Near-coincidence-sites modeling of the edge facet dislocation structures of α precipitates in a Ti–7.26 wt.% Cr alloy

2020

Crystals

The orientation relationship (OR) between phases related by a phase transformation is often reproducible. This study interprets and predicts the reproducible ORs with a two-stage approach. The initial OR formed at the nucleation stage tends to allow a periodic structure of a preferred state to form in the interface. A matching correspondence of either a one-to-one or n-to-m nature can be specified in the periodic structure. An initial OR will become the final reproducible OR if there is no misfit. Otherwise, a reproducible OR developed at the growth stage tends to permit a singular dislocation structure to form in an interface where the preferred state must be sustained locally. The actual change in the OR is subject to the given material system and the phase-transformation condition. Various singular dislocation structures and their constraints on the ORs are analyzed, with thermodynamics and kinetics applied conceptually. The resulting ORs can be specified by following one or more Δg parallelism rules. A set of workable steps is provided to facilitate the interpretation of observed reproducible ORs. Some unsolved problems are identified, which call for further studies that can quantitatively combine the thermodynamics, kinetics and crystallography of phase transformations.

Section: Analysis With ∆Gsmentioning

confidence: 99%

Reproducible Orientation Relationships Developed from Phase Transformations—Role of Interfaces

2020

Crystals

“…[11][12][13] To allow a small degree of misfit, we have evaluated the interfacial matching status according to the distribution of near coincidence sites (NCS), as suggested by Liang et al 14 Planes or directions containing dense NCS are likely to be favoured by nature. [14][15][16] The threshold of the NCS is taken to be 15%a a , where a a is the smallest lattice distance of a-Mg. If the distance between two points from different lattices is smaller than 15%a a , then either of the points is considered to be an NCS.…”

Section: Interpretation Of Crystallographic Morphologymentioning

confidence: 99%

Crystallography of Mg₂Sn precipitates with two newly observed orientation relationships in an Mg–Sn–Mn alloy

Shi

Dai

Materials Science and Technology

2012

Two new orientation relationships between β-Mg2Sn precipitates and α-Mg matrix have been observed by transmission electron microscopy. One is (1 1 0) β//(0 0 0 1) α, [0 0 1] β//[1 −1 0 0] α, and the other is (1 1 0) β//(0 0 0 1) α, [−1 1 −1] β//[1 −1 0 0] α. The precipitates with both orientation relationships exhibit a lath shaped morphology, with the long axis lying along [1 1 −2 0] α. The morphology is interpreted by a three-dimensional near coincidence sites model.

“…In the top insert, there is an Mg 2 Sn precipitate surrounded by three well-defined side facets, marked by dashed lines. The OR between the precipitate (β, fcc) and the matrix (α, hcp) is that [32] [0001] α is parallel to [111] β and (2-1-10) α deviates from (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) β about 9º, as shown in the lower insert. Three ∆g between nearby {0 -1 1 0} α and {0 2 -2} β are marked by elliptic circles in the diffraction pattern.…”

Section: Solid State Phenomena Vols 172-174mentioning

confidence: 99%

Description of Crystallographic Morphologies of Product Phases with Singularity and Δg Distribution

Shi

2011

SSP

Product phases from various phase transformations often exhibit fascinating morphologies. Facets of unique crystallographic orientations are characteristic of the morphologies. Based on a comparison of facets in the surfaces and interfaces of crystals, this paper proposes to use singularity as the common features of facets on a crystal. While association of facets with energy singularity has been established from the Wulff construction, we defined singularity in structure with an absence of one or more types of defects common to a vicinal surface or interface. Singularity in an interfacial structure is described in terms of both ledges and dislocations. When dislocations are involved, the candidates of the singular interfaces derive mainly from the principal O-lattice planes. The orientations of these planes are defined by Δg’s, which are measurable in diffraction patterns. Singularity with respect to the orientation relationship results from further eliminating defects, which is permitted by a special arrangement of Δg’s. The candidates of singular interface confined by the arrangement of discrete Δg’s are helpful for understanding the crystallographic morphology. One example from an Mg alloy is provided to show the association of the singular interfaces with Δg’s. The effect of the potential presence of a long-range strain and kinetic effects are briefly discussed.