Scaling behaviour of pair correlation functions for randomly faulted hexagonal close-packed structures

Tiwary, Pratyush; Pandey, Dhananjai

doi:10.1107/s0108767307017990

Cited by 5 publications

(15 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, s 2 < 0 corresponds to the average h.c.p. disordered stacking arrangement also as reported earlier by Tiwary & Pandey (2007a).…”

Section: Case Iii: S 2 <supporting

confidence: 89%

“…We did not manage to reduce the sum of two exponentials to a single exponential. The particular cases treated by Tiwary & Pandey (2007a), though, are valid and similar to the results presented here. Fig.…”

Section: The Probability Correlation Functionsupporting

confidence: 86%

“…Thus, s 2 > 0 corresponds to the average f.c.c. disordered stacking arrangement as reported earlier by Tiwary & Pandey (2007a). Combining equations (32), (33) and (34), the following expression can be obtained,…”

Section: The Probability Correlation Functionmentioning

confidence: 66%

“…In Tiwary & Pandey (2007a) an equivalent expression [equation (15) in their article] to equation (29) is made equal to a single exponential decaying function [equation (16) in their article], thus defining a single characteristic length for the decaying behavior. Care must be taken: to make a sum of two exponentials equal to a single exponential is in general not mathematically justified.…”

Section: The Probability Correlation Functionmentioning

confidence: 99%

See 3 more Smart Citations

Stacking and twin faults in close-packed crystal structures: exact description of random faulting statistics for the full range of faulting probabilities

et al. 2008

View full text Add to dashboard Cite

The classical model of independent random single deformation faults and twin faulting in face-centered-cubic and hexagonal close packing is revisited. The model is extended to account for the whole range of faulting probabilities. The faulting process resulting in the final stacking sequences is described by several equivalent computational models. The probability sequence tree is established. Random faulting is described as a finite-state automaton machine. An expression giving the percent of hexagonality from the faulting probabilities is derived. The average sizes of the cubic and hexagonal domains are given as a function of single deformation and twinning fault probabilities. An expression for the probability of finding a given sequence within the complete stacking arrangement is also derived. The probability P(0)(Delta) of finding two layers of the same type Delta layers apart is derived. It is shown that previous generalizations did not account for all terms in the final probability expressions. The different behaviors of the P(0)(Delta) functions are discussed.

show abstract

“…Thus, s 2 < 0 corresponds to the average h.c.p. disordered stacking arrangement also as reported earlier by Tiwary & Pandey (2007a).…”

Section: Case Iii: S 2 <supporting

confidence: 89%

Section: The Probability Correlation Functionsupporting

confidence: 86%

Section: The Probability Correlation Functionmentioning

confidence: 66%

Section: The Probability Correlation Functionmentioning

confidence: 99%

See 2 more Smart Citations

Stacking and twin faults in close-packed crystal structures: exact description of random faulting statistics for the full range of faulting probabilities

et al. 2008

View full text Add to dashboard Cite

show abstract

“…But the conventional methods (random-walk technique, difference equation or matrixequation methods), even if applied to the structures with a small concentration and/or random distribution of SFs, proved to be mathematically cumbersome. Satisfactory solutions have been obtained merely for only two low period polytypes, i.e., 2H and 3C [16][17][18]. Therefore, they were applied to limited number of simple cp structures [19][20][21][22][23] and few phase transformations between them [24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Modelling diffraction patterns from one‐dimensionally disordered structures of A^IIB^VI crystals by Monte Carlo Technique IV. The 6H structure with different kinds of stacking faults

Gosk

2010

Cryst. Res. Technol.

View full text Add to dashboard Cite

To investigate the one-dimensionally disordered structures (ODDS) in the close packed (cp) crystals, the Monte Carlo computer simulation technique has been applied. Calculations of the diffraction intensity distributions along the 10.L reciprocal lattice row from the 6H(33) structure with the four different kinds of the stacking faults (SFs): growth, deformation, layer displacement and extrinsic fault are presented. In particular, using the simple frequency functions of the fault to fault distances, both random and non-random distributions of the SFs are considered. Distinctive features of the diffraction patterns corresponding to the chosen examples of the transformations from the parent 6H(33) structure into another small-period polytypes are discussed in detail.

show abstract

A Unique Example of Structural Diversity Tuned by Apparently Innocent o-, m-, and p-Nitro Substituents of Benzoate in Their Complexes of Mn(II) with 4,4′-Bipyridine: 1D Ladder, 2D Sheet, and 3D Framework

Kar

Biswas

Ida

et al. 2011

Crystal Growth & Design

View full text Add to dashboard Cite

Four new Mn(II) coordination polymers [Mn(4,4′-bpy)(C6H5COO)2] n (1), [Mn(4,4′-bpy)(o-(NO2)C6H4COO)2] n (2), [Mn(4,4′-bpy)(m-(NO2)C6H4COO)2] n (3), and [Mn(4,4′-bpy)(p-(NO2)C6H4COO)2] n (4) (where 4,4′-bpy = 4,4′-bipyridine) have been synthesized by self-assembly of the primary ligands, benzoate and the o-, m-, and p-isomers of nitrobenzoates, respectively, together with 4,4′-bpy as the secondary spacer. All four complexes were characterized by elemental analyses, IR spectroscopy, single-crystal X-ray diffraction analyses, and variable-temperature magnetic measurements. The structural analyses reveal that complexes 1 and 3 are constructed by linear fused chains through double syn-syn (for 1) or syn-anti (for 3) carboxylate-bridged Mn(II), which are further linked to one another by trans coordinated 4,4′-bpy bridges, giving rise to a rectangular grid-like two-dimensional (2D) net. Complex 2 features one-dimensional (1D) molecular ladder formed by both syn-syn and syn-anti carboxylate-bridged dimeric Mn(II) units which are joined alternately by 4,4′-bpy. Complex 4 is formed by fused zigzag chains of double syn-syn carboxylate-bridged Mn(II) that are connected by cis oriented 4,4′-bpy to generate an unprecedented three-dimensional (3D) framework. The dimensionality of the complexes thus varies from 1D to 2D to 3D on changing the position of the nitro group from o- to m- to p- in the benzoate, showing explicitly the tuning ability of this apparently innocent substituent on the topology of the coordination polymer. Variable-temperature (1.8–300 K) magnetic susceptibility measurements showed the presence of antiferromagnetic coupling in all four complexes that have been fitted with an infinite classical-spin chain model derived by Fisher for 1, 3, and 4 (J = −0.779(2), −0.855(2), and −0.536(2) cm–1, respectively) and van Vleck equation for 2 (J = −0.354(2) cm–1).

show abstract

Scaling behaviour of pair correlation functions for randomly faulted hexagonal close-packed structures

Cited by 5 publications

References 24 publications

Stacking and twin faults in close-packed crystal structures: exact description of random faulting statistics for the full range of faulting probabilities

Stacking and twin faults in close-packed crystal structures: exact description of random faulting statistics for the full range of faulting probabilities

Modelling diffraction patterns from one‐dimensionally disordered structures of A^IIB^VI crystals by Monte Carlo Technique IV. The 6H structure with different kinds of stacking faults

A Unique Example of Structural Diversity Tuned by Apparently Innocent o-, m-, and p-Nitro Substituents of Benzoate in Their Complexes of Mn(II) with 4,4′-Bipyridine: 1D Ladder, 2D Sheet, and 3D Framework

Contact Info

Product

Resources

About

Scaling behaviour of pair correlation functions for randomly faulted hexagonal close-packed structures

Cited by 5 publications

References 24 publications

Stacking and twin faults in close-packed crystal structures: exact description of random faulting statistics for the full range of faulting probabilities

Stacking and twin faults in close-packed crystal structures: exact description of random faulting statistics for the full range of faulting probabilities

Modelling diffraction patterns from one‐dimensionally disordered structures of AIIBVI crystals by Monte Carlo Technique IV. The 6H structure with different kinds of stacking faults

A Unique Example of Structural Diversity Tuned by Apparently Innocent o-, m-, and p-Nitro Substituents of Benzoate in Their Complexes of Mn(II) with 4,4′-Bipyridine: 1D Ladder, 2D Sheet, and 3D Framework

Contact Info

Product

Resources

About

Modelling diffraction patterns from one‐dimensionally disordered structures of A^IIB^VI crystals by Monte Carlo Technique IV. The 6H structure with different kinds of stacking faults