Magnesium has an energy density of 43.0 MJ/ℓ and a specific energy of 24.7 MJ/kg. This is among the highest energy densities of any easily burnable fuel — iron, polystyrene, polyethylene, and lithium borohydride are similar, while the more difficult aluminum, carbon, and silicon are up in the 70–84 MJ/ℓ range. (See, however, the note on aluminum-air batteries and the note on lithum as a fuel.) It excels iron at specific energy, and polystyrene, polyethylene, and lithium borohydride excel it. But burning polystyrene, polyethylene, and lithium borohydride produces a lot of gas, spreading out the heat a great deal. So, for compact, easily ignited fuel to produce a high temperature, magnesium is pretty much tops. As a bonus, it’s pretty abundant and easily obtained from seawater; see notes below on smelting.
Magnesia has a molar mass of 40.3 g/mol and a heat capacity around room temperature of 37.2 J/mol/K; dividing these two gives an unremarkable specific heat of 0.923 J/g/K. Magnesium itself has a molar mass of 24.3 g/mol, so magnesia (MgO) is 60.3% magnesium; burning a kg of magnesium yields 1.66 kg of magnesia, and, as mentioned above, 24.7 MJ. From this we can derive that, if its specific heat remained constant, the resulting magnesia would be at 26500°, which means that in practice the upper limit to the temperature will be imposed by heat loss mechanisms and the finite speed of combustion, since this is several times hotter than the surface of the sun.
Thus we have magnesium flashbulbs.
Consider a kilojoule. We can store it in 23 microliters of magnesium weighing 40 mg. Liberating it requires another 26 mg of oxygen, for example from the air, which contains it at about 210 mg/ℓ, so about 130 mℓ of atmospheric-pressure air are needed; the reaction can be arranged to proceed at rates of anywhere from tens of watts or so up to a megawatt by controlling the introduction of the air, as long as the hot magnesium doesn’t start reducing its reaction chamber, or of course melting it. If it is necessary to carry the oxidizer as well, water works well once the reaction is going, since water is 89% oxygen; 26 mg of oxygen as water thus occupies 29 μl. (See below, though.)
This makes magnesium appealing as a compact way to store energy capable of safe, controlled high-power release. One of the few examples of this being done in practice is the MAGIC engine developed by Mitsubishi and Takashi Yabe and others at the Tokyo Institute of Technology, which also used a water oxidizer; Yabe has also worked on magnesium-air fuel cells.
The oxygen-magnesium reaction produces no gaseous products unless the temperature is allowed to go very high (magnesia boils at 3600°, though magnesium melts at 650° and boils at 1091°), but the water-magnesium reaction produces hydrogen. The MAGIC engine secondarily burns the hydrogen produced in air to recover the enthalpy of formation of the water, which was drawn from the initial water–magnesium reaction. Water’s standard enthalpy of formation is -285.83 ±0.04 kJ/mol and its molar mass is 18.01528(33) g/mol. Magnesia’s are -601.6 ±0.3 kJ/mol and 40.304 g/mol (compared to, say, -1675.7 kJ/mol and 101.960 g/mol for alumina, nearly the same energy density); although I’m not very sure of my understanding of the thermodynamics, I think this means that splitting the water sucks up about half of the heat you’d otherwise get out of the reaction, since both MgO and H₂O have a single oxygen, so a mole of H₂O produces a mole of MgO; so you would need about twice the amount of magnesium to produce a given amount of energy.
The hydrogen also soaks up 28.836 J/mol/K of heat, lowering the potential maximum temperature further, but I think by another factor of less than 2. So we’re still talking about maximum temperatures that exceed magnesia’s boiling point.
(Under appropriate conditions you can generate hydrogen at room temperature from magnesium and water.)
Using oxygen rather than water you should get the full 601.6 kJ/mol, which divided by magnesium’s 24.3 g/mol works out to 24.8 MJ/kg, close to the 24.7 cited above. This makes me think I am understanding the thermodynamics properly.
For controlling the reaction rate, the most appealing option would seem to be preheating the magnesium to somewhat below its melting point, then introducing the oxidizer at a controlled rate. The temperature will immediately rise enough to melt the magnesium, which over a long enough timescale will reduce the available area for the reaction to take place; but in many circumstances the reaction can be run to completion on a shorter timescale than that, and the increasing temperature may be an effective countervailing force.
Maintaining the magnesium fuel in large solid pieces until near time to use would be a useful safety measure. These would be much harder to ignite accidentally. Perhaps the simplest approach would be a round magnesium rod that twists in a device exactly like a manual pencil sharpener to shave off shavings of a calibrated thickness.
Under some circumstances, it might be best to first preheat some magnesia by burning magnesium, with little or no gas release, and then use a second, later burst of gas to move the generated heat to where it’s needed. This decouples the time during which the combustion happens — which may be limited by, for example, considerations such as the one mentioned above of burning the magnesium to solid magnesia fast enough that it doesn’t melt into a round mass with little surface area, or inversely by the inability to burn the magnesium as fast as would be desired because of limited surface area — from the time during which the heat is transferred to where it will be used, which might be shorter or longer than the combustion time.
Recharging spent magnesium fuel should be considerably easier than the analogous process for aluminum, which is especially interesting for use as a motor vehicle fuel. Something like three fourths of magnesium today is produced in China by the Pidgeon silicothermic process, boiling magnesium vapor at sub-atmospheric pressures out of mixed MgO and ferrosilicon powders at 1200°–1400°, and further stabilizing the silica byproduct with CaO. However, the historically dominant process was electrolysis of molten MgCl₂ produced from HCl and MgO; the electrolysis releases the Cl₂, which can be exothermically recombined with H₂ with ultraviolet light, even in aqueous solution, which tames the process a bit. Pure MgCl₂ melts at 714°, but, e.g., Davy fluxed it with corrosive sublimate to discover magnesium at a tamer temperature; so a recharging apparatus of a reasonably small size and temperature might be feasible.
A new, more direct process uses a solid zirconia electrolyte to directly electrolyze MgO at 1150°–1300°, in order to drop the cost of magnesium for structural applications in vehicles. The cathode is a bath of molten MgO through which argon is bubbled, coming out containing Mg vapor. The O₂ can travel through the zirconia to the cathode, made, for example, of molten copper, tin, or silver, or of a zirconia–nickel cermet coating on the zirconia. Magnesia-stabilized zirconia is more stable in the molten salt bath, but lower conductivity; they found some kind of sooper seekrit ingredient to keep the molten MgO from corroding regular yttria-stabilized zirconia. Like the Pidgeon process, the magnesium produced is in vapor form, and so a distillation step inherently purifies the reaction product. (With appropriate “fluxes” or molten-salt solvents, this same SOM process has been used to smelt iron, silicon, tantalum, and titanium.)
Sulfur is an alternative oxidant; MgS has a molar mass of 56.38 g/mol and an enthalpy of formation of -347 kJ/mol, which works out to 14.3 MJ per kg of magnesium or 6.2 MJ per kg accounting for the oxidant as well. This reaction is used commercially to remove unwanted sulfur from steel. It doesn’t melt until 2226°, and its boiling point is not known, though probably a bit lower than magnesia’s. Interestingly, it can react with oxygen to give epsom salt rather than the little-known sulfite.
The sulfide’s heat capacity at room temperature is 45.6 J/mol/K, which works out to a specific heat of 0.809 J/g/K. This extrapolates out to 7600 K. This is a lot cooler than the extrapolated temperature for magnesia but still pretty toasty.
This might be useful in cases where limiting the reaction rate is not desired, but it probably isn’t safe in more than milligram quantities because of the rapidity of the reaction.
Although, as explained above, you can smelt magnesia with ferrosilicon at 1200°–1400° with lime, because the gaseous magnesium leaves the reaction and the lime stabilizes the silica product as larnite, under normal conditions the reaction tends in the opposite direction: magnesium will reduce silica to silicon. As the International Magnesium Association cautions:
The refractories used in the furnace should be high in alumina or magnesia because molten magnesium can react violently with even small amounts of silica (often [sic] present in ceramic materials).
SiO₂ has an enthalpy of formation of -911 kJ/mol, while MgO’s enthalpy of formation is -601.6 kJ/mol. So at room temperature I think the reaction would be SiO₂ + 2Mg → 2MgO + Si + 293 kJ per mol of silica, noticeably exothermic, though of course a very low reaction rate. Magnesia’s 40.304 g/mol and silica’s 60.08 g/mol add up to 140.69 g for the left side of this reaction, which works out to about 2.08 MJ/kg with both reagents in the denominator. Counting just the magnesium, 3.63 MJ/kg, so (I think) that’s the intrinsic energetic cost of the Pidgeon process’s endothermic aspect. The intrinsic energetic cost of the silicon in the ferrosilicon feedstock is three times as much per kg of magnesium produced.
The easily-accessible temperature-dependent equilibrium reversal of this reaction interestingly makes magnesium somewhat interconvertible with silicon, even in the impure form of ferrosilicon, assuming you have ample supplies of their ubiquitous oxides. Metallurgical-grade silicon is mostly produced by carbothermal reduction, though aluminothermal reduction is also performed; this suggests a mostly solar thermal route to smelt magnesium.
One of the most interesting aspects of the solid oxide electrolyte process for magnesium production mentioned above is that the resulting white-hot magnesium vapor is capable of reducing not oxides only of silicon but indeed of nearly any metal, including exotics like titanium and tantalum (though not, apparently, zirconium and yttrium, at least not fast enough to prevent the electrolysis from proceeding). Magnesium’s first ionization energy is 737.7 kJ/mol, kind of a middle-of-the-road value for metals, so I don’t think the issue is that it’s extremely easy to oxidize magnesium. And from an entropic point of view you would think temperatures well above magnesium’s boiling point would tend to favor the reduction of magnesium, as it does in the Pidgeon process — presumably at a high enough temperature titanium would instead reduce magnesia to magnesium vapor, just as silicon does. I guess I need to go read about Gibbs free energy.
At 1200° titanium dioxide is solid (melting point 1843°), magnesia is solid (melting point 2852°), and titanium is solid (melting point 1668°), but magnesium is a gas (boiling point 1091°, as mentioned above).
A practical aspect of the silica-magnesium reaction is that you maybe shouldn’t throw silica sand on an unwanted magnesium fire. You will be disappoint.