1 | r""" |
---|
2 | Definition |
---|
3 | ---------- |
---|
4 | |
---|
5 | This model fits the Guinier function |
---|
6 | |
---|
7 | .. math:: |
---|
8 | |
---|
9 | I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2R_g^2}{3} \right]} |
---|
10 | + \text{background} |
---|
11 | |
---|
12 | to the data directly without any need for linearisation (*cf*. the usual |
---|
13 | plot of $\ln I(q)$ vs $q^2$\ ). Note that you may have to restrict the data |
---|
14 | range to include small q only, where the Guinier approximation actually |
---|
15 | applies. See also the guinier_porod model. |
---|
16 | |
---|
17 | For 2D data the scattering intensity is calculated in the same way as 1D, |
---|
18 | where the $q$ vector is defined as |
---|
19 | |
---|
20 | .. math:: q = \sqrt{q_x^2 + q_y^2} |
---|
21 | |
---|
22 | References |
---|
23 | ---------- |
---|
24 | |
---|
25 | A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*, |
---|
26 | John Wiley & Sons, New York (1955) |
---|
27 | """ |
---|
28 | |
---|
29 | from numpy import inf |
---|
30 | |
---|
31 | name = "guinier" |
---|
32 | title = "" |
---|
33 | description = """ |
---|
34 | I(q) = scale.exp ( - rg^2 q^2 / 3.0 ) |
---|
35 | |
---|
36 | List of default parameters: |
---|
37 | scale = scale |
---|
38 | rg = Radius of gyration |
---|
39 | """ |
---|
40 | category = "shape-independent" |
---|
41 | |
---|
42 | # ["name", "units", default, [lower, upper], "type","description"], |
---|
43 | parameters = [["rg", "Ang", 60.0, [0, inf], "", "Radius of Gyration"]] |
---|
44 | |
---|
45 | Iq = """ |
---|
46 | double exponent = rg*rg*q*q/3.0; |
---|
47 | double value = exp(-exponent); |
---|
48 | return value; |
---|
49 | """ |
---|
50 | |
---|
51 | # parameters for demo |
---|
52 | demo = dict(scale=1.0, rg=60.0) |
---|
53 | |
---|
54 | # parameters for unit tests |
---|
55 | tests = [[{'rg' : 31.5}, 0.005, 0.992756]] |
---|