Changes in / [1a3c0c6:5601947] in sasmodels


Ignore:
File:
1 edited

Legend:

Unmodified
Added
Removed
  • sasmodels/models/spinodal.py

    r475ff58 ref07e95  
    33---------- 
    44 
    5 This model calculates the SAS signal of a phase separating system  
    6 undergoing spinodal decomposition. The scattering intensity $I(q)$ is calculated  
    7 as  
     5This model calculates the SAS signal of a phase separating solution 
     6under spinodal decomposition. The scattering intensity $I(q)$ is calculated as 
    87 
    98.. math:: 
    109    I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 
    1110 
    12 where $x=q/q_0$, $q_0$ is the peak position, $I_{max}$ is the intensity  
    13 at $q_0$ (parameterised as the $scale$ parameter), and $B$ is a flat  
    14 background. The spinodal wavelength is given by $2\pi/q_0$.  
    15  
    16 The exponent $\gamma$ is equal to $d+1$ for off-critical concentration  
    17 mixtures (smooth interfaces) and $2d$ for critical concentration mixtures  
    18 (entangled interfaces), where $d$ is the dimensionality (ie, 1, 2, 3) of the  
    19 system. Thus 2 <= $\gamma$ <= 6. A transition from $\gamma=d+1$ to $\gamma=2d$  
    20 is expected near the percolation threshold.  
    21  
    22 As this function tends to zero as $q$ tends to zero, in practice it may be  
    23 necessary to combine it with another function describing the low-angle  
    24 scattering, or to simply omit the low-angle scattering from the fit. 
     11where $x=q/q_0$ and $B$ is a flat background. The characteristic structure 
     12length scales with the correlation peak at $q_0$. The exponent $\gamma$ is 
     13equal to $d+1$ with d the dimensionality of the off-critical concentration 
     14mixtures. A transition to $\gamma=2d$ is seen near the percolation threshold 
     15into the critical concentration regime. 
    2516 
    2617References 
     
    3122Physica A 123,497 (1984). 
    3223 
    33 Revision History 
    34 ---------------- 
     24Authorship and Verification 
     25---------------------------- 
    3526 
    36 * **Author:**  Dirk Honecker **Date:** Oct 7, 2016 
    37 * **Revised:** Steve King    **Date:** Sep 7, 2018 
     27* **Author:** Dirk Honecker **Date:** Oct 7, 2016 
    3828""" 
    3929 
     
    4434title = "Spinodal decomposition model" 
    4535description = """\ 
    46       I(q) = Imax ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma)) + background 
     36      I(q) = scale ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma))+background 
    4737 
    4838      List of default parameters: 
    49        
    50       Imax = correlation peak intensity at q_0 
    51       background = incoherent background 
    52       gamma = exponent (see model documentation) 
     39      scale = scaling 
     40      gamma = exponent 
     41      x = q/q_0 
    5342      q_0 = correlation peak position [1/A] 
    54       x = q/q_0""" 
    55        
     43      background = Incoherent background""" 
    5644category = "shape-independent" 
    5745 
Note: See TracChangeset for help on using the changeset viewer.