WebThe Frank-Bilby equation has been utilized to develop a general approach in which a simple criterion is proposed to classify interfaces with discrete misfit dislocation arrays … A general deformation matrix A relating two lattices can be simply calculated from A = X B X −1A ,[17] where X B and X A are 3×3 matrixes containing column vectors x Ai and x Bi from lattices A and B, respectively. All vectors must be defined in a common orthonormal coordinate. Therefore, the elements in A depend on … See more As stated in the previous section, the multiplicity of A is caused by the multiple lattice correspondences. When matrix A is used for calculating … See more Influence of reference lattice on the description of dislocations has been a key issue in a geometric model. The description of a dislocation structure with a geometric model includes two features: the Burgers vectors … See more So far we have shown how to determine the possible dislocation structure in a general interface based on the effective O-cell traces. … See more Atomic steps are defects in a general interface, because they are usually associated with a higher energy than the terrace region.[51] Traditionally, the terrace-step-kink … See more
Micromechanics of crystalline interfaces - University of Illinois ...
WebDec 6, 2024 · In order to relieve the misfitting elastic energy, the hetero-interfaces become semicoherent by forming networks of dislocations. These microscopic structures strongly influence the materials properties associated with the development of advanced materials. We develop a continuum model for the dislocation structures of semicoherent interfaces. … WebFeb 19, 2024 · The Frank-Bilby equation (FBE) can give many solutions for the dislocation content of a grain boundary (GB); most of them are considered to have little physical … town of queen creek traffic signal details
A pseudoinverse for Frank
WebOct 10, 2024 · The first two factors are common to all materials, and the resulting dislocation patterns can be described by continuum elasticity models such as the Frank-Bilby equation. 25 25. J. P. Hirth, R. C. Pond, R. G. Hoagland, X.-Y. Liu, and J. Wang, “ Interface defects, reference spaces and the Frank–Bilby equation,” Prog. Mater. WebJun 1, 2016 · The Frank–Bilby formula predicts an average spacing between misfit dislocations of about 2.8 nm, which is the same as the MD result. WebOct 1, 2009 · The Frank–Bilby equation has been utilized to develop a general approach in which a simple criterion is proposed to classify interfaces with discrete misfit dislocation arrays into four types so ... town of queen creek az planning department