source: sasmodels/sasmodels/models/core_shell_sphere.py @ 42356c8

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 42356c8 was 42356c8, checked in by Paul Kienzle <pkienzle@…>, 8 years ago

label all sld parameters

  • Property mode set to 100644
File size: 3.9 KB
Line 
1r"""
2.. _core_shell_sphere:
3
4This model provides the form factor, $P(q)$, for a spherical particle with a core-shell structure.
5The form factor is normalized by the particle volume.
6
7Definition
8----------
9
10The 1D scattering intensity is calculated in the following way (Guinier, 1955)
11
12.. math::
13
14    P(q) = \frac{\text{scale}}{V} F^2(q) + \text{background}
15
16where
17
18.. math::
19
20    F^2(q)=\frac{3}{V_s}\left[V_c(\rho_c-\rho_s)\frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3}+
21    V_s(\rho_s-\rho_{solv})\frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}\right]
22
23where $V_s$ is the volume of the whole particle, $V_c$ is
24the volume of the core, $r_s$ = $radius$ + $thickness$ is the radius of the particle, $r_c$ is the radius of the
25core, $\rho_c$ is the scattering length density of the core, $\rho_s$ is the scattering length
26density of the shell, $\rho_{solv}$ is the scattering length density of the solvent.
27
28The 2D scattering intensity is the same as $P(q)$ above, regardless of the
29orientation of the $q$ vector.
30
31NB: The outer most radius (ie, = radius + thickness) is used as the
32effective radius for $S(Q)$ when $P(Q) \cdot S(Q)$ is applied.
33
34References
35----------
36
37A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955)
38
39Validation
40----------
41
42Validation of our code was done by comparing the output of the 1D model to the output of
43the software provided by NIST (Kline, 2006). Figure 1 shows a comparison of the output of
44our model and the output of the NIST software.
45
46"""
47
48from numpy import pi, inf
49
50name = "core_shell_sphere"
51title = "Form factor for a monodisperse spherical particle with particle with a core-shell structure."
52description = """
53    F^2(q) = 3/V_s [V_c (sld_core-sld_shell) (sin(q*radius)-q*radius*cos(q*radius))/(q*radius)^3
54                   + V_s (sld_shell-sld_solvent) (sin(q*r_s)-q*r_s*cos(q*r_s))/(q*r_s)^3]
55
56            V_s: Volume of the sphere shell
57            V_c: Volume of the sphere core
58            r_s: Shell radius = radius + thickness
59"""
60category = "shape:sphere"
61
62# pylint: disable=bad-whitespace, line-too-long
63#             ["name", "units", default, [lower, upper], "type","description"],
64parameters = [["radius",      "Ang",        60.0, [0, inf],    "volume", "Sphere core radius"],
65              ["thickness",   "Ang",        10.0, [0, inf],    "volume", "Sphere shell thickness"],
66              ["sld_core",    "1e-6/Ang^2", 1.0,  [-inf, inf], "sld",    "core scattering length density"],
67              ["sld_shell",   "1e-6/Ang^2", 2.0,  [-inf, inf], "sld",    "shell scattering length density"],
68              ["sld_solvent", "1e-6/Ang^2", 3.0,  [-inf, inf], "sld",    "Solvent scattering length density"]]
69# pylint: enable=bad-whitespace, line-too-long
70
71source = ["lib/sph_j1c.c", "lib/core_shell.c", "core_shell_sphere.c"]
72
73demo = dict(scale=1, background=0, radius=60, thickness=10,
74            sld_core=1.0, sld_shell=2.0, sld_solvent=0.0)
75
76def ER(radius, thickness):
77    """
78        Equivalent radius
79        @param radius: core radius
80        @param thickness: shell thickness
81    """
82    return radius + thickness
83
84def VR(radius, thickness):
85    """
86        Volume ratio
87        @param radius: core radius
88        @param thickness: shell thickness
89    """
90    return (1,1)
91    whole = 4.0 * pi / 3.0 * pow((radius + thickness), 3)
92    core = 4.0 * pi / 3.0 * radius * radius * radius
93    return whole, whole - core
94
95tests = [[{'radius': 20.0, 'thickness': 10.0}, 'ER', 30.0],
96         # TODO: VR test suppressed until we sort out new product model
97         # and determine what to do with volume ratio.
98         #[{'radius': 20.0, 'thickness': 10.0}, 'VR', 0.703703704],
99
100         # The SasView test result was 0.00169, with a background of 0.001
101         [{'radius': 60.0,
102           'thickness': 10.0,
103           'sld_core': 1.0,
104           'sld_shell':2.0,
105           'sld_solvent':3.0,
106           'background':0.0
107          }, 0.4, 0.000698838]]
Note: See TracBrowser for help on using the repository browser.