[66d119f] | 1 | double form_volume(double core_thick, |
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| 2 | double layer_thick, |
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| 3 | double radius, |
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| 4 | double n_stacking); |
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| 5 | |
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| 6 | double Iq(double q, |
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| 7 | double core_thick, |
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| 8 | double layer_thick, |
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| 9 | double radius, |
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| 10 | double n_stacking, |
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| 11 | double sigma_d, |
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| 12 | double core_sld, |
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| 13 | double layer_sld, |
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| 14 | double solvent_sld); |
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| 15 | |
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| 16 | double Iqxy(double qx, double qy, |
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| 17 | double core_thick, |
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| 18 | double layer_thick, |
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| 19 | double radius, |
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| 20 | double n_stacking, |
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| 21 | double sigma_d, |
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| 22 | double core_sld, |
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| 23 | double layer_sld, |
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| 24 | double solvent_sld, |
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| 25 | double theta, |
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| 26 | double phi); |
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| 27 | |
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| 28 | static |
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| 29 | double _kernel(double qq, |
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| 30 | double radius, |
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| 31 | double core_sld, |
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| 32 | double layer_sld, |
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| 33 | double solvent_sld, |
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| 34 | double halfheight, |
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| 35 | double layer_thick, |
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| 36 | double zi, |
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| 37 | double sigma_d, |
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| 38 | double d, |
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| 39 | double n_stacking) |
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| 40 | |
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| 41 | { |
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| 42 | // qq is the q-value for the calculation (1/A) |
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| 43 | // radius is the core radius of the cylinder (A) |
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| 44 | // *_sld are the respective SLD's |
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| 45 | // halfheight is the *Half* CORE-LENGTH of the cylinder = L (A) |
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| 46 | // zi is the dummy variable for the integration (x in Feigin's notation) |
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| 47 | |
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| 48 | const double besarg1 = qq*radius*sin(zi); |
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| 49 | const double besarg2 = qq*radius*sin(zi); |
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| 50 | |
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| 51 | const double sinarg1 = qq*halfheight*cos(zi); |
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| 52 | const double sinarg2 = qq*(halfheight+layer_thick)*cos(zi); |
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| 53 | |
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| 54 | const double be1 = J1(besarg1)/besarg1; |
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| 55 | const double be2 = J1(besarg2)/besarg2; |
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| 56 | const double si1 = sin(sinarg1)/sinarg1; |
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| 57 | const double si2 = sin(sinarg2)/sinarg2; |
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| 58 | |
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| 59 | const double dr1 = (core_sld-solvent_sld); |
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| 60 | const double dr2 = (layer_sld-solvent_sld); |
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| 61 | const double area = M_PI*radius*radius; |
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| 62 | const double totald=2.0*(layer_thick+halfheight); |
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| 63 | |
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| 64 | const double t1 = 2.0*area*(2.0*halfheight)*dr1*(si1)*(be1); |
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| 65 | const double t2 = 2.0*area*dr2*(totald*si2-2.0*halfheight*si1)*(be2); |
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| 66 | |
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| 67 | |
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| 68 | double retval =((t1+t2)*(t1+t2))*sin(zi); |
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| 69 | |
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| 70 | // loop for the structure facture S(q) |
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| 71 | double sqq=0.0; |
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| 72 | for(int kk=1;kk<n_stacking;kk+=1) { |
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| 73 | double dexpt=qq*cos(zi)*qq*cos(zi)*d*d*sigma_d*sigma_d*kk/2.0; |
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| 74 | sqq=sqq+(n_stacking-kk)*cos(qq*cos(zi)*d*kk)*exp(-1.*dexpt); |
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| 75 | } |
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| 76 | |
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| 77 | // end of loop for S(q) |
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| 78 | sqq=1.0+2.0*sqq/n_stacking; |
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| 79 | |
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| 80 | retval *= sqq; |
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| 81 | |
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| 82 | return(retval); |
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| 83 | } |
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| 84 | |
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| 85 | |
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| 86 | static |
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| 87 | double stacked_disks_kernel(double q, |
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| 88 | double core_thick, |
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| 89 | double layer_thick, |
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| 90 | double radius, |
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| 91 | double n_stacking, |
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| 92 | double sigma_d, |
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| 93 | double core_sld, |
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| 94 | double layer_sld, |
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| 95 | double solvent_sld) |
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| 96 | { |
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| 97 | /* StackedDiscsX : calculates the form factor of a stacked "tactoid" of core shell disks |
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| 98 | like clay platelets that are not exfoliated |
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| 99 | */ |
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| 100 | double summ = 0.0; //initialize integral |
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| 101 | |
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| 102 | double d=2.0*layer_thick+core_thick; |
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| 103 | double halfheight = core_thick/2.0; |
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| 104 | |
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| 105 | for(int i=0;i<N_POINTS_76;i++) { |
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| 106 | double zi = (Gauss76Z[i] + 1.0)*M_PI/4.0; |
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| 107 | double yyy = Gauss76Wt[i] * |
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| 108 | _kernel(q, |
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| 109 | radius, |
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| 110 | core_sld, |
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| 111 | layer_sld, |
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| 112 | solvent_sld, |
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| 113 | halfheight, |
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| 114 | layer_thick, |
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| 115 | zi, |
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| 116 | sigma_d, |
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| 117 | d, |
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| 118 | n_stacking); |
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| 119 | summ += yyy; |
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| 120 | } |
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| 121 | |
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| 122 | double answer = M_PI/4.0*summ; |
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| 123 | |
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| 124 | //Convert to [cm-1] |
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| 125 | answer *= 1.0e-4; |
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| 126 | |
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| 127 | return answer; |
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| 128 | } |
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| 129 | |
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| 130 | static double stacked_disks_kernel_2d(double q, double q_x, double q_y, |
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| 131 | double core_thick, |
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| 132 | double layer_thick, |
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| 133 | double radius, |
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| 134 | double n_stacking, |
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| 135 | double sigma_d, |
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| 136 | double core_sld, |
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| 137 | double layer_sld, |
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| 138 | double solvent_sld, |
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| 139 | double theta, |
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| 140 | double phi) |
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| 141 | { |
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| 142 | |
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| 143 | double ct, st, cp, sp; |
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[d507c3a] | 144 | |
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| 145 | //convert angle degree to radian |
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| 146 | theta = theta * M_PI/180.0; |
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| 147 | phi = phi * M_PI/180.0; |
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| 148 | |
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[66d119f] | 149 | SINCOS(theta, st, ct); |
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| 150 | SINCOS(phi, sp, cp); |
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| 151 | |
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| 152 | // silence compiler warnings about unused variable |
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| 153 | (void) sp; |
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| 154 | |
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| 155 | // parallelepiped orientation |
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| 156 | const double cyl_x = ct * cp; |
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| 157 | const double cyl_y = st; |
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| 158 | |
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| 159 | // Compute the angle btw vector q and the |
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| 160 | // axis of the parallelepiped |
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| 161 | const double cos_val = cyl_x*q_x + cyl_y*q_y; |
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| 162 | |
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| 163 | // Note: cos(alpha) = 0 and 1 will get an |
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| 164 | // undefined value from Stackdisc_kern |
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| 165 | double alpha = acos( cos_val ); |
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| 166 | |
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| 167 | // Call the IGOR library function to get the kernel |
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| 168 | double d = 2 * layer_thick + core_thick; |
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| 169 | double halfheight = core_thick/2.0; |
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| 170 | double answer = _kernel(q, |
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| 171 | radius, |
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| 172 | core_sld, |
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| 173 | layer_sld, |
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| 174 | solvent_sld, |
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| 175 | halfheight, |
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| 176 | layer_thick, |
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| 177 | alpha, |
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| 178 | sigma_d, |
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| 179 | d, |
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| 180 | n_stacking); |
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| 181 | |
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| 182 | answer /= sin(alpha); |
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| 183 | //convert to [cm-1] |
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| 184 | answer *= 1.0e-4; |
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| 185 | |
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| 186 | return answer; |
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| 187 | } |
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| 188 | |
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| 189 | double form_volume(double core_thick, |
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| 190 | double layer_thick, |
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| 191 | double radius, |
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| 192 | double n_stacking){ |
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| 193 | double d = 2 * layer_thick + core_thick; |
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| 194 | return acos(-1.0) * radius * radius * d * n_stacking; |
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| 195 | } |
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| 196 | |
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| 197 | double Iq(double q, |
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| 198 | double core_thick, |
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| 199 | double layer_thick, |
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| 200 | double radius, |
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| 201 | double n_stacking, |
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| 202 | double sigma_d, |
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| 203 | double core_sld, |
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| 204 | double layer_sld, |
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| 205 | double solvent_sld) |
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| 206 | { |
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| 207 | return stacked_disks_kernel(q, |
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| 208 | core_thick, |
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| 209 | layer_thick, |
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| 210 | radius, |
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| 211 | n_stacking, |
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| 212 | sigma_d, |
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| 213 | core_sld, |
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| 214 | layer_sld, |
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| 215 | solvent_sld); |
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| 216 | } |
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| 217 | |
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| 218 | // Iqxy is never called since no orientation or magnetic parameters. |
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| 219 | double Iqxy(double qx, double qy, |
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| 220 | double core_thick, |
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| 221 | double layer_thick, |
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| 222 | double radius, |
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| 223 | double n_stacking, |
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| 224 | double sigma_d, |
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| 225 | double core_sld, |
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| 226 | double layer_sld, |
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| 227 | double solvent_sld, |
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| 228 | double theta, |
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| 229 | double phi) |
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| 230 | { |
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| 231 | double q = sqrt(qx*qx + qy*qy); |
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| 232 | return stacked_disks_kernel_2d(q, qx/q, qy/q, |
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| 233 | core_thick, |
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| 234 | layer_thick, |
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| 235 | radius, |
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| 236 | n_stacking, |
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| 237 | sigma_d, |
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| 238 | core_sld, |
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| 239 | layer_sld, |
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| 240 | solvent_sld, |
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| 241 | theta, |
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| 242 | phi); |
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| 243 | } |
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| 244 | |
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