[ec392464] | 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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[da456fb] | 6 | .. _SANS_Calculator_Tool: |
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| 7 | |
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[a9dc4eb] | 8 | Generic SANS Calculator Tool |
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| 9 | ============================ |
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[ec392464] | 10 | |
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[a9dc4eb] | 11 | Description |
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| 12 | ----------- |
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[ec392464] | 13 | |
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[a9dc4eb] | 14 | This tool attempts to simulate the SANS expected from a specified |
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| 15 | shape/structure or scattering length density profile. The tool can |
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| 16 | handle both nuclear and magnetic contributions to the scattering. |
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[850c753] | 17 | |
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[a9dc4eb] | 18 | Theory |
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| 19 | ------ |
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[ec392464] | 20 | |
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[850c753] | 21 | In general, a particle with a volume *V* can be described by an ensemble |
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| 22 | containing *N* 3-dimensional rectangular pixels where each pixel is much |
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| 23 | smaller than *V*. |
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[ec392464] | 24 | |
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[850c753] | 25 | Assuming that all the pixel sizes are the same, the elastic scattering |
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| 26 | intensity from the particle is |
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[ec392464] | 27 | |
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| 28 | .. image:: gen_i.gif |
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| 29 | |
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[850c753] | 30 | Equation 1. |
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| 31 | |
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| 32 | where |beta|\ :sub:`j` and *r*\ :sub:`j` are the scattering length density and |
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| 33 | the position of the j'th pixel respectively. |
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| 34 | |
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| 35 | The total volume *V* |
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[ec392464] | 36 | |
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| 37 | .. image:: v_j.gif |
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| 38 | |
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[850c753] | 39 | for |beta|\ :sub:`j` |noteql|\0 where *v*\ :sub:`j` is the volume of the j'th |
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| 40 | pixel (or the j'th natural atomic volume (= atomic mass / (natural molar |
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| 41 | density * Avogadro number) for the atomic structures). |
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| 42 | |
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| 43 | *V* can be corrected by users. This correction is useful especially for an |
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| 44 | atomic structure (such as taken from a PDB file) to get the right normalization. |
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| 45 | |
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| 46 | *NOTE!* |beta|\ :sub:`j` *displayed in the GUI may be incorrect but this will not |
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| 47 | affect the scattering computation if the correction of the total volume V is made.* |
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| 48 | |
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| 49 | The scattering length density (SLD) of each pixel, where the SLD is uniform, is |
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| 50 | a combination of the nuclear and magnetic SLDs and depends on the spin states |
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| 51 | of the neutrons as follows. |
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| 52 | |
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[a9dc4eb] | 53 | Magnetic Scattering |
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| 54 | ^^^^^^^^^^^^^^^^^^^ |
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[850c753] | 55 | |
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| 56 | For magnetic scattering, only the magnetization component, *M*\ :sub:`perp`\ , |
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| 57 | perpendicular to the scattering vector *Q* contributes to the magnetic |
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| 58 | scattering length. |
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[ec392464] | 59 | |
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| 60 | .. image:: mag_vector.bmp |
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| 61 | |
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| 62 | The magnetic scattering length density is then |
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| 63 | |
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| 64 | .. image:: dm_eq.gif |
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| 65 | |
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[850c753] | 66 | where the gyromagnetic ratio |gamma| = -1.913, |mu|\ :sub:`B` is the Bohr |
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| 67 | magneton, *r*\ :sub:`0` is the classical radius of electron, and |sigma| is the |
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| 68 | Pauli spin. |
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[ec392464] | 69 | |
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[850c753] | 70 | For a polarized neutron, the magnetic scattering is depending on the spin states. |
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[ec392464] | 71 | |
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[850c753] | 72 | Let us consider that the incident neutrons are polarised both parallel (+) and |
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| 73 | anti-parallel (-) to the x' axis (see below). The possible states after |
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| 74 | scattering from the sample are then |
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[ec392464] | 75 | |
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[850c753] | 76 | * Non-spin flips: (+ +) and (- -) |
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| 77 | * Spin flips: (+ -) and (- +) |
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[ec392464] | 78 | |
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| 79 | .. image:: gen_mag_pic.bmp |
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| 80 | |
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[850c753] | 81 | Now let us assume that the angles of the *Q* vector and the spin-axis (x') |
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| 82 | to the x-axis are |phi| and |theta|\ :sub:`up` respectively (see above). Then, |
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[ec392464] | 83 | depending upon the polarization (spin) state of neutrons, the scattering |
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[850c753] | 84 | length densities, including the nuclear scattering length density (|beta|\ :sub:`N`\ ) |
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| 85 | are given as |
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[ec392464] | 86 | |
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[850c753] | 87 | * for non-spin-flips |
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[ec392464] | 88 | |
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[850c753] | 89 | .. image:: sld1.gif |
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[ec392464] | 90 | |
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[850c753] | 91 | * for spin-flips |
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| 92 | |
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| 93 | .. image:: sld2.gif |
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[ec392464] | 94 | |
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| 95 | where |
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| 96 | |
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| 97 | .. image:: mxp.gif |
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| 98 | |
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| 99 | .. image:: myp.gif |
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| 100 | |
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| 101 | .. image:: mzp.gif |
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| 102 | |
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| 103 | .. image:: mqx.gif |
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| 104 | |
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| 105 | .. image:: mqy.gif |
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| 106 | |
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[850c753] | 107 | Here the *M0*\ :sub:`x`\ , *M0*\ :sub:`y` and *M0*\ :sub:`z` are the x, y and z |
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| 108 | components of the magnetisation vector in the laboratory xyz frame. |
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[ec392464] | 109 | |
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| 110 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 111 | |
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[a9dc4eb] | 112 | Using the tool |
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| 113 | -------------- |
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[ec392464] | 114 | |
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| 115 | .. image:: gen_gui_help.bmp |
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| 116 | |
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[850c753] | 117 | After computation the result will appear in the *Theory* box in the SasView |
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| 118 | *Data Explorer* panel. |
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| 119 | |
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| 120 | *Up_frac_in* and *Up_frac_out* are the ratio |
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[ec392464] | 121 | |
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[850c753] | 122 | (spin up) / (spin up + spin down) |
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| 123 | |
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| 124 | of neutrons before the sample and at the analyzer, respectively. |
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[ec392464] | 125 | |
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[850c753] | 126 | *NOTE 1. The values of* Up_frac_in *and* Up_frac_out *must be in the range |
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| 127 | 0.0 to 1.0. Both values are 0.5 for unpolarized neutrons.* |
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[ec392464] | 128 | |
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[850c753] | 129 | *NOTE 2. This computation is totally based on the pixel (or atomic) data fixed |
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| 130 | in xyz coordinates. No angular orientational averaging is considered.* |
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| 131 | |
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| 132 | *NOTE 3. For the nuclear scattering length density, only the real component |
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[ec392464] | 133 | is taken account.* |
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| 134 | |
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| 135 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 136 | |
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[a9dc4eb] | 137 | Using PDB/OMF or SLD files |
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| 138 | -------------------------- |
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[ec392464] | 139 | |
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[a9dc4eb] | 140 | The SANS Calculator tool can read some PDB, OMF or SLD files but ignores |
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[850c753] | 141 | polarized/magnetic scattering when doing so, thus related parameters such as |
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| 142 | *Up_frac_in*, etc, will be ignored. |
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[ec392464] | 143 | |
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[850c753] | 144 | The calculation for fixed orientation uses Equation 1 above resulting in a 2D |
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| 145 | output, whereas the scattering calculation averaged over all the orientations |
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| 146 | uses the Debye equation below providing a 1D output |
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[ec392464] | 147 | |
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| 148 | .. image:: gen_debye_eq.gif |
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| 149 | |
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[850c753] | 150 | where *v*\ :sub:`j` |beta|\ :sub:`j` |equiv| *b*\ :sub:`j` is the scattering |
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| 151 | length of the j'th atom. The calculation output is passed to the *Data Explorer* |
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| 152 | for further use. |
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[ec392464] | 153 | |
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| 154 | .. image:: pdb_combo.jpg |
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[850c753] | 155 | |
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| 156 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 157 | |
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[a9dc4eb] | 158 | .. note:: This help document was last changed by Steve King, 01May2015 |
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