# source:sasmodels/sasmodels/models/core_shell_sphere.py@edc9f8d

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since edc9f8d was edc9f8d, checked in by Mathieu Doucet <doucetm@…>, 8 years ago

Converting core-shell sphere model

• Property mode set to 100644
File size: 4.0 KB
Line
1r"""
2This model provides the form factor, $P(q)$, for a spherical particle with a core-shell structure.
3The form factor is normalized by the particle volume.
4
5Definition
6----------
7
8The 1D scattering intensity is calculated in the following way (Guinier, 1955)
9
10.. math::
11
12    P(q) = \frac{\text{scale}}{V} F^2(q) + \text{background}
13
14where
15
16.. math::
17    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}+
18    V_s(\rho_s-\rho_{solv})\frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}\right]
19
20
21where $V_s$ is the volume of the outer shell, $V_c$ is
22the volume of the core, $r_s$ is the radius of the shell, $r_c$ is the radius of the
23core, $\rho_c$ is the scattering length density of the core, $\rho_s$ is the scattering length
24density of the shell, $\rho_{solv}$ is the scattering length density of the solvent.
25
26The 2D scattering intensity is the same as $P(q)$ above, regardless of the
27orientation of the $q$ vector.
28
29NB: The outer most radius (ie, = radius + thickness) is used as the
30effective radius for $S(Q)$ when $P(Q) \cdot S(Q)$ is applied.
31
32Reference
33---------
34
35A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955)
36
37Validation
38----------
39
40Validation of our code was done by comparing the output of the 1D model to the output of
41the software provided by NIST (Kline, 2006). Figure 1 shows a comparison of the output of
42our model and the output of the NIST software.
43
44.. image:: img/core_shell_sphere_1d.jpg
45
46    Figure 1: Comparison of the SasView scattering intensity for a core-shell sphere with
47    the output of the NIST SANS analysis software. The parameters were set to:
48    *scale* = 1.0, *radius* = 60 , *contrast* = 1e-6 |Ang^-2|, and
49    *background* = 0.001 |cm^-1|.
50"""
51
52from numpy import pi, inf
53
54name = "core_shell_sphere"
55title = "Form factor for a monodisperse spherical particle with particle with a core-shell structure."
56description = """
58                   + V_s (shell_sld-solvent_sld) (sin(q*r_s)-q*r_s*cos(q*r_s))/(q*r_s)^3]
59
60            V_s: Volume of the sphere shell
61            V_c: Volume of the sphere core
63"""
64category = "shape:sphere"
65
67#             ["name", "units", default, [lower, upper], "type","description"],
69              ["thickness",   "Ang",        10.0, [0, inf],    "volume", "Sphere shell thickness"],
70              ["core_sld",    "1e-6/Ang^2", 1.0,  [-inf, inf], "",       "Sphere core scattering length density"],
71              ["shell_sld",   "1e-6/Ang^2", 2.0,  [-inf, inf], "",       "Sphere shell scattering length density"],
72              ["solvent_sld", "1e-6/Ang^2", 3.0,  [-inf, inf],  "",      "Solvent scattering length density"]]
74
75source = ["lib/sph_j1c.c", "core_shell_sphere.c"]
76
77demo = dict(scale=1, background=0, radius=60, thickness=10,
78            core_sld=1.0, shell_sld=2.0, solvent_sld=0.0)
79
80oldname = 'CoreShellModel'
81oldpars = {}
82
84    """
87        @param thickness: shell thickness
88    """
90
92    """
93        Volume ratio
95        @param thickness: shell thickness
96    """
97    whole = 4.0 * pi / 3.0 * pow((radius + thickness), 3)
99    return whole, whole - core
100
101tests = [
102         [{'radius': 20.0, 'thickness': 10.0}, 'ER', 30.0 ],
103         [{'radius': 20.0, 'thickness': 10.0}, 'VR', 0.703703704 ],
104
105         # The SasView test result was 0.00169, with a background of 0.001