Evolution of speckle during spinodal decomposition

Time-dependent properties of the speckled intensity patterns created by sca ttering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equati on. For binary systems which obey a local conservation law, the characteris tic domain size is known to grow in time tau as R=[B tau](n) with n=1/3, wh ere B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance a t wave vector k can be collapsed onto a scaling function Cov(delta t,(t) ov er bar), where delta t= k(1/n)B\tau(2)-tau(1)\ and (t) over bar= k(1/n)B(ta u(1)+tau(2))/2 Both analytically and numerically, the covariance is found t o depend on st only through delta t/(t) over bar in the small-(t) over bar limit and delta t/(t) over bar(1-n) in the large-(t) over bar limit, consis tent with a simple theory of moving interfaces that applies to any universa lity class described by a scalar order parameter. The speckle-intensity cov ariance is numerically demonstrated to be equal to the square of the two-ti me structure factor of the scattering material, for which an analytic scali ng function is obtained for large t. In addition, the two-time, two-point o rder-parameter correlation function is found to scale as C(r/(B(n)root tau( 1)(2n)+tau(2)(2n)), tau(1)/tau(2)), even for quite large distances r. The a symptotic power-law exponent for the autocorrelation function is found to b e lambda approximate to 4.47, violating an upper bound conjectured by Fishe r and Huse. [S1063-651X(99)00311-6].