Model of the radial distribution function of pores in a layer of porous aluminum oxide

Cherkas, N. L.; Cherkas, S. L.

doi:10.1134/s106377451506005x

Cited by 10 publications

(10 citation statements)

References 23 publications

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“…This method was applied to describe the structure of some simple liquids [9][10][11][12][13][14][15]. A similar method of smearing of coordinate circles was used to describe artificial 2D crystals [16,17]. Here we consider a slightly different method consisting in the random shifting of the crystal nodes.…”

Section: Introductionmentioning

confidence: 99%

Smeared Lattice Model as a Framework for Order to Disorder Transitions in 2D Systems

Cherkas

2018

Crystals

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Order to disorder transitions are important for two-dimensional (2D) objects such as oxide films with cellular porous structure, honeycomb, graphene, Bénard cells in liquid, and artificial systems consisting of colloid particles on a plane. For instance, solid films of porous alumina represent almost regular crystalline structure. We show that in this case, the radial distribution function is well described by the smeared hexagonal lattice of the two-dimensional ideal crystal by inserting some amount of defects into the lattice.Another example is a system of hard disks in a plane, which illustrates order to disorder transitions. It is shown that the coincidence with the distribution function obtained by the solution of the Percus-Yevick equation is achieved by the smoothing of the square lattice and injecting the defects of the vacancy type into it. However, better approximation is reached when the lattice is a result of a mixture of the smoothed square and hexagonal lattices. Impurity of the hexagonal lattice is considerable at short distances. Dependencies of the lattice constants, smoothing widths, and contributions of the different type of the lattices on the filling parameter are found. The transition to order looks to be an increase of the hexagonal lattice fraction in the superposition of hexagonal and square lattices and a decrease of their smearing.

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Section: Introductionmentioning

confidence: 99%

Smeared Lattice Model as a Framework for Order to Disorder Transitions in 2D Systems

Cherkas

2018

Crystals

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“…The radial distribution function is one of the most widely used approaches for characterizing particle clustering in turbulent flows (Monchaux et al, 2012), and is also currently widely used in a variety of other fields including stochastic geometry (e.g., Stoyan et al, 1995), astrophysics (e.g., Martinez and Saar, 2001), granular media (e.g., Lee and Seong, 2016), crystallography (e.g., Cherkas and Cherkas, 2016), and plasma physics (e.g., Erimbetova et al, 2013). The ideas behind its use go back at least a century (e.g., Ornstein and Zernike, 1914), and its wide use permits a large number of different conceptual and notational conventions.…”

Section: Introduction To the Radial Distribution Functionmentioning

confidence: 99%

A Method for Computing the Three-Dimensional Radial Distribution Function of Cloud Particles from Holographic Images

Larsen¹,

Shaw²

2018

Preprint

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Abstract. Reliable measurements of the three-dimensional radial distribution function for cloud droplets are desired to help characterize microphysical processes that depend on local drop environment. Existing numerical techniques to estimate this three-dimensional radial distribution function are not well suited to in situ or laboratory data gathered from a finite experimental domain. This manuscript introduces and tests a new method designed to reliably estimate the three-dimensional radial distribution function in contexts where (i) physical considerations prohibit the use of periodic boundary conditions and (ii) particle positions are measured inside a convex volume that may have a large aspect ratio. The method is then utilized to measure the three-dimensional radial distribution function from laboratory data taken in a cloud chamber from the Holographic Detector for Clouds (HOLODEC).

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Section: Introduction To the Radial Distribution Functionmentioning

confidence: 99%

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Larsen¹

2018

Preprint

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Model of the radial distribution function of pores in a layer of porous aluminum oxide

Cited by 10 publications

References 23 publications

Smeared Lattice Model as a Framework for Order to Disorder Transitions in 2D Systems

Smeared Lattice Model as a Framework for Order to Disorder Transitions in 2D Systems

A Method for Computing the Three-Dimensional Radial Distribution Function of Cloud Particles from Holographic Images

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