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Liquid fluorine has great potential as a rocket fuel; per the Encyclopedia Astronautica, LF2/LH2 has a specific impulse of 470 seconds. http://www.astronautix.com/l/lf2lh2.html Lithium/LF2/LH2 can get you over 500 seconds, but requires you to have molten lithium at over 450K stored near cryogenic liquid hydrogen. Krypton difluoride (KrF2) is a compound with some interesting properties, aside from being a noble gas compound. Annoyingly, it breaks apart at temperatures above about 195K. More importantly for the purpose of using it as a rocket propellant, it is an incredibly strong oxidizing agent. In fact, it is a more powerful oxidizer than fluorine gas, a consequence of the extremely dissociation energy (delta Hf) of the krypton-fluorine bond (54 kJ/mol, vs 157 kJ/mol for F2, via https://labs.chem.ucsb.edu/zakarian/armen/11---bonddissociationenergy.pdf ) Hydrogen fluoride (HF), the product of burning hydrogen with fluoride compounds, has a bond dissociation energy of 568 kJ/mol. Modelling the combustion of KrF2 and H2, we get the following equation; KrF2 + H2 = Kr + 2HF -(2*55 + 436) = -2*569 + E for a net energy production of 592 kJ/mol. Compared to 545 kJ/mol for hydrogen/fluorine combustion, this is slightly better. Also, it has the advantage that your fuel is at a higher temperature (195K for KrF2 vs. 85K for LF2), and KrF2 is more dense than liquid fluorine. Unfortunately, KrF2 is a solid with no known liquid phase, and as mentioned, is unstable above 195K. A better option might be xenon fluorides. The xenon-fluorine bond has a bond energy of a mere 13 kJ/mol, and xenon compounds are much more understood than krypton compounds. Likely the best option is Xenon Hexafluoride (XeF6). Xenon hexafluoride melts at 322K, and boils at 348K. A fairly narrow temperature range, and unfortunately one that would require heating, but likely not insurmountable. (Sadly, I cannot find information on the liquid density of XeF6). XeF6 would react with H2 according to the following formula. XeF6 + 3H2 = Xe + 6HF -(6*13+3*436) = -6*569 + E for a net energy production of 2028 kJ/mol Granted, this combination would almost certainly have lower specific impulse than LH2/LF2 due to the large size of the xenon atom (average mass of exhaust products is 35.8 vs. 19, so exhaust velocity would be roughly 37% less). Assume roughly 300 isp assuming flame temp is equal to LH2/LF2, possibly more if the flame temp for xenon hexafluoride is higher. However, xenon hexafluoride fuel would give a higher thrust, in addition to being more dense and making your first stage smaller. Although at that point, why not use kerolox and ditch liquid hydrogen altogether. Still, an interesting theoretical exercise, and I'd be keen to see data on xenon hexafluoride flame temps if anyone has it.
Put here since this forum needs more love. One of the major benefits of nuclear rocket engines such as NERVA is they are capable of using almost any working fluid as propellant (provided they are appropriately designed). As the source of energy in a nuclear rocket comes from fission, rather than combustion, an oxidizer is not needed. The propellant can be chosen based on other properties. Hydrogen is a common choice, as the light molecular mass of H2 gives a good exhaust velocity and specific impulse. Methane and other hydrocarbons are also considered; they give good thrust (generally better with heavier hydrocarbons), and decent specific impulse (methane is best). Additionally, hydrocarbons are found on numerous bodies in the solar system, including in liquid form on Titan. Robert Zubrin writes about in-situ resource utilization to obtain propellant for nuclear rockets here and here. One of the biggest drawbacks of using hydrogen as fuel for a nuclear rocket is its low density. Even if liquid hydrogen is used (requiring cryogenic storage), the fuel tank mass (and therefore structural mass) will be much larger than if another fuel was used. Compounds of hydrogen and other light elements could give good performance, but have better storage density and not require cryogenic storage. Ammonia, methane, and water have already been examined. Borane (BH3) is unstable, and diborane (B2H6) has a high molar mass (yielding lower isp unless it dissociates), and still requires cryogenic temperatures to keep liquid; it boils at 181K. Two interesting options would be the lightest metal hydrides; lithium hydride and beryllium dihydride. Both of these compounds are solid at room temperature; and would have decent volumetric efficiency (though they are both less dense than water in solid form). Additionally, their molar masses are very light; lithium hydride has a molar mass of roughly 8, and beryllium dihydride is roughly 11. This is superior to ammonia, methane, or water. The only better options are hydrogen, or helium (good luck keeping liquid helium cool for years on a spacecraft). Even better, these compounds actually decompose when heated to their melting points, yielding hydrogen (and metal atoms). As the specific impulse is dependent on the average molar mass of the exhaust products, this means your efficiency will be almost as good as hydrogen (with much better volumetric efficiency). I suspect that storing your propellant in solid form could also simplify your fuel tank construction. However, there are some drawbacks. LiH and BeH2 both require heating to decompose. There are several options for a source of heat, but it seems to me the easiest would be heating elements strategically placed throughout the fuel mass. Another major problem would be deposition of lithium or beryllium metal in the reactor compartment. I am uncertain whether lithium or beryllium in elemental form would react with zirconium carbide cladding in NERVA; I suspect there is little research on this topic. Even if the metals are nonreactive in gaseous form, the whole of the reactor compartment would have to be kept above the melting point of lithium (454K) or beryllium (1560K). Additionally, the aft end of the reactor compartment would have to be hot enough to boil lithium (1615K) or beryllium (3243K) to avoid two-phase losses in the exhaust. 3243K is close to the maximum of performance possible today (I believe my nuclear propulsion professor said that 3500K was the "holy grail" of solid core NTR design). Beryllium is highly toxic when inhaled, though this could be avoided by only using the rockets in space (chemical rockets are better optimized for ground launch). Lithium is less toxic, but computer simulations have apparently shown that unless almost all lithium-6 is removed from the hydride, it functions as a neutron poison. To my knowledge, beryllium hydride is not a neutron poison. Beryllium hydride has at least been mentioned as a fuel for normal rockets; https://arxiv.org/ftp/arxiv/papers/1105/1105.0998.pdf, but I have yet to find any mention of its use as a nuclear rocket propellant. I would be quite curious to know if more research on this topic exists. On the surface, though, beryllium hydride looks like a good propellant, provided its issues can be overcome.