1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
|
double form_volume(double radius_lg, double radius_sm, double penetration);
double Iq(double q,
double sld_lg, double sld_sm, double sld_solvent,
double volfraction_lg, double volfraction_sm, double surf_fraction,
double radius_lg, double radius_sm, double penetration);
double form_volume(double radius_lg, double radius_sm, double penetration)
{
//Because of the complex structure, volume normalization must
//happen in the Iq code below. Thus the form volume is set to 1.0 here
double volume=1.0;
return volume;
}
static double
radius_effective(int mode, double radius_lg, double radius_sm, double penetration)
{
switch (mode) {
default:
case 1: // radius_large
return radius_lg;
case 2: // radius_outer
return radius_lg + 2.0*radius_sm - penetration;
}
}
double Iq(double q,
double sld_lg, double sld_sm, double sld_solvent,
double volfraction_lg, double volfraction_sm, double surface_fraction,
double radius_lg, double radius_sm, double penetration)
{
// Ref: J. coll. inter. sci. (2010) vol. 343 (1) pp. 36-41.
double vfL, rL, sldL, vfS, rS, sldS, deltaS, delrhoL, delrhoS, sldSolv;
double VL, VS, Np, f2, fSs;
double psiL,psiS;
double sfLS,sfSS;
double slT;
vfL = volfraction_lg;
rL = radius_lg;
sldL = sld_lg;
vfS = volfraction_sm;
fSs = surface_fraction;
rS = radius_sm;
sldS = sld_sm;
deltaS = penetration;
sldSolv = sld_solvent;
delrhoL = fabs(sldL - sldSolv);
delrhoS = fabs(sldS - sldSolv);
VL = M_4PI_3*rL*rL*rL;
VS = M_4PI_3*rS*rS*rS;
//Number of small particles per large particle
Np = vfS*fSs*VL/vfL/VS;
//Total scattering length difference
slT = delrhoL*VL + Np*delrhoS*VS;
//Form factors for each particle
psiL = sas_3j1x_x(q*rL);
psiS = sas_3j1x_x(q*rS);
//Cross term between large and small particles
sfLS = psiL*psiS*sas_sinx_x(q*(rL+deltaS*rS));
//Cross term between small particles at the surface
sfSS = psiS*psiS*sas_sinx_x(q*(rL+deltaS*rS))*sas_sinx_x(q*(rL+deltaS*rS));
//Large sphere form factor term
f2 = delrhoL*delrhoL*VL*VL*psiL*psiL;
//Small sphere form factor term
f2 += Np*delrhoS*delrhoS*VS*VS*psiS*psiS;
//Small particle - small particle cross term
f2 += Np*(Np-1)*delrhoS*delrhoS*VS*VS*sfSS;
//Large-small particle cross term
f2 += 2*Np*delrhoL*delrhoS*VL*VS*sfLS;
//Normalise by total scattering length difference
if (f2 != 0.0){
f2 = f2/slT/slT;
}
//I(q) for large-small composite particles
f2 = f2*(vfL*delrhoL*delrhoL*VL + vfS*fSs*Np*delrhoS*delrhoS*VS);
//I(q) for free small particles
f2+= vfS*(1.0-fSs)*delrhoS*delrhoS*VS*psiS*psiS;
// normalize to single particle volume and convert to 1/cm
f2 *= 1.0e8; // [=] 1/cm
f2 *= 1.0e-12; // convert for (1/A^-6)^2 to (1/A)^2
return f2;
}
|
