P. Politi, KINK DYNAMICS IN A ONE-DIMENSIONAL GROWING SURFACE, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(1), 1998, pp. 281-294
A high-symmetry crystal surface may undergo a kinetic instability duri
ng the growth, such that its late stage evolution resembles a phase se
paration process. Th.is parallel is rigorous in one dimension, if the
conserved surface current is derivable from a free energy. We study th
e problem in the presence of a physically relevant term breaking the u
p-down symmetry of the surface and that cannot be derived from a free
energy: Following the treatment introduced by Kawasaki and Ohta [Physi
ca A 116, 573 (1982)] for the symmetric case, we are able to translate
the problem of the surface evolution into a problem of nonlinear dyna
mics of I;inks (domain walls). Because of the break of symmetry, two d
ifferent classes (A-aad B) of kinks appear and their analytical form i
s derived. The effect of the adding term is to shrink; a kink A and to
widen the neighboring kink B in such a way that the product of their
widths keeps constant. Concerning the dynamics, this implies that kink
s A move much faster than kinks B. Since the kink profiles approach ex
ponentially the asymptotical values, the time dependence of the averag
e distance L(t)between kinks does not change: L(t)similar to lnt in th
e absence of noise, and L(t)similar to t(1/3) in the presence of (shot
) noise. However, the crossover lime between the first and the second
regime may increase even of some orders of magnitude. Finally, our res
ults show that kinks A may be so narrow that their width is comparable
to the lattice constant: in this case, they indeed represent a discon
tinuity of the surface slope, that is, an angular point, and a differe
nce approach to coarsening; should be used.