Microstructure morphology transitions at mesoscopic epitaxial surfaces

Spiral surface growth is well understood in the limit where motion of the spiral ridge is controlled by the local supersaturation of adatoms in its surrounding. In liquid epitaxial growth, however, spirals can form governed by both, transport of heat as well as solute. We propose for the first time a two-scale model of epitaxial growth which takes into account all of these transport processes. This new model assumes a separation of length scales for the transport of heat compared to that of the solutal field. It allows for the first time numerical simulations of extended surface regions by at the same time taking into account microstructure evolution and microstructure interaction. We apply this model successfully to extend the scaling relation for the step spacing given by the BCF theory Phil. Trans. R. Soc. London, Ser. A 243, 299 (1951)] to microstructure evolution governed by heat and solute diffusion. Further applications to understand the mechanisms and consequences of spiral interaction at epitaxial surfaces, in particular the resulting morphology transitions, are discussed.