Tangible Nanomoney

by Robert A. Freitas Jr.

Research Scientist
Zyvex Corp. 1321 North Plano Road. Richardson, TX 75081
Copyright 2000 Robert A. Freitas Jr. All Rights Reserved.
This paper was written in December 1999 and was originally published in the July 2000 issue of Nanotechnology Industries Newsletter. The correct literature citation and URL for this document are:

Robert A. Freitas Jr., "Tangible Nanomoney," Nanotechnology Industries Newsletter, Issue II, July 2000, pp. 2-11.

http://www.rfreitas.com/Nano/TangibleNanomoney.htm http://www.zyvex.com/Publications/papers/nanomoney (alternate)


Robert Freitas, author of the recently-published groundbreaking technical book Nanomedicine, reflects on how we might pay for very advanced medicine -- or indeed, pay for anything at all -- in a world where artificial molecular machine systems are commonplace. Hint: Perhaps we'll be using coins made of tantalum or ununquadium!

I'm sometimes asked how we're going to pay for nanomedicine [1], once medical nanorobotic treatments become available. Surely all this advanced technology will be so expensive that only the rich will be able to afford it? I usually reply that it is a rational and defensible expectation that nanomedicine may actually cost far less, per treatment, than today's traditional medical interventions. But these questions about costs have gotten me thinking. How will we pay for anything in a future world of ubiquitous artificial molecular machine systems?

I won't try to pass judgment on whether electronic money or some other intangible form of currency might be sufficient for all necessary economic purposes. I'll simply note that tangible money has always played a role in human commerce, so for now the safest assumption is that tangibles will probably continue to do so, though perhaps with somewhat lesser importance in the overall economy.

What Is Money?

Assuming some form of physical specie will still be useful in a nanotechnology-rich society, what form should it take? We recognize that money generally serves two well-known primary functions: A store of value, and a medium of transaction. As a result, we can postulate that in the ideal form:
  1. Money should be an efficient store of value, having high value per unit volume or per unit mass.
  2. Money should be available in small enough physical sizes to be readily portable, even in the largest denominations, by human users, thus facilitating exchange transactions and specie warehousing.
  3. Money should be physically stable for a duration of time spanning at least the maximum intended period of transactions and/or the maximum value storage horizon.
  4. Money should not be inherently physically dangerous to its owner (e.g. radioactive, poisonous, explosive, etc.).
But money must also be trustworthy, which has several additional implications:
  1. Money should be difficult to counterfeit.
  2. Money should be difficult or impossible to replicate at a cost less than its cost of manufacture even by the most efficient means possible. That is, production costs (aka "intrinsic value") should approximate face value; seigniorage should be minimal to nil.
  3. Money should be immediately recognizable as the intended denomination of the intended specie. Once revealed, the intrinsic value of the specie should be difficult to disguise. If unrevealed, the specie should still be compact enough to hide (from thieves or tax authorities) on one's person or elsewhere; see (2) above.
  4. Money should be self-validating by its own physical form, and not rely upon any legalistic governmental imprimatur, easily-altered surface stamping, or monopoly minting authority to partake of value (e.g., no "fiat" specie).
In a nanotechnology-intensive world, any form of physical currency whose value depends solely upon the physical arrangement of common atoms must likely fail one or more of the above criteria. For example, today's paper money and base-metal coins are easily counterfeited. A perfect replica hundred-dollar bill of mass ~1 gram can be manufactured by Drexler's ~1 kg desktop manufacturing appliance [2] at the rate of one banknote per second, an output providing the operator with an income of $360,000 per hour. It may take 30 years to catch up to deci-trillionaire Bill Gates, but then again, the counterfeiter can always buy more manufacturing appliances. The desktop machine can also produce 5 carats/sec of already-cut investment-grade diamonds, reproducing the entire 1995 world demand for polished stone (19 million carats [3]) in 44 days. Goodbye, DeBeers. Another expensive substance that can probably be cheaply replicated is the relatively simple mixture of minerals and molecules comprising moondust, a material which nonetheless in 1999 cost $3 million/gram on the rare occasions it has gone on sale [4].

The same objection applies to any specimen of complexly structured ordinary matter, such as sculpted gemstones [5] or other 3-dimensional art pieces constructed with nanoscale features, or atomically-encoded data storage blocks. With a mature nanotechnology, many if not most physically stable 3-D atomic structures should become accessible to cheap fabrication, and pure information has different values in different contexts. If we someday conceive of exotic molecular structures that cannot be manufactured by any known molecular assembler technology, then by definition these structures also cannot be manufactured by biological or other natural (e.g. geological) self-assembly processes -- as these processes may be regarded as subsets of the nanotechnology toolchest. Hence such exotic structures would not exist in nature and are impossible to fabricate as specie, and so cannot be used as money.

Gold

Coins made of gold, the rarest of the traditional precious metals in the Earth's crust, are a step in the right direction because gold atoms are inherently somewhat scarce (Table 1). This scarcity may hold true even in a world of abundant nanotechnology. Consider: One of every 3 billion atoms in ordinary crustal rock is a gold atom, or 3.1 ppb (parts-per-billion) by weight. All natural gold atoms are of one isotope, Au197. A ~10 kg nanotech desktop refinery wholly dedicated to sorting gold atoms from crustal rock, perhaps employing ~1 kg of the input ordering and reagent preparation subsystems found in Drexler's original manufacturing appliance [2], could in theory sort ~1025 crustal atoms per second, extracting ~3 1015 gold atoms/sec or ~1 microgram/sec, which is a net output of about 1 troy ounce of gold per year. To achieve this paltry output, the desktop refinery must process 16,000 tons/yr of rock (~100 cm3/sec) and the unit draws about 1 megawatt of continuous power assuming a minimum waste heat generation of 3 106 joules per kilogram of input materials [2]. So you get about $300/yr worth of gold, but the energy costs you $900,000/yr at today's $0.10/Kw-hr electric rates. Cost breakeven occurs if the crustal rock can be ~3,000 preconcentrated in gold content, using bulk chemical processes, but this may be uneconomical and hardly seems worth the trouble.


Table 1. Precious Metal Abundances
(relative mass of atoms, in parts-per-billion or ppb) [12]
Source of Metal Abundance of Gold Abundance of Platinum Abundance of Silver
   (ppb)  (ppb)  (ppb)
Meteorite 170 1000 140
Human body
100
- -
Crustal rocks
       3.1
  37
  80
Sun
   1
   9
   1
Universe
      0.6
   5
      0.6
Seawater
        0.05
-
      0.1
River water
          0.002
-
      0.3


Even diverting the entire present-day human energy consumption of ~1013 watts, already approaching the hypsithermal limit for Earth [1], exclusively to nanotech gold extraction from crustal rock would produce only ~300 tons/yr of new gold. This won't seriously disrupt international gold prices, because world gold production already averages ~1500 tons/yr [6] using 5,000-10,000 ppb ores, and because a total of ~100,000 tons of gold has been extracted throughout history [7], most of it still extant, worth ~$1 trillion at today's prices.

Perhaps you are thinking that it might make more sense to do a little environmental remediation while reworking the mining industry tailings, which are typically ~1,000 ppb gold [6], and extracting all of the remaining precious metal. Working on the richer tailings rather than raw crustal rock, our nanotech desktop refinery could produce ~300 troy ounces of pure gold per year, worth $100,000/yr at current market prices. Unfortunately, the energy cost is still $900,000/yr at today's $0.10/Kw-hr electric rates. If future energy rates are a lot cheaper than today's rates, well and good. But note that only ~108 tons of new mine tailings are piled up annually, with each year's leavings containing ~100 tons of unextracted gold. Even if completely extracted, all of the gold in these tailings would still be far less than the total aboveground worldwide stockpile of the metal. What about seawater extraction [8]? Gold is ~100 times less plentiful in seawater than in the crust, though gross filtration and bulk preprocessing might improve throughput. Other potentially inflationary imports into the world economy from future extraterrestrial sources of monetary gold -- such as metal-rich asteroids -- may be largely offset by relatively high prospecting and shipping/insurance costs, and by a fast-growing economy able to fully absorb a rapidly expanding money supply.

The bottom line is that at ~$200/cm3, gold at least minimally satisfies our eight criteria for an ideal tangible nanomoney. Its rareness will not be decisively altered by nanotechnology. But the "precious yellow" owes its historical preeminence to the fact that gold is the most easily extractible inert rare element in the Earth's crust. In the nanotech era, other alternatives may exist.

Antimatter

In 1999, the rarest and most expensive nonradioactive material available on Earth was antimatter, which could be artificially created in the laboratory at a cost of $62.5 trillion/gram [9]. The cost is high because current production and storage methods are crude. Harold Gerrish at NASA/Marshall estimates that improvements in modern antiproton traps could bring the cost down to $5 billion/gm in a few years [9], and a new injector at Fermilab outside Chicago should allow that facility to increase its annual production tenfold to 15 nanograms/yr, up from 1.5 nanograms/yr today [9].

To be practical as currency, however, the antimatter would have to be passively stable, else it would be too dangerous for common use. (Antimatter in contact with ordinary matter, such as container walls or pants pockets, decomposes explosively into a shower of nuclear particles and high-energy photons.) Matter-friendly stabilized antimatter has been proposed theoretically [10], and it has been suggested [1] that a two-component hypergolic antimatter fuel could permit controlled energy recovery up to a theoretical maximum energy storage density of ~2 1021 J/m3. At today's $0.10/Kw-hr electric rates, this maximum energy density would correspond to a recoverable energy value of $56 million/cm3. However, stabilized antimatter remains a purely speculative possibility.

Ordinary Matter

If we restrict our analysis of tangible nanomoney to ordinary matter, then the question becomes: What is the rarest stable isotope that could possibly serve as monetary specie? To help answer this question, I compiled a list of all known stable isotopes ranked by measured natural abundance in Earth's crust. Table 2 gives all such isotopes present at less than 1 ppb, just below the crustal abundance for gold, along with their abundance relative to the total for that element, in parentheses, and the current market price. The values for gold, platinum, silver, and diamonds are listed for comparison.


Table 2. The Rarest Natural Isotopes and Their Current Prices [11-13]
Element  Relative Isotopic
Abundance
Terrestrial Crustal
Rock Abundance
Actual or Estimated
Current Prices
Notes
Tc97 (Note 1) - ~0 $30,000,000,000/gm (est.)
Tc98 (Note 2) - ~0 $30,000,000,000/gm (est.)
He3 (0.000137%) 0.000007535 $637.31/gm  
Xe126 (0.090%) 0.000018  $28,948.49/gm  
Xe124 (0.096%) 0.0000192  $15,483.24/gm  
Os184 (0.018%) 0.000324  $30,000,000/gm (est.)
Xe128 (1.92%) 0.000384  $7,000/gm (est.)
Kr78 (0.35%) 0.000525  $6,923.26/gm  
Xe130 (4.08%) 0.000816  $3,900/gm (est.)
Te120 (0.089%) 0.00089  $1,400,000/gm (est.)
Xe136 (8.87%) 0.001774  $2,156.21/gm  
Xe134 (10.44%) 0.002088  $2,389.46/gm (Note 3)
Kr80 (2.28%) 0.00342  $5,791.52/gm  
Xe131 (21.18%) 0.004236  $1,658.94/gm  
Pt190 (0.0127%) 0.00470  $1,347,960/gm (Note 4)
Xe129 (26.44%) 0.005288  $691.31/gm  
Xe132 (26.89%) 0.005378  $700/gm (est.)
Te123 (0.89%) 0.0089  $140,000/gm (est.)
Kr83 (11.49%) 0.017235  $2,600/gm (est.)
Kr82 (11.58%) 0.01737  $2,580.90/gm  
Ru98 (1.87%) 0.0187  $323,040/gm  
Te122 (2.55%) 0.0255  $76,850/gm  
Kr86 (17.30%) 0.02595  $196.51/gm  
Os186 (1.59%) 0.02862  $600,500/gm (Note 5)
Os187 (1.96%) 0.03528  $159,060/gm (Note 6)
Te124 (4.74%) 0.0474  $29,230/gm  
Ru96 (5.54%) 0.0554  $100,000/gm (est.)
Pd102 (1.02%) 0.06426  $893,800/gm (Note 7)
Te125 (7.07%) 0.0707  $16,040/gm  
Kr84 (57.00%) 0.0855  $338.33/gm  
Hg196 (0.146%) 0.09782  $3,141,500/gm (Note 8)
Ru100 (12.60%) 0.1260  $43,170/gm  
Ru99 (12.76%) 0.1276  $39,040/gm  
Ir191 (37.3%) 0.1492  $12,070/gm  
Ru101 (17.06) 0.1706  $35,050/gm  
Ru104 (18.62%) 0.1862  $27,300/gm  
Te126 (18.84%) 0.1884  $8,950/gm  
Ta180m (0.0123%) 0.2091  $17,095,890/gm (Note 9)
U234 (0.0057%) 0.228  $61,800/gm (Note 10)
Os188 (13.24%) 0.23832  $31,200/gm
 
Ir193 (62.7%) 0.2508  $6,070/gm
 
Pt192 (0.782%) 0.28934  $139,600/gm (Note 11)
Os189 (16.15%) 0.2907  $25,260/gm  
Ru102 (31.55%) 0.3155  $20,410/gm  
Te128 (31.74%) 0.3174  $4,340/gm  
Te130 (34.08%) 0.3408  $4,490/gm  
Se74 (0.89%) 0.445  $761,190/gm (Note 12)
Os190 (26.26%) 0.47268  $13,720/gm  
Rh103 (100%) 0.70  $29/gm  
Pd104 (11.14%) 0.70182  $63,800/gm  
Os192 (40.78%) 0.73404  $10,400/gm  
Pd110 (11.72%) 0.73836  $67,090/gm  
Re185 (37.40%) 0.9724  $9,400/gm  
Ag (nat. isot. mix) 80  $0.20/gm  
Au   3.1  $10/gm  
Pt (nat. isot. mix) 37  $12/gm  
Diamond (natural) - $28,000/gm (Note 13)

NOTES:
    1. moderately radioactive, decays by gamma emission and electron capture to Mo97, t1/2 = 2.6 106 yr;
    2. moderately radioactive, decays by gamma and beta emission to Ru98, t1/2 = 4.2 106 yr;
    3. only 51% enrichment;
    4. only 4.19% enrichment of this slightly radioactive alpha emitter, t1/2 = 7 1011 yr;
    5. only 79.48% enrichment;
    6. only 70.43% enrichment;
    7. only 78.18% enrichment;
    8. only 31%-48% enrichment;
    9. only 5.70% enrichment, as oxide;
    10. moderately radioactive alpha emitter, t1/2 = 2.48 105 yr;
    11. only 41.63% enrichment of this slightly radioactive alpha emitter, t1/2 ~ 1015 yr;
    12. 77.71% enrichment;
    13. investment grade D flawless, cut gemstones, 1-carat size (1997 JCK market quotes).




     

Technetium

Technetium (Tc) is present in the Earth's crust only as minute traces from the spontaneous fission of natural uranium; the short half-life precludes primordial technetium on Earth. The element is also observed in the stellar atmospheres of S-, M-, and N-type stars. Tc is artificially created on Earth by bombarding molybdenum or rhodium targets with protons or deuterium nuclei, producing some isotopes at a cost of ~$30 billion/gm [14] (~$350 billion/cm3). Alternatively, technetium-99 is a fission byproduct of nuclear reactors and is harvested by the nuclear fuel reprocessing industry, a vastly cheaper source which allows kilogram-quantity production of Tc99 at a cost of ~$100/gm [15]. Technetium is a silvery grey metal that tarnishes slowly in moist air, density 11.5 gm/cm3, melting point 2157C. It would require airtight encapsulation in a shell of chemically inert metal such as gold or platinum. But its use in specie is unlikely because the metal is moderately radioactive. For example, even with a 2.6 million-year half-life, Tc97 emits ~30 microwatts/cm3 of decay energy or ~600 million Bq/cm3 (~0.3 rad/sec), compared to a background count of ~7000 Bq [16] for the natural human body.

Helium and Xenon

The rarest nonradioactive isotopes found naturally on Earth are the three gaseous isotopes He3 (1 atom per 24 trillion atoms in Earth's crust), Xe126 (1 atom per 370 trillion crust atoms), and Xe124 (~1 atom per 350 trillion crust atoms), all available commercially [17]. The precious metal atoms gold, silver, and platinum are about 10 million times more abundant.

Noble gas atoms may be encapsulated in fullerene cages such as C60 [18, 19]. One present-day encapsulation technique involves heating bulk fullerenes to 650C at 3000 atm gas pressure, a procedure which entrains 1 of every 1000 fullerene molecules with a single noble gas atom [19]. With proper chemical treatment, a C60 molecule can also have a stable orifice of fixed diameter opened up in its side, only allowing atoms smaller than a certain size to enter [90, 91]; radioactive holmium atoms trapped in C82 cages are already used in biodistribution experiments [92]. If we can find a low-cost method of purifying the gas-entrained cage molecules, or can devise a more efficient production method that achieves closer to ~100% entrainment, then closely-packed roughly spherical C60 molecules each of volume ~0.70 nm3 with a volumetric packing factor of 68% would allow ~0.95 1021 noble gas atoms/cm3 to be stably stored, equivalent to a net storage pressure of 30-40 atm. This gives an effective storage density of 0.005 gm/cm3 for He3 (specie value $3/cm3 [20]) but 0.20 gm/cm3 for Xe126 (specie value $5,800/cm3 [21]). Although very rare, He3 is paradoxically a relatively cheap isotope because of the vast supply of helium produced by the petroleum industry -- gas-well helium averages 1.5 10-5 % He3 [22].

If we could raise the storage pressure to 1000 atm (12.3 1021 He3 atoms/cm3 or 9.48 1021 Xe atoms/cm3) and pack these gas atoms into sturdy single-walled carbon nanotubes (SWCTs), then storage density rises to ~0.061 gm/cm3 for He3 (specie value $39/cm3) and ~2.0 gm/cm3 for Xe126 (specie value $58,000/cm3). Note that the Van der Waals gas equation governs at such high pressures [1], not the ideal gas law, so still greater compression permits little improvement in packing density.

For comparison, the volumetric values of more traditional specie are $2/cm3 for silver, $200/cm3 for gold, $260/cm3 for platinum, and $100,000/cm3 for late-20th-century investment-grade diamonds.

NMR (nuclear magnetic resonance) could be used to noninvasively measure the quantity of fullerene-entrained He3 present inside the cladding because He3 is an excellent spin-1/2 NMR nucleus with a high gyromagnetic ratio [19] at a resonance frequency of ~7618 MHz. Xe129 (spin 1/2, ~2781 MHz) and Xe131 (spin 3/2, ~824 MHz) are also known to be NMR active [12]. Gold cladding would be NMR active at ~175 MHz (Au197, nuclear spin 3/2), the only natural isotope [12]. The most abundant platinum isotope (Pt195, 33.832%) is also NMR active with a nuclear spin of 1/2 and a resonance at ~2141 MHz, but the other two most common natural platinum isotopes (Pt194 at 32.967% and Pt196 at 25.242%) would provide a completely NMR-inactive cladding [12]. Diamond cladding with pure C12 crystal would also be NMR-inactive, but may be too brittle for practical use in circulating coinage.

Helium is not known to form covalent compounds, but by 1999 ~80 covalent compounds had been produced with xenon bonded to fluorine and oxygen [23], one of which possibly might provide a slightly higher effective storage density of rare-isotope atoms than the compressed gas. Unfortunately, xenon compounds tend to be highly toxic because of their strong oxidizing character [23], hence represent a health threat to users in the event of breach of the cladding material. Pure He and Xe are biologically harmless in trace quantities, though in larger quantities xenon gas has been used as an experimental surgical anesthetic in humans for several decades [11, 24].

Osmium

The rarest and possibly most expensive nonradioactive isotope found naturally on Earth that is a solid at normal room temperature and pressure is an isotope of osmium, Os184. Osmium [25] is a lustrous bluish white metal that is extremely hard. After iridium, it is the densest known element (22.61 gm/cm3) and has the highest melting point (3033C) of the platinum group metals. Solid metal won't tarnish in air, but finely powdered or spongy metal slowly oxidizes, giving off caustic osmium tetroxide. OsO4 is highly toxic and is a powerful oxidizing agent with a low vapor pressure (e.g. boiling point is 130C at 1 atm) -- air concentrations as low as 100 nanograms/m3 can cause lung congestion, skin or eye damage [25]. Since the tetroxide has a strong odor, osmium particles that oxidized and volatized after being exposed to ambient air following a breach of the inert cladding would be immediately detectable. Still, the potential for toxicity is a distinct drawback to its use in nanospecie.

Os184 is so rare that its price is not conveniently available, but a linear extrapolation of a log-log plot of price vs. abundance for six other natural osmium isotopes whose prices are readily available (ranging from $10,400/gm for Os192 up to $600,500/gm for Os186 [26] would imply a price for Os184 (~100 times rarer than Os186) of ~$30 million/gm, or ~$700 million/cm3. Natural mixed-isotope osmium is several times rarer than gold in Earth's crust, so a nanotech desktop refinery won't make this metal cheap.

Tantalum

Another candidate for the most expensive nonradioactive solid natural isotope -- and perhaps the ideal candidate for tangible nanomoney -- is an isotope of tantalum, Ta180m. After He3 and Ca46, Ta180m is the third rarest naturally occurring stable isotope on Earth on a relative abundance basis. First discovered in 1954 [27], tantalum-180m has long been believed to be so rare because it is largely bypassed in the two processes that produced most of the heavy elements found in the ground here on Earth -- (1) the s-process (slow neutron capture during stellar helium burning) and (2) the r-process (rapid neutron capture during supernova explosions) [27-30]. Apparently in 1999, the entire world's supply of Ta180m was only 6.7 milligrams [30].

Interestingly, the naturally-occurring isotope is not in the ground state but is a nuclear isomer at an excitation energy of 73 KeV with a spin parity of Jp = 9- [28]. In the ground state, Ta180 decays in 8.15 hours by electron-capture (EC) to Hf180 and by beta-decay to W180. It was originally predicted that Ta180m would exhibit similar decay routes, but the most recent experimental search [28] has found no evidence of radioactive decay products distinguishable from background levels, establishing a lower limit on the Ta180m half-life of > 3.0 1015 yr for EC and > 1.9 1015 yr for beta-decay and raising the possibility that these atoms are completely stable.

Tantalum is a hard, greyish-silver, heavy (16.6 gm/cm3) metal that can be drawn into a very fine wire (high ductility), and has a high melting point (3017C) exceeded only by osmium, rhenium, and tungsten. The metal is completely immune to chemical attack at temperatures below 150C and above this temperature is attacked only by hydrofluoric acid, acidic solutions containing the fluoride ion, and free sulfur trioxide, and only very slowly by alkalis. Coins minted of pure Ta180m extracted using current bulk separation methods would have a value of at least $284 million/cm3, or even more because the value given in Table 2 is for 5.7%-enriched metal only. Natural tantalum metal and its stable pentoxide are biologically inert [31-34], so the metal is widely used in medical implants such as sutures, cranial repair plates, and other prostheses. But Ta180m coins might still be cladded with gold or platinum to forestall a decline in their value due to wear abrasion. Coin purity can be determined by bremsstrahlung irradiation photoactivation analysis [30] or by other means; a cheap cladding made of Ta181, the most abundant natural isotope, would be NMR-active (spin 7/2, ~1199 MHz).

Couldn't we just buy some natural bulk pure tantalum (mostly Ta181), currently costing $1.20/gm [89], then use nanotech concentrators to perform an isotopic separation to extract the 1 atom in every 81,300 that is a Ta180m atom? We could indeed! Neglecting chemical pre- and post-processing expenses, a 0.02 M aqueous solution of TaF5 fed into a 32-stage teragravity nanocentrifuge cascade [1] could have its Ta180m content enriched from 0.0123% to 5.7% for an energy cost of ~$1,000/gm ($16,600/cm3), assuming $0.10/Kw-hr.

But keep in mind that today's relatively cheap natural tantalum is derived from concentrated tantalite ores, not from random crustal rocks. The total quantity of Ta180m available in the entire 1996 world reserve base of tantalum (including all known economic, marginal, and even subeconomic reserves still in the ground) was a mere 4,200 kg [93]. At $1,000/gm, our 4,200 kg of metal is only worth $4.2 billion -- a spit in the bucket against today's $20 trillion world money supply. Once the whole 4,200 kg has been extracted and there is still demand, the metal price must rise sharply or else new (but presumably poorer, harder to find) ore deposits must be discovered. How high could the price go? Who knows? But we do know that the world reserve base for gold in 1996 was 61,000,000 kg [93], and at ~$350/oz the market was valuing this reserve base of monetary metal at ~$0.7 trillion. If the world reserve base of Ta180m is assigned gold's monetary function and is similarly valued at $0.7 trillion, and if vast new tantalum ore deposits prove difficult to find, then the price of Ta180m could rise to ~$170,000/gm ($2.8 million/cm3). Note also that tantalum is more than 1000 times rarer than gold, in seawater [12].

Ta181 would be a convenient "base" substance with which to dilute the Ta180m down to minute concentrations, in order to make lower-denomination coins. Nanotech coin-verifying machines could quickly clean and map the worn, scratched exterior surface of a specimen coin to atomic resolution, then weigh the specimen coin to single-proton mass accuracy [1], allowing the computation of the precise number of Ta180m atoms present within the cladding on the assumption that Ta180m is the only impurity in the Ta181 base metal. In theory, a more detailed assay could be done, with the coin completely deconstructed, counted and verified atom by atom, then reconstructed back into the original form in a few minutes, perhaps using a verification machine similar in size and speed to the desktop manufacturing appliance mentioned earlier.

Can we breed new Ta180m atoms more cheaply by artificial means, avoiding the costly enrichment process from limited and dilute natural sources? Maybe, maybe not. Five nucleosynthetic techniques have been proposed for making Ta180m [29, 30]. Two seem to require Type II supernova conditions, and another is now believed not to work. The other two methods involve a rare s-process neutron capture synthesis. One of these is at most ~0.01% efficient [29]. The other method requires nuclear precursors to be held near 300,000,000 degrees K to induce transformation, but at this temperature the normally stable Ta180m has a half-life of only 130,000 sec [30]. Additionally, the high-nuclear-energy Ta180m isomer thus produced then decays into the stable Ta180m isomer with only 3.8% probability, so this method also appears very inefficient. A 0.01% production efficiency, requiring ~10,000 26-KeV neutrons per atom of Ta180m synthesized, would imply a minimum energy cost of $40,000/gm (~$600,000/cm3) to manufacture stable Ta180m, assuming the current $0.10/Kw-hr electric rate. The apparent difficulty of making this isotope may be a fundamental physical limitation which the future advent of nanotechnology is not likely to substantially alter.

Superheavy Elements

One drawback to any natural material is that a plentiful natural source might conceivably be found someday, devaluing the currency and triggering rampant inflation. Ideally, we'd prefer a substance for which no natural sources are available or likely, and which is intrinsically very difficult to produce artificially. This leads us to the superheavy elements or SHEs [70-74].

The number of elements is limited because nuclei become increasingly unstable against spontaneous fission and alpha-decay as proton number increases. For example, between thorium and the heavy fermium isotopes, the spontaneous fission half-life plunges by 30 orders of magnitude [76]. But in 1948, Goeppert-Mayer [35] pointed out that nuclear shell closure effects would substantially increase nuclear stability, and Wheeler [36] in 1955 and Scharff-Goldhaber in 1957 [37] postulated the existence of transactinide elements with atomic numbers above 103, the SHEs. By equating Coulombic and surface energy of the nucleus, Huizenga [38] had argued that the maximum number of chemical elements should be ~125, but in 1990 Seaborg estimated that more than 500 undiscovered transuranic isotopes might exist [73], and in 1996 Seaborg reproduced a "Futuristic Periodic Table" with atomic numbers running as high as hypothetical element 168 [39] similar to other hypothetical tables published decades earlier [40, 62]. There have been speculations on the possible chemical properties of elements with atomic numbers up to 184 [61, 64] and on the nuclear stability of elements with atomic numbers up to 274 [41].

Starting in the 1960s and 1970s, theoretical research on the SHEs largely centered on a hypothesized nuclear "island of stability" centered on element 114298 [42-48], with half-life predictions ranging from a few months [49] for 114310, 5 years [74] for 118302, 1000 years [41] for 112296, and 1079 years [74] for 116300, up to as high as 0.1 million years [41, 50], 20 million years [51], 1 billion years [41], or 2.5 billion years [52] for 110294. The stabilization near 114298 is due to the complete filling of nuclear proton and neutron shells, analogous to the complete filling of electronic shells in the noble gases in chemistry. Another "island of stability" was predicted to exist around element 164472 by Sobiczewski et al [53], with half-lives ranging from 105-107 years. Taking spontaneous fission, alpha and beta decay, proton emission and electron-capture decay modes simultaneously into account, others have estimated more pessimistic half-lives [74-78]. On the other hand, if certain unconventional assumptions are made about nuclear shapes and deformations [54], some elements with atomic numbers above 134 might be stable.

The possibility of very long-lived SHEs triggered a major hunt for these atoms in nature. Searches of various ores and minerals, meteorites and hot brines, leaded glass, cosmic rays, and even lunar samples for evidence of SHEs came up empty [45, 74]. Flerov and Ter-Akopian [45] report negative detection limits as low as 10-14 - 10-17 gm/gm. Thus any natural SHEs that might be present must be 1-1000 times rarer than He3 atoms and 0.01-10 million times rarer than Ta180m atoms. Current thinking is that it is unlikely that the r-process (rapid neutron capture in supernovae, >~1027 neutrons/cm2-sec for 1-100 sec [55]) of heavy element nucleosynthesis will lead to the production of SHE nuclei [56, 73]. (Nuclear explosions typically produce neutron fluxes of >~1031 neutrons/cm2-sec for ~10-6 sec [55, 57]; light-water nuclear reactors generate 2-5 1015 neutrons/cm2-sec for > 107 sec [73].) However unlikely, the possible existence of SHEs in nature cannot yet be positively excluded [58]. For instance, a black hole/neutron star binary system might provide an appropriate mechanism [59].

The chemical nature of hypothetical SHEs has been extensively investigated [60-70] although the theory is complicated by the need to include relativistic effects [70] -- e.g., for atomic numbers greater than 90, orbital electron velocities exceed 50% of the speed of light [73]. Pitzer [63] concluded that elements 112 ("eka-mercury") and 114 ("eka-lead") might be slightly metallic gases or volatile liquids near room temperature, and element 118 ("eka-radon") should also be a gas or volatile liquid. Fricke [64] agreed that element 112 should be "a distinctly noble metal" in macroscopic quantities with a density of 16.8 gm/cm3, but "the interatomic attraction in the metallic state will be small, possibly leading to high volatility as in the noble gases." Hulet [79] predicted that element 112 will boil at or below room temperature. Keller et al [60] estimated a melting point for element 113 ("eka-thallium") of 430C and a density of 16 gm/cm3. For element 114, Keller et al [60] estimated a melting point of 67C, a boiling point of 147C, and a density of 14 gm/cm3. Element 114 is likely to be very chemically inert [64, 69]. (Note again that gaseous or liquid atoms can be entrained in fullerene cages, and thereby embodied in useful specie.) Fricke [64] estimated a density of 13.5 gm/cm3 and a melting point of 400C for element 115. Stable element 164, if it exists, might have the highest density of any element, ~46 gm/cm3 [64].

During the 1970s and 1980s, SHE element 106 was produced from O18 + Cf249 with a cross section of 0.3 nanobarns [81] and element 108 was made from the Fe58 + Pb208 reaction at 0.02 nanobarns [82]. In the 1990s, efforts to create SHEs met with increasing success. For example, by 1999 four isotopes of the famed element 114 (eka-lead or "ununquadium" (symbol "UUQ"), the provisional IUPAC designation) had been created artificially [83-86], including 114285 (t1/2 = 0.6 millisec), 114287 (t1/2 ~ 5 sec), 114288 (t1/2 < 0.03 sec), and 114289 (t1/2 = 30.4 sec). In Oganessian's group [85], 114289 was produced by bombarding a Pu244 target with a 236-MeV Ca48 beam of intensity 4 1012 ions/sec, making just one atom of the SHE with a cross-section of ~1 picobarn -- out of 5.2 x 1018 incident calcium ions over a 34-day period, only one fusion event corresponded to a compound nucleus that survived to give a Z = 114 nucleus [48]. By late 1999, elements 110277, 112281, 116289, and 118293 had also been synthesized [84].

Even if stable, long-lived SHEs can be artificially manufactured, they are likely to remain extremely rare. There is a rapid decrease in the production cross section, with increasing nuclear charge, typically <~1 nanobarn for elements above 105 [79, 80]. For example, Wolf et al [87] predicted the peak cross-section for making element 106 from the Es253 + Xe136 deep inelastic transfer reaction to be 10 nanobarns, but only ~1 picobarn for producing element 110 and ~0.1 picobarn for making 114290 in the same reaction. Nitschke [88] estimated the cross-section to produce element 114 from the U238 + U238 reaction as ~0.1 nanobarns, and from a variety of other reactions as from 0.00002-20,000 picobarns. Production rates of SHEs are on the order 1 atom/hour or less [70] and Coulomb barrier energies are on the order of 200-300 MeV [79]. Seaborg and Loveland [73] note that the predicted cross-sections for heaviest element formation by heavy ion bombardment are less than 10-8 of the total reaction cross section, "corresponding to the production of less than 1 atom per day of irradiation" using incident beam particle fluxes of 1013-1015 ions/sec from modern accelerators.

We see that stable superheavy atoms could be perhaps a trillion times more costly to manufacture than artificial Ta180m, suggesting a very speculative value of ~$0.001/atom (~$2 1018/gm) using our customary electric rate assumptions. Even if the material was slightly radioactive, very few SHE atoms would be required to impart great value to the specie, substantially eliminating the radiation risk. For example, a coin with $1 million face value need contain only 109 SHE atoms worth $0.001/atom. Assuming a 106-year half life, there are only ~2 disintegrations per day, well below the background count from today's circulating base-metal coins (~3-30 counts/day, per gram). Our million-dollar coin would lose only ~$0.50/yr (~$500/millennium) of intrinsic value due to radioactive decay.

Aside from the radioactivity, any biotoxicity of SHEs is unlikely to be of much importance since the concentration of SHE would be so low and because the bulk of the coin would consist primarily of "cheap" bioinert material such as gold, platinum (failure strength ~100 times greater than gold), or diamond. Such coins, perhaps containing trace amounts of ununquadium or some other relatively stable SHE, might prove to be the ultimate tangible nanomoney.


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Original hypertext version of this document prepared by Robert J. Bradbury, February 2001.

Last updated by the author on 18 May 2003.