  We studied scaling in kinetic roughening and phase ordering during growth of
binary systems using 1+1 dimensional single-step solid-on-solid model with two
components interacting via Ising-like interaction with the strength K. We found
that the model exhibits crossover from the intermediate regime, with effective
scaling exponents for kinetic roughening significantly larger than for the
ordinary single-step growth model, to asymptotic regime with exponents of the
Kardar-Parisi-Zhang class. Crossover time and length are exponentially
increasing with K. For a given large K, scaling with enhanced exponents is
valid over many decades. The effective scaling exponents are continuously
increasing with K. Surface ordering proceeds up to crossover. Average size of
surface domains increases during growth with the exponent close to 1/2, the
spin-spin correlation function and the distribution of domains obey scaling
with the same exponent.
