1. Categories
2. Cylinder
3. Stacked Disks
4. stacked_disks.c

Stacked Disks - stacked_disks.c

    static double
stacked_disks_kernel(
    double qab,
    double qc,
    double halfheight,
    double thick_layer,
    double radius,
    int n_stacking,
    double sigma_dnn,
    double core_sld,
    double layer_sld,
    double solvent_sld,
    double d)

{
    // q is the q-value for the calculation (1/A)
    // radius is the core radius of the cylinder (A)
    // *_sld are the respective SLD's
    // halfheight is the *Half* CORE-LENGTH of the cylinder = L (A)
    // zi is the dummy variable for the integration (x in Feigin's notation)

    const double besarg1 = radius*qab;
    //const double besarg2 = radius*qab;

    const double sinarg1 = halfheight*qc;
    const double sinarg2 = (halfheight+thick_layer)*qc;

    const double be1 = sas_2J1x_x(besarg1);
    //const double be2 = sas_2J1x_x(besarg2);
    const double be2 = be1;
    const double si1 = sas_sinx_x(sinarg1);
    const double si2 = sas_sinx_x(sinarg2);

    const double dr1 = core_sld - solvent_sld;
    const double dr2 = layer_sld - solvent_sld;
    const double area = M_PI*radius*radius;
    const double totald = 2.0*(thick_layer + halfheight);

    const double t1 = area * (2.0*halfheight) * dr1 * si1 * be1;
    const double t2 = area * dr2 * (totald*si2 - 2.0*halfheight*si1) * be2;

    double pq = square(t1 + t2);

    // loop for the structure factor S(q)
    double qd_cos_alpha = d*qc;
    //d*cos_alpha is the projection of d onto q (in other words the component
    //of d that is parallel to q.
    double debye_arg = -0.5*square(qd_cos_alpha*sigma_dnn);
    double sq=0.0;
    for (int kk=1; kk<n_stacking; kk++) {
        sq += (n_stacking-kk) * cos(qd_cos_alpha*kk) * exp(debye_arg*kk);
    }
    // end of loop for S(q)
    sq = 1.0 + 2.0*sq/n_stacking;

    return pq * sq * n_stacking;
    // volume normalization should be per disk not per stack but form_volume
    // is per stack so correct here for now.  Could change form_volume but
    // if one ever wants to use P*S we need the ER based on the total volume
}


static double
stacked_disks_1d(
    double q,
    double thick_core,
    double thick_layer,
    double radius,
    int n_stacking,
    double sigma_dnn,
    double core_sld,
    double layer_sld,
    double solvent_sld)
{
/*    StackedDiscsX  :  calculates the form factor of a stacked "tactoid" of core shell disks
like clay platelets that are not exfoliated
*/
    double summ = 0.0;    //initialize integral

    double d = 2.0*thick_layer+thick_core;
    double halfheight = 0.5*thick_core;

    for(int i=0; i<GAUSS_N; i++) {
        double zi = (GAUSS_Z[i] + 1.0)*M_PI_4;
        double sin_alpha, cos_alpha; // slots to hold sincos function output
        SINCOS(zi, sin_alpha, cos_alpha);
        double yyy = stacked_disks_kernel(q*sin_alpha, q*cos_alpha,
                           halfheight,
                           thick_layer,
                           radius,
                           n_stacking,
                           sigma_dnn,
                           core_sld,
                           layer_sld,
                           solvent_sld,
                           d);
        summ += GAUSS_W[i] * yyy * sin_alpha;
    }

    double answer = M_PI_4*summ;

    //Convert to [cm-1]
    return 1.0e-4*answer;
}

static double
form_volume(
    double thick_core,
    double thick_layer,
    double radius,
    double fp_n_stacking)
{
    int n_stacking = (int)(fp_n_stacking + 0.5);
    double d = 2.0 * thick_layer + thick_core;
    return M_PI * radius * radius * d * n_stacking;
}

static double
Iq(
    double q,
    double thick_core,
    double thick_layer,
    double radius,
    double fp_n_stacking,
    double sigma_dnn,
    double core_sld,
    double layer_sld,
    double solvent_sld)
{
    int n_stacking = (int)(fp_n_stacking + 0.5);
    return stacked_disks_1d(q,
                    thick_core,
                    thick_layer,
                    radius,
                    n_stacking,
                    sigma_dnn,
                    core_sld,
                    layer_sld,
                    solvent_sld);
}


static double
Iqac(double qab, double qc,
    double thick_core,
    double thick_layer,
    double radius,
    double fp_n_stacking,
    double sigma_dnn,
    double core_sld,
    double layer_sld,
    double solvent_sld)
{
    int n_stacking = (int)(fp_n_stacking + 0.5);
    double d = 2.0 * thick_layer + thick_core;
    double halfheight = 0.5*thick_core;
    double answer = stacked_disks_kernel(qab, qc,
                     halfheight,
                     thick_layer,
                     radius,
                     n_stacking,
                     sigma_dnn,
                     core_sld,
                     layer_sld,
                     solvent_sld,
                     d);

    //convert to [cm-1]
    answer *= 1.0e-4;

    return answer;
}

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