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We present a critical view of the analysis of experimental island densities acquired as a function of temperature in terms of barriers and prefactors for tracer diffusion at surfaces. We investigate the achievable precision for methods ranging from simple application of scaling laws, via integration of mean-field rate equations within various approximations for the capture rates, to kinetic Monte Carlo simulations that account for the various island shapes realized on square and hexagonal lattices. The discussion of theoretical models will be accompanied by variable temperature STM data for the nucleation of Ag on a Pt͑111͒ surface. We introduce experimental methods to test for dimer diffusion and dissociation, as well as for transient mobility of monomers. Density scaling is analyzed in the presence of post-deposition mobility and easy adatom attachment to islands and other monomers. From extended kinetic Monte Carlo simulations we establish density scaling for the various island shapes on square and hexagonal lattices for coverages up to percolation, which is particularly relevant for methods working in reciprocal space. ͓S0163-1829͑99͒01231-X͔

Dynamical growth aspects of symmetry-breaking, first-order phase transitions for which the primary order parameter is a second-rank tensor, e.g., strain describing diffusionless structural phase transitions, are considered. It is found that a single domain does not always grow inside the parent phase matrix, but instead a perpetually twinning interface propagates through the system, a result of the system attempting to minimize its kinetic energy.

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