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Likely-feasible non-flux-deposition powder-bed 3-D printing processes
=====================================================================

I just wrote this long thing in `glass-fluxing-3d-printing` 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 file `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.

Magnesium oxychloride (Sorel cement) or zinc oxychloride
--------------------------------------------------------

[Sorel cement][0] is a combination of highly water-soluble [magnesium
chloride][1] (nigari) with highly water-insoluble [magnesium oxide][2]
(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.

[0]: https://en.wikipedia.org/wiki/Sorel_cement
[1]: https://en.wikipedia.org/wiki/Magnesium_chloride
[2]: https://en.wikipedia.org/wiki/Periclase

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!

Selective hammering
-------------------

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.)

Selective electrical sintering
------------------------------

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][3].

[3]: https://en.wikipedia.org/wiki/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.

Cement precipitation by cross-linking with calcium or other polyvalent cations
------------------------------------------------------------------------------

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][4].  This is used in
[molecular gastronomy spherification][5] of foods, forming a flexible
calcium alginate membrane around a liquid center with sodium alginate
dissolved in it.

[4]: https://en.wikipedia.org/wiki/Salt_metathesis_reaction
[5]: https://en.wikipedia.org/wiki/Spherification

(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.)

### Candidate cements and fillers ###

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:

- [Aluminum phosphate] — the rare mineral berlinite, with Mohs
  hardness 6.5, or, when hydrated, the unusual mineral variscite, with
  Mohs hardness 4.5, used as a dental cement; or, sometimes, aluminum
  triphosphate, aluminum hexametaphosphate, or aluminum
  tetrametaphosphate.
- [Calcium phosphate] — probably hydroxyapatite, like tooth enamel, Mohs
  hardness 5; can incorporate iron(II) and manganese substituting
  freely for calcium to form the equally hard graftonite;
- [Calcium carbonate] — calcite, Mohs hardness 3;
- [Calcium alginate] — a silicone-like insoluble, nontoxic organic
  water-gel-forming elastomer;
- [Ammonium magnesium phosphate] — the light, very soft (Mohs ≤ 2)
  mineral struvite, which might be formed if ammonium phosphate is the
  phosphate salt used;
- [Magnesium phosphate] is a GRAS food additive for buffering acidity,
  but I don’t know anything about its mechanical properties;
- [Magnesium carbonate] — the soft mineral magnesite, Mohs hardness
  3.5–4.5, which can be calcined at only 500–800° to magnesium oxide,
  or magnesia alba ([periclase][2], as mentioned above), which doesn’t
  melt until 2852° and is used as a stronger alternative to gypsum in
  drywall;
- [Calcium magnesium carbonate] — the mineral dolomite, Mohs 3.5–4,
  which probably will *not* form even if its constituents are
  available (because it’s picky about crystallizing);
- Magnesium alginate ought to exist and be similar to calcium
  alginate;
- [Copper phosphate] — a blue-to-green insoluble copper salt;
- [Copper carbonate] — a bright blue to green pigment, depending on
  degree of hydration, occurring as malachite and azurite in nature
  (which differ in their degree of carbonation); “very sensitive to
  acids”.  Mohs 3.5–4.
- [Zinc phosphate] — one of the oldest and most widely used dental
  cements, so nontoxic and biocompatible, made in something like the
  way I’m suggesting here (mixing zinc oxide and magnesium oxide
  powder with buffered aqueous phosphoric acid); occurs naturally as
  the rare mineral hopeite (Mohs 3–3.5);
- [Zinc carbonate] — the mineral smithsonite (Mohs 4.5), one of the two
  minerals known as calamine (the other being zinc silicate);
- [Ferric phosphate] — non-toxic, except to mollusks, and sometimes used
  as an iron nutritional supplement, but almost insoluble in
  water; “heterosite” or “wolfeite”?
- [Ferrous phosphate] — the soft deep blue to bluish green mineral
  vivianite, used to kill garden slugs, Mohs 1.5–2;
- [Iron carbonate] — the dense yellow mineral siderite, Mohs 3.75–4.25;
- [Manganese carbonate] — the rose-red mineral rhodochrosite, Mohs 3.5–4.

[Aluminum phosphate]: https://en.wikipedia.org/wiki/Aluminum_phosphate
[Calcium phosphate]: https://en.wikipedia.org/wiki/Calcium_phosphate
[Calcium carbonate]: https://en.wikipedia.org/wiki/Calcium_carbonate
[Calcium alginate]: https://en.wikipedia.org/wiki/Calcium_alginate
[Ammonium magnesium phosphate]: https://en.wikipedia.org/wiki/Ammonium_magnesium_phosphate
[Magnesium phosphate]: https://en.wikipedia.org/wiki/Magnesium_phosphate
[Magnesium carbonate]: https://en.wikipedia.org/wiki/Magnesium_carbonate
[Calcium magnesium carbonate]: https://en.wikipedia.org/wiki/Calcium_magnesium_carbonate
[Copper phosphate]: https://en.wikipedia.org/wiki/Copper_phosphate
[Copper carbonate]: https://en.wikipedia.org/wiki/Copper_carbonate
[Zinc phosphate]: https://en.wikipedia.org/wiki/Zinc_phosphate
[Zinc carbonate]: https://en.wikipedia.org/wiki/Zinc_carbonate
[Ferric phosphate]: https://en.wikipedia.org/wiki/Ferric_phosphate
[Ferrous phosphate]: https://en.wikipedia.org/wiki/Ferrous_phosphate
[Iron carbonate]: https://en.wikipedia.org/wiki/Iron_carbonate
[Manganese carbonate]: https://en.wikipedia.org/wiki/Manganese_carbonate

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.

### Liquid tank systems ###

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.

### Nucleation control ###

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.

### Densification ###

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.

### Electrolytic injection of cations ###

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.

### Alternative solvents ###

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.

Bicarbonate as a hydroxyl donor
-------------------------------

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.

Bicarbonate as a CO₂ donor
--------------------------

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.

Metastable redox systems such as thermites
------------------------------------------

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 file
`glass-fluxing-3d-printing` and file `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.

[WP claims]: https://en.wikipedia.org/wiki/Thermite

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.

Some materials pricing
----------------------

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%.)

- Silica sand for construction (not very pure, but without stones or
  salt) has costs that vary greatly by location, but are generally
  around
  [AR$1200/m<sup>3</sup>](https://articulo.mercadolibre.com.ar/MLA-768679609-arena-fina-para-construccion-por-m3-zona-norte-_JM#position=10&type=item),
  which works out to about AR$750/tonne at 1.6 g/cc, or AR$0.75/kg
  (US$0.012/kg).
- Portland cement costs
  [US$9.64/kg](https://articulo.mercadolibre.com.ar/MLA-797321571-cemento-loma-negra-x-50kg-_JM#position=6&type=item)
  (US$0.15/kg).
- Calcium hydroxide (slaked lime) costs
  [AR$7.8/kg](https://articulo.mercadolibre.com.ar/MLA-757939942-cal-comun-hidrat-25kg-materiales-moreno-_JM?quantity=1#position=6&type=item)
  (US$0.12/kg).
- Fine pine sawdust costs around
  [AR$10/kg](https://articulo.mercadolibre.com.ar/MLA-780311310-aserrin-fino-o-harina-de-madera-_JM?quantity=1#position=3&type=item)
  (US$0.16/kg) although prices vary by a factor of 2 or 3.
- Coke (carbon) costs
  [AR$45/kg](https://articulo.mercadolibre.com.ar/MLA-705399385-carbon-de-coque-ideal-para-fragua-herreria-cuchilleria-_JM#position=6&type=item)
  (US$0.70/kg).
- Magnesium sulfate (Epsom salt) costs
  [AR$116/kg](https://articulo.mercadolibre.com.ar/MLA-799605787-sales-de-epsom-sulfato-de-magnesio-x-1-kg-cerveza-beerman-_JM?variation=40283751673&quantity=1#reco_item_pos=1&reco_backend=machinalis-seller-items&reco_backend_type=low_level&reco_client=vip-seller_items-above&reco_id=12377ec4-2ff4-4b43-8da2-72e510d1c6cc)
  for beer brewing or
  [AR$112/kg](https://articulo.mercadolibre.com.ar/MLA-734568990-sales-de-epson-sulfato-de-magnesio-1-kg-en-caba-belgrano-_JM#position=22&type=item)
  as medicine or
  [AR$83/kg](https://articulo.mercadolibre.com.ar/MLA-782695567-fertilizante-sulfato-de-magnesio-1kg-hidroponia-fertirriego-_JM#position=1&type=item)
  or as low as
  [AR$60/kg](https://articulo.mercadolibre.com.ar/MLA-743192007-fertilizante-sulfato-de-magnesio-25-kg-_JM#position=4&type=item)
  as a hydroponics fertilizer (US$0.90/kg).
- Diammonium phosphate costs
  [AR$150/kg](https://articulo.mercadolibre.com.ar/MLA-788997362-fosfato-diamonico-bertinat-x-1-kg-_JM#position=3&type=item)
  as a hydroponic fertilizer or
  [AR$60/kg](https://articulo.mercadolibre.com.ar/MLA-740956087-fosfato-diamonico-profertil-x-25-kg-fertilizante-siembra-_JM#position=5&type=item)
  in bulk (US$0.90/kg).
- Magnetite is I think
  [AR$70/kg](https://articulo.mercadolibre.com.ar/MLA-687582531-oxido-de-hierro-magnetico-color-negro-_JM?quantity=1#position=1&type=item)
  ("oxido de hierro magnetico color negro") but it isn't totally clear
  whether the AR$350 price is for a 5-kg bag or not.  (US$1.10/kg)
- Sodium silicate solution (waterglass) costs
  [AR$72/kg](https://articulo.mercadolibre.com.ar/MLA-614113867-sikafloor-cure-hard-24-20kg-curador-silicato-sodico-hormigon-_JM?quantity=1#position=10&type=item)
  for waterproofing and surface-hardening concrete ("curador
  silicato", in this case Sikafloor CureHard 24).  (US$1.10/kg)
- Quicklime, calcium oxide, costs
  [AR$75/kg](https://articulo.mercadolibre.com.ar/MLA-785354481-cal-viva-en-piedra-4-kilos-_JM#position=3&type=item).
  (US$1.20/kg).  Note that this is almost ten times the price of
  slaked lime, suggesting that either the slaked lime is adulterated
  or the safe handling of quicklime is very costly.
- Bentonite clay costs
  [AR$232/kg](https://articulo.mercadolibre.com.ar/MLA-726626245-bentonita-uso-alimentario-por-1-kilo-para-vino-artesanal-_JM#position=16&type=item)
  or more when food-grade, but as clumping cat litter, only
  [AR$83/kg](https://articulo.mercadolibre.com.ar/MLA-827234517-piedras-aglomerantes-para-gatos-bentonita-cancat-x-24kg-_JM#position=27&type=item)
  (US$1.30/kg).  The cat litter might be contaminated with other
  clays, with silt, or with sand, but for these purposes that might be
  acceptable.
- Aluminum in ingots costs
  [AR$100/kg](https://articulo.mercadolibre.com.ar/MLA-769852785-lingotes-de-aluminio-_JM?quantity=1#reco_item_pos=0&reco_backend=machinalis-seller-items&reco_backend_type=low_level&reco_client=vip-seller_items-above&reco_id=de0ed817-5520-473d-be6b-f9028b946fdd)
  (US$1.60/kg).
- Calcium chloride costs
  [AR$106/kg](https://articulo.mercadolibre.com.ar/MLA-801292925-cloruro-de-calcio-5-kg-anti-humedad-microcentro-oferta-_JM#position=1&type=item)
  as a desiccant (US$1.60/kg), or
  [AR$125/kg](https://articulo.mercadolibre.com.ar/MLA-801293094-cloruro-de-calcio-1-kg-anti-humedad-microcentro-oferta-_JM#position=2&type=item)
  if you only buy one kilo.  For beer brewing they charge
  [AR$165/kg](https://articulo.mercadolibre.com.ar/MLA-799700836-cloruro-de-calcio-x-1-kg-sales-cerveza-beerman-_JM?quantity=1#position=5&type=item)
  which seems like it might be purer.  For bath salts,
  [AR$155/kg](https://articulo.mercadolibre.com.ar/MLA-692807595-cloruro-calcio-5-kg-antihumedad-quimicaxquimicos-_JM?quantity=1&variation=38352669199#position=7&type=item)
  with a purity of 77-80%.
- Calcium nitrate costs
  [AR$111/kg](https://articulo.mercadolibre.com.ar/MLA-782697675-nitrato-de-calcio-soluble-1kg-fertilizante-hidroponia-fertir-_JM#position=13&type=item)
  as a fertilizer (US$1.70/kg).  It's deliquescent above 50% humidity.
- Green vitriol costs
  [AR$111/kg](https://articulo.mercadolibre.com.ar/MLA-782694358-sulfato-de-hierro-1kg-fertilizante-hidroponia-fertirriego-_JM#position=4&type=item)
  (US$1.70/kg) to
  [AR$165/kg](https://articulo.mercadolibre.com.ar/MLA-773096315-fertilizante-sulfato-de-hierro-heptahidrato-x-1-kg-ferroso-_JM#position=15&type=item)
  as a fertilizer.
- Sodium bicarbonate costs
  [AR$129/kg](https://articulo.mercadolibre.com.ar/MLA-609806294-bicarbonato-de-sodio-puro-x-1-kilo-consumo-alimenticio-_JM?variation=39010468391&quantity=1#reco_item_pos=2&reco_backend=mp2v-combos-multiseller-v5-without-promise&reco_backend_type=low_level&reco_client=vip_combo&reco_id=004ec0bd-816d-4399-9e19-2dd9c50edb77)
  (US$2.00/kg).
- Monoammonium phosphate costs
  [AR$143/kg](https://articulo.mercadolibre.com.ar/MLA-782687002-fosfato-monoamonico-soluble-1kg-hidroponia-fertirr-orquideas-_JM#position=1&type=item)
  as a hydroponic fertilizer (US$2.20/kg)
- Lead in ingots costs
  [AR$145/kg](https://articulo.mercadolibre.com.ar/MLA-758197821-plomo-en-lingotes-precio-por-kilo--_JM?quantity=1#reco_item_pos=2&reco_backend=machinalis-v2p-pdp&reco_backend_type=low_level&reco_client=vip-v2p&reco_id=df3a03ea-0823-49a4-9bfd-d0ffbb644631)
  from BATERIAS INDIANAPOLIS in Burzaco.  (US$2.20/kg)
- Trisodium phosphate costs
  [AR$150/kg](https://articulo.mercadolibre.com.ar/MLA-788648580-fosfato-trisodico-_JM#position=6&type=item)
  for industrial use.  (US$2.30/kg)
- 85% phosphoric acid costs
  [AR$495/liter](https://articulo.mercadolibre.com.ar/MLA-800599354-acido-fosforico-85-uso-alimenticio-x-1l-cerveza-artesanal-_JM#position=1&type=item)
  for beer brewing, or
  [AR$350/liter](https://articulo.mercadolibre.com.ar/MLA-824889997-acido-fosforico-al-85-oxidial-x-5kg-cerveza-artesanal-_JM#position=6&type=item)
  in bulk or as low as
  [AR$170/liter](https://articulo.mercadolibre.com.ar/MLA-768698447-fertilizante-acido-fosforico-85-35-kg-grado-alimenticio-_JM#position=26&type=item).
  That's [1.6845
  g/cc](https://en.wikipedia.org/wiki/Phosphoric_acid#cite_ref-Density_85%_1-0)
  so that's reasonably close to being AR$495 or AR$350 or AR$170
  (US$2.60) per kg of phosphoric acid.
- Alumina costs
  [AR$298/kg](https://articulo.mercadolibre.com.ar/MLA-757407097-alumina-calcinada-x-5-kgs-ideal-ceramica-refractaria-_JM#position=3&type=item)
  from Alcoa, or, in bulk, as little as
  [AR$194/kg](https://articulo.mercadolibre.com.ar/MLA-705053769-oxido-de-aluninio-_JM?quantity=1#position=2&type=item)
  (US$3/kg).
- Magnesium chloride costs
  [AR$221/kg](https://articulo.mercadolibre.com.ar/MLA-704309565-cloruro-de-magnesio-importado-de-alemania-1-kilo-_JM#position=17&type=item)
  or
  [AR$249/kg](https://articulo.mercadolibre.com.ar/MLA-790169873-cloruro-de-magnesio-puro-de-israel-1-kilo-_JM#position=11&type=item)
  for food or nutritional supplement use, or as low as
  [AR$195/kg](https://articulo.mercadolibre.com.ar/MLA-801300287-cloruro-de-magnesio-x-1-kg-grs-microcentro-oferta-_JM#position=49&type=item)
  for bath-salts use (US$3/kg).
- Brass filings from keys (probably mostly free-machining brass) can
  cost
  [AR$230/kg](https://articulo.mercadolibre.com.ar/MLA-826151385-1-kg-viruta-de-bronce-de-llaves-lanus-envios-_JM#position=3&type=item),
  (US$4/kg) although the price seems to vary quite a bit; another
  listing has it at
  [AR$1500/kg](https://articulo.mercadolibre.com.ar/MLA-810839346-1-kg-viruta-de-bronce-_JM?quantity=1#position=7&type=item).
- Scrap brass in ingots costs
  [AR$230/kg](https://articulo.mercadolibre.com.ar/MLA-769839038-lingotes-de-bronce-_JM?quantity=1#reco_item_pos=1&reco_backend=machinalis-seller-items&reco_backend_type=low_level&reco_client=vip-seller_items-above&reco_id=de0ed817-5520-473d-be6b-f9028b946fdd)
  (US$4/kg).
- Powdered sulfur costs
  [AR$329/kg](https://articulo.mercadolibre.com.ar/MLA-702668486-azufre-en-polvo-uso-agricola-certificado-x-1-kilo-aranuela-_JM#position=1&type=item)
  or
  [AR$244/kg](https://articulo.mercadolibre.com.ar/MLA-702668711-azufre-en-polvo-uso-agricola-certificado-x-5-kilos-_JM#position=3&type=item)
  in bulk (US$4/kg).
- Potassium nitrate costs
  [AR$245/kg](https://articulo.mercadolibre.com.ar/MLA-782678595-nitrato-de-potasio-1kg-fertilizante-hidroponia-_JM#position=22&type=item)
  (US$4/kg) to
  [AR$289/kg](https://articulo.mercadolibre.com.ar/MLA-814892875-nitrato-de-potasio-x-1000gr-grado-tecnico-_JM#position=33&type=item)
  as a fertilizer.
- White vitriol costs
  [AR$258/kg](https://articulo.mercadolibre.com.ar/MLA-819343339-sulfato-de-zinc-25kg-hidroponia-indoor-frutales-_JM#position=2&type=item)
  (US$4/kg) as a fertilizer.
- Magnesium nitrate costs
  [AR$262/kg](https://articulo.mercadolibre.com.ar/MLA-818728076-fertilizante-nitrato-de-magnesio-soluble-25kg-fertirriego-_JM#position=24&type=item)
  (US$4/kg) as a fertilizer.
- Sodium carbonate costs
  [AR$690/kg](https://articulo.mercadolibre.com.ar/MLA-628345764-carbonato-de-sodio-puro-x-1-kg-_JM#position=3&type=item)
  for bath-salts use, or
  [AR$860/kg](https://articulo.mercadolibre.com.ar/MLA-768801312-carbonato-de-sodio-x-1kg-soda-solvay-_JM#position=1&type=item),
  or
  [AR$280/kg](https://articulo.mercadolibre.com.ar/MLA-824295056-carbonato-de-sodio-10-kilos-envio-gratis-_JM#position=4&type=item)
  (US$4/kg) in bulk.  It's also available in small quantities in
  supermarkets mixed with sodium percarbonate for laundry use.
- Manganese sulfate costs
  [AR$381/kg](https://articulo.mercadolibre.com.ar/MLA-782695861-fertilizante-sulfato-de-manganeso-1kg-hidroponia-fertirriego-_JM?quantity=1&variation=41856095567)
  (US$6/kg) as a fertilizer.
- Chopped 4.5-mm glass fiber costs
  [AR$381/kg](https://articulo.mercadolibre.com.ar/MLA-753742872-hilo-de-fibra-de-vidrio-cortada-45-mm-20-kg-carga-placas-_JM?quantity=1#position=22&type=item)
  (US$6/kg) ("Hilo De Fibra De Vidrio Cortada 4,5 Mm - 20 Kg Carga
  Placas", "Comercial San José", 12 blocks from the Tigre station), or
  in 3-mm cuts, as low as
  [AR$337/kg](https://articulo.mercadolibre.com.ar/MLA-626789126-fibra-de-vidrio-cortada-227kg-friccion-frenos-embragues-_JM?quantity=1#position=11&type=item)
  ("mecha cortada", "chemia.com.ar").
- Copper sulfate costs
  [AR$400/kg](https://articulo.mercadolibre.com.ar/MLA-728428461-sulfato-de-cobre-x-1-kg-pentahidratado-alguicida-swimclor-_JM?quantity=1#position=1&type=item)
  (US$6/kg) as a swimming-pool fungicide and algicide.
- Silicon carbide costs
  [AR$420/kg](https://articulo.mercadolibre.com.ar/MLA-768525886-carburo-de-silicio-1-kg-_JM?quantity=1&variation=34521887207&onAttributesExp=true#position=41&type=item)
  (US$7/kg) ("Carbeto de silicio", in Portuguese, imported from
  Brazil, brand Imerys Fused Minerals.)
- Monopotassium phosphate costs
  [AR$483/kg](https://articulo.mercadolibre.com.ar/MLA-782689480-fosfato-monopotasico-soluble-1kg-hidroponia-fertirriego-_JM#position=4&type=item)
  (US$7/kg) as a hydroponic fertilizer.
- Calcium citrate costs
  [AR$520/kg](https://articulo.mercadolibre.com.ar/MLA-696873565-citrato-de-calcio-puro-usp-1-kilo-_JM?quantity=1&variation=36215312715#position=1&type=item)
  (US$8/kg) as a nutritional supplement.  Its solubility is a bit
  under 1 g/liter: 100x higher than calcium carbonate, but 1000x lower
  than chloride and nitrate.
- Zinc oxide costs
  [AR$1600/kg](https://articulo.mercadolibre.com.ar/MLA-821674738-oxido-de-zinc-500gr-uso-cosmetico-_JM#position=2&type=item)
  to
  [AR$3300/kg](https://articulo.mercadolibre.com.ar/MLA-821674155-oxido-de-zinc-100gr-uso-cosmetico-_JM#position=5&type=item)
  for cosmetics use, or
  [AR$540/kg](https://articulo.mercadolibre.com.ar/MLA-815571838-oxido-de-zinc-x-1-kg-zona-oeste-_JM?quantity=1#position=13&type=item)
  (US$8/kg) for use in paint ("purity 99.5%, contact with skin
  dangerous").  Also [zinc phosphate dental cement is for
  sale](https://articulo.mercadolibre.com.ar/MLA-814398983-cemento-de-fosfato-de-zinc-polvo-90g-de-trey-zinc-dentsply-_JM?quantity=1#position=16&type=item)
  for AR$2080 for 90 grams; presumably this is the zinc oxide and
  phosphoric acid mentioned above.
- Iron filings ("limaduras de hierro") cost
  [AR$600/kg](https://articulo.mercadolibre.com.ar/MLA-635344275-polvo-de-hierro-por-5-kgs-_JM#position=20&type=item)
  (US$9/kg) to
  [AR$850/kg](https://articulo.mercadolibre.com.ar/MLA-612106699-polvo-limaduras-de-hierro-muy-fina-para-magnetizar-x-1-kg-_JM#position=2&type=item).
- Magnesium citrate costs
  [AR$650/kg](https://articulo.mercadolibre.com.ar/MLA-692362188-citrato-de-magnesio-puro-usp-1-kilo-_JM?searchVariation=26231558871#position=4&type=item)
  (US$10/kg) as a supplement.
- Powdered lead costs
  [AR$700/kg](https://articulo.mercadolibre.com.ar/MLA-708482010-plomo-en-polvo-envases-por-1-kilo-_JM),
  (US$11/kg) but see above about lead in ingots.
- Magnesium oxide costs
  [AR$845/kg](https://articulo.mercadolibre.com.ar/MLA-716898108-oxido-de-magnesio-grado-usp-999-apto-consumo-1kg-_JM#position=3&type=item)
  (US$13/kg) to
  [AR$1040/kg](https://articulo.mercadolibre.com.ar/MLA-716899617-oxido-de-magnesio-grado-usp-999-apto-consumo-250-gr-_JM#position=2&type=item)
  in 99.9% USP food-grade form.
- Copper filings ("polvo de cobre puro") cost
  [AR$850/kg](https://articulo.mercadolibre.com.ar/MLA-762274650-polvo-de-cobre-puro-1kg-_JM?quantity=1#position=2&type=item)
  (US$13/kg).
- Potassium chloride costs
  [AR$996/kg](https://articulo.mercadolibre.com.ar/MLA-810688910-sal-udable-sal-con-003-de-sodio-70-grs-_JM?variation=42320647286&quantity=1#reco_item_pos=0&reco_backend=machinalis-domain-pads&reco_backend_type=low_level&reco_client=vip-pads&reco_id=d5c1979e-1933-415a-a50c-d86c80635853&is_advertising=true&ad_domain=VIPCORE_RECOMMENDED&ad_position=1&ad_click_id=NzU0YmMxMzUtMjI5YS00MzQxLTg4YjAtMGNmZWRkZDE5NTE1)
  (US$15/kg) as a salt substitute.
- Fine brass powder costs
  [AR$1200/kg](https://articulo.mercadolibre.com.ar/MLA-637439920-bronce-puro-en-polvo-por-kilo-_JM?quantity=1#position=25&type=item)
  (US$19/kg).
- Potassium silicate solution costs
  [AR$1450/kg](https://articulo.mercadolibre.com.ar/MLA-716496949-top-crop-barrier-250-ml-silicato-de-potasio-_JM?quantity=1#position=6&type=item)
  (US$22/kg) as a fertilizer.
- Calcium acetate hypothetically costs
  [AR$2000/kg](https://articulo.mercadolibre.com.ar/MLA-818209811-acetato-de-calcio-_JM?quantity=1#position=1&type=item)
  (US$30/kg) but a lot of people complain about that vendor.
- Powdered zinc costs
  [AR$2600/kg](https://articulo.mercadolibre.com.ar/MLA-706162251-zinc-puro-en-polvo-precio-por-kilo-_JM#position=18&type=item)
  (US$40/kg).
- 97%-pure powdered aluminum costs
  [AR$2900/kg](https://articulo.mercadolibre.com.ar/MLA-637123855-aluminio-pureza-97-en-polvo-p-pinturas-uso-industrial-_JM)
  (US$40/kg) though I've seen other listings at lower prices.
- 99%-pure powdered tin costs
  [AR$3700/kg](https://articulo.mercadolibre.com.ar/MLA-637126985-estano-en-polvo-pureza-999-ultrafino-envases-de-1-kgs-_JM)
  (US$60/kg).
- Sodium alginate costs
  [AR$40000/kg](https://articulo.mercadolibre.com.ar/MLA-675431636-alginato-de-sodio-modernist-pantry-50gr-cocina-molecular-_JM#position=1&type=item).
  or as low as
  [AR$10050/kg](https://articulo.mercadolibre.com.ar/MLA-782955884-alginato-de-sodio-materia-prima-premium-por-100g-envio-_JM#position=3&type=item)
  (US$160/kg) for culinary use.
- Nitrates of iron and copper are not available.
- Zinc chloride is not available.
- Potassium carbonate is not available, which is a shame, since it's
  much more water-soluble than sodium carbonate.
- Ammonium carbonate is not available, although it's used in some
  cookies here in Argentina.
- Aside from the possibility of prying them out of dead batteries,
  carbon electrodes are available for arc gouging: [4 mm diameter, 305
  mm long for
  AR$83](https://articulo.mercadolibre.com.ar/MLA-670322016-electrodos-de-carbon-para-repelado-arcair-4x305mmx-3-unid-_JM?quantity=1#position=1&type=item),
  [6 mm diameter of some unknown length for
  AR$43](https://articulo.mercadolibre.com.ar/MLA-825520594-electrodo-de-carbon-60-mm-x-1-unidad-_JM?quantity=1#position=4&type=item),
  [10 mm diameter of some unknown length for
  AR$72](https://articulo.mercadolibre.com.ar/MLA-825520595-electrodo-de-carbon-10-mm-x-1-unidad-_JM?quantity=1#position=11&type=item),
  or [13 mm diameter of some unknown length for
  AR$136](https://articulo.mercadolibre.com.ar/MLA-825520599-electrodo-de-carbon-13-mm-x-1-unidad-_JM?quantity=1#position=12&type=item).
- Several vendors sell bars of magnesium as sacrificial anodes for
  solar hot water heaters for a few hundred pesos, and there are a few
  magnesium firestarters like the one I had as a kid.
- Someone is selling ["glass basalt
  fiber"](https://articulo.mercadolibre.com.ar/MLA-829232912-fibra-de-vidrio-basalto-de-alta-calidad-resistencia-directa-_JM#position=4&type=item)
  for "SMC roving", for AR$100 for 1.5 meters.  I have no idea if this
  is actually basalt fiber but I suspect it's just glass fiber.

Some candidate mixtures explored in more detail
-----------------------------------------------

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.

### Cat-litter bentonite or other clay body by itself ###

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.

### Quartz sand and calcium hydroxide ###

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.

### Quartz sand and portland cement ###

This is the classic hydraulic mortar; it sets up faster if you add
some slaked lime.

### Quartz sand, wood flour, cat-litter bentonite, diammonium phosphate, calcium chloride ###

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 CaCl<sub>2</sub>, with a molar mass of 111 and a
solubility of 650 g/liter of water at 10°; [diammonium phosphate] is
(NH<sub>4</sub>)<sub>2</sub>HPO<sub>4</sub>, 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
Ca<sub>5</sub>(PO<sub>4</sub>)<sub>3</sub>OH, 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.

[diammonium phosphate]: https://en.wikipedia.org/wiki/Diammonium_phosphate
[Calcium chloride]: https://en.wikipedia.org/wiki/Calcium_chloride
[ammonium chloride]: https://en.wikipedia.org/wiki/Ammonium_chloride
[Hydroxyapatite]: https://en.wikipedia.org/wiki/Hydroxyapatite

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.)

[Poinern et al. 2009]: https://www.ncbi.nlm.nih.gov/pubmed/19232507

(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.)

[Hielscher's sono-synthesis report]: https://www.hielscher.com/sono-synthesis-of-nano-hydroxyapatite.htm

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 &beta;-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](https://civiltoday.com/civil-engineering-materials/sand/299-bulk-density-of-sand)
([see also
rfcafe](http://www.rfcafe.com/references/general/density-building-materials.htm)),
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:

<table><tr><th>Ingredient<th>Mass/liter<th>US$/kg<th>US$/liter
       <tr><td>Sand      <td>1.6 kg    <td>0.012 <td>0.019
       <tr><td>Cat litter<td>170 g     <td>1.30  <td>0.22
       <tr><td>CaCl<sub>2</sub>
                         <td>270 g     <td>1.60  <td>0.43
       <tr><td>(NH<sub>4</sub>)<sub>2</sub>HPO<sub>4</sub>
                         <td>190 g     <td>0.90  <td>0.17
       <tr><th>Total     <td>2.23 kg   <td>      <td>0.84
</table>

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.

### Phosphoric acid is not a cheaper phosphate source but might permit denser cement ###

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.

### Calcium nitrate is more expensive than calcium chloride ###

[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.

[Rey, Combes, Drouet, and Grossin]: https://www.sciencedirect.com/science/article/pii/B9780080552941000234?via%3Dihub

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.

### Berlinite-bonded alumina ###

[Grover et al.] at Argonne published a paper in 1999 on this,
reporting a rather astonishing result: "We hydrothermally cured a
mixture of Al<sub>2</sub>O<sub>3</sub> and H<sub>3</sub>PO<sub>4</sub>
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, AlPO<sub>4</sub>, 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 file
`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 file `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.

[Grover et al.]: https://inis.iaea.org/search/search.aspx?orig_q=RN:33000620

### Sawdust, diammonium phosphate, sodium bicarbonate, and calcium chloride ###

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.

### Magnesium sulfate, sodium carbonate, and silica sand ###

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.

### Green vitriol and trisodium phosphate ###

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,
Cu<sub>5</sub>(PO<sub>4</sub>)<sub>2</sub>OH<sub>4</sub>.  Again, I
haven't worked out the stoichiometry.

### Spot-welding brass filings with a carbon or TIG electrode ###

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 file `filled-fdm` and file
`phase-change-soldering-iron` for more on related systems).  If so, as
described in file `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.