Changeset c64a68e in sasmodels for sasmodels/models/parallelepiped.py


Ignore:
Timestamp:
May 2, 2018 4:58:15 PM (6 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
96153e4
Parents:
b343226 (diff), 33969b6 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.
Message:

Merge branch 'master' into ticket-896

File:
1 edited

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  • sasmodels/models/parallelepiped.py

    ref07e95 rb343226  
    22# Note: model title and parameter table are inserted automatically 
    33r""" 
    4 The form factor is normalized by the particle volume. 
    5 For information about polarised and magnetic scattering, see 
    6 the :ref:`magnetism` documentation. 
    7  
    84Definition 
    95---------- 
    106 
    11  This model calculates the scattering from a rectangular parallelepiped 
    12  (\:numref:`parallelepiped-image`\). 
    13  If you need to apply polydispersity, see also :ref:`rectangular-prism`. 
     7This model calculates the scattering from a rectangular parallelepiped 
     8(:numref:`parallelepiped-image`). 
     9If you need to apply polydispersity, see also :ref:`rectangular-prism`. For 
     10information about polarised and magnetic scattering, see 
     11the :ref:`magnetism` documentation. 
    1412 
    1513.. _parallelepiped-image: 
    … …  
    2624error, or fixing of some dimensions at expected values, may help. 
    2725 
    28 The 1D scattering intensity $I(q)$ is calculated as: 
     26The form factor is normalized by the particle volume and the 1D scattering 
     27intensity $I(q)$ is then calculated as: 
    2928 
    3029.. Comment by Miguel Gonzalez: 
    … …  
    3938 
    4039    I(q) = \frac{\text{scale}}{V} (\Delta\rho \cdot V)^2 
    41            \left< P(q, \alpha) \right> + \text{background} 
     40           \left< P(q, \alpha, \beta) \right> + \text{background} 
    4241 
    4342where the volume $V = A B C$, the contrast is defined as 
    44 $\Delta\rho = \rho_\text{p} - \rho_\text{solvent}$, 
    45 $P(q, \alpha)$ is the form factor corresponding to a parallelepiped oriented 
    46 at an angle $\alpha$ (angle between the long axis C and $\vec q$), 
    47 and the averaging $\left<\ldots\right>$ is applied over all orientations. 
     43$\Delta\rho = \rho_\text{p} - \rho_\text{solvent}$, $P(q, \alpha, \beta)$ 
     44is the form factor corresponding to a parallelepiped oriented 
     45at an angle $\alpha$ (angle between the long axis C and $\vec q$), and $\beta$ 
     46(the angle between the projection of the particle in the $xy$ detector plane 
     47and the $y$ axis) and the averaging $\left<\ldots\right>$ is applied over all 
     48orientations. 
    4849 
    4950Assuming $a = A/B < 1$, $b = B /B = 1$, and $c = C/B > 1$, the 
    50 form factor is given by (Mittelbach and Porod, 1961) 
     51form factor is given by (Mittelbach and Porod, 1961 [#Mittelbach]_) 
    5152 
    5253.. math:: 
    … …  
    6667    \mu &= qB 
    6768 
    68 The scattering intensity per unit volume is returned in units of |cm^-1|. 
     69where substitution of $\sigma = cos\alpha$ and $\beta = \pi/2 \ u$ have been 
     70applied. 
    6971 
    7072NB: The 2nd virial coefficient of the parallelepiped is calculated based on 
    … …  
    120122.. math:: 
    121123 
    122     P(q_x, q_y) = \left[\frac{\sin(\tfrac{1}{2}qA\cos\alpha)}{(\tfrac{1}{2}qA\cos\alpha)}\right]^2 
    123                   \left[\frac{\sin(\tfrac{1}{2}qB\cos\beta)}{(\tfrac{1}{2}qB\cos\beta)}\right]^2 
    124                   \left[\frac{\sin(\tfrac{1}{2}qC\cos\gamma)}{(\tfrac{1}{2}qC\cos\gamma)}\right]^2 
     124    P(q_x, q_y) = \left[\frac{\sin(\tfrac{1}{2}qA\cos\alpha)}{(\tfrac{1} 
     125                   {2}qA\cos\alpha)}\right]^2 
     126                  \left[\frac{\sin(\tfrac{1}{2}qB\cos\beta)}{(\tfrac{1} 
     127                   {2}qB\cos\beta)}\right]^2 
     128                  \left[\frac{\sin(\tfrac{1}{2}qC\cos\gamma)}{(\tfrac{1} 
     129                   {2}qC\cos\gamma)}\right]^2 
    125130 
    126131with 
    … …  
    160165---------- 
    161166 
    162 P Mittelbach and G Porod, *Acta Physica Austriaca*, 14 (1961) 185-211 
    163  
    164 R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 
     167.. [#Mittelbach] P Mittelbach and G Porod, *Acta Physica Austriaca*, 
     168   14 (1961) 185-211 
     169.. [#] R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 
    165170 
    166171Authorship and Verification 
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