Suppose you want to fabricate a grid of wires, like for a capacitive touchscreen. In theory there are lots of ways you can do this: etching or electroless plating of printed circuit boards (especially including flex), weaving insulated wires (ideally multistranded) into a flexible cloth, slicing aluminized mylar into ribbons and then gluing the ribbons onto paper, drawing graphite lines on both sides of a sheet of paper, etc., but I wanted to focus on the case of glazed ceramic.
Let’s say you start by making a bisque ceramic plate with a bunch of narrow gold-leaf ribbons running in parallel across it. Then you can add an engobe or other glaze on top of those ribbons (except, perhaps, along one edge where you are going to attach electrodes), then another set of ribbons running across that, perpendicular to the first. With the proper choice of glaze, this new set of ribbons will be insulated from the first set by the glaze. If you then want them to be insulated from the world, you can do a second glaze firing of the plate with another, lower-melting glaze on top of the ribbons, again with the possible exception of one edge.
This procedure should give you a grid of capacitively-coupled wires whose coupling is dependent on you touching the plate. This is also potentially useful as a macroscopic ROM: if you add some conductive paint to the surface at some junctions, it can act to increase the capacitive coupling at those junctions, thus representing information. Under suitable circumstances, this reader might even be able to capacitively read heavy graphite marks on paper.
Consider the case where each layer of glaze is 100 μm thick and has a relative permittivity of 5 (that of glass — see Measuring the moisture content of coffee and other things with dielectric spectroscopy), the ribbons are 1 mm wide and 5 mm apart, and you place a conductive circle of 11 mm in diameter over one of these junctions. The capacitance ε A / d between the wires without the circle is 5 ε₀ 1 mm² / 100 μm = 0.44 pF, a capacitance small enough to be hard to measure. (ε₀, the vacuum permittivity, is about 8.85 picofarads / meter.) The capacitance between the upper wire and the circle is 5 ε₀ 11 mm² / 100 μm ≈ 4.9 pF, and the capacitance between the lower wire and the circle is 5 ε₀ 11 mm² / 200 μm ≈ 2.4 pF. So the series capacitance between the two wires is 1.62 pF, about four times larger than the capacitance without the conductive thing.
Detecting an extra 1.2 pF in a circuit usually requires a relatively carefully built measurement circuit to keep stray capacitances from drifting, but it’s entirely feasible. A thinner glaze or one with higher permittivity, or wider ribbons, would provide larger capacitances which would be even easier to measure; but wider ribbons would also reduce the relative difference in capacitance between the finger-present and finger-absent states. A thicker glaze would probably necessitate either high-permittivity ingredients or wider ribbons.
At 10 MHz, which is a convenient frequency, 1.62 pF gives a capacitive reactance of (2πfC)⁻¹ = 9.8 kΩ, while 0.44 pF gives 36 kΩ. These numbers are large compared to the expected resistance of the wires in the plate: according to Paper/foil relays, gold’s resistivity is 2.44×10⁻⁸ Ωm, so a 1 mm × 100 nm × 100 mm wire is 24.4 Ω. (See Spark particulate sieve for information on metal thicknesses.) But they are small compared to the input impedance of any random op-amp.
Gold leaf has the advantages of being cheap and of not oxidizing, even
when ceramic is being fired. (Most of the ceramic I’ve done was fired
at 1020° (see file ceramics-notes) but porcelain can be fired at up
to 1400°; some earthenware made from ferrous clay can be fired as low
as 600°.) I have the impression that the usual pottery gilding
technique is somewhat more complicated than merely gluing gold leaf to
the greenware or bisqueware before a firing, but I’m not sure why.
Some oxides are also conductive; indium tin oxide is the one commonly used for transparent conductors in LCDs, but zinc oxide and some heavy metal titanates are also semiconductors. Yttria-stabilized zirconia is conductive at high enough temperatures, and was formerly used as an incandescent element in Nernst lamps, and silicon carbide, though not an oxide, oxidizes slowly enough to survive ceramic firing. Some of these might be practical to deposit on the surface as part of a glaze, but I suspect that others would dissolve in the common glazes.
If you’re firing in a sufficiently reducing atmosphere, you may be able to use powdered copper or copper oxide to get copper traces rather than gold leaf; for uses like printed circuits, this could offer immensely higher conductivity. (Gold is very nearly as conductive as copper, but gold’s cost advantage in this context would come from being able to use a very thin layer of it, which gives it substantial resistance.) Carbon and many different metals might work in a reducing atmosphere.
Of course you can solder other components to the traces thus produced and make a more or less conventional printed-circuit board, though perhaps at somewhat higher cost.
The HP 9100 used a ROM design somewhat similar to the above, but using inductive coupling rather than capacitive coupling, and using a now-traditional multilayer printed-circuit board rather than layers of ceramic glaze. Such an inductive ROM could totally work, and inductive sensing could also be used to detect the proximity of ferromagnetic materials rather than conductive ones.
The traditional reason for applying gold leaf to thin sheets of vitrified silicon dioxide was for a burglar alarm: the gold leaf running around the outside of a glass window was part of a Wheatstone bridge, and either breaking it along with the glass, or shorting it out to avoid breaking it, would change its resistance enough to trigger the alarm. So you could use such embedded conductors for detecting not only touch but also breakage.
The resistance calculated above for the gold-leaf traces is in a range that would be usable for resistance heating, although common pottery is somewhat fragile to thermal shock, so the heating would need to be fairly slow. (I suspect this can be improved in the body of the pottery by foaming, but I don’t know how to improve it in the glaze.) The gold itself will withstand fairly high temperatures. Silicon carbide and zirconia are other promising materials for printed heaters.
An induction coil, for example for a pancake motor, can be printed on a ceramic surface in this way. If it’s to be used for high-power applications like motors, cooking, or other bulk heating, rather than sensing, you probably want the lower resistances achievable more cheaply with copper.
Gold leaf’s extreme thinness could conceivably be used to fabricate extremely fine circuit details, if you can pattern it finely enough. For example, you could imagine traces of 100 nm thickness, as above, but only 100 nm width rather than 1 mm, spaced 100 nm apart. This would provide 5 parallel conductors per micron, so a 10-mm-diameter circle could contain a spiral pancake coil of 50’000 turns, which would be a fairly sensitive detector of varying magnetic fields.
The (presumably) high resistance and high dielectric strength of the glaze could enable electrostatic-like fields, perhaps capable of moving macroscopic objects such as bits of aluminum foil. According to How would you maximize the energy density of a capacitor?, fused quartz doesn’t break down until 30 MV/m; if the glaze is 10 MV/m, you could safely use voltages of up to about 1000 V with the 100-μm glaze thickness I guessed at above.
By exposing spark gaps on the surface of the plate, not placing glaze over them, you could fabricate a kind of multiplexed matrix display. Probably you could only illuminate one spark gap at a time, and you’d probably need a few hundred volts to reliably get a spark going in air. Unlike conventional printed-circuit boards, glazed ceramic will not become conductive when you arc across it (there’s nothing to char) and the gases produced by the spark will not attack it; however, the plasma will gradually vaporize it, and perhaps more importantly, vaporize the spark-gap contacts, especially if they are thin gold leaf. Also, the device produces nitrogen oxides and ozone.
Since arcing produces substantial UV, you could possibly get pixels of different colors by depositing different fluorescent colored dyes under different spark gaps.
Selectively generating arcs as you sweep paper across the ceramic could be used to selectively char the paper, thus printing on it, though not in an archival-safe manner.
Glow/corona discharge in air might permit longer life than arcing. Such spatially selective application of glow discharge in air could be useful not only for making visible images with light but also for selectively activating chemically-inert surfaces such as glass or polyethylene, or selectively initiating polymerization or ozone bleaching.
Glow discharge in a low-pressure inert-gas atmosphere, of course, gives you a neon bulb. I think that’s also how gas-plasma displays work.
Such exposed pairs of contacts are also, of course, how rubber-dome keyboards work, at lower voltages than those needed for spark gaps; these can usually be operated by touching them with fingers as well.
Air-quartz flash bulbs are the gold standard for short non-laser light pulses for high-speed photography; such a spark gap over (largely-quartz) fired clay amounts to something similar to an air-quartz flash bulb. Aside from the uses in stroboscopy, an array of such spark gaps firing in a raster sequence produces short flashes of light emanating from different points; by focusing these through a lens onto an object, they scan a spot of light across it in a fashion similar to a flying-spot TV camera, but without moving parts. The resulting waveform of reflected light detected at some point P produces an image of the scene as seen through the lens, as if illuminated from point P. (See Flying spot reilluminatable stage for more thoughts on this.)