Crystal Coordination Number

Background

Ionic compounds are made up of + and - ions (Na+ and Cl-) in a regular arrangement that is arranged so that + isn't next to a -. You would've thought that there is one or at best two or three ways of doing this, actually there are loads (visit this link to see 14 of them http://en.wikipedia.org/wiki/Crystal_structure#Lattice_systems of them) depending on the ratio of + to - ions and the relative sizes of + and - ions. Luckily for you, you only need to recognise and explain about two of them.

The two structures - NaCl and CsCl 

Think of a theoretical situation where all the ions are exactly the same size like in a box of bowling balls. When you have a box of bowling balls (or any identically sized spheres) the natural arrangement they will settle in will have each bowling ball being touched by 12 others (this is the maximum number of spheres that can touch a central sphere when they are all the same size, trust me its true!). 

Now to really exaggerate the situation imagine a similar scenario where you have a mixed bag of bowling balls and table tennis balls in a 1:1 ratio and for some weird reason when they arrange themselves naturally the bowling balls can only be touched by table tennis balls (and vice versa). Now there is a problem, because bowling balls are bigger than table tennis balls you can get maybe 50 around a bowling ball but in the reverse situation you can only get maybe 3 bowling balls to touch a table tennis. So in this theoretical box of bowling balls and table tennis balls there is a problem if you are to maintain this 1:1 ratio we can't have 50 of 1 and 3 of the other. So, the structure will have to take the smaller number of 3 as the number of each that touch each other. 

So now we have a pattern, when spheres are identically sized we can fit 12 around the opposite one, when they are different sizes this number decreases (down to possibly 3 for bowling balls and table tennis balls). This is called crystal coordination number. i.e. bowling balls have a crystal coordination number of 12. Mixed bowling balls and table tennis balls have a crystal coordination number of 3

Right to ions. 

Cs and Cl are v similar sizes (think bowling balls) so the crystal coordination number will be high (i.e. 8). Na and Cl are different sizes (think mixed bowling balls and table tennis balls) so the crystal coordination number must be lower (i.e. 6). 

This means that in the NaCl crystal there are 6 Nas next to every Cl and 6 Cls next to every Na.

The total crystal coordination number of the crystal is 6,6.  The crystal coordination number of sodium in the crystal is 6 and the crystal coordination of chloride in the crystal is 6.

What does NaCl and CsCl look like?

I am not going to try and draw this here so look at your notes or google them!

What are they going to ask you in the exam?

Firstly, there are the obvious questions like, what do they look like? what is the crystal coordination number? but what about the more descriptive questions that will involve a bit more thought.

1. Why do they have different crystal coordination numbers?

Cs is bigger than Na, so you can fit more Cl ions around a Cs than an Na. Hence CsCl is 8,8 and NaCl is 6,6

2. Why can't MgCl2 have a 6,6 coordination number?

In MgCl2 there are twice as many Cl ions as Mg ions and the crystal coordination number must reflect this, so the crystal coordination might be 4,8 or 6,12 or any structure that involves there being twice as many of one ion compared to another.