skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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 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 = L 2 or L(L+1), for L = 3, 4,… having unique ground state shapes, for moderate sizes 9 ≤ N ≤ O(10 2); 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(10 2); (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(10 2) to N = O(10 3); and (v) classic scaling with β = 3/2 for very large N = O(103) and above. The specified size ranges apply for typical modelmore » 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.« less

Authors:
 [1];  [2];  [1]
  1. Ames Lab., Ames, IA (United States); Iowa State Univ., Ames, IA (United States)
  2. Ames Lab., Ames, IA (United States)
Publication Date:
Research Org.:
Ames Lab., Ames, IA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1411960
Alternate Identifier(s):
OSTI ID: 1411280
Report Number(s):
IS-J-9487
Journal ID: ISSN 2469-9950; PRBMDO; TRN: US1800291
Grant/Contract Number:  
CHE-1507223; AC02-07CH11358
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 23; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Lai, King C., Liu, Da -Jiang, and Evans, James W. Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.235406.
Lai, King C., Liu, Da -Jiang, & Evans, James W. Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes. United States. doi:10.1103/PhysRevB.96.235406.
Lai, King C., Liu, Da -Jiang, and Evans, James W. Tue . "Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes". United States. doi:10.1103/PhysRevB.96.235406. https://www.osti.gov/servlets/purl/1411960.
@article{osti_1411960,
title = {Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes},
author = {Lai, King C. and Liu, Da -Jiang and Evans, James W.},
abstractNote = {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 = Np = 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 = Np +3, Np + 4,… (iii) facile diffusion but with large β > 2 for N = Np + 1 and Np + 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 Np + 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.},
doi = {10.1103/PhysRevB.96.235406},
journal = {Physical Review B},
number = 23,
volume = 96,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share: