source: sasmodels/sasmodels/models/sphere.py @ 9a4811a

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Last change on this file since 9a4811a was 9a4811a, checked in by wojciech, 8 years ago

Magnetic documentation is properly referrenced now

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1r"""
2For information about polarised and magnetic scattering, see
3the :ref:`magnetism` documentation.
4documentation.
5
6Definition
7----------
8
9The 1D scattering intensity is calculated in the following way (Guinier, 1955)
10
11.. math::
12
13    I(q) = \frac{\text{scale}}{V} \cdot \left[
14        3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3}
15        \right]^2 + \text{background}
16
17where *scale* is a volume fraction, $V$ is the volume of the scatterer,
18$r$ is the radius of the sphere, *background* is the background level and
19*sld* and *sld_solvent* are the scattering length densities (SLDs) of the
20scatterer and the solvent respectively.
21
22Note that if your data is in absolute scale, the *scale* should represent
23the volume fraction (which is unitless) if you have a good fit. If not,
24it should represent the volume fraction times a factor (by which your data
25might need to be rescaled).
26
27The 2D scattering intensity is the same as above, regardless of the
28orientation of $\vec q$.
29
30Validation
31----------
32
33Validation of our code was done by comparing the output of the 1D model
34to the output of the software provided by the NIST (Kline, 2006).
35
36
37References
38----------
39
40A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*,
41John Wiley and Sons, New York, (1955)
42
43*2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.*
44"""
45
46from numpy import inf
47
48name = "sphere"
49title = "Spheres with uniform scattering length density"
50description = """\
51P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr))
52                /(qr)^3]^2 + background
53    r: radius of sphere
54    V: The volume of the scatter
55    sld: the SLD of the sphere
56    sld_solvent: the SLD of the solvent
57"""
58category = "shape:sphere"
59
60#             ["name", "units", default, [lower, upper], "type","description"],
61parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld",
62               "Layer scattering length density"],
63              ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld",
64               "Solvent scattering length density"],
65              ["radius", "Ang", 50, [0, inf], "volume",
66               "Sphere radius"],
67             ]
68
69source = ["lib/sph_j1c.c", "lib/sphere_form.c"]
70
71# No volume normalization despite having a volume parameter
72# This should perhaps be volume normalized?
73form_volume = """
74    return sphere_volume(radius);
75    """
76
77Iq = """
78    return sphere_form(q, radius, sld, sld_solvent);
79    """
80
81def ER(radius):
82    """
83    Return equivalent radius (ER)
84    """
85    return radius
86
87# VR defaults to 1.0
88
89demo = dict(scale=1, background=0,
90            sld=6, sld_solvent=1,
91            radius=120,
92            radius_pd=.2, radius_pd_n=45)
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