Polyvalent machine-learned potential for cobalt: From bulk to nanoparticles

We present the development and applications of a quadratic spectral neighbor analysis potential (q-SNAP) for ferromagnetic cobalt. Trained on density functional theory calculations using the Perdew-Burke-Ernzerhof (DFT-PBE) functional, this machine-learned potential enables simulations of large systems over extended time scales across a wide range of temperatures and pressures at near DFT accuracy. It is validated by closely reproducing the phonon dispersions of hexagonal close-packed (hcp) and face-centered cubic (fcc) Co, surface energies, and the relative stability of nanoparticles of various shapes. An important feature of this potential is its numerical stability in long molecular dynamics simulations. This robustness is exploited to compute the heat capacity of nanoparticles containing up to 9201 atoms, showing convergence to less than 2 $\mathrm{J}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}$ after 100 ns. Computations of the melting temperature of nanoparticles as a function of their size revealed a convergence to the bulk limit in excellent agreement with the experimental value. This highly accurate machine-learned potential for Co opens exciting opportunities for further applications such as the dynamics of nanoparticles in catalytic reactions.