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Solutions HW3 F10

# Solutions HW3 F10 - Department of Materials Science and...

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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.

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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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Solutions HW3 F10 - Department of Materials Science and...

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