source: sasview/src/sas/qtgui/Calculators/media/sas_calculator_help.rst @ 417c03f

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[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]8Generic SANS Calculator Tool
9============================
[ec392464]10
[a9dc4eb]11Description
12-----------
[ec392464]13
[a9dc4eb]14This tool attempts to simulate the SANS expected from a specified
15shape/structure or scattering length density profile. The tool can
16handle both nuclear and magnetic contributions to the scattering.
[850c753]17
[a9dc4eb]18Theory
19------
[ec392464]20
[5ed76f8]21In general, a particle with a volume $V$ can be described by an ensemble
22containing $N$ 3-dimensional rectangular pixels where each pixel is much
23smaller than $V$.
[ec392464]24
[5ed76f8]25Assuming that all the pixel sizes are the same, the elastic scattering
[850c753]26intensity from the particle is
[ec392464]27
[6aad2e8]28.. image:: gen_i.png
[ec392464]29
[850c753]30Equation 1.
31
[5ed76f8]32where $\beta_j$ and $r_j$ are the scattering length density and
33the position of the $j^\text{th}$ pixel respectively.
[850c753]34
[5ed76f8]35The total volume $V$
[ec392464]36
[5ed76f8]37.. math::
[ec392464]38
[5ed76f8]39    V = \sum_j^N v_j
40
41for $\beta_j \ne 0$ where $v_j$ is the volume of the $j^\text{th}$
42pixel (or the $j^\text{th}$ natural atomic volume (= atomic mass / (natural molar
[850c753]43density * Avogadro number) for the atomic structures).
44
[5ed76f8]45$V$ can be corrected by users. This correction is useful especially for an
46atomic 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]49affect the scattering computation if the correction of the total volume V is made.*
50
[5ed76f8]51The scattering length density (SLD) of each pixel, where the SLD is uniform, is
52a combination of the nuclear and magnetic SLDs and depends on the spin states
[850c753]53of the neutrons as follows.
54
[a9dc4eb]55Magnetic Scattering
56^^^^^^^^^^^^^^^^^^^
[850c753]57
[5ed76f8]58For magnetic scattering, only the magnetization component, $M_\perp$,
59perpendicular to the scattering vector $Q$ contributes to the magnetic
[850c753]60scattering length.
[ec392464]61
[6aad2e8]62.. image:: mag_vector.png
[ec392464]63
64The magnetic scattering length density is then
65
[6aad2e8]66.. image:: dm_eq.png
[ec392464]67
[5ed76f8]68where the gyromagnetic ratio is $\gamma = -1.913$, $\mu_B$ is the Bohr
69magneton, $r_0$ is the classical radius of electron, and $\sigma$ is the
[850c753]70Pauli spin.
[ec392464]71
[850c753]72For a polarized neutron, the magnetic scattering is depending on the spin states.
[ec392464]73
[5ed76f8]74Let us consider that the incident neutrons are polarised both parallel (+) and
75anti-parallel (-) to the x' axis (see below). The possible states after
76scattering 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]83Now let us assume that the angles of the *Q* vector and the spin-axis (x')
84to the x-axis are $\phi$ and $\theta_\text{up}$ respectively (see above). Then,
85depending upon the polarization (spin) state of neutrons, the scattering
86length densities, including the nuclear scattering length density ($\beta_N$)
[850c753]87are 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
97where
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]109Here the $M0_x$, $M0_y$ and $M0_z$ are the $x$, $y$ and $z$
110components of the magnetisation vector in the laboratory $xyz$ frame.
[ec392464]111
112.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
113
[a9dc4eb]114Using the tool
115--------------
[ec392464]116
[6aad2e8]117.. image:: gen_gui_help.png
[ec392464]118
[5ed76f8]119After 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]126of 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]1290.0 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]132in xyz coordinates. No angular orientational averaging is considered.*
133
[5ed76f8]134*NOTE 3. For the nuclear scattering length density, only the real component
[ec392464]135is taken account.*
136
137.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
138
[a9dc4eb]139Using PDB/OMF or SLD files
140--------------------------
[ec392464]141
[a9dc4eb]142The SANS Calculator tool can read some PDB, OMF or SLD files but ignores
[5ed76f8]143polarized/magnetic scattering when doing so, thus related parameters such as
[850c753]144*Up_frac_in*, etc, will be ignored.
[ec392464]145
[5ed76f8]146The calculation for fixed orientation uses Equation 1 above resulting in a 2D
147output, whereas the scattering calculation averaged over all the orientations
[850c753]148uses the Debye equation below providing a 1D output
[ec392464]149
[6aad2e8]150.. image:: gen_debye_eq.png
[ec392464]151
[5ed76f8]152where $v_j \beta_j \equiv b_j$ is the scattering
153length of the $j^\text{th}$ atom. The calculation output is passed to the *Data Explorer*
[850c753]154for 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
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