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

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

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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 languageEnglish
Pages (from-to)4874-4881
Number of pages8
JournalActa Materialia
Issue number16
Publication statusPublished - 2009 Sept


  • Analytical methods
  • Dislocations
  • Grain boundary structure
  • Interface structure


Dive into the research topics of 'Quantization of the Frank-Bilby equation for misfit dislocation arrays in interfaces'. Together they form a unique fingerprint.

Cite this