Changeset 5ed76f8 in sasview for src/sas/sasgui/perspectives/calculator/media/sas_calculator_help.rst
- Timestamp:
- Apr 7, 2017 1:11:41 AM (7 years ago)
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- master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, magnetic_scatt, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
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- 727c05f
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src/sas/sasgui/perspectives/calculator/media/sas_calculator_help.rst
r6aad2e8 r5ed76f8 19 19 ------ 20 20 21 In general, a particle with a volume *V* can be described by an ensemble22 containing *N* 3-dimensional rectangular pixels where each pixel is much23 smaller than *V*.21 In general, a particle with a volume $V$ can be described by an ensemble 22 containing $N$ 3-dimensional rectangular pixels where each pixel is much 23 smaller than $V$. 24 24 25 Assuming that all the pixel sizes are the same, the elastic scattering 25 Assuming that all the pixel sizes are the same, the elastic scattering 26 26 intensity from the particle is 27 27 … … 30 30 Equation 1. 31 31 32 where |beta|\ :sub:`j` and *r*\ :sub:`j` are the scattering length density and33 the position of the j'thpixel respectively.32 where $\beta_j$ and $r_j$ are the scattering length density and 33 the position of the $j^\text{th}$ pixel respectively. 34 34 35 The total volume *V*35 The total volume $V$ 36 36 37 .. image:: v_j.png37 .. math:: 38 38 39 for |beta|\ :sub:`j` |noteql|\0 where *v*\ :sub:`j` is the volume of the j'th 40 pixel (or the j'th natural atomic volume (= atomic mass / (natural molar 39 V = \sum_j^N v_j 40 41 for $\beta_j \ne 0$ where $v_j$ is the volume of the $j^\text{th}$ 42 pixel (or the $j^\text{th}$ natural atomic volume (= atomic mass / (natural molar 41 43 density * Avogadro number) for the atomic structures). 42 44 43 *V* can be corrected by users. This correction is useful especially for an 44 atomic structure (such as taken from a PDB file) to get the right normalization. 45 $V$ can be corrected by users. This correction is useful especially for an 46 atomic structure (such as taken from a PDB file) to get the right normalization. 45 47 46 *NOTE! * |beta|\ :sub:`j` *displayed in the GUI may be incorrect but this will not48 *NOTE! $\beta_j$ displayed in the GUI may be incorrect but this will not 47 49 affect the scattering computation if the correction of the total volume V is made.* 48 50 49 The scattering length density (SLD) of each pixel, where the SLD is uniform, is 50 a combination of the nuclear and magnetic SLDs and depends on the spin states 51 The scattering length density (SLD) of each pixel, where the SLD is uniform, is 52 a combination of the nuclear and magnetic SLDs and depends on the spin states 51 53 of the neutrons as follows. 52 54 … … 54 56 ^^^^^^^^^^^^^^^^^^^ 55 57 56 For magnetic scattering, only the magnetization component, *M*\ :sub:`perp`\ ,57 perpendicular to the scattering vector *Q* contributes to the magnetic58 For magnetic scattering, only the magnetization component, $M_\perp$, 59 perpendicular to the scattering vector $Q$ contributes to the magnetic 58 60 scattering length. 59 61 … … 64 66 .. image:: dm_eq.png 65 67 66 where the gyromagnetic ratio |gamma| = -1.913, |mu|\ :sub:`B` is the Bohr67 magneton, *r*\ :sub:`0` is the classical radius of electron, and |sigma| is the68 where the gyromagnetic ratio is $\gamma = -1.913$, $\mu_B$ is the Bohr 69 magneton, $r_0$ is the classical radius of electron, and $\sigma$ is the 68 70 Pauli spin. 69 71 70 72 For a polarized neutron, the magnetic scattering is depending on the spin states. 71 73 72 Let us consider that the incident neutrons are polarised both parallel (+) and 73 anti-parallel (-) to the x' axis (see below). The possible states after 74 scattering from the sample are then 74 Let us consider that the incident neutrons are polarised both parallel (+) and 75 anti-parallel (-) to the x' axis (see below). The possible states after 76 scattering from the sample are then 75 77 76 78 * Non-spin flips: (+ +) and (- -) … … 79 81 .. image:: gen_mag_pic.png 80 82 81 Now let us assume that the angles of the *Q* vector and the spin-axis (x') 82 to the x-axis are |phi| and |theta|\ :sub:`up` respectively (see above). Then,83 depending upon the polarization (spin) state of neutrons, the scattering 84 length densities, including the nuclear scattering length density ( |beta|\ :sub:`N`\ )83 Now let us assume that the angles of the *Q* vector and the spin-axis (x') 84 to the x-axis are $\phi$ and $\theta_\text{up}$ respectively (see above). Then, 85 depending upon the polarization (spin) state of neutrons, the scattering 86 length densities, including the nuclear scattering length density ($\beta_N$) 85 87 are given as 86 88 … … 105 107 .. image:: mqy.png 106 108 107 Here the *M0*\ :sub:`x`\ , *M0*\ :sub:`y` and *M0*\ :sub:`z` are the x, y and z108 components of the magnetisation vector in the laboratory xyz frame.109 Here the $M0_x$, $M0_y$ and $M0_z$ are the $x$, $y$ and $z$ 110 components of the magnetisation vector in the laboratory $xyz$ frame. 109 111 110 112 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 115 117 .. image:: gen_gui_help.png 116 118 117 After computation the result will appear in the *Theory* box in the SasView 119 After computation the result will appear in the *Theory* box in the SasView 118 120 *Data Explorer* panel. 119 121 120 *Up_frac_in* and *Up_frac_out* are the ratio 122 *Up_frac_in* and *Up_frac_out* are the ratio 121 123 122 124 (spin up) / (spin up + spin down) 123 125 124 126 of neutrons before the sample and at the analyzer, respectively. 125 127 126 *NOTE 1. The values of* Up_frac_in *and* Up_frac_out *must be in the range 128 *NOTE 1. The values of* Up_frac_in *and* Up_frac_out *must be in the range 127 129 0.0 to 1.0. Both values are 0.5 for unpolarized neutrons.* 128 130 129 *NOTE 2. This computation is totally based on the pixel (or atomic) data fixed 131 *NOTE 2. This computation is totally based on the pixel (or atomic) data fixed 130 132 in xyz coordinates. No angular orientational averaging is considered.* 131 133 132 *NOTE 3. For the nuclear scattering length density, only the real component 134 *NOTE 3. For the nuclear scattering length density, only the real component 133 135 is taken account.* 134 136 … … 139 141 140 142 The SANS Calculator tool can read some PDB, OMF or SLD files but ignores 141 polarized/magnetic scattering when doing so, thus related parameters such as 143 polarized/magnetic scattering when doing so, thus related parameters such as 142 144 *Up_frac_in*, etc, will be ignored. 143 145 144 The calculation for fixed orientation uses Equation 1 above resulting in a 2D 145 output, whereas the scattering calculation averaged over all the orientations 146 The calculation for fixed orientation uses Equation 1 above resulting in a 2D 147 output, whereas the scattering calculation averaged over all the orientations 146 148 uses the Debye equation below providing a 1D output 147 149 148 150 .. image:: gen_debye_eq.png 149 151 150 where *v*\ :sub:`j` |beta|\ :sub:`j` |equiv| *b*\ :sub:`j` is the scattering151 length of the j'th atom. The calculation output is passed to the *Data Explorer*152 where $v_j \beta_j \equiv b_j$ is the scattering 153 length of the $j^\text{th}$ atom. The calculation output is passed to the *Data Explorer* 152 154 for further use. 153 155
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