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Unformatted text preview: EMSE 312 Midterm Exam Solutions to selected problems FALL 2010 KPDL: 10-18-10 1 1. (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) Centering (Space Lattice) (d) (2 p) Glide Symmetry (e) (2 p) Symmorphic Space Group (a) A rotation followed by a reflection (Roto-Reflection) or a rotation followed by an inversion (Roto-Inversion). (b) A point group is a unique and particular combination of point symmetry operations 32 possible combinations. (c) The addition of a lattice point (making the lattice non-primitive) without changing the point symmetry. (d) A partial translation followed by a reflection. (e) A unique combination of the 32 point symmetries and the 14 Bravais Lattices (the improper translations such as a screw axis and/or a glide planes are excluded) 73 possible combinations. 2. (10 p) The crystal system required for a substance is determined by the point group symmetry associated with its chemical bonding; i.e., the point symmetry must be compatible with a particular crystal system. Match the following 10 point symmetries with the appropriate crystal systems using the Table below (you can use either the full point group notation OR a, b, c, e, f, g, h, i, and j, in the space for the appropriate crystal system).. Crystal System Point Groups Triclinic None Monoclinic j) 2 m Orthorhombic e) , h) 2 mm mmm Tetragonal f) 4 mmm , i) 4 Cubic a) , d) 23 432 Trigonal c) 3 , g) 32 Hexagonal b) 6 mm EMSE 312 Midterm Exam FALL 2010 KPDL: 10-18-10 2 3. (10 p) Starting with a RH object placed at the coordinate ( , , ) x y z , determine the object type (RH / LH) and object locations (coordinates) for the following situations: (a) (3 p) 4 symmetry + RH: +x, +y, +z (b) (4 p) The 4 m point group (c) (3 p)...
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- Spring '08