## Methodology
### System and Simulation Set-Up  
A constant power density, \(P\), of 22 W is applied at the first cell with a system-wide convection coefficient of 100 W\(\cdot\)m\({}^{-2}\cdot\)K until initiation. The cell is considered initiated once the runaway exothermic combustion reaction takes precedence over the external heating ramp--this is calculated as surpassing a minimum initiation temperature with a rapid temperature rise. This condition is customized for each fuel/oxidizer pairing as the variable heat capacities affect the initial heating ramp for a given power density, \(P\), as well as the different heat of reactions for each combustive pair. The initiation delay is defined as the time for initiation to occur in the first, externally heated cell. Initially, the entire system is at the ambient temperature (300 K). As the model does not account for reactions in the gas phase, the reaction is stopped when reactants or products are vaporized. A temperature limit, corresponding to the lowest vaporization temperature among the different materials constituting each considered thermite couple, is therefore imposed, after which the system is considered to have dispersed into the environment. These vaporization temperature limits and corresponding materials are listed in Table 1. Other main parameters that have been used for the calculations are listed in the Supplementary Information file S1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**Fuel Species**} & \multicolumn{3}{c}{**Disruption**} & \multirow{3}{*}{**Initiation**} & \multirow{3}{*}{**Initiation**} & \multirow{3}{*}{**Delay (ms)**} & \multirow{3}{*}{**Burn Rate**} \\  & & & & & & \\  & **Oxide** & & & & & \\  & **Cyaporized Species** & & & & \\ \hline \multirow{4}{*}{**Al**} & CuO & 2070 (Cu\({}_{2}\)O) & 2.9 & 943 & 91 & 60 \\  & Fe\({}_{2}\)O\({}_{3}\) & 2743 (AI) & 6.7 & 1994 & 350 & 38 \\  & WO\({}_{3}\) & 1973 (WO\({}_{3}\)) & 1.6 & 718 & 63 & 17 \\  & Pb\({}_{3}\)O\({}_{4}\) & 1808 (PbO) & 1.6 & 1194 & 127 & 2.1 \\ \hline \multirow{4}{*}{**B**} & CuO & 2070 (Cu\({}_{2}\)O) & 2.4 & 1285 & 192 & 4.3 \\  & Fe\({}_{2}\)O\({}_{3}\) & 2130 (B\({}_{2}\)O\({}_{3}\)) & 5 & 1577 & 360 & 17 \\  & WO\({}_{3}\) & 1973 (WO\({}_{3}\)) & 1.4 & 1228 & 186 & 14.5 \\  & Pb\({}_{3}\)O\({}_{4}\) & 1808 (PbO) & 1.3 & 1192 & 165 & 8 \\ \hline \multirow{4}{*}{**Zr**} & CuO & 2070 (Cu\({}_{2}\)O) & 2.6 & 1643 & 270 & 6.7 \\  & Fe\({}_{2}\)O\({}_{3}\) & 3135 (Fe) & 6.8 & 1957 & 334 & 37 \\ \cline{1-1}  & WO\({}_{3}\) & 1973 (WO\({}_{3}\)) & 1.5 & 1862 & 245 & 14.3 \\ \cline{1-1}  & Pb\({}_{3}\)O\({}_{4}\) & 1808 (PbO) & 1.5 & no initiation & no initiation & no initiation \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculated system disruption, defined as the temperature of first vaporization among all thermite basic components, effective thermal conductivity, initiation temperature, initiation delay, and burn rate for Al, B, and Zr fuel based nanothermites. This work includes a number of metallic fuel and metal oxides that are utilized to form the thermite materials, namely Al, B, and Zr for the metal fuels and CuO, WO\({}_{3}\), Fe\({}_{2}\)O\({}_{3}\), and Pb\({}_{3}\)O\({}_{4}\) for the oxide materials. Their main chemical reactions are detailed in the Supplementary Information file S2. These different thermite couples are benchmark tested using identical parameters for comparison. We only consider stoichiometric mixtures of thermites composed of nanoscale fuel and oxidizer particles. All fuel particles are considered 80 nm in diameter with oxidizer sizes spanning from 90 to 120 nm calculated according to the stoichiometric ratio (\(\zeta=1\)) (detailed particle sizes are given in the Supplementary Information Table S2). Thermite mixtures are placed in a 3 mm long open-air system, considered with an axisymmetric geometry (2 mm in diameter). The one-dimensional mesh size is set at \(\Delta\)x = 1 \(\upmu\)m, and populated at a %TMD of 60% compaction to place ourselves in a conductively dominant reaction regime.