SS - Radius ratio rules for predicting crystal structures

Question 1

State three factors and how they affect ionic radii

Answer 1

1. Ionic radii increases down a group
2. Ionic radii decrease with oxidation state
3. Ionic radii increases with coordination number

Question 2

Describe how coordination number changes with cation size

Answer 2

As cation size increases, it gets easier to put more anions around the cation.

Note that if the cation and anion are roughly the same size, the coordination number is 8. If there is a large difference between the two, coordination number is 4 and anywhere in the middle, coordination number is 6.

Question 3

Describe how to use the ratio of cation to anion sizes to predict structure.

Answer 3

Where the radius of the cation is r+ and the radius of the anion is r-.

We assume the ions touch and we can use Pythagoras to find the ratio.

Question 4

Summarise the radius ratios and how they relate to crystal structure

Answer 4

Question 5

Describe perovskite structures

Answer 5

Perovskite structures have the formula ABX₃ where A (black) and B (blue) are cations and X (red) is an anion.

Question 6

Give and describe Goldschmidt’s tolerance factor

Answer 6

The tolerance factor determines whether or not a perovskite structure will be formed.

If t=1, a perovskite structure is predicted.

If 0.8 ≤ t ≤ 1, perovskite generally do form but there will be tilting within the structure

If t > 1, the central cation is too large to form a perovskite

If t < 0.8, the central cation is too small to form a perovskite