source: sasmodels/sasmodels/models/core_shell_sphere.py @ 2d81cfe

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 2d81cfe was 2d81cfe, checked in by Paul Kienzle <pkienzle@…>, 22 months ago

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[edc9f8d]1r"""
[55b2b232]2.. _core_shell_sphere:
3
[40a87fa]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.
[edc9f8d]6
[9f60c06]7For information about polarised and magnetic scattering, see
[9a4811a]8the :ref:`magnetism` documentation.
[9f60c06]9
[edc9f8d]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::
[fa8011eb]22
[40a87fa]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]
[8c9dbc9]27
[40a87fa]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.
[edc9f8d]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
[3556ad7]40References
41----------
[edc9f8d]42
[40a87fa]43A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*,
44John Wiley and Sons, New York, (1955)
[edc9f8d]45
46Validation
47----------
48
[40a87fa]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.
[edc9f8d]52"""
53
[2d81cfe]54import numpy as np
[edc9f8d]55from numpy import pi, inf
56
57name = "core_shell_sphere"
58title = "Form factor for a monodisperse spherical particle with particle with a core-shell structure."
59description = """
[d49ca5c]60    F^2(q) = 3/V_s [V_c (sld_core-sld_shell) (sin(q*radius)-q*radius*cos(q*radius))/(q*radius)^3
[3556ad7]61                   + V_s (sld_shell-sld_solvent) (sin(q*r_s)-q*r_s*cos(q*r_s))/(q*r_s)^3]
[edc9f8d]62
63            V_s: Volume of the sphere shell
64            V_c: Volume of the sphere core
65            r_s: Shell radius = radius + thickness
66"""
67category = "shape:sphere"
68
69# pylint: disable=bad-whitespace, line-too-long
70#             ["name", "units", default, [lower, upper], "type","description"],
71parameters = [["radius",      "Ang",        60.0, [0, inf],    "volume", "Sphere core radius"],
72              ["thickness",   "Ang",        10.0, [0, inf],    "volume", "Sphere shell thickness"],
[42356c8]73              ["sld_core",    "1e-6/Ang^2", 1.0,  [-inf, inf], "sld",    "core scattering length density"],
74              ["sld_shell",   "1e-6/Ang^2", 2.0,  [-inf, inf], "sld",    "shell scattering length density"],
75              ["sld_solvent", "1e-6/Ang^2", 3.0,  [-inf, inf], "sld",    "Solvent scattering length density"]]
[edc9f8d]76# pylint: enable=bad-whitespace, line-too-long
77
[925ad6e]78source = ["lib/sas_3j1x_x.c", "lib/core_shell.c", "core_shell_sphere.c"]
[edc9f8d]79
80demo = dict(scale=1, background=0, radius=60, thickness=10,
[3556ad7]81            sld_core=1.0, sld_shell=2.0, sld_solvent=0.0)
[edc9f8d]82
83def ER(radius, thickness):
84    """
85        Equivalent radius
86        @param radius: core radius
87        @param thickness: shell thickness
88    """
89    return radius + thickness
90
91def VR(radius, thickness):
92    """
93        Volume ratio
94        @param radius: core radius
95        @param thickness: shell thickness
96    """
[40a87fa]97    return (1, 1)
[4962519]98    whole = 4.0/3.0 * pi * (radius + thickness)**3
99    core = 4.0/3.0 * pi * radius**3
[edc9f8d]100    return whole, whole - core
101
[d49ca5c]102def random():
[8f04da4]103    outer_radius = 10**np.random.uniform(1.3, 4.3)
104    # Use a distribution with a preference for thin shell or thin core
105    # Avoid core,shell radii < 1
106    radius = np.random.beta(0.5, 0.5)*(outer_radius-2) + 1
[9f6823b]107    thickness = outer_radius - radius
[d49ca5c]108    pars = dict(
109        radius=radius,
110        thickness=thickness,
111    )
112    return pars
113
[40a87fa]114tests = [
115    [{'radius': 20.0, 'thickness': 10.0}, 'ER', 30.0],
[8f04da4]116    # TODO: VR test suppressed until we sort out new product model
117    # and determine what to do with volume ratio.
118    #[{'radius': 20.0, 'thickness': 10.0}, 'VR', 0.703703704],
119
120    # The SasView test result was 0.00169, with a background of 0.001
121    [{'radius': 60.0, 'thickness': 10.0, 'sld_core': 1.0, 'sld_shell': 2.0,
122      'sld_solvent': 3.0, 'background': 0.0}, 0.4, 0.000698838],
[40a87fa]123]
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