[ec392464] | 1 | .. sas_calculator_help.rst |
---|
| 2 | |
---|
| 3 | .. This is a port of the original SasView html help file to ReSTructured text |
---|
| 4 | .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. |
---|
| 5 | |
---|
[da456fb] | 6 | .. _SANS_Calculator_Tool: |
---|
| 7 | |
---|
[a9dc4eb] | 8 | Generic SANS Calculator Tool |
---|
| 9 | ============================ |
---|
[ec392464] | 10 | |
---|
[a9dc4eb] | 11 | Description |
---|
| 12 | ----------- |
---|
[ec392464] | 13 | |
---|
[a9dc4eb] | 14 | This tool attempts to simulate the SANS expected from a specified |
---|
| 15 | shape/structure or scattering length density profile. The tool can |
---|
| 16 | handle both nuclear and magnetic contributions to the scattering. |
---|
[850c753] | 17 | |
---|
[a9dc4eb] | 18 | Theory |
---|
| 19 | ------ |
---|
[ec392464] | 20 | |
---|
[5ed76f8] | 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 $V$. |
---|
[ec392464] | 24 | |
---|
[5ed76f8] | 25 | Assuming that all the pixel sizes are the same, the elastic scattering |
---|
[850c753] | 26 | intensity from the particle is |
---|
[ec392464] | 27 | |
---|
[6aad2e8] | 28 | .. image:: gen_i.png |
---|
[ec392464] | 29 | |
---|
[850c753] | 30 | Equation 1. |
---|
| 31 | |
---|
[5ed76f8] | 32 | where $\beta_j$ and $r_j$ are the scattering length density and |
---|
| 33 | the position of the $j^\text{th}$ pixel respectively. |
---|
[850c753] | 34 | |
---|
[5ed76f8] | 35 | The total volume $V$ |
---|
[ec392464] | 36 | |
---|
[5ed76f8] | 37 | .. math:: |
---|
[ec392464] | 38 | |
---|
[5ed76f8] | 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 |
---|
[850c753] | 43 | density * Avogadro number) for the atomic structures). |
---|
| 44 | |
---|
[5ed76f8] | 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. |
---|
[850c753] | 47 | |
---|
[5ed76f8] | 48 | *NOTE! $\beta_j$ displayed in the GUI may be incorrect but this will not |
---|
[850c753] | 49 | affect the scattering computation if the correction of the total volume V is made.* |
---|
| 50 | |
---|
[5ed76f8] | 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 |
---|
[850c753] | 53 | of the neutrons as follows. |
---|
| 54 | |
---|
[a9dc4eb] | 55 | Magnetic Scattering |
---|
| 56 | ^^^^^^^^^^^^^^^^^^^ |
---|
[850c753] | 57 | |
---|
[5ed76f8] | 58 | For magnetic scattering, only the magnetization component, $M_\perp$, |
---|
| 59 | perpendicular to the scattering vector $Q$ contributes to the magnetic |
---|
[850c753] | 60 | scattering length. |
---|
[ec392464] | 61 | |
---|
[6aad2e8] | 62 | .. image:: mag_vector.png |
---|
[ec392464] | 63 | |
---|
| 64 | The magnetic scattering length density is then |
---|
| 65 | |
---|
[6aad2e8] | 66 | .. image:: dm_eq.png |
---|
[ec392464] | 67 | |
---|
[5ed76f8] | 68 | 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 |
---|
[850c753] | 70 | Pauli spin. |
---|
[ec392464] | 71 | |
---|
[850c753] | 72 | For a polarized neutron, the magnetic scattering is depending on the spin states. |
---|
[ec392464] | 73 | |
---|
[5ed76f8] | 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 |
---|
[ec392464] | 77 | |
---|
[850c753] | 78 | * Non-spin flips: (+ +) and (- -) |
---|
| 79 | * Spin flips: (+ -) and (- +) |
---|
[ec392464] | 80 | |
---|
[6aad2e8] | 81 | .. image:: gen_mag_pic.png |
---|
[ec392464] | 82 | |
---|
[5ed76f8] | 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 ($\beta_N$) |
---|
[850c753] | 87 | are given as |
---|
[ec392464] | 88 | |
---|
[850c753] | 89 | * for non-spin-flips |
---|
[ec392464] | 90 | |
---|
[6aad2e8] | 91 | .. image:: sld1.png |
---|
[ec392464] | 92 | |
---|
[850c753] | 93 | * for spin-flips |
---|
| 94 | |
---|
[6aad2e8] | 95 | .. image:: sld2.png |
---|
[ec392464] | 96 | |
---|
| 97 | where |
---|
| 98 | |
---|
[6aad2e8] | 99 | .. image:: mxp.png |
---|
[ec392464] | 100 | |
---|
[6aad2e8] | 101 | .. image:: myp.png |
---|
[ec392464] | 102 | |
---|
[6aad2e8] | 103 | .. image:: mzp.png |
---|
[ec392464] | 104 | |
---|
[6aad2e8] | 105 | .. image:: mqx.png |
---|
[ec392464] | 106 | |
---|
[6aad2e8] | 107 | .. image:: mqy.png |
---|
[ec392464] | 108 | |
---|
[5ed76f8] | 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. |
---|
[ec392464] | 111 | |
---|
| 112 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
---|
| 113 | |
---|
[a9dc4eb] | 114 | Using the tool |
---|
| 115 | -------------- |
---|
[ec392464] | 116 | |
---|
[6aad2e8] | 117 | .. image:: gen_gui_help.png |
---|
[ec392464] | 118 | |
---|
[5ed76f8] | 119 | After computation the result will appear in the *Theory* box in the SasView |
---|
[850c753] | 120 | *Data Explorer* panel. |
---|
| 121 | |
---|
[5ed76f8] | 122 | *Up_frac_in* and *Up_frac_out* are the ratio |
---|
[ec392464] | 123 | |
---|
[850c753] | 124 | (spin up) / (spin up + spin down) |
---|
[5ed76f8] | 125 | |
---|
[850c753] | 126 | of neutrons before the sample and at the analyzer, respectively. |
---|
[ec392464] | 127 | |
---|
[5ed76f8] | 128 | *NOTE 1. The values of* Up_frac_in *and* Up_frac_out *must be in the range |
---|
[850c753] | 129 | 0.0 to 1.0. Both values are 0.5 for unpolarized neutrons.* |
---|
[ec392464] | 130 | |
---|
[5ed76f8] | 131 | *NOTE 2. This computation is totally based on the pixel (or atomic) data fixed |
---|
[850c753] | 132 | in xyz coordinates. No angular orientational averaging is considered.* |
---|
| 133 | |
---|
[5ed76f8] | 134 | *NOTE 3. For the nuclear scattering length density, only the real component |
---|
[ec392464] | 135 | is taken account.* |
---|
| 136 | |
---|
| 137 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
---|
| 138 | |
---|
[a9dc4eb] | 139 | Using PDB/OMF or SLD files |
---|
| 140 | -------------------------- |
---|
[ec392464] | 141 | |
---|
[a9dc4eb] | 142 | The SANS Calculator tool can read some PDB, OMF or SLD files but ignores |
---|
[5ed76f8] | 143 | polarized/magnetic scattering when doing so, thus related parameters such as |
---|
[850c753] | 144 | *Up_frac_in*, etc, will be ignored. |
---|
[ec392464] | 145 | |
---|
[5ed76f8] | 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 |
---|
[850c753] | 148 | uses the Debye equation below providing a 1D output |
---|
[ec392464] | 149 | |
---|
[6aad2e8] | 150 | .. image:: gen_debye_eq.png |
---|
[ec392464] | 151 | |
---|
[5ed76f8] | 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* |
---|
[850c753] | 154 | for further use. |
---|
[ec392464] | 155 | |
---|
| 156 | .. image:: pdb_combo.jpg |
---|
[850c753] | 157 | |
---|
| 158 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
---|
| 159 | |
---|
[a9dc4eb] | 160 | .. note:: This help document was last changed by Steve King, 01May2015 |
---|