[5d4777d] | 1 | r""" |
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| 2 | Polydispersity in the bilayer thickness can be applied from the GUI. |
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| 3 | |
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| 4 | Definition |
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| 5 | ---------- |
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| 6 | |
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[eb69cce] | 7 | The scattering intensity $I(q)$ is |
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[5d4777d] | 8 | |
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| 9 | .. math:: |
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| 10 | |
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[eb69cce] | 11 | I(q) = \frac{2\pi P(q)}{\delta q^2} |
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[5d4777d] | 12 | |
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| 13 | |
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| 14 | The form factor is |
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| 15 | |
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| 16 | .. math:: |
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| 17 | |
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[eb69cce] | 18 | P(q) = \frac{2\Delta\rho^2}{q^2}(1-cos(q\delta)) |
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[5d4777d] | 19 | |
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| 20 | |
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[eb69cce] | 21 | where $\delta$ is the bilayer thickness. |
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[5d4777d] | 22 | |
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[eb69cce] | 23 | The 2D scattering intensity is calculated in the same way as 1D, where |
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| 24 | the $q$ vector is defined as |
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[5d4777d] | 25 | |
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| 26 | .. math:: |
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| 27 | |
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[eb69cce] | 28 | q = \sqrt{q_x^2 + q_y^2} |
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[5d4777d] | 29 | |
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| 30 | |
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[19dcb933] | 31 | .. figure:: img/lamellar_1d.jpg |
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[5d4777d] | 32 | |
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| 33 | 1D plot using the default values (w/1000 data point). |
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| 34 | |
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| 35 | |
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[eb69cce] | 36 | References |
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| 37 | ---------- |
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[5d4777d] | 38 | |
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| 39 | F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502 |
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| 40 | |
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| 41 | also in J. Phys. Chem. B, 105, (2001) 11081-11088 |
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| 42 | |
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| 43 | |
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| 44 | """ |
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| 45 | |
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[3c56da87] | 46 | from numpy import inf |
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[5d4777d] | 47 | |
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| 48 | name = "lamellar" |
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| 49 | title = "Lyotropic lamellar phase with uniform SLD and random distribution" |
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| 50 | description = """\ |
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[3e428ec] | 51 | [Dilute Lamellar Form Factor](from a lyotropic lamellar phase) |
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| 52 | I(q)= 2*pi*P(q)/(delta *q^(2)), where |
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| 53 | P(q)=2*(contrast/q)^(2)*(1-cos(q*delta))^(2)) |
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| 54 | thickness = layer thickness |
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| 55 | sld = layer scattering length density |
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| 56 | sld_solvent = solvent scattering length density |
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| 57 | background = incoherent background |
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| 58 | scale = scale factor |
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[5d4777d] | 59 | """ |
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[a5d0d00] | 60 | category = "shape:lamellae" |
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[5d4777d] | 61 | |
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[3e428ec] | 62 | # ["name", "units", default, [lower, upper], "type","description"], |
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| 63 | parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "", |
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| 64 | "Layer scattering length density" ], |
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| 65 | ["solvent_sld", "1e-6/Ang^2", 6, [-inf, inf], "", |
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| 66 | "Solvent scattering length density" ], |
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| 67 | ["thickness", "Ang", 50, [0, inf], "volume","Bilayer thickness" ], |
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| 68 | ] |
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[5d4777d] | 69 | |
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| 70 | |
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| 71 | # No volume normalization despite having a volume parameter |
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| 72 | # This should perhaps be volume normalized? |
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| 73 | form_volume = """ |
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[994d77f] | 74 | return 1.0; |
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[5d4777d] | 75 | """ |
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| 76 | |
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| 77 | Iq = """ |
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[994d77f] | 78 | const double sub = sld - solvent_sld; |
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| 79 | const double qsq = q*q; |
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[38d8774] | 80 | // Original expression |
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| 81 | //return 4.0e-4*M_PI*sub*sub/qsq * (1.0-cos(q*thickness)) / (thickness*qsq); |
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| 82 | // const double alpha = fmod(q*thickness+0.1, 2.0*M_PI)-0.1; |
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| 83 | // Use small angle fix 1-cos(theta) = 2 sin^2(theta/2) |
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| 84 | const double sinq2 = sin(0.5*q*thickness); |
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| 85 | return 4.0e-4*M_PI*sub*sub/qsq * 2.0*sinq2*sinq2 / (thickness*qsq); |
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[5d4777d] | 86 | """ |
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| 87 | |
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| 88 | Iqxy = """ |
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[bfb195e] | 89 | return Iq(sqrt(qx*qx+qy*qy), IQ_PARAMETERS); |
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[5d4777d] | 90 | """ |
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| 91 | |
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| 92 | # ER defaults to 0.0 |
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[d547f16] | 93 | # VR defaults to 1.0 |
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| 94 | |
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[3e428ec] | 95 | demo = dict(scale=1, background=0, |
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| 96 | sld=6, solvent_sld=1, |
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| 97 | thickness=40, |
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| 98 | thickness_pd=0.2, thickness_pd_n=40) |
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[a503bfd] | 99 | oldname = 'LamellarModel' |
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| 100 | oldpars = dict(sld='sld_bi', solvent_sld='sld_sol', thickness='bi_thick') |
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[348557a] | 101 | tests = [ |
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| 102 | [ {'scale': 1.0, 'background' : 0.0, 'thickness' : 50.0, 'sld' : 1.0,'solvent_sld' : 6.3, 'thickness_pd' : 0.0, |
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| 103 | }, [0.001], [882289.54309]] |
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| 104 | ] |
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| 105 | # ADDED by: converted by PAK? (or RKH?) ON: 16Mar2016 - RKH adding unit tests from sasview to early 2015 conversion |
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| 106 | # [(qx1, qy1), (qx2, qy2), ...], [I(qx1,qy1), I(qx2,qy2), ...]], |
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