Muons and Fukushima

Dear Reader,

One of the great problems right now is working out where the fuel in the damaged cores and the ponds is, and in what condition the fuel is in. We can take for granted that the fuel which was in units 1, 2 and 3 has been damaged by overheating. But the state of the fuel in the ponds was a bit more of a mystery to us.

After clearing the rubbish out of the pond at unit three it has been possible to inspect the pond, the pond is frankly in a bit of a mess. But the fuel seems to have escaped serious damage. Photographs have been taken of the fuel racks in the pond and it does not look like there has been been any dire melting or explosions in the pond.

I have seen that some samples have been taken from the pond at unit four to allow them to be examined (these were samples of unused fuel which were being stored in the pond at the time of the accident). The work so far suggests that the fuel in the pond is in good condition. This suggests strongly that no nuclear explosion occurred in the pond.

The other great question is the state of the reactors. I saw something interesting recently, it is a sensing system based on cosmic rays (muons). This looks to me like a good method for finding the fuel inside the damaged reactors without having to get up close and personal with the stricken reactors.

Another thing which needs to be done is for society to recover from the accident, I have seen some advice from the IAEA on the subject of remediation of the contaminated land (outside the nuclear reactor park). This document might be of interest to some of my readers. It includes a discussion of the cleaning of different types of areas which include farmland. As I predicted it does include the question of deep ploughing the land.

Clay again

Dear Reader,

Again we are turning out attention to clay, clay is a wonderful substance on which we play tennis on, make pots from and create art with. Clay is also important when cesium gets into our soil. I recently wrote a little on the subject of the clay minerals in the soils in Japan. Here is a useful set of lecture notes on silicate minerals, most clays seem to be silicates.

I have recently read that the soil from Japan holds tightly onto cesium, when soil which was contaminated by the Fukushima event was soaked in 1 M ammonium chloride solution (at 25 oC) only about 20 % of the cesium radioactivity was liberated from the soil. Then when this soil was treated with 1 M acetic acid only about 10 % more of the cesium was liberated from the soil.

It was also found that treatment with 1 milimole per litre sulphuric acid only was able to liberate less than 1 % of the radioactivity while 1 mole per litre sulphuric acid was able to liberate about half the cesium.

These findings suggest it will be hard to wash the cesium out of the soil, but if the soil is washed with ammonium chloride then the remaining cesium will be hard to transfer to plants. I suspect that as time goes on that the amount of cesium which can be transferred to the plants will become less and less as the cesium becomes more and more fixed to the minerals in the soil.

Update on your new best friend

Dear Reader,

Slightly more than one year ago I wrote about the new best friend of the Japanese people. Rather than a person who will go out and go for a karaoke session with you, drink beer with you or go for a walk in the park with you this new friend is one who can clean up your drinking water and keep your fruit and veg safe. Also this friend can help keep the milk healthy. Now you might ask what sort of super nice person can do all these things, or what sort of imp or kappa is able to do all these things.

The identity of this new friend is a bit more humble sounding, it is the clay in the soil. I have seen a recent paper by Naofumi Kozai, Toshihiko Ohnuki, Makoto Arisaka, Masayuki Watanabe, Fuminori Sakamoto, Shinya Yamasaki and Mingyu Jiang (Journal of Nuclear Science and Technology, 2012, 49(5), pages 473 to 478) in which the cesium behaviour in the soil is reported.

In this paper the soil was examined with X-ray diffraction. This found smectite, mica, hornblende, kaolinite, quartz, orthoclose, cistobalite, feldspar, stishovite, gibbsite, sodalite, olivine and sorosilicate minerals in the soils.

The smectite clay is rather similar to the illite clay which I showed a picture of recently. The two clays are related, I have seen a thesis which explains how the smectite clay transforms into illite clay. For your information the thesis is here. The difference between these two layered clays is in the anionic bread layers between the potassium jam. The smectite and the illite have slightly different layers.

A smectite clay, the oxygens are in orange red, the potassium ions in blue, the aluminium/silicon atoms are in sea green. Note that layers of potassium ions which look like slices of bread.

I think that both the smectite and illite are formed from mica, so I would say that the more mica in the rocks which formed the soil the better when you are considering cesium in soil. The mica is very similar to the two clays, again it is a layered solid.

Many of us know mica, it is a mineral which can be made into thin sheets. We will soon see why it is possible to split mica into thin sheets. It is easy to separate the mica by peeling apart the layers.

Here is a view of a mica (Muscovite) which was studied some time ago. (O.V. Sidorenko, B.B. Zvyagin and S.V. Soboleva, Kristallografiya, 1975, 20, 543-549). Should should see again that the solid is layered, the potassiums (blue) have anionic layers of alumo-magnesium silicate between them. I have shown all the non oxygen atoms in the layers as green.

Mica showing the layers of potassium ions between the anionic layers

The important thing about the mica is that the aluminium atoms are randomly mixed with magnesium and silicon atoms in the two layers. The authors of the paper I am working from expressed the view that one of the types of layers (the middle layer in the trilayer anionic layer) has 20 % magnesium and 80 % aluminium. While the two outer layers of the anionic trilayer have 28.4 % aluminium and 71.6 % silicon. The mica also contains some hydroxyl anions which I have been unable to locate in that solid. I have made a new drawing of the mica which shows the mixed aluminium/silicon and aluminium/magnesium layers in different colours to show you how the solid fits together.

Diagram of mica. The potassium ions are in blue. The mixed aluminium/magnesium sites are in grey. The mixed aluminium/silicon sites are in green. The oxygens are in a rather fetching shade of orange.

It is important to note that the green aluminium/silicon sites have a tetrahedral arrangement of oxygen atoms around the central atoms while the grey mixed magnesium/aluminium sites have a distorted octahedral arrangement of oxygens around the central atoms.

The hornblende clay is a very different mineral, I have looked at the crystal structure and it looks in some ways like a SBA-15 or MCM-41 to me. It has tube like holes which pass in one direction through the clay. These tubes are then filled with sodium and potassium cations. As the clay is so different, I suspect that it may behave differently to the layered clays which I showed you.

The mica based minerals can change the spacing between the anionic layers to suit a new cation which has a larger diameter than the potassium. In this way the larger cesium ions can be held in the solid. But in the case of the hornblende, I do not think it will be so easy to add a larger cation. I think that the holes will get plugged up and blocked by the larger cations.

Here is a view of several unit cells of the hornblende clay, the solid is a little disordered. It has a mixture of sodium (yellow) and potassium (blue) cations in the solid. Also note that it has grey calcium ions in the alumosilicate layers. The aluminiums are purple, the silicons are sea green and the iron atoms in the clay are orange. The oxygen is in a rather fetching orange/red as before.

A view of hornblende clay showing the holes in which the potassium/sodium ions go.

I will try and give you an update soon on the clay and the cesium.

Sheep and Chernobyl

Dear Reader,

I have just discovered that the Chernobyl related controls which were imposed on sheep farms in England and Wales have just been lifted. The radioactive cesium from Chernobyl will have become weaker because of the radioactive (physical) decay, while the cesium-137 will only have decayed slightly the cesium-134 will have decayed a lot by now.

I imagine that by now that the cesium will have migrated deeper into the soil, this makes the cesium less able to enter the grass. Also I am hoping that the cesium will be more tightly bonded now to the soil minerals, one of the problems with the hill sheep farms is that the soil is poor in potassium and the minerals which will bind the cesium are not present in large amounts. This will lower the Kd value for cesium in the soil as a result the plants will be more able to absorb the cesium via their roots.

I saw with interest that Naofumi Kozai, Toshihiko Ohnuki, Makoto Arisaka, Masayuki Watanabe, Fuminori Sakamoto, Shinya Yamasaki & Mingyu Jiang published an article (Chemical states of fallout radioactive Cs in the soils deposited at Fukushima Daiichi Nuclear Power Plant accident) in the Journal of Nuclear Science and Technology, 2012, volume 49, issue 5, pages 473 to 478.

In this paper the authors report some leaching experiments which have been done on cesium contaminated soil from Japan, they found that the majority of the cesium stayed in the soil even when the soil was treated with ammonium chloride and acetic acid solution. This suggests to me that much of the cesium is locked up inside the soil which will prevent both the easy washing of the cesium out of the soil and also prevent the plants absorbing the cesium with ease.

Mike Adams

Dear Reader,

It has come to my attention that a Mike Adams has published a claim that the spent fuel ponds at Fukushima are a dire threat which is likely to exterminate mankind. He claims that the release of “radiation would turn North America into a “dead zone” for humans… mutated (and failed) crops, radioactive groundwater, skyrocketing infant mortality, an explosion in cancer and infertility”

Now before I go any further I will address some of these bold claims. I think that on many things Mike is very wrong.

1. A radiation release from the spent fuel pond is very different to a release of radioactivity. I sincerely wish people would learn the difference ! The best way to think of it for the layman is to consider my dog, he sometimes barks and you could imagine the waves of sound coming from his mouth to be like radiation. His bark travels through the air obeying an inverse square law and with some distance from him the bark soon becomes less irksome. The dog is the object which emits the barks, you should think of the dog as being like the radioactivity. The barks from my dog might escape from the house when I open a window but the thing which emits the bark can not escape with the same ease.
2. As cesium (the most mobile of the medium to long term irksome radioisotopes) sticks like glue to clay, almost all ground water and wells will remain radiologically safe to drink from no matter what happens.

So with these two important mistakes, omissions, distortions or whatever you want to call them lets take a look at the rest of his article using the our intellect !

Mike wrote that the cesium release will snuff out all life in mainland USA; I very much doubt that this would be possible.

He assumes that all the cesium will be released, and that 85 times as much ¹³⁷Cs is in the ponds as was released at Chernobyl. I want to use the Chernobyl cesium in Scotland as a model for his proposed doomsday event.

I looked up the average level of ¹³⁷Cs in soil in the UK, in Scotland the level of this radioisotope as a result of Chernobyl is 1580 give or take 310 Bq m^-2 on moorland while it is 2510 give or take 510 Bq m^-2.[1] This might seem like a lot of radioactivity, but for a beta/gamma isotope this is not much. If we take the standard data[2] on ¹³⁷Cs we will find that the dose rate one meter above the surface of ground which is uniformly contaminated with 1 Bq m^-2 is 1.6 pSv hr^-1. So the dose rate due to the Chernobyl cesium in Scotland is 4.016 nSv hr^-1. Which works out as 35 microSv per year. This is not much !

If we assume that the Chernobyl release had been 85 times larger, then the yearly dose would be now 3 mSv per year. This dose will not exterminate humans ! The chances of getting cancer as a result of living 60 years in such a place will be small. Only 1 in 111 people will get cancer as a result of this exposure even if we ignore the radioactive decay of the cesium. Sadly about 1 in 4 people die of cancer from other causes such as bad diet, smoking and simple bad luck. As a result I would not expect to see any noticeable change in the population.

So we have caught him in another error, not too good !

I would also like to point out that Mike has not fully explained the mechanism by which he proposes that the cesium will be released from the pond.

The great problem with his idea is that the heat production in the fuel in the pond has gone down greatly, the fuel will hardly be emitting any heat by now. This makes it much harder for the cesium to be released from the pond. I would be very interested to see how he proposes the pond will belch forth the cesium.

To give you some idea of what Mike is like here is what he thinks of the UN, he thinks it is “a criminal globalist organization engaged in widespread sex slave trafficking, child abuse and mass murder”. The last time I looked the UN appeared to be much more benign than that. I recall that recently part of the UN (the IAEA) got a noble peace prize (they spent the money part of the prize on cancer care for people in the third world).

Some years ago the United Nations High Commissioner for Refugees (UNHCR), United Nations International Children’s Emergency Fund (UNICEF) and United Nations Peace-Keeping Forces have all been given Noble Peace Prizes.

I thought that the people in Norway who issue Noble peace prizes are careful not to issue them to bloodthirsty cut-throats and brigands.

This scorching condemnation of the UN does suggest to me that there is either something terribly wrong with either my understanding or Mike’s understanding of the UN. I think I will leave it up to my reader to judge the UN.

Before I do go, I would like to point out something. Fukushima was (and is) a horrible accident, but the horrible nature of the accident is not a license to exaggerate or lie. I fear that members of the Green movement who exaggerate or lie will do the environment a great harm, what will happen is that they will discredit the genuine concerns of those who want to protect the environment.

---

[1] A.S. Likuku, D. Branford, D. Fowler and K.J. Weston, Journal of Environmental Radioactivity, 2006, 90(1), 37-47.

[2] http://www-pub.iaea.org/MTCD/publications/PDF/Pub815_web.pdf

The big earthquake one year on

Dear Reader,

We are coming up to the first anniversary of the Fukushima accident which was provoked by a big earthquake. Now as ever it is important to avoid going to one extreme or another. When we get sick a spoon full of medicine might make us feel better but that fact is not a license to drink the whole bottle in one go !

While I am very strongly in favour of improving safety standards in the nuclear industry and I am sure that some important lessons can be learnt from the Fukushima event, but we should not close down the whole nuclear industry just because of this accident. I always do point out that the burning of coal does release a vast amount of radioactivity into the air.

The majority of radioisotopes from nuclear power plants are short lived beta emitters which tend to go away quickly, the radioactivity in coal tends to be long lived alpha activity. As the alpha emitters tend to be so much more toxic and as they are long lived this is a nasty menace which people tend to forget about. So do not allow anyone to talk you into switching to coal as a way to close down scary looking nuclear plants.

Now on the subject of radioactivity, it is important to bear in mind that wind farms need neodymium for the magnets. The extraction of this metal often requires it to be extracted from monazite which is a radioactive mineral. So before anyone trys to sell you the idea of clean green wind power as an alternative to nuclear power then ask where the neodymium for the magnets comes from. The great problem with “greenness” is that you need to look at the whole life cycle of the object or the system, you also need to look at where the materials required for a device come from as well as what waste the device forms and how you are going to dispose of the device when it is no longer wanted.

I worry that unless the right degree of care is taken with the ore processing that the extraction of the neodymium will create large amounts of radioactive waste which might not be managed in a safe, environmentally sound or reasonable way.

But lets think for a moment about the radioactivity from the Fukushima accident, in common with chernobyl after the short lived iodines the most important radioisotope is Cs-137. This is a medium to long lived isotope which contributes to much of the dose which members of the public will get in the medium and long term after the accident. I saw a paper in the literature by J. Jandl, J. Novosad, J. Francová and H. Procházka, Veterniarni Medicina (Praha), 1989, 34(8), 485 to 490 which is on the subject of cesium removal from deer meat. What these Czech workers did was to pickle meat, by ion exchange the cesium came out of the meat and was lost into the pickling liquid. As only the meat and not the pickling liquid is consumed by humans this offers a method for the decontamination of meat.

The same idea has been written about by some Germans (R. Wahl and E. Kallee) in Nature, 1986, 323, 208. These workers reported that after five days 95 % of the cesium had been lost from the meat. They also reported that the meat tasted very good. So based on this work I would like to suggest that we should consider treating some foods after gathering them to lower their radioactivity content and thus make them fit for human consumption.

The calculations are going well

Dear Reader,

I am currently in the process of doing the calculations, the good news is that they are working and that the answers are in agreement with the answers which I obtained using graph paper.

It is important to understand that for these calculations when they are done by hand using graph paper then a mathematical treatment similar to that used for Fraunhofer diffraction which is diffraction where the distance between the observer and the diffraction grating is infinite. While when the problem is being considered with a spreadsheet it is much more easy to use maths which is similar to that used for Fresnel diffraction where the distance between the slits and the observer is small.

Control rod chemistry

Dear Reader,

In the blogosphere I have noticed that one blogger claimed that the radioactive silver spread around by the Fukushima accident was due to the use of silver in control rods. While one paper I read suggested that the reactor one used boron carbide, I can not rule out that the reactors used silver control rods.

Control rods are used on almost all reactors to control the rate of reaction, the further out they are pulled from the core the faster the reaction occurs. You can think of the control rods as the accelerator pedal of the reactor.

Silver has a high cross section for neutrons and as a result would make a good control rod material, the ideal control rod would.

1. Last forever
2. Cost nothing to make
3. Not become radioactive while in service
4. Behave nicely even during a horrible accident

The first issue is an interesting one, designs for control rods vary from reactor to reactor. One common choice is to use boron; this is because one of the isotopes of boron has a very large cross section for neutrons.

The cross section for neutrons is expressed in barns; this is an old unit of measurement which dates back to the Manhattan project. The idea was that if everyone expressed the cross section areas in barns rather than square meters then if a spy saw a cross section then it would be just a meaningless number. I suspect that the term barn relates to barn door.

The choice of boron has a sting in the tale which can come back to bite you on the arse. The problem is that any isotope with a very high cross section for neutrons will not be needed in large atom numbers. Each time it catches a neutron then one less atom will be present, so this can cause a change in the effectiveness of the control rod. This idea is known as burning out the neutron poison.

While the slow weakening of a control rod’s effect is an undesirable effect, this effect can be used in a beneficial way. Some fuels which have very high fissile contents have a little boron blended in. The idea is that as the fissile atoms are used up the boron is also burnt up by the neutron bombardment. The overall idea is that the fuel keeps the same reactivity level throughout its whole life inside the reactor.

The reaction by which the boron works is

n + ¹⁰B –> ⁴He + ⁷Li

This reaction generates helium gas; one Russian design for a control rod uses a boron steel alloy. The problem with this design is that the life of the control rod is limited because the helium starts to form bubbles in the steel. These bubbles then harm the properties of the rod.

A common western design is to use boron carbide (B₄C), the rods are made of a steel and have holes into which are place pellets of boron carbide. As the steel is separated from the boron we do not have the helium bubble problem, but if the rod is overheated then a reaction can occur between the stainless steel and the boron carbide. This is an exothermic reaction which forms metal borides and some carbon. For example

B₄C + 4Fe –> 4FeB + C

One other disadvantage of boron carbide is that during an accident it can form methane; the methane can lead to the formation of methyl iodide during an accident.

An alternative is to use a cadmium-silver alloy; the nice thing about cadmium is that it is very selective. It has a very large cross section for slow thermal neutrons while for fast neutrons is has next to no cross section. As the thermal neutrons are more able to cause fission then the cadmium has the nice effect of selectively mopping up these neutrons thus altering the energy spectrum of the neutrons in the core.

As a result of the fact that cadmium is selective for slow neutrons, I think that a control rod based on only cadmium would be a poor choice for a fast reactor such as a sodium cooled fast breeder, for such a reactor I would be inclined to use boron as it has a simple broad graph of absorption cross section as a function of neutron energy.

Cadmium is a metal which has a series of non radioactive isotopes, so when the cadmium-113  (the isotope with the largest thermal cross section) swallows up a neutron it forms cadmium-114 which is non radioactive and has a small capture cross section for neutrons. In this way many of the cadmium atoms can swallow up a series of neutrons without forming much radioactivity. Also the radioactive isotopes of cadmium are mostly well behaved short lived isotopes.

¹⁰⁶Cd, 1.25 %

¹⁰⁷Cd, half life of 6.5 hours decays to ¹⁰⁷Ag

¹⁰⁸Cd, 0.89 %

¹⁰⁹Cd, half life of 463 days decays to ¹⁰⁹Ag

¹¹⁰Cd, 12.49 %

¹¹¹Cd, 12.80 %

¹¹²Cd, 24.13 %

¹¹³Cd, 12.22 %, very long half life (7.7 x 10¹⁵ years or 7.700000000000000 years)

¹¹⁴Cd, 28.73 %

¹¹⁵Cd, half life of 53.46 hours decays to ¹¹⁵In

¹¹⁶Cd, 7.49 %

¹¹⁷Cd half life of 2.49 hours decays to ¹¹⁷In

On the other hand silver has two stable isotopes, both of which form radioisotopes when they swallow up a neutron. This means that silver control rods will make more long (half life > 1 day) radioactivity per million neutrons which they absorb than a cadmium control rod will.

Some time ago I visited a disused nuclear power plant in Sweden; it was a small heavy water plant which produced only 10 MW of electric power and heat for district heating. In the reactor containment I saw the area where the used fuel used to be stored (the fuel had been taken away long ago) but the control rods remained locked inside the storage area. They were being left there to decay while everyone is waiting to decommission the reactor building. The thing about decommissioning is that the longer you wait the lower the levels of many irksome isotopes. For example the ⁶⁰Co which forms as a result of the cobalt impurities in stainless steel will become half as strong every five years, thus by waiting for 50 years this radiation source will become one thousand times weaker.

Due to the fact that the control rods are exposed to such high neutron fluxes when in use, and as they are intended to absorb neutrons they can become very active.

When an accident occurs and a core melt occurs, it is likely that silver containing control rods will melt and start to form fine silver rich particles. This is likely to be a good thing as iodine has a strong affinity for the silver; this aerosol of silver may help to trap out radioactive iodine inside the plant. On the other hand if the silver particles are of the “wrong size” then maybe they will assist the escape of the radioactive iodine. One of the key features of the Chernobyl accident was that ruthenium tetroxide (RuO₄) was formed; this is a very volatile and strongly
oxidizing metal oxide. The RuO₄  enabled the ¹⁰³Ru and ¹⁰⁶Ru to form a coating on steel surfaces. These steel surfaces included both parts of the plant and also fine steel particles which were then able to escape from the plant. This is likely to be the reason why ruthenium rich hot particles were observed after the Chernobyl accident.

Ruthenium is a nice metal which I have a deep love of; I picked up this liking for it when I worked for Tony Hill. He joked that he had a special attraction to [RuHCl(CO)(PPh₃)₃] which is a complex formed by heating ruthenium chloride in methoxyethanol with triphenyl phosphine. I think I can see why Tony likes this complex; it is a useful starting material for a series of other things. It is also possible to make an osmium version of this complex but I will save my views on osmium for another day. The formation of this rather interesting looking compound is related to the work of Vaska. Vaska is a chemist from Eastern Europe who is something of a genius, he did a lot of nice chemistry with elements such as iridium. But lets get back to control rods.

So sometimes formation of solids or particles are a good thing and sometimes a bad thing.

One alternative to boron carbide, boron steel and indium-silver-cadmium alloys is to use hafnium. This is an interesting element; while zirconium has a very low cross section for neutrons (it is close to transparent to neutrons) hafnium is a very strong absorber of neutrons. As the elements are so similar in chemistry hafnium is commonly found in zirconium minerals, the zirconium used for nuclear reactor applications is normally a special low hafnium grade.

The hafnium is used in the form of hafnium hydride in control rods; these control rods are unlikely to react violently during a reactor accident or to form troublesome gases.

Tellurium-129m maps

Dear Reader,

It has come to my attention that the Japanese government have published a map of the tellurium-129m contamination levels in the countryside near to Fukushima. Here is a link to the maps from Japan.

Now before we get going we might want to consider what tellurium is.

Tellurium is a heavy version of sulphur (sulfur), it is named after the earth while selenium (the element) above it is named after the moon. Tellurium has some rather interesting chemistry it is more than just a heavy version of sulphur.

Many organisms are able to transform it from one chemical form to another, one of the typical symptoms of tellurium poisoning in humans is that the unlucky person who is stricken with tellurium will start to stink to high heaven of garlic.

This is because inside the human body the tellurium is converted into dimethyl tellurium, while I do not think that the tellurium will leave the reactor in the form of dimethyl tellurium I think it is likely that bacteria or animals will convert the tellurium into this volatile form. It is possible that the ability of living things to form this volatile organometallic may make the environmental chemistry of the tellurium more complex.

Now I hope that it is OK with my readers but right now I do not want to get sucked into a discussion of the environmental chemistry of tellurium, but I am willing to comment on another aspect of tellurium chemistry.

One of my all time favourites in chemistry is VSEPR, or Valence Shell Electron Pair Repulsion theory. For those of you who are not in the know, this is a simple theory which predicts correctly the majority of covalent compounds which lack transition metals. Be careful of the transition metals the electrons in the d orbitals can throw you a bit of a weirdo ball, on the other hand the main group elements tend to just play nicely with a normal over the shoulder delivery of the cricket ball without trying to do things like spin bowling.

The core idea of VSEPR is that the central atom has a series of electron clouds (orbitals) which poke out of the atom to form sigma bonds. The sigma bonds would look like sausages if we could see them. Think it is a nice thing that s is for sausages and also for sigma bond.

These sausage like clouds of electron density will repel each other, this is a plain simple electrostatic effect much like the effects you get if you comb your hair and then wave the comb near some small scraps of paper.

If an atom has two such sausages (opps I mean bonds) then the furthest they can be from each other on a sphere is at 180 degrees (pi radians) from each other, an example of this would be the arrangement of atoms in acetylene.

If an atom has three sausages then the furthest they will be from each other is at 0, 120 and 240 degrees around the equator of a perfect sphere. An example of this type of arrangement would be the atoms in benzene or styrene. While we are at it be thankful for styrene, without styrene there would be no polystyrene or ABS plastic. The chances are that your computer screen has a case made of ABS.

If an atom has four sausages then these bonds will be arranged in a tetrahedral manner, this is the arrangement which makes them the furthest from each other.

If the atom has five sausages then the geometry which puts the bonds the furthest apart would be to stick one at each of the poles, and three spaced at 120 degrees apart on the equator. One alternative would be a square based pyramid but I have done the maths for that
yet.

If the atom has six sausages then the geometry which puts all the bonds in an octahedral arrangement.

When an atom has a lone pair this should be regarded as a sigma bond which goes to nowhere. Treat it as if it almost as it it was just another bond, as the electrons are on average closer to the atom the lone pair is more able to repel other other bonds than a normal sigma bond.

The fun thing about tellurium is that sometimes its lone pair is stereochemically active this means that it repels other electron pairs just like any other electron pair. But sometimes the tellurium lone pairs are stereochemically inactive which means that these lone pairs do not repel other electron pairs (bonds and lone pairs). The non-stereochemically active lone pair does not normally appear in light elements such as sulfur and oxygen, it tends to be something which only happens with heavy elements such as tellurium and lead.

Molecular boxes

OK a bit more about prussian blue and what are known as coordination polymers. The idea of a coordination polymer is that it is a repeating network where bridging ligands link each metal centre to the next, thus making a polymer.

To understand them we need to build up to it, it is not a good idea to try to run before you walk. Lets start with a metal complex which has lone pairs poking out into space ready to bind to something else. Err Oh Err how about [CpFe(PR₃)(CN)₂]^- this is a 18 VE complex. For those of you who do not know what the 18 VE rule is then I suggest that you read Tony Hill‘s book which will explain the 18 VE rule. A copy of organotransition metal chemistry by Anthony Hill can be obtained from the RSC.

Here is a picture of the anion, you can see it has the two nitrile groups which each have a lone pair on the nitrogen atom.

The cyclopentadienyl iron triphenylphosphine dicyanide anion

Now here is a complex where the Cu(PCy₃) group is used, this group is a weak lewis acid so it has the ability to bind to lewis bases such as the lone pairs of the cyanide groups of the iron fragment.

You can now see the square-ish arrangement of two copper atoms (green) and two irons (yellow), what you are looking at may be a bit of an “atomic fog” but do not worry yourselves too much.

The diiron dicopper square complex

As I feel kind here is a picture of the inner core of the complex, I have removed the carbon groups attached to the phosphorus atoms.

Copper iron square complex without some of the groups to give you a better look

Now if we use three cyanides to link a metal to three other metals we can make a cube, well it is a bit of a distorted cube. I am sure that the more able minded persons reading this can understand how this is step towards a infinite solid with lots of cubes in it. Here is a picture of it. Before you ask the cage is anionic, and the atom at the centre of the cage is a potassium. This complex was published by T.B.Rauchfuss in the Journal of the American Chemical Society, 2007, 129, 1931.

The cube of eight cobalt atoms bridged by 12 cyanide ligands

The cube is capped with cyclopentadienyl and tetramethylcyclobutadiene ligands. For those of you who can not see through the atomic soup (or atomic fog) here is the cube without the capping ligands.

The cobalt cage without the capping groups

* If as a university teacher you do not get on with Tony Hill’s book then you can always replace this with another book.