  We study the formation of nanostructures with alternating stripes composed of
bulk-immiscible adsorbates during submonolayer heteroepitaxy. We evaluate the
influence of two mechanisms considered in the literature: (i) strain relaxation
by alternating arrangement of the adsorbate species, and (ii) kinetic
segregation due to chemically induced diffusion barriers. A model ternary
system of two adsorbates with opposite misfit relative to the substrate, and
symmetric binding is investigated by off-lattice as well as lattice kinetic
Monte Carlo simulations. We find that neither of the mechanisms (i) or (ii)
alone can account for known experimental observations. Rather, a combination of
both is needed. We present an off-lattice model which allows for a qualitative
reproduction of stripe patterns as well as island ramification in agreement
with recent experimental observations for CoAg/Ru(0001) [R. Q. Hwang, Phys.
Rev. Lett. 76, 4757 (1996)]. The quantitative dependencies of stripe width and
degree of island ramification on the misfit and interaction strength between
the two adsorbate types are presented. Attempts to capture essential features
in a simplified lattice gas model show that a detailed incorporation of
non-local effects is required.
