[dc02af0] | 1 | # Note: model title and parameter table are inserted automatically |
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| 2 | r""" |
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| 3 | This model provides the scattering intensity, *I(q)*, for a lyotropic lamellar phase where a random distribution in |
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| 4 | solution are assumed. The SLD of the head region is taken to be different from the SLD of the tail region. |
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| 5 | |
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| 6 | *2.1.31.1. Definition* |
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| 7 | |
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| 8 | The scattering intensity *I(q)* is |
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| 9 | |
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| 10 | .. math:: |
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| 11 | |
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| 12 | I(Q) = 2\pi{P(Q) \over (2(|delta|\ H +|delta|\ T) Q^2) |
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| 13 | |
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| 14 | The form factor is |
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| 15 | |
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| 16 | .. image:: img/lamellarFFHG_.jpg |
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| 17 | |
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| 18 | where |delta|\ T = tail length (or *tail_length*), |delta|\ H = head thickness (or *h_thickness*), |
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| 19 | |drho|\ H = SLD(headgroup) - SLD(solvent), and |drho|\ T = SLD(tail) - SLD(solvent). |
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| 20 | |
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| 21 | The 2D scattering intensity is calculated in the same way as 1D, where the *q* vector is defined as |
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| 22 | |
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| 23 | .. math:: |
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| 24 | |
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| 25 | Q = \sqrt{Q_x^2 + Q_y^2} |
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| 26 | |
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| 27 | The returned value is in units of |cm^-1|, on absolute scale. In the parameters, *sld_tail* = SLD of the tail group, |
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| 28 | and *sld_head* = SLD of the head group. |
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| 29 | |
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| 30 | ============== ======== ============= |
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| 31 | Parameter name Units Default value |
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| 32 | ============== ======== ============= |
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| 33 | background |cm^-1| 0.0 |
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| 34 | head_sld |Ang^-2| 3e-06 |
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| 35 | scale None 1 |
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| 36 | solvent_sld |Ang^-2| 6e-06 |
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| 37 | head_length |Ang| 10 |
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| 38 | tail_length |Ang| 15 |
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| 39 | sld (tail) |Ang^-2| 0 |
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| 40 | ============== ======== ============= |
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| 41 | |
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| 42 | .. image:: img/lamellarFFHG_138.jpg |
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| 43 | |
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| 44 | *Figure. 1D plot using the default values (w/1000 data point).* |
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| 45 | |
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| 46 | Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research |
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| 47 | (Kline, 2006). |
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| 48 | |
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| 49 | REFERENCE |
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| 50 | |
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| 51 | F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502 |
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| 52 | |
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| 53 | also in J. Phys. Chem. B, 105, (2001) 11081-11088 |
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| 54 | |
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| 55 | *2014/04/17 - Description reviewed by S King and P Butler.* |
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| 56 | """ |
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| 57 | |
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| 58 | from numpy import pi, inf |
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| 59 | |
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| 60 | name = "lamellar_FFHG" |
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| 61 | title = "Random lamellar phase with Head Groups " |
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| 62 | description = """\ |
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| 63 | [Random lamellar phase with Head Groups] |
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| 64 | I(q)= 2*pi*P(q)/(2(H+T)*q^(2)), where |
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| 65 | P(q)= see manual |
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| 66 | layer thickness =(H+T+T+H) = 2(Head+Tail) |
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| 67 | sld = Tail scattering length density |
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| 68 | sld_head = Head scattering length density |
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| 69 | sld_solvent = solvent scattering length density |
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| 70 | background = incoherent background |
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| 71 | scale = scale factor |
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| 72 | """ |
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[a5d0d00] | 73 | category = "shape:lamellae" |
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[dc02af0] | 74 | |
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| 75 | parameters = [ |
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| 76 | # [ "name", "units", default, [lower, upper], "type", |
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| 77 | # "description" ], |
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| 78 | [ "tail_length", "Ang", 15, [0, inf], "volume", |
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| 79 | "Tail thickness" ], |
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| 80 | [ "head_length", "Ang", 10, [0, inf], "volume", |
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| 81 | "head thickness" ], |
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| 82 | [ "sld", "1e-6/Ang^2", 0.4, [-inf,inf], "", |
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| 83 | "Tail scattering length density" ], |
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| 84 | [ "head_sld", "1e-6/Ang^2", 3.0, [-inf,inf], "", |
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| 85 | "Head scattering length density" ], |
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| 86 | [ "solvent_sld", "1e-6/Ang^2", 6, [-inf,inf], "", |
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| 87 | "Solvent scattering length density" ], |
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| 88 | ] |
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| 89 | |
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| 90 | # No volume normalization despite having a volume parameter |
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| 91 | # This should perhaps be volume normalized? |
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| 92 | form_volume = """ |
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| 93 | return 1.0; |
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| 94 | """ |
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| 95 | |
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| 96 | Iq = """ |
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| 97 | const double qsq = q*q; |
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| 98 | const double drh = head_sld - solvent_sld; |
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| 99 | const double drt = sld - solvent_sld; //correction 13FEB06 by L.Porcar |
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| 100 | const double qT = q*tail_length; |
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| 101 | double Pq, inten; |
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| 102 | Pq = drh*(sin(q*(head_length+tail_length))-sin(qT)) + drt*sin(qT); |
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| 103 | Pq *= Pq; |
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| 104 | Pq *= 4.0/(qsq); |
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| 105 | |
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| 106 | inten = 2.0e-4*M_PI*Pq/qsq; |
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| 107 | |
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| 108 | return inten /= 2.0*(head_length+tail_length); //normalize by the bilayer thickness |
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| 109 | |
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| 110 | """ |
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| 111 | |
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| 112 | Iqxy = """ |
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| 113 | // never called since no orientation or magnetic parameters. |
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| 114 | return -1.0; |
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| 115 | """ |
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| 116 | |
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| 117 | # ER defaults to 0.0 |
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| 118 | # VR defaults to 1.0 |
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| 119 | |
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| 120 | demo = dict( |
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| 121 | scale=1, background=0, |
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| 122 | tail_length=15,head_length=10, |
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| 123 | sld=0.4, head_sld=3.0, solvent_sld=6.0, |
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| 124 | tail_length_pd= 0.2, tail_length_pd_n=40, |
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| 125 | head_length_pd= 0.01, head_length_pd_n=40, |
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| 126 | ) |
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| 127 | oldname = 'LamellarFFHGModel' |
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| 128 | oldpars = dict(head_length='h_thickness', sld='sld_tail', head_sld='sld_head', solvent_sld='sld_solvent') |
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| 129 | |
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