Gap-size and capture-zone distributions in one-dimensional point-island nucleation and growth simulations: Asymptotics and models

O'Neill, Kenneth Peter; Grinfeld, Michael; Lamb, Wilson; Mulheran, Paul A.

doi:10.1103/physreve.85.021601

Cited by 23 publications

(62 citation statements)

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“…Here too the capture zone size s is scaled by the average. From (1) we were able to find the asymptotics of P (s) as s → 0, and subsequently showed good agreement with Monte-Carlo simulation data [13].…”

Section: Introductionsupporting

confidence: 63%

“…The values we reported for the exponents were, to 2 significant figures, 3.8, 5.5 and 6.5 respectively for i = 1, 2, 3 (see [13] for details including error estimates which are smaller than 0.1). Our predictions for this exponent depend on the mechanism that dominates nucleation.…”

Section: Discussionmentioning

confidence: 60%

“…(4). We also found higher exponents for higher critical island sizes [13], but had concrete theoretical results to compare them to at that time.…”

Section: Discussionmentioning

confidence: 80%

“…In [13] we presented results from Monte Carlo simulations for one-dimensional island nucleation and growth during submonolayer deposition, numerically analysing the asymptotics of the capture zone distributions. We found that in the spontaneous nucleation case i = 0, the measured exponent was 3.04 ± 0.04, very close to the value of 3 predicted by Eqn.…”

Section: Discussionmentioning

confidence: 99%

“…In Section 3, we compare this new result with data from our previously published Monte Carlo simulations [13], which is the only source we know of for large-size CZD asymptotics for a range of critical island sizes.…”

Section: Introductionmentioning

confidence: 97%

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Asymptotics of capture zone distributions in a fragmentation-based model of submonolayer deposition

Blackman

Grinfeld²,

Mulheran³

2015

Physics Letters A

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This version is available at https://strathprints.strath.ac.uk/55558/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the AbstractWe consider the asymptotics of the distribution of the capture zones associated with the islands nucleated during submonolayer deposition onto a one-dimensional substrate. We use a convolution of the distribution of inter-island gaps, the asymptotics of which is known for a class of nucleation models, to derive the asymptotics for the capture zones. The results are in broad agreement with published Monte Carlo simulation data [Phys. Rev. E 85, 021601].

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Section: Introductionsupporting

confidence: 63%

Section: Discussionmentioning

confidence: 60%

“…(4). We also found higher exponents for higher critical island sizes [13], but had concrete theoretical results to compare them to at that time.…”

Section: Discussionmentioning

confidence: 80%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

See 3 more Smart Citations

Asymptotics of capture zone distributions in a fragmentation-based model of submonolayer deposition

Blackman

Grinfeld²,

Mulheran³

2015

Physics Letters A

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Random Processes

Cruise

Hryniv

Wade

2015

Digital Encyclopedia of Applied Physics

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The theory of stochastic processes is concerned with mathematical models of systems whose behavior is time dependent and incorporates randomness or uncertainty. The statistical structure of the system can be determined from the physical application in mind: a rich class consists of Markov processes whose future evolution depends on the past only through the present state of the system. We give a tour through some important examples of stochastic processes, primarily (but not exclusively) in a discrete setting where technicalities are minimized. Our tour is facilitated by a selection of mathematical tools of broad applicability, with a focus on generating functions and renewal ideas. We investigate in detail some illustrative specimens chosen for their relevance to applications in the physical sciences and for the mathematical ideas they elucidate.

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

Einstein¹,

Pimpinelli²,

González³

2014

Journal of Crystal Growth

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We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) P (s) = as β exp(−bs 2 ), where s is the CZ area divided by its average value. This approach offers arguably the best 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 < s < 2, where the data is sufficiently large to be reliably accessible experimentally. We summarize and catalog the many experiments in which this method has been applied. I. PRELUDE

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Gap-size and capture-zone distributions in one-dimensional point-island nucleation and growth simulations: Asymptotics and models

Cited by 23 publications

References 25 publications

Asymptotics of capture zone distributions in a fragmentation-based model of submonolayer deposition

Asymptotics of capture zone distributions in a fragmentation-based model of submonolayer deposition

Random Processes

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

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