The crystallite size–disorder relationship based on the spiral paracrystal

Eads, J.L.; Millane, Rick P.

doi:10.1107/s0108767300010205

Acta Cryst Sect A

2000

DOI: 10.1107/s0108767300010205

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The crystallite size–disorder relationship based on the spiral paracrystal

J.L. Eads

Rick P. Millane

Abstract: A simple physical model of the relationship between crystallite size and disorder for paracrystalline materials is presented, based on the spiral paracrystal and distortion of the lattice cells. Simulations show that the model leads to relationships similar to the Ã rule. Average crystallite sizes predicted by the model are in agreement with experimental data and also allow crystallite-size distributions to be proposed. The model provides a more satisfactory and complete explanation of this relationship than d… Show more

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Cited by 3 publications

References 14 publications

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Five Metal(II) Coordination Polymers Constructed from Two Vanillin Derivatives: From Discrete Structure to 3D Diamondoid Network

Gao

Liu

et al. 2009

Crystal Growth & Design

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Two vanillin derivatives, 4-hydroxy-3-methoxybenzaldehyde nicotinoylhydrazone (L 1 ) and 4-hydroxy-3-methoxybenzaldehyde salicyloylhydrazone (L 2 ), were synthesized. The two flexible ligands have been employed to assemble with Pb(II), Cu(II), or Co(II) ion, leading to the formation of five coordination polymers varying from zero-to three-dimensional structures. Complex [Pb 2 (L 1 ) 2 (NO 3 ) 2 ] 3 3H 2 O (1) features a novel 3D diamond-like coordination network based on binuclear units as binodes and hydrazone ligands, L 1 , as linkers. However, complex Pb 2 (L 1 ) 2 (OAc) 2 (H 2 O) 2 (2) presents a 1D doublestrand chain structure. Two factors, the second ligand (acid ligand) and different coordination ability of water molecules, are investigated to further explore its relationship with the resultant crystalline architectures in complexes 1 and 2. The donor atoms in the two lead(II) complexes 1 and 2 can cluster to one side leaving an "open" coordination site to accommodate the stereochemically active 6s 2 lone pair. Complex Cu(L 2 ) 2 (3) shows a 1D double-strand chain structure. There is an extended onedimensional structure in complex [Co 3þ (L 2 ) 2 (C 5 H 5 N) 2 ] 3 ClO 4 (4), while [Co 2þ (L 2 ) 2 (C 5 H 5 N) 2 ] 3 2CH 3 OH 3 H 2 O (5) displays a discrete structure.

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Five Metal(II) Coordination Polymers Constructed from Two Vanillin Derivatives: From Discrete Structure to 3D Diamondoid Network

Gao

Liu

et al. 2009

Crystal Growth & Design

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Diffraction by the ideal paracrystal

Eads¹,

Millane²

2001

Acta Cryst Sect A

Self Cite

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A detailed analysis is made of the statistics and diffraction by a general, finite, two-dimensional ideal paracrystal. The statistics of the diagonal chain through the ideal paracrystal are derived, and the special cases of square and hexagonal ideal paracrystals are considered. Expressions for the diffraction are derived and characteristics of diffraction patterns are discussed in terms of the different parameters of the model for square and hexagonal ideal paracrystals. The variation of peak widths with scattering angle along different directions in reciprocal space is examined.

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Effects of near-neighbor correlations on the diffuse scattering from a one-dimensional paracrystal

Leroy¹,

Lazzari²,

Renaud³

2004

Acta Cryst Sect A

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The one-dimensional paracrystal model is generalized by folding the lattice sites with objects whose scattering lengths or sizes and separation display a spatial correlation from cell to cell. A general theory to calculate the diffuse scattering and the scattering-length autocorrelation function is developed. The investigated models of coupling along the paracrystalline chain are the correlations between (i) the sizes of the scatterers, (ii) the sizes of scatterers and their separations, and (iii) the sizes of scatterers and the fluctuation of their separation distances. In the first case (i), the size of a scatterer is, on average, linked to that of its neighbors. As a result, a continuous transition from the total lack of size correlation (known as decoupling approximation or DA) to the scattering from monodisperse domains (local monodisperse approximation or LMA) is obtained. In the second case of correlation (ii), the mean interobject distance is assumed to depend on the respective sizes of nearest neighbors. Depending on the introduced correlation parameter, aggregation or hard-core-type effects can be accounted for. Surprisingly, in some cases, it is possible to find a peak in the scattering curve without any structure in the total interference function. The size-separation correlations may also dramatically reduce the scattering intensity close to the origin compared to the completely uncorrelated case. The last model (iii) foresees a coupling between the sizes of neighboring objects and the variance of the separation between neighbors. Within this model, on average along the chain, the fluctuations of distances between scatterers become dependent on the respective sizes of neighbors, while the mean distance between objects remains constant.

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The crystallite size–disorder relationship based on the spiral paracrystal

Cited by 3 publications

References 14 publications

Five Metal(II) Coordination Polymers Constructed from Two Vanillin Derivatives: From Discrete Structure to 3D Diamondoid Network

Five Metal(II) Coordination Polymers Constructed from Two Vanillin Derivatives: From Discrete Structure to 3D Diamondoid Network

Diffraction by the ideal paracrystal

Effects of near-neighbor correlations on the diffuse scattering from a one-dimensional paracrystal

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