If you want to form phosphates of calcium, magnesium, or aluminum with a reaction between a finely divided solid and a liquid, for maximum strength, it would be desirable for a maximum amount of the reaction mass to be incorporated into the final phosphate product, and a minimal amount to be lost as waste products. But you’d also like the reaction product to not be too much larger than the original finely divided solid.
What would the ideal materials be?
The phosphate anion alone has a molar mass of 94.9714 g/mol.
Monoammonium phosphate has a molar mass of 115.025 g/mol (containing one phosphate, so it’s 83% phosphate by weight), weighs 1.80 g/cc, dissolves 36g in 100ml of water at 20°, and dissolves 173g in 100ml of water at 100°. So one ml of solid MAP contains 1.49 g of phosphate. It decomposes at 200°.
Diammonium phosphate is 132.06 g/mol (72% phosphate) and 1.619 g/cc, dissolves 57.5g/100ml at 10°, and decomposes at 155°. So one ml of solid DAP contains 1.16 g of phosphate.
Phosphoric acid, of course, has a molar mass of 97.994 g/mol and also contains one phosphate, so it’s 97% phosphate. Its density is 1.834 g/cc when solid. It dissolves 548 g per 100ml of water at 20°, and melts at 40-42.4°, so above that temperature no water is needed at all to make it liquid; but dehydrating it can be very difficult. One ml of solid phosphoric acid contains 1.78 g of phosphate.
Trisodium phosphate is 163.939 g/mol (58% phosphate), has a density of 2.536 g/cc (when not hydrated!), and dissolves 12g/100ml of water at 20° or 94.6g/100ml at 100°. So one ml of solid TSP contains 1.47 g of phosphate.
Disodium phosphate is 141.96/mol (67% phosphate) and 1.7 g/cc and dissolves 7.7 g/100ml at 20°, so one cc of it contains 1.14 g of phosphate.
Calcium weighs 40.078 g/mol.
Calcium chloride is 110.98 g/mol (36% calcium) and weighs 2.15 g/cc (0.8 g Ca/cc), and water dissolves 74.5 g/100ml at 20°. It’s also soluble in acetic acid, ethanol, methanol, pyridine, all kinds of crazy stuff. It’s a sticky pain in the ass to dry out, though.
Slaked lime is 74.093 g/mol (54% calcium) and 2.211 g/cc, so each cc contains 1.2 g of calcium. At 20° water only dissolves 0.173 g/100ml of it, but apparently it’s soluble in glycerol?
Quicklime is 56.0774 g/mol (71% calcium) and 3.34 g/cc (2.4 g Ca/cc) but reacts with water rather than dissolving in it.
Calcium nitrate is 164.088 g/mol (24% calcium) and 2.504 g/cc, so each cc contains only 0.6 g of calcium. Water dissolves 121 g/100ml at 20° or 271g/100ml at 40°.
Calcium acetate is 158.166 g/mol when anhydrous (25% calcium) and 1.509 g/cc (0.4 g Ca/cc) but very hygroscopic, dissolving 34.7 g/100ml in water at 20°.
Calcium formate is 130.113 g/mol (31% calcium) and 2.02 g/cc (0.6 g Ca/cc) and water dissolves 16 g/100ml at 0°. It decomposes at 300°.
Aluminum itself weighs 26.9815384 g/cc, and is a candidate source for aluminum ions. However, it ordinarily resists attack by phosphoric acid reasonably well.
Aluminum trihydroxide is 78.00 g/mol (35% Al) and 2.42 g/cc (0.8 g Al/cc). It starts releasing its hydroxyls at 300°. Water only dissolves 0.1 mg/100ml of it.
Sodium aluminate is 81.97 g/mol (33% Al) and 1.5 g/cc. Its advantage over the hydroxide is that it’s highly water-soluble, especially at high temperature and pH.
(Di)aluminum (tri)sulfate (papermaker’s alum) is one of the standard water-soluble aluminum salts; it weighs 342.15 g/mol (15.8% Al) when anhydrous, and 2.672 g/cc. Water dissolves 36.4g/100ml of it at 20°, making it acidic.
Aluminum (tri)chloride is the other, even more soluble one; it weighs 133.341 g/mol (20% Al) (when anhydrous) and 2.48 g/cc (0.5 g Al/cc). Water dissolves 45.8 g/100ml at 20°. Interestingly, the anhydrous form sublimes at 180°, suggesting the possibility of gassing a mixture with aluminum. However, you cannot dehydrate the hexahydrate by heating it, and the anhydrous compound fumes in moist air! You have to form the anhydrous form anhydrously, perhaps via SHS from copper chloride an aluminum metal.
There are also soluble acetates of aluminum.
Aluminum oxide weighs 101.960 g/mol (53% aluminum) and can be extremely stable, or it can be relatively reactive, depending on how it’s been treated since it was formed. It’s totally insoluble in anything.
Tricalcium (di)phosphate, one possible end goal, is 310.18 g/mol (containing two phosphates, so 61% phosphate by weight, the rest being calcium) and weighs 3.14 g/cc. Its solubility in water is 1.2 mg/kg, which I guess is 0.12 mg/100ml.
Monocalcium (di)phosphate, another, is 234.05 g/mol when unhydrated (81% phosphate) but tends to disproportionate into phosphoric acid and “dicalcium” (di)phosphate, especially above 203°. It’s dramatically more water-soluble than the tricalcium salt, at 2 g/100ml. Soluble acid monobasic phosphates like this may be useful not only as phosphate sinks but also as phosphate sources to calm down the reaction with things like calcium oxide, which might otherwise be too violent.
Dicalcium (mono)phosphate, a third, is actually CaHPO4, 136.06 g/mol (70% phosphate). WP says:
In a continuous process CaCl2 can be treated with [diammonium phosphate] to form the dihydrate:
CaCl2 + (NH4)2HPO4 → CaHPO4•2H2O + 2NH4Cl
A slurry of the dihydrate is then heated to around 65–70 °C to form anhydrous CaHPO4 as a crystalline precipitate, typically as flat diamondoid crystals, which are suitable for further processing.
There’s also a “dicalcium diphosphate”, to which it converts when heated to 240°-500°, which is actually calcium pyrophosphate.
Aluminum orthophosphate (AlPO4) weighs 121.9529 g/mol and 2.566 g/cc, thus being 78% phosphate and 22% aluminum, and containing 2.0 g/cc of phosphate and 0.57 g/cc of aluminum.
Monoaluminum phosphate is commonly used as a refractory cement since Kingery’s dissertation, but unfortunately is not in Wikipedia.
The idea of all this stuff is to form a lasting solid precipitate, especially for 3-D printing applications. There are several possible problems to solve.
The first is reactions that are too slow and allow the materials to escape.
The second is reactions that complete adequately fast, but do not produce enough solid product to form a solid mass.
The third is reactions that are too fast and throw the materials apart rather than producing a solid product.
The fourth is that the phosphate material, even when fully formed, may not be very strong, or may have other undesirable properties such as being electrically insulating.
Inert fillers should help with all four of these problems. The filler particles impede diffusion and convection, allowing more time for the reaction to complete. The new crystals need only bridge the existing filler particles together rather than interlocking with other new crystals. The filler particles add a great deal of thermal mass and reduce the temperature rise associated with any exothermic reaction, allowing even very exothermic reactions to take place safely in the insterstices. And they can contribute many, though not all, desired properties to the finished product.
Kingery’s dissertation used kaolin and quartz sand as fillers for his various refractory “bonds” such as monoaluminum phosphate.
Wet-ground vermiculite may be an expedient functional filler for this purpose, since vermiculite is easy to find and wet grinding is easy to do. I suspect that talc and clays are probably superior for most purposes.
Other promising fillers include apatite, berlinite, synthetic aluminum phosphates, sapphire, quartz sand, mullite, glass fiber, basalt fiber, carbon fiber, recycled glass, glass microspheres, graphite, carbon black, carborundum, and zeolites.