I just wrote this long thing in Flux deposition for 3-D printing in glass and metals about a powder-bed 3-D printing technique that deposits a binder that’s completely inert at room temperature, but upon firing the print in a kiln, becomes active. (See also 3-D printing by flux deposition.)
I think there are a variety of other possibilities in powder-bed 3-D printing that have not yet been fully explored.
Powder-bed 3-D printing, in general, consists of depositing one layer after another of powder, alternating with selectively applying some kind of treatment to the top layer of powder which results in causing it to solidify. The classic inkjet-binder-deposition 3-D printing is one example, but selective laser sintering and selective laser melting are other processes in this category.
Sorel cement is a combination of highly water-soluble magnesium chloride (nigari) with highly water-insoluble magnesium oxide (milk of magnesia); it’s a cement similar to Portland cement, but more refractory, less water-resistant (and won’t harden underwater), and nearly twice as strong.
So, although I’d have to investigate more, I think you could use an aqueous solution of magnesium chloride to moisten a powder bed of sand and dry magnesium oxide to form a very strong mortar.
Zinc oxychloride might work in the same way: zinc oxide is insoluble, like magnesium oxide, while zinc chloride is so soluble it’s deliquescent; and zinc oxychloride or zinc hydroxychloride formed in precisely this way was formerly used as a dental cement, like the zinc phosphate mentioned below. Zinc chloride, however, is acidic, corrosive, and a skin irritant, while magnesium chloride is free of these problems. In fact, Sorel investigated zinc oxychloride before settling on magnesium oxychloride!
Instead of squirting binders onto a powder bed like an inkjet printer, you could bang the shit out of it with hammers like a dot-matrix printer, ideally under vacuum so that you don’t generate explosive gas expulsions. The impact will stick together the particles in the vicinity, affecting a total mass of powder material similar to the total mass of the hammer. (This suggests that low-mass hammers are in some sense optimal.)
For beds of metal particles, instead of squirting binders, you could touch the surface of the powder with an electrode and drive a large current into it, sintering the nearby particles together through joule heating of their contact points, like an old-fashioned coherer.
The electrode would probably have to be a carbon rod, since any other plausible material is likely to stop working due to surface oxidation.
This probably won’t produce a strongly bonded part, but might be enough to produce a solid part that can then be solidified further by other means.
A number of anions, such as phosphate, carbonate, and alginate, form water-soluble compounds with monovalent cations like those of the alkali metals (sodium, potassium) and ammonium, while forming water-insoluble compounds with divalent cations like those of the alkaline earth metals (calcium, magnesium). Calcium and magnesium also have highly water-soluble salts, such as their nontoxic chlorides. Phosphate is also water-soluble in the form of phosphoric acid.
This means that by mixing two liquids you can precipitate a solid through a double ion replacement reaction. This is used in molecular gastronomy spherification of foods, forming a flexible calcium alginate membrane around a liquid center with sodium alginate dissolved in it.
(I’m pretty sure this is because these anions are polyvalent and are strongly enough bonded to their cations that they are solvated together with them, rather than separately, so that once the cations are also polyvalent, the individual anions floating around with their individual cation harems are replaced by endless chains in which each cation links together different anions. But I’m no chemist.)
Other polyvalent cations, like Cu₂₊, Zn₂₊, Fe₃₊, Fe₂₊, and Al₃₊, should also work for this. Most of these also have relatively innocuous water-soluble salts; ZnCl₂, Fe(NO₃)₃, Cu(NO₃)₂, FeCl₃, and AlCl₃, as well as blue, white, and green vitriol, of course, which last are innocuous enough to use as nutritional supplements, but are subject to onerous reporting paperwork in places nowadays; acetates of calcium, magnesium, copper, zinc, and ferrous iron (II) are also all soluble, though acetate of zinc only a bit, and acetate of ferric iron (III) not at all. Ferrous citrate is also soluble.
So the plan is that you precipitate a solid cement in the interstices of an aggregate or filler, such as quartz, grog, carbon black, fumed silica, mullite needles, aluminum oxide crystals, rutile needles, zircon crystals, mica, chopped carbon fiber, chopped basalt fiber, chopped glass fiber, powdered graphite, powdered copper, powdered silver, hollow glass spheres, hollow steel spheres, chopped cellulose fiber (such as sawdust), silicon carbide, clay (especially finely dispersed bentonite), diatomaceous earth, etc.; or a mixture. If the cement is relatively inert, unlike the aggressively alkaline slaked lime and portland cement, a wide variety of fillers are possible that couldn't withstand the harsh chemistry of everyday building materials.
Different possible resulting cements include the following; I’m including Mohs hardnesses as an imprecise but readily available and roughly accurate guide to strength:
So you should be able to get relatively high strength, almost as high as portland cement (whose strength comes mainly from belite, which is known as larnite in nature, Mohs 6), by precipitating calcium phosphate crystals from a water-soluble calcium salt such as calcium chloride and a water-soluble phosphate salt such as monoammonium phosphate; you may be able to get a highly refractory bond by calcining the phosphate or carbonate of magnesium into magnesia; you can get an instant nontoxic aqueous elastomeric gel with calcium alginate; you can get biocompatibility (and guaranteed-working recipes) from zinc and magnesium oxides with buffered aqueous phosphoric acid; and there are thirteen other combinations that will probably work as well.
Further alternative polycations might include nickel, mercury, and vanadium ions, but these have some disadvantages (carcinogenicity, higher toxicity) and not much in the way of available information. Further alternative polyanions might include sulfate (which does have some insoluble salts, notably calcium sulfate (gypsum) and barium sulfate), oxalate, silicate (see below), sulfide (soluble with lithium, sodium, and ammonium, but should precipitate transition metals) and perhaps some carrageenans.
Iron sulfide in particular — fool’s gold — is 6–6.5 on the Mohs scale, harder than apatite. It has the disadvantage of gradually oxidizing in air, though, with corrosive results, and of course the soluble sulfides are toxic.
It might be advantageous to work with a mixture that is liquid until the cement is precipitated, rather than consisting mostly of a packed granular filler. This doesn’t exclude the use of fillers; especially bentonite clay can remain in suspension in water up to fairly high concentrations of clay without solidifying the water. It might be worthwhile to mix a little sodium or potassium alginate in with the phosphate so that the initial introduction of the calcium donor will gel things in place in milliseconds and prevent the liquid from flowing further, even if the calcium phosphate or other cement takes some time to fully crystallize. (This might be useful to limit diffusion even in a powder-bed system.)
(The advantage of Newtonian or at least non-thixotropic liquids is that their surfaces are reliably quite flat and horizontal; they have no angle of repose.)
Other plant gelling agents such as pectins and carrageenans can also be precipitated into a gel by pH control and in some cases by polyvalent cations (though there are many different types of pectin and many different types of carrageenan, and they can sometimes react in opposite ways to pH changes), and aluminum sulfate precipitates insoluble, gelatinous aluminum hydroxide when the water is insufficiently acidic. Things like alcohol or salt may be sufficient to precipitate some of these by reducing the amount of water.
It may be desirable to prevent homogeneous nucleation in order for the cement particles to be big enough to bridge the gaps between grains of filler. For of these most cements, if the temperature is kept high enough, cement particles will only nucleate on the surfaces of grains of filler; this may help to produce a solid mass. (More speculatively, pressure control is another possible lever to control nucleation, but this would probably require a liquid-filled chamber.) It may also be possible to solve this problem by making the precipitation mass-transport-limited.
Filler particles with more extreme aspect ratios — clays such as bentonite being the champion here, though a less expansive clay may be more practical for this use — should lower the critical percolation threshold needed to form a solid mass, thus placing less stringent demands on the nucleation process.
Once you have the “green” article made out of filler grains cemented together, you can use water to wash off the unhardened mixture of filler (“powder”) and unprecipitated solute, as well as washing out leftover reaction products other than the cement. Densification may be needed after the initial precipitation, since when the cement precipitates from solution, the water and other solute remain. (For example, if reacting aqueous dipotassium phosphate (which dissolves 150 g per 100 mℓ of water) with calcium chloride to produce hydroxyapatite, you have potassium chloride and water taking up space in the result.) Densification can be carried out by passing a supersaturated solution of the same cement, or a compatible cement, over the printed object once it is removed from the powder bed; or it can be carried out by infusing the pores with a different material, perhaps a melt, again after powder removal.
As an alternative source of polyvalent cations, you could use small anodes of suitable metals (zinc, copper, manganese, or iron, although maybe it might be possible with a suitable alloy of calcium or magnesium) with a controllable current; this might allow you to switch on and off the cementing action with much higher precision and frequency than pumping solute liquids in and out of a pipette or inkjet, and would avoid the need for the extra water content to maintain those cementing ions in solution.
This approach should be especially suitable to introducing controlled amounts of impurities into particular places in the printed object — for example, copper or iron ions would probably produce a bright blue color, or manganese ions a rose-red color. You could probably get a wide variety of other colors by using other metals not otherwise mentioned here; cations introduced for the purpose of adding color need not be polyvalent or form physically strong compounds.
More generally, the precise control of mixing provided by the electrolytic mechanism can be used to produce precisely controlled gradients of material properties in the cementing material, for example to produce controllable optical or acoustic refraction.
In theory you could also use a sacrificial cathode that released anions such as phosphate or carbonate when electrolytically reduced, but that seems much more difficult; I know of no such material.
Water is a terribly convenient solvent for facilitating such double-metathesis reactions, since it’s capable of dissolving a very wide variety of ions, it’s fairly nontoxic, and it is liquid at room temperature. But it has the major disadvantage that it contains oxygen, so to metals like calcium, water is utter death. Other polar solvents might be feasible alternatives; for example, anhydrous ammonia at low temperature and/or high pressure, or molten-salt mixtures like FLiNaK and FLiBe at somewhat higher temperatures, or the truly outlandish polar organic solvent systems used in current lithium-ion batteries.
Cyanoacrylates polymerize in the presence of hydroxyl ions; dripping cyanoacrylate onto NaHCO₃, stealing hydroxyl ions and converting it to sodium carbonate, is a well-known manual additive manufacturing technique which can probably be improved by adding filler to the NaHCO₃.
Waterglass (sodium or potassium silicate) forms a silica gel rapidly upon exposure to CO₂; maybe you can use NaHCO₃ as a CO₂ donor for this purpose. Certainly you can harden it with acids instead, or with ethanol.
There are other materials that harden or recrystallize upon exposure to CO₂, most notably Ca(OH)₂, slaked lime, which produces calcium carbonate. Normally they harden fairly slowly once wet by absorbing CO₂ from the air, but maybe you could get them to harden faster by supplying them with NaHCO₃.
Rather than using chemicals that react immediately on contact, as in the above, or initiating some kind of interaction by slowly heating the entire powder bed after careful deposition, as in Flux deposition for 3-D printing in glass and metals and 3-D printing by flux deposition, it might be worthwhile to use chemicals that can react quite energetically, but which remain almost completely inert during the printing process; and, once the printing is complete, ignite them and allow the self-sustaining reaction to run to completion. The trick is to identify reactions that would produce enough heat to produce interesting materials, but without producing enough gas to blow the nascent object to bits.
Thermites, such as the classic aluminum-powder/magnetite system formerly widely used for welding, are one example; you could selectively deposit aluminum powder into a bed of magnetite, and then ignite the thermite once the printing is done (traditionally, using magnesium ribbon). This produces molten iron and molten (!!) aluminum oxide, which I expect would then quickly quench in the much larger body of magnetite, producing a solid object consisting of a magnetite shell around a core consisting of phases of iron and amorphous or cryptocrystalline corundum; plausibly both phases might initially be continuous, as in an open-cell foam, but the corundum would almost certainly fracture severely during cooling. With some luck, the purified iron thus produced will be sufficiently ductile to remain intact.
(The temperature is 2500° when the oxidizer is hematite rather than magnetite, but I think this is limited by aluminum boiling at 2519° rather than by the energy available.)
Magnetite has some disadvantages; it will melt onto the outside of the printed object, its own properties are not all that desirable, and it adds iron (thus, weight) to the piece. Other oxygen donors might solve or at least ameliorate these problems. However, the traditional alternatives are hematite (red iron oxide), silica, diboron trioxide (boria), a mixture of manganese dioxide with manganese monoxide, lead tetroxide, cupric oxide (CuO, the toxic tenorite), and viridian. Of these, I think silica is the one with the highest melting point (1600°), and it has the benefit of being transparent; but the metallic silicon thus formed is even more brittle than corundum. Viridian and cupric oxide offer the fascinating prospect of 3-D printing in purified chromium and copper, but cupric-oxide thermite can be explosive. Additionally, chromite (FeCr₂O₄) might work — I think aluminothermic reduction of chromite is used for commercial chromium smelting.
Sometimes people use teflon instead of an oxygen donor, thus producing a metal fluoride (and carbon) rather than a metal oxide.
Typically when burning aluminum with quartz as the oxidizer, sulfur is included in an aluminum–sulfur–sand composition; WP claims this functions as an extra oxidizer to add energy, as well as to ease ignition. Sulfur is sometimes used with magnetite, aluminum, and barium nitrate to make “thermate,” a higher-temperature thermite with mostly military uses.
Aluminum is not the only possible fuel metal, only one of the cheapest and safest; other possibilities include zirconium, calcium (!), zinc, titanium, silicon, boron, and magnesium.
Common fillers for thermite welding include high-carbon steel, cast iron, or pig iron, which melt and mix with the purified iron to produce a steel with the desired level of carbon.
Alternatively, at somewhat higher cost, you could attempt to make the oxidizer rather than the metal the limiting reagent — for example, depositing a small amount of magnetite powder in a bed of aluminum powder, rather than the reverse; then, the newly formed material will quench in the aluminum, acquiring an aluminum coating rather than a magnetite coating. This is very risky, though, because the aluminum powder burns fiercely in air. You’d need to do it under an inert or reducing gas, or in vacuum.
The reaction between zinc and sulfur, every chemistry teacher’s favorite, is another candidate. The sphalerite or wurtzite thus produced is a reasonably strong mineral (Mohs 3.5–4). Other metals, such as aluminum and I think iron, have similar reactions, but the sulfides thus formed are less stable and tend to hydrolyze.
Looking at Mercado Libre here in Argentina this weekend (2019-12-13 to 2019-12-15) I found some vendors for most of the materials I mentioned above; today the dollar is around AR$62 bid, AR$67 ask; I'm using AR$64.50/US$ for the conversion. I've ordered the materials I was able to price roughly by price.
(Addendum 2019-12-20: the dollar is AR$73 today. I spot-checked three of the prices below; none of the three have changed, in pesos, although this means they have fallen by something like 10% to 15% in dollars. This clearly means that the error bars on these prices are like 20% or 30%.)
Although there are of course a very large number of combinations drawn from the above that are likely to work, I thought it would be useful to work out some properties and approximate recipes for a few of the variants.
Although mostly I'm considering a binder-jetting process here, keep in mind that in fact the "binder" being jetted is in most cases just water, or water thinned with alcohol, and its only function is to solvate the actual cement grains so that they can react, and in some cases to drive the reaction kinetics toward water-insoluble cement products. In most cases, another polar solvent such as ammonia, or heat from a laser or arc, could be substituted for the water "binder".
Also, many of these mixtures would benefit from additional ingredients; the U Washington Open3DP project has published a number of recipes they found worked well. In many cases, for example, they added carboxymethylcellulose or a similar plant gum to provide both wet strength and green strength.
If we jet water, perhaps thinned with a little alcohol, onto a powder bed made of clumping cat litter, it will clump. If left to dry, perhaps without even depowdering, it will form a dried unfired clay object. If some sand or grog is included, this object can even be strong enough to survive handling, and such additives will also reduce shrinkage on drying, as would non-expansive clays.
This is the classic cal y arena mortar, cured by absorbing carbon dioxide from the air, mostly in 24 hours. It has the attractive feature of being bright white. I think U Washington Open3DP has done some work with this recipe.
This is the classic hydraulic mortar; it sets up faster if you add some slaked lime.
Upon jetting water thinned with a little alcohol onto this dry powder-bed mixture, ammonium chloride and calcium phosphate are formed; bentonite crystals serve to provide extra nucleation centers for the precipitating calcium phosphate, to bridge gaps between precipitate crystals (especially initially, when they are small), to add tensile strength to the weaker calcium phosphate crystals, and to stop the propagation of cracks through the calcium phosphate. The highly soluble ammonium chloride remains in solution in the pore water; if desired, it can be leached out later by immersing the finished part in water. The quartz sand fills the majority of the material and provides mostly compressive strength. The wood flour serves to reduce density and provide tensile strength, like collagen in bone.
The mixture is kept dry and must be protected from air exposure when not in use, because the calcium chloride is deliquescent at ordinary humidities; even then, the ammonium has a limited shelf life, especially when warm.
The needle-like morphology of typical apatite nanocrystals is well-suited for bridging gaps between clay particles and other fillers, and would pose no barrier to further diffusion to carry the reaction to completion; even the platelet-like morphology that sometimes occurs with apatites and often with triclinic octacalcium phosphate would work well. The spherical morphology that occurs with amorphous tricalcium diphosphate (called tricalcium phosphate, TCP) would be pessimal, and when TCP precipitates from aqueous solutions, it always precipitates in amorphous form, requiring heat-treatment to crystallize. Apatite is favored at high pH; TCP is favored at more acidic pH; and OCP is favored in between, at a slightly acidic pH.
Calcium chloride is CaCl2, with a molar mass of 111 and a solubility of 650 g/liter of water at 10°; diammonium phosphate is (NH4)2HPO4, with a molar mass of 132 and a solubility of 575 g/liter of water at 10°. Hydroxyapatite, which is the mineral cement we are hoping for, is Ca5(PO4)3OH, with a Ca:P ratio of 5:3 and a molar mass of 502; Wikipedia says it is commonly prepared as nanocrystals from a mixture of calcium nitrate and diammonium phosphate, including at non-stoichiometric ratios. So for every 5 moles (555 g) of calcium chloride we want 3 moles (396 g) of diammonium phosphate and get some miscellaneous products plus one mole (502 g) of hydroxyapatite, 10 moles of chloride ions, and 6 moles of ammonium ions, which I think will result in 6 moles of ammonium chloride (53.5 g/mol, so 321 g) and 4 moles of excess chloride. Also we have a couple of extra hydrogens floating around, so maybe we'll get hydrochloric acid or something; might be a good idea to include some calcium hydroxide or something if that's happening. (I should work out the side products in more detail; the formation of chlorapatite rather than hydroxyapatite may be a possibility, and seems guaranteed if you heat the result to dissociate the ammonium chloride.)
Solvating that amount of calcium chloride simultaneously would take 850 g of water, and of diammonium phosphate, 690 g of water, at 10°. So, dividing, for every gram of hydroxyapatite, we need 3.1 g of water, 1.1 g of calcium chloride, and 0.79 g of diammonium phosphate. Actually we might need somewhat more or somewhat less water than that: more because some of the water molecules are tied up by the "pore walls" of the bentonite, or less because when hydroxyapatite precipitates out of solution, the water remains to solvate new calcium chloride and diammonium phosphate. It will gradually become saturated with ammonium chloride (solubility: about 240 g/liter at 10°) and lose its ability to solvate more calcium and phosphate so they can react.
I'm not sure whether you would expect such a water deficiency to also slow the formation of the calcium phosphate crystals, allowing them to grow larger, by limiting the speed at which calcium phosphate can diffuse to the crystal growth sites, or to result in smaller crystals because the solution is more fully saturated. Both seem worth a try. Also, though, the papers I've seen on hydroxyapatite wet precipitation, like Poinern et al. 2009, required hours for the crystallization to produce particles of tens to hundreds of nanometers, and ideally we'd like it to happen at subsecond time scales, or in minutes at most. (But Victor Chen's YouTube demo of reacting sodium phosphate with calcium chloride produced a solid and completed within a few seconds; similarly Arieus Alcide's reacting calcium gluconate with potassium phosphate produced a white precipitate instantly.)
(Carbonates or hydroxides might work to liberate ammonium from the solution, and would prevent the pH from dropping (Hielscher's sono-synthesis report says they tried to keep their pH around 10 with NaOH in order to get hydroxyapatite instead of a different calcium phosphate) but the chlorides they formed would also be soluble, except in a few problematic cases like chlorides of silver, thallium, lead (plumbous, II), mercury (I) (calomel), and copper(cuprous, I), all of which are alarmingly toxic, absurdly expensive, or both. Also, I suspect any of these would form soluble complexes with the ammonium ligands, leaving us back where we started. Perhaps it would help to use trisodium phosphate, which is pretty alkaline, in place of some or all of the diammonium phosphate.)
The apatite crystals can incorporate a little magnesium, which can transform them into whitlockite, but it is reported to inhibit apatite nucleation and growth, as does carbonate. Magnesium I think favors the precipitation of tricalcium phosphate, since β-TCP shares whitlockite's crystal structure.
So, if the amount of water is about right --- as set by the amount of pore space available for the reaction --- then every 5 kg (or, say, 5 nanograms) of pore space will produce 1 kg (or, respectively, 1 ng) of cement. Because hydroxyapatite has a density of about 3.2 g/cc, this means that the cement will fill up only about 8% of the pore space, so we'd better hope that we can get by with a smaller amount of water.
(8% was arrived at as follows: anhydrous calcium chloride weighs 2.15 g/cc, and undissolved diammonium phosphate weighs 1.619 g/cc, so the 5 g of solution that yielded each gram of hydroxyapatite actually occupied 4.1 milliliters before the water began to solvate the salts, and the gram of hydroxyapatite occupies 1 ml/3.2 = 0.31 ml, which works out to about 7.6%.)
How much pore space is there? Building sand weighs d = 1.52-1.68 g/cc (see also rfcafe), which suggests a void fraction of (1 - d/2.4) = 30% to 37%, 2.4 g/cc being the density of quartz; let's say one third. The bentonite particles might occupy 50% of the remaining space, one sixth of the total, and the phyllosilicate bentonite crystalline material might have a density of 2 g/cc (I'm not sure). Let's forget about the sawdust for the time being. So we have one sixth of the space available as pore space.
For each 4.1 milliliters of pore space, we need 1.1 g of calcium chloride and 0.79 g of diammonium phosphate. So for each milliliter of powder, we need 270 mg of calcium chloride, 190 mg of diammonium phosphate, 1600 mg of construction sand, and 170 mg of bentonite cat litter. Or, per liter of mix:
| Ingredient | Mass/liter | US$/kg | US$/liter |
|---|---|---|---|
| Sand | 1.6 kg | 0.012 | 0.019 |
| Cat litter | 170 g | 1.30 | 0.22 |
| CaCl2 | 270 g | 1.60 | 0.43 |
| (NH4)2HPO4 | 190 g | 0.90 | 0.17 |
| Total | 2.23 kg | 0.84 |
It's probably important to make sure that the formation of the calcium phosphate take place mostly between the bentonite grains. In the powder bed, the bentonite is I think unavoidably going to be aggregated into clumps of tens to hundreds of microns in size, and water, when wetting the powder, will reach the centers of those clumps last. But the centers of those clumps are precisely where the calcium phosphate is most needed --- in other places it runs the risk of forming crystals that don't attach to anything. I think the way to solve this is to thoroughly wet-mix the calcium chloride into the bentonite before drying the bentonite and breaking it into those clumps; then mix the clumps with the sand and the crystals of diammonium phosphate. That way, when the water wets the powder, it will first dissolve all the diammonium phosphate, then begin to diffuse into the bentonite clumps, where it can cement them by forming calcium phosphate there.
If the bentonite in question is not already a calcium bentonite, it may eat some of your calcium in this process, diffusing out sodium to replace it, so you may need to use somewhat more calcium than suggested.
We can see that if we were to replace all the sand 1:1 with sawdust, assuming 1 kg/liter, it would add US$0.16 to the cost and bring it up to US$1/liter. However, sawdust has much higher porosity than sand, so it would also increase the amount of bentonite and cement that could be included; perhaps the cost might increase to as much as US$2/liter.
The diammonium phosphate mentioned above contains one phosphorus atom per 132-dalton formula unit, and additionally it needs more than its own mass in water to dissolve it. Phosphoric acid also contains one phosphorus atom per molecule, but its molecules are only 98 daltons, and it only needs a very small amount of water. So if diammonium phosphate costs US$0.90/kg, phosphoric acid could cost as much as $1.20/kg and still actually be cheaper. But in fact phosphoric acid costs US$2.60/kg.
Jetting 85%-pure phosphoric acid out of nozzles is not going to work; it's too viscous. But you could maybe use powdered solid phosphoric acid. However, although it's not toxic, it's pretty caustic; most of the other chemicals described above are less dangerous.
Rey, Combes, Drouet, and Grossin explain that the usual way to deposit apatites in lab wet synthesis, with also some use in industry, is by reacting calcium nitrate with an ammonium phosphate; one reason for this is that nitrate and ammonium groups are easily driven out of the reaction product by heating. Calcium nitrate at US$1.70/kg would seem to be very nearly the same price as calcium chloride at US$1.60/kg, but calcium chloride's molar mass is 111 (or 219 as hexahydrate), while calcium nitrate's is 164 (or 236 as tetrahydrate), so you get considerably less calcium for your money unless that calcium chloride is fully hydrated and the nitrate is desiccated.
The bigger issue is that nitrates are a certain amount of hassle to deal with, due to both their toxicity to the humans and ongoing chimpanzee dominance games the humans like to play.
There are presumably cases where the greater ease of driving nitrate residues out of the structure is a decisive advantage, however.
Grover et al. at Argonne published a paper in 1999 on this, reporting a rather astonishing result: "We hydrothermally cured a mixture of Al2O3 and H3PO4 solution between 130°C and 150°C to form a hard and dense berlinite-bonded alumina ceramic." I would not have thought that phosphoric acid could attack sapphire so easily, much less that the result would be a low-temperature way to bond alumina grains. They got a "putty-like" gel of aluminum phosphates after heating alumina in aqueous phosphoric acid, which could dry (to a hydrated xerogel I suppose) and then redissolve in water; by heating it to 150° they drove off not only the water but also the remaining hydrogen, converting the water-soluble aluminum phosphates into berlinite, aluminum orthophosphate, AlPO4, which is covalently bonded to the remaining alumina.
This is such an astounding development that I wonder why I haven't heard of it before; perhaps it has some fatal flaw not mentioned in the paper. The cement described would cost close to US$3 per kilogram and requires baking to cure, so it's not going to replace portland cement unless some material prices change dramatically, but it's both cheaper and presumably much stronger than common petroleum-based plastics, while sharing most of their advantages, although requiring a slow curing process to reach its full strength.
It might work for a variant of this binder-jetting process, too. Although the soluble aluminum phosphates are probably too syrupy to squirt out of jets, you can reportedly dry them to a hard, rocky form that dissolves again in water; squirting water onto it may be sufficient to stick particles of a filler such as sapphire together into a green body that can then be baked at 150°, perhaps with a preliminary aging step. And, like the processes described in 3-D printing by flux deposition, it might be possible to bake the whole powder bed, since the water is an essential reagent in the hardening process; if this works, it would make the green strength irrelevant, but might irreversibly cure the unused aluminum-phosphate binder. And of course you can use an FDM-like selective paste deposition process like those used for adobe and clay-paste "3-d printing".
More on this berlinite-gel process in Berlinite gel.
The double-metathesis-type reactions described above might be a more comfortable way to precipitate aluminum phosphates in situ than pressure-cooking alumina in strong phosphoric acid for several days. For example, you could produce an aluminum phosphate by mixing solutions of aluminum chloride and diammonium phosphate --- even if the aluminum phosphates you get are water-soluble, they won't be nearly as water-soluble as the reagents, so you might get enough precipitation. But it seems likely that, without baking, you'll only get soluble aluminum hydrogen and dihydrogen phosphates.
You should be able to make a kind of inexpensive waterproof fiberboard by precipitating apatite between the wood fibers in the same way described above, but a larger fraction of the resulting substance will be made of apatite, because you don't have sand grains taking up two thirds of the volume. Sodium bicarbonate can keep the combination alkaline, like trisodium phosphate above, which not only favors the precipitation of apatite rather than less-stable calcium phosphates, but also protects the wood fiber from acid. Bicarbonate will buffer the system, preventing it from becoming too alkaline, and additionally serves as a fire retardant.
The elasticity of the mix may pose problems for a powder-bed 3-D printer, since it will spring back after you compact it. You can compact the whole mass at the end of the process, squeezing both air and water out of the mix and causing the water to spread somewhat. The alternative of maintaining the bed under compression while you squirt binder onto it seems impractical. Just adding binders like carboxymethylcellulose won't help because it's the dry part of the powder bed that causes the problem.
A reasonable mix might be 500 g sawdust, 100 g sodium bicarbonate, 235 g calcium chloride, 165 g diammonium phosphate; this works out to US$0.80/kg.
These two soluble chemicals (Epsom salt and washing soda) ought to form magnesium carbonate (magnesite). Magnesium sulfate is US$0.90/kg and sodium carbonate is US$4/kg. I haven't worked out the stoichiometry, but probably the article of commerce is the heptahydrate, which will have an impact on that.
At respectively US$1.70/kg and US$2.30/kg, with some luck, these two highly soluble salts should react to make an insoluble basic copper phosphate, the deep green pigment pseudomalachite and its polymorphs ludjibaite and reichenbachite, Cu5(PO4)2OH4. Again, I haven't worked out the stoichiometry.
Brass filings can be bought as cheaply as US$4/kg. There are a couple of ways you could easily melt a controlled-size spot on the surface of a bed of brass filings using a carbon-rod or TIG electrode. First, you could charge up a capacitor and move the rod closer to the surface until there is an arc, with the rod being positive and the filings being negative; this will deposit most of the energy into the filings. Second, you could bring the rod into contact with the filings, run a current through the rod and an inductor, and then break contact, again inducing an arc, again with the electrons impacting the rod and the ionized air or other gas molecules impacting the filings. In each of these cases the spot size is controlled by the amount of energy built up in the energy-storage device.
Third, you could run an arc more or less continuously from the electrode to the bed, as in normal TIG welding or carbon arc gouging.
Lead particles in the powder bed might help with the sintering; I think molten lead can dissolve a signficant amount of copper, and I don't know about zinc (see Filling hollow FDM things with other materials and A phase-change soldering iron for more on related systems). If so, as described in 3-D printing by flux deposition, it might be possible to later bake the finished piece to induce the lead to diffuse away from what were initially the sintering boundaries, thus preventing the evolution of any liquid until a substantially higher temperature.
Other powdered metals, such as copper, lead, stainless steel, steel, or aluminum, would also work to a greater or lesser extent, but steel and aluminum are relatively hazardous and would probably need to be done under an inert gas such as argon.