Fig. 1. (a) Variation of longest (red circles) and average (black circles) bond lengths of BP-N with pressure. The relaxation proceeds from high to low pressure, leading to an increase in bond lengths as the pressure decreases. (b) and (c) BP-N structures at 25 and 23 GPa, respectively. Stability is maintained at 25 GPa, whereas decomposition into N-chains occurs at 23 GPa owing to breaking of the longest bonds. (d) and (e) Phonon spectra of BP-N at 40 and 30 GPa, respectively.

Fig. 2. Variations of enthalpy with pressure at different P-atom doping concentrations for cg-N, BP-N, LP-N, and HLP-N: (a) without P-atom doping; (b) 3.125% doping; (c) 6.25% doping. The enthalpy values are referenced to those of cg-N. For 3.25% doping, there is one unique configuration for cg-N, one for BP-N, four for LP-N, and four for HLP-N (only stable configurations with minimal enthalpy were used). The same is found for 6.25% doping concentration.

Fig. 3. (a) Relationships between structural stability and uniformity at 0 and 50 GPa. The blue circles represent stable structures, and the orange circles depict unstable structures for structural relaxation. (b) Relationship between energy and uniformity at 0 GPa for 12.5% and 25% doping concentrations. The circles represent stable configurations, while the black lines are to guide the eye.

Fig. 4. Structures alongside their respective phonon dispersions for (a) the configuration possessing the lowest energy and (b) a representative dynamically unstable configuration with 12.5% doping concentration. The black arrows in (b) indicate the direction of vibration for the Z-point imaginary frequency. (c) Variation of energy as a function of interlayer P–P distances. Each circle represents a unique configuration, with the red triangle indicating the configuration with the lowest energy and the blue triangle one of the dynamically unstable configurations. (d) Schematic of interlayer electrostatic interaction for configurations with N–P dipoles. Atoms with charged labels (positive or negative) contribute to interlayer stability. The orange waves visually depict the electrostatic interaction between P and N atoms, highlighting its key role in stabilizing the system. For all structures, blue spheres represent N atoms and red spheres P atoms.

Fig. 5. Structures and corresponding phonon dispersions for 25% doping concentration. (a) Configuration with four N–P dipoles. (b) Configuration with two N–P dipoles. The orange waves visually depict the electrostatic interaction between P and N atoms. Blue spheres represent N atoms and red spheres P atoms, and atoms with charged labels contribute to interlayer stability.

Fig. 6. Calculated density ρ, energy density E_d, volumetric energy density E_v, detonation velocity V_d, and detonation pressure P_d of 12.5% and 25% P-atom-doped BP-N. For comparison, the values for TNT and HMX explosives are also listed. Superscript “Expt.” indicates experimental data.