Changes in sasmodels/models/hollow_rectangular_prism.py [455aaa1:2d81cfe] in sasmodels
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sasmodels/models/hollow_rectangular_prism.py
r455aaa1 r2d81cfe 2 2 # Note: model title and parameter table are inserted automatically 3 3 r""" 4 5 This model provides the form factor, $P(q)$, for a hollow rectangular 6 parallelepiped with a wall of thickness $\Delta$. 7 It computes only the 1D scattering, not the 2D. 8 4 9 Definition 5 10 ---------- 6 11 7 This model provides the form factor, $P(q)$, for a hollow rectangular 8 parallelepiped with a wall of thickness $\Delta$. The 1D scattering intensity 9 for this model is calculated by forming the difference of the amplitudes of two 10 massive parallelepipeds differing in their outermost dimensions in each 11 direction by the same length increment $2\Delta$ (\ [#Nayuk2012]_ Nayuk, 2012). 12 The 1D scattering intensity for this model is calculated by forming 13 the difference of the amplitudes of two massive parallelepipeds 14 differing in their outermost dimensions in each direction by the 15 same length increment $2\Delta$ (Nayuk, 2012). 12 16 13 17 As in the case of the massive parallelepiped model (:ref:`rectangular-prism`), … … 57 61 \rho_\text{solvent})^2 \times P(q) + \text{background} 58 62 59 where $\rho_\text{p}$ is the scattering length densityof the parallelepiped,60 $\rho_\text{solvent}$ is the scattering length densityof the solvent,63 where $\rho_\text{p}$ is the scattering length of the parallelepiped, 64 $\rho_\text{solvent}$ is the scattering length of the solvent, 61 65 and (if the data are in absolute units) *scale* represents the volume fraction 62 (which is unitless) of the rectangular shell of material (i.e. not including 63 the volume of the solvent filled core). 66 (which is unitless). 64 67 65 For 2d data the orientation of the particle is required, described using 66 angles $\theta$, $\phi$ and $\Psi$ as in the diagrams below, for further details 67 of the calculation and angular dispersions see :ref:`orientation` . 68 The angle $\Psi$ is the rotational angle around the long *C* axis. For example, 69 $\Psi = 0$ when the *B* axis is parallel to the *x*-axis of the detector. 70 71 For 2d, constraints must be applied during fitting to ensure that the inequality 72 $A < B < C$ is not violated, and hence the correct definition of angles is 73 preserved. The calculation will not report an error if the inequality is *not* 74 preserved, but the results may be not correct. 75 76 .. figure:: img/parallelepiped_angle_definition.png 77 78 Definition of the angles for oriented hollow rectangular prism. 79 Note that rotation $\theta$, initially in the $xz$ plane, is carried out first, then 80 rotation $\phi$ about the $z$ axis, finally rotation $\Psi$ is now around the axis of the prism. 81 The neutron or X-ray beam is along the $z$ axis. 82 83 .. figure:: img/parallelepiped_angle_projection.png 84 85 Examples of the angles for oriented hollow rectangular prisms against the 86 detector plane. 68 **The 2D scattering intensity is not computed by this model.** 87 69 88 70 … … 97 79 ---------- 98 80 99 .. [#Nayuk2012] R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 100 101 102 Authorship and Verification 103 ---------------------------- 104 105 * **Author:** Miguel Gonzales **Date:** February 26, 2016 106 * **Last Modified by:** Paul Kienzle **Date:** December 14, 2017 107 * **Last Reviewed by:** Paul Butler **Date:** September 06, 2018 81 R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 108 82 """ 109 83 … … 139 113 ["thickness", "Ang", 1, [0, inf], "volume", 140 114 "Thickness of parallelepiped"], 141 ["theta", "degrees", 0, [-360, 360], "orientation",142 "c axis to beam angle"],143 ["phi", "degrees", 0, [-360, 360], "orientation",144 "rotation about beam"],145 ["psi", "degrees", 0, [-360, 360], "orientation",146 "rotation about c axis"],147 115 ] 148 116
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