Changeset 475ff58 in sasmodels
 Timestamp:
 Sep 7, 2018 11:49:04 AM (10 months ago)
 Branches:
 master, core_shell_microgels, magnetic_model, ticket1257vesicleproduct, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
 Children:
 c11d09f, 1a3c0c6
 Parents:
 992299c
 File:

 1 edited
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sasmodels/models/spinodal.py
ref07e95 r475ff58 3 3  4 4 5 This model calculates the SAS signal of a phase separating solution 6 under spinodal decomposition. The scattering intensity $I(q)$ is calculated as 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 7 8 8 9 .. math:: 9 10 I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 10 11 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 offcritical concentration 14 mixtures. A transition to $\gamma=2d$ is seen near the percolation threshold 15 into the critical concentration regime. 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 offcritical 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 lowangle 24 scattering, or to simply omit the lowangle scattering from the fit. 16 25 17 26 References … … 22 31 Physica A 123,497 (1984). 23 32 24 Authorship and Verification 25  33 Revision History 34  26 35 27 * **Author:** Dirk Honecker **Date:** Oct 7, 2016 36 * **Author:** Dirk Honecker **Date:** Oct 7, 2016 37 * **Revised:** Steve King **Date:** Sep 7, 2018 28 38 """ 29 39 … … 34 44 title = "Spinodal decomposition model" 35 45 description = """\ 36 I(q) = scale ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma))+background46 I(q) = Imax ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma)) + background 37 47 38 48 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) 42 53 q_0 = correlation peak position [1/A] 43 background = Incoherent background""" 54 x = q/q_0""" 55 44 56 category = "shapeindependent" 45 57
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