source: sasmodels/sasmodels/models/lamellar_hg.py @ d2bb604

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Last change on this file since d2bb604 was d2bb604, checked in by Paul Kienzle <pkienzle@…>, 8 years ago

fix models so all dll tests pass

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1# Note: model title and parameter table are inserted automatically
2r"""
3This model provides the scattering intensity, $I(q)$, for a lyotropic lamellar
4phase where a random distribution in solution are assumed. The SLD of the head
5region is taken to be different from the SLD of the tail region.
6
7Definition
8----------
9
10The scattering intensity $I(q)$ is
11
12.. math::
13
14   I(q) = 2\pi\frac{\text{scale}}{2(\delta_H + \delta_T)}  P(q) \frac{1}{q^2}
15
16The form factor $P(q)$ is
17
18.. math::
19
20    P(q) = \frac{4}{q^2}
21        \left\lbrace
22            \Delta \rho_H
23            \left[\sin[q(\delta_H + \delta_T)\ - \sin(q\delta_T)\right]
24            + \Delta\rho_T\sin(q\delta_T)
25        \right\rbrace^2
26
27where $\delta_T$ is *tail_length*, $\delta_H$ is *head_length*,
28$\Delta\rho_H$ is the head contrast (*sld_head* $-$ *sld_solvent*),
29and $\Delta\rho_T$ is tail contrast (*sld* $-$ *sld_solvent*).
30
31The total thickness of the lamellar sheet is $\delta_H$ + $\delta_T$ + $\delta_T$ + $\delta_H$.
32Note that in a non aqueous solvent the chemical "head" group may be the
33"Tail region" and vice-versa.
34
35The 2D scattering intensity is calculated in the same way as 1D, where
36the $q$ vector is defined as
37
38.. math::
39
40    q = \sqrt{q_x^2 + q_y^2}
41
42
43References
44----------
45
46F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502
47
48also in J. Phys. Chem. B, 105, (2001) 11081-11088
49
50*2014/04/17 - Description reviewed by S King and P Butler.*
51"""
52
53from numpy import inf
54
55name = "lamellar_hg"
56title = "Random lamellar phase with Head and Tail Groups"
57description = """\
58    [Random lamellar phase with Head and Tail Groups]
59        I(q)= 2*pi*P(q)/(2(H+T)*q^(2)), where
60        P(q)= see manual
61        layer thickness =(H+T+T+H) = 2(Head+Tail)
62        sld = Tail scattering length density
63        sld_head = Head scattering length density
64        sld_solvent = solvent scattering length density
65        background = incoherent background
66        scale = scale factor
67"""
68category = "shape:lamellae"
69
70# pylint: disable=bad-whitespace, line-too-long
71#             ["name", "units", default, [lower, upper], "type","description"],
72parameters = [["tail_length", "Ang",       15,   [0, inf],  "volume",  "Tail thickness ( total = H+T+T+H)"],
73              ["head_length", "Ang",       10,   [0, inf],  "volume",  "Head thickness"],
74              ["sld",         "1e-6/Ang^2", 0.4, [-inf,inf], "",       "Tail scattering length density"],
75              ["sld_head",    "1e-6/Ang^2", 3.0, [-inf,inf], "",       "Head scattering length density"],
76              ["sld_solvent", "1e-6/Ang^2", 6,   [-inf,inf], "",       "Solvent scattering length density"]]
77# pylint: enable=bad-whitespace, line-too-long
78
79# No volume normalization despite having a volume parameter
80# This should perhaps be volume normalized?
81form_volume = """
82    return 1.0;
83    """
84
85Iq = """
86    const double qsq = q*q;
87    const double drh = sld_head - sld_solvent;
88    const double drt = sld - sld_solvent;    //correction 13FEB06 by L.Porcar
89    const double qT = q*tail_length;
90    double Pq, inten;
91    Pq = drh*(sin(q*(head_length+tail_length))-sin(qT)) + drt*sin(qT);
92    Pq *= Pq;
93    Pq *= 4.0/(qsq);
94
95    inten = 2.0e-4*M_PI*Pq/qsq;
96
97    // normalize by the bilayer thickness
98    inten /= 2.0*(head_length+tail_length);
99
100    return inten;
101    """
102
103# ER defaults to 0.0
104# VR defaults to 1.0
105
106demo = dict(scale=1, background=0,
107            tail_length=15, head_length=10,
108            sld=0.4, sld_head=3.0, sld_solvent=6.0,
109            tail_length_pd=0.2, tail_length_pd_n=40,
110            head_length_pd=0.01, head_length_pd_n=40)
111
112#
113tests = [[{'scale': 1.0, 'background': 0.0, 'tail_length': 15.0, 'head_length': 10.0,
114           'sld': 0.4, 'sld_head': 3.0, 'sld_solvent': 6.0}, [0.001], [653143.9209]]]
115# ADDED by: RKH  ON: 18Mar2016  converted from sasview previously, now renaming everything & sorting the docs
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