Paracrystals and growth-disorder models

Welberry, T. R.; Miller, Glenn H.; Carroll, C. E.

doi:10.1107/s0567739480001921

Cited by 33 publications

(42 citation statements)

References 4 publications

(4 reference statements)

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“…As discussed above for the square paracrystals, for values of σ L > ∼0.3 the diffraction pattern contains no Bragg peaks and only diffuse paracrystal peaks remain [4]. The diffraction pattern of the example in Figure 4A shows two orders of the diffuse paracrystal peaks.…”

Section: Examples Effect Of Variance σ 2 Lmentioning

confidence: 82%

“…Paracrystalline models based on interacting Gausssian random variables that were described previously for a square lattice [4] have proved useful in a number of different fields. These include the analysis of fibre diffraction patterns [8,9], the description of the distribution of defect clusters in the non-stoichiometric iron oxide wüstite, Fe 1-x O [10] and recently in interpreting diffraction from semiconductor structures with self-organized quantum dots (QDs) [11].…”

Section: Discussionmentioning

confidence: 99%

“…Following the line advocated by Hammersley [3] Welberry and co-workers [4][5][6] developed a model for distorted lattices in which sets of Gaussian distributed random variables were associated with each site of a regular lattice and then correlations introduced between these variables. In the remainder of this paper the term paracrystal is used (rather loosely) to refer to highly distorted examples of these perturbed regular lattices.…”

Section: Introductionmentioning

confidence: 99%

“…However, the accompanying very high values of the correlations, ρ L and ρ T , means that the variance, 2 , d σ of the distance between nearest neighbours is quite small. This may be quantified (see reference [4]) using the formula, Figure 2 shows three examples of paracrystals produced in this way that are based on a square lattice. In Figure The aim of the present paper is to extend the use of Gaussian variables to produce highly distorted hexagonal lattices or hexagonal paracrystals, which have not previously been treated.…”

Section: Introductionmentioning

confidence: 99%

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Hexagonal paracrystals

Welberry

2014

Zeitschrift Für Kristallographie - Crystalline Materials

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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, 2 , L σ 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.

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Section: Examples Effect Of Variance σ 2 Lmentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hexagonal paracrystals

Welberry

2014

Zeitschrift Für Kristallographie - Crystalline Materials

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“…Incorporation of correlated lattice distortions into a model of polycrystalline fibers, and calculation of associated diffraction patterns, is the subject of this paper. Two models of lattices with correlated distortions are the paracrystal (Hosemann & Bagchi, 1962) and the perturbed lattice (Welberry, Miller & Carroll, 1980;Welberry & Carroll, 1982, 1983. In the paracrystal model, a distorted lattice is generated by replacing vectors that form the edges of the unit cell of a periodic lattice with vectors that vary in both length and direction.…”

Section: Introductionmentioning

confidence: 99%

Diffraction by Polycrystalline Fibers with Correlated Disorder

Stroud¹,

Millane²

1996

Acta Cryst Sect A

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Theory is developed for describing diffraction from polycrystalline fibers of helical molecules, in which the constituent crystallites contain correlated lattice disorder and uncorrelated substitution disorder. The theory utilizes a recently reported description of cylindrically averaged diffraction by distorted lattices that is based in real space and uses an imposed correlation field to describe correlated disorder [Stroud & Millane (1996). Proc. R. Soc. London Ser. A, 452,. The theory developed here is implemented as an efficient numerical algorithm for calculating diffraction patterns from fibers containing correlated disorder. Simulations are used to explore the effects of this kind of disorder and to characterize the disorder in a polynucleotide fiber whose diffraction pattern indicates its presence. This leads to a significant improvement in the agreement between the calculated and measured diffraction patterns over that from a model of only uncorrelated lattice disorder.

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Methods of Analysis of Diffuse Scattering from Disordered Structures of Polymers

2013

Crystals and Crystallinity in Polymers

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Paracrystals and growth-disorder models

Cited by 33 publications

References 4 publications

Hexagonal paracrystals

Hexagonal paracrystals

Diffraction by Polycrystalline Fibers with Correlated Disorder

Methods of Analysis of Diffuse Scattering from Disordered Structures of Polymers

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