Thinking more about 3-D printing phosphate rocks. The prince of phosphates is the quartz-like berlinite, an aluminum phosphate. Obvious solution: squirt soluble aluminum salts like aluminum chloride into soluble phosphate salts like diammonium phosphate, or vice versa, to precipitate it, maybe in the interstices of some dirt.
(The other soluble aluminum salts are the sulfate, the nitrate, the lactate, and the perchlorate, as well as the alums, and any of them could be used; sodium aluminate might also be worth a mention, since it precipitates out the insoluble aluminum hydroxide gibbsite in anything but a very alkaline environment. Potassium aluminate, which has very similar properties, is sold for phosphorus-precipitation water treatment.)
Next step: what if we produce the aluminum salt electrolytically on demand from an aluminum electrode? Maybe run NaCl over the electrode to produce aluminum chloride or sodium aluminate. Probably you still need to do the electrolysis in a clean chamber and squirt the result into some kind of powder or solution instead of just sticking the electrode into mud and applying a voltage, unless buildup on the electrode itself is what you’re going for.
But producing aluminum itself is costly and demanding in a variety of ways. What if we don’t have aluminum metal, just an aluminum ore like bauxite? Maybe we could electrolytically produce soluble aluminum salts from it and squirt them out; for example, with a chloride electrolyte like NaCl and a silver-plated, gold-plated, or graphite anode, or a sulfate electrolyte and a lead or graphite anode, or a sodium-salt electrode and a steel cathode. The alums occur naturally on Earth in water-soluble form, so in their cases you wouldn’t even need electrolysis.
What if you instead want to extract the phosphate electrolytically? Maybe a slurry of apatite with a sulfate salt (sodium, say) and a lead or graphite anode could solubilize phosphate while immobilizing most of the calcium, and the result could be directly squirted onto a power containing aluminum cations, maybe even in an insoluble form like the trihydroxide, to form the phosphate of aluminum.
You might even be able to carry out both processes simultaneously, thus eliminating the need to neutralize unwanted ions from the other half of the electrolysis.
In both these aluminum-metal-free processes, you could probably skip most or all of the usual refining of the mineral feedstocks, because the usual contaminants either mostly won’t dissolve or won’t harm the desired cement-formation reactions. For example, bauxite often contains troublesome impurities of reactive silica, hematite, rutile/perovskite, and lime, all of whose cations would react with phosphate to form hard, insoluble rocks in much the same way as aluminum. Such a mix might have more favorable properties than pure aluminum phosphate; for example, species like hydroxyapatite that nucleate and grow rapidly could provide early strength, especially if they form acicular or platy crystals, allowing time for slower-growing crystals of other minerals to form over a longer period of time.
Aside from the potential for 3-D printing, this family of processes could also be used for grouting soil to stabilize it as a foundation for buildings or civil-engineering projects like highways.
Massive crystalline berlinite is fairly hard and inert, so if that can be persuaded to form, it should be possible to reveal the resulting shape by abrading or dissolving away the softer or more reactive ingredients.
Another interesting possibility is the mineralization of wood (or other porous substances that are easy to shape, such as carbon foam or plaster of Paris) by soaking such materials into it one after the other (perhaps forcing them in under high pressure), hopefully forming a surface layer of wood enhanced with the incombustible, hard, stiff, insoluble phosphate mineral. This obviously has potential disadvantages: the phosphate is not the only product of the reaction --- aluminum chloride and diammonium phosphate, for example, will also produce ammonium chloride; the solvent remains, and may have difficulty escaping the low-porosity material; and the ingredients may not be completely consumed, and in some cases may attack the wood over time, for example hydrolyzing it.
This sort of thing seems like a potential appealing low-cost hydrothermal route to “ceramic-matrix composites”, somewhat similar to the bargain-basement gypsum remineralization described in Making mirabilite and calcite from drywall. First, layup and fixation of the reinforcing fibers (perhaps zirconia, alumina, mullite, carborundum, graphite, basalt, metals like steel, or ordinary glass fiber), using some sort of very porous adhesive (perhaps a minimal amount of plaster of Paris), and sizing of the fibers with a lower-strength material to enable fiber pull-out. (Traditional CMC manufacturing uses pyrolytic carbon or boron nitride for this sizing.) Second, saturation of the fiber reinforcement with one of the salts that will produce the matrix, followed by drying it to remove the unnecessary water. Third, application of the other salt to form the desired mineral matrix, such as berlinite.
To form large crystals, capable of bridging larger gaps, it’s desirable for reaction conditions to be just barely favorable for crystal nucleation. For some systems, this can be achieved by temperature control, but that seems unlikely to help much in this case, given the very low solubility of the aluminum phosphate in water at any reasonable temperature. If the amount of aluminum phosphate dissolved in the water never rises very high, this could help, although at the cost of making the reaction take a long time. This requires limiting the rate of the reaction that produces it, either (unlikely) by very low temperatures, or by having a very low concentration of one of the ingredients.
For example, if solid gibbsite is the source of the aluminum, you could flow an abundant amount of very dilute diammonium phosphate through it, perhaps forming aluminum phosphate at a low enough rate that nearly all of it would deposit on existing phosphate crystals rather than forming their own. But this might simply encase the gibbsite crystals in an inert layer of berlinite, passivating them. The difficulty with doing this with two water-soluble ingredients is that flowing an abundant amount of a very dilute ingredient through the porous object would wash away the other ingredient.
If it’s possible to supply one of the salts as a vapor instead of a liquid solution, that could perhaps solve this problem, because a low concentration could be applied for a period of time. Aluminum chloride sublimes at 180°, for example, while the soluble phosphate remains liquid even after losing all its water at 212°, so perhaps hot aluminum chloride vapor could form berlinite on phosphate-bearing surfaces in the 100°-200° range.
If using the phosphate as a cement to selectively join an aggregate (a functional filler), obvious candidates for the aggregate include clay grains, quartz, and sapphire, aside from the fibers and whiskers mentioned previously.