Question

3) In diopside, CaMgSi,O. Si is coordinated to 4 oxygens. What is the coordination of Ca (Ca ionic radius 1.12A, O ionic radius = 1.4 Å)? Mg is found in octahedral coordination, what are the largest and smallest radii that Mg could have to be stable in this coordination? (hint: remember, O is the only anion here!) (20)

Answer 1

Here, we will be using radius ratio rule. The radius ratio is defined as radius of Cation divided by radius of anion.

Radius Ratio	Coordination Number	Geometry
< 0.155	2	Linear
0.155 - 0.225	3	Triangular Planar
0.225 - 0.414	4	Tetrahedral
0.414 - 0.732	6	Octahedral
0.732 - 1.000	8	Cubic

a)

For Ca, radius of cation = 1.12 A and for Oxygen, radius of anion = 1.4 A

Thus the radius ratio equals 1.12/1.4 = 0.8

Thus, from the above table it can be deduced that the coordination number should be 8.

b)

Mg is found in octahedral void. Thus, the coordination number will be 6. For this, we have,

TO 0.414 < "Mg <0.732 = 0.414 < "Mg < 0.732 0.414 x 1.44 <IM, < 0.732 x 1.44 0.58À <IM, < 1.024 1.4A

Thus, the radius of Magnesium should be between 0.58 A and 1.02 A