1 | #correlation length model |
---|
2 | # Note: model title and parameter table are inserted automatically |
---|
3 | r""" |
---|
4 | Definition |
---|
5 | ---------- |
---|
6 | |
---|
7 | The scattering intensity I(q) is calculated as |
---|
8 | |
---|
9 | .. math:: |
---|
10 | I(Q) = \frac{A}{Q^n} + \frac{C}{1 + (Q\xi)^m} + B |
---|
11 | |
---|
12 | The first term describes Porod scattering from clusters (exponent = n) and the |
---|
13 | second term is a Lorentzian function describing scattering from polymer chains |
---|
14 | (exponent = m). This second term characterizes the polymer/solvent interactions |
---|
15 | and therefore the thermodynamics. The two multiplicative factors A and C, the |
---|
16 | incoherent background B and the two exponents n and m are used as fitting |
---|
17 | parameters. The final parameter ξ is a correlation length for the polymer |
---|
18 | chains. Note that when m=2 this functional form becomes the familiar Lorentzian |
---|
19 | function. |
---|
20 | |
---|
21 | For 2D data: The 2D scattering intensity is calculated in the same way as 1D, |
---|
22 | where the q vector is defined as |
---|
23 | |
---|
24 | .. math:: |
---|
25 | q = \sqrt{q_x^2 + q_y^2} |
---|
26 | |
---|
27 | .. figure:: img/correlation_length_1d.jpg |
---|
28 | |
---|
29 | 1D plot using the default values (w/500 data points). |
---|
30 | |
---|
31 | REFERENCE |
---|
32 | B Hammouda, D L Ho and S R Kline, Insight into Clustering in |
---|
33 | Poly(ethylene oxide) Solutions, Macromolecules, 37 (2004) 6932-6937 |
---|
34 | """ |
---|
35 | |
---|
36 | from numpy import inf, sqrt |
---|
37 | |
---|
38 | name = "correlation_length" |
---|
39 | title = """Calculates an empirical functional form for SAS data characterized |
---|
40 | by a low-Q signal and a high-Q signal.""" |
---|
41 | description = """ |
---|
42 | """ |
---|
43 | category = "shape-independent" |
---|
44 | # pylint: disable=bad-continuation, line-too-long |
---|
45 | # ["name", "units", default, [lower, upper], "type","description"], |
---|
46 | parameters = [ |
---|
47 | ["lorentz_scale", "", 10.0, [0, inf], "", "Lorentzian Scaling Factor"], |
---|
48 | ["porod_scale", "", 1e-06, [0, inf], "", "Porod Scaling Factor"], |
---|
49 | ["cor_length", "Ang", 50.0, [0, inf], "", "Correlation length"], |
---|
50 | ["exponent_p", "", 3.0, [0, inf], "", "Porod Exponent"], |
---|
51 | ["exponent_l", "1/Ang^2", 2.0, [0, inf], "", "Lorentzian Exponent"], |
---|
52 | ] |
---|
53 | # pylint: enable=bad-continuation, line-too-long |
---|
54 | |
---|
55 | def Iq(q, lorentz_scale, porod_scale, cor_length, exponent_p, exponent_l): |
---|
56 | """ |
---|
57 | 1D calculation of the Correlation length model |
---|
58 | """ |
---|
59 | porod = porod_scale / pow(q, exponent_p) |
---|
60 | lorentz = lorentz_scale / (1.0 + pow(q * cor_length, exponent_l)) |
---|
61 | inten = porod + lorentz |
---|
62 | return inten |
---|
63 | |
---|
64 | def Iqxy(qx, qy, lorentz_scale, porod_scale, cor_length, exponent_p, exponent_l): |
---|
65 | """ |
---|
66 | 2D calculation of the Correlation length model |
---|
67 | There is no orientation contribution. |
---|
68 | """ |
---|
69 | q = sqrt(qx ** 2 + qy ** 2) |
---|
70 | return Iq(q, lorentz_scale, porod_scale, cor_length, exponent_p, exponent_l) |
---|
71 | |
---|
72 | # parameters for demo |
---|
73 | demo = dict(lorentz_scale=10.0, porod_scale=1.0e-06, cor_length=50.0, |
---|
74 | exponent_p=3.0, exponent_l=2.0, background=0.1, |
---|
75 | ) |
---|
76 | |
---|
77 | # For testing against the old sasview models, include the converted parameter |
---|
78 | # names and the target sasview model name. |
---|
79 | oldname = 'CorrLengthModel' |
---|
80 | |
---|
81 | oldpars = dict(lorentz_scale='scale_l', porod_scale='scale_p', |
---|
82 | cor_length='length_l', exponent_p='exponent_p', |
---|
83 | exponent_l='exponent_l') |
---|
84 | |
---|
85 | tests = [[{}, 0.001, 1009.98], |
---|
86 | [{}, 0.150141, 0.174645], |
---|
87 | [{}, 0.442528, 0.0203957]] |
---|