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Unformatted text preview: EMS 162, page 1/4 Prof. Y. Takamura, 2010 UNIVERSITY OF CALIFORNIA, DAVIS Department of Chemical Engineering and Materials Science EMS 162: Structure and Characterization of Engineering Materials Homework 8 – OPTIONAL BUT HIGHLY RECOMMENDED - SOLUTIONS Due Date: Monday, March 15th, 2010 – 3096 Bainer Hall by 12noon 1. Atomic Arrangement on Planes [30 pts] (a) The perovskite crystal structure consists of alternating layers with different chemical composition, which add up to the overall stoichiometry of ABX 3 . Draw 2-dimensional images of the atom arrangement for each of these layers for the ( h 00), ( hh 0), and ( hhh ) planes of a single crystal material with the perovskite crystal structure. Label the atomic positions (uvw) for each atom and identify each position as being an A, B, or X atom. Indicate the composition of each layer. (b) For the ( h 00) planes, consider the case for SrTiO 3 and LaAlO 3 where the valence states are Sr 2+ , Ti 4+ , La 3+ , Al 3+ , and O 2- . What are the formal charges for each of the layers? (c) For the case for SrTiO 3, calculate the number of atoms per nm 2 on the ( h 00), ( hh 0), and ( hhh ) planes. Which plane has the most number of atoms per unit area? You don’t have to distinguish between the type of atom. The lattice parameter of SrTiO 3 is a = 0.3905 nm. Solution: (see attached hand written sheets) 2. Crystallite Size [12 pts] Note: Only computer generated plots will be given full credit for this problem. (a) Using the Scherrer equation, create a plot showing the breadth, B , (in degrees of 2theta) vs. particle diameter (Å) due to the small crystal effect alone. Assume 2theta = 90°, λ = 1.5418 Å, and use a range of particle diameter between 50 and 1000 Å. What is the value of B at t = 50 Å? At t = 500 Å? At t = 1000 Å? (b) Using the Scherrer equation, create a plot showing B (in degrees of 2theta) vs. 2theta (degrees) for a particle diameter of 250 Å. Assume λ = 1.5418 Å and vary 2theta from 20 to 160 degrees. What is the value of B at 2 theta = 20 degrees? At 2 theta = 100 degrees? At 2 theta = 160 degrees?...
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This note was uploaded on 05/14/2010 for the course EMS 162 taught by Professor Howitt during the Winter '08 term at UC Davis.
- Winter '08