# 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

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.

**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**Last Modified by:****Last Reviewed by:**