1. Coordination Principle
GLY 4200
Fall, 2018

2. Electrostatic Attraction
Anions and cations cluster together because they are attracted electrostatically
The clusters form coordination arrays

3. Ionic Bonding
The coordinated ions always cluster about the coordinating ion in such a way that their centers lie at the apices of a polyhedron
For bonding that is non-ionic, the same general principles hold

4. Coordination Number
The number of coordinated ions around a central ion is known as the coordination number (CN)
This usually refers to anions around a cation, but is occasionally used for cations around anion.
The ions may, in a first approximation, be thought of as hard spheres. Ideally, the anions around a cation will be arranged so that the spheres just touch. As we will see in lab, the first coordination shell (nearest neighbors) will be arranged in a pattern which depends on the relative size of the anion and cation.

5. Radius Ratio
The radius ratio is the ratio of the cation radius (note: this is Rc) to the anion radius (Ra) or (R+/R-)
Since anions are almost always larger than cations, the ratio is between zero and one

6. Fit Perfect Cation large, pushes anions apart
Cation small, rattles around (unstable)
If the fit is perfect, that is, if the cation is just large enough to fit when the anions are touching the ratios will be the minimum value given below for each range.

7. Common Configurations
Rc/Ra CN
Configuration
<0.155 II
linear
III
trigonal IV
tetragonal
square planar VI
octahedral
VIII
cubic

8. Linear
These numbers are derivable (except for the linear case) but only two derivations are straight-forward.

9. Trigonal Planar

10. Tetrahedral

11. Square Planar Square Planar – Octahedral
Both sides of the triangle are = 1
1**2 + 1**2 = Z** ∴ Z**2 = Z = 2**0.5 = 1.414
Z = ½ + ½ + x (where x = diameter of cation)
x = RC = 0.212
(0.212)/0.5 = = RC/RA
This is the minimum size the cation must be – if it were smaller it would rattle around – this is forbidden by the “no rattling – around” rule.

12. Octahedral

13. Cubic Cubic – Dimension of each side is 1.0
1**2 + 1**2 = 2 = diagonal measurement of each side
Vertical = 1
1**2 + (1.414)**2 = 3
Z =Body diagonal = 3**0.5 = 1.732
Z – 1 = x = 0.732

14. Radius Ratio Computation
Although the ratios thus derived are for exact fits, larger cations occasionally will fit in a smaller structure.
That is, the observed coordination number will be smaller than the predicted CN.
Example: Ca & O
RC/RA = 0.82
Predicted CN = VIII
Observed = VI