| 1 | double form_volume(double radius_lg, double radius_sm, double penetration); |
|---|
| 2 | |
|---|
| 3 | double Iq(double q, |
|---|
| 4 | double sld_lg, double sld_sm, double sld_solvent, |
|---|
| 5 | double volfraction_lg, double volfraction_sm, double surf_fraction, |
|---|
| 6 | double radius_lg, double radius_sm, double penetration); |
|---|
| 7 | |
|---|
| 8 | double form_volume(double radius_lg, double radius_sm, double penetration) |
|---|
| 9 | { |
|---|
| 10 | //Because of the complex structure, volume normalization must |
|---|
| 11 | //happen in the Iq code below. Thus the form volume is set to 1.0 here |
|---|
| 12 | double volume=1.0; |
|---|
| 13 | return volume; |
|---|
| 14 | } |
|---|
| 15 | |
|---|
| 16 | static double |
|---|
| 17 | effective_radius(int mode, double radius_lg, double radius_sm, double penetration) |
|---|
| 18 | { |
|---|
| 19 | if (mode == 1) { |
|---|
| 20 | return radius_lg; |
|---|
| 21 | } else { |
|---|
| 22 | return radius_lg + 2.0*radius_sm - penetration; |
|---|
| 23 | } |
|---|
| 24 | } |
|---|
| 25 | |
|---|
| 26 | double Iq(double q, |
|---|
| 27 | double sld_lg, double sld_sm, double sld_solvent, |
|---|
| 28 | double volfraction_lg, double volfraction_sm, double surface_fraction, |
|---|
| 29 | double radius_lg, double radius_sm, double penetration) |
|---|
| 30 | { |
|---|
| 31 | // Ref: J. coll. inter. sci. (2010) vol. 343 (1) pp. 36-41. |
|---|
| 32 | |
|---|
| 33 | |
|---|
| 34 | double vfL, rL, sldL, vfS, rS, sldS, deltaS, delrhoL, delrhoS, sldSolv; |
|---|
| 35 | double VL, VS, Np, f2, fSs; |
|---|
| 36 | double psiL,psiS; |
|---|
| 37 | double sfLS,sfSS; |
|---|
| 38 | double slT; |
|---|
| 39 | |
|---|
| 40 | vfL = volfraction_lg; |
|---|
| 41 | rL = radius_lg; |
|---|
| 42 | sldL = sld_lg; |
|---|
| 43 | vfS = volfraction_sm; |
|---|
| 44 | fSs = surface_fraction; |
|---|
| 45 | rS = radius_sm; |
|---|
| 46 | sldS = sld_sm; |
|---|
| 47 | deltaS = penetration; |
|---|
| 48 | sldSolv = sld_solvent; |
|---|
| 49 | |
|---|
| 50 | delrhoL = fabs(sldL - sldSolv); |
|---|
| 51 | delrhoS = fabs(sldS - sldSolv); |
|---|
| 52 | |
|---|
| 53 | VL = M_4PI_3*rL*rL*rL; |
|---|
| 54 | VS = M_4PI_3*rS*rS*rS; |
|---|
| 55 | |
|---|
| 56 | //Number of small particles per large particle |
|---|
| 57 | Np = vfS*fSs*VL/vfL/VS; |
|---|
| 58 | |
|---|
| 59 | //Total scattering length difference |
|---|
| 60 | slT = delrhoL*VL + Np*delrhoS*VS; |
|---|
| 61 | |
|---|
| 62 | //Form factors for each particle |
|---|
| 63 | psiL = sas_3j1x_x(q*rL); |
|---|
| 64 | psiS = sas_3j1x_x(q*rS); |
|---|
| 65 | |
|---|
| 66 | //Cross term between large and small particles |
|---|
| 67 | sfLS = psiL*psiS*sas_sinx_x(q*(rL+deltaS*rS)); |
|---|
| 68 | //Cross term between small particles at the surface |
|---|
| 69 | sfSS = psiS*psiS*sas_sinx_x(q*(rL+deltaS*rS))*sas_sinx_x(q*(rL+deltaS*rS)); |
|---|
| 70 | |
|---|
| 71 | //Large sphere form factor term |
|---|
| 72 | f2 = delrhoL*delrhoL*VL*VL*psiL*psiL; |
|---|
| 73 | //Small sphere form factor term |
|---|
| 74 | f2 += Np*delrhoS*delrhoS*VS*VS*psiS*psiS; |
|---|
| 75 | //Small particle - small particle cross term |
|---|
| 76 | f2 += Np*(Np-1)*delrhoS*delrhoS*VS*VS*sfSS; |
|---|
| 77 | //Large-small particle cross term |
|---|
| 78 | f2 += 2*Np*delrhoL*delrhoS*VL*VS*sfLS; |
|---|
| 79 | //Normalise by total scattering length difference |
|---|
| 80 | if (f2 != 0.0){ |
|---|
| 81 | f2 = f2/slT/slT; |
|---|
| 82 | } |
|---|
| 83 | |
|---|
| 84 | //I(q) for large-small composite particles |
|---|
| 85 | f2 = f2*(vfL*delrhoL*delrhoL*VL + vfS*fSs*Np*delrhoS*delrhoS*VS); |
|---|
| 86 | //I(q) for free small particles |
|---|
| 87 | f2+= vfS*(1.0-fSs)*delrhoS*delrhoS*VS*psiS*psiS; |
|---|
| 88 | |
|---|
| 89 | // normalize to single particle volume and convert to 1/cm |
|---|
| 90 | f2 *= 1.0e8; // [=] 1/cm |
|---|
| 91 | f2 *= 1.0e-12; // convert for (1/A^-6)^2 to (1/A)^2 |
|---|
| 92 | |
|---|
| 93 | return f2; |
|---|
| 94 | } |
|---|
