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 = Δωi/Δxj 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 Δ
R with the change in a position from (
x1,
x2,
x3) to (
x1 + Δ
x1,
x2 + Δ
x2,
x3 + Δ
x3). δ
R is a small-angle rotation which satisfies Δ
R ≈ (δ
R)
N where
N is a sufficiently large positive integer. The relationship Δ
R ≈ (δ
R)
N means that the
N-times successive rotations of δ
R with an interval of δ
x = (Δ
x1/
N, Δ
x2/
N, Δ
x3/
N) is equivalent to Δ
R. The angles δϕ
i are the small rotation angles of δ
R around the
xi axes.
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