Spontaneous flattening of randomly corrugated unstructured surfaces

A simple kinetic theory of the spontaneous flattening of randomly corrugated solid surface is presented, based on Mullins equation for idealized surfaces given by the equation z=ζ(x,y,t), t>0. We define ζ(x,y,t) as a statistically homogeneous random function centred at zero. <ζ(x,y,t)>=0. The coefficients A > 0 and B > 0 are proportional to the surface tension and correspond to the evaporation-condensation and surface-diffusion mechanism, respectively. The autocorrelation function of ζ(x,y,0) (at time t0 =0) is modelled as a function of the Gaussian shape. Two situations are treated: the case where ζ is a statistically isotropic (in lateral directions) random function and the case where ζ is a random function in the x-direction, not dependent on the perpendicular coordinate y. Attention is focussed on the r.m.s deviation η(t) =√ {[ζ(x,y,t)]2}. It is shown for both the situations that the long-time dependence of η(t) is of the form t-μ, μ > 0, in contrast with the exponential time-dependence which was formerly derived by Mullins for sinusoidally corrugated surfaces. (author)