We study scaling in kinetic roughening and phase ordering during growt
h of binary systems. We use a 1 + 1-dimensional single-step solid-on-s
olid model with Ising-like interaction between two components. We obse
rved that the model exhibits a crossover from an intermediate regime,
with effective scaling exponents for kinetic roughening significantly
larger than for the ordinary single-step growth model, to an asymptoti
c regime with exponents of the Kardar-Parisi-Zhang class. The crossove
r time and length are exponentially increasing with the strength of in
teraction K. For a given large K, scaling with enhanced exponents is v
alid over many decades. The effective scaling exponents are continuous
ly increasing with K. Surface ordering proceeds up to the crossover. T
he average size of surface domains increases during growth with the ex
ponent close to 1/2; the spin-spin correlation function and the distri
bution of domains obey scaling with the same exponent. [SO163-1829(98)
02039-6].