[d1fe925] | 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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| 7 | The scattering intensity *I(Q)* is |
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| 8 | |
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| 9 | .. math:: |
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| 10 | |
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| 11 | I(Q) = 2\pi{P(Q) \over \delta Q^2} |
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| 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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| 18 | P(Q) = {2\Delta\rho^2 \over Q^2}(1-cos(Q\delta)) |
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| 19 | |
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| 20 | |
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| 21 | where |delta| = bilayer thickness. |
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| 22 | |
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| 23 | The 2D scattering intensity is calculated in the same way as 1D, where the $Q$ vector is defined as |
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| 24 | |
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| 25 | .. math:: |
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| 26 | |
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| 27 | Q = \sqrt{Q_x^2 + Q_y^2} |
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| 28 | |
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| 29 | |
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| 30 | |
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| 31 | Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research |
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| 32 | (Kline, 2006). |
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| 33 | |
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| 34 | .. figure:: img/lamellar_1d.jpg |
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| 35 | |
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| 36 | 1D plot using the default values (w/1000 data point). |
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| 37 | |
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| 38 | |
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| 39 | Reference |
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| 40 | --------- |
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| 41 | |
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| 42 | F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502 |
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| 43 | |
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| 44 | also in J. Phys. Chem. B, 105, (2001) 11081-11088 |
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| 45 | |
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| 46 | |
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| 47 | """ |
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| 48 | |
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| 49 | from numpy import inf |
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| 50 | |
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| 51 | name = "lamellar" |
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| 52 | title = "Lyotropic lamellar phase with uniform SLD and random distribution" |
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| 53 | description = """\ |
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| 54 | [Dilute Lamellar Form Factor](from a lyotropic lamellar phase) |
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| 55 | I(q)= 2*pi*P(q)/(delta *q^(2)), where |
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| 56 | P(q)=2*(contrast/q)^(2)*(1-cos(q*delta))^(2)) |
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| 57 | thickness = layer thickness |
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| 58 | sld = layer scattering length density |
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| 59 | sld_solvent = solvent scattering length density |
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| 60 | background = incoherent background |
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| 61 | scale = scale factor |
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| 62 | """ |
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| 63 | category = "shape:lamellae" |
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| 64 | |
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| 65 | # ["name", "units", default, [lower, upper], "type","description"], |
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| 66 | parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "", |
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| 67 | "Layer scattering length density" ], |
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| 68 | ["solvent_sld", "1e-6/Ang^2", 6, [-inf, inf], "", |
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| 69 | "Solvent scattering length density" ], |
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| 70 | ["thickness", "Ang", 50, [0, inf], "volume","Bilayer thickness" ], |
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| 71 | ] |
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| 72 | |
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| 73 | |
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| 74 | # No volume normalization despite having a volume parameter |
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| 75 | # This should perhaps be volume normalized? |
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| 76 | form_volume = """ |
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| 77 | return 1.0; |
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| 78 | """ |
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| 79 | |
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| 80 | Iq = """ |
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| 81 | const double sub = sld - solvent_sld; |
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| 82 | const double qsq = q*q; |
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| 83 | return 4.0e-4*M_PI*sub*sub/qsq * (1.0-cos(q*thickness)) |
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| 84 | / (thickness*qsq); |
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| 85 | """ |
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| 86 | |
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| 87 | Iqxy = """ |
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| 88 | return Iq(sqrt(qx*qx+qy*qy), IQ_PARAMETERS); |
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| 89 | """ |
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| 90 | |
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| 91 | # ER defaults to 0.0 |
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| 92 | # VR defaults to 1.0 |
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| 93 | |
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| 94 | demo = dict(scale=1, background=0, |
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| 95 | sld=6, solvent_sld=1, |
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| 96 | thickness=40, |
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| 97 | thickness_pd=0.2, thickness_pd_n=40) |
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| 98 | oldname = 'LamellarModel' |
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| 99 | oldpars = dict(sld='sld_bi', solvent_sld='sld_sol', thickness='bi_thick') |
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| 100 | |
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