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Faceting of a growing crystal surface by surface diffusion.
T V Savina1, A A Golovin, S H Davis
1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208-3100, USA.
Summary
This study explores crystal surface faceting driven by anisotropic surface tension and diffusion. It reveals transitions in faceting dynamics from coarsening to chaotic surfaces as growth rates increase.
Area of Science:
- Surface science
- Materials science
- Nonlinear dynamics
Background:
- Crystal surfaces exhibit faceting due to anisotropic surface tension and diffusion.
- Surface evolution is influenced by deposition or etching fluxes.
- Understanding these processes is crucial for materials engineering and nanotechnology.
Purpose of the Study:
- To analytically and numerically study nonlinear evolution equations for 1+1 and 2+1 crystal surface faceting.
- To investigate the stationary shapes and dynamics of faceted pyramidal structures.
- To characterize the transitions in faceting behavior as a function of growth rate.
Main Methods:
- Analytical methods, including matched asymptotic expansions for small growth rates.
- Numerical simulations for larger growth rates.
- Investigation of nonlinear evolution equations governing surface diffusion and deposition/etching.
Main Results:
- Unique solitary hill and periodic hill-and-valley solutions were found for 1+1 surfaces.
- Solitary valley solutions for 1+1 surfaces form a one-parameter family.
- Faceting dynamics transition from power-law coarsening to fixed-size pyramidal structures and finally to spatiotemporally chaotic surfaces with increasing growth rates.
Conclusions:
- The study provides a comprehensive understanding of crystal surface faceting dynamics.
- Transitions in surface morphology are characterized across different growth regimes.
- The findings contribute to predicting and controlling surface structures in materials science.