Coincidence site lattice theory of multicrystalline ensembles

Gertsman, V.Y.

doi:10.1107/s0108767301009102

Cited by 43 publications

(9 citation statements)

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“…It follows that the volume of the CSL n lattice is AE multi = 3 3n . This result could also probably be derived from the general formula suggested by Gertsman (2001b).…”

Section: Figuresupporting

confidence: 66%

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ⁿgrain boundaries

Cayron

2006

Acta Crystallogr A Found Crystallogr

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Multiple twinning in cubic crystals is represented geometrically by a threedimensional fractal and algebraically by a groupoid. In this groupoid, the variant crystals are the objects, the misorientations between the variants are the operations, and the AE3 n operators are the different types of operations (expressed by sets of equivalent operations). A general formula gives the number of variants and the number of AE3 n operators for any twinning order. Different substructures of this groupoid (free group, semigroup) can be equivalently introduced to encode the operations with strings. For any coding substructure, the operators are expressed by sets of equivalent strings. The composition of two operators is determined without any matrix calculation by string concatenations. It is multivalued due to the groupoid structure. The composition table of the operators is used to identify the AE3 n grain boundaries and to reconstruct the twin related domains in the electron back-scattered diffraction maps.

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“…It follows that the volume of the CSL n lattice is AE multi = 3 3n . This result could also probably be derived from the general formula suggested by Gertsman (2001b).…”

Section: Figuresupporting

confidence: 66%

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ⁿgrain boundaries

Cayron

2006

Acta Crystallogr A Found Crystallogr

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“…Another way to classify gain boundaries is by the degree of fit ( ) between the lattice structures of the two grains, which is expressed in the coincident site lattice (CSL) theory by the reciprocal of the ratio of coincidence sites to the total number of sites. 9 Grain boundaries with high-valus (higher than 30) are regarded as random grain boundaries. On the other hand, the grain boundaries with low-values (less than 30) are categorized as CSL boundaries.…”

mentioning

confidence: 99%

Local Electrochemistry and In Situ Microscopy of Pitting at Sensitized Grain Boundary of Type 304 Stainless Steel in NaCl Solution

Ida

Muto

Sugawara

et al. 2017

J. Electrochem. Soc.

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To elucidate the pit initiation behavior of sensitized stainless steels, the anodic polarization of a single grain boundary was examined in 0.1 M NaCl (pH 5.4) at 298 K using a micro-electrochemical system. For Type 304 heat-treated at 923 K for 2 h, no pitting was initiated on a small area (ca. 100 μm × 100 μm) with a sensitized grain boundary without MnS inclusions. However, stable pitting was observed on the electrode area that was larger than ca. 200 μm × 200 μm. In situ microscopy revealed that the first step in corrosion was a spherical pit generated at a MnS inclusion at a sensitized grain boundary, and that intergranular corrosion started at the pit. The local depassivation of the Cr-depleted zone along the sensitized grain boundary was thought to be introduced by the dissolution of the inclusion. The co-existence of the MnS inclusion and the Cr-depleted zone was considered to be the critical factor in the pit initiation of sensitized stainless steels in NaCl solutions. Stainless steels are widely used in chloride environments because of their high corrosion resistance, which is attributed to their high Cr content, at above 12 mass%.1 When stainless steels are heated to around 900 K (e.g., welding), sensitization occurs due to the formation of Cr-depleted zones at the grain boundaries. The susceptibility to intergranular corrosion and pitting at the grain boundaries increases as a result of sensitization-treatments. 2To assess the degree of sensitization and/or the mechanisms of intergranular corrosion, acidic solutions are usually used. ASTM A262 testing specification contains the following intergranular corrosion tests: 1) Huey test (boiling HNO 3 ), 2) Strauss test (boiling H 2 SO 4 + CuSO 4 + metallic Cu), 3) and Streicher test (boiling H 2 SO 4 + Fe 2 (SO 4 ) 3 ). After immersion, the specimens are visually examined and/or measured for weight loss. These methods have been widely and successfully used in corrosion engineering. ISO 12732 specifies a method that uses the double loop electrochemical potentiodynamic reactivation test (based onĈihal's method 3 ). In this method, the standard solution is 0.5 M H 2 SO 4 -0.01 M KSCN, and the degree of sensitization can be evaluated quantitatively from the comparison of the peak current densities between the anodic scan and the subsequent cathodic scan.Although acidic solutions are generally used to evaluate the degree of sensitization, in practical applications, pitting and stress corrosion cracking occur in stainless steels in near-neutral pH environments. NaCl solutions are used to evaluate the pitting corrosion resistance and the susceptibility of sensitized stainless steels to stress corrosion cracking (SCC). Cheng et al. studied the pitting corrosion of sensitized Type 304 stainless steel under wet-dry cycling and demonstrated that both the probability of pitting and the average size of the pit increased as a result of sensitization. 4 It was suggested that the observed change in the pit morphology from round to an irregular shape could be attributed t...

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“…Several authors have speculated that longer-range correlations may exist [10][11][12], but apart from our most recent study on quadruple junction character [9], there has been no quantitative exploration of this issue. In this note, we offer the first study of correlations at the second and third nearest-neighbor levels in two-dimensional (2D) grain boundary networks, and point to critical issues for the development of a comprehensive percolation theory for grain boundary networks.…”

Section: Introductionmentioning

confidence: 89%

Correlations beyond the nearest-neighbor level in grain boundary networks

Schuh

Frary

2006

Scripta Materialia

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This is an author-produced, peer-reviewed version of this article. © 2009, Elsevier. Licensed under the Creative Commons AttributionNonCommercial-NoDerivatives 4.0 International License (https://creativecommons.org/licenses/by-nc-nd/4.0/). The final, definitive version of this document can be found online at Scripta Materialia, doi: 10.1016Materialia, doi: 10. /j.scriptamat.2005 This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Scripta Materialia Abstract Correlations among 'special' and 'general' grain boundaries are studied on two-dimensional networks, by examining the configurational entropy of boundary structures as well as percolation thresholds. Consideration of crystallographic constraints at various length scales reveals that higher-order constraints play a role in boundary connectivity and network structure. Implications for grain boundary engineering are discussed and directions for future work highlighted.

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Coincidence site lattice theory of multicrystalline ensembles

Cited by 43 publications

References 10 publications

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ⁿgrain boundaries

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ⁿgrain boundaries

Local Electrochemistry and In Situ Microscopy of Pitting at Sensitized Grain Boundary of Type 304 Stainless Steel in NaCl Solution

Correlations beyond the nearest-neighbor level in grain boundary networks

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Coincidence site lattice theory of multicrystalline ensembles

Cited by 43 publications

References 10 publications

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ngrain boundaries

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ngrain boundaries

Local Electrochemistry and In Situ Microscopy of Pitting at Sensitized Grain Boundary of Type 304 Stainless Steel in NaCl Solution

Correlations beyond the nearest-neighbor level in grain boundary networks

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Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ⁿgrain boundaries

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ⁿgrain boundaries