MATERIALS TRANSACTIONS
Online ISSN : 1347-5320
Print ISSN : 1345-9678
ISSN-L : 1345-9678
Representation of Nye’s Lattice Curvature Tensor by Log Angles
Ryosuke MatsutaniSusumu Onaka
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JOURNALS RESTRICTED ACCESS Advance online publication

Article ID: M2019049

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Abstract

The log angles of a rotation matrix are three independent elements of the logarithm of the rotation matrix. Nye’s lattice curvature tensor κij is discussed by using the log angles. For the change in a crystal orientation ΔR with the change in a position Δxi, it is shown that the elements of κij are written as κij = Δωixj using the log angles Δωi of ΔR. The log angles for the crystal rotation given by the axis/angle pair are also discussed.

 

This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 82 (2018) 415–418.

Fig. 2 The change in a crystal orientation as much as ΔR with the change in a position from (x1, x2, x3) to (x1 + Δx1, x2 + Δx2, x3 + Δx3). δR is a small-angle rotation which satisfies ΔR ≈ (δR)N where N is a sufficiently large positive integer. The relationship ΔR ≈ (δR)N means that the N-times successive rotations of δR with an interval of δx = (Δx1/N, Δx2/N, Δx3/N) is equivalent to ΔR. The angles δϕi are the small rotation angles of δR around the xi axes. Fullsize Image
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© 2019 The Japan Institute of Metals and Materials
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