# Changeset 475ff58 in sasmodels

Ignore:
Timestamp:
Sep 7, 2018 11:49:04 AM (2 months ago)
Branches:
master, beta_approx, cuda-test, py3, ticket-1015-gpu-mem-error, ticket-1015-quick-fix, ticket-1157, ticket-608-user-defined-weights, ticket_1156
Children:
cc8b183, 1a3c0c6
Parents:
992299c
Message:

Clarified documentation for spinodal model. Closes #1167

File:
1 edited

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Unmodified
 ref07e95 ---------- This model calculates the SAS signal of a phase separating solution under spinodal decomposition. The scattering intensity $I(q)$ is calculated as This model calculates the SAS signal of a phase separating system undergoing spinodal decomposition. The scattering intensity $I(q)$ is calculated as .. math:: I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B where $x=q/q_0$ and $B$ is a flat background. The characteristic structure length scales with the correlation peak at $q_0$. The exponent $\gamma$ is equal to $d+1$ with d the dimensionality of the off-critical concentration mixtures. A transition to $\gamma=2d$ is seen near the percolation threshold into the critical concentration regime. where $x=q/q_0$, $q_0$ is the peak position, $I_{max}$ is the intensity at $q_0$ (parameterised as the $scale$ parameter), and $B$ is a flat background. The spinodal wavelength is given by $2\pi/q_0$. The exponent $\gamma$ is equal to $d+1$ for off-critical concentration mixtures (smooth interfaces) and $2d$ for critical concentration mixtures (entangled interfaces), where $d$ is the dimensionality (ie, 1, 2, 3) of the system. Thus 2 <= $\gamma$ <= 6. A transition from $\gamma=d+1$ to $\gamma=2d$ is expected near the percolation threshold. As this function tends to zero as $q$ tends to zero, in practice it may be necessary to combine it with another function describing the low-angle scattering, or to simply omit the low-angle scattering from the fit. References Physica A 123,497 (1984). Authorship and Verification ---------------------------- Revision History ---------------- * **Author:** Dirk Honecker **Date:** Oct 7, 2016 * **Author:**  Dirk Honecker **Date:** Oct 7, 2016 * **Revised:** Steve King    **Date:** Sep 7, 2018 """ title = "Spinodal decomposition model" description = """\ I(q) = scale ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma))+background I(q) = Imax ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma)) + background List of default parameters: scale = scaling gamma = exponent x = q/q_0 Imax = correlation peak intensity at q_0 background = incoherent background gamma = exponent (see model documentation) q_0 = correlation peak position [1/A] background = Incoherent background""" x = q/q_0""" category = "shape-independent"