Changeset c88f983 in sasmodels for sasmodels/models/spinodal.py


Ignore:
Timestamp:
Sep 8, 2018 5:29:57 AM (6 years ago)
Author:
Torin Cooper-Bennun <torin.cooper-bennun@…>
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
c11d09f, 0159b5e
Parents:
84f2962 (diff), 475ff58 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
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Message:

Merge branch 'master' into beta_approx

File:
1 edited

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  • sasmodels/models/spinodal.py

    r71b751d rc88f983  
    33---------- 
    44 
    5 This model calculates the SAS signal of a phase separating solution 
    6 under spinodal decomposition. The scattering intensity $I(q)$ is calculated as 
     5This model calculates the SAS signal of a phase separating system  
     6undergoing spinodal decomposition. The scattering intensity $I(q)$ is calculated  
     7as  
    78 
    89.. math:: 
    910    I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 
    1011 
    11 where $x=q/q_0$ and $B$ is a flat background. The characteristic structure 
    12 length scales with the correlation peak at $q_0$. The exponent $\gamma$ is 
    13 equal to $d+1$ with d the dimensionality of the off-critical concentration 
    14 mixtures. A transition to $\gamma=2d$ is seen near the percolation threshold 
    15 into the critical concentration regime. 
     12where $x=q/q_0$, $q_0$ is the peak position, $I_{max}$ is the intensity  
     13at $q_0$ (parameterised as the $scale$ parameter), and $B$ is a flat  
     14background. The spinodal wavelength is given by $2\pi/q_0$.  
     15 
     16The exponent $\gamma$ is equal to $d+1$ for off-critical concentration  
     17mixtures (smooth interfaces) and $2d$ for critical concentration mixtures  
     18(entangled interfaces), where $d$ is the dimensionality (ie, 1, 2, 3) of the  
     19system. Thus 2 <= $\gamma$ <= 6. A transition from $\gamma=d+1$ to $\gamma=2d$  
     20is expected near the percolation threshold.  
     21 
     22As this function tends to zero as $q$ tends to zero, in practice it may be  
     23necessary to combine it with another function describing the low-angle  
     24scattering, or to simply omit the low-angle scattering from the fit. 
    1625 
    1726References 
    … …  
    2231Physica A 123,497 (1984). 
    2332 
    24 Authorship and Verification 
    25 ---------------------------- 
     33Revision History 
     34---------------- 
    2635 
    27 * **Author:** Dirk Honecker **Date:** Oct 7, 2016 
     36* **Author:**  Dirk Honecker **Date:** Oct 7, 2016 
     37* **Revised:** Steve King    **Date:** Sep 7, 2018 
    2838""" 
    2939 
    … …  
    3444title = "Spinodal decomposition model" 
    3545description = """\ 
    36       I(q) = scale ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma))+background 
     46      I(q) = Imax ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma)) + background 
    3747 
    3848      List of default parameters: 
    39       scale = scaling 
    40       gamma = exponent 
    41       x = q/q_0 
     49       
     50      Imax = correlation peak intensity at q_0 
     51      background = incoherent background 
     52      gamma = exponent (see model documentation) 
    4253      q_0 = correlation peak position [1/A] 
    43       background = Incoherent background""" 
     54      x = q/q_0""" 
     55       
    4456category = "shape-independent" 
    4557 
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