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Non cubic cells

Dear Reader,

When I was at my brother in law’s wedding I took the chance to bring to Sweden a book which I consider to be one of my “secret weapons” in chemistry. It is not the most advanced book in my collection but it is a fun book. It is a 1960s text book which is intended to be a bridge between A-level chemistry and university chemistry.

Now if any of you have a copy of “Chemistry: A Unified Approuch” by Buttle, Daniels and Beckett then I suggest that you turn to page 70 of the third edition. But the rest of you will have to keep on reading my blog.

I want to discuss with you some crystal systems and unit cells which are a little different to the rock salt cubic one which I have already considered.

Now if we make a start with a cube which has been stretched or squeezed in one direction we will have tetragonal. The example which the book gives is mercury(II) cyanide. Now this is a compound which I suspect will get some less mature people angry. The mercury part may outrage them while the cyanide part will also get them in a pickle.

Before we go any further I need to share something with you, sometimes when we learn about chemistry we need to learn about the chemistry of not so nice to handle substances. If I was to try to write a chemistry course which either only included “nice” harmless substances or only contained wild and scary compounds then I would have done the students a great wrong. To understand chemistry you will need to understand both nice innocent compounds and some real nasties. While I do not advocate giving the undergraduates things like plutonium, acrylamide, brucine and large amounts of KCN to do experiments with I still need to teach them about these things as they will need to have an understanding of these things for the good of society.

To fail to teach chemistry students about “horrible” chemicals is as stupid as not teaching law students about “what to do when people break the law”. While law students could be taught about all the laws which relate to nice people who make a point of obeying the law, they need to know about legal reasoning of criminal law, and the details of the laws which deal with bad people.

I have very little sympathy for the idea that I should not teach students about chemicals which they can not handle in their teaching lab. I also have precious little sympathy for people who use (or want to use) the more hazardous chemicals in a reckless manner, I am strongly in favour of responsible chemistry.

Now I am coming down from my soap box, and returning to the chemistry.

O. Reckeweg and A. Simon, Zeitschrift fuer Naturforschung, Teil B. Anorganische Chemie, Organische Chemie, 2002, 57, 895-900 is the most modern determination of mercury(II) cyanide. This compound is in a cube which has been squashed. The cell has two sides which are 9.6922 Å long and one which is 8.9015 Å long. The first two are the x and y axis while the last is the z axis. The z axis is blue while the other two are red and green.

We need to add the mercury atoms at the following locations

0,2500 0,7880 0,8750
0,2500 0,7120 0,3750
0,2120 0,2500 0,1250
0,2880 0,2500 0,6250
0,7500 0,2120 0,1250
0,7500 0,2880 0,6250
0,7880 0,7500 0,8750
0,7120 0,7500 0,3750

Here is what our cell will look like with the metal atoms

The mercury atoms in the cell

Next we should add the cyanide carbons at the following locations

0,0464 0,7950 0,8366
0,0464 0,7050 0,4134
0,4536 0,7950 0,9134
0,4536 0,7050 0,3366
0,7050 0,9536 0,5866
0,7050 0,5464 0,6634
0,7950 0,9536 0,1634
0,7950 0,5464 0,0866
0,9536 0,2050 0,1634
0,9536 0,2950 0,5866
0,5464 0,2050 0,0866
0,5464 0,2950 0,6634
0,2950 0,0464 0,4134
0,2950 0,4536 0,3366
0,2050 0,0464 0,8366
0,2050 0,4536 0,9134

Here is the cell with the carbons and the mercury atoms

The cell with the carbon and mercury atoms in it

Lastly we add the cyanide nitrogens, I know that this might be a lot for you to read but think of how I have to type all the the values !

0,2035 0,9280 0,1785
0,2965 0,9280 0,5715
0,2035 0,5720 0,0715
0,2965 0,5720 0,6785
0,5720 0,7035 0,3215
0,5720 0,7965 0,9285
0,9280 0,7035 0,4285
0,9280 0,7965 0,8215
0,7965 0,0720 0,8215
0,7035 0,0720 0,4285
0,7965 0,4280 0,9285
0,7035 0,4280 0,3215
0,4280 0,2965 0,6785
0,4280 0,2035 0,0715
0,0720 0,2965 0,5715
0,0720 0,2035 0,1785

Now we have all the atoms in the cell, here it is in all its glory.

Here is the cell with all the atoms in it

Now we have the whole of the cell, the interesting question is what is the coordination number of the mercury. Now at first look it might appear that the coordination number of the mercury is four. But it is only two. If we look at the coordination environment of a mercury we will see that we only have two cyanide carbons in the right places.

The coordination environment of a mercury atom

Lead(II) iodide has a series of different hexagonal crystal forms, but the most simple one is described by B. Palosz, W. Steurer and H. Schulz, Journal of Physics: Condensed Matter, 1990, 2, 5285-5295.

After the endurance test of typing the values for the mercury cyanide this one should be quite a nice rest.

The cell is a hexagonal cell, the a and b edges are 4.558 Å long (these are the x and y axis {red and green}) while the z axis is blue and the c edge is 6.986 Å long.

We have a lead atom at each vertex of the cell, so the fractional coordinates of the lead is 0 0 0 (well that was easy).

The first iodine is at 0.3333, 0.6667, 0.2675 while the other is at 0.6667, 0.3333, 0.7325.

Here is what the cell looks like.

Lead(II) iodide cell

Potassium chromate, well I do not know why the book seems to choose toxic examples so much but this is a good example of an orthorhombic cell.

We start with a box which is 7.662 Å by 5.919 Å by 10.391 Å.

Then we add the potassium atoms at the following fractional coordinates

0.1656, 0.2500, 0.0857

0.5100, 0.7500, 0.1998

0.6656, 0.2500, 0.4143

0.0100, 0.7500, 0.3002

0.990, 0.2500, 0.6998

0.3344, 0.7500, 0.5857

0.4900, 0.2500, 0.8002

0.8344, 0.7500, 0.9143

As all of these potassium atoms are totally inside the cell, we have eight potassium atoms in our cell.

Next we need to start to add the chromium atoms these are at

0.7291, 0.2500, 0.0794

0.2291, 0.2500, 0.4206

0.7709, 0.7500, 0.5794

0.2709, 0.7500, 0.9206

As all the chromiums are fully inside the cell we have four chromiums in the unit cell which means that the potassium to chromium ratio is 2:1. This is in agreement with the formula which we are expecting for the solid.

Lastly we add the oxygen atoms to the cell.

We have four groups of four oxygens which are at

0,1982 0,7500 0,0704
0,1971 0,5225 0,8471
0,4846 0,7500 0,9200
0,1971 0,9775 0,8471
0,6971 0,9775 0,6529
0,9846 0,7500 0,5800
0,6982 0,7500 0,4296
0,6971 0,5225 0,6529
0,8018 0,2500 0,9296
0,8029 0,4775 0,1529
0,5154 0,2500 0,0800
0,8029 0,0225 0,1529
0,3029 0,0225 0,3471
0,0154 0,2500 0,4200
0,3018 0,2500 0,5704
0,3029 0,4775 0,3471

I hope by now that the penny will have dropped the cell has a magic point at 0.5, 0.5, 0.5, this is a centre of symmetry. If an atom appears at fractional coordinates q, w, e then another atom will appear at 1-q, 1-w, 1-e.

If we add the oxygens to the cell we will get a tetrahedral arrangement around the chromium atoms, for two of the chromium atoms we have to borrow an oxygen from another unit cell. This finishes off the potassium chromate cell. It also helps explain why chromate is so toxic, the chromate anion is so similar to a sulfate anion that it can pass through cell and nuclear membranes in the same way as a sulfate anion can. The chromate which enters the nucleoplasm can get reduced to chromium(III) which can then form very long lived complexes with the DNA in the cell.

The other crystal systems which have angles which are not right angles are much more of a pain to draw so we will not do them today.

I will put up the pictures of the potassium chromate later.


One Response

  1. Interesting!

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