source: sasmodels/sasmodels/models/core_multi_shell.py @ 2d73a53

core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 2d73a53 was 2d73a53, checked in by butler, 6 years ago

added more references and more documentation cleanup

  • Property mode set to 100644
File size: 4.4 KB
Line 
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 $\vec q$ 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 :ref:`magnetism` documentation.
29
30Our model uses the form factor calculations implemented in a c-library provided
31by the NIST Center for Neutron Research (Kline, 2006) [#kline]_.
32
33References
34----------
35
36.. [#] See the :ref:`core-shell-sphere` model documentation.
37.. [#kline] S R Kline, *J Appl. Cryst.*, 39 (2006) 895
38.. [#] L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray and
39   Neutron Scattering*, Plenum Press, New York, 1987.
40
41Authorship and Verification
42----------------------------
43
44* **Author:** NIST IGOR/DANSE **Date:** pre 2010
45* **Last Modified by:** Paul Kienzle **Date:** September 12, 2016
46* **Last Reviewed by:** Paul Kienzle **Date:** September 12, 2016
47"""
48
49
50
51from __future__ import division
52
53import numpy as np
54from numpy import inf
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], "sld",
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], "sld",
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], "sld",
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    Returns the SLD profile *r* (Ang), and *rho* (1e-6/Ang^2).
108    """
109    z = []
110    rho = []
111
112    # add in the core
113    z.append(0)
114    rho.append(sld_core)
115    z.append(radius)
116    rho.append(sld_core)
117
118    # add in the shells
119    for k in range(int(n)):
120        # Left side of each shells
121        z.append(z[-1])
122        rho.append(sld[k])
123        z.append(z[-1] + thickness[k])
124        rho.append(sld[k])
125    # add in the solvent
126    z.append(z[-1])
127    rho.append(sld_solvent)
128    z.append(z[-1]*1.25)
129    rho.append(sld_solvent)
130
131    return np.asarray(z), np.asarray(rho)
132
133def ER(radius, n, thickness):
134    """Effective radius"""
135    n = int(n[0])  # n cannot be polydisperse
136    return np.sum(thickness[:n], axis=0) + radius
137
138demo = dict(sld_core=6.4,
139            radius=60,
140            sld_solvent=6.4,
141            n=2,
142            sld=[2.0, 3.0],
143            thickness=20,
144            thickness1_pd=0.3,
145            thickness2_pd=0.3,
146            thickness1_pd_n=10,
147            thickness2_pd_n=10,
148            )
Note: See TracBrowser for help on using the repository browser.