core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 925ad6e was 925ad6e, checked in by wojciech, 4 years ago

sph_j1c translated to sas_3j1x_x

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Line
1r"""
2Definition
3----------
4This model calculates the scattering from fractal-like aggregates of spherical
5building blocks according the following equation:
6
7.. math::
8
9    I(q) = \phi\ V_\text{block} (\rho_\text{block}
10          - \rho_\text{solvent})^2 P(q)S(q) + \text{background}
11
12where $\phi$ is The volume fraction of the spherical "building block" particles
13of radius $R_0$, $V_{block}$ is the volume of a single building block,
14$\rho_{solvent}$ is the scattering length density of the solvent, and
15$\rho_{block}$ is the scattering length density of the building blocks, and
16P(q), S(q) are the scattering from randomly distributed spherical particles
17(the building blocks) and the interference from such building blocks organized
18in a fractal-like clusters.  P(q) and S(q) are calculated as:
19
20.. math::
21
22    P(q)&= F(qR_0)^2
23
24    F(q)&= \frac{3 (\sin x - x \cos x)}{x^3}
25
26    V_\text{particle} &= \frac{4}{3}\ \pi R_0
27
28    S(q) &= 1 + \frac{D_f\  \Gamma\!(D_f-1)}{[1+1/(q \xi)^2\  ]^{(D_f -1)/2}}
29    \frac{\sin[(D_f-1) \tan^{-1}(q \xi) ]}{(q R_0)^{D_f}}
30
31where $\xi$ is the correlation length representing the cluster size and $D_f$
32is the fractal dimension, representing the self similarity of the structure.
33Note that S(q) here goes negative if $D_f$ is too large, and the Gamma function
34diverges at $D_f$=0 and $D_f$=1.
35
36**Polydispersity on the radius is provided for.**
37
38For 2D data: The 2D scattering intensity is calculated in the same way as
391D, where the *q* vector is defined as
40
41.. math::
42
43    q = \sqrt{q_x^2 + q_y^2}
44
45
46References
47----------
48
49J Teixeira, *J. Appl. Cryst.*, 21 (1988) 781-785
50
51**Author:** NIST IGOR/DANSE **on:** pre 2010
52
54
55**Last Reviewed by:** Paul Butler **on:** March 20, 2016
56
57"""
58
59from numpy import inf
60
61name = "fractal"
62title = "Calculates the scattering from fractal-like aggregates of spheres \
63following theTexiera reference."
64description = """
65        The scattering intensity is given by
66        I(q) = scale * V * delta^(2) * P(q) * S(q) + background, where
68        F(x) = 3*[sin(x)-x cos(x)]/x**3
69        delta = sld_block -sld_solv
70        scale        =  scale * volfraction
72        sld_block    =  SDL block
73        sld_solv  =  SDL solvent
74        background   =  background
75        and S(q) is the interference term between building blocks given
76        in the full documentation and depending on the parameters
77        fractal_dim  =  Fractal dimension
78        cor_length  =  Correlation Length    """
79
80category = "shape-independent"
81
83#             ["name", "units", default, [lower, upper], "type","description"],
84parameters = [["volfraction", "", 0.05, [0.0, 1], "",
85               "volume fraction of blocks"],
86              ["radius",    "Ang",  5.0, [0.0, inf], "",
88              ["fractal_dim",      "",  2.0, [0.0, 6.0], "",
89               "fractal dimension"],
90              ["cor_length", "Ang", 100.0, [0.0, inf], "",
91               "cluster correlation length"],
92              ["sld_block", "1e-6/Ang^2", 2.0, [-inf, inf], "sld",
93               "scattering length density of particles"],
94              ["sld_solvent", "1e-6/Ang^2", 6.4, [-inf, inf], "sld",
95               "scattering length density of solvent"],
96             ]
98
99source = ["lib/sas_3j1x_x.c", "lib/sas_gamma.c", "lib/fractal_sq.c", "fractal.c"]
100
101demo = dict(volfraction=0.05,