Changeset caddb14 in sasmodels
 Timestamp:
 Oct 1, 2016 9:48:49 AM (5 years ago)
 Branches:
 master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket1257vesicleproduct, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
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 69ef533
 Parents:
 a807206
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sasmodels/models/teubner_strey.py
r40a87fa rcaddb14 5 5 This model calculates the scattered intensity of a twocomponent system 6 6 using the TeubnerStrey model. Unlike :ref:`dab` this function generates 7 a peak. 7 a peak. A twophase material can be characterised by two length scales  8 a correlation length and a domain size (periodicity). 9 10 The original paper by Teubner and Strey defined the function as: 8 11 9 12 .. math:: 10 13 11 I(q) =\frac{1}{a_2 + c_1 q^2 + c_2 q^4} + \text{background}14 I(q) \propto \frac{1}{a_2 + c_1 q^2 + c_2 q^4} + \text{background} 12 15 13 The parameters $a_2$, $c_1$ and $c_2$ can be used to determine the 14 characteristic domain size $d$, 16 where the parameters $a_2$, $c_1$ and $c_2$ are defined in terms of the 17 periodicity, $d$, and correlation length $\xi$ as: 18 19 .. math:: 20 21 a_2 &= \biggl[1+\bigl(\frac{2\pi\xi}{d}\bigr)^2\biggr]\\ 22 c_1 &= 2\xi^2\bigl(\frac{2\pi\xi}{d}\bigr)^2+2\xi^2\\ 23 c_2 &= \xi^4 24 25 and thus, the periodicity, $d$ is given by 15 26 16 27 .. math:: 17 28 18 29 d = 2\pi\left[\frac12\left(\frac{a_2}{c_2}\right)^{1/2} 19 +\frac14\frac{c_1}{c_2}\right]^{1/2}30  \frac14\frac{c_1}{c_2}\right]^{1/2} 20 31 21 22 and the correlation length $\xi$, 32 and the correlation length, $\xi$, is given by 23 33 24 34 .. math:: 25 35 26 36 \xi = \left[\frac12\left(\frac{a_2}{c_2}\right)^{1/2} 27 \frac14\frac{c_1}{c_2}\right]^{1/2}37 + \frac14\frac{c_1}{c_2}\right]^{1/2} 28 38 39 Here the model is parameterised in terms of $d$ and $\xi$ and with an explicit 40 volume fraction for one phase, $\phi_a$, and contrast, 41 $\delta\rho^2 = (\rho_a  \rho_b)^2$ : 42 43 .. math:: 44 45 I(q) = \frac{8\pi\phi_a(1\phi_a)(\Delta\rho)^2c_2/\xi} 46 {a_2 + c_1q^2 + c_2q^4} 47 48 where :math:`8\pi\phi_a(1\phi_a)(\Delta\rho)^2c_2/\xi` is the constant of 49 proportionality from the first equation above. 50 51 In the case of a microemulsion, $a_2 > 0$, $c_1 < 0$, and $c_2 >0$. 29 52 30 53 For 2D data, scattering intensity is calculated in the same way as 1D, … … 34 57 35 58 q = \sqrt{q_x^2 + q_y^2} 36 37 59 38 60 References … … 44 66 *J. Chem. Phys.*, 101 (1994) 5343 45 67 68 H Endo, M Mihailescu, M. Monkenbusch, J Allgaier, G Gompper, D Richter, 69 B Jakobs, T Sottmann, R Strey, and I Grillo, *J. Chem. Phys.*, 115 (2001), 580 46 70 """ 47 71 48 72 import numpy as np 49 from numpy import inf 73 from numpy import inf,power,pi 50 74 51 75 name = "teubner_strey" 52 76 title = "TeubnerStrey model of microemulsions" 53 77 description = """\ 54 Scattering model class for the TeubnerStrey model given by 55 Provide F(x) = 1/( a2 + c1 q^2+ c2 q^4 ) + background 56 a2>0, c1<0, c2>0, 4 a2 c2  c1^2 > 0 78 Calculates scattering according to the TeubnerStrey model 57 79 """ 58 80 category = "shapeindependent" … … 60 82 # ["name", "units", default, [lower, upper], "type","description"], 61 83 parameters = [ 62 ["a2", "", 0.1, [0, inf], "", "a2"], 63 ["c1", "1e6/Ang^2", 30., [inf, 0], "", "c1"], 64 ["c2", "Ang", 5000., [0, inf], "volume", "c2"], 84 ["volfraction_a", "", 0.5, [0, 1.0], "", "Volume fraction of phase a"], 85 ["sld_a", "1e6/Ang^2", 0.3, [inf, inf], "", "SLD of phase a"], 86 ["sld_b", "1e6/Ang^2", 6.3, [inf, inf], "", "SLD of phase b"], 87 ["d", "Ang", 100.0, [0, inf], "", "Domain size (periodicity)"], 88 ["xi", "Ang", 30.0, [0, inf], "", "Correlation length"], 65 89 ] 66 90 67 def Iq(q, a2, c1, c2):91 def Iq(q, volfraction, sld, sld_solvent,d,xi): 68 92 """SAS form""" 69 return 1. / np.polyval([c2, c1, a2], q**2) 93 drho2 = (sldsld_solvent)*(sldsld_solvent) 94 a2 = power(1.0+power(2.0*pi*xi/d,2.0),2.0) 95 c1 = 2.0*xi*xi*power(2.0*pi*xi/d,2.0)+2*xi*xi 96 c2 = power(xi,4.0) 97 prefactor = 8.0*pi*volfraction*(1.0volfraction)*drho2*c2/xi 98 #k2 = (2.0*pi/d)*(2.0*pi/d) 99 #xi2 = 1/(xi*xi) 100 #q2 = q*q 101 #result = prefactor/((xi2+k2)*(xi2+k2)+2.0*(xi2k2)*q2+q2*q2) 102 return 1.0e4*prefactor / np.polyval([c2, c1, a2], q**2) 103 70 104 Iq.vectorized = True # Iq accepts an array of q values 71 105 72 demo = dict(scale=1, background=0, a2=0.1, c1=30.0, c2=5000.0) 73 tests = [[{}, 0.2, 0.145927536232]] 106 demo = dict(scale=1, background=0, volfraction_a=0.5, 107 sld_a=0.3, sld_b=6.3, 108 d=100.0, xi=30.0) 109 tests = [[{}, 0.06, 41.5918888453]]
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