Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

Abstract

To clarify whether a surface can be rough with faceted macrosteps that maintain their shape on the surface, crystal surface roughness is studied by a Monte Carlo method for a nucleation-limited crystal-growth process. As a surface model, the restricted solid-on-solid (RSOS) model with point-contact-type step–step attraction (p-RSOS model) is adopted. At equilibrium and at sufficiently low temperatures, the vicinal surface of the p-RSOS model consists of faceted macrosteps with (111) side surfaces and smooth terraces with (001) surfaces (the step-faceting zone). We found that a surface with faceted macrosteps has an approximately self-affine-rough structure on a ‘faceted-rough surface’; the surface width is strongly divergent at the step-disassembling point, which is a characteristic driving force for crystal growth. A ‘faceted-rough surface’ is realized in the region between the step-disassembling point and a crossover point where the single nucleation growth changes to poly-nucleation growth.

Slope–temperature faceting diagram for macrosteps at equilibrium

“…In our previous work regarding the step-faceting zone in the non-equilibrium steady state 22 , 26 , 55 , we showed that the mean height of a faceted macrostep for in the step-faceting zone is sensitive to the initial configuration. Here, represents the bulk chemical difference between the crystal and the ambient phases, represents a crossover point between the 2D single nucleation and the poly-nucleation processes at the edge of the faceted macrosteps, and L is the linear size of the system.…”

“…We found zipping phenomena 50 and pinning phenomena 51 , 56 . At a slope of , we observed disassembling/assembling of faceted macrosteps 22 , 25 , 26 and a faceted rough surface 55 between the atomically rough and thermodynamic rough surfaces. From the slope dependence of the surface width, which is the standard deviation of the surface height, in the RSOS model ( ), the roughness exponent near (001) is different from that near (111) for large 35 .…”

Induced side-branching in smooth and faceted dendrites: theory and phase-field simulations

“…With all due caution, namely the difference of Péclet number and growth regime (diffusion limited growth versus slow growth), origin of growth anisotropy (capillary versus kinetic), as well as the peculiarities of smooth and rough faceting [49], the presently described mechanism for ISB might provide an alternative scenario for the sprouting of side branches in snowflake as was experimentally observed upon changing growth conditions in [30]. In his book, Libbrecht ascribes ISB to a purely morphological origin.…”

Induced side-branching in smooth and faceted dendrites: theory and Phase-Field simulations

“…With all due caution, namely the difference of Péclet number and growth regime (diffusion limited growth vs. slow growth), origin of growth anisotropy (capillary vs. kinetic), as well as the peculiarities of smooth and rough faceting [46], the presently described mechanism for ISB might provide an alternative scenario for the sprouting of side branches in snowflake as was experimentally observed upon changing growth conditions in [31]. In his book, Libbrecht ascribes ISB to a purely morphological origin.…”