1 | r""" |
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2 | Definition |
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3 | ---------- |
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4 | |
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5 | The large and small spheres have their own SLD, as well as the solvent. The |
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6 | surface coverage term is a fractional coverage (maximum of approximately 0.9 |
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7 | for hexagonally-packed spheres on a surface). Since not all of the small |
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8 | spheres are necessarily attached to the surface, the excess free (small) |
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9 | spheres scattering is also included in the calculation. The function calculate |
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10 | follows equations (8)-(12) of the reference below, and the equations are not |
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11 | reproduced here. |
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12 | |
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13 | No inter-particle scattering is included in this model. |
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14 | |
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15 | |
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16 | .. figure:: img/raspberry_geometry.jpg |
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17 | |
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18 | Schematic of the raspberry model |
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19 | |
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20 | where *Ro* is the radius of the large sphere, *Rp* the radius of the smaller |
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21 | spheres on the surface and |delta| = the fractional penetration depth. |
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22 | |
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23 | For 2D data: The 2D scattering intensity is calculated in the same way as 1D, |
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24 | where the *q* vector is defined as |
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25 | |
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26 | .. math:: |
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27 | |
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28 | q = \sqrt{q_x^2 + q_y^2} |
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29 | |
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30 | |
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31 | References |
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32 | ---------- |
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33 | |
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34 | K Larson-Smith, A Jackson, and D C Pozzo, *Small angle scattering model for Pickering emulsions and raspberry* |
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35 | *particles*, *Journal of Colloid and Interface Science*, 343(1) (2010) 36-41 |
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36 | |
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37 | **Author:** Andrew jackson **on:** 2008 |
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38 | |
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39 | **Modified by:** Paul Butler **on:** March 18, 2016 |
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40 | |
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41 | **Reviewed by:** Paul Butler **on:** March 18, 2016 |
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42 | """ |
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43 | |
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44 | from numpy import pi, inf |
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45 | |
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46 | name = "raspberry" |
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47 | title = "Calculates the form factor, *P(q)*, for a 'Raspberry-like' structure \ |
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48 | where there are smaller spheres at the surface of a larger sphere, such as the \ |
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49 | structure of a Pickering emulsion." |
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50 | description = """ |
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51 | RaspBerryModel: |
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52 | volf_Lsph = volume fraction large spheres |
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53 | radius_Lsph = radius large sphere (A) |
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54 | sld_Lsph = sld large sphere (A-2) |
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55 | volf_Ssph = volume fraction small spheres |
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56 | radius_Ssph = radius small sphere (A) |
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57 | surfrac_Ssph = fraction of small spheres at surface |
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58 | sld_Ssph = sld small sphere |
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59 | delta_Ssph = small sphere penetration (A) |
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60 | sld_solv = sld solvent |
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61 | background = background (cm-1) |
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62 | Ref: J. coll. inter. sci. (2010) vol. 343 (1) pp. 36-41.""" |
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63 | category = "shape:sphere" |
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64 | |
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65 | # [ "name", "units", default, [lower, upper], "type", "description"], |
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66 | parameters = [["sld_lg", "1e-6/Ang^2", -0.4, [-inf, inf], "", |
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67 | "large particle scattering length density"], |
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68 | ["sld_sm", "1e-6/Ang^2", 3.5, [-inf, inf], "", |
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69 | "small particle scattering length density"], |
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70 | ["sld_solvent", "1e-6/Ang^2", 6.36, [-inf, inf], "", |
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71 | "solvent scattering length density"], |
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72 | ["volfraction_lg", "", 0.05, [-inf, inf], "", |
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73 | "volume fraction of large spheres"], |
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74 | ["volfraction_sm", "", 0.005, [-inf, inf], "", |
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75 | "volume fraction of small spheres"], |
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76 | ["surf_fraction", "", 0.4, [-inf, inf], "", |
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77 | "fraction of small spheres at surface"], |
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78 | ["radius_lg", "Ang", 5000, [0, inf], "volume", |
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79 | "radius of large spheres"], |
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80 | ["radius_sm", "Ang", 100, [0, inf], "", |
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81 | "radius of small spheres"], |
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82 | ["penetration", "Ang", 0.0, [0, inf], "", |
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83 | "penetration depth of small spheres into large sphere"], |
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84 | ] |
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85 | |
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86 | source = ["lib/sph_j1c.c", "raspberry.c"] |
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87 | |
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88 | # parameters for demo |
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89 | demo = dict(scale=1, background=0.001, |
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90 | sld_lg=-0.4, sld_sm=3.5, sld_solvent=6.36, |
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91 | volfraction_lg=0.05, volfraction_sm=0.005, surf_fraction=0.4, |
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92 | radius_lg=5000, radius_sm=100, penetration=0.0, |
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93 | radius_lg_pd=.2, radius_lg_pd_n=10) |
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94 | |
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95 | # For testing against the old sasview models, include the converted parameter |
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96 | # names and the target sasview model name. |
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97 | oldname = 'RaspBerryModel' |
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98 | oldpars = dict(sld_lg='sld_Lsph', sld_sm='sld_Ssph', sld_solvent='sld_solv', |
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99 | volfraction_lg='volf_Lsph', volfraction_sm='volf_Ssph', |
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100 | surf_fraction='surfrac_Ssph', |
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101 | radius_lg='radius_Lsph', radius_sm='radius_Ssph', |
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102 | penetration='delta_Ssph') |
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103 | |
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104 | |
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105 | # NOTE: test results taken from values returned by SasView 3.1.2, with |
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106 | # 0.001 added for a non-zero default background. |
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107 | tests = [[{}, 0.0412755102041, 0.286669115234], |
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108 | [{}, 0.5, 0.00103818393658], |
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109 | ] |
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