A short time ago I chickened (lost my courage) out of the harder unit cells, then it started to rain which stops me doing my project in the garden. I have come back into the house and I am now sitting in front of the PC again.
We will be attempting to deal with a rhombohohdral cell, we will use the suggested example of sodium nitrate from that book which I mentioned recently. This cell has three equal lengths for the sides which are 6.3108 Å long. The angles alpha, beta and gamma are all 47.267 degrees.
N. Elliott, Annales Academiae Scientiarum Fennicae, Series A6: Physica, 1962, 94, 1 to 34 publishes the crystal strcutre. I will use this person’s data to make our cell.
The first part is to draw the box for the cell, this is not so easy as the angles in the cell are not 90 degrees. After you have been able to draw the cell we should start to add the atoms.
The sodiums are easy as we have them at fractional coordinates of 0 0 0 and 0.5 0.5 0.5, those of you who have been paying attention should quickly understand that we have two sodium atoms in each unit cell.
We have nitrogens at two fractional coordinates 0.25 0.25 0.25 and 0.75 0.75 0.75. This means we have two nitrogen atoms in our unit cell.
Finally we have oxygens at six sites, here are the fractional coordinates for these oxygen atoms.
Here is one view of what is inside the cell
Sadly one of the sodiums blocks the view of a nitrate anion, so here is a second view.
Finally here is a table of the cartesian coordinates of the atoms, this will allow some of my readers at home to recreate the unit cell. The sodium at 0 0 0 is the sodium at the centre of the cell. This will help you recreate a cell for yourselves.