Changeset 393facf in sasmodels


Ignore:
Timestamp:
Nov 6, 2017 2:25:04 AM (6 years ago)
Author:
dirk
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
49eb251
Parents:
8de1477
Message:

update documentation for core_shell_parallelepiped, hollow_rectangular_prism and rectangular_prism

Location:
sasmodels/models
Files:
3 edited

Legend:

Unmodified
Added
Removed

  • sasmodels/models/core_shell_parallelepiped.py

    rfc0b7aa r393facf  
    55Calculates the form factor for a rectangular solid with a core-shell structure. 
    66The thickness and the scattering length density of the shell or 
    7 "rim" can be different on each (pair) of faces. However at this time 
    8 the 1D calculation does **NOT** actually calculate a c face rim despite the presence of 
    9 the parameter. Some other aspects of the 1D calculation may be wrong. 
    10  
    11 .. note:: 
    12    This model was originally ported from NIST IGOR macros. However, it is not 
    13    yet fully understood by the SasView developers and is currently under review. 
     7"rim" can be different on each (pair) of faces. 
     8 
    149 
    1510The form factor is normalized by the particle volume $V$ such that 
    … …  
    4136    V = ABC + 2t_ABC + 2t_BAC + 2t_CAB 
    4237 
    43 **meaning that there are "gaps" at the corners of the solid.**  Again note that 
    44 $t_C = 0$ currently. 
     38**meaning that there are "gaps" at the corners of the solid.** 
    4539 
    4640The intensity calculated follows the :ref:`parallelepiped` model, with the 
    4741core-shell intensity being calculated as the square of the sum of the 
    48 amplitudes of the core and shell, in the same manner as a core-shell model. 
    49  
    50 .. math:: 
    51  
    52     F_{a}(Q,\alpha,\beta)= 
    53     \left[\frac{\sin(\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha \sin\beta)}{\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha\sin\beta} 
    54     - \frac{\sin(\tfrac{1}{2}QL_A\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_A\sin\alpha \sin\beta} \right] 
    55     \left[\frac{\sin(\tfrac{1}{2}QL_B\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_B\sin\alpha \sin\beta} \right] 
    56     \left[\frac{\sin(\tfrac{1}{2}QL_C\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_C\sin\alpha \sin\beta} \right] 
    57  
    58 .. note:: 
    59  
    60     Why does t_B not appear in the above equation? 
    61     For the calculation of the form factor to be valid, the sides of the solid 
    62     MUST (perhaps not any more?) be chosen such that** $A < B < C$. 
    63     If this inequality is not satisfied, the model will not report an error, 
    64     but the calculation will not be correct and thus the result wrong. 
     42amplitudes of the core and the slabs on the edges. 
     43 
     44the scattering amplitude is computed for a particular orientation of the core-shell 
     45parallelepiped with respect to the scattering vector and then averaged over all 
     46possible orientations, where $\alpha$ is the angle between the $z$ axis and the longest axis $C$ 
     47of the parallelepiped, $\beta$ is the angle between projection of the particle in the $xy$ detector plane and the $y$ axis. 
     48 
     49.. math:: 
     50    \begin{align*} 
     51    F(Q)&=A B C (\rho_\text{core}-\rho_\text{solvent})  S(A \sin\alpha \sin\beta)S(B \sin\alpha \cos\beta)S(C \cos\alpha) \\ 
     52    &+ 2t_A B C (\rho_\text{A}-\rho_\text{solvent})  \left[S((A+t_A) \sin\alpha \sin\beta)-S(A \sin\alpha \sin\beta)\right] S(B \sin\alpha \cos\beta) S(C \cos\alpha)\\ 
     53    &+ 2 A t_B C (\rho_\text{B}-\rho_\text{solvent})  S(A \sin\alpha \sin\beta) \left[S((B+t_B) \sin\alpha \cos\beta)-S(B \sin\alpha \cos\beta)\right] S(C \cos\alpha)\\ 
     54    &+ 2 A B t_C (\rho_\text{C}-\rho_\text{solvent}) S(A \sin\alpha \sin\beta) S(B \sin\alpha \cos\beta) \left[S((C+t_C) \cos\alpha)-S(C \cos\alpha)\right] 
     55    \end{align*} 
     56 
     57with 
     58 
     59.. math:: 
     60 
     61    S(x) = \frac{\sin \tfrac{1}{2}Q x}{\tfrac{1}{2}Q x} 
     62 
     63where $\rho_\text{core}$, $\rho_\text{A}$, $\rho_\text{B}$ and $\rho_\text{C}$ are 
     64the scattering length of the parallelepiped core, and the rectangular slabs of 
     65thickness $t_A$, $t_B$ and $t_C$, respectively. 
     66$\rho_\text{solvent}$ is the scattering length of the solvent. 
    6567 
    6668FITTING NOTES 
    … …  
    7375known values, or you will certainly end up at a solution that is unphysical. 
    7476 
    75 Constraints must be applied during fitting to ensure that the inequality 
    76 $A < B < C$ is not violated. The calculation will not report an error, 
    77 but the results will not be correct. 
    78  
    7977The returned value is in units of |cm^-1|, on absolute scale. 
    8078 
    … …  
    9189$\Psi = 0$ when the *short_b* axis is parallel to the *x*-axis of the detector. 
    9290 
     91For 2d, constraints must be applied during fitting to ensure that the inequality 
     92$A < B < C$ is not violated, and hence the correct definition of angles is preserved. The calculation will not report an error, 
     93but the results may be not correct. 
     94 
    9395.. figure:: img/parallelepiped_angle_definition.png 
    9496 
    9597    Definition of the angles for oriented core-shell parallelepipeds. 
    9698    Note that rotation $\theta$, initially in the $xz$ plane, is carried out first, then 
    97     rotation $\phi$ about the $z$ axis, finally rotation $\Psi$ is now around the axis of the cylinder. 
     99    rotation $\phi$ about the $z$ axis, finally rotation $\Psi$ is now around the axis of the parallelepiped. 
    98100    The neutron or X-ray beam is along the $z$ axis. 
    99101 

  • sasmodels/models/hollow_rectangular_prism.py

    r8de1477 r393facf  
    55This model provides the form factor, $P(q)$, for a hollow rectangular 
    66parallelepiped with a wall of thickness $\Delta$. 
    7 It computes only the 1D scattering, not the 2D. 
     7 
    88 
    99Definition 
    … …  
    6666(which is unitless). 
    6767 
    68 **The 2D scattering intensity is not computed by this model.** 
     68For 2d data the orientation of the particle is required, described using 
     69angles $\theta$, $\phi$ and $\Psi$ as in the diagrams below, for further details 
     70of the calculation and angular dispersions see :ref:`orientation` . 
     71The angle $\Psi$ is the rotational angle around the long *C* axis. For example, 
     72$\Psi = 0$ when the *B* axis is parallel to the *x*-axis of the detector. 
     73 
     74For 2d, constraints must be applied during fitting to ensure that the inequality 
     75$A < B < C$ is not violated, and hence the correct definition of angles is preserved. The calculation will not report an error, 
     76but the results may be not correct. 
     77 
     78.. figure:: img/parallelepiped_angle_definition.png 
     79 
     80    Definition of the angles for oriented hollow rectangular prism. 
     81    Note that rotation $\theta$, initially in the $xz$ plane, is carried out first, then 
     82    rotation $\phi$ about the $z$ axis, finally rotation $\Psi$ is now around the axis of the prism. 
     83    The neutron or X-ray beam is along the $z$ axis. 
     84 
     85.. figure:: img/parallelepiped_angle_projection.png 
     86 
     87    Examples of the angles for oriented hollow rectangular prisms against the 
     88    detector plane. 
    6989 
    7090 
    … …  
    181201         [{}, [0.2], [0.76687283098]], 
    182202        ] 
    183  

  • sasmodels/models/rectangular_prism.py

    r8de1477 r393facf  
    1212the prism (e.g. setting $b/a = 1$ and $c/a = 1$ and applying polydispersity 
    1313to *a* will generate a distribution of cubes of different sizes). 
    14 Note also that, contrary to :ref:`parallelepiped`, it does not compute 
    15 the 2D scattering. 
    1614 
    1715 
    … …  
    2624that reference), with $\theta$ corresponding to $\alpha$ in that paper, 
    2725and not to the usual convention used for example in the 
    28 :ref:`parallelepiped` model. As the present model does not compute 
    29 the 2D scattering, this has no further consequences. 
     26:ref:`parallelepiped` model. 
    3027 
    3128In this model the scattering from a massive parallelepiped with an 
    … …  
    6562units) *scale* represents the volume fraction (which is unitless). 
    6663 
    67 **The 2D scattering intensity is not computed by this model.** 
     64For 2d data the orientation of the particle is required, described using 
     65angles $\theta$, $\phi$ and $\Psi$ as in the diagrams below, for further details 
     66of the calculation and angular dispersions see :ref:`orientation` . 
     67The angle $\Psi$ is the rotational angle around the long *C* axis. For example, 
     68$\Psi = 0$ when the *B* axis is parallel to the *x*-axis of the detector. 
     69 
     70For 2d, constraints must be applied during fitting to ensure that the inequality 
     71$A < B < C$ is not violated, and hence the correct definition of angles is preserved. The calculation will not report an error, 
     72but the results may be not correct. 
     73 
     74.. figure:: img/parallelepiped_angle_definition.png 
     75 
     76    Definition of the angles for oriented core-shell parallelepipeds. 
     77    Note that rotation $\theta$, initially in the $xz$ plane, is carried out first, then 
     78    rotation $\phi$ about the $z$ axis, finally rotation $\Psi$ is now around the axis of the cylinder. 
     79    The neutron or X-ray beam is along the $z$ axis. 
     80 
     81.. figure:: img/parallelepiped_angle_projection.png 
     82 
     83    Examples of the angles for oriented rectangular prisms against the 
     84    detector plane. 
     85 
    6886 
    6987 
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