Epitaxial interactions between molecular overlayers and ordered substrates

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Abstract
A framework for evaluating the epitaxy of crystalline organic overlayers of generic symmetry on ordered substrates is described, which combines a computationally efficient analytical method for explicit determination of the type of epitaxy (i.e., commensurism, coincidence, or incommensurism) and overlayer azimuthal orientation with an analysis of the elastic properties of the overlayer and the overlayer-substrate interface. The azimuthal orientations predicted by the analytical method agree with values predicted by semiempirical potential-energy calculations and observed experimentally for previously reported organic overlayers which are demonstrated here to be coincident. Calculations based on this analytical approach are much less computationally intensive than potential-energy calculations, as the number of computational operations is independent of the overlayer size chosen for analysis. This enables analyses to be performed for the large overlayer basis sets common for molecular overlayers. Furthermore, this facilitates the analysis of coincident overlayers, for which the overlayer size needs to be large enough to establish a phasing relationship between a substrate and a large nonprimitive overlayer supercell so that the global minimum with respect to azimuthal angle can be determined. The computational efficiency of this method also enables a convenient examination of numerous possible reconstructed overlayer configurations in which the lattice parameters are bracketed around those of the native overlayer, thereby allowing examination of possible epitaxy-driven overlayer reconstructions. When combined with calculated intralayer- and overlayer-substrate elastic constants, this method provides a strategy for the design of heteroepitaxial molecular films. © 1996 The American Physical Society.