1 | r""" |
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2 | |
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3 | Definition |
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4 | ---------- |
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5 | This model provides the form factor for a circular cylinder with a core-shell |
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6 | scattering length density profile. The form factor is normalized by the |
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7 | particle volume. |
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8 | |
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9 | .. _core-shell-bicelle-geometry: |
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10 | |
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11 | .. figure:: img/core_shell_bicelle_geometry.png |
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12 | |
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13 | (Graphic from DOI: 10.1039/C0NP00002G) |
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14 | |
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15 | |
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16 | The output of the 1D scattering intensity function for randomly oriented |
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17 | cylinders is then given by the equation above. |
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18 | |
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19 | The *theta* and *phi* parameters are not used for the 1D output. |
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20 | Our implementation of the scattering kernel and the 1D scattering intensity |
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21 | use the c-library from NIST. |
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22 | |
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23 | .. figure:: img/cylinder_angle_definition.jpg |
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24 | |
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25 | Definition of the angles for the oriented core shell bicelle tmodel. |
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26 | |
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27 | .. figure:: img/cylinder_angle_projection.jpg |
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28 | |
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29 | Examples of the angles for oriented pp against the detector plane. |
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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 | L A Feigin and D I Svergun, |
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35 | *Structure Analysis by Small-Angle X-Ray and Neutron Scattering,* |
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36 | Plenum Press, New York, (1987) |
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37 | |
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38 | """ |
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39 | |
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40 | from numpy import inf, sin, cos |
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41 | |
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42 | name = "core_shell_bicelle" |
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43 | title = "Circular cylinder with a core-shell scattering length density profile.." |
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44 | description = """ |
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45 | P(q,alpha)= scale/Vs*f(q)^(2) + bkg, where: f(q)= 2(core_sld |
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46 | - solvant_sld)* Vc*sin[qLcos(alpha/2)] |
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47 | /[qLcos(alpha/2)]*J1(qRsin(alpha)) |
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48 | /[qRsin(alpha)]+2(shell_sld-solvent_sld) |
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49 | *Vs*sin[q(L+T)cos(alpha/2)][[q(L+T) |
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50 | *cos(alpha/2)]*J1(q(R+T)sin(alpha)) |
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51 | /q(R+T)sin(alpha)] |
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52 | |
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53 | alpha:is the angle between the axis of |
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54 | the cylinder and the q-vector |
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55 | Vs: the volume of the outer shell |
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56 | Vc: the volume of the core |
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57 | L: the length of the core |
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58 | shell_sld: the scattering length density |
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59 | of the shell |
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60 | solvent_sld: the scattering length density |
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61 | of the solvent |
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62 | bkg: the background |
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63 | T: the thickness |
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64 | R+T: is the outer radius |
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65 | L+2T: The total length of the outershell |
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66 | J1: the first order Bessel function |
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67 | theta: axis_theta of the cylinder |
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68 | phi: the axis_phi of the cylinder... |
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69 | """ |
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70 | category = "shape:cylinder" |
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71 | |
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72 | # pylint: disable=bad-whitespace, line-too-long |
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73 | # ["name", "units", default, [lower, upper], "type", "description"], |
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74 | parameters = [ |
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75 | ["radius", "Ang", 20, [0, inf], "volume", "Cylinder core radius"], |
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76 | ["rim_thickness", "Ang", 10, [0, inf], "volume", "Rim shell thickness"], |
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77 | ["face_thickness", "Ang", 10, [0, inf], "volume", "Cylinder face thickness"], |
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78 | ["length", "Ang", 400, [0, inf], "volume", "Cylinder length"], |
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79 | ["core_sld", "1e-6/Ang^2", 1, [-inf, inf], "", "Cylinder core scattering length density"], |
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80 | ["face_sld", "1e-6/Ang^2", 4, [-inf, inf], "", "Cylinder face scattering length density"], |
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81 | ["rim_sld", "1e-6/Ang^2", 4, [-inf, inf], "", "Cylinder rim scattering length density"], |
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82 | ["solvent_sld", "1e-6/Ang^2", 1, [-inf, inf], "", "Solvent scattering length density"], |
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83 | ["theta", "degrees", 90, [-inf, inf], "orientation", "In plane angle"], |
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84 | ["phi", "degrees", 0, [-inf, inf], "orientation", "Out of plane angle"], |
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85 | ] |
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86 | |
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87 | # pylint: enable=bad-whitespace, line-too-long |
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88 | |
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89 | source = ["lib/Si.c","lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "core_shell_bicelle.c"] |
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90 | |
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91 | demo = dict(scale=1, background=0, |
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92 | radius=20.0, |
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93 | rim_thickness=10.0, |
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94 | face_thickness=10.0, |
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95 | length=400.0, |
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96 | core_sld=1.0, |
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97 | face_sld=4.0, |
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98 | rim_sld=4.0, |
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99 | solvent_sld=1.0, |
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100 | theta=90, |
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101 | phi=0) |
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102 | |
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103 | oldname = 'CoreShellBicelleModel' |
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104 | |
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105 | oldpars = dict(rim_thickness='rim_thick', |
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106 | face_thickness='face_thick', |
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107 | theta='axis_theta', |
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108 | phi='axis_phi') |
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109 | |
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110 | qx, qy = 0.4 * cos(90), 0.5 * sin(0) |
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111 | tests = [ |
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112 | # Accuracy tests based on content in test/utest_other_models.py |
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113 | [{'radius': 20.0, |
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114 | 'rim_thickness': 10.0, |
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115 | 'face_thickness': 10.0, |
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116 | 'length': 400.0, |
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117 | 'core_sld': 1.0, |
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118 | 'face_sld': 4.0, |
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119 | 'rim_sld': 4.0, |
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120 | 'solvent_sld': 1.0, |
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121 | 'background': 0.0, |
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122 | }, 0.001, 353.550], |
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123 | |
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124 | [{'radius': 20.0, |
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125 | 'rim_thickness': 10.0, |
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126 | 'face_thickness': 10.0, |
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127 | 'length': 400.0, |
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128 | 'core_sld': 1.0, |
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129 | 'face_sld': 4.0, |
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130 | 'rim_sld': 4.0, |
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131 | 'solvent_sld': 1.0, |
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132 | 'theta': 90.0, |
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133 | 'phi': 0.0, |
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134 | 'background': 0.00, |
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135 | }, (qx, qy), 24.9167], |
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136 | |
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137 | # Additional tests with larger range of parameters |
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138 | [{'radius': 3.0, |
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139 | 'rim_thickness': 100.0, |
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140 | 'face_thickness': 100.0, |
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141 | 'length': 1200.0, |
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142 | 'core_sld': 5.0, |
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143 | 'face_sld': 41.0, |
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144 | 'rim_sld': 42.0, |
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145 | 'solvent_sld': 21.0, |
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146 | }, 0.05, 1670.1828], |
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147 | ] |
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