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Coincidence Site Lattices in Non‐Cubic Lattices
Author(s) -
Fortes M. A.
Publication year - 1977
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220820143
Subject(s) - lattice (music) , orthorhombic crystal system , coincidence , cubic crystal system , cubic form , reciprocal lattice , crystallography , grain boundary , combinatorics , reciprocal , condensed matter physics , crystal structure , physics , mathematics , geometry , chemistry , quantum mechanics , microstructure , medicine , linguistics , alternative medicine , philosophy , pathology , acoustics , diffraction
Except for trivial cases, which are not relevant in coincidence site lattice (c.s.l.) models of grain boundary structure, c.s.l. rotations can only exist in C‐lattices, i.e. those which contain an orthorhombic cell with edges o 1 o 2 , o 3 so that o 1 2 : o 2 2 : o 3 2 : = n 1 : n 2 : n 3 , the n i being integers. It is also shown that there is a one‐to‐one correspondence between the c.s.l. rotations of a C‐lattice and those of a cubic lattice. However, the reciprocal fraction of coincident points, Σ, tends to be larger in non‐cubic lattices. The implications, for the c.s.l. model of grain boundaries, of the weak incidence of low Σ c.s.l. orientations in non‐cubic crystals are discussed.