
image->sfacs = malloc(image->width * image->height
* sizeof(double complex));
if ( image->molecule->reflections == NULL ) {
get_reflections_cached(image->molecule, image->xray_energy);
}
for ( x=0; x<image->width; x++ ) {
for ( y=0; y<image->height; y++ ) {
double f_lattice;
double complex f_molecule;
struct threevec q;
double complex val;
q = image->qvecs[x + image->width*y];
f_lattice = lattice_factor(q, ax,ay,az,bx,by,bz,cx,cy,cz);
f_molecule = molecule_factor(image->molecule, q,
ax,ay,az,bx,by,bz,cx,cy,cz);
val = f_molecule * f_lattice;
image->sfacs[x + image->width*y] = val;
}
progress_bar(x, image->width-1, "Calculating lattice factors");
}
}
|
