EMS 162, page
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
, 2010, in class
Note: You must show all the steps you used to obtain your answer in order to receive full credit.
include units in your answers.
Consider the ordered structures, L1
, shown below, where the black circles are Au atoms and the white
atoms are Cu atoms.
What is the chemical formula for the L1
For the L1
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?
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.
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?
To emphasize the cubic nature of the crystal structure, we could choose the simple cubic Bravais
with a 4 atom basis
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)
Looking at the diagrams below, for the L1
, 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
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]