FinalExam2010-sol

FinalExam2010-sol - EMSE 312 Final Exam Solutions FALL 2010...

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Unformatted text preview: EMSE 312 Final Exam Solutions FALL 2010 1. Crystallography: (10 p) Explain briefly each of the following (use simple sketches to illustrate when suitable): (a) (2 p) Improper Rotation (b) (2 p) Point Group (c) (2 p) Bravais Lattice (d) (2 p) Screw Axis Symmetry (e) (2 p) Space Group (a) A rotation followed by a reflection (roto-reflection) or an inversion (roto-inversion). (b) A unique combination of the 10 point symmetry operations (proper rotations 1, 2, 3, 4, and 6, and improper rotations 1 , 2 m = , 3, 4and 3 6 m = ). (c) A unique combination of a crystal system (7 crystal systems) and a space lattice (5 space lattices: P, A (B, C), I , F and R). (d) A rotation followed by a partial translation: ; m n m n < and both and are integers and where the partial translation is n m m t n = . The rotation can take the values of 1, 2, 3, 4, and 6. For example, the screw axis symmetry corresponds to a rotation followed by a partial translation of n 1 4 90 1 0.25 4 t = = along the rotation axis. (e) A unique combination of one of the 32 Point Groups (which defined the crystal system) and one of the 5 Space Lattices (P, A (B, C), I , F and R), where a rotation axis can be a screw axis and a mirror plane can be a glide plane. KPDL: 12-15-10 1 EMSE 312 Final Exam Solutions FALL 2010 KPDL: 12-15-10 2 2. Optical Diffraction/Fourier Transforms: (10 p) (a) (5 p) Draw the most intense features of an optical diffractogram that would be obtained from one of the square apertures shown below. (b) (5 p) Draw the most intense features of an optical diffractogram that would be obtained from all three square apertures punched out from an opaque screen in an arrangement shown below. Try to draw the diffractogram to scale, and specify what features of the diffractogram which are due to the shape of the objects (apertures) and due to interference between the objects, respectively. (10 p) 3a a 2a Solution: a) b) EMSE 312 Final Exam Solutions FALL 2010 KPDL: 12-15-10 3 3. (20 p) Consider the Ewald sphere construction of a "Laue Back-Reflection" experiment on an orthorhombic single crystal with the lattice parameters , 2.0 a = 2.0 b = , and 3.0 c = . (a) (3p) Use a graphic construction to determine the d-spacing of the ( ) 704 plane ( ) hkl d : The length of the ( ) 704 g-vector) is -1 704 3.75 0.2667 d = Note: calculated d-spacing 720 0.266996 d = (b) (3p) Use a graphic construction to determine the wavelength of the X-ray that will satisfy the Braggs law (first order reflection); i.e., 2 s i n hkl hkl d = The radius of the Ewald sphere (circle) is -1 704 704 1 1.95 0.526 = = (c) (3p) Use a graphic construction to determine the Bragg angle of the ( ) 704 plane....
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FinalExam2010-sol - EMSE 312 Final Exam Solutions FALL 2010...

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