Changes in / [1a3c0c6:5601947] in sasmodels
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sasmodels/models/spinodal.py
r475ff58 ref07e95 3 3 ---------- 4 4 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 5 This model calculates the SAS signal of a phase separating solution 6 under spinodal decomposition. The scattering intensity $I(q)$ is calculated as 8 7 9 8 .. math:: 10 9 I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 11 10 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. 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. 25 16 26 17 References … … 31 22 Physica A 123,497 (1984). 32 23 33 Revision History 34 ---------------- 24 Authorship and Verification 25 ---------------------------- 35 26 36 * **Author:** Dirk Honecker **Date:** Oct 7, 2016 37 * **Revised:** Steve King **Date:** Sep 7, 2018 27 * **Author:** Dirk Honecker **Date:** Oct 7, 2016 38 28 """ 39 29 … … 44 34 title = "Spinodal decomposition model" 45 35 description = """\ 46 I(q) = Imax ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma)) +background36 I(q) = scale ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma))+background 47 37 48 38 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 53 42 q_0 = correlation peak position [1/A] 54 x = q/q_0""" 55 43 background = Incoherent background""" 56 44 category = "shape-independent" 57 45
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