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/*
* 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"
/* Density of water in kg/m^3 */
#define WATER_DENSITY (1.0e6)
/* Molar mass of water, in kg/mol */
#define WATER_MOLAR_MASS (18.01528e3)
/* Avogadro's number */
#define AVOGADRO (6.022e23)
/* Number of slices to divide water column into, where the
* slices are coplanar with the beam and the cylinder axis */
#define N_WATER_SLICES 100
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;
}
/* Return structure factor for molecule 'mol' at energy 'en' (J/photon) at
* scattering vector 'q' */
static double complex molecule_factor(struct molecule *mol, struct threevec q,
double en)
{
int i;
double complex F = 0.0;
double s;
/* s = sin(theta)/lambda = 1/2d = (1/d)/2.0 */
s = modulus(q.u, q.v, q.w) / 2.0;
/* Atoms are grouped by species for faster calculation */
for ( i=0; i<mol->n_species; i++ ) {
double complex sfac;
double complex contrib = 0.0;
struct mol_species *spec;
int j;
spec = mol->species[i];
for ( j=0; j<spec->n_atoms; j++ ) {
double ph;
ph = q.u*spec->x[j] + q.v*spec->y[j] + q.w*spec->z[j];
/* Conversion from revolutions to radians is required */
contrib += cos(2.0*M_PI*ph) + I*sin(2.0*M_PI*ph);
}
sfac = get_sfac(spec->species, s, en);
F += sfac * contrib * exp(-2.0 * spec->B[j] * s);
}
return F;
}
static double complex water_factor(struct threevec q, double en)
{
double x;
double complex res = 0.0;
int n = 0;
double s;
double molecules_per_m3;
double molecules_per_m;
const double rc = 0.5e-6; /* Radius of cylinder (m) */
const double rb = 1.5e-6; /* Radius of beam (m) */
/* Density of water molecules */
molecules_per_m3 = WATER_DENSITY * (AVOGADRO / WATER_MOLAR_MASS);
/* Number of water molecules per slice per metre of thickness */
molecules_per_m = (2*rb*2*rc) * molecules_per_m3 / N_WATER_SLICES;
/* s = sin(theta)/lambda = 1/2d = (1/d)/2.0 */
s = modulus(q.u, q.v, q.w) / 2.0;
for ( x=-rc; x<=rc; x+=rc/(N_WATER_SLICES/2) ) {
double ph;
double thickness;
/* The thickness of a cylinder in a direction parallel
* to the beam. The cylinder axis is perpendicular to
* the beam */
thickness = 2.0 * sqrt((rc*rc)-(x*x));
ph = q.u*x;
res += thickness * (cos(2.0*M_PI*ph) + I*sin(2.0*M_PI*ph));
n++;
}
res *= (get_sfac("O", s, en) + 2.0*get_sfac("H", s, en))
* molecules_per_m;
/* Correct for sampling of integration */
return (res/(double)n) * (2.0*rc);
}
void get_diffraction(struct image *image, UnitCell *cell)
{
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(cell, &ax, &ay, &az,
&bx, &by, &bz,
&cx, &cy, &cz);
image->sfacs = malloc(image->width * image->height
* sizeof(double complex));
progress_bar(0, image->width-1);
for ( x=0; x<image->width; x++ ) {
for ( y=0; y<image->height; y++ ) {
double f_lattice;
double complex f_molecule;
double complex f_water;
struct threevec q;
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,
image->xray_energy);
/* Nasty approximation follows */
if ( y == image->height/2 ) {
f_water = water_factor(q, image->xray_energy);
} else {
f_water = 0.0;
}
image->sfacs[x + image->width*y] = (f_lattice * f_molecule)
+ f_water;
}
progress_bar(x, image->width-1);
}
}
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