source: sasmodels/sasmodels/models/sphere.py @ ec45c4f

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since ec45c4f was ec45c4f, checked in by Paul Kienzle <pkienzle@…>, 8 years ago

remove oldname/oldpars from new models

  • Property mode set to 100644
File size: 2.8 KB
Line 
1r"""
2For information about polarised and magnetic scattering, see
3the :doc:`magnetic help <../sasgui/perspectives/fitting/mag_help>` documentation.
4
5Definition
6----------
7
8The 1D scattering intensity is calculated in the following way (Guinier, 1955)
9
10.. math::
11
12    I(q) = \frac{\text{scale}}{V} \cdot \left[
13        3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3}
14        \right]^2 + \text{background}
15
16where *scale* is a volume fraction, $V$ is the volume of the scatterer,
17$r$ is the radius of the sphere, *background* is the background level and
18*sld* and *sld_solvent* are the scattering length densities (SLDs) of the
19scatterer and the solvent respectively.
20
21Note that if your data is in absolute scale, the *scale* should represent
22the volume fraction (which is unitless) if you have a good fit. If not,
23it should represent the volume fraction times a factor (by which your data
24might need to be rescaled).
25
26The 2D scattering intensity is the same as above, regardless of the
27orientation of $\vec q$.
28
29Validation
30----------
31
32Validation of our code was done by comparing the output of the 1D model
33to the output of the software provided by the NIST (Kline, 2006).
34
35
36References
37----------
38
39A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*,
40John Wiley and Sons, New York, (1955)
41
42*2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.*
43"""
44
45from numpy import inf
46
47name = "sphere"
48title = "Spheres with uniform scattering length density"
49description = """\
50P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr))
51                /(qr)^3]^2 + background
52    r: radius of sphere
53    V: The volume of the scatter
54    sld: the SLD of the sphere
55    sld_solvent: the SLD of the solvent
56"""
57category = "shape:sphere"
58
59#             ["name", "units", default, [lower, upper], "type","description"],
60parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "",
61               "Layer scattering length density"],
62              ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "",
63               "Solvent scattering length density"],
64              ["radius", "Ang", 50, [0, inf], "volume",
65               "Sphere radius"],
66             ]
67
68source = ["lib/sph_j1c.c", "lib/sphere_form.c"]
69
70# No volume normalization despite having a volume parameter
71# This should perhaps be volume normalized?
72form_volume = """
73    return sphere_volume(radius);
74    """
75
76Iq = """
77    return sphere_form(q, radius, sld, sld_solvent);
78    """
79
80Iqxy = """
81    // never called since no orientation or magnetic parameters.
82    //return -1.0;
83    return Iq(sqrt(qx*qx + qy*qy), sld, sld_solvent, radius);
84    """
85
86def ER(radius):
87    """
88    Return equivalent radius (ER)
89    """
90    return radius
91
92# VR defaults to 1.0
93
94demo = dict(scale=1, background=0,
95            sld=6, sld_solvent=1,
96            radius=120,
97            radius_pd=.2, radius_pd_n=45)
Note: See TracBrowser for help on using the repository browser.