THE UNIVERSITY OF LETHBRIDGE
CHEMISTRY 4000 B
1.
TEST #1
DEPARTMENT OF CHEMISTRY
February 5th, 1999
ANSWERS
Given the point group 4 , shown at left, construct an accurate stereograph of the resultant point group obtained by adding a
two-fold rotation axis perpendicular to the vertical 4 axis. Note: there is already a two-fold axis along the same
direction as the principal axis.
2. An atom in a cubic unit cell has fractional coordinates (0.2, 0.3, 0.4). Give the coordinates of a second atom within the unit
cell related to the first by the following symmetry. Start from the original point in each case, and show your work!
a) F-centering
b) An inversion centre (i.e. 1 )at the origin of the unit cell.
3. A certain oxide of barium, BaO2, crystallizes in the space group I4/mmm with a = 3.8154 and c = 6.8513 Å, and its density was
measured as 5.6 g cm–3. Using this information and the page from the International Tables Vol.4 attached to this exam, answer
the following questions:
a) To what crystal class and Bravais lattice does this structure belong?
Tetragonal crystal class; Tetragonal-I Bravais lattice (body centred)
b) Show how the point group of the unit cell can be derived from the space group symbol.
c) Calculate Z.
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d) This is a crystal structure for which you need additional information. Read carefully. One of the Ba atoms is located at
coordinates (0,0,0). One of the O atoms is located at the coordinates (0,0,0.39). Which Wyckoff positions are occupied by the
Ba and O atoms?
e) What are the coordinates of the other Ba and O atoms in the unit cell?
f) Using the information you have already obtained, make a careful sketch of the contents of a single unit cell of BaO2. Label all
atoms, coordinates and axes in your diagram!
g) BONUS [4 pts]: if you deduced the correct crystal structure, you should have obtained some valuable chemical information
about BaO2. What kind of compound is this? What are the likely oxidation states of the two constituent elements? Can you
propose the correct chemical name for the compound? Why might this oxide of barium form in the first place?
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