Analyzing capture zone distributions (CZD) in growth: Theory and applications

• Published in: Journal of crystal growth 2014-09, Vol.401, p.67-71
• Main Authors: Einstein, Theodore L., Pimpinelli, Alberto, Luis González, Diego
• Format: Article
• Language: English
• Subjects: A1. Crystal morphology; A1. Growth models; A1. Low dimensional structures; A1. Surface structure; A2. Single crystal growth; Accessibility; Asymptotic properties; Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Crystal growth; Diffusion in solids; Exact sciences and technology; Materials science; Mathematical analysis; Mathematical models; Methods of crystal growth; physics of crystal growth; Nuclei; Physics; Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation; Transport; Transport properties of condensed matter (nonelectronic); Wigner distribution
• ISSN: 0022-0248; 1873-5002
• DOI: 10.1016/j.jcrysgro.2014.01.053

We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) P(s)=asβexp(−bs2), where s is the CZ area divided by its average value. This approach offers arguably the most robust (least sensitive to mass transport) method to find the critical nucleus size i, since β≈i+2. Various analytical and numerical investigations, which we discuss, show that the simple GWD expression is inadequate in the tails of the distribution, it does account well for the central regime 0.5