| 1 | double form_volume(double radius_lg, double radius_sm, double penetration); |
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| 2 | |
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| 3 | double Iq(double q, |
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| 4 | double sld_lg, double sld_sm, double sld_solvent, |
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| 5 | double volfraction_lg, double volfraction_sm, double surf_fraction, |
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| 6 | double radius_lg, double radius_sm, double penetration); |
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| 7 | |
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| 8 | double form_volume(double radius_lg, double radius_sm, double penetration) |
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| 9 | { |
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| 10 | //Because of the complex structure, volume normalization must |
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| 11 | //happen in the Iq code below. Thus the form volume is set to 1.0 here |
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| 12 | double volume=1.0; |
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| 13 | return volume; |
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| 14 | } |
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| 15 | |
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| 16 | static double |
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| 17 | effective_radius(int mode, double radius_lg, double radius_sm, double penetration) |
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| 18 | { |
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| 19 | switch (mode) { |
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| 20 | case 1: // radius_large |
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| 21 | return radius_lg; |
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| 22 | case 2: // radius_outer |
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| 23 | return radius_lg + 2.0*radius_sm - penetration; |
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| 24 | } |
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| 25 | } |
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| 26 | |
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| 27 | double Iq(double q, |
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| 28 | double sld_lg, double sld_sm, double sld_solvent, |
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| 29 | double volfraction_lg, double volfraction_sm, double surface_fraction, |
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| 30 | double radius_lg, double radius_sm, double penetration) |
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| 31 | { |
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| 32 | // Ref: J. coll. inter. sci. (2010) vol. 343 (1) pp. 36-41. |
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| 33 | |
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| 34 | |
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| 35 | double vfL, rL, sldL, vfS, rS, sldS, deltaS, delrhoL, delrhoS, sldSolv; |
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| 36 | double VL, VS, Np, f2, fSs; |
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| 37 | double psiL,psiS; |
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| 38 | double sfLS,sfSS; |
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| 39 | double slT; |
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| 40 | |
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| 41 | vfL = volfraction_lg; |
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| 42 | rL = radius_lg; |
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| 43 | sldL = sld_lg; |
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| 44 | vfS = volfraction_sm; |
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| 45 | fSs = surface_fraction; |
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| 46 | rS = radius_sm; |
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| 47 | sldS = sld_sm; |
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| 48 | deltaS = penetration; |
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| 49 | sldSolv = sld_solvent; |
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| 50 | |
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| 51 | delrhoL = fabs(sldL - sldSolv); |
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| 52 | delrhoS = fabs(sldS - sldSolv); |
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| 53 | |
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| 54 | VL = M_4PI_3*rL*rL*rL; |
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| 55 | VS = M_4PI_3*rS*rS*rS; |
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| 56 | |
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| 57 | //Number of small particles per large particle |
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| 58 | Np = vfS*fSs*VL/vfL/VS; |
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| 59 | |
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| 60 | //Total scattering length difference |
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| 61 | slT = delrhoL*VL + Np*delrhoS*VS; |
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| 62 | |
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| 63 | //Form factors for each particle |
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| 64 | psiL = sas_3j1x_x(q*rL); |
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| 65 | psiS = sas_3j1x_x(q*rS); |
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| 66 | |
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| 67 | //Cross term between large and small particles |
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| 68 | sfLS = psiL*psiS*sas_sinx_x(q*(rL+deltaS*rS)); |
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| 69 | //Cross term between small particles at the surface |
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| 70 | sfSS = psiS*psiS*sas_sinx_x(q*(rL+deltaS*rS))*sas_sinx_x(q*(rL+deltaS*rS)); |
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| 71 | |
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| 72 | //Large sphere form factor term |
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| 73 | f2 = delrhoL*delrhoL*VL*VL*psiL*psiL; |
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| 74 | //Small sphere form factor term |
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| 75 | f2 += Np*delrhoS*delrhoS*VS*VS*psiS*psiS; |
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| 76 | //Small particle - small particle cross term |
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| 77 | f2 += Np*(Np-1)*delrhoS*delrhoS*VS*VS*sfSS; |
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| 78 | //Large-small particle cross term |
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| 79 | f2 += 2*Np*delrhoL*delrhoS*VL*VS*sfLS; |
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| 80 | //Normalise by total scattering length difference |
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| 81 | if (f2 != 0.0){ |
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| 82 | f2 = f2/slT/slT; |
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| 83 | } |
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| 84 | |
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| 85 | //I(q) for large-small composite particles |
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| 86 | f2 = f2*(vfL*delrhoL*delrhoL*VL + vfS*fSs*Np*delrhoS*delrhoS*VS); |
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| 87 | //I(q) for free small particles |
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| 88 | f2+= vfS*(1.0-fSs)*delrhoS*delrhoS*VS*psiS*psiS; |
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| 89 | |
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| 90 | // normalize to single particle volume and convert to 1/cm |
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| 91 | f2 *= 1.0e8; // [=] 1/cm |
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| 92 | f2 *= 1.0e-12; // convert for (1/A^-6)^2 to (1/A)^2 |
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| 93 | |
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| 94 | return f2; |
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| 95 | } |
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