SOLID STTAE

COORDINATION NUMBER CHANGES WITH PRESSURE AND TEMPERATURE

Coordination Number (CN) and Radius Ratio

           

            In an ionic structure each cation tends to surround itself with anions; the number that can be grouped around it will depend on the relative size of the cations and anions. If you use the analogy of a soccer ball, tennis balls, and golf balls, you can fit more golf balls around a soccer ball than you can around a tennis ball. 

The Coordination Number (CN) is defined as the number of anions that can fit around a cation.  This number increases as the radius ratio increases.   The number of anions that can ‘fit’ around a cation is related to the relative size difference between the ions, and this size difference can be described using the radius ratio, which is given by:

                                                r cation/r anion.

When this number is small, then only a few anions can fit around a cation.  When this number is large, then more anions can fit around a cation.  When CN is 4, it is known as tetrahedral coordination; when it is 6, it is octahedral; and when it is 8, it is known as cubic coordination.  See the following table.

Radius Ratio	Arrange of Anions around the cation	Coordination Number (CN)
0.15 - 0.22	Corners of equilateral triangle	3
0.22 - 0.41	Corners of a tetrahedron	4
0.41 - 0.73	Corners of an octahedron	6
0.73 - 1	corners of a cube	8
1	Midpoints of cube edges	12

We can represent a silicon in tetrahedral coordination in two ways:

Examples: Predict the coordination of NaCl and CsCl

The radius of Cl ^-1 is 1.81 Å  and the radius of Na ⁺¹ is 0.99Å.  The radius ratio is therefore 0.99/1.81 or 0.55.  This would predict that Na is in octahedral coordination with Cl.  The radius of Cs ⁺¹ is 1.67 Å and thus the radius ratio is 0.92 which would predict that Cs is surrounded by 8 (cubic) Cl’s in its structure.

The effect of pressure and temperature on coordination number:

Al ⁺³ can occur in both octahedral and tetrahedral sites in silicates.  In such cases, the coordination number is to some extent controlled by pressure and temperature.  One can make the assumption that high temperature and low pressure promote low CN whereas low temperature and high pressure promote high CN.