[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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| 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 Scattering Calculator Tool |
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| 17 | ================================== |
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| 18 | |
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| 19 | Polarization and Magnetic Scattering |
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| 20 | |
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| 21 | Theory_ |
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| 22 | GUI_ |
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| 23 | PDB_Data_ |
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| 24 | |
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| 25 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 26 | |
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| 27 | .. _Theory: |
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| 28 | |
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| 29 | Theory |
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| 30 | ------ |
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| 31 | |
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| 32 | In general, a particle with a volume V can be described by an ensemble |
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| 33 | containing N 3-dimensional rectangular pixels where each pixels are much |
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| 34 | smaller than V. Assuming that all the pixel sizes are same, the elastic |
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| 35 | scattering intensity by the particle |
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| 36 | |
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| 37 | .. image:: gen_i.gif |
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| 38 | |
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| 39 | where /beta/jand rj are the scattering length density and the position of the |
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| 40 | j'th pixel respectively. And the total volume |
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| 41 | |
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| 42 | .. image:: v_j.gif |
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| 43 | |
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| 44 | for /beta/j/noteql/0 where vj is the volume of the j'th pixel (or the j'th |
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| 45 | natural atomic volume (= atomic mass/natural molar density/Avogadro number) for |
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| 46 | the atomic structures). The total volume V can be corrected by users. This |
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| 47 | correction is useful especially for an atomic structure (taken from a pdb file) |
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| 48 | to get the right normalization. Note that the /beta/j displayed in GUI may be |
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| 49 | incorrect but will not affect the scattering computation if the correction of |
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| 50 | the total volume is made. The scattering length density (SLD) of each pixel |
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| 51 | where the SLD is uniform, is a combination of the nuclear and magnetic SLDs and |
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| 52 | depends on the spin states of the neutrons as follows:For magnetic scattering, |
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| 53 | only the magnetization component, *M*perp, perpendicular to the scattering |
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| 54 | vector *Q* contributes to the the magnetic scattering length. (Figure below). |
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| 55 | |
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| 56 | .. image:: mag_vector.bmp |
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| 57 | |
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| 58 | The magnetic scattering length density is then |
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| 59 | |
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| 60 | .. image:: dm_eq.gif |
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| 61 | |
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| 62 | where /gamma/= -1.913 the gyromagnetic ratio, /mu/B is the Bohr magneton, r0 is |
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| 63 | the classical radius of electron, and */sigma/* is the Pauli spin. |
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| 64 | |
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| 65 | For polarized neutron, the magnetic scattering is depending on the spin states. |
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| 66 | |
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| 67 | Let's consider that the incident neutrons are polarised parallel (+)/ |
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| 68 | anti-parallel (-) to the x' axis (See both Figures above). The possible |
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| 69 | out-coming states then are + and - states for both incident states, where |
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| 70 | |
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| 71 | - Non-spin flips: (+ +) and (- -) |
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| 72 | - Spin flips: (+ -) and (- +) |
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| 73 | |
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| 74 | .. image:: gen_mag_pic.bmp |
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| 75 | |
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| 76 | Now, let's assume that the angles of the *Q* vector and the spin-axis (x') |
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| 77 | from x-axis are /phi/ and /theta/up respectively (See Figure above). Then, |
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| 78 | depending upon the polarization (spin) state of neutrons, the scattering |
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| 79 | length densities, including the nuclear scattering length density (/beta/N) |
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| 80 | are given as, for non-spin-flips |
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| 81 | |
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| 82 | .. image:: sld1.gif |
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| 83 | |
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| 84 | and for spin-flips |
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| 85 | |
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| 86 | .. image:: sld2.gif |
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| 87 | |
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| 88 | where |
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| 89 | |
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| 90 | .. image:: mxp.gif |
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| 91 | |
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| 92 | .. image:: myp.gif |
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| 93 | |
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| 94 | .. image:: mzp.gif |
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| 95 | |
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| 96 | .. image:: mqx.gif |
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| 97 | |
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| 98 | .. image:: mqy.gif |
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| 99 | |
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| 100 | Here, the M0x, M0yand M0zare the x, y and z components of the magnetisation |
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| 101 | vector given in the xyz lab frame. |
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| 102 | |
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| 103 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 104 | |
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| 105 | .. _GUI: |
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| 106 | |
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| 107 | GUI |
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| 108 | --- |
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| 109 | |
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| 110 | .. image:: gen_gui_help.bmp |
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| 111 | |
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| 112 | After the computation, the result will be listed in the 'Theory' box in the |
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| 113 | data explorer panel on the main window.The 'Up_frac_in' and 'Up_frac_out' are |
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| 114 | the ratio, (spin up) /(spin up + spin down) neutrons before the sample and at |
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| 115 | the analyzer, respectively. |
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| 116 | |
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| 117 | *Note I: The values of 'Up_frac_in' and 'Up_frac_out' must be in the range |
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| 118 | between 0 and 1. For example, both values are 0.5 for unpolarized neutrons.* |
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| 119 | |
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| 120 | *Note II: This computation is totally based on the pixel (or atomic) data |
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| 121 | fixed in the xyz coordinates. Thus no angular orientational averaging is |
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| 122 | considered.* |
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| 123 | |
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| 124 | *Note III: For the nuclear scattering length density, only the real component |
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| 125 | is taken account.* |
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| 126 | |
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| 127 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 128 | |
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| 129 | .. _PDB_Data: |
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| 130 | |
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| 131 | PDB Data |
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| 132 | -------- |
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| 133 | |
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| 134 | This Generic scattering calculator also supports some pdb files without |
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| 135 | considering polarized/magnetic scattering so that the related parameters |
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| 136 | such as Up_*** will be ignored (see the Picture below). The calculation for |
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| 137 | fixed orientation uses (the first) Equation above resulting in a 2D output, |
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| 138 | whileas the scattering calculation averaged over all the orientations uses |
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| 139 | the Debye equation providing a 1D output |
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| 140 | |
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| 141 | .. image:: gen_debye_eq.gif |
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| 142 | |
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| 143 | where vj /beta/j /equiv/ bj the scattering length of the j'th atom. The resultant outputs |
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| 144 | will be displayed in the DataExplorer for further uses. |
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| 145 | |
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| 146 | .. image:: pdb_combo.jpg |
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