Crystal Structures: Efficiency of Packing

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Presentation transcript:

Crystal Structures: Efficiency of Packing Loosely based on Jespersen 6th Ed Sec 12.11 (p.566-568) Dr. C. Yau Fall 2014

Efficiency of Packing We now examine packing of metals which have atoms of the same size (as opposed to ionic compounds that have cations and anions, which are different sizes). We will think of the atoms being in layers. What kind of packing is involved in getting the atoms as close together as possible? “Efficiency of packing” refers to how closely packed the atoms can be: the closer they are, the more efficient it is.

If we put a 2nd layer exactly on top of the 1st, we have the simple cubic cell. Packing Efficiency = 54% If we put the 2nd layer over the holes of the 1st layer, we have the body cubic cell. Packing Efficiency = 68%

There is another way of packing the 1st layer There is another way of packing the 1st layer. Do you see the difference in the two way of packing the first layer? Note that there are bigger holes in the first one, thus less packing efficiency. Let us now consider the 2nd type of packing of the 1st layer.

The 2nd layer would sit on top of the holes of the 1st layer. There are two ways of placing the 3rd layer over the holes of the 2nd layer (see arrows).

Placing the 3rd layer on top of the holes indicated by the black arrow leads to the cubic closest packing (abcabc arrangement) or ccp. If placed on top of the holes indicated by the red arrow, we have the hexagonal closest packing (abab arrangement) or hcp. Packing efficiency is 74% for both.

This is a playground for you to experiment with closest packing.