Evolution of speckle during spinodal decomposition

Abstract

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time $\tau$ as $R=[B\tau {]}^n$ with n=1/3, where B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance at wave vector $\mathbf{k}$ can be collapsed onto a scaling function $Cov(\delta t,\bar{t})$, where $\delta t=k^{1/n}B|{\tau }_2-{\tau }_1|$ and $\bar{t}=k^{1/n}B({\tau }_1+{\tau }_2)/2$. Both analytically and numerically, the covariance is found to depend on $\delta t$ only through $\delta t/\bar{t}$ in the small-$\bar{t}$ limit and $\delta t/{\bar{t}}^{1-n}$ in the large-$\bar{t}$ limit, consistent with a simple theory of moving interfaces that applies to any universality class described by a scalar order parameter. The speckle-intensity covariance is numerically demonstrated to be equal to the square of the two-time structure factor of the scattering material, for which an analytic scaling function is obtained for large $\bar{t}.$ In addition, the two-time, two-point order-parameter correlation function is found to scale as $C(r/(B^n\sqrt{{\tau }_1^{2n}+{\tau }_2^{2n}}),{\tau }_1/{\tau }_2)$, even for quite large distances $r$. The asymptotic power-law exponent for the autocorrelation function is found to be $\lambda \approx 4.47$, violating an upper bound conjectured by Fisher and Huse.

RevTex: 11 pages + 12 figures, submitted to PRE

References in corpus (3)

• Speckle from phase ordering systems
• Persistence, Poisoning, and Autocorrelations in Dilute Coarsening
• Universality and Scaling for the Structure Factor in Dynamic Order-Disorder Transitions

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