Equilibrium shapes of solid particles on elastically mismatched substrates

Small particles or islands bonded to a substrate can be profoundly influenc ed by both interfacial and elastic driving forces that tend to have opposin g influences on the apparent wetting behavior. The superposition of these t wo driving forces can therefore lead to a rich set of particle properties, most notably their equilibrium shapes. Here we present a variational analys is leading directly to an Euler-Lagrange equation that can be solved to yie ld the equilibrium shapes of partially wetting particles as a function of t heir size, interface energy densities, and elastic interaction with a rigid substrate. The solutions are used to gain insight into the variables that most significantly influence the equilibrium morphology, and to derive the approximate driving force for surface area reduction by coarsening among a dispersion of unequally sized particles. The relatively simple analytical m odel can also form a foundation upon which more realistic numerical simulat ions may be built and compared. (C) 1999 Academic Press.