source: sasmodels/sasmodels/models/bcc.c @ 754c454

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Last change on this file since 754c454 was 754c454, checked in by ajj, 9 years ago

Adding BCC paracrystal model

  • Property mode set to 100644
File size: 5.6 KB
Line 
1double form_volume(double radius);
2double Iq(double q,double dnn,double d_factor, double radius,double sld, double solvent_sld);
3double Iqxy(double qx, double qy, double dnn,
4    double d_factor, double radius,double sld, double solvent_sld,
5    double theta, double phi, double psi);
6
7double _BCC_Integrand(double q, double dnn, double d_factor, double theta, double phi);
8double _BCCeval(double Theta, double Phi, double temp1, double temp3);
9double _sphereform(double q, double radius, double sld, double solvent_sld);
10
11
12double _BCC_Integrand(double q, double dnn, double d_factor, double theta, double phi) {
13
14        const double Da = d_factor*dnn;
15        const double temp1 = q*q*Da*Da;
16        const double temp3 = q*dnn;
17
18        double retVal = _BCCeval(theta,phi,temp1,temp3)/(4.0*M_PI);
19        return(retVal);
20}
21
22double _BCCeval(double Theta, double Phi, double temp1, double temp3) {
23
24        double temp6,temp7,temp8,temp9,temp10;
25        double result;
26
27        temp6 = sin(Theta);
28        temp7 = sin(Theta)*cos(Phi)+sin(Theta)*sin(Phi)+cos(Theta);
29        temp8 = -1.0*sin(Theta)*cos(Phi)-sin(Theta)*sin(Phi)+cos(Theta);
30        temp9 = -1.0*sin(Theta)*cos(Phi)+sin(Theta)*sin(Phi)-cos(Theta);
31        temp10 = exp((-1.0/8.0)*temp1*((temp7*temp7)+(temp8*temp8)+(temp9*temp9)));
32        result = pow(1.0-(temp10*temp10),3)*temp6/((1.0-2.0*temp10*cos(0.5*temp3*(temp7))+(temp10*temp10))*(1.0-2.0*temp10*cos(0.5*temp3*(temp8))+(temp10*temp10))*(1.0-2.0*temp10*cos(0.5*temp3*(temp9))+(temp10*temp10)));
33
34        return (result);
35}
36
37double _sphereform(double q, double radius, double sld, double solvent_sld){
38    const double qr = q*radius;
39    double sn, cn;
40    SINCOS(qr, sn, cn);
41    const double bes = qr==0.0 ? 1.0 : 3.0*(sn-qr*cn)/(qr*qr*qr);
42    const double fq = bes * (sld - solvent_sld)*form_volume(radius);
43    return 1.0e-4*fq*fq;
44}
45
46double form_volume(double radius){
47    return 1.333333333333333*M_PI*radius*radius*radius;
48}
49
50
51double Iq(double q, double dnn,
52  double d_factor, double radius,
53  double sld, double solvent_sld){
54
55        //Volume fraction calculated from lattice symmetry and sphere radius
56        const double s1 = dnn/sqrt(0.75);
57        const double latticescale = 2.0*(4.0/3.0)*M_PI*(radius*radius*radius)/(s1*s1*s1);
58
59    const double va = 0.0;
60    const double vb = 2.0*M_PI;
61    const double vaj = 0.0;
62    const double vbj = M_PI;
63
64    double summ = 0.0;
65    double answer = 0.0;
66        for(int i=0; i<150; i++) {
67                //setup inner integral over the ellipsoidal cross-section
68                double summj=0.0;
69                const double zi = ( Gauss150Z[i]*(vb-va) + va + vb )/2.0;               //the outer dummy is phi
70                for(int j=0;j<150;j++) {
71                        //20 gauss points for the inner integral
72                        double zij = ( Gauss150Z[j]*(vbj-vaj) + vaj + vbj )/2.0;                //the inner dummy is theta
73                        double yyy = Gauss150Wt[j] * _BCC_Integrand(q,dnn,d_factor,zi,zij);
74                        summj += yyy;
75                }
76                //now calculate the value of the inner integral
77                double answer = (vbj-vaj)/2.0*summj;
78
79                //now calculate outer integral
80                summ = summ+(Gauss150Wt[i] * answer);
81        }               //final scaling is done at the end of the function, after the NT_FP64 case
82
83        answer = (vb-va)/2.0*summ;
84        answer = answer*_sphereform(q,radius,sld,solvent_sld)*latticescale;
85
86    return answer;
87
88
89}
90
91
92double Iqxy(double qx, double qy, double dnn,
93    double d_factor, double radius,double sld, double solvent_sld,
94    double theta, double phi, double psi){
95
96  double b3_x, b3_y, b1_x, b1_y, b2_x, b2_y; //b3_z,
97  double q_z;
98  double cos_val_b3, cos_val_b2, cos_val_b1;
99  double a1_dot_q, a2_dot_q,a3_dot_q;
100  double answer;
101  double Zq, Fkq, Fkq_2;
102
103  //convert to q and make scaled values
104  double q = sqrt(qx*qx+qy*qy);
105  double q_x = qx/q;
106  double q_y = qy/q;
107
108  //convert angle degree to radian
109  theta = theta * M_PI_180;
110  phi = phi * M_PI_180;
111  psi = psi * M_PI_180;
112
113  const double Da = d_factor*dnn;
114  const double qDa_2 = q*q*Da*Da;
115  const double s1 = dnn/sqrt(0.75);
116
117
118  //the occupied volume of the lattice
119  const double latticescale = 2.0*(4.0/3.0)*M_PI*(radius*radius*radius)/(s1*s1*s1);
120  // q vector
121  q_z = 0.0; // for SANS; assuming qz is negligible
122  /// Angles here are respect to detector coordinate
123  ///  instead of against q coordinate(PRB 36(46), 3(6), 1754(3854))
124    // b3 axis orientation
125    b3_x = cos(theta) * cos(phi);
126    b3_y = sin(theta);
127    //b3_z = -cos(theta) * sin(phi);
128    cos_val_b3 =  b3_x*q_x + b3_y*q_y;// + b3_z*q_z;
129
130    //alpha = acos(cos_val_b3);
131    // b1 axis orientation
132    b1_x = -cos(phi)*sin(psi) * sin(theta)+sin(phi)*cos(psi);
133    b1_y = sin(psi)*cos(theta);
134    cos_val_b1 = b1_x*q_x + b1_y*q_y;
135    // b2 axis orientation
136    b2_x = -sin(theta)*cos(psi)*cos(phi)-sin(psi)*sin(phi);
137        b2_y = cos(theta)*cos(psi);
138    cos_val_b2 = b2_x*q_x + b2_y*q_y;
139
140    // The following test should always pass
141    if (fabs(cos_val_b3)>1.0) {
142      //printf("bcc_ana_2D: Unexpected error: cos()>1\n");
143      cos_val_b3 = 1.0;
144    }
145    if (fabs(cos_val_b2)>1.0) {
146      //printf("bcc_ana_2D: Unexpected error: cos()>1\n");
147      cos_val_b2 = 1.0;
148    }
149    if (fabs(cos_val_b1)>1.0) {
150      //printf("bcc_ana_2D: Unexpected error: cos()>1\n");
151      cos_val_b1 = 1.0;
152    }
153    // Compute the angle btw vector q and the a3 axis
154    a3_dot_q = 0.5*dnn*q*(cos_val_b2+cos_val_b1-cos_val_b3);
155
156    // a1 axis
157    a1_dot_q = 0.5*dnn*q*(cos_val_b3+cos_val_b2-cos_val_b1);
158
159    // a2 axis
160    a2_dot_q = 0.5*dnn*q*(cos_val_b3+cos_val_b1-cos_val_b2);
161
162
163    // Get Fkq and Fkq_2
164    Fkq = exp(-0.5*pow(Da/dnn,2.0)*(a1_dot_q*a1_dot_q+a2_dot_q*a2_dot_q+a3_dot_q*a3_dot_q));
165    Fkq_2 = Fkq*Fkq;
166    // Call Zq=Z1*Z2*Z3
167    Zq = (1.0-Fkq_2)/(1.0-2.0*Fkq*cos(a1_dot_q)+Fkq_2);
168    Zq *= (1.0-Fkq_2)/(1.0-2.0*Fkq*cos(a2_dot_q)+Fkq_2);
169    Zq *= (1.0-Fkq_2)/(1.0-2.0*Fkq*cos(a3_dot_q)+Fkq_2);
170
171  // Use SphereForm directly from libigor
172  answer = _sphereform(q,radius,sld,solvent_sld)*Zq*latticescale;
173
174  return answer;
175 }
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