On the crystallography of precipitation

Zhang, W.-Z.; Weatherly, G. C.

doi:10.1016/j.pmatsci.2004.04.002

Cited by 228 publications

(180 citation statements)

References 134 publications

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“…Therefore, the POPs are candidates for singular interfaces. 15,25 It is convenient to express the orientation of a POP with a reciprocal vector, Δg. 36 The associated g must be related by the lattice correspondence and contain two Burgers vectors.…”

Section: Singularity Based On Defect Structuresmentioning

confidence: 99%

“…Therefore, the total number of POPs for a given OR is limited, usually less than 10. An O-line interface is normal to a group of Δg's 37 (Δg parallelism rule II 15 ), and an O-plane, as an invariant plane, is normal to all Δg' s. 38 Thus, the IO of the interface is fixed. The Δg parallelism condition associated with the elimination of dislocations also restricts the OR, namely, two of the three DOF in the OR for an O-line interface, and all three DOF in the OR for an O-plane is fixed, as it is for a coherent interface.…”

Section: Singularity Based On Defect Structuresmentioning

confidence: 99%

“…15 The ORs for the interfaces in the red, light-blue, blue and green zones are limited by at least two rules. The corresponding interfaces are fully singular in the five degrees of boundary geometrical phase space, but this is only possible with particular lattice parameters.…”

Section: Integrated Considerationsmentioning

confidence: 99%

“…The corresponding interfaces are fully singular in the five degrees of boundary geometrical phase space, but this is only possible with particular lattice parameters. 15 The ORs for the interfaces in the other coloured zones are constrained by one rule plus a pair of parallel low-index vectors. The OR for such an interface is also completely fixed, and can be determined with a 2D model in the plane normal to the parallel vectors.…”

Section: Integrated Considerationsmentioning

confidence: 99%

“…The major models have been reviewed previously in detail in lengthy review papers. 15,16 More recently, Howe 17 has provided an updated comprehensive review of major models in a book chapter.…”

Section: Introductionmentioning

confidence: 99%

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Faceted interfaces: a key feature to quantitative understanding of transformation morphology

Zhang

Dai

2016

npj Comput Mater

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Faceted interfaces are a typical key feature of the morphology of many microstructures generated from solid-state phase transformations. Interpretation, prediction and simulation of this faceted morphology remain a challenge, especially for systems where irrational orientation relationships (ORs) between two phases and irrational interface orientations (IOs) are preferred. In terms of structural singularities, this work suggests an integrated framework, which possibly encompasses all candidates of faceted interfaces. The structural singularities are identified from a matching pattern, a dislocation structure and/or a ledge structure. The resultant singular interfaces have discrete IOs, described with low-index g's (rational orientations) and/or Δg's (either rational or irrational orientations). Various existing models are grouped according to their determined results regarding the OR and IO, and the links between the models are clarified in the integrated framework. Elimination of defect types as far as possible in a dominant singular interface often exerts a central restriction on the OR. An irrational IO is usually due to the elimination of dislocations in one direction, i.e., an O-line interface. Analytical methods using both three-dimensional and two-dimensional models for quantitative determinations of O-line interfaces are reviewed, and a detailed example showing the calculation for an irrational interface is given. The association between structural singularities and local energy minima is verified by atomistic calculations of interfacial energies in fcc/bcc alloys where it is found that the calculated equilibrium cross-sections are in a good agreement with observations from selected alloys.

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Section: Singularity Based On Defect Structuresmentioning

confidence: 99%

Section: Singularity Based On Defect Structuresmentioning

confidence: 99%

Section: Integrated Considerationsmentioning

confidence: 99%

Section: Integrated Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Faceted interfaces: a key feature to quantitative understanding of transformation morphology

Zhang

Dai

2016

npj Comput Mater

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Orientation Relationship of Dispersoids Precipitated in an AA3xxx Alloy during Annealing at Low Temperatures

Muggerud¹,

Li²,

Holmestad³

2012

ICAA13: 13th International Conference on Aluminum Alloys

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Crystal Interfaces

and

Knowles

2012

Crystallography and Crystal Defects

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Every real crystal must have at least one imperfection -its surface. It is useful to introduce crystal interfaces by thinking of a surface that is parallel to a prominent crystallographic plane and represents a smooth sheet of atoms, of which the pattern is the same as that of a parallel plane inside the crystal. We shall use this simple clear idea, but recognize it is not strictly true. Surfaces show the phenomenon of reconstruction, whereby even in high vacuum the outer layers of atoms rearrange into a more energetically favourable situation. A well-known example is the 7 × 7 structure found on (111) Si [1]. Similar surface reconstructions occur on clean metal surfaces [2]. These reconstructions can be rationalized in terms of the coordination of the atoms at the surface and the electronic structure at the surface being different from the bulk (which, in practice, typically means distances of > 1 nm from the surface).Rather than such outer surfaces, we are mainly concerned in this chapter with internal interfaces in crystalline solids, for example grain boundaries and boundaries between different phases, such as epitaxial interfaces, although we begin in this section with the concept of surface free energy to achieve this. The topic of internal interfaces covers a very wide field [3], from which we have attempted here to distil the essential aspects relevant to a basic understanding of the crystallography of internal interfaces. Books listed in the Suggestions for Further Reading direct the reader to more advanced treatments of this topic.We shall formally define a flat surface parallel to any given rational plane by removing all the atoms whose centres lie to one side of a plane of this orientation located within the bulk crystal. With this assumption, in highly symmetrical crystal structures with one atom per lattice point, such as the c.c.p. and b.c.c. crystal structures, the location of the defining plane will not affect the structure of this idealized surface, because each atom has identical surroundings within the bulk.

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On the crystallography of precipitation

Cited by 228 publications

References 134 publications

Faceted interfaces: a key feature to quantitative understanding of transformation morphology

Faceted interfaces: a key feature to quantitative understanding of transformation morphology

Orientation Relationship of Dispersoids Precipitated in an AA3xxx Alloy during Annealing at Low Temperatures

Crystal Interfaces

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