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Our Friend Gadolinium

Brian Wang directs our attention to one important part of Rob Freitas' radionuclide page:

The mass of the alpha-particle is ~7000 times greater than that of an electron, so the velocity and hence the range of a-particles in matter is considerably less than for beta-particles of equal energy. Consequently the optimum radionuclide for medical nanorobots is predominantly an alpha emitter.

Among all gamma-free alpha-only emitters with t1/2 > 106 sec, the highest volumetric power density is available using Gd148 (gadolinium) which a-decays directly to Sm144 (samarium), a stable rare-earth isotope. A solid sphere of pure Gd148 (~7900 kg/m3) of radius r = 95 microns surrounded by a 5-micron thick platinum shield (total device radius R = 100 microns) and a thin polished silver coating of emissivity er = 0.02 suspended in vacuo would initially maintain a constant temperature T2 (far from a surface held at T1 = 310 K)

75-year half-life, initially generating 17 microwatts of thermal power which can be converted to 8 microwatts of mechanical power by a Stirling engine operating at ~50% efficiency. (Smaller spheres of Gd148 run cooler.) While probably too large for most individual nanorobot designs, such spheres could be an ideal long-term energy source for a swallowable or implantable "power pill" (Chapter 26) or dedicated energy organ (Section 6.4.4). A ~0.2 kg block of pure Gd148 (~1 inch3) initially yields ~120 watts, sufficient in theory to meet the complete basal power needs of an entire human body for ~1 century (given suitable nucleochemical energy conversion and load buffering mechanisms, and a sufficiently well-divided structure).

The last part is the punchline, of course. Freitas acknowledges future design challenges such as energy conversion, load buffering, and division of structure. If these challenges are overcome, a large block of Gd148 (or simply gadolinite ready to be processed into pure gadolinium) could supply nutrition to millions of people for millennia. Gadolinium has a half-life of 75 years, so you'd need double as much for each 75-year period you wish to avoiding refueling for, but storing gadolinium in its stable gadolinite form seems avoid this problem. Unfortunately, gadolinite is fairly rare and gadolinium itself is only found in the Earth's crust at a 6.2 ppm level. By comparison, the abundance of gold in the Earth's crust is only 0.0011 ppm. According to this page, annual production of gadolinium is 200 tons.

Just to throw some numbers out there, if one cubic inch is enough per person per century, a million people would require a million cubic inches. That can fit in a cube 9 x 9 x 9 ft large. According to Freitas' numbers, this would weigh about 200,000 kg, or 200 metric tonnes, which is on par with today's annual production. If demand for gadolinium grew, it seems plausible that its cost would fall greatly -- after all, gold is about 6,000 times rarer and our annual production is 2,800 tons. Feeding ten billion people with gadolinium, if that were possible, would require about 2,000,000 metric tonnes for the first century. At an extraction rate of 200,000 metric tonnes per year, it could be done in a decade. This would require increasing current production by a factor of 1,000. According to this book, gadolinite can contain 40% rare earth oxides, 5% of which consists of gadolinium itself. That means that gadolinium makes up about 2% of the total. (Wrong: see comments.) Processing ten million metric tonnes of the ore annually would yield the required amount. For comparison, we extract 1.2 billion tons of iron from the Earth's crust annually.

Update: all of the above is wrong for one reason or another, as pointed out in the comments, but at least I had fun. I was confusing chemical stability with nuclear stability and made the mistake that I thought gadolinium-148 would be nuclear-stable in its gadolinite form, which is wrong. The atomic number of gadolinium is 64 meaning that gadolinium-148 contains 20 extra neutrons above neutron-proton parity. It seems to me that we'd eventually have to find a less safe and cheaper isotope to make this work on a large level if it's suitable in practice and we ever want to.

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  1. From WP: “Gadolinium is never found in nature as the free element, but is contained in many rare minerals such as monazite and bastnäsite. It occurs only in trace amounts in the mineral gadolinite, which was also named after Johan Gadolin. The abundance in the earth crust is about 6.2 mg/kg.[2]”

    “Monazite sand deposits are inevitably of the monazite-(Ce) composition. Typically the lanthanides in such monazites contain about 45 – 48 % cerium, about 24% lanthanum, about 17% neodymium, about 5% praseodymium, and minor quantities of samarium, gadolinium, and yttrium.”

    On Bastnasite: “The composition of the lanthanides was about 49% cerium, 33% lanthanum, 12% neodymium, and 5% praseodymium, with some samarium and gadolinium.”

    The main economic issue would appear to be refining Gd, since it exists in such trace amounts. Uranium is much more abundant and more abundantly mined than Gd (“The worldwide production of uranium in 2006 amounted to 39 655 tonnes”), but “[i]n nature, uranium atoms exist as uranium-238 (99.284%), uranium-235 (0.711%), and a very small amount of uranium-234 (0.0058%),” and 235-U is what it needs to be purified down to. That would be the expensive and difficult part. Gold is cheaper and easier to refine, even though we only mine 2800 tons (compared to 40,000 tons of uranium) because it’s much more pure when it comes out of the ground.

    Michael says: “If demand for gadolinium grew, it seems plausible that its cost would fall greatly”

    Not sure what economics you’re using there.

  2. MZ, ceteris paribus, increased demand leads to increased price. Importantly, increased demand does not necessarily lead to increased cost. Economies of scale and technological innovation (due to industry growth) can mitigate cost and counteract the price increase. However, there’s the supply problem too! If there isn’t much gadolinium or it becomes increasingly hard to obtain, price will increase.

    Anyway, this is all very strange for other reasons. First, this idea does not eliminate eating, because nutrition is still necessary. Second, to do this for one person is very expensive, even for a futuristic idea. Using Michael’s numbers, it’d have cost the entire world GDP in 2006 to obtain the gadolinium for one person. That’s not including the as yet unknown costs of the nanorobots, the surgery, etc… Furthermore, not only must total cost be considered but also relative cost- that is how this procedure compares to simply eating and paying for groceries. New futurist technologies are likely to make food cheaper at a fast rate too, so the “future technologies will make this cheaper” wildcard does not automatically help. It’s hard to say when or if this procedure would be competitive, even were it not so costly. From my standpoint, there’s too many variables.

    At any rate, this is highly speculative but very interesting.

  3. Michael, this is all very interesting, but the gadolinium one mines from the ground doesn’t contain any of the nuclide Ga148 at all (for the obvious reason that it is radioactive with a rather short half-life). I believe that you make Ga148 by spallation, by hitting a tungsten block with a proton beam from an accelerator (such as the advanced neutron source at Oak Ridge). I doubt if you could make more than a few grams a year, even if you did nothing else with your accelerator.

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