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Last change
on this file since d86967b was
9f60c06,
checked in by wojciech, 8 years ago
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Magnetism help file moved to sasmodels - fixing ticket #607
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File size:
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[19dcb933] | 1 | |
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| 2 | .. _models-intro: |
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| 3 | |
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| 4 | ************ |
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| 5 | Introduction |
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| 6 | ************ |
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| 7 | |
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| 8 | Many of our models use the form factor calculations implemented in a c-library provided by the NIST Center for Neutron |
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| 9 | Research and thus some content and figures in this document are originated from or shared with the NIST SANS Igor-based |
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| 10 | analysis package. |
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| 11 | |
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| 12 | This software provides form factors for various particle shapes. After giving a mathematical definition of each model, |
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| 13 | we show the list of parameters available to the user. Validation plots for each model are also presented. |
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| 14 | |
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| 15 | Instructions on how to use SasView itself are available separately. |
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| 16 | |
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| 17 | To easily compare to the scattering intensity measured in experiments, we normalize the form factors by the volume of |
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| 18 | the particle |
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| 19 | |
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| 20 | .. math:: |
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| 21 | |
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| 22 | P(\vec q) = \frac{P_o(\vec q)}{V} = \frac{1}{V} F(\vec q) F^*(\vec q) |
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| 23 | |
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| 24 | with |
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| 25 | |
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| 26 | F(\vec q) = \int\int\int dV\rho(\vec r) e^{-i\vec q \cdot \vec r} |
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| 27 | |
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| 28 | where $P_0(\vec q)$ is the un-normalized form factor, $\rho(\vec r)$ is the scattering length density at a given |
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| 29 | point in space and the integration is done over the volume $V$ of the scatterer. |
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| 30 | |
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| 31 | For systems without inter-particle interference, the form factors we provide can be related to the scattering intensity |
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| 32 | by the particle volume fraction |
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| 33 | |
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| 34 | .. math:: |
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| 35 | |
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| 36 | I(\vec q) = \Phi P(\vec q) |
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| 37 | |
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| 38 | Our so-called 1D scattering intensity functions provide $P(Q)$ for the case where the scatterer is randomly oriented. In |
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| 39 | that case, the scattering intensity only depends on the length of $Q$ . The intensity measured on the plane of the SAS |
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| 40 | detector will have an azimuthal symmetry around $Q=0$. |
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| 41 | |
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| 42 | Our so-called 2D scattering intensity functions provide $P(Q,\phi)$ for an oriented system as a function of a |
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| 43 | $q$ vector in the plane of the detector. We define the angle $\phi$ as the angle between the $q$ vector and the horizontal |
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| 44 | ($x$) axis of the plane of the detector. |
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| 45 | |
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[9f60c06] | 46 | For information about polarised and magnetic scattering, see :ref:`magnetism`. |
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[19dcb933] | 47 | |
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