[edf1e8b] | 1 | static double stacked_disks_kernel( |
---|
| 2 | double q, |
---|
| 3 | double halfheight, |
---|
| 4 | double thick_layer, |
---|
| 5 | double radius, |
---|
[19f996b] | 6 | int n_stacking, |
---|
[edf1e8b] | 7 | double sigma_dnn, |
---|
| 8 | double core_sld, |
---|
| 9 | double layer_sld, |
---|
| 10 | double solvent_sld, |
---|
| 11 | double sin_alpha, |
---|
| 12 | double cos_alpha, |
---|
| 13 | double d) |
---|
[66d119f] | 14 | |
---|
| 15 | { |
---|
[3ac4e1b] | 16 | // q is the q-value for the calculation (1/A) |
---|
| 17 | // radius is the core radius of the cylinder (A) |
---|
| 18 | // *_sld are the respective SLD's |
---|
| 19 | // halfheight is the *Half* CORE-LENGTH of the cylinder = L (A) |
---|
| 20 | // zi is the dummy variable for the integration (x in Feigin's notation) |
---|
| 21 | |
---|
| 22 | const double besarg1 = q*radius*sin_alpha; |
---|
| 23 | //const double besarg2 = q*radius*sin_alpha; |
---|
| 24 | |
---|
| 25 | const double sinarg1 = q*halfheight*cos_alpha; |
---|
| 26 | const double sinarg2 = q*(halfheight+thick_layer)*cos_alpha; |
---|
| 27 | |
---|
[592343f] | 28 | const double be1 = sas_2J1x_x(besarg1); |
---|
[6c3e266] | 29 | //const double be2 = sas_2J1x_x(besarg2); |
---|
[3ac4e1b] | 30 | const double be2 = be1; |
---|
[1e7b0db0] | 31 | const double si1 = sas_sinx_x(sinarg1); |
---|
| 32 | const double si2 = sas_sinx_x(sinarg2); |
---|
[3ac4e1b] | 33 | |
---|
| 34 | const double dr1 = core_sld - solvent_sld; |
---|
| 35 | const double dr2 = layer_sld - solvent_sld; |
---|
| 36 | const double area = M_PI*radius*radius; |
---|
| 37 | const double totald = 2.0*(thick_layer + halfheight); |
---|
| 38 | |
---|
| 39 | const double t1 = area * (2.0*halfheight) * dr1 * si1 * be1; |
---|
| 40 | const double t2 = area * dr2 * (totald*si2 - 2.0*halfheight*si1) * be2; |
---|
| 41 | |
---|
| 42 | double pq = square(t1 + t2); |
---|
| 43 | |
---|
| 44 | // loop for the structure factor S(q) |
---|
| 45 | double qd_cos_alpha = q*d*cos_alpha; |
---|
[98ce141] | 46 | //d*cos_alpha is the projection of d onto q (in other words the component |
---|
| 47 | //of d that is parallel to q. |
---|
[3ac4e1b] | 48 | double debye_arg = -0.5*square(qd_cos_alpha*sigma_dnn); |
---|
| 49 | double sq=0.0; |
---|
| 50 | for (int kk=1; kk<n_stacking; kk++) { |
---|
| 51 | sq += (n_stacking-kk) * cos(qd_cos_alpha*kk) * exp(debye_arg*kk); |
---|
| 52 | } |
---|
| 53 | // end of loop for S(q) |
---|
| 54 | sq = 1.0 + 2.0*sq/n_stacking; |
---|
| 55 | |
---|
[98ce141] | 56 | return pq * sq * n_stacking; |
---|
| 57 | // volume normalization should be per disk not per stack but form_volume |
---|
| 58 | // is per stack so correct here for now. Could change form_volume but |
---|
| 59 | // if one ever wants to use P*S we need the ER based on the total volume |
---|
[66d119f] | 60 | } |
---|
| 61 | |
---|
| 62 | |
---|
[edf1e8b] | 63 | static double stacked_disks_1d( |
---|
| 64 | double q, |
---|
| 65 | double thick_core, |
---|
| 66 | double thick_layer, |
---|
| 67 | double radius, |
---|
[19f996b] | 68 | int n_stacking, |
---|
[edf1e8b] | 69 | double sigma_dnn, |
---|
| 70 | double core_sld, |
---|
| 71 | double layer_sld, |
---|
| 72 | double solvent_sld) |
---|
[66d119f] | 73 | { |
---|
[3ac4e1b] | 74 | /* StackedDiscsX : calculates the form factor of a stacked "tactoid" of core shell disks |
---|
[66d119f] | 75 | like clay platelets that are not exfoliated |
---|
| 76 | */ |
---|
[3ac4e1b] | 77 | double summ = 0.0; //initialize integral |
---|
| 78 | |
---|
| 79 | double d = 2.0*thick_layer+thick_core; |
---|
| 80 | double halfheight = 0.5*thick_core; |
---|
| 81 | |
---|
| 82 | for(int i=0; i<N_POINTS_76; i++) { |
---|
| 83 | double zi = (Gauss76Z[i] + 1.0)*M_PI_4; |
---|
| 84 | double sin_alpha, cos_alpha; // slots to hold sincos function output |
---|
| 85 | SINCOS(zi, sin_alpha, cos_alpha); |
---|
[edf1e8b] | 86 | double yyy = stacked_disks_kernel(q, |
---|
| 87 | halfheight, |
---|
| 88 | thick_layer, |
---|
[3ac4e1b] | 89 | radius, |
---|
[edf1e8b] | 90 | n_stacking, |
---|
| 91 | sigma_dnn, |
---|
[3ac4e1b] | 92 | core_sld, |
---|
| 93 | layer_sld, |
---|
| 94 | solvent_sld, |
---|
| 95 | sin_alpha, |
---|
| 96 | cos_alpha, |
---|
[edf1e8b] | 97 | d); |
---|
[3ac4e1b] | 98 | summ += Gauss76Wt[i] * yyy * sin_alpha; |
---|
| 99 | } |
---|
| 100 | |
---|
| 101 | double answer = M_PI_4*summ; |
---|
| 102 | |
---|
| 103 | //Convert to [cm-1] |
---|
| 104 | return 1.0e-4*answer; |
---|
[66d119f] | 105 | } |
---|
| 106 | |
---|
[edf1e8b] | 107 | static double form_volume( |
---|
| 108 | double thick_core, |
---|
| 109 | double thick_layer, |
---|
| 110 | double radius, |
---|
| 111 | double fp_n_stacking) |
---|
| 112 | { |
---|
| 113 | int n_stacking = (int)(fp_n_stacking + 0.5); |
---|
[6831fa0] | 114 | double d = 2.0 * thick_layer + thick_core; |
---|
| 115 | return M_PI * radius * radius * d * n_stacking; |
---|
[66d119f] | 116 | } |
---|
| 117 | |
---|
[edf1e8b] | 118 | static double Iq( |
---|
| 119 | double q, |
---|
| 120 | double thick_core, |
---|
| 121 | double thick_layer, |
---|
| 122 | double radius, |
---|
| 123 | double fp_n_stacking, |
---|
| 124 | double sigma_dnn, |
---|
| 125 | double core_sld, |
---|
| 126 | double layer_sld, |
---|
| 127 | double solvent_sld) |
---|
[66d119f] | 128 | { |
---|
[edf1e8b] | 129 | int n_stacking = (int)(fp_n_stacking + 0.5); |
---|
| 130 | return stacked_disks_1d(q, |
---|
[a807206] | 131 | thick_core, |
---|
| 132 | thick_layer, |
---|
[66d119f] | 133 | radius, |
---|
| 134 | n_stacking, |
---|
[a807206] | 135 | sigma_dnn, |
---|
[66d119f] | 136 | core_sld, |
---|
| 137 | layer_sld, |
---|
| 138 | solvent_sld); |
---|
| 139 | } |
---|
[6831fa0] | 140 | |
---|
| 141 | |
---|
[edf1e8b] | 142 | static double Iqxy(double qx, double qy, |
---|
| 143 | double thick_core, |
---|
| 144 | double thick_layer, |
---|
| 145 | double radius, |
---|
| 146 | double fp_n_stacking, |
---|
| 147 | double sigma_dnn, |
---|
| 148 | double core_sld, |
---|
| 149 | double layer_sld, |
---|
| 150 | double solvent_sld, |
---|
| 151 | double theta, |
---|
| 152 | double phi) |
---|
[6831fa0] | 153 | { |
---|
[edf1e8b] | 154 | int n_stacking = (int)(fp_n_stacking + 0.5); |
---|
[6831fa0] | 155 | double q, sin_alpha, cos_alpha; |
---|
| 156 | ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); |
---|
| 157 | |
---|
| 158 | double d = 2.0 * thick_layer + thick_core; |
---|
| 159 | double halfheight = 0.5*thick_core; |
---|
[edf1e8b] | 160 | double answer = stacked_disks_kernel(q, |
---|
| 161 | halfheight, |
---|
| 162 | thick_layer, |
---|
[6831fa0] | 163 | radius, |
---|
[edf1e8b] | 164 | n_stacking, |
---|
| 165 | sigma_dnn, |
---|
[6831fa0] | 166 | core_sld, |
---|
| 167 | layer_sld, |
---|
| 168 | solvent_sld, |
---|
| 169 | sin_alpha, |
---|
| 170 | cos_alpha, |
---|
[edf1e8b] | 171 | d); |
---|
[6831fa0] | 172 | |
---|
| 173 | //convert to [cm-1] |
---|
| 174 | answer *= 1.0e-4; |
---|
| 175 | |
---|
| 176 | return answer; |
---|
| 177 | } |
---|
| 178 | |
---|