Problem Set #2

1. For columns I-V in the periodic table, plot ionic radius on the y-axis vs. row number on the x-axis. Choose the ionic radii for 6-fold coordination from Table 3.11. You should end up with five lines on one plot. Describe and explain the trends that you see: how does ionic radius depend on Row number? Column number? Atomic number? Number of electrons?

2. a) Draw the following cubic structure

coordinates of A atoms: 1/2,0,0; 0,1/2,0; 0,0,1/2; 1/2,1/2,1/2

coordinates of B atoms: 0,0,0; 1/2,1/2,0; 1/2,0,1/2; 0,1/2,1/2

b) What is the coordination polyhedron surrounding the A atom?

c) What shared elements exist between these coordination polyhedra

d) Identify the structure

Extra credit (more challenging): draw the following structure and answer the same questions:

This is a tetragonal structure with a=4.2 Å, b=4.2 Å, and c=2.7 Å

coordinates of A atoms: 0,0,0; 1/2,1/2,1/2

coordinates of B atoms: 0.3,0.3,0; 0.7,0.7,0; 0.2,0.8,0.5; 0.8,0.2,0.5

3. As we saw in class, the coordination number is limited by the radius ratio, the ratio of the cation radius to the anion radius. For each coordination number, there is a minimum value of the radius ratio. Derive the minimum values of the radius ratio for 3-fold, 6-fold, and 8-fold coordination. You may find figures 3.34 and 3.36 helpful, but you must show your own work. Extra credit: derive the minimum value of the radius ratio for four-fold coordination.

4. The following table contains chemical analyses of four minerals. Plot compositions A, B, and C on a ternary diagram with components: MgO, FeO, and SiO₂. Identify all four minerals. Remember that measurements always contain errors, which in this case are typically 1 percent. You may find useful the section in your book: “Recalculation of chemical analyses”.

Weight Percent oxides

Oxide A B C D

SiO₂ 58 50 35 43

Al₂O₃ 0 0 0 37

FeO 7 36 42 0

MgO 35 13 23 0

CaO 0 0 0 20

Na₂O 0 0 0 0

K₂O 0 0 0 0