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  • sasmodels/models/hollow_rectangular_prism.py

    r455aaa1 r2d81cfe  
    22# Note: model title and parameter table are inserted automatically 
    33r""" 
     4 
     5This model provides the form factor, $P(q)$, for a hollow rectangular 
     6parallelepiped with a wall of thickness $\Delta$. 
     7It computes only the 1D scattering, not the 2D. 
     8 
    49Definition 
    510---------- 
    611 
    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). 
     12The 1D scattering intensity for this model is calculated by forming 
     13the difference of the amplitudes of two massive parallelepipeds 
     14differing in their outermost dimensions in each direction by the 
     15same length increment $2\Delta$ (Nayuk, 2012). 
    1216 
    1317As in the case of the massive parallelepiped model (:ref:`rectangular-prism`), 
     
    5761  \rho_\text{solvent})^2 \times P(q) + \text{background} 
    5862 
    59 where $\rho_\text{p}$ is the scattering length density of the parallelepiped, 
    60 $\rho_\text{solvent}$ is the scattering length density of the solvent, 
     63where $\rho_\text{p}$ is the scattering length of the parallelepiped, 
     64$\rho_\text{solvent}$ is the scattering length of the solvent, 
    6165and (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). 
    6467 
    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.** 
    8769 
    8870 
     
    9779---------- 
    9880 
    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 
     81R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 
    10882""" 
    10983 
     
    139113              ["thickness", "Ang", 1, [0, inf], "volume", 
    140114               "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"], 
    147115             ] 
    148116 
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