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The mechanical properties of nanoparticles like strength or toughness dramatically depend on their size and shape. This statement is the main conclusion resulting from a large number of experimental and theoretical studies of nanoparticles with sizes ranging from 10 to 1000 nm. Less information is available for smaller sizes. For such small systems, experiments are difficult to perform, and the reliability of classical molecular dynamics calculations is questionable because of the high surface-volume ratio and of large strains. First-principles calculations appears as a suitable option, at least for system sizes lower than 2 nm. We perform such calculations for FCC (Al), BCC (W), and cubic diamond (Si, SiC) nanoparticles [1,2]. We find that high strength values are obtained in all cases, with a clear dependence on the nanoparticle shape. They are close and often greater than the theoretical bulk strength. We propose several possible explanations for this surprising finding. It is observed that amorphization becomes the favored plasticity mechanism at this scale, which can be understood using thermodynamics arguments. In specific cases the homogeneous nucleations of a dislocation (SiC) and of a twin (W) are identified. All these results are discussed in relation with the literature and classical molecular dynamics calculations of larger nanoparticles. [1] L. Pizzagalli, J. Godet, Ultrahigh Strength and Plasticity Mechanisms of Si and SiC Nanoparticles Revealed by First-Principles Molecular Dynamics. Phys. Rev. Lett. 131, 236201, 2023. [2] L. Pizzagalli, J. Durinck, S. Brochard, J. Godet, First-principles molecular dynamics compression of small metallic nanoparticles. Scripta Materialia 241, 115683, 2024.