Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

Journal Article · 05 December 2017 · Physical Review B

DOI: https://doi.org/10.1103/PhysRevB.96.235406 · OSTI ID:1411960

Lai, King C. ^[1]; Liu, Da -Jiang ^[2]; Evans, James W. ^[1]

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1. Ames Lab., Ames, IA (United States); Iowa State Univ., Ames, IA (United States)
2. Ames Lab., Ames, IA (United States)

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal(100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN ~ N^-β with β = 3/2. However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N < 9; (ii) slow nucleation-mediated diffusion with small β < 1 for “perfect” sizes N = N_p = L² or L(L+1), for L = 3, 4,… having unique ground state shapes, for moderate sizes 9 ≤ N ≤ O(10²); the same also applies for N = N_p +3, N_p + 4,… (iii) facile diffusion but with large β > 2 for N = Np + 1 and N_p + 2 also for moderate sizes 9 ≤ N ≤ O(10²); (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲ β < 3/2, reflecting the quasi-facetted structure of clusters, for larger N = O(10²) to N = O(10³); and (v) classic scaling with β = 3/2 for very large N = O(103) and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where show that diffusivity cycles quasi-periodically from the slowest branch for N_p + 3 (not Np) to the fastest branch for Np + 1. Behavior is quantified by Kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back-correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground state and low-lying excited state cluster configurations, and also of kink populations.

• Research Organization: Ames Lab., Ames, IA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-07CH11358
• OSTI ID: 1411960
• Report Number(s): IS-J--9487
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 23 Vol. 96; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English