The Egg of the Phoenix: a computational time capsule


Could you build a portable computer that would still work if you buried it in the ground for a century?

The Legend

As retold in Sandman, the legend is as follows: There is a bird called the phoenix, which one day spontaneously bursts into flame. In the ashes left behind are two eggs, one dark and one light.

When the time comes, the light egg hatches into the new phoenix.

Nobody knows what comes from the dark egg.


photo by Moosa Khan, cc-by-nc

In the year 2150, long after the collapse of the globalized praxic [0] early-21st-century society into nuclear warfare in the wake of diminishing oil production, farmer Iangatu Awidum [1] is plowing his field, when his plow hits a smallish egg-shaped rock, about a kilogram. He digs it out, and discovers that it’s not actually a rock, but some kind of fascinating manufactured object from the praxic age.

Awidum takes it home at the end of the day, and discovers that it’s some kind of computing machine that still works, called the Egg of the Phoenix, left over from the praxic age. He has never seen a working computing machine before. It contains an immense archive of praxic knowledge, including, among other things, instructions for synthesis of antibiotics, and full instructions on how to build more such devices, starting from raw materials. Furthermore, it can be programmed to do computations for him, which turns out to be very useful; and it is in occasional communication with another similar device that has been discovered several thousand kilometers away, allowing him to converse with someone in another part of the world.

Awidum begins to share his knowledge, and life expectancies in his community begin to grow.


What would it take for this scenario to come to pass?

  1. A societal collapse between now and 2050, allowing enough time before Awidum’s birth for all the existing computers to break down.
  2. Biological human beings still existing in 2150.
  3. A computing machine that can survive in working condition for 100 years without maintenance or repair.
  4. A general lack of other working computing machines in the post-collapse age, so that none are left in 2150.
  5. A user interface sufficiently captivating and comprehensible that a normal biological human person would be likely to figure out how to program the machine to perform complex problem solving, without a community of practitioners to encourage and teach them.
  6. An immense archive of praxic knowledge organized to be useful without an industrial society.
  7. A post-praxic society that doesn’t burn people at the stake for knowing things. (Consider that the cover art from the Scorpions’ 1976 album “Virgin Killer” got the English Wikipedia blocked from the internet in England a couple of years ago, having been categorized as child pornography. So any large, moderately old archive of information is likely to contain Forbidden Knowledge, in any society.)
  8. Low-power long-range radio communication.
  9. Enough Eggs manufactured that a few of them survive.

Items #1, #2, #4, and #7 are so difficult to predict that I won’t discuss them further, except to point out that, objectively speaking, my scenario is pretty improbable.

I think item #5 is an unsolved problem at this point.

Item #6 is more or less Diderot’s project with the Encyclopédie, which has finally been more or less fulfilled, after centuries of false starts and disappointments, by the Wikipedia.

Most of the rest of this essay is devoted to #3 and #8, which are mere engineering problems, and #9, which is partly an engineering problem.

Possible bad outcomes

Even if my scenario above were to come to pass, it’s not entirely clear that it would be a good thing; I’ve been thinking about my doubts on this count for some time.

First, it seems clear from our experience that mathematical, praxic, and historical knowledge — all that could conceivably be conveyed by a book or an automatic computer — are not sufficient to make people happy. They empower human will, that is, they provide people with more power over their environment, which they can use to get things they want. However, the things people want don’t always make them happy, and often people use them to get more power over other people, which makes the other people unhappy. It’s far from clear that they make warfare less likely or less harmful. And so, although societies with more widespread knowledge of these kinds are generally somewhat happier and have lower peacetime homicide rates (in part because the structures of social control are much stronger), they have higher suicide rates, and they still make war.

Second, our hypothesis #1, a societal collapse into nuclear war between now and 2050, would provide some sort of strong evidence about human nature and praxic knowledge — greatly reducing the probability that we live in a universe where human nature is really benefited by knowledge.

That is, such a time capsule is inconsequential if modern liberal human society remains prosperous and relatively peaceful; but perhaps if liberal human society destroys itself, we should try a different approach rather than leaving Eggs around from which liberalism could be reincarnated after having failed catastrophically once.

Third, even if the knowledge is useful, getting it out of a book is not the same thing at all as discovering it, and a computer is barely better than a book. Europe suffered through centuries of argumentum-ad-authoritam epistemology, in which the primary means of discovering the truth was the interpretation of ancient texts. You can urge skepticism and empiricism all you want, but in the long run, if interpreting ancient texts works better, people will do that. So you could conceivably end up with a calcified world society that’s a sort of copy of the 21st-century world technically, but without any new discoveries being made.

In sum, instead of returning material prosperity to the world, Awidum might use his newfound knowledge to conquer and enslave first nearby villages, and then faraway nations, who would be unable to resist his autonomous drones and plastic explosives; Awidum might learn to refine methamphetamine from Ephedra and shoot up until he dies; Awidum might spend all his time masturbating to ancient pornography and playing Doom; Awidum might return material prosperity to the world, resulting in another nuclear war in 2167; the Egg of the Phoenix might be stolen by first one thief and then another, leaving a trail of death and betrayal in its wake like many famous diamonds; or the Egg of the Phoenix might become the new Aristotle or Ptolemy, the ancient deluded fool whose errors crippled the intellectual life of a civilization for a millennium.

Is this an Egg of light or of darkness? What can we expect to hatch from it?

I remain optimistic that access to knowledge and tools is a net benefit for humanity, even if it’s unequally distributed.

(It is interesting to note that, according to the Wikipedia, Diderot himself was skeptical about the value of technical progress.)

Still, XXX I’ll talk about ways to attempt to mitigate these two risks.

Phoenix Egg antecedents

Image 2010-11-16 by perhaps Michel Blom, no license provided

The idea of a "durable computer" is not new; the Zero-energy Device Challenge is one example:

designed and build by Michel Blom, who is fascinated by the challenge of gathering energy without generating chemical waste.

XXX more

Phoenix Egg design

The dimensions and shape of the Egg are the least essential to the scenario, but it’s useful to be concrete about them.

I said “a smallish egg-shaped rock, about a kilogram”. I’m thinking of a specific gravity of around 3 (thus a volume of about 300cc), and an aspect ratio of around 8, an oblate spheroid, about 36cm across and 4.5cm thick, with an area of about 1000 square centimeters on each side.

(I know eggs are usually prolate rather than oblate, but that’s okay with me.)

Given that, the remaining questions are: where does the Egg get the energy it needs to compute and communicate? XXX How does it store it until it needs to use it? How does it compute and store information? XXX How much power does it use? XXX How does it communicate with other Eggs? XXX How does it talk to people, and how do people talk to it? How is it protected from the hazards it must endure during the decades or centuries before it hatches, whether it’s being used by people or lying buried in a landfill during that time? XXX How little could it cost to produce, and what might induce people to buy it when it’s new, in order to be able to produce many of them?

XXX tin whiskers from solder

The following sections are about those questions.

Protecting the Egg of the Phoenix from hazards

Electronic circuitry is vulnerable to damage from a few major causes: impact and shock, crushing and grinding, chemical attack, high-voltage discharge, and electromagnetic pulses. (However, I consider nanotech attacks out of scope.) The Egg would need to be protected from each of these without entirely eliminating its ability to interact with the rest of the world.

Impact and shock can be largely mitigated by potting the Egg’s electronics, i.e. embedding them in a solid block. Epoxy resin is a traditional material for this, in part because it is opaque and very difficult to remove, and thus hinders competitors’ reverse-engineering efforts; however, it needs to be shielded from ultraviolet. Other possible materials include poly(methyl methacrylate), also known as Plexiglas or Lucite, and silicone rubber (long-chain polydimethylsiloxane), both of which have the advantage (from my perspective) that they are transparent. Silicone rubber additionally should do a much better job of protecting from shocks, and it is used for this currently.

(Transparency is a major advantage for solar-powered devices; flexibility is a major advantage for mechanical buttons.)

Potting also protects somewhat from chemical attack, the most common example of which is probably spilling a Coke in your keyboard, which will dissolve copper traces from the circuit board if left to dry. Internal-source chemical attack is also a problem, so the Egg must not include, for example, chemical batteries, which are unstable and tend to leak caustic chemicals. Epoxy is immune to almost all chemical attacks; PMMA is immune to fewer; silicone is vulnerable to many kinds of corrosion and can absorb many nonpolar liquids. In any case, it might be a good idea to include an additional layer of an even more inert substance, such as Teflon, Kynar, or Kapton, or to mix the potting compounds with mineral fillers to reduce chemical vulnerability further, such as mica, montmorillonite, or aluminum oxide; these fillers could also improve mechanical strength.

A PMMA manufacturer lists the following compounds that it’s vulnerable to: glacial acetic acid, acetone, aniline, benzene, butyl acetate, carbon tetrachloride, chloroform, diethyl ether, dimethyl formamide, dioctyl phthalate, ethyl acetate, 95% ethyl alcohol, ethylene dichloride, 25% hydrofluoric acid, lacquer thinner, 100% methanol, MEK, methylene chloride, concentrated nitric acid, 5% phenol solution, concentrated sulfuric acid, toluene, trichloroethylene, and xylene. It seems to be pretty sturdy against alkalis, salts, less concentrated acids (including hydrochloric), and oxidizing agents.

Potting also protects from crushing and grinding. Silicone, being soft, would help less with crushing and grinding, but it could be reinforced with an outer frame, for example of steel or PMMA. An aluminum oxide filler could also slow damage from grinding.

High-voltage discharge, such as electrostatic discharge, is a problem largely due to exposed electrical contacts being touched by electrically charged people. A device with no exposed electrical contacts, for example because it’s entirely covered with a thick layer of some nonconductive potting compound, will be well-protected from this hazard.

Electromagnetic pulses are perhaps the most difficult problem, particularly with the desire to include a long-range radio. A metal shell around the electronic parts, with only small holes penetrating it (e.g. for LEDs) would protect it, but would also make radio communication impossible. I think it might be possible to shunt an antenna with metal-oxide varistors to protect the rest of the circuitry, but I don’t really know.

So, roughly, you might have inner circuitry embedded in a donut of silicone, coated with a thin layer of Teflon, embedded in the middle of a rounded disc of Lucite with an invisible admixture of thinly flaked mica; a centimeter or so below both surfaces of the disc is a layer of solar panels, and a pocket of silicone with mechanical buttons underneath it, connected to the inner circuitry through wires. If you don’t worry about EMP, anyway.

A Phoenix’s Egg like that could be sunk to the bottom of the ocean, boiled in sulfuric acid, and run over by a series of trucks without suffering any real damage. It would probably continue to work if shot with buckshot or a machine gun and perhaps struck by lightning a few times, but it would suffer some damage.

The computing hardware of the Egg of the Phoenix

Solid-state semiconductor electronic integrated circuits are the only plausible current option for the computing hardware of the Egg. They’re very stable, as long as they aren’t overheated or directly subjected to high voltages, and they can carry out computation many orders of magnitude more efficiently than any other current option, as well as faster.

Crystalline silicon is an extremely stable substance. It’s very similar to diamond, and it forms a passivating layer of quartz on its surface when exposed to air, and an extra-thick layer of quartz is added during the normal manufacturing process for these chips. Silicon solar panels sitting out in direct sunlight have survived for several decades without losing much of their capacity. Silicon doesn’t melt until around 1900°C — much higher than the aluminum, copper, and gold used to interconnect parts of electronic circuits --- and chips will often continue to work after being inadvertently heated to red or even white heat and allowed to cool.

The aluminum, copper, and gold conductors also have extremely long lives.

Heating chips to high heat, even without melting them, can permit dopant migration, ruining them. I don’t think this effect is substantial at ordinary temperatures and current densities. (Sufficiently high current densities in semiconductors will damage them by nonthermal means.)

In short, the expected wear lifetime of silicon chips is actually many times longer than needed for an Egg.

To keep its power usage low, it’s probably good to include processors of different capacities and specializations: a small 8-bit processor for less demanding tasks (e.g. monitoring a keyboard, perhaps putting text onto a screen in response) and a higher-power 32-bit processor that’s rarely powered on, perhaps along with specialized chips for specific tasks like DSP and radio communication, which are kept powered off almost all the time.

An example “high-powered” chip might be the NXP (ex Philips) LPC1343, a 72MHz 32-bit ARM Cortex-M0 which costs about US$3.62, with 8KiB of RAM and 32KiB of program Flash.

The data storage hardware of the Egg of the Phoenix

Mask ROM is just as stable as any other silicon chip, but it’s an awfully expensive way to store massive amounts of data. In 2010, CMP (a multi-project wafer broker like MOSIS and Europractice) was charging €350 / mm² for 25 prototypes from one 0.35μm vendor, with a minimum of 3mm², €1050, which I estimate at around 600 000 transistors, or perhaps a few more diodes. So you get 25 copies of maybe one kilobit per Euro. This is not a desirable way to preserve a copy of Wikipedia.

The price per copy ought to go way down from there, though, to maybe a quarter of a Euro per chip (thus, four megabits per Euro). I think nonerasable, one-time-programmable (OTP) PROMs ought to be just as stable as mask ROMs, since you’re basically just electrically vaporizing some bits on an empty mask-ROM chip.

Mass-market PROMs are still being made, such as the Altera EPC1PC8, which is US$11 for a megabit, but I suspect they’re actually just EPROMs without a way to erase them. So unless you design your own chips and fab them through CMP or something, you might have to pay 1970s prices.

Re-recordable nonvolatile digital storage hardware, on the other hand, is flaky.

It looks like FeRAM is currently commercially available and relatively cheap but not popular enough for Digi-Key to keep in stock. Onlinecomponents claims to have stock and charges about US$30 per megabit. However, Fujitsu only claims 10-year data retention.

Flash memory supposedly has a retention lifetime of a century or so before the charge bleeds away from the floating gate, and supports being erased ten or a hundred thousand times. I don’t know if I believe it, though. Flash or FRAM might be acceptable for long-term storage if the Egg can keep some energy in reserve to rewrite its Flash every ten years or so, or its FRAM every year. XXX how much?

Unfortunately I think Flash may be the only current option. CD-R dyes tend to fade over time, oxide flakes off tapes and floppy disks, hard disks develop stiction and finally fail to start, and so on. I think magnetization domains themselves can be stable over a timescale of centuries, but perhaps that depends on the size of the bits, and anyway it hardly matters if none of the options available realize that potential. Perhaps magnetic bubble memories from the late 1970s could provide an option.


| nonvolatile memory type | unique per € | lifetime                        |
| CMP custom mask ROMs    | 1 kilobit?   | thousands or millions of years  |
| CMP custom PROMs        | 25 kilobits? | "                               |
| FeRAM                   | 40 kilobits  | “10 years”                      |
| mass-market PROMs       | 100 kilobits | thousands or millions of years? |
| Flash                   | 500 megabits | “100 years”                     |

There are other more speculative options.

If memristor memories, phase-change chalcogenide-glass RAM, or MRAM become available soon, perhaps they will have better stability characteristics than the existing erasable semiconductor memories. Phase-change RAM is supposed to retain its memory for 300 years.

If stability rather than speed is of the essence, you could perhaps use an inexpensive homebrew Atomic Force Microscope to scribe onto a glass slide. Ordinary glass, if not broken or exposed to abrasion, can hold its shape down to a wavelength of light or so at timescales of millennia, and has no crystalline structure to impose a minimum bit size; you ought to be able to record nanoscopic bits, if not erase them. I’m not sure how reliable these devices are or how large an area they can cover, i.e. what their storage capacity is. XXX

A Scanning Tunneling Microscope might be XXX easier to build, but only works on conductive substances, most of which are, unfortunately, crystalline. Metglas or other amorphous metals might be suitable. XXX

I’m skeptical that AFMs, STMs, or piezoresponse force microscopes have the long-term reliability under harsh circumstances needed for an Egg. XXX Could a single shock at an inopportune time permanently blunt their tip? XXX Do they depend on a sealed vacuum chamber that could be spoiled by outgassing? XXX Could ambient vibration at a resonant frequency scribble scratches all over their recording medium?

If you’re using AFMs or STMs to store data, you might be able to mass-produce things for them to read by means of the same casting process that the Grating Lab (XXX get URL) uses to produce laboratory-quality diffraction gratings.

The energy source of the Egg of the Phoenix

Where would the Egg get the energy to compute?

Solar panels

Crystalline silicon solar panels are one possibility. In direct sunlight, one side of the Egg would receive about 100 watts of sunlight, which could straightforwardly provide 15 watts of electricity for computation, which is more than a modern notebook computer uses when it’s not charging its batteries. You probably wouldn’t really want to cover the entire upper surface of the device with panels, though, because then there’s no room for a display.

As discussed later, some output options are a lot easier in the dark.

Nuclear energy

I considered nuclear energy (a nuclear thermoelectric generator, for example), but I don’t think it’s a good idea for several reasons. First, in the current political environment, it would be very difficult either to manufacture or to transport nuclear-powered Eggs. Second, if the Egg gets buried, the lack of convection would cause its temperature to rise without bound, eventually destroying it and potentially releasing hazardous radioisotopes. Third, as shown by the medical nuclear spill in Brazil and by experience with Strontium-71-powered weather stations in the former Soviet Union, ignorant people hoping to profitably salvage valuable materials can break open nearly any container, so it’s not a good idea to leave sealed containers of dangerously radioactive materials around the landscape. Fourth, the power supplies lose their potency over time, rapidly if they use radioisotopes with short half-lives.

It might be possible to power the Egg with nuclear energy if there’s a way to harness an extremely small amount of some radioisotope with a half-life measured in centuries or longer. Extremely small amounts of radioisotopes are routinely manufactured, shipped, and sold freely for purposes such as americium smoke detectors, gas-lantern mantles, and uranium pottery glazes. If e.g. an alpha or beta emitter could be harnessed to charge a capacitor by sending individual particles across a dielectric vacuum gap, it might be feasible to use nuclear energy to supply a tiny amount of power without running into the above roadblocks.


One variant of mechanical energy is vibration: Greg Sittler suggested that you could power it from a sort of high-power microphone, piezoelectric perhaps, inside a resonating cavity, so that wind blowing over the top would cause it to whistle and generate electricity.

Vibration-energy harvesting devices are finding some use these days in HVAC monitoring, but it seems like too much to hope for that the Egg would find itself in an environment with constant vibration while it’s still intact enough to hatch. Perhaps if it were exposed in the open to a hailstorm.

Thermal energy

Thermal energy, other than direct solar heating, is unlikely to provide a useful amount of energy on Earth. Photovoltaic cells are probably a better way to get energy from direct sunlight than some kind of heat engine, because the heat engine can only work with the black-body temperature of the environment of the hot side of the Egg, so it’s necessarily of very low efficiency.

(You could imagine some kind of very small concentrating solar power generator, but that probably involves a lot of complicated, unreliable mechanical parts.)

Mechanical energy

Mechanical energy will probably have to be supplied by the human user of the device, so it’s worth considering how much energy humans could conceivably supply.

At the low end, typing on a keyboard puts energy into it. A finger might weigh 30g. A typical keystroke might be 4mm, and at 160wpm, it needs to be completed within a time window of 60s/5/160 = 75ms, so the whole downward part of the keystroke might take 150ms, I’m guessing accelerating more or less uniformly downward the whole time. That means that, at the impact at the end, you’re going 8mm/150ms, or 53mm/s, so your 30g finger has a kinetic energy of about 43mJ. Someone typing 160wpm is delivering a 43mJ keystroke every 75ms, or a whopping 570mW! A normal keyboard just turns that energy into heat.

Even if you’re typing at a more amateurish pace, you could probably manage to dump 50mW into the keyboard.

At the high end of human mechanical energy, a normal person pedaling a bicycle hard might be putting 80W into it. Accelerating an 80kg person-plus-bike from 0 to 20 kilometers per hour in 30 seconds would be 82 watts without friction.

(I’m not suggesting that bicycle pedals would be a reasonable thing to add to the Egg. Bicycle pedal bottom bracket mechanisms are relatively unreliable, with a mean time to failure of under ten years, and they need lubrication. I’m just saying that it probably represents the very high end of what a single person can do, regardless of the machinery available.)

The magnetic key

There’s still the question of how to harvest the mechanical energy of keystrokes. You could use a variable capacitor, like a condenser microphone: mechanically forcing charged plates apart raises the voltage, and you can then bleed off some of the charge before allowing them to come back together. Or you could strike a piezoelectric crystal, such as PZT. I have another idea in mind, though.

Take a thin strip of sheet steel and bend it into a U shape, wrap a coil around the U, and put a permanent magnet across the gap at the top of the U. The electrical steel used for transformer cores has a magnetic permeability of about 80000 times the permeability of free space or air, until it saturates, anyway. Suppose the length of the strip is about 20cm. Then the path reluctance is equivalent to the reluctance of about 2.5 microns of air. Now, if you elastically deform one of the arms of the U until it’s 4mm out of contact with the magnet at 53mm/s, you’ve increased the path reluctance by 1600 times, and therefore (IIRC) decreased the magnetic flux by 1600 times. Better, half of that decrease was in the first 2.5 microns of travel, which took about 50 microseconds at 53mm/s. So if your maximum flux was some quantity Φ₀, you had a moment where you were decreasing it at about 10000Φ₀ per second. (If you let it spring back, the process reverses as the metal strikes the magnet.)

This produces a pulse of voltage in the coil, and if current flows, it will briefly slow down the rate of flux disappearance. If you have it hooked up to a rectifier and a high-voltage capacitor, the current flowing will limit the rate of flux change and therefore the voltage produced. I think this means that the process can be very efficient, burning only a very minimal amount of the harvested power in resistances or voltage drops in the circuit.

Ideally, most of the energy of the keystroke is taken up by the force of thus breaking the magnetic circuit, leaving only a small amount to push the metal against the backstop 4mm away, and there isn’t so much potential energy in the magnetic field that too much gets wasted by mechanical vibration when the “contacts” come back together.

(I don’t know how to calculate the limits to the efficiency of this mechanism.)

The high-voltage pulses should also be easy to sense, for use as input.

Such magnetic contacts should have a big reliability advantage over electrical-contact switches: they don’t arc (there are induced currents, but they’re eddy currents inside the steel) and surface fouling won’t impair their functioning, as long as the reluctance of the surface fouling is small compared to the reluctance of the whole magnetic circuit, which is to say, as long as it’s not more than a micron or so thick.

Plating the metal with nickel or chromium to prevent corrosion may be a good idea. Keeping it inside a hermetically-sealed chamber will probably also help.

EnOcean ECO 100 energy harvesting button pictured (with a similar operating principle, but a different design)

Steel does not fatigue detectably in a few hundred million cycles as long as it’s not stressed past its endurance limit, although recent research suggests that it will eventually fatigue. In this case, suppose the strip is about 1mm thick. Bending by 4mm over a distance of 20cm means the metal is bent into an arc (two arcs, actually) of about cos⁻¹((20cm-4mm)/20cm) = 0.2 radians, which means the radius of bending is about 100cm on the inside and 100.1cm on the outside, so the strain is about 0.05% in compression and 0.05% in tension at the outside edges, and half that on average. Steel’s Young’s modulus is about 29 Mpsi or 200 GPa, so this is a stress of about 100MPa. Steels’ tensile strengths vary widely, but the lowest in Machinery’s Handbook are around 55kpsi, 379MPa, so if I haven’t screwed up my calculation too badly, the stress at the surface is a bit over a fourth of the ultimate tensile strength.

Typical endurance limits for steels are either around half of ultimate tensile strength, or 690 MPa, whichever is less, so in the 190-690 MPa range. So, at 100MPa, the strip probably won’t fatigue from the bending, although it could conceivably fatigue from the impact against the magnet.

I think a ferrite permanent magnet will not lose its magnetization in this situation.

I don’t know of any other potential wear mechanisms in this device, other than fatigue and corrosion.

There are existing commercial products which I believe work like this, like the EnOcean ECO 100 energy-harvesting switch pictured above. However, the ECO 100 is only rated for 50 000 keypresses. If you were using two of them like iambic telegraph keys, that would be a few hours of operation. By avoiding fatigue and sliding contacts, my design should work to at least a billion keystrokes.

Energy source summary

Here are some guesses about the energy sources that seem like plausible options:

|                      | maximum | average | storage |
| Photovoltaic panels  | 15 W    | 5 W     | 16 h    |
| Rapid typing         | 500 mW  | 25 mW   | 1 s     |
| Slow typing          | 50 mW   | 2.5 mW  | 5 s     |
| Great human exertion | 80 W    | 800mW   | 24 h    |

Energy storage in the Egg of the Phoenix

Most of the energy-source options provide intermittent power, so it needs to be able to store energy until it needs it. There are existing chips to manage energy-harvesting applications, such as the LTC3588 (US$4.22), which uses a capacitor charged as high as 20V to store the harvested energy until it’s needed.

Batteries: not an option

The standard way to store energy in portable computing devices today is in chemical batteries, which achieve much higher energy densities than capacitors. Unfortunately, they aren’t very stable over time; their normal operation involves chemical reactions that erode and rebuild their electrodes as they are discharged and recharged, sometimes producing short circuits and fires. Worse, they usually use their outer case as one of their electrodes, and so eroding it can cause them to leak; and some types, like lithium batteries, degrade spontaneously even if you don’t discharge and recharge them.

So I don’t think chemical batteries are an option.


I had been thinking about small, high-capacitance capacitors, but Greg pointed out that you can probably store more energy in a low-capacitance high-voltage capacitor than in a high-capacitance low-voltage capacitor. Here’s why. Every volt added to a capacitor requires one microcoulomb of charge per microfarad of capacitance, and putting that microcoulomb there requires doing work of one microjoule per volt. So the first microcoulomb is easy, but the next one is harder, since the voltage is higher, and each one after that gets harder and harder, storing more and more energy. Consequently the total energy stored is CV²/2.

High voltages have advantages and disadvantages. Solar panels don’t natively produce very high voltages unless you put an awful lot of them in series. XXX how many? Converting from a high voltage to a low voltage with a switch-mode power supply is a lot easier than converting from a low voltage to a high voltage with a buck/boost converter. High voltages mean less current, and therefore less energy lost in wires of a given diameter or in diode rectifiers. And of course high voltages pose the risk of arcing.

The energy density limit is imposed by the dielectric strength of the insulating dielectric that separates the plates of the capacitor. If the electric field gets strong enough — a large enough number of volts per meter — it rips apart the atoms of the dielectric into ions, forming a conductive path, either temporarily or permanently, and discharging the capacitor.

So you can get a higher-voltage capacitor by using a proportionally thicker dielectric. Twice the dielectric thickness gives you twice the voltage. That also lowers the capacitance, though: twice the dielectric thickness gives you half the capacitance.

However, since it’s CV²/2 and not CV/2, that still gives you twice the energy storage. It turns out that the energy is actually stored in the electric field in the dielectric, so at a given flux density (field strength), it’s proportional to the volume of the dielectric; increasing the plate area leaves the maximum voltage unchanged while proportionally increasing the capacitance.

High-voltage, low-capacitance capacitors are also appealing for another reason: they should be easier to produce to make more Eggs of the Phoenix. Benjamin Franklin made his own high-voltage capacitors; Iangatu Awidum can too.

Dielectric choice

How much energy could you store, then? Capacitance C is εA/d, where A is the area, d is the distance between the plates, and ε is the absolute permittivity, and breakdown voltage is d S, where S is the dielectric strength. So CV²/2 = dεAS²/2. dA is simply the volume of the dielectric, so E = VεS²/2. In a sense, the plates and insulation of the capacitor are just overhead; to maximize capacitive energy density, you want to maximize the fraction of the capacitor that is made of dielectric, and maximize the product of the square of the dielectric strength (breakdown voltage per meter) and the dielectric constant.

ε is sometimes written kε₀, where k is the “dielectric constant” or “relative permittivity”, and ε₀ is the permittivity of free space, 8.854 × 10⁻¹² farads per meter. So it suffices to maximize kS².

So, what dielectric would allow us to store the most energy?

XXX the references in this table are getting lost. I probably need to use <table> tags, sigh.

|                 | S (MV/m)  | dielectric constant k |    kS² |
| distilled water | 65 [13]   | 80 [15]               | 340000 |
| dielectric PZT  | 9 [30]    | 3850 [16]             | 310000 |
| mica            | 118 [13]  | 8 [25]                | 111000 |
| polyimide       | 150 [31]  | 3.4 [15]              |  77000 |
| benzene         | 163 [13]  | 2.3 [29]              |  61000 |
| waxed paper     | 40 [13]   | 3.7 [26]              |   5900 |
| BaTiO₃          | 2 [24]    | 1250 [15]             |   5000 |
| Teflon          | 60 [13]   | 2.1 [15]              |   7600 |
| fused quartz    | 25 [27]   | 3.75 [12]             |   2300 |
| corundum        | 13.4 [13] | 9.8 [32]              |   1800 |
| silicone        | 20 [39]   | 2.8 [39]              |   1120 |
| PMMA            | 17 [38]   | 3.6 [38]              |   1040 |
| epoxy           | 16.5 [37] | 3.4 [37]              |    930 |
| vacuum          | 20 [13]   | 1                     |    400 |
| mineral oil     | 10 [13]   | 2.1 [33]              |    210 |
| air             | 3.3 [36]  | 1.0                   |     11 |

The “vacuum” entry in this table requires some explanation. Vacuum doesn’t suffer dielectric breakdown the way that materials do, but a vacuum capacitor above about 20 megavolts per meter will lose charge through Fowler-Nordheim tunneling, aka “field emission”. There are many dielectric materials (e.g. distilled water, Teflon, mica, benzene, fused silica) with a higher dielectric strength than that.

(Note: the dielectric strength of fused quartz is given as 8MV/m by [26] and as 470-670 MV/m by the CRC Handbook, 86th edition, page 15-44. This very large discrepancy concerns me. So I used a third value, provided by a vendor of the stuff, which is in between the other two. The Physics Factbook entry [28] demonstrates this to an even greater extent. If the CRC handbook’s value were correct, fused quartz would be competitive with and perhaps dramatically better than PZT.)

A disadvantage of solid dielectrics is that they can’t recover from a dielectric breakdown. So it might be the case that a liquid-dielectric capacitor would be more durable than a solid-dielectric capacitor.

PZT: probably too expensive

It’s clear that PZT is head and shoulders above all the other solid options in this table.

Ramtron has requested an exemption from RoHS for PZT, commenting that there’s already an exemption for high-voltage capacitors, but saying:

Lead-zirconium-titanate (PZT) material has the highest known dielectric constant (εr = 1000 – 1200) and thus can be used as a planar metal/insulator/metal (MIM) capacitor with a breakdown voltage of more than 100 V. No alternative to PZT is currently known for thin film capacitors and ferroelectric RAM (F-RAM) memories that achieves the same combination of high dielectric constant, high breakdown field and temperature stability of 20% in a temperature range from -25 to +85 °C.

They apparently got their exemption (European Commission Decision 2011/534/EC).

I’m not sure if high-voltage ceramic capacitors are actually using PZT or another related perovskite. I can’t find a vendor that explicitly markets a discrete PZT-dielectric capacitor, which frustrates my desire to estimate how much energy a PZT device could store.

A good guess, though, might be Vishay’s Cera-Mite line of high-voltage disc capacitors, which Octopart claims are RoHS exempt; the biggest of them, the 30AED33, is 3300 pF at up to 30kVDC: a 37mm-long cylinder 24mm in diameter. This works out to an energy capacity of 1.5 J, or 89 J / liter, if the capacitor behaves perfectly ideally. Digi-Key has Vishay’s similar 40kV 715C40DKD33 listed at US$54; it’s 34mm long and 58mm in diameter.

The dielectric in these capacitors is described as “Y5U”, which apparently means a large family of perovskite dielectrics that often include lead. Whether it’s actually PZT or some other related compound is unknown.

What is clear is that it’s incredibly expensive: about US$600 / liter, or US$0.60 per milliliter.

Distilled water: apparently the right choice but flaky

A distilled-water dielectric is slightly more energy-dense at breakdown than PZT, and it costs an enormous amount less.

Water is unfortunately fairly corrosive. When pure, it’s not very corrosive, but corrosion might be able to add ions to it which make it progressively more corrosive. Background radiation and dissociation into hydroxyl and hydronium will unavoidably create ions in the water.

However, all is not lost. Suppose you want a water-dielectric capacitor with 100kV breakdown. At 65 MV/m, that’s a plate spacing of 1.54 mm. Your plates can then be 0.1mm thick without occupying a substantial fraction of the capacitor volume, so you have plenty of space for a 25-micron-thick coating of some inert material, such as Teflon, Kynar, or Kapton, between the plates and the water. Then the water won’t have the opportunity to corrode the plates. The plates can alternate between positive and negative, just as in a multilayer ceramic capacitor.

This does, however, mean that a dielectric breakdown would render the device inoperable.

XXX This page about dielectric breakdown of water suggests that I have the breakdown voltage too high by an order of magnitude, and the Sandia paper it references says that the empirical equations currently used to model water dielectrics have a limiting breakdown voltage of 0 as time approaches infinity. The paper is specifically about designing energy-storage water-dielectric capacitors for particle accelerators. This is probably why I’d never heard of a water-dielectric capacitor for sale. (It might also be that water has high dielectric losses.) XXX More discussions

Water has another disadvantage: even deionized water has high conductivity, even before breakdown streamers form, compared to other candidate dielectrics. Fused quartz has a conductivity of 1.3×10⁻¹⁸ mhos per meter; air is in the 10⁻¹⁵ to 10⁻¹⁴ range; and deionized water is 5.5 × 10⁻⁶. That’s still six orders of magnitude less than seawater and 12 orders of magnitude less than conductors, but it’s sufficient to cause problems for this application.

XXX calculate that.


[0]: Yes, I read Anathem. If you haven’t read it, you should read it too. It’s thought-provoking. Fire Upon the Deep too. They both touch frequently on topics discussed in this post. As in Anathem, where I refer to “praxis”, read “praxis and poiesis”.

[1]: Fictional name “scientifically” generated from English bigram distributions.