EMS162-2010-Homework4_Solutions - UNIVERSITY OF CALIFORNIA,...

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EMS 162, page 1/3 Prof. Y. Takamura, 2010 UNIVERSITY OF CALIFORNIA, DAVIS Department of Chemical Engineering and Materials Science EMS 162: Structure and Characterization of Engineering Materials Homework 4 - Solutions Due Date: Tuesday, Feb. 2 nd , 2010, in class Note: You must show all the steps you used to obtain your answer in order to receive full credit. Remember to include units in your answers. 1. Crystal Structures [12 pts] Consider the ordered structures, L1 0 and L1 2 , shown below, where the black circles are Au atoms and the white atoms are Cu atoms. (a) What is the chemical formula for the L1 0 structure? For the L1 2 structure? (b) If we would like to emphasize the cubic nature of both of the crystal structures, what combination of Bravais lattice and basis can we use for each structure? (c) For only one of the structures, it is possible to redefine the unit cell as a tetragonal unit cell. For which structure is it possible? Explain why this type of redefined unit cell allowed for one crystal structure but not for the other structure. Include in your answer a diagram for each structure. (d) What is the new basis for this unit cell? What is the relationship for the volume of the new unit cell compared to the original unit cell? Solution: (a) L1 0 structure: CuAu [1 pt] ; L1 2 structure: AuCu 3 [1 pt] (b) To emphasize the cubic nature of the crystal structure, we could choose the simple cubic Bravais lattice [1 pt] with a 4 atom basis [1 pt] consisting of the atoms in the corner (0,0,0), bottom face center (½, ½, 0), back face center (0, ½, ½) and the left side face center (½ , 0, ½) (c) Looking at the diagrams below, for the L1 0 structure [1 pt] , we can define a tetragonal unit cell where the Au atom (now denoted in blue) sits in the body center, while the Cu atoms (white circles) are at the corner positions. However, a similar reconstruction of the L1 2 structure leads to a combination of black and white circles in the corner position, which is not a valid unit cell. [1 pt for explanation][2 pts for each diagram]
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EMS162-2010-Homework4_Solutions - UNIVERSITY OF CALIFORNIA,...

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