How To Draw A Unit Cell - Inorganic Teaching

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How to draw a unit cell

I will be kind to you and we will only do it with a cubic cell, todays solid will be rhodium. For those of you who do not know what copper looks like here is a a photograph of a strip of copper metal.

Copper metal

But we are much more interested in the atomic scale than the macroscopic scale. Lets go to work.

We start by looking at the size and shape of the unit cell, the unit cell is cubic and the length of one side is 3.615 Å. So the first thing to do is to draw a cube shaped box. NB I have distorted the cube to make the later stages of the task a little more easy.

First view of the cube, showing a cube as a solid object.

This is a bad drawing as you need to be able to see the back edges of the cube, so it is better to redraw so it is like a fish tank.

Cube as a fish tank

Now we are ready to start to add the atoms to the cube. We need to first define one corner of the cube as the origin. I have now marked the origin with an O.

Origin added to cube

Now I add labels for the three different axes (a, b and c). As a = b = c it does not matter which way around you get them for this example.

Axes now with labels

Now we need the fractional coordinates.

Cu at 0, 0, 0 ; 0.5, 0.5, 0 ; 0.5, 0, 0.5 and 0, 0.5, 0.5.

We will start with the coppers at 0, 0, 0

Cu at 0, 0, 0 ; 0.5, 0.5, 0 ; 0.5, 0, 0.5 and 0, 0.5, 0.5.

So now add a single copper atom at the origin.

First copper atom added

Now move along the a axis the length of the unit cell edge and add another copper atom. These two atoms are related by a simple linear translation.

Second copper atom added, atoms are related by translation

Now using a related translation along the b axis add the next two copper atoms.

Now with four atoms of copper

Next do the same using the c axis to finish off the coppers at the corners. Now you have a primitive cubic cell just like that found in alpha polonium. But copper is a little more complex than alpha-Po. So we need to some more work.

Coppers at all the corners now

Now it is time to start on the coppers which are in the centre of the faces of the cube. Start by measuring half way along the a and c axes. Mark the point where the lines cross.

Marked out where to add the copper at 0.5, 0.0, 0.5

Now add the copper where the dotted lines cross.

Copper now added at 0.5, 0.0, 0.5

Now by translation along the b axis add the copper at the other end of the unit cell which is at 0.5, 1.0, 0.5

Copper added at 0.5, 1.0, 0.5

Now repeat the operations to add the next two coppers.

Added the coppers at 0.5, 0.5, 0.0 and 0.5, 0.5, 1.0

Now the next bit is hard to see, as things are going to get crowded. I will now change colour of the atoms to blue to make it a little more easy to see. So add the copper at 1.0, 0.5, 0.5

Almost there now, keep going please !

And to finish off the job we add the last atom.

Great we have finished our copper unit cell. Relax for a moment but do not go away we still have plenty of work to do !

Please be aware that other metals (such as zinc metal) can have non cubic unit cells. For those of you who do not recall what zinc looks like here is a zinc coated flower pot tray.

A zinc coated steel tray

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This entry was posted on March 15, 2010 at 8:51 am and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

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