Solutions HW3 F10 - Page 1 of 9 Department of Materials...

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Unformatted text preview: Page 1 of 9 Department of Materials Science and Engineering University of Maryland College Park, MD ENMA 300: Problem Set #3 SOLUTIONS 1. Lattices (2D and 3D) Identify the lattices and the unit cell in the following images: (a) [Source: M. C. Escher] The white outline shows a unit cells (other outlines are possible). The green dots show the lattice, which is a 2D rectangular Bravais lattice. Page 2 of 9 (b) [Source: M.C. Escher] An oblique (nearly hexagonal) 2D Bravais lattice. (c) The Schwarz P surface defines two 3D networks of channels (the inside and the outside), that are actually identical in shape. On the right is a magnified portion of the surface. [Source: Min Lai et al., Chem. Comm. 2007] There are two acceptable answers. The simplest answer is that this is a Simple Cubic lattice, with the unit cell shown in the right frame. The answer that reflects the highest symmetry in the problem is that this is a Body Centered Cubic lattice, with a unit cell that is only half of surface shown in the right frame. Indeed, any BCC or FCC lattice can be reduced to a Simple Cubic lattice with a larger unit cell when convenient. Page 3 of 9 (d) A Face-Centered Cubic Bravais lattice. The basis is (blue sphere+green sphere+the same color sticks that are attached to them). 2. Packing Densities - Ceramics Compute the Atomic Packing Factor for a rock salt crystal with r cation /r anion = 0.414, 0.54 and 1....
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This note was uploaded on 08/02/2011 for the course ENMA 300 taught by Professor Alsheikhly during the Spring '11 term at University of Maryland Baltimore.

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Solutions HW3 F10 - Page 1 of 9 Department of Materials...

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