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