Changeset 07300ea in sasmodels


Ignore:
Timestamp:
Nov 28, 2016 12:52:56 AM (7 years ago)
Author:
butler
Branches:
master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
bdd08df
Parents:
98ce141
Message:

update, correct and standardize documentation for fractal_core_shell as
well as small tweak to stacked_disk documentation. Addresses #646

Location:
sasmodels/models
Files:
2 edited

Legend:

Unmodified
Added
Removed
  • sasmodels/models/fractal_core_shell.py

    r217590b r07300ea  
    11r""" 
     2Definition 
     3---------- 
    24Calculates the scattering from a fractal structure with a primary building 
    35block of core-shell spheres, as opposed to just homogeneous spheres in 
    4 the fractal model. 
    5 This model could find use for aggregates of coated particles, or aggregates 
    6 of vesicles. 
    7  
    8 Definition 
    9 ---------- 
     6the fractal model. It is an extension of the well known Teixeira\ [#teixeira]_ 
     7fractal model replacing the $P(q)$ of a solid sphere with that of a core-shell 
     8sphere. This model could find use for aggregates of coated particles, or 
     9aggregates of vesicles for example. 
    1010 
    1111.. math:: 
    1212 
    13     I(q) = \text{background} + P(q)S(q) 
     13    I(q) = P(q)S(q) + \text{background} 
    1414 
    15 The form factor $P(q)$ is that from core_shell model with $bkg$ = 0 
    16  
     15Where $P(q)$ is the core-shell form factor and $S(q)$ is the 
     16Teixeira\ [#teixeira]_ fractal structure factor both of which are given again 
     17below: 
    1718 
    1819.. math:: 
    1920 
    20     P(q)=\frac{scale}{V_s}\left[3V_c(\rho_c-\rho_s) 
     21    P(q) &= \frac{\phi}{V_s}\left[3V_c(\rho_c-\rho_s) 
    2122    \frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3}+ 
    2223    3V_s(\rho_s-\rho_{solv}) 
    2324    \frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}\right]^2 
    2425 
     26    S(q) &= 1 + \frac{D_f\ \Gamma\!(D_f-1)}{[1+1/(q\xi)^2]^{(D_f-1)/2}}  
     27    \frac{\sin[(D_f-1)\tan^{-1}(q\xi)]}{(qr_s)^{D_f}} 
    2528 
    26 while the fractal structure factor $S(q)$ is 
     29where $\phi$ is the volume fraction of particles, $V_s$ is the volume of the 
     30whole particle, $V_c$ is the volume of the core, $\rho_c$, $\rho_s$, and 
     31$\rho_{solv}$ are the scattering length densities of the core, shell, and 
     32solvent respectively, $r_c$ and $r_s$ are the radius of the core and the radius 
     33of the whole particle respectively, $D_f$ is the fractal dimension, and |xi| the 
     34correlation length. 
     35  
     36Polydispersity of radius and thickness are also provided for. 
    2737 
    28 .. math:: 
    29  
    30     S(q) = \frac{D_f\Gamma(D_f-1)\sin((D_f-1)\tan^{-1}(q\xi))} 
    31     {(qr_c)^{D_f}\left(1+\frac{1}{q^2\xi ^2} \right)^{\frac{D_f-1}{2}}} 
    32  
    33 where $D_f$ = fractal_dim, |xi| = cor_length, $r_c$ = (core) radius, and 
    34 $scale$ = volume fraction. 
    35  
    36 The fractal structure is as documented in the fractal model. 
    37 Polydispersity of radius and thickness is provided for. 
    38  
    39 For 2D data: The 2D scattering intensity is calculated in the same way as 1D, 
    40 where the $q$ vector is defined as 
     38This model does not allow for anisotropy and thus the 2D scattering intensity 
     39is calculated in the same way as 1D, where the $q$ vector is defined as 
    4140 
    4241.. math:: 
     
    4443    q = \sqrt{q_x^2 + q_y^2} 
    4544 
     45Our model is derived from the form factor calculations implemented in IGOR 
     46macros by the NIST Center for Neutron Research\ [#Kline]_ 
     47 
    4648References 
    4749---------- 
    4850 
    49 See the core_shell and fractal model descriptions 
     51.. [#teixeira] J Teixeira, *J. Appl. Cryst.*, 21 (1988) 781-785 
     52.. [#Kline]  S R Kline, *J Appl. Cryst.*, 39 (2006) 895 
     53 
     54Authorship and Verification 
     55---------------------------- 
     56 
     57* **Author:** NIST IGOR/DANSE **Date:** pre 2010 
     58* **Last Modified by:** Paul Butler and Paul Kienzle **on:** November 27, 2016 
     59* **Last Reviewed by:** Paul Butler and Paul Kienzle **on:** November 27, 2016 
    5060 
    5161""" 
     
    5464 
    5565name = "fractal_core_shell" 
    56 title = "" 
    57 description = """ 
     66title = "Scattering from a fractal structure formed from core shell spheres" 
     67description = """\ 
     68    Model for fractal aggregates of core-shell primary particles. It is based on 
     69    the Teixeira model for the S(q) of a fractal * P(q) for a core-shell sphere 
    5870 
    59 """ 
     71    radius =  the radius of the core 
     72    thickness = thickness of the shell 
     73    thick_layer = thickness of a layer 
     74    sld_core = the SLD of the core 
     75    sld_shell = the SLD of the shell 
     76    sld_solvent = the SLD of the solvent 
     77    volfraction = volume fraction of core-shell particles 
     78    fractal_dim = fractal dimension 
     79    cor_length = correlation length of the fractal like aggretates 
     80    """ 
    6081category = "shape-independent" 
    6182 
  • sasmodels/models/stacked_disks.py

    r98ce141 r07300ea  
    8383 
    8484Our model is derived from the form factor calculations implemented in a 
    85 c-library provided by the NIST Center for Neutron Research 
    86 (Kline, 2006)\ [#CIT_Kline]_ 
     85c-library provided by the NIST Center for Neutron Research\ [#CIT_Kline]_ 
    8786 
    8887References 
Note: See TracChangeset for help on using the changeset viewer.