“Cyclic fabrication systems” is a term Matthew Moses, Hiroshi Yamaguchi, and Gregory Chirikjian invented to describe a collection of materials, tools, and processes capable of reproducing itself. A CFS is the keystone of economic autarky, of resilience against faraway catastrophes, and of escaping resource scarcity traps, and its exponential growth rate has historically been the major limit on worldwide economic growth; consequently the study of CFSs is, or should be, central to economics, although it is a relatively neglected topic, involving as it does cross-disciplinary concerns from engineering, materials science, chemistry, metrology, and economics.
A programmable, fully automated autotrophic CFS with a growth rate exceeding that of the economy would eliminate the scarcity of capital goods that has been the foundation of human economics for two million years.
With that in mind, I thought it would be worthwhile to survey historically and potentially existing CFSs. There are various aspects of cyclicity: there’s the simple geometric question of how a machine can reproduce the shapes of its own parts in the same materials; there’s the metrology question of how to measure half a millimeter on a ruler measured in millimeters; there’s the control question of how a negative-feedback system can produce another working active negative-feedback system, there’s the chemistry question of how to produce a large amount of materials with the necessary degree of purity, starting from impure and unknown natural materials and a small amount of known and pure materials; and there’s the energy question of how such an assemblage of machines can continue harvesting energy from its environment, for example building an engine that can harness the available solar or chemical energy.
The first category of CFSs to survey are those concerned with imposing some existing geometry on some existing material. For now we’re not so concerned with how the geometry or the material is created.
A feature common to many geometry CFSs is a sort of rock-paper-scissors dynamic; in a given manufacturing process, typically one material is stabler than another, so perhaps it can be used to shape that other material.
For example, you can melt wax into a pewter mold, you can melt pewter into a steel mold, and you can melt steel into a greensand mold; but you can’t melt greensand into any kind of mold, both because it requires unreasonably high temperatures and because it ceases to be greensand when you melt it. Instead we rely on the fact that greensand at room temperature is soft enough to be rammed around patterns, made of materials such as wax, with tools made of materials such as steel.
Pewter beats wax, steel beats pewter, greensand beats steel, and wax beats greensand. Thus we form the cycle that makes our fabrication system cyclic.
Since the Paleolithic, the humans have shaped tools by banging rocks together, a process called “knapping”. Arguably this is not a CFS, because typically the hammerstones and other flintknapping tools such as antlers and copper pressure-flaking tools are not themselves shaped by flintknapping or flintknapped tools.
Knapping is somewhat limited in the geometries it can achieve, and it can only shape materials that break in the right way, such as glass, obsidian, and flint.
A major innovation in manufacturing technology some 35 millennia ago, perhaps in Japan, was shaping stones by grinding them with abrasives, rather than chipping. It had spread to the Levant and Europe by some 10-18 millennia ago, where it is considered a distinguishing mark of the Neolithic. Grinding permits greater liberty of materials, surface finishes, and geometry; abrasives can shape any solid material and can achieve arbitrary geometry down to submicron scales. In particular, in the late Japanese Paleolithic and in the Mesolithic and Neolithic, polished stone axes were much more durable than traditional knapped axes; hole-drilling permitted much more adaptable and secure forms of assembly; and Kebaran mortars and pestles began to automate the more mechanical aspects of food digestion.
From a CFS perspective, there are several great features of grinding. One is that the geometry of the workpiece can be more precise than the geometry of the tool, because it is determined primarily by the movement of the tool, as constrained by the workpiece and other external systems, rather than the tool’s geometry. Another is that, by grinding three surfaces against each other with abrasive between, a precisely flat surface can be achieved without any flatness reference. A third is that some hard materials are relatively easy to break, so we can get a rock-paper-scissors cycle with only two materials: a hard, brittle abrasive such as sapphire or quartz and a softer, tougher hammering material such as copper or iron. A fourth is that, because of the aforementioned movement feature, it’s actually possible to get a CFS with just a single material such as sandstone or concrete; you can dress a grinding wheel with an abrasive dressing stick just by moving the stick back and forth across the wheel’s face while spinning it. A fifth is that grinding generally does not require heat or a minimum tool pressure, so it can be done while the workpiece is not deformed, providing more precise geometry than other ways of shaping materials.
Consequently various kinds of grinding, including lapping, play central roles in all kinds of precision manufacturing even today. Especially on glass materials, deep submicron precision is feasible. Grinding is also commonly the only cutting process used for applications like cutting rebar or concrete on construction sites and smoothing over weld beads, where its material flexibility and low equipment cost outweigh its low material removal rate. In modern machine shops, grinding is used for cutting nearly-finished parts to final dimensions and for shaping metal-cutting tools out of materials that are too hard to drill or cut on the mill or lathe.
Since the late Paleolithic or early Neolithic, the humans have made pottery by sintering (“firing”) composites of clays, sintering aids, fillers, and sand into a sort of ceramic. Sintering in general has the advantage that the sintered material can remain solid at temperatures exceeding those necessary to sinter it in the first place (for pottery, in the 700°–1500° range depending on composition), so if the temperature remains relatively predictable, a kiln for sintering such pottery can itself be made of the same pottery. Moreover, it is possible (and, in historical practice, usual) to sinter the kiln itself in place, rather than sintering firebricks in a separate kiln and then assembling them into a kiln.
Clays go through a series of states of plasticity according to their hydration. Above about 25% water, they are colloidal liquids called “slips”; around 22%, purely plastic solids or thixotropic liquids, which shrink substantially as they dry further; around 20%, they remain plastic over a large range of deformations but become capable of brittle fracture (“leather-hard”) and almost do not shrink upon further drying; and below about 18%, they are fragile, brittle solids, which do not shrink on further drying. (The precise transition points vary by clay composition, soaking time, and aqueous solute content.) Firing results in further shrinkage. The other components of the so-called “clay body” can enhance plasticity and reduce sintering temperatures, and they tend to decrease shrinkage. The sintered clay body is much stronger and can be nonporous, especially if sintered a second time coated with a so-called “glaze” which melts fully rather than just sintering; typically this results in further shrinkage.
Because fired or even dried clay can plastically deform leather-hard or fully plastic clay, it is straightforward to use so-called clay “seals” to reproduce geometry (in negative), and such “bullae” have been a key security measure for commercial transactions for some 12 millennia, since the beginning of agriculture if not before; recently metals are more commonly used instead of clay, but this innovation was unknown until just a couple of millennia ago. This process of molding can be carried through multiple generations of clay seals, though not without significant loss of fidelity, including, in particular, shrinkage.
Such a clay-on-clay “sealing” process is probably responsible for the oldest instance of movable-type printing, the Phaistos disk; and of course movable type in Asia was made from pottery long before Gutenberg.
In the leather-hard state, the clay body is still plastic enough to take the impressions of seals, but also brittle enough to be cut with blades. Typically these are made of metal in current practice, but blades made of fired clay also work. Because most of the shrinkage has already happened, forming clay in the leather-hard state results in much more precise dimensions.
Clay is commonly “slipcast” in porous molds made of plaster of Paris: a slip is poured into a mold, and the absorption of water into the mold solidifies a layer of the slip in contact with the mold. The remaining slip is poured out, and the cast piece contracts as it dries and can then be demolded. Presumably it is possible to make the molds of porous fired clay instead of plaster, though I have never heard of it being done and have not attempted it myself.
Dried clay is also friable enough to be easily abraded or carved by tools, including tools made of fired clay.
The precision of all of these shaping processes is limited by the shrinkage and deformation of the ceramic during sintering, if sintering is done; by the grain size of non-clay tempers, such as sand, in the clay body; and by the shrinkage and deformation of the clay body to its dry state, for shaping processes that rely on plasticity.
Fired-clay ceramics play a key role in many more elaborate CFSs as well, because (depending on composition) they can withstand relatively high temperatures without losing their shape, they can easily be shaped to complex geometries while plastic (especially if dimensional precision is not critical), they are themselves relatively hard and can embed even harder abrasives, and they are very inexpensive.
Like most ceramics, clay has extremely small elastic deformation in all states, including the fired state, on the order of 0.01% strain at failure. This permits relatively high geometric precision, especially when shaping dried clay, but it complicates the use of fired clay for springs and other flexures.
Worth mentioning is the standard procedure for foaming pottery, which is to mix a granular organic material such as sawdust or used yerba mate into the clay body. In an oxidizing kiln the organic material burns out completely, leaving voids in the clay which reduce its weight, impede crack propagation, and improve its thermal insulating capabilities, and at higher void fractions permit easy fluid flow through the fired piece. Because of the crack-propagation improvement, the foamed pottery can be cut to shape almost as if it were wood. I’ve tried void fractions from 50% yerba up to 85% yerba, which last was quite fragile; above 66% yerba, the material permitted easy airflow. This porosity can be beneficial to the firing process in allowing the fabrication of thicker shapes without steam explosions.
So, the cycles here are: fired clay shapes plastic clay (by sealing, slipcasting, or cutting), plastic clay dries into dried clay, and dried clay is fired into fired clay; and fired clay carves dried clay, and dried clay is fired into fired clay.
Cold iron is harder than hot iron or even hot steel, so if you press them together the cold iron will reshape the hot metal without itself being reshaped. This is common to a number of metal-shaping processes including hot rolling, hot forging, and wire drawing; commonly hammering is used to achieve sufficiently high pressures to deform the hot metal. (It is also the reason the World Trade Center collapsed, despite the temperatures not being hot enough to melt its steel beams; the heat softened them.)
However, the metal thus formed deforms during cooling, so these processes generally cannot achieve tight dimensional tolerances.
So the cycle here is that cold iron forges hot iron, and hot iron cools into cold iron.
Files and other hardened iron and steel tools can be used to cut unhardened iron and steel, which can then be hardened. Similarly, hardened iron and steel hammers can be used to cold-forge unhardened iron and steel.
There are several ways to harden ferrous metals, but nearly all of them involve a great deal of heat, and so impose a certain amount of uncontrolled deformation. “Case hardening” by diffusing carbon (and possibly nitrogen) into the surface of iron is a form of solid-solution hardening known for two or three millennia; “quenching”, applicable to carbon steels, is another. In quenching, the metal is heated until it converts from ferrite to austenite, then cooled too rapidly for it to reform ferrite at the surface, leaving it in the metastable state of martensite, which is much harder than ferrite. (Sometimes the term “case hardening” is also used for quenching only the surface of a piece of metal.)
Another is “work hardening” by hammering the surface (“cold working” or “cold forging”), but typically the resulting hardening is relatively small. Cutting highly work-hardenable metals like copper is difficult, because work hardening hardens the surface as soon as you have cut it, and perhaps even before; consequently, the carburization and quenching processes described above are the ones used for cyclic fabrication systems. Work hardening plays many critical roles in metallurgy, but historically not in CFSs.
(Other forms of hardening, such as precipitation hardening, are not applicable to iron and ordinary steels, though they are applicable to some other alloys, like 17-4 stainless and beryllium copper.)
So the cycle here is that hardened steel cuts unhardened steel, and then quenching or carburizing unhardened steel makes hardened steel.
As mentioned above, sandcasting is a common CFS, in the sense that once you have a pattern for a castable shape, you can ram soft greensand around the pattern in a flask to make a mold, disassemble the flask, remove the pattern, reassemble the flask, and pour molten metal into it to reproduce the shape of the pattern — first perhaps arsenical bronze, but also copper, and more recently tin bronze, cast iron, tin, pewter, pot metal, Zamak, pig iron, high-silicon aluminum alloys, brass, and so on.
Greensand is sand (typically quartz; minerals that outgas at high temperatures such as calcite or gypsum are forbidden) containing a small amount of wet clay as a binder. There is little enough clay so that the mold is very porous, thus permitting easy passage of gas through the sand, among other things to allow the mold to dry before casting. Typically the clay used is bentonite, since it can function as a binder at the lowest levels, and those levels are low enough that its expansivity is not a problem.
Aside from the raw materials, sandcasting requires minimally a pattern, a riddle, a ram, a flask, a crucible, and a kiln (called a “furnace”). The crucible and the furnace are necessarily formed of refractory materials, and in usual practice must be exposed to air, so pottery is the traditional material for them, making this CFS dependent on the pottery CFS when used for ferrous metals; the non-ferrous metals mentioned above can instead use ferrous crucibles, and in theory could use ferrous furnaces as well, but pottery is much more practical. The pattern and flask are traditionally made of wood, but metal would also work fine. The ram can be made of wood or metal. The riddle probably cannot be practically cast of metal, because it needs to have many small holes, and casting is bad at those. The standard nowadays is to use a riddle of woven wires on a wooden frame, but I think you could make one of fired clay (though my first attempt to do so was not very successful) or woven flax sized with some kind of abrasion-resistant coating.
In sandcasting, although the mold is destroyed when the casting is shaken out of it, the pattern can be reused many times. Nowadays the patterns are often 3-D printed, but another bootstrapping option might be to carve the pattern from foamed pottery.
I think older than sandcasting is lost-wax casting, which is similar, but with a pattern of wax (traditionally a mix of beeswax and pine resin, perhaps with some dry powdered clay as a filler) and a mold of pottery. Rather than removing the pattern from the mold before firing the mold, the wax is simply left in the pattern, where it melts and then burns out, just like the organic fillers used for foaming pottery. This does not permit the reuse of the pattern, but can reproduce finer details than sandcasting, though with worse dimensional precision.
A modern innovation in these processes is “lost foam casting”, where the pattern is burned out as with lost-wax casting, but the mold is sand as with sand casting. By making the pattern from an organic foam such as styrofoam, it produces little enough gas that it need not be removed from the mold ahead of time, but is instead burned out by the hot metal; this eliminates the need for a binder and the need to disassemble the flask, and styrofoam is easier to cut than the traditional wood or, especially, metal.
EDM is capable of holding very tight tolerances (on the order of a micron, or somewhat higher at larger material removal rates) and cutting very hard materials, even diamond. You bring an electrically conductive workpiece together with a tool (“die”) in an insulating liquid, such as diesel fuel or deionized water, holding a voltage across them, until a spark occurs, vaporizing some of both the workpiece and the die. The vapor immediately condenses in the liquid, and some time later you move them toward each other until a new spark occurs somewhere else. This repeats, thus eroding both the workpiece and the die. They never quite make contact, and they never heat up except in a very thin surface layer, so the deformations that limit the precision of mechanical cutting processes are absent.
The die can be of the same material as the workpiece. However, to minimize the necessity to manufacture new dies, it’s desirable to use die materials that are eroded less than the workpiece because of having higher boiling points, higher enthalpy of fusion and/or vaporization, or higher thermal conductivity; graphite, copper, brass, and tungsten-copper are ideal, but even things like aluminum last longer than steel (I think?), which in turn lasts longer than stainless steel, which in turn lasts longer than tungsten carbide and similar materials.
In particular, copper and graphite electrodes can cut steel with almost no wear, removing more than 100× as much workpiece as electrode.
“Small hole EDM” is a variant of this approach, usually categorized
separately, in which the tool electrode is a thin tube used to “drill”
a hole into or through the workpiece. Dielectric fluid is fed through
the tool at high speed. The tool is rotated as it is fed into the
hole, eliminating circumferential variation, and also permitting the
hole to be significantly wider than the tool itself if the center of
rotation is eccentric. EDM drilling can thus produce very accurately
cylindrical holes, even in very hard materials. (And this is a
crucial supporting process for wire EDM, as explained later.)
Small-hole EDM drills are often insulated up to the tip so that the hole only widens near the tip, enabling it to remain the same diameter over a long distance.
Hypothetically, if the die were of a shape that can be produced by helical extrusion, then it could be fed into the cut in the helical path along which it was extruded. The end of the die might be consumed in the process, but, especially for through holes, this is unimportant.
An EDM die can also be moved to cut out a shape as if it were an end mill, known as “orbiting”; if this is done with a die with a thread profile (“EDM tapping”), it cuts a thread into the hole it’s in with the same thread pitch as the die’s thread, but a larger diameter. Small pits in the threads of the die are unimportant, as they will be covered by the orbital motion.
Hypothetically, you could also move the die in two directions of motion at once, as if for lapping; although I do not know of this process being used in practice, the same process could produce three accurately flat surfaces by translating and rotating them relative to each other while using them to erode one another via EDM.
EDM is also done at times with dies that are wheels analogous to grinding wheels; as with grinding wheels, small irregularities in the wheel surface are inconsequential, so they can make surfaces that are more accurately cylindrical than they are themselves. Presumably these EDM wheels must periodically be dressed like grinding wheels, but using EDM rather than grinding. Vollmer calls this process “disc erosion”, and their process uses copper-tungsten wheels and an oil dielectric to sharpen cutting tools made of polycrystalline diamond or tungsten carbide, while Setco calls it “spark erosion grinding” and uses cold-rolled steel wheels and I think a water dielectric to cut delicate metal honeycomb parts for jet engines.
A CFS based on die-sink EDM might be able to use a single conductive material as both a workpiece and a tool, reorienting the tool during the cutting process to produce on it the kinds of radii and edges that will be needed for later features to be cut into the workpiece.
However, a much more efficient die-sink-EDM-based CFS would use at least two materials, one harder and easier to cut with EDM, such as steel or tungsten carbide, and the other softer and more resistant to spark erosion, such as graphite, brass, or copper. A single steel cutting tool can cut hundreds of brass electrodes to precise shapes, and a single brass electrode can erode hundreds of steel workpieces to precise shapes.
However, an EDM machine cannot be made entirely from metal parts, because the only electrical path between the cutting tool and the workpiece must be the cutting arc. Thus some insulating material, such as a plastic or ceramic, is needed to complete the cycle.
(These accounts of EDM-based CFSs take the electronic servo control systems necessary to control the EDM motion as given, a lacuna I will remedy later on.)
In many cases, however, wire EDM supplemented with small-hole EDM is orders of magnitude faster than die-sink EDM. Normally die-sinking EDM is only used to finish parts to final dimensions after cutting them to approximate shape using faster processes.
Wire EDM removes material from a conductive workpiece through the same spark-erosion process as other kinds of EDM, but the tool electrode is a thin brass wire, tens to hundreds of microns in thickness. This wire passes through a thin kerf in the workpiece, cutting it to an arbitrary two-dimensional shape with an arbitrary taper, while running through the workpiece at high speed. Given a starting hole made by some other process, such as drilling or small-hole EDM, wire EDM can enlarge the hole to an arbitrary shape. By cutting a stack of sheets, typically welded together at the edge, wire EDM can cut the same shape into many sheets at once.
The eroded brass wire must be melted and redrawn before being used again, since it has spark-erosion pits at unknown places along its length which could cause it to break if used a second time.
Die-sink EDM can cut arbitrary three-dimensional shapes, while wire EDM is more restricted in the geometry it can produce. But die-sink EDM must vaporize and wash away all the negative space of the desired part, while wire EDM need only vaporize a kerf of tens or hundreds of microns around its surface, thus potentially permitting a speedup of a thousand or so.
Wire EDM and small-hole EDM can cut through a meter or more of material in a single operation, so it’s straightforward to imagine a sheet-cutting operation producing 20,000 identical parts from 50-μm-thick sheet stock in a single operation. (Other sheet-cutting processes, like waterjet, plasma, oxy-gas, bandsaw, and laser, are not so flexible; they tend to blow the layers apart.) But it’s not clear that this would be an especially fast or cheap way to do it.
A CFS based on wire EDM could surely cut most of the parts of the EDM machine itself from steel or brass stock, then assemble them using an assembly system made similarly. The wire itself, if not treated as a “vitamin” provided from outside the system, could be drawn from brass stock using EDM-cut drawing dies. (These might even be workable without small-hole EDM.) Again, I will postpone the question of the necessary control electronics, and again an insulator is required.
As mentioned earlier, grinding plays an important role in modern machining, as does hardening of steels for cutting tools, but its overall cycle is more complex. Metal is mostly cut with a lathe, drill press, milling machine, or hand file, using ceramic/cermet (“hardmetal”) or hardened steel cutting tools (“machining”). These tools are typically shaped and resharpened with a grinding wheel, which can be silicon carbide, cubic boron nitride (“borazon” or “qingsongite”), or diamond, or (for hardened steel tools only) aluminum oxide, garnet, or zirconia†. Aluminum oxide, zirconia, and silicon carbide are the usual materials. This grinding wheel wears and loads, and must be brought back to shape (“dressed”) periodically; Adam Martin of Helical Solutions explains that a diamond grinding wheel requires dressing every 500 to 600 tungsten-carbide tools.‡ Dressing a diamond or silicon-carbide wheel can be done with another silicon-carbide wheel, as Helical does; aluminum-oxide wheels can be dressed with a diamond tool or with a star wheel.
A star wheel is a steel wheel with many points that is free to rotate; bringing it in contact with a spinning grinding wheel sets it to rotating, and its points whack into the surface of the grinding wheel, chipping it and knocking off grains. Moving the star wheel back and forth as it spins evens out the local variations in its shape, making the surface of the grinding wheel accurately cylindrical or conical, depending on whether the movement is parallel to the grinding-wheel axis.
Star wheels can be made by grinding their parts from steel stock and assembling them, or more rapidly by cutting the steel stock with cermet or hardened steel tools.
Grinding wheels are made by casting a mix of abrasive and binder in a mold, and often then firing the piece to harden the binder. The mold can be cut from metal; common binders include clay, magnesium oxychloride, and organic polymer resins including rubbers, and have historically included sodium silicate and shellac; but a wide variety of cements work at low speeds. Historically, grinding wheels were often simply cut from sandstone, whose quartz grains are hard enough to cut steel but not tungsten carbide; they are typically bonded together by calcite deposited hydrothermally. Wheels using the “superabrasives”, diamond and cubic boron nitride, commonly use metals as binders.
As mentioned above, bonded-abrasive sticks can also be used to dress bonded-abrasive grinding wheels. They can be made in the same way as the wheels, but are normally more porous. Traditionally this porosity is achieved in a similar way to foamed fired-clay pottery, with a filler that burns out during firing, but, for low-firing binders like rubbers and shellac, a lower-boiling-point filler such as naphthalene is needed.
Grinding done fast can easily produce temperatures high enough to dissolve diamond into transition metals like iron, so diamond abrasives are usually not used on metals. Cubic boron nitride is nearly as hard and does not suffer from this problem. Also, diamond burns in air at 650°, while boron nitride does not burn at all — it forms an impermeable boria layer (though this melts at 490° and starts vaporizing at 1100°, well below its boiling point of 1860°), then begins to react with transition metals around 1400°.
Silicon carbide abrasives don’t last as long as alumina, accounting for their lower popularity despite their higher hardness.
Sometimes the ratio between the workpiece wear and the grinding-wheel wear is called the “G ratio”; the G ratio depends on the abrasive material, the bond, machining speed, feed rate, and workpiece material. Typical G ratios are 2–200, but can even be smaller than unity. This is orders of magnitude smaller than the ratio between the wear on a machining tool and the chips removed from the workpiece, which is in the neighborhood of tens of thousands up to millions, so in the machine shop grinding is only used as a finishing operation, similar to die-sink EDM. This permits a machining CFS to achieve much higher offspring numbers than a simpler grinding CFS.
So, among the geometry-production CFSs in modern machine shops, we find: hardened steel cuts steel, which is then hardened, then ground with an aluminum-oxide grinding wheel, which in turn is dressed with a steel star wheel, which was also cut with hardened steel; tungsten carbide is ground with a diamond wheel, which is dressed with a silicon-carbide dressing stick, and both the wheel and the stick were cast in steel molds cut with tungsten carbide; silicon-carbide grinding wheels are dressed by grinding them with other silicon-carbide wheels; and many variations.
Tungsten carbide cutters are themselves mostly shaped by other processes and may not be ground at all; in particular, they are mostly made by hot isostatic pressing (“HIP”) of tungsten-carbide powder, cemented with cobalt. This is done mostly with steel equipment made by the processes described above.
† I’m not sure whether zirconia can be used to cut tungsten carbide, why nobody makes grinding wheels out of tungsten carbide, or why zirconia is usually used together with aluminum oxide instead of alone.
‡ However, in the same video, Martin also claims that tungsten carbide is made by sintering tungsten with cobalt, so he may not be an entirely reliable narrator.
This involves several different applications of the same process, one which is somewhat less familiar from daily life than grinding, cutting, and spark erosion. It involves a current between two electrodes in an electrolyte; typically the electrolyte is aqueous, although ionic liquids are possible, including deep eutectic systems.
A paradigmatic case is nickel plating of steel, in which a nickel anode and steel cathode are immersed in a solution of, for example, sodium chloride. The power supply sucks electrons out of the nickel anode, ionizing nickel atoms at the surface of the electrode, which float freely in the electrolyte as positive Ni²⁺ ions, attracted to the negatively charged cathode, where they are reunited with electrons and form metallic nickel again. Thus the anode is gradually dissolved while metal is deposited on the cathode.
In this case the sodium does not deposit on the cathode because it is much easier to ionize — its ionization energy is 495.8 kJ/mol, its reduction potential is -2.71 volts, and its electronegativity is 0.93 Pauling units — not only than the nickel, but even than the water itself. Nickel’s ionization energy is 737.1 kJ/mol (and its second ionization energy is 1753.0 kJ/mol), its reduction potential to the hydroxide is -0.72 volts, its reduction potential to the nickel(II) ion is -0.25 volts, and its electronegativity is 1.91 Pauling units. Water’s reduction potential to electrolyze hydrogen is -0.8277 volts. So nickel precipitates at a lower voltage than is required to produce hydrogen, and hydrogen is produced at a lower voltage than is required to produce sodium, although mercury electrodes can change the situation by amalgamating the produced sodium.
(I’m not sure about this, for a couple of reasons. Nickel cations go into the solution, turning it light green, but the bulk solution does not become positively charged like a positive electret, so either it must be losing other cations like the sodium, or it must be gaining additional anions to compensate, which would have to be hydroxyl anions formed by producing hydrogen gas. But nickel chloride is highly acidic, not basic.)
Because the nickel’s crystal structure is relatively compatible with the steel’s, it can form a strongly adherent film on the surface.
This process, and analogous processes using other metals, is used in seven main ways, three of which are more or less geometry production:
Electroplating of a thin film of metal on the surface of some substrate, which might even be a film of graphite paint. This can be used for appearance’s sake (as in the case of gold-plating base metals for costume jewelry) or to modify some other aspect of the object’s properties. For example, steel thus plated with nickel or chrome is harder and less prone to corrosion. (I think it might also be less prone to fatigue.)
Galvanoplasty of bulk metal shapes, also known as electroforming or electrotyping, where the electroplating action is continued until it is much thicker than just a thin film. Historically geometry was imposed on the resulting shape by depositing it on the inside of a mold, like slipcasting of pottery, or on the outside of a mandrel in the shape of the desired object, but nowadays it should feasible to use electronic control of anode position and current to deposit metal selectively. Electroforming can hit nanometer tolerances, thus being suitable for reproduction even of holograms. Sometimes the term “electroforming” is limited to the case where the mandrel or mold is conductive and “electrotyping” to the case where it is not.
Electrochemical machining simply reverses the roles of the electrodes from galvanoplasty: instead of using the cathode as the workpiece and the anode as the tool, it uses the anode as the workpiece and removes parts of it using the cathode, much like EDM. But EDM passes a current between electrodes separated by a dielectric by producing an avalanche breakdown of that dielectric which produces plasma hot enough to vaporize part of the workpiece electrode and, usually, the tool electrode. ECM, by contrast, passes a current between electrodes separated by an electrolyte, carried by ions. As with EDM, by positioning the tool electrode, erosion can be carried out selectively in some places and not others.
The other uses of electrochemistry are corrosion removal, sacrificial anode corrosion protection, electrochemical batteries, and electrowinning of metals, which are not geometry-reproduction processes and so do not concern us here.
There is a gray area between electroforming and electroplating, “dimensional recovery”, where a film is plated onto a metal part to enlarge it by microns to hundreds of microns. Since the non-mandrel side of the electroformed object has relatively uncontrolled geometry, this is usually preliminary to a later subtractive process such as grinding which produces the final geometry.
The electrochemical processes, both deposition and erosion, take place faster at some places and times and slower at others. They can be limited by ionic availability, especially for deposition, and by voltage. Generally the deposits are smoother when the limit is from ionic availability, while voltage limits tend to deposit dendrites (I do not understand why) so it is common to add organic thickeners to the water as “leveler brighteners” — originally gelatin and nowadays mostly secret chemicals, although some people have reported success with things like dishwashing detergent, vanillin, and corn syrup. (There are other kinds of “brighteners” also used in electroplating which work by other means.)
There have been some experiments using electrochemical machining to shape nonconductive materials such as soda-lime glass; the idea is that the electric field through the workpiece is balanced by an accumulation of ions on its opposite surfaces, one of which (in close proximity to a “cutting” electrode) is attacked by them. Since this section is dedicated to CFSs that are demonstrated to work, I will not further consider here these experiments, nor other possibilities like using anodic dissolution as a source of divalent cations to precipitate silicates, phosphates, organic anions, and so on.
In cases where dissolution of an anode is unacceptable, for example because no suitable anode is available, anodes of graphite, amorphous carbon, platinum, or palladium can be used; these will not dissolve anodically. I assume this is because they’re held together by covalent bonds rather than metallic bonds, but I don’t really know.
Deposition of metal onto the cathode is unavoidable — even coal and graphite can be electroplated, and have been since the very inception of the process — but if the cathode is not itself vulnerable to such erosion, the deposits can be removed thereafter simply by reversing the current.
A simple geometric CFS using electrotyping might make a mold using wax, paint graphite onto it, electrotype copper onto the graphite, remove the copper from the mold, then cast a new wax mold on the copper. A more advanced version that avoids the dimensional-imprecision problem of wax shrinkage would use a parting layer, perhaps of graphite dust, to electrotype copper directly onto copper. My understanding is that this was common practice from a year after the invention of the process in 1848 until the 1930s.
A more complex geometric CFS using electrotyping and electrochemical machining would first use moving electrodes to selectively electrodeposit a metal, such as copper, into a rough pattern, then use electrochemical machining with moving electrodes to trim it to the precise shape. Each of these processes is individually well-explored.
A soft resin such as latex or silicone can form a mold for casting a hard resin such as a polyester or epoxy, and vice versa. Moreover, either type of resin can be used to manipulate the other kind in its semi-polymerized state. Resin polymerization differs from the liquid–solid phase change of conventional forms of casting in that it does not necessarily, or indeed normally, involve any change in dimensions. (Dimensional changes can be achieved by impregnating a soft resin with a solvent before or after casting, respectively shrinking or growing the product.) Resin casting is used by the Grating Lab to mass-produce research-grade diffraction gratings from a single master grating ruled on glass by a ruling engine.
Resin casting can of course also make molds for many other kinds of casting, use forms or patterns made by them, or modify the resin systems with fillers.
There are a lot of other possibilities; I will mention a few of them here.
Selective etching is widely used in semiconductor and MEMS manufacturing; for example, hydrofluoric acid removes silicon dioxide, but not silicon or organic photoresists, while piranha removes organic photoresists but none of the layers in chips, including silicon dioxide. But it’s also used in more prosaic ways: hot water with alum in it, for example, will eat steel but not aluminum, copper, tin, or zinc, a fact commonly used to remove broken drillbits; so you could imagine a CFS using alum in place of grinding to shape steel cutting tools for brass. Nonpolar solvents like carbon dioxide, alcohol, acetone, xylene, or toluene will usually dissolve many nonpolar organic resins but usually not sugar or ionic solids, while polar solvents like water, ammonia, glacial acetic acid, and ionic liquids (including deep eutectic systems) can dissolve many ionic solids like salt, sugar, or potassium silicate, but usually not nonpolar solids.
Bread dough is easy to shape. Calcining bread in a reducing atmosphere produces carbon foam, which is refractory to 6000°, more than hot enough to bake more bread in and even calcine it, or for that matter for casting metals, carbothermic reduction of iron, or even carbothermic reduction of aluminum. On Earth such a device may oxidize on the outside during operation, where it’s exposed to air, but this can be tolerated in various ways: making it large enough to survive one or more operations, coating the outside with a layer of something more resistant to oxidation (but not necessarily heat), or operating it in deep space or in a nitrogen atmosphere, for example. At human scales, amorphous carbon foam is a disappointingly weak material, but this is less of a problem at the micron scale where all the real action is.
Above I mentioned that clay bodies for pottery form a single-material CFS because they can be sintered into a kiln suitable for firing more of the same kind of clay; this is because of a curious property of sintering, that the material being sintered holds its form throughout, though not its dimensions. This is a general property of the sintering process, not limited to clay; granular polymers, glasses, metals, and other ceramics can all be sintered at temperatures below their melting points and while holding their shapes, and this is routinely done in many industrial processes. So in fact nearly any solid can be granulated and used in place of clay with appropriate binders, sintering aids, and atmosphere, and adequate temperature control; thus you can form a furnace capable of doing more of the same kind of sintering.
I have previously written about the possibility of using solid-solution “hardening” on sintered objects. The general outline of the process is that, before sintering, the “green” object contains at least a low-melting sintering aid and a high-melting filler; during sintering, the sintering aid solidifies and densifies the object (perhaps without fully melting, and perhaps partly dissolving the filler). Then you soak the object at a near-sintering temperature for quite a while so that the sintering aid diffuses into the still-solid filler. Given sufficient solubility of the sintering aid in the filler, the interstitial areas with pure sintering aid will disappear, leaving only solid solutions of the two (or more) materials, with the expanded solid grains in intimate contact with one another. For suitable mixtures, the resulting solid solution will remain stable even up to considerably higher temperatures.
If you squint hard enough, you could describe the hardening process of plaster of paris in this way; calcium sulfate hemihydrate is the “filler”, water is the “sintering aid”, and room temperature is the “sintering temperature” at which the water dissolves into the plaster, forming calcium sulfate dihydrate as the solid solution, which then remains stable up to some 150°. I suspect a similar dynamic is at play in the well-known use of boron donors as fluxes for soda-lime quartz glass, which I believe produces a borosilicate glass with a higher softening point than even the original soda-lime glass. (Boria melts at only 450°, but laboratory borosilicate glasses like type-7740 Pyrex can be used up to 500°, soften around 820°, and finally melt at 1648°, a temperature at which neat boria vaporizes rapidly.)
If the sintering aid forms a eutectic with the filler, it need not even be lower-melting; for example, a tiny amount of table salt can be used in this way to stick ice cubes together at temperatures between the melting points of the eutectic (-21.2°) and pure water ice (0°), even though salt’s melting point is higher. The eutectic water-salt solution is initially liquid at the interface between ice and salt crystals, but after several minutes the salt diffuses into the ice until no salt or eutectic is left. So you can do this process at -20° and get a solid that is stable, though weak and creep-plagued, up to 0°.
A very large number of binary, ternary, and quaternary solid-solution systems can be coaxed to perform in this super-sintering way at the right temperature in the right proportions. (The need to control the ice–salt reaction described above to within ±10.6°, i.e., ±3.9%, may be atypically demanding.) Moreover, their properties can be improved further by using the sinterable material itself as a binder for a different filler that is inert at the process temperatures; for example, you could thus use salted ice as a binder for sawdust (pykrete), or brass as a binder for steel (whether in the form of powder, chopped fiber, hollow spheres, solid spheres, some other shape, or some combination).
This is classified as a “geometry” possibility, since the circularity involved is that of using, say, brass tools to give the desired geometry to a “brass clay”, which are then fired in a brass furnace made from the same material, to produce finished brass parts.
Stick, flame, wire, or friction welding might be a plausible way to additively build up the parts of a stick, flame, wire, or friction welder; the only part of the welding apparatus that experiences welding temperatures is the filler metal and the workpieces. As with EDM and ECM machines, parts of the welding machine need to be electrical insulators as well.
Earlier I mentioned that work hardening is not typically used as a way to harden metal so that it can cut or hammer out copies of itself, because the hardening process takes place during cutting or hammering. This may be less of a concern for cyclic fabrication systems than for traditional production systems, because the objective is to maximize reproductive rate rather than tool life, but there’s also another possibility: bending and forming. You could imagine, for example, folding fingers out of aluminum foil which were sufficiently stiff to grasp other aluminum foil and fold it into more fingers, or bending a wire into a tight coil that is then used as a tube to guide other similar wire to be similarly bent. And of course you can clearly use wadded-up aluminum foil to make forms between which you press virgin foil. In cases like these, where it is possible to bring many folds or coils of tool to bear on a single fold or coil of workpiece, work-hardening might be more practical — desirable, in fact, since work hardening is the negative-feedback mechanism that distributes the bending evenly along a curve instead of concentrating it at a kink, as happens when you try to bend a drinking straw.
(Aluminum foil in particular is an appealing raw material for experimentation because it’s cheaply and easily available, ships pre-annealed, work-hardens readily, has good mechanical properties in the tempered state, and is typically of some 10 μm in thickness, with submicron roughness on one side.)
I mentioned foamed clay earlier, as well as carbon foam from bread. Foamed materials have a variety of potentially appealing properties for cyclic fabrication systems: they tend to be much better thermal insulators than the fully-dense material, which helps make chambers capable of heating and cooling; achieving a given stiffness with the foamed material requires much less mass, though more volume, than doing it with the fully-dense material; and they have very appealing cutting properties. Sintering clay or other materials causes them to shrink, and not perfectly uniformly, so it is common to grind sintered parts to precise dimensions after sintering. Foaming greatly facilitates such cutting because the bubbles tend to arrest crack propagation and reduce the material’s hardness. The 25%-dense foamed pottery I made was soft enough to be carved with a fingernail, and it is common for people to cut foamed refractory silica-alumina firebricks with woodcutting tools. Foams also tend to have a Poisson ratio close to 0, which is potentially helpful for dimensional precision. Finally, foams tend to be much more flexible, even elastically, than the fully-dense materials they are made from, which can facilitate the use of flexures.
Polymer-derived ceramics are a very interesting possibility discussed in some detail in Pyrolysis 3-D printing, which also mentions another “supersintering” alternative to the diffusion-based system mentioned earlier: if the “sintering aid” responds to heat by pyrolyzing into a solid substance that is stable to higher temperatures, like the bread dough mentioned earlier, it will produce a solid object with geometry stable up to those higher temperatures. Depending on the geometry and strength of the filler particles, the pyrolysis products need not even be particularly strong to produce a strong object.
I’ve previously written about using various kinds of chemical cements for 3-D printing, whether powder-bed or extrusion, focusing on those that can be activated relatively quickly, including things like double-metathesis reactions, pH-activated gelling agents, heat-induced solvent evaporation, and the precipitation induced by divalent cations in a number of aqueous ionic systems. Almost any of these approaches, if workable, would provide a CFS.
For example, in “Likely-feasible non-flux-deposition powder-bed 3-D printing processes” in Dercuano, I suggested selectively jetting water onto a powder bed consisting of 1.6 kg/l quartz sand, 170 g/l unfired-bentonite clumping cat litter, 270 g/l calcium chloride, and 190 g/l diammonium phosphate, with the calcium chloride wet-mixed with the cat-litter bentonite, then the mixture dried and powdered, then dry-mixed with the other ingredients and thereafter protected from air; perhaps adding a minority of wood flour, I suggested, would help with tensile strength. This mixture was hypothesized to set up rock-solid immediately upon being moistened by precipitating calcium phosphate in the interstices of the bentonite. If such a mixture works and produces a strong solid, you could probably build the entire 3-D printing machine out of it. (Except for the electronics, of course. And perhaps a little sealant for the water pipes.) None of the ingredients or their processing would cause any difficulty to the cemented product, unlike the case with trying to grind steel with the same steel or cast brass into a mold made of the same brass.
The fundamental difficulty of metrology is to make finer measuring instruments. With feedback and incremental refinement, it is easy to make geometry finer than our manufacturing processes: we alternate between measuring the geometry and refining it, thus approaching perfection to within the limits of our materials and measurement capability, however crude our tools may be. Thus, for example, a patient worker with pine pitch, fine abrasive, two glass blanks, a razor blade, and a candle can grind a parabolic mirror to within a fraction of a wavelength of light.
However, making measurement instruments that can measure more finely than our existing measurement instruments can measure, that is a real difficulty. There are many aspects to this difficulty! To name a few axes, there is the kind of quantity being measured: mass, length, volume, luminous intensity, time, angle, information, temperature, frequency, force, pressure, speed, density, voltage, electric current, energy, power, magnetic flux, magnetic flux density, electrical resistance, inductance, capacitance, area, stress, elasticity, tensile strength, compressive strength, roughness, viscosity, refractive index, specific heat, spectral radiance, pH, chemical concentration, magnetic permeability, electrical permittivity, etc.; the measurement to a desired precision of an absolute standard, such as a given number of oscillations of a given spectral line, or the distance traveled by light in a given time; the accurate subdivision of such an absolute standard or a standard derived from it; the shielding, balancing, or cancelation of unwanted effects that disturb a given measurement; the estimation of how successful such efforts have been; and so on.