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Island nucleation and growth with anomalous diffusion in one-dimension
Ehsan H Sabbar1, Jacques G Amar1
1Department of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606, USA.
The Journal of Chemical Physics
|February 24, 2017
Summary
This study validates a general rate-equation theory for submonolayer island nucleation and growth in 1D. Simulations confirm excellent agreement with the theory for both superdiffusion and subdiffusion anomalous diffusion cases.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Statistical Mechanics
Background:
- A general rate-equation (RE) theory for submonolayer island nucleation and growth was previously established for 2D substrates.
- This theory accounts for critical island size (i), fractal dimension (df), substrate dimension (d), and diffusion exponent (μ).
- Prior work showed good agreement for irreversible growth (i=1) on 2D substrates (d=2).
Purpose of the Study:
- To extend the validation of the general RE theory to one-dimensional (1D) systems (d=1).
- To investigate island nucleation and growth under anomalous diffusion conditions (superdiffusion μ>1 and subdiffusion μ<1) in 1D.
- To compare simulation results with the RE theory for both irreversible (i=1) and reversible (i=2) growth scenarios.
Main Methods:
- Conducting simulations of island nucleation and growth in a 1D system.
- Implementing anomalous diffusion models with varying diffusion exponents (μ) from 0 to 2.
- Analyzing simulation data for irreversible (i=1) and reversible (i=2) growth processes.
Main Results:
- Simulations were performed for 1D island nucleation and growth with anomalous diffusion (μ values ranging from 0 to 2).
- Excellent agreement was observed between simulation results and the general rate-equation theory.
- The agreement holds for both superdiffusion (μ>1) and subdiffusion (μ<1) across irreversible (i=1) and reversible (i=2) growth models.
Conclusions:
- The general rate-equation theory accurately describes submonolayer island nucleation and growth in 1D systems.
- The theory's validity is confirmed even with anomalous diffusion (superdiffusion and subdiffusion).
- This work extends the applicability of the RE theory to lower-dimensional systems and diverse diffusion behaviors.
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