source: sasmodels/sasmodels/models/core_multi_shell.py @ 263daec

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 263daec was 263daec, checked in by Paul Kienzle <pkienzle@…>, 8 years ago

add unified power Rg

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1r"""
2Definition
3----------
4
5This model is a trivial extension of the CoreShell function to a larger number
6of shells. The scattering length density profile for the default sld values
7(w/ 4 shells).
8
9.. figure:: img/core_multi_shell_sld_default_profile.jpg
10
11    SLD profile of the core_multi_shell object from the center of sphere out
12    for the default SLDs.*
13
14The 2D scattering intensity is the same as $P(q)$ above, regardless of the
15orientation of the $q$ vector which is defined as
16
17.. math::
18
19    q = \sqrt{q_x^2 + q_y^2}
20
21.. note:: **Be careful!** The SLDs and scale can be highly correlated. Hold as
22         many of these parameters fixed as possible.
23
24.. note:: The outer most radius (= *radius* + *thickness*) is used as the
25          effective radius for $S(Q)$ when $P(Q)*S(Q)$ is applied.
26
27For information about polarised and magnetic scattering, see
28the :doc:`magnetic help <../sasgui/perspectives/fitting/mag_help>` documentation.
29
30Our model uses the form factor calculations implemented in a c-library provided
31by the NIST Center for Neutron Research (Kline, 2006).
32
33References
34----------
35See the :ref:`core_shell_sphere <core_shell_sphere>` model documentation.
36
37L A Feigin and D I Svergun,
38*Structure Analysis by Small-Angle X-Ray and Neutron Scattering*,
39Plenum Press, New York, 1987.
40
41**Author:** NIST IGOR/DANSE **on:** pre 2010
42
43**Last Modified by:** in progress **on:** March 20, 2016
44
45**Last Reviewed by:** in progress **on:** March 20, 2016
46"""
47
48
49
50from __future__ import division
51
52import numpy as np
53from numpy import inf, nan
54from math import fabs, exp, expm1
55
56name = "core_multi_shell"
57title = "This model provides the scattering from a spherical core with 1 to 4 \
58 concentric shell structures. The SLDs of the core and each shell are \
59 individually specified."
60
61description = """\
62Form factor for a core muti-shell (up to 4) sphere normalized by the volume.
63Each shell can have a unique thickness and sld.
64
65        background:background,
66        rad_core0: radius of sphere(core)
67        thick_shell#:the thickness of the shell#
68        sld_core0: the SLD of the sphere
69        sld_solv: the SLD of the solvent
70        sld_shell: the SLD of the shell#
71        A_shell#: the coefficient in the exponential function
72       
73       
74    scale: 1.0 if data is on absolute scale
75    volfraction: volume fraction of spheres
76    radius: the radius of the core
77    sld: the SLD of the core
78    thick_shelli: the thickness of the i'th shell from the core
79    sld_shelli: the SLD of the i'th shell from the core
80    sld_solvent: the SLD of the solvent
81    background: incoherent background
82
83"""
84
85category = "shape:sphere"
86
87
88#             ["name", "units", default, [lower, upper], "type","description"],
89parameters = [["sld_core", "1e-6/Ang^2", 1.0, [-inf, inf], "",
90               "Core scattering length density"],
91              ["radius", "Ang", 200., [0, inf], "volume",
92               "Radius of the core"],
93              ["sld_solvent", "1e-6/Ang^2", 6.4, [-inf, inf], "",
94               "Solvent scattering length density"],
95              ["n", "", 1, [0, 10], "volume",
96               "number of shells"],
97              ["sld[n]", "1e-6/Ang^2", 1.7, [-inf, inf], "",
98               "scattering length density of shell k"],
99              ["thickness[n]", "Ang", 40., [0, inf], "volume",
100               "Thickness of shell k"],
101              ]
102
103source = ["lib/sph_j1c.c", "core_multi_shell.c"]
104
105def profile(sld_core, radius, sld_solvent, n, sld, thickness):
106    """
107    SLD profile
108   
109    :return: (r, beta) where r is a list of radius of the transition points\
110      and beta is a list of the corresponding SLD values.
111
112    """
113    total_radius = 1.25*(sum(thickness[:n]) + radius + 1)
114
115    r = []
116    beta = []
117
118    # add in the core
119    r.append(0)
120    beta.append(sld)
121    r.append(radius)
122    beta.append(sld)
123
124    # add in the shells
125    for k in range(n):
126        # Left side of each shells
127        r0 = r[-1]
128        r.append(r0)
129        beta.append(sld[k])
130        r.append(r0 + thickness[k])
131        beta.append(sld[k])
132    # add in the solvent
133    r.append(r[-1])
134    beta.append(sld_solvent)
135    r.append(total_radius)
136    beta.append(sld_solvent)
137
138    return np.asarray(r), np.asarray(beta)
139
140def ER(radius, n, thickness):
141    n = n[0]  # n cannot be polydisperse
142    return np.sum(thickness[:n], axis=0) + radius
143
144def VR(radius, n, thickness):
145    return 1.0, 1.0
146
147demo = dict(sld_core = 6.4,
148            radius = 60,
149            sld_solvent = 6.4,
150            n = 2,
151            sld = [2.0, 3.0],
152            thickness = 20,
153            thickness1_pd = 0.3,
154            thickness2_pd = 0.3,
155            thickness1_pd_n = 10,
156            thickness2_pd_n = 10,
157            )
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