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Evolution of speckle during spinodal decomposition | | Gregory Brown
; Per Arne Rikvold
; Mark Sutton
; Martin Grant
; | | Date: |
24 May 1999 | | Journal: | Phys. Rev. E 60, 5151 (1999) | | Subject: | Statistical Mechanics; Materials Science | cond-mat.stat-mech cond-mat.mtrl-sci | | Affiliation: | McGill & Florida State), Per Arne Rikvold (Florida State), Mark Sutton(McGill), and Martin Grant(McGill | | 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 $ au$ as $R = [B au]^n$ 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 ${f k}$ can be collapsed onto a scaling function $Cov(delta t,ar{t})$, where $delta t = k^{1/n} B | au_2- au_1|$ and $ar{t} = k^{1/n} B ( au_1+ au_2)/2$. Both analytically and numerically, the covariance is found to depend on $delta t$ only through $delta t/ar{t}$ in the small-$ar{t}$ limit and $delta t/ar{t} ^{1-n}$ in the large-$ar{t}$ 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 $ar{t}.$ In addition, the two-time, two-point order-parameter correlation function is found to scale as $C(r/(B^nsqrt{ au_1^{2n}+ au_2^{2n}}), au_1/ au_2)$, 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. | | Source: | arXiv, cond-mat/9905343 | | Services: | Forum | Review | PDF | Favorites | |
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