1 | /* Lamellar_ParaCrystal - Pedersen's model |
---|
2 | |
---|
3 | */ |
---|
4 | double Iq(double qval, |
---|
5 | double th, |
---|
6 | double Nlayers, |
---|
7 | double davg, |
---|
8 | double pd, |
---|
9 | double sld, |
---|
10 | double solvent_sld); |
---|
11 | double paraCryst_sn(double ww, double qval, double davg, long Nlayers, double an); |
---|
12 | double paraCryst_an(double ww, double qval, double davg, long Nlayers); |
---|
13 | |
---|
14 | double Iq(double qval, |
---|
15 | double th, |
---|
16 | double Nlayers, |
---|
17 | double davg, |
---|
18 | double pd, |
---|
19 | double sld, |
---|
20 | double solvent_sld) |
---|
21 | { |
---|
22 | |
---|
23 | double inten,contr,xn; |
---|
24 | double xi,ww,Pbil,Znq,Snq,an; |
---|
25 | long n1,n2; |
---|
26 | |
---|
27 | contr = sld - solvent_sld; |
---|
28 | //get the fractional part of Nlayers, to determine the "mixing" of N's |
---|
29 | |
---|
30 | n1 = (long)trunc(Nlayers); //rounds towards zero |
---|
31 | n2 = n1 + 1; |
---|
32 | xn = (double)n2 - Nlayers; //fractional contribution of n1 |
---|
33 | |
---|
34 | ww = exp(-qval*qval*pd*pd*davg*davg/2.0); |
---|
35 | |
---|
36 | //calculate the n1 contribution |
---|
37 | an = paraCryst_an(ww,qval,davg,n1); |
---|
38 | Snq = paraCryst_sn(ww,qval,davg,n1,an); |
---|
39 | |
---|
40 | Znq = xn*Snq; |
---|
41 | |
---|
42 | //calculate the n2 contribution |
---|
43 | an = paraCryst_an(ww,qval,davg,n2); |
---|
44 | Snq = paraCryst_sn(ww,qval,davg,n2,an); |
---|
45 | |
---|
46 | Znq += (1.0-xn)*Snq; |
---|
47 | |
---|
48 | //and the independent contribution |
---|
49 | Znq += (1.0-ww*ww)/(1.0+ww*ww-2.0*ww*cos(qval*davg)); |
---|
50 | |
---|
51 | //the limit when Nlayers approaches infinity |
---|
52 | // Zq = (1-ww^2)/(1+ww^2-2*ww*cos(qval*davg)) |
---|
53 | |
---|
54 | xi = th/2.0; //use 1/2 the bilayer thickness |
---|
55 | Pbil = (sin(qval*xi)/(qval*xi))*(sin(qval*xi)/(qval*xi)); |
---|
56 | |
---|
57 | inten = 2.0*M_PI*contr*contr*Pbil*Znq/(qval*qval); |
---|
58 | inten *= 1.0e-04; |
---|
59 | //printf("q=%.7e wwm1=%g ww=%.5e an=% 12.5e Snq=% 12.5e Znq=% 12.5e Pbil=% 12.5e\n",qval,wwm1,ww,an,Snq,Znq,Pbil); |
---|
60 | return(inten); |
---|
61 | } |
---|
62 | |
---|
63 | // functions for the lamellar paracrystal model |
---|
64 | double |
---|
65 | paraCryst_sn(double ww, double qval, double davg, long Nlayers, double an) { |
---|
66 | |
---|
67 | double Snq; |
---|
68 | |
---|
69 | Snq = an/( (double)Nlayers*pow((1.0+ww*ww-2.0*ww*cos(qval*davg)),2) ); |
---|
70 | |
---|
71 | return(Snq); |
---|
72 | } |
---|
73 | |
---|
74 | double |
---|
75 | paraCryst_an(double ww, double qval, double davg, long Nlayers) { |
---|
76 | |
---|
77 | double an; |
---|
78 | |
---|
79 | an = 4.0*ww*ww - 2.0*(ww*ww*ww+ww)*cos(qval*davg); |
---|
80 | an -= 4.0*pow(ww,(Nlayers+2))*cos((double)Nlayers*qval*davg); |
---|
81 | an += 2.0*pow(ww,(Nlayers+3))*cos((double)(Nlayers-1)*qval*davg); |
---|
82 | an += 2.0*pow(ww,(Nlayers+1))*cos((double)(Nlayers+1)*qval*davg); |
---|
83 | |
---|
84 | return(an); |
---|
85 | } |
---|
86 | |
---|