Quantization of the Frank-Bilby equation for misfit dislocation arrays in interfaces

J. B. Yang; Y. Nagai; Z. G. Yang; M. Hasegawa

doi:10.1016/j.actamat.2009.06.042

Quantization of the Frank-Bilby equation for misfit dislocation arrays in interfaces

J. B. Yang, Y. Nagai, Z. G. Yang, M. Hasegawa

Materials Design Division

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

A quantization procedure for the Frank-Bilby equation to calculate the periodic structure of interphase interfaces and grain boundaries with one, two and three sets of discrete misfit dislocation arrays is presented mainly in terms of the basic O-lattice equation. The line directions and spacings of misfit dislocation arrays are derived to account for the full relaxation of the long-range strains in the interface without the ad hoc assumption proposed by Bollmann who assumed that misfit dislocation arrays are the lines of intersection between the O-cell walls and the interface. It has been found that the discrete dislocation arrangement derived from the above Bollmann's assumption cannot always ensure that the interface is free of long-range strains.

Original language	English
Pages (from-to)	4874-4881
Number of pages	8
Journal	Acta Materialia
Volume	57
Issue number	16
DOIs	https://doi.org/10.1016/j.actamat.2009.06.042
Publication status	Published - 2009 Sept

Keywords

Analytical methods
Dislocations
Grain boundary structure
Interface structure

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Ceramics and Composites
Polymers and Plastics
Metals and Alloys

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10.1016/j.actamat.2009.06.042

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title = "Quantization of the Frank-Bilby equation for misfit dislocation arrays in interfaces",

abstract = "A quantization procedure for the Frank-Bilby equation to calculate the periodic structure of interphase interfaces and grain boundaries with one, two and three sets of discrete misfit dislocation arrays is presented mainly in terms of the basic O-lattice equation. The line directions and spacings of misfit dislocation arrays are derived to account for the full relaxation of the long-range strains in the interface without the ad hoc assumption proposed by Bollmann who assumed that misfit dislocation arrays are the lines of intersection between the O-cell walls and the interface. It has been found that the discrete dislocation arrangement derived from the above Bollmann's assumption cannot always ensure that the interface is free of long-range strains.",

keywords = "Analytical methods, Dislocations, Grain boundary structure, Interface structure",

author = "Yang, {J. B.} and Y. Nagai and Yang, {Z. G.} and M. Hasegawa",

note = "Funding Information: We would like to thank Dr. Yu.N. Osetsky at Oak Ridge National Laboratory, Dr. R.C. Pond at the University of Liverpool and Dr. W.Z. Zhang at Tsinghua University for helpful comments on the manuscript. This work was partially supported by Grant-in-Aids for Scientific Research of the Ministry of Education, Science and Culture (Nos. 17002009, 18686077 and 15106015). Z.G.Y. would also like to acknowledge the support of the National Natural Science Foundation of China (No. 50871059).",

year = "2009",

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doi = "10.1016/j.actamat.2009.06.042",

language = "English",

volume = "57",

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AU - Yang, J. B.

AU - Nagai, Y.

AU - Yang, Z. G.

AU - Hasegawa, M.

N1 - Funding Information: We would like to thank Dr. Yu.N. Osetsky at Oak Ridge National Laboratory, Dr. R.C. Pond at the University of Liverpool and Dr. W.Z. Zhang at Tsinghua University for helpful comments on the manuscript. This work was partially supported by Grant-in-Aids for Scientific Research of the Ministry of Education, Science and Culture (Nos. 17002009, 18686077 and 15106015). Z.G.Y. would also like to acknowledge the support of the National Natural Science Foundation of China (No. 50871059).

PY - 2009/9

Y1 - 2009/9

N2 - A quantization procedure for the Frank-Bilby equation to calculate the periodic structure of interphase interfaces and grain boundaries with one, two and three sets of discrete misfit dislocation arrays is presented mainly in terms of the basic O-lattice equation. The line directions and spacings of misfit dislocation arrays are derived to account for the full relaxation of the long-range strains in the interface without the ad hoc assumption proposed by Bollmann who assumed that misfit dislocation arrays are the lines of intersection between the O-cell walls and the interface. It has been found that the discrete dislocation arrangement derived from the above Bollmann's assumption cannot always ensure that the interface is free of long-range strains.

AB - A quantization procedure for the Frank-Bilby equation to calculate the periodic structure of interphase interfaces and grain boundaries with one, two and three sets of discrete misfit dislocation arrays is presented mainly in terms of the basic O-lattice equation. The line directions and spacings of misfit dislocation arrays are derived to account for the full relaxation of the long-range strains in the interface without the ad hoc assumption proposed by Bollmann who assumed that misfit dislocation arrays are the lines of intersection between the O-cell walls and the interface. It has been found that the discrete dislocation arrangement derived from the above Bollmann's assumption cannot always ensure that the interface is free of long-range strains.

KW - Analytical methods

KW - Dislocations

KW - Grain boundary structure

KW - Interface structure

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JO - Acta Materialia

JF - Acta Materialia

IS - 16

ER -

Quantization of the Frank-Bilby equation for misfit dislocation arrays in interfaces

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Keywords

ASJC Scopus subject areas

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