# source:sasmodels/sasmodels/models/fractal_core_shell.py@ef07e95

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
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1r"""
2Definition
3----------
4Calculates the scattering from a fractal structure with a primary building
5block of core-shell spheres, as opposed to just homogeneous spheres in
6the fractal model. It is an extension of the well known Teixeira\ [#teixeira]_
7fractal model replacing the $P(q)$ of a solid sphere with that of a core-shell
8sphere. This model could find use for aggregates of coated particles, or
9aggregates of vesicles for example.
10
11.. math::
12
13    I(q) = P(q)S(q) + \text{background}
14
15Where $P(q)$ is the core-shell form factor and $S(q)$ is the
16Teixeira\ [#teixeira]_ fractal structure factor both of which are given again
17below:
18
19.. math::
20
21    P(q) &= \frac{\phi}{V_s}\left[3V_c(\rho_c-\rho_s)
22    \frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3}+
23    3V_s(\rho_s-\rho_{solv})
24    \frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}\right]^2 \\
25    S(q) &= 1 + \frac{D_f\ \Gamma\!(D_f-1)}{[1+1/(q\xi)^2]^{(D_f-1)/2}}
26    \frac{\sin[(D_f-1)\tan^{-1}(q\xi)]}{(qr_s)^{D_f}}
27
28where $\phi$ is the volume fraction of particles, $V_s$ is the volume of the
29whole particle, $V_c$ is the volume of the core, $\rho_c$, $\rho_s$, and
30$\rho_{solv}$ are the scattering length densities of the core, shell, and
31solvent respectively, $r_c$ and $r_s$ are the radius of the core and the radius
32of the whole particle respectively, $D_f$ is the fractal dimension, and $\xi$ the
33correlation length.
34
35Polydispersity of radius and thickness are also provided for.
36
37This model does not allow for anisotropy and thus the 2D scattering intensity
38is calculated in the same way as 1D, where the $q$ vector is defined as
39
40.. math::
41
42    q = \sqrt{q_x^2 + q_y^2}
43
44Our model is derived from the form factor calculations implemented in IGOR
45macros by the NIST Center for Neutron Research\ [#Kline]_
46
47References
48----------
49
50.. [#teixeira] J Teixeira, *J. Appl. Cryst.*, 21 (1988) 781-785
51.. [#Kline]  S R Kline, *J Appl. Cryst.*, 39 (2006) 895
52
53Authorship and Verification
54----------------------------
55
56* **Author:** NIST IGOR/DANSE **Date:** pre 2010
57* **Last Modified by:** Paul Butler and Paul Kienzle **Date:** November 27, 2016
58* **Last Reviewed by:** Paul Butler and Paul Kienzle **Date:** November 27, 2016
59"""
60
61import numpy as np
62from numpy import pi, inf
63
64name = "fractal_core_shell"
65title = "Scattering from a fractal structure formed from core shell spheres"
66description = """\
67    Model for fractal aggregates of core-shell primary particles. It is based on
68    the Teixeira model for the S(q) of a fractal * P(q) for a core-shell sphere
69
71    thickness = thickness of the shell
72    thick_layer = thickness of a layer
73    sld_core = the SLD of the core
74    sld_shell = the SLD of the shell
75    sld_solvent = the SLD of the solvent
76    volfraction = volume fraction of core-shell particles
77    fractal_dim = fractal dimension
78    cor_length = correlation length of the fractal like aggretates
79    """
80category = "shape-independent"
81
83#   ["name", "units", default, [lower, upper], "type","description"],
84parameters = [
86    ["thickness",   "Ang",        10.0, [0.0, inf],  "volume", "Sphere shell thickness"],
87    ["sld_core",    "1e-6/Ang^2", 1.0,  [-inf, inf], "sld",    "Sphere core scattering length density"],
88    ["sld_shell",   "1e-6/Ang^2", 2.0,  [-inf, inf], "sld",    "Sphere shell scattering length density"],
89    ["sld_solvent", "1e-6/Ang^2", 3.0,  [-inf, inf], "sld",    "Solvent scattering length density"],
90    ["volfraction", "",           1.0,  [0.0, inf],  "",       "Volume fraction of building block spheres"],
91    ["fractal_dim",    "",        2.0,  [0.0, 6.0],  "",       "Fractal dimension"],
92    ["cor_length",  "Ang",      100.0,  [0.0, inf],  "",       "Correlation length of fractal-like aggregates"],
93]
95
96source = ["lib/sas_3j1x_x.c", "lib/sas_gamma.c", "lib/core_shell.c",
97          "lib/fractal_sq.c", "fractal_core_shell.c"]
98
99def random():
101    # Use a distribution with a preference for thin shell or thin core
102    # Avoid core,shell radii < 1
103    thickness = np.random.beta(0.5, 0.5)*(outer_radius-2) + 1
106    volfraction = 10**np.random.uniform(-3, -1)
107    fractal_dim = 2*np.random.beta(3, 4) + 1
108    pars = dict(
109        #background=0, sld_block=1, sld_solvent=0,
110        volfraction=volfraction,
112        cor_length=cor_length,
113        fractal_dim=fractal_dim,
114    )
115    return pars
116
117demo = dict(scale=0.05,
118            background=0,
120            thickness=5,
121            sld_core=3.5,
122            sld_shell=1.0,
123            sld_solvent=6.35,
124            volfraction=0.05,
125            fractal_dim=2.0,
126            cor_length=100.0)
127
129    """
132        @param thickness: shell thickness
133    """
135
137    """
138        Volume ratio
140        @param thickness: shell thickness
141    """
142    whole = 4.0/3.0 * pi * (radius + thickness)**3
143    core = 4.0/3.0 * pi * radius**3
144    return whole, whole-core
145
146tests = [[{'radius': 20.0, 'thickness': 10.0}, 'ER', 30.0],
147         [{'radius': 20.0, 'thickness': 10.0}, 'VR', 0.703703704]]
148
149#         # The SasView test result was 0.00169, with a background of 0.001
150#         # They are however wrong as we now know.  IGOR might be a more
151#         # appropriate source. Otherwise will just have to assume this is now
152#         # correct and self generate a correct answer for the future. Until we
153#         # figure it out leave the tests commented out