spinodal

Spinodal decomposition model

Parameter Description Units Default value
scale Source intensity None 1
background Source background cm-1 0.001
scale Scale factor None 1
gamma Exponent None 3
q_0 Correlation peak position Å-1 0.1

The returned value is scaled to units of cm-1 sr-1, absolute scale.

Definition

This model calculates the SAS signal of a phase separating solution under spinodal decomposition. The scattering intensity \(I(q)\) is calculated as

\[I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B\]

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.

../../_images/spinodal_autogenfig.png

Fig. 103 1D plot corresponding to the default parameters of the model.

References

H. Furukawa. Dynamics-scaling theory for phase-separating unmixing mixtures: Growth rates of droplets and scaling properties of autocorrelation functions. Physica A 123,497 (1984).

Authorship and Verification

  • Author: Dirk Honecker Date: Oct 7, 2016
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