HW03Solution - PROBLEM 2-14 B.D Cullity and S.R Stock...

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2-14 Pole A, whose coordinates are 20°N, 50°E, is to be rotated about the axes described below. In each case, find the coordinates of the final position of pole A and show the path traced out during its rotation. a) 100° rotation about the NS axis, counterclockwise looking from N to S. b) 60° rotation about an axis normal to the plane of projection, clockwise to the observer. c) 60° rotation about an inclined axis B, whose coordinates are 10°S, 30°W, clockwise to the observer. Solution a ) This rotation of 100° causes pole A to rotate into the lower hemisphere of the projection sphere after 40°, so its “negative” pole reappears to complete the remaining 60°, as shown below. Final location: 20°S, 30°W. A A’ PROBLEM 2-14 B.D. Cullity and S.R. Stock, Elements of X-Ray Diffraction, 3 rd Ed., Prentice Hall, (2001) MSE 104 Materials Characterization Professor R. Gronsky page 1 of 3
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b ) This rotation of 60° is simply done by spinning about a pin through the center, shown below. Final location: 27°S, 48°E. A A’ 60° PROBLEM 2-14 B.D. Cullity and S.R. Stock, Elements of X-Ray Diffraction, 3 rd Ed., Prentice Hall, (2001) MSE 104 Materials Characterization Professor R. Gronsky page 2 of 3
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c ) Rotation about an inclined axis requires that the rotation axis be moved into a useful orientation. That makes this solution a three-step procedure. First, move the rotation axis to the center of the stereographic projection, which makes the rotation axis normal to the page. This is done by rotating the Wulff Net (shown dimmed here) to put pole B on the equator.
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