[5d4777d] | 1 | r""" |
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[40a87fa] | 2 | For information about polarised and magnetic scattering, see |
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[9a4811a] | 3 | the :ref:`magnetism` documentation. |
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[19dcb933] | 4 | |
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| 5 | Definition |
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| 6 | ---------- |
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| 7 | |
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| 8 | The 1D scattering intensity is calculated in the following way (Guinier, 1955) |
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| 9 | |
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| 10 | .. math:: |
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| 11 | |
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[eb69cce] | 12 | I(q) = \frac{\text{scale}}{V} \cdot \left[ |
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| 13 | 3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3} |
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[19dcb933] | 14 | \right]^2 + \text{background} |
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| 15 | |
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| 16 | where *scale* is a volume fraction, $V$ is the volume of the scatterer, |
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[7e6bea81] | 17 | $r$ is the radius of the sphere and *background* is the background level. |
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[49da079] | 18 | *sld* and *sld_solvent* are the scattering length densities (SLDs) of the |
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[7e6bea81] | 19 | scatterer and the solvent respectively, whose difference is $\Delta\rho$. |
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[19dcb933] | 20 | |
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| 21 | Note that if your data is in absolute scale, the *scale* should represent |
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| 22 | the volume fraction (which is unitless) if you have a good fit. If not, |
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| 23 | it should represent the volume fraction times a factor (by which your data |
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| 24 | might need to be rescaled). |
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| 25 | |
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| 26 | The 2D scattering intensity is the same as above, regardless of the |
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| 27 | orientation of $\vec q$. |
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| 28 | |
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| 29 | Validation |
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| 30 | ---------- |
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| 31 | |
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| 32 | Validation of our code was done by comparing the output of the 1D model |
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| 33 | to the output of the software provided by the NIST (Kline, 2006). |
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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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[19dcb933] | 38 | |
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[0507e09] | 39 | .. [#] A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) |
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[19dcb933] | 40 | |
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[0507e09] | 41 | Source |
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| 42 | ------ |
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| 43 | |
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| 44 | `sphere.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/sphere.py>`_ |
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| 45 | |
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| 46 | `sphere.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/sphere.c>`_ |
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| 47 | |
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| 48 | Authorship and Verification |
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| 49 | ---------------------------- |
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| 50 | |
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| 51 | * **Author:** |
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| 52 | * **Last Modified by:** |
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[ef07e95] | 53 | * **Last Reviewed by:** S King and P Parker **Date:** 2013/09/09 and 2014/01/06 |
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[0507e09] | 54 | * **Source added by :** Steve King **Date:** March 25, 2019 |
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[5d4777d] | 55 | """ |
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| 56 | |
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[2d81cfe] | 57 | import numpy as np |
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[3c56da87] | 58 | from numpy import inf |
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[5d4777d] | 59 | |
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| 60 | name = "sphere" |
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[19dcb933] | 61 | title = "Spheres with uniform scattering length density" |
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[5d4777d] | 62 | description = """\ |
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[49da079] | 63 | P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr)) |
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[eb69cce] | 64 | /(qr)^3]^2 + background |
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| 65 | r: radius of sphere |
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[19dcb933] | 66 | V: The volume of the scatter |
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| 67 | sld: the SLD of the sphere |
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[49da079] | 68 | sld_solvent: the SLD of the solvent |
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[5d4777d] | 69 | """ |
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[a5d0d00] | 70 | category = "shape:sphere" |
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[5d4777d] | 71 | |
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[3e428ec] | 72 | # ["name", "units", default, [lower, upper], "type","description"], |
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[42356c8] | 73 | parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld", |
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[3e428ec] | 74 | "Layer scattering length density"], |
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[42356c8] | 75 | ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld", |
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[3e428ec] | 76 | "Solvent scattering length density"], |
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| 77 | ["radius", "Ang", 50, [0, inf], "volume", |
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| 78 | "Sphere radius"], |
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| 79 | ] |
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[5d4777d] | 80 | |
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[b297ba9] | 81 | source = ["lib/sas_3j1x_x.c", "sphere.c"] |
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[71b751d] | 82 | have_Fq = True |
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[d277229] | 83 | effective_radius_type = ["radius"] |
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[c036ddb] | 84 | |
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[404ebbd] | 85 | def random(): |
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[b297ba9] | 86 | """Return a random parameter set for the model.""" |
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[404ebbd] | 87 | radius = 10**np.random.uniform(1.3, 4) |
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| 88 | pars = dict( |
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| 89 | radius=radius, |
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| 90 | ) |
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| 91 | return pars |
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| 92 | |
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[7e6bea81] | 93 | tests = [ |
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| 94 | [{}, 0.2, 0.726362], |
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| 95 | [{"scale": 1., "background": 0., "sld": 6., "sld_solvent": 1., |
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| 96 | "radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, |
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| 97 | 0.2, 0.228843], |
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[304c775] | 98 | [{"radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, |
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| 99 | 0.1, None, None, 120., None, 1.0], |
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[265c657] | 100 | [{"@S": "hardsphere"}, |
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[facb052] | 101 | 0.1, 0.7940350343881906], # Q=0.1 this is current value, not verified elsewhere yet |
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[265c657] | 102 | [{"@S": "hardsphere", # hard sphere structure factor |
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[0b8a1fc] | 103 | "structure_factor_mode": 1, # decoupling approximation |
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[facb052] | 104 | "effective_radius_type": 1, "radius_effective":27.0 # equivalent sphere Currently have hardwired model_test to accept radius_effective |
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| 105 | # direct_model has the name & value BUT does it get passed to S(Q)??? What about volfracion, plus the many parameters used by other S(Q) ? |
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| 106 | # effective_radius_type does NOT appear in the list, has it been stripped out??? |
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[265c657] | 107 | }, 0.1, 0.7940350343881906], |
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[facb052] | 108 | # [{"@S": "hardsphere", # hard sphere structure factor |
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| 109 | # "structure_factor_mode": 3, # - WHY same result? |
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| 110 | # "effective_radius_type": 3, "radius_effective":23.0 # |
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| 111 | # }, 0.1, 0.7940350343881906] |
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[7e6bea81] | 112 | ] |
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[2464785] | 113 | # putting None for expected result will pass the test if there are no errors from the routine, but without any check on the value of the result |
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