EMS162-2010-Homework6_Solutions - UNIVERSITY OF CALIFORNIA,...

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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 6 – Solutions [50 pts] Due Date: Tuesday, Feb. 23rd, 2010, in class Note: You must show all your steps in order to receive full credit. Remember to include your units! 1. Term Paper Outline [5% of term paper grade] The second benchmark for the term paper is to create an outline of your term paper. Your outline (in the form of a few bullet points or sentences) should provide more detail about the specific aspects of your selected topic that will be covered in your term paper. Remember that these aspects should fall under the broad umbrella of structure and characterization of materials. Good sources of information include published works such as textbooks or journal articles. Web of Science is a good database for searching through scientific journals. 2. Structure Factors in Reciprocal Space [10 pts] In class we showed that the reciprocal lattice cell for the body centered cubic structure has a face centered cubic array of points, and that the reciprocal lattice cell for the face centered cubic structure has a body centered cubic array of points. Both of these cells are double-sized, meaning the corners are two reciprocal lattice translation units from the origin. (a) Perform a similar derivation for the ionic crystal structure, rock salt: NaCl by deriving the structure factor, F hkl . (b) Draw the reciprocal lattice cell for this crystal structure and label all the allowed reflections. Represent the magnitude of the structure factor as the size of the dot at each reciprocal lattice position, and a missing position as an open circle. (c) What type of array is formed in reciprocal space for the NaCl crystal structure? Why? Solution: (a) For NaCl, the uvw positions are Na: 0 0 0; ½ ½ 0; ½ 0 ½; 0 ½ ½ Cl: ½ ½ ½; 0 0 ½; 0 ½ 0; ½ 0 0 () ( ) ( ) [] [ ] ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 1 1 l k h i Cl Na l k i l h i k h i ih ik il l k h i l k i l h i k h i lw kv hu i n hkl e f f e e e e e e e f e e e f e f F Cl Na n n n + + + + + + + + + + + + + + + + = + + + + + + + = =
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EMS162-2010-Homework6_Solutions - UNIVERSITY OF CALIFORNIA,...

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