Hardness Enhancement by Metal–Metal Bonding in Mn 4 N, Mn 3 NiN, and Mn 3 PdN Antiperovskites

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PdN, were synthesized via high-pressure and high-temperature methods combined with high-temperature denitrogenation. Vickers hardness measurements revealed a consistent increase in hardness with rising valence electron concentration. Structural and bonding analyses showed that metal-metal bonding is often considered unfavorable for hardness, but in these Mn-N antiperovskites it contributes positively to the measured hardness. First-principles calculations were employed to elucidate this mechanism, leading us to propose a new interaction model describing the role of metal-metal bonding in strengthening ionic crystal frameworks. This study not only advances the theoretical understanding of hardness but also offers guidance for designing high-hardness materials.