1 | .. sas_calculator_help.rst |
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2 | |
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3 | .. This is a port of the original SasView html help file to ReSTructured text |
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4 | .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. |
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5 | |
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6 | .. |beta| unicode:: U+03B2 |
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7 | .. |gamma| unicode:: U+03B3 |
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8 | .. |theta| unicode:: U+03B8 |
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9 | .. |mu| unicode:: U+03BC |
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10 | .. |sigma| unicode:: U+03C3 |
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11 | .. |phi| unicode:: U+03C6 |
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12 | |
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13 | .. |equiv| unicode:: U+2261 |
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14 | .. |noteql| unicode:: U+2260 |
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15 | |
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16 | Generic SANS Calculator Tool |
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17 | ============================ |
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18 | |
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19 | Description |
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20 | ----------- |
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21 | |
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22 | This tool attempts to simulate the SANS expected from a specified |
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23 | shape/structure or scattering length density profile. The tool can |
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24 | handle both nuclear and magnetic contributions to the scattering. |
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25 | |
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26 | Theory |
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27 | ------ |
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28 | |
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29 | In general, a particle with a volume *V* can be described by an ensemble |
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30 | containing *N* 3-dimensional rectangular pixels where each pixel is much |
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31 | smaller than *V*. |
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32 | |
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33 | Assuming that all the pixel sizes are the same, the elastic scattering |
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34 | intensity from the particle is |
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35 | |
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36 | .. image:: gen_i.gif |
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37 | |
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38 | Equation 1. |
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39 | |
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40 | where |beta|\ :sub:`j` and *r*\ :sub:`j` are the scattering length density and |
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41 | the position of the j'th pixel respectively. |
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42 | |
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43 | The total volume *V* |
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44 | |
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45 | .. image:: v_j.gif |
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46 | |
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47 | for |beta|\ :sub:`j` |noteql|\0 where *v*\ :sub:`j` is the volume of the j'th |
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48 | pixel (or the j'th natural atomic volume (= atomic mass / (natural molar |
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49 | density * Avogadro number) for the atomic structures). |
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50 | |
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51 | *V* can be corrected by users. This correction is useful especially for an |
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52 | atomic structure (such as taken from a PDB file) to get the right normalization. |
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53 | |
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54 | *NOTE!* |beta|\ :sub:`j` *displayed in the GUI may be incorrect but this will not |
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55 | affect the scattering computation if the correction of the total volume V is made.* |
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56 | |
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57 | The scattering length density (SLD) of each pixel, where the SLD is uniform, is |
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58 | a combination of the nuclear and magnetic SLDs and depends on the spin states |
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59 | of the neutrons as follows. |
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60 | |
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61 | Magnetic Scattering |
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62 | ^^^^^^^^^^^^^^^^^^^ |
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63 | |
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64 | For magnetic scattering, only the magnetization component, *M*\ :sub:`perp`\ , |
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65 | perpendicular to the scattering vector *Q* contributes to the magnetic |
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66 | scattering length. |
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67 | |
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68 | .. image:: mag_vector.bmp |
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69 | |
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70 | The magnetic scattering length density is then |
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71 | |
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72 | .. image:: dm_eq.gif |
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73 | |
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74 | where the gyromagnetic ratio |gamma| = -1.913, |mu|\ :sub:`B` is the Bohr |
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75 | magneton, *r*\ :sub:`0` is the classical radius of electron, and |sigma| is the |
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76 | Pauli spin. |
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77 | |
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78 | For a polarized neutron, the magnetic scattering is depending on the spin states. |
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79 | |
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80 | Let us consider that the incident neutrons are polarised both parallel (+) and |
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81 | anti-parallel (-) to the x' axis (see below). The possible states after |
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82 | scattering from the sample are then |
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83 | |
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84 | * Non-spin flips: (+ +) and (- -) |
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85 | * Spin flips: (+ -) and (- +) |
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86 | |
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87 | .. image:: gen_mag_pic.bmp |
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88 | |
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89 | Now let us assume that the angles of the *Q* vector and the spin-axis (x') |
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90 | to the x-axis are |phi| and |theta|\ :sub:`up` respectively (see above). Then, |
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91 | depending upon the polarization (spin) state of neutrons, the scattering |
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92 | length densities, including the nuclear scattering length density (|beta|\ :sub:`N`\ ) |
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93 | are given as |
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94 | |
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95 | * for non-spin-flips |
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96 | |
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97 | .. image:: sld1.gif |
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98 | |
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99 | * for spin-flips |
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100 | |
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101 | .. image:: sld2.gif |
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102 | |
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103 | where |
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104 | |
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105 | .. image:: mxp.gif |
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106 | |
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107 | .. image:: myp.gif |
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108 | |
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109 | .. image:: mzp.gif |
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110 | |
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111 | .. image:: mqx.gif |
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112 | |
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113 | .. image:: mqy.gif |
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114 | |
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115 | Here the *M0*\ :sub:`x`\ , *M0*\ :sub:`y` and *M0*\ :sub:`z` are the x, y and z |
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116 | components of the magnetisation vector in the laboratory xyz frame. |
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117 | |
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118 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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119 | |
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120 | Using the tool |
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121 | -------------- |
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122 | |
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123 | .. image:: gen_gui_help.bmp |
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124 | |
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125 | After computation the result will appear in the *Theory* box in the SasView |
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126 | *Data Explorer* panel. |
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127 | |
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128 | *Up_frac_in* and *Up_frac_out* are the ratio |
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129 | |
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130 | (spin up) / (spin up + spin down) |
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131 | |
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132 | of neutrons before the sample and at the analyzer, respectively. |
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133 | |
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134 | *NOTE 1. The values of* Up_frac_in *and* Up_frac_out *must be in the range |
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135 | 0.0 to 1.0. Both values are 0.5 for unpolarized neutrons.* |
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136 | |
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137 | *NOTE 2. This computation is totally based on the pixel (or atomic) data fixed |
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138 | in xyz coordinates. No angular orientational averaging is considered.* |
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139 | |
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140 | *NOTE 3. For the nuclear scattering length density, only the real component |
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141 | is taken account.* |
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142 | |
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143 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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144 | |
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145 | Using PDB/OMF or SLD files |
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146 | -------------------------- |
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147 | |
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148 | The SANS Calculator tool can read some PDB, OMF or SLD files but ignores |
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149 | polarized/magnetic scattering when doing so, thus related parameters such as |
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150 | *Up_frac_in*, etc, will be ignored. |
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151 | |
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152 | The calculation for fixed orientation uses Equation 1 above resulting in a 2D |
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153 | output, whereas the scattering calculation averaged over all the orientations |
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154 | uses the Debye equation below providing a 1D output |
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155 | |
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156 | .. image:: gen_debye_eq.gif |
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157 | |
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158 | where *v*\ :sub:`j` |beta|\ :sub:`j` |equiv| *b*\ :sub:`j` is the scattering |
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159 | length of the j'th atom. The calculation output is passed to the *Data Explorer* |
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160 | for further use. |
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161 | |
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162 | .. image:: pdb_combo.jpg |
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163 | |
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164 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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165 | |
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166 | .. note:: This help document was last changed by Steve King, 01May2015 |
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