Hexagonal paracrystals

Thomas Richard Welberry

doi:10.1515/zkri-2014-1732

Hexagonal paracrystals

Thomas Richard Welberry^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Spatially interacting Gaussian random variables arranged on a hexagonal lattice are used to construct examples of hexagonal paracrystals. As for previously described paracrystals on a square lattice the distributions may be specified by a variance, σ_L², defining the magnitude of the displacement away from the underlying perfect lattice together with parameters defining transverse and longitudinal correlations (ρ_T and ρ_L) between neighbouring displacements. A strong longitudinal correlation indicates a small variation from cell to cell in the length of the cell edge whereas a strong transverse correlation indicates a small variation in the cell edge direction. For values of σ_L>~0.30 of the unit cell spacing the diffraction patterns contain diffuse peaks only with no evidence of Bragg peaks arising from the underlying regular lattice.

Original language	English
Pages (from-to)	69-74
Number of pages	6
Journal	Zeitschfrift fur Kristallographie
Volume	230
Issue number	1
DOIs	https://doi.org/10.1515/zkri-2014-1732
Publication status	Published - 1 Jan 2015

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title = "Hexagonal paracrystals",

abstract = "Spatially interacting Gaussian random variables arranged on a hexagonal lattice are used to construct examples of hexagonal paracrystals. As for previously described paracrystals on a square lattice the distributions may be specified by a variance, σL2, defining the magnitude of the displacement away from the underlying perfect lattice together with parameters defining transverse and longitudinal correlations (ρT and ρL) between neighbouring displacements. A strong longitudinal correlation indicates a small variation from cell to cell in the length of the cell edge whereas a strong transverse correlation indicates a small variation in the cell edge direction. For values of σL>~0.30 of the unit cell spacing the diffraction patterns contain diffuse peaks only with no evidence of Bragg peaks arising from the underlying regular lattice.",

keywords = "diffraction, diffuse scattering, distorted lattices, paracrystals",

author = "Welberry, {Thomas Richard}",

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N2 - Spatially interacting Gaussian random variables arranged on a hexagonal lattice are used to construct examples of hexagonal paracrystals. As for previously described paracrystals on a square lattice the distributions may be specified by a variance, σL2, defining the magnitude of the displacement away from the underlying perfect lattice together with parameters defining transverse and longitudinal correlations (ρT and ρL) between neighbouring displacements. A strong longitudinal correlation indicates a small variation from cell to cell in the length of the cell edge whereas a strong transverse correlation indicates a small variation in the cell edge direction. For values of σL>~0.30 of the unit cell spacing the diffraction patterns contain diffuse peaks only with no evidence of Bragg peaks arising from the underlying regular lattice.

AB - Spatially interacting Gaussian random variables arranged on a hexagonal lattice are used to construct examples of hexagonal paracrystals. As for previously described paracrystals on a square lattice the distributions may be specified by a variance, σL2, defining the magnitude of the displacement away from the underlying perfect lattice together with parameters defining transverse and longitudinal correlations (ρT and ρL) between neighbouring displacements. A strong longitudinal correlation indicates a small variation from cell to cell in the length of the cell edge whereas a strong transverse correlation indicates a small variation in the cell edge direction. For values of σL>~0.30 of the unit cell spacing the diffraction patterns contain diffuse peaks only with no evidence of Bragg peaks arising from the underlying regular lattice.

KW - diffraction

KW - diffuse scattering

KW - distorted lattices

KW - paracrystals

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JO - Zeitschfrift fur Kristallographie

JF - Zeitschfrift fur Kristallographie

IS - 1

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Hexagonal paracrystals

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