Kitchen aluminum foil is a remarkable material.
It’s typically 10 μm thick and 400 mm wide, giving it an aspect ratio of 40000 in that dimension, and rolls are commonly some ten meters in length, for an aspect ratio of 1 000 000; heavy-duty versions can reach 30 μm or more. Despite their thinness, foils of 25 μm or more are impermeable to oxygen, water, and light, though Wikipedia claims thinner foils typically are plagued with pinholes. It comes in a fully annealed state, so it rapidly work-hardens when bent, and because of its thinness can be bent at deep submillimeter scales to form metamaterials. It’s highly reflective (88% on the bright side across the visible spectrum and even higher in the infrared) and conductive, rivaling copper. It resists corrosion for years in weather, it’s nontoxic, it’s light (2.71 g/cc), and it’s damn cheap, under 50¢/m².
Robert Lang recommends laminating tissue paper on one or both sides of kitchen aluminum foil to make “tissue foil”, which for years he considered the ideal origami material. Notably, he uses a weak sacrificial adhesive layer to hold the foil in place for the lamination process.
Typical alloys include especially 1100 and 1200, but also 8111, 8015, and 8006, with 0.06%–0.6% silicon and 0.4%–1.6% iron, and in some cases also some copper or manganese, under 0.5%. (1100 is sometimes described as an “unalloyed aluminum grade” but it’s specified to contain 0.05%–0.20% of copper, and it unavoidably has other impurities.) Room-temperature yield strengths of these alloys range from 30–170 MPa, with ultimate tensile strengths of 70–200 MPa, and of course they all have a Young’s modulus around 70 GPa. Because its crystal structure is fcc, it remains ductile down to absolute zero, making it suitable for cryogenic applications; indeed, aluminum becomes stronger at cryogenic temperatures. And, although it weakens dramatically at higher temperatures, it doesn’t melt until almost 650°, enabling it to be used at higher temperatures than organic materials.
If oxidized (for example, with a soda solution, an arc, or anodization) it yields amorphous sapphire, which if crystallized is an excellent insulator, refractory, and abrasive. The oxidation process produces a great deal of heat, making aluminum a very-high-energy-density fuel, and, thanks to aluminum’s sternly trivalent nature, electrical current; aluminum-foil fuel cells are routinely produced by amateurs, though these typically oxidize the aluminum to the chloride rather than the hydroxide or the oxide.
50¢/m² is 50¢/kWp in a solar concentrator, or 0.05¢/Wp, which is noticeably cheaper than photovoltaic cells, currently around 18¢/Wp, 360 times more expensive. (However, the foil number there is sunlight watts; if you’re making a PV solar concentrator you have to divide by the efficiency of the solar cells, say 21%, which gives you 0.24¢/Wp electric.) A large aluminum-foil assembly would be vulnerable to significant deflections, but many small assemblies could be placed on a hard, stable surface such as a rock or an adobe wall.
Alternatively, though, it might be possible to stiffen the foil by making the equivalent of corrugated cardboard out of it, maybe using aqueous boric acid (US$1.70/kg according to Potential local sources and prices of refractory materials) or borax as the glue. The surface tension of water is ample to hold aluminum foil in place until the water dries.
The feature that currently attracts my attention is the possibility of work-hardening, which suggests the tempting possibility of making tooling from aluminum foil that can itself work aluminum foil at room temperature, a possibility reinforced by the immense aspect ratios routinely available. As a simple example, you can in theory roll some foil into a cone, and the point of this cone can dent, form a rib in, or even pierce more of the same foil; but this is much easier in practice if you first fold the foil 16 layers thick, form ribs converging to a point on the last-formed fold, then roll the cone around that point. If the last-formed fold is reversed, the aluminum along the outer edge of the fold is the aluminum that was most strained previously, having been bent double with as small a radius as possible, and so will be the most work-hardened.
I was able to use such a cone to pierce not just aluminum foil but the skin of an apple. I folded it from some foil which, folded 256 layers thick, measured 2.57 mm in my shitty digital calipers; the resulting square measured 27–29 mm on each side and weighed 1.8 g, giving a density of only 0.8–1.0 g/cc, so it’s probably more than half air, though it rapidly sinks in water, so probably the density is a little higher than that.
Using such a cone point to form ribs without piercing foil is tricky, because it tends to have significant asperities around the tip, which tend to tear the foil if it is unbacked. These can presumably be removed, permitting traditional SPIF processing of raw foil by sliding the point over the foil; a better alternative might be to produce a sequence of dents in the foil, then add new dents between them, eventually producing a continuous groove in a way analogous to how chain drilling cuts through a block of metal. However, when the foil “workpiece” is backed by something reasonably hard (I’ve used corrugated cardboard and the above-mentioned packed 256-layer aluminum-foil square) and I’m using one of the other point types described below, tears are relatively uncommon; in this situation it fairly reliably just forms ribs. (I need to test more rigorously to find out if the point type, the backing, or both is relevant here.)
Because such ribs are work-hardened, they are able to imprint their shape on fully-annealed foil repeatedly. I wrote a short word in cursive on foil using a layered aluminum-foil point (“single-point incremental forming”), with the foil simply backed by the somewhat-hard 256-layer square, then pressed this master against another piece of foil in several places, pressing the two foils between my fingers in each position (“stamping”). This resulted in very readable copies of the word in several locations, although I’m guessing there was substantial springback, so repeating this sort of stamping through multiple generations would make the stamping shallower at each generation.
I’ve tried smoking and annealing this foil with candle flames and butane lighter flames, but so far I’ve only managed to melt it (in under a second, usually) without ever smoking it. Maybe if I put water in it I could get it to smoke up so I could tell when it was on the point of overheating, but probably a different method of temperature control would be more practical to anneal such a thin material, such as a temperature-controlled heat gun.
A more reproducible point construction with a sharper, lower-volume point was able to pierce the foil and apple even more easily. I folded the foil three times to get 8 layers with a right-angle corner; bisected the corner twice to get a 22½° angle; formed a rib bisecting that angle with thumbnail pressure; then opened the final fold to about 30° so that the two sides of the point would stiffen one another.
By laying the foil into a form with a 90° valley in it and dragging such a point over it, I was able to get a bend into the foil. When there were ribs running perpendicular to the bend, this required multiple passes in one case; a second attempt resulted in neatly cutting through the foil at the intended bend location.
Another way to look at the 40 000:1 aspect ratio is to consider making a tight cylindrical roll from a strip of the foil, 400 mm long and, say, 10 mm wide, comprising 40 mm³, a cylinder whose ends are 4 mm³. The cylinder thus has radius 1.13 mm and diameter 2.26 mm, so a section through the center of it will go through 226 10-μm layers of foil. That is, instead of being 40 000 as you’d expect, it’s about √(40000) · 4/π.
The significance of ribs for folding is not that the ribs themselves become more flexible — the material in the rib is work-hardened and thus less flexible in plastic deformation, though its elastic properties remain unchanged — but that they prevent curvature of the material around them in any other direction, so if it’s going to bend, the bend will be parallel to the ribs.
By making many parallel slits in the foil (with a steel box-cutter blade, backing the foil with cardboard), I was able to make expanded sheet metal, expanding a bit of foil by more than a factor of 2.
I was also able to fold a rather ugly origami crane by hand from the foil, about 700 mg and 70 mm wingspan.
This assemblage of techniques seems promising for matter compiler bootstrapping, although it’s clearly just a beginning. Many of the problematic aspects of kitchen aluminum foil result from trying to work with it at the 10-mm scale rather than the 10-μm scale. Wrinkles, rips, and so on are going to happen unintentionally when trying to manipulate 10-μm foil with 10-mm human fingers.
(Also, the natural frequencies of such macroscopic objects made by folding such foil rarely exceed 100 Hz. The wing of the foil crane resonates at around 100 Hz.)
As a test of alternatives, I also folded an origami crane from a square cut from an aluminum Monster can, which is normally expected to be about 100 μm thick. The square was about 125 mm on a side, and the crane weighs about 3.8 g. One layer of the square measured 0.12 mm; two layers 0.33 mm; three layers 0.38 mm; and four layers 0.52 mm. We can conclude from this that (a) my caliper technique is shitty, (b) the can (including paint) is about 120 μm thick, and (c) the actual aluminum part of the can is more like 90 μm thick (3.8 g / 125 mm / 125 mm / 2.71 (g/cc)).
It’s a fucking miracle that I didn’t cut myself on the damn crane. It was all knife edges and burrs, and every time I folded the damn thing it cracked and ripped more, exposing new cutting edges. Aluminum-can bodies are typically aluminum 3004, hardened with manganese and magnesium, and work-hardened from the deep-drawing process rather than annealed, so it’s not a perfect analogy, but it seems at least suggestive.
Aluminum flashing for roofing is 0.024 inches, or in modern units, 610 μm, but I think it’s annealed; aluminum is sold as sheet metal down to 0.004 inches, 100 μm in modern units.
If we figure that the foil can meaningfully change direction every 20 μm, then we might think of an aluminum-foil machine as being made of “moving parts” on the order of 1000 μm² (50 μm × 20 μm), 1000 “parts” per square millimeter of foil; a roll of kitchen aluminum foil is enough to fabricate some 4 billion “parts”. A bootstrapping compiler might require 100 000 parts and thus a square centimeter of aluminum foil, cut and folded around into a shape a couple of millimeters in diameter. If it were doing only one thing at a time, and needed 10 seconds to construct/assemble each moving part, it would take about 12 days to recompile itself. This is probably adequately fast, barely, but probably not adequately robust against errors. It would probably be better to design it to have more parts and do many things at once, enabling it to be faster and correct errors.
It would be astonishing if no other materials were needed: you can’t build anything electrical out of aluminum, at least at sub-microwave frequencies, because the whole device is at the same electrical potential. Similarly with getting mechanical power from thermal expansion and contraction: it would just expand isotropically rather than bending or sliding to do useful work. It might be possible to use just aluminum foil coated on one side with something else, such as glass or a few microns of aluminum oxide.
An interesting way to think of the density of aluminum foil is that 10 μm of 2.71-g/cc aluminum foil is 27.1 g/m², which is the same areal density as a 23-mm-high column of air.
Other processes that may be very interesting to apply to aluminum foil include electrolytic machining, electric discharge machining, scanning probe microscopy, and anodization. Electrolytic machining might make it possible to use an aluminum-foil tool to cut arbitrary shapes into metals such as steel, invar, brass, inconel, monel, or tungsten, and also to transform a scrap of aluminum foil (either flat or of a known geometry) into a white-light hologram of an arbitrary optical system, Fresnel-reflector-style.