## 3 Results and Discussion
### Benchmark Study
Zirconium-Based ThermitesIn a similar capacity to boron metal, nanosized zirconium has been proposed as an additive to improve the properties of conventional Al micron-sized fuel, with these three-material composite thermites showing higher reactivity in terms of initiation time, increased energy delivery and longer combustion duration [66]. Importantly, the poor oxygen diffusivity across ZrO\({}_{2}\), the lowest of all considered fuels in the initiation temperature range (1000-2000 K, see Supplementary Information file S1) is a strong limit to the reactivity of thermites using only Zr as the fuel, even more limiting than the case of boron, which also exhibits difficulties for initiation for the same reason. This leads to longer initiation times and temperatures despite similar thermal conductivities compared with aluminum and boron-based thermites in most cases. Initiation times exceed 200 ms for all systems. Note that Zr/Pb\({}_{3}\)O\({}_{4}\) cannot be initiated under these conditions, requiring an initiation/propagation formulation that relies solely on gas phase mechanisms for systems brought to the disruption temperature. At this time, there are no explicit studies on the reaction characteristics of purely zirconium-based systems, and so the results will be discussed in comparison with the other fuel propositions. It is interesting to note that the CuO oxidizer gives again the slowest propagating reaction when mixed with Zr fuel: 6.7 cm\(\cdot\)s\({}^{-1}\) as in the case of B fuel. It is probable that the relatively low vaporization limit for this system at 2070 K (Cu\({}_{2}\)O) is not sufficiently hot to allow enough freed oxygen to escape into the fuel particle until just before the system disruption. CuO is generally a high gas-producing oxidizer, and, thus, this couple would likely see enhanced performance in experimental studies or in multiphasic simulations including gas phase reactions. The Zr/Fe\({}_{2}\)O\({}_{3}\) thermite couple shows comparable behavior  
Figure 4: Temperature profiles taken at regular time intervals dt and calculated burn rate V\({}_{\rm SS}\) for: (**a**) B/CuO, (**b**) B/Fe\({}_{2}\)O\({}_{3}\), (**c**) B/WO\({}_{3}\), and (**d**) B/Pb\({}_{3}\)O\({}_{4}\) systems at \(\xi=1.0\) with 80-nm boron particles. to the other thermite couples utilizing this oxide (see Figure 5). The reaction remains dominantly driven by the decomposition of Fe\({}_{2}\)O\({}_{3}\) at the high temperature of 1957 K. This is similar to Zr/CuO that does not see high flux of oxygen towards the Zr fuel, necessary for the runaway reaction to initiate until this high temperature. However, this system is limited by a much higher vaporization temperature at 3135 K for the final Fe product, which allows more time for the oxidation of the fuel, and more activation for diffusion, before the disruption temperature is reached. This couple was found to have the highest propagation rate at 37 cm:s\({}^{-1}\). It is interesting to note that this propagation velocity is as fast as that of the Al/Fe\({}_{2}\)O\({}_{3}\) thermite, despite the large difference in oxygen diffusivity between Al\({}_{2}\)O\({}_{3}\) and ZrO\({}_{2}\), and the very similar heats of reactions (275 vs. 281 kJ\(\cdot\)mol\({}^{-1}\) for Zr/Fe\({}_{2}\)O\({}_{3}\) and Al/Fe\({}_{2}\)O\({}_{3}\), respectively). In contrast to the limitation of the Zr/CuO system, the very high oxygen diffusivity in WO\({}_{3}\) at low temperature likely moderates the deficit caused by limited diffusion through the native oxide layer. The freed oxygen reservoir is available in this case to maximize the oxidation of the fuel from about 800 K. This is still significantly smaller than the comparative temperature gradients of this oxide coupled with the other fuels. Finally, the Zr/Pb\({}_{3}\)O\({}_{4}\) couple was the only thermite considered that does not manage to initiate under the simulated conditions.