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

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
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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Line 
1r"""
2.. _core_shell_sphere:
3
4This model provides the form factor, $P(q)$, for a spherical particle with
5a core-shell structure. The form factor is normalized by the particle volume.
6
7For information about polarised and magnetic scattering, see
8the :ref:`magnetism` documentation.
9
10Definition
11----------
12
13The 1D scattering intensity is calculated in the following way (Guinier, 1955)
14
15.. math::
16
17    P(q) = \frac{\text{scale}}{V} F^2(q) + \text{background}
18
19where
20
21.. math::
22
23    F^2(q) = \frac{3}{V_s}\left[
24       V_c(\rho_c-\rho_s)\frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3} +
25       V_s(\rho_s-\rho_\text{solv})\frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}
26       \right]
27
28where $V_s$ is the volume of the whole particle, $V_c$ is the volume of the
29core, $r_s$ = $radius$ + $thickness$ is the radius of the particle, $r_c$
30is the radius of the core, $\rho_c$ is the scattering length density of the
31core, $\rho_s$ is the scattering length density of the shell,
32$\rho_\text{solv}$, is the scattering length density of the solvent.
33
34The 2D scattering intensity is the same as $P(q)$ above, regardless of the
35orientation of the $q$ vector.
36
37NB: The outer most radius (ie, = radius + thickness) is used as the
38effective radius for $S(Q)$ when $P(Q) \cdot S(Q)$ is applied.
39
40References
41----------
42
43A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*,
44John Wiley and Sons, New York, (1955)
45
46Validation
47----------
48
49Validation of our code was done by comparing the output of the 1D model to
50the output of the software provided by NIST (Kline, 2006). Figure 1 shows a
51comparison of the output of our model and the output of the NIST software.
52"""
53
54from numpy import pi, inf
55
56name = "core_shell_sphere"
57title = "Form factor for a monodisperse spherical particle with particle with a core-shell structure."
58description = """
59    F^2(q) = 3/V_s [V_c (sld_core-sld_shell) (sin(q*radius)-q*radius*cos(q*radius))/(q*radius)^3
60                   + V_s (sld_shell-sld_solvent) (sin(q*r_s)-q*r_s*cos(q*r_s))/(q*r_s)^3]
61
62            V_s: Volume of the sphere shell
63            V_c: Volume of the sphere core
64            r_s: Shell radius = radius + thickness
65"""
66category = "shape:sphere"
67
68# pylint: disable=bad-whitespace, line-too-long
69#             ["name", "units", default, [lower, upper], "type","description"],
70parameters = [["radius",      "Ang",        60.0, [0, inf],    "volume", "Sphere core radius"],
71              ["thickness",   "Ang",        10.0, [0, inf],    "volume", "Sphere shell thickness"],
72              ["sld_core",    "1e-6/Ang^2", 1.0,  [-inf, inf], "sld",    "core scattering length density"],
73              ["sld_shell",   "1e-6/Ang^2", 2.0,  [-inf, inf], "sld",    "shell scattering length density"],
74              ["sld_solvent", "1e-6/Ang^2", 3.0,  [-inf, inf], "sld",    "Solvent scattering length density"]]
75# pylint: enable=bad-whitespace, line-too-long
76
77source = ["lib/sph_j1c.c", "lib/core_shell.c", "core_shell_sphere.c"]
78
79demo = dict(scale=1, background=0, radius=60, thickness=10,
80            sld_core=1.0, sld_shell=2.0, sld_solvent=0.0)
81
82def ER(radius, thickness):
83    """
84        Equivalent radius
85        @param radius: core radius
86        @param thickness: shell thickness
87    """
88    return radius + thickness
89
90def VR(radius, thickness):
91    """
92        Volume ratio
93        @param radius: core radius
94        @param thickness: shell thickness
95    """
96    return (1, 1)
97    whole = 4.0 * pi / 3.0 * pow((radius + thickness), 3)
98    core = 4.0 * pi / 3.0 * radius * radius * radius
99    return whole, whole - core
100
101tests = [
102    [{'radius': 20.0, 'thickness': 10.0}, 'ER', 30.0],
103     # TODO: VR test suppressed until we sort out new product model
104     # and determine what to do with volume ratio.
105     #[{'radius': 20.0, 'thickness': 10.0}, 'VR', 0.703703704],
106
107     # The SasView test result was 0.00169, with a background of 0.001
108     [{'radius': 60.0, 'thickness': 10.0, 'sld_core': 1.0, 'sld_shell':2.0,
109       'sld_solvent':3.0, 'background':0.0},
110      0.4, 0.000698838],
111]
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