Nuclear Waste: Untapped Potential

Oh man, This is great, I get to mix nuclear advocacy and my actual degree in Nano-materials Engineering together in one post!

I’ve noticed news about the Diamond Battery cropping up again lately since I first heard about it back in 2017, and oh man this thing is so exciting for a few reasons. First because it’s a new potential method of producing steady energy for small devices such as hearing aids, pacemakers, remote sensors for things like ecological monitoring, and other such devices that need to operate for long periods of time but don’t need much energy. Second, because it’s something that squares with what I’ve said before when talking about nuclear waste, namely that Nuclear Waste is only Waste if you Waste it.

To showcase how useful this technology could be, and how we might be able to benefit from the utilization of nuclear “waste” material, I’m going to dive right into the physics and practicality of this Diamond Battery. A bit of a warning, this will probably be one of the more math heavy articles I’ve written but I will do my best to explain everything I use.

Mechanisms

So how can a Diamond make energy? We don’t see anyone plugging their phones into their engagement rings. Well honestly it’s almost the same way that a solar panel works. Diamond, like silicon, is a semiconductor. It’s just much lazier than silicon and takes significantly more energy to get it to do anything. So if a sufficiently energetic particle like a photon or an electron hits the diamond, it can release lots of electrons from the atoms in the diamond and cause a current to flow. But that’s just how we can harness the electricity, how does this design actually produce them?

This is where the radiation comes in. The articles state that the designers have been planning to use radioactive carbon-14 (an isotope of carbon that has an approximately 5700 year half life) as a source of beta-particles to stimulate the semi-conductive properties of the diamond. Since beta-particles are just very fast moving electrons, they are blocked quite easily by thin sheets of material (the articles about the diamond battery state that the test samples are only 0.5 mm thick and have effectively no radiation leakage) and are easily used to create showers of ionized electrons. This is the electricity for the battery.

(A neat aside that I recently figured out about these battery designs: Since diamond is so dense, it actually has a fairly slow effective speed of light through its crystal, about 40% of the speed of light in a vacuum. This means that it is highly likely that the beta-particles that are released from the radioactive carbon will actually be travelling Faster than the speed of light in the diamond, and thus will actively release Cherenkov radiation. This is the cool blue glow you might have seen in some youtube videos about reactor start-ups. Depending on how much faster than this the electrons are travelling, this lightspeed sonic boom might actually be a contributing factor in producing electricity via ionization of the diamonds, and that is a ridiculously cool sci-fi feature that makes me feel like it’s actually from the goddamned future.)

How Much Energy/Power?

So how much energy can one of these batteries produce? Well, we know the half life of the C-14 isotope (5730 years) which means that it’s activity is approximately 1.648×10^11 Bq/g according to this formula from the link. (a Bq is a Becquerel, the standard unit of radioactive activity equal to one decay event per second), and each decay has an average energy of 50,000 electron volts (eV). Since eV is a measure of energy and not actually a voltage (I mean, it’s technically also a voltage since we are talking about individual electrons, but lets just ignore that) we can change it directly into Joules (1 eV = 1.60218e-19 J). Then we multiply it by the specific activity to find out the specific power of a diamond made from pure carbon-14. The units work out to a Joule/(second*gram), and a Watt, the unit for Power, is just a Joule per second. Some quick napkin math gives us a specific power density of 1.32 milliwatts per gram.

Of course this is for just a pure chunk of C-14 diamond, which we can’t do because a) that would let a lot of the energy escape out into free space and not be harvested to do useful work for us, and b) purposefully exposing people to radiation without shielding is generally considered a no-no. So we have to put a coating of regular Carbon-12 diamond around it to capture those last electrons and provide a conduction pathway to the electrodes that connect the battery to the rest of the system you are trying to power. Now, we know that penetration of radiation is determined generally by the density of the blocking material, so C-12 diamond, with a density of 3.5 g/cm^3, should have a maximum penetration depth of approximately 0.1 mm. Therefore, we need a layer approximately 0.1 mm thick surrounding the C-14 core to keep everything kosher.

Practical Numbers

So to make these numbers start making a little more sense, let’s put this in a familiar form factor. A standard AA battery is a cylinder approximately 49.5 mm long (without the little nub), and 14 mm in diameter. If we assume that we have a 0.15 mm thick layer of C-12 as the outermost layer (extra 0.05 mm cause we are all about safety with our Power Crystals) then we have a central core of C-14 diamond that is 49.2 mm long and 13.7 mm wide giving us a total volume of 7.25 cm^3 of power producing core, surrounded by 0.367 cm^3 of C-12 diamond. It’s important to differentiate these two sections because C-14 diamond and standard C-12 diamond have different densities. The crystal stays the same size, but we cram a couple more neutrons into every atom. C-14 diamond works out to about 4.05g/cm^3 so about a 16% increase giving us a core mass of our diamond battery/energy crystal.

For those of you wondering why this is at all important, it’s because we earlier calculated the Power Density of the C-14 diamond as 1.32 milliwatts per gram. Since we now know the mass of the core of our Energy Crystal, we can determine that it would produce up to 29.36 milliwatts steadily. Doesn’t sound very impressive until you realize that it would produce this power every minute of every day for Hundreds of years before it started dropping by noticeable levels. If we used this to power something for 100 years then that would be approximately 92.6 Megajoules of energy which is about 26.7 kWh. So the same amount of energy it takes to run your fridge for a day, spread out over a century from an AA battery.

Drawbacks

How realistic is this battery? Could we power a car? Sadly, probably not. At 1.32 mW/g you would need a chunk of diamond weighing about 15 tonnes to make the approximately 20 kW that normally lets a car maintain highway speeds, So it’s not super practical for cars, but a smaller chunks could be good for trickle charging a battery to keep some small electronics like mentioned earlier that need to be able to operate continuously for long periods of time. And a side benefit would be that the heat from these diamond batteries would keep those items warm even if they were operating in extreme environments like Antarctica, so maybe we could use little chunks to replace block heaters in cars for winter? God knows I’d love to never have to worry about my car being frozen again. But that heat leads to a small oversight we made in our previous calculations. Namely that no energy collection method is 100% efficient, which is what we were assuming with our previous numbers. Now there are no publicly available numbers for the predicted energy generation from these batteries in a final state. Some sources state that they would only make about 15 J per day per gram, which when compared with our calculated value of 1.32 mW/g means that the conversion efficiency is around 13%, but it doesn’t state what the ratio of C-14 to C-12 is, so there’s no way to know. 13% is not a bad estimate for conversion efficiency though in my opinion. Single crystal silicon solar cells are only about 24% efficient and they’ve had decades of research into optimizing them. A brand new technology getting 13% is pretty impressive.

Potentials

So the carbon based batteries won’t be putting any serious power out, But C-14 isn’t the only kind of nuclear waste that produces beta particles that can be harvested for electricity in this manner. My personal favourite would be Strontium-90, because it’s one of the portions of High Level Waste that people are most concerned about storing. Thus I think that putting it to use instead of just letting it linger and be wasted would be of great benefit. It’s about 8 times heavier than carbon but it produces about 0.536 W/g of heat due to it’s two beta decays to the stable Zirconium-90. To find out how much energy can be captured from that we need to estimate how much of that energy is in the electron and how much is from the atom rebounding after the decay (Newton’s laws of motion, Every action has an equal and opposite reaction and all that jazz.) If we assume the two parts of each decay have equal energy because of this, then there is the potential to capture up to 0.268 W/g of electricity from the initial strontium.

Even if the conversion efficiency is still 13%, this seems to indicate that Strontium-90 would still produce 34.8 mW/g of electricity which is about 26 times the power density of the carbon 14 diamond. However, there is a slight problem. Namely, the strontium is not a semi-conductor like diamond. We cannot generate electricity from the beta particles that do not escape the strontium, meaning that we must disperse it throughout the diamond itself. Thankfully, we can offset this problem by encasing the strontium in the C-14 diamond, thus boosting the power generation a tiny amount (waste not, want not). There is all sorts of interesting process design work that could be done to explore what the most efficient mixture of Strontium to Carbon would be: how the particles should be sized and dispersed, what geometry is most effective yadda yadda, but none of you came here to read a Masters degree thesis so I will attempt to summarize it now.

~Two Days Later~

Okay it’s been two days since I wrote that last paragraph because I fell into a math hole trying to optimize this energy crystal and let me just say, hoo-boy the theoretical limits on it are actually pretty ridiculous. We’re talking up to 7 kW of energy split between heat and electricity from a cube that is 10 cm on a side and glowing blue… (If you are interested in the math let me know and we can get in touch. FYI, it’s Super not practical, but you can think of it as every single strontium atom wearing a little tetrahedral party hat made of 5 carbon atoms)

Conclusions

I know this all seems like a ridiculous flight of fancy, but it is an important point. Nuclear materials are a poorly utilized class of materials due to the general misunderstandings of radiation. It’s not something to be afraid of for no other reason than it is a nuclear material. We have literal tonnes of materials like this sitting in dry cask storage all over the world that might have unexplored applications just as useful as this, but we don’t know because peoples’ fears have kept them locked away.