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MidtermExam2009-sol

# MidtermExam2009-sol - EMSE 312 Midterm Exam – Solutions...

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Unformatted text preview: EMSE 312 Midterm Exam – Solutions to selected problems FALL 2009 KPDL: 10-16-07 1 1. (10 p) Explain briefly each of the following (use simple sketches to illustrate when suitable): (a) (2 p) Proper Rotation (b) (2 p) Point Group (c) (2 p) Bravais Lattice (d) (2 p) Screw Axis Symmetry (e) (2 p) Space group (a) A motion of a RH-object by a 1, 2, 3, 4 or 6-fold rotation around a rotation axis. (b) A point group is a unique and particular combination of point symmetry operations – 32 possible combinations. (c) A Bravais Lattice is a combination of a crystal system (defined by the point symmetry) and a space lattice (P, A, [B, C,] I, F or R) – 14 possible combinations. (d) An improper translation obtained by a partial translation followed by a rotation. (e) A unique combination of point symmetry, Bravais Lattice and improper translations such as a screw axis and/or a glide plane – 230 possible combinations. 2. (10 p) The crystal system is determined by the point group symmetry, and the space lattice (i.e., centering) must be compatible with a particular crystal system. Complete the two tables below by making check marks ( √ ) where appropriate ( Note : all crystal systems are compatible with 1-fold proper rotation and all crystal systems can be primitive). (a) (5 p) Crystal systems and proper rotation symmetries. Crystal System 1 2 3 4 6 Triclinic √ Monoclinic √ √ Orthorhombic √ √ Tetragonal √ √ √ Cubic √ √ √ √ Trigonal √ √ Hexagonal √ √ √ √ (b) (5 p) Crystal systems and space lattices. Crystal System P A , B , C I F R Triclinic √ Monoclinic √ √ ( √ ) = B ( √ ) = B Orthorhombic √ √ √ √ Tetragonal √ ( √ ) = P √ ( √ ) = I Cubic √ √ √ Trigonal √ √ Hexagonal √ ( √ ) = Trigonal R Note: Some combinations will result in related Bravais Lattices Monoclinic 1 st setting (unique c-axis): C ≡ P, B ≡ A ≡ I ≡ F Tetragonal: C ≡ P, I ≡ F, A and B violates the 4-fold rotation axis EMSE 312 Midterm Exam FALL 2009 KPDL: 10-18-09 2 3. (10 p) Determine the symmetry operations required to relate the object type (RH and LH objects)...
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MidtermExam2009-sol - EMSE 312 Midterm Exam – Solutions...

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