It is well accepted that dendrites grow on anode surface of lithium-metal based batteries, while magnesium-metal batteries do not exhibit such a behavior. However, it has been recently shown experimentally and theoretically that magnesium can form uneven deposits that lead to similar safety concerns as lithium dendrites. To investigate a complex phenomenon such as dendritic growth from a theoretical point of view, it is necessary to study it on a multiscale level, i.e. from atomistic to meso scale. Herein we investigate thermodynamics, kinetics and morphology evolution of magnesium and lithium surfaces using density functional theory (DFT) and kinetic Monte Carlo (kMC) simulations. To be realistic for a device such as a battery, the electrochemical dimension has also to be included: this study was done within the framework of Grand canonical DFT approach that enables potential dependent DFT calculations, simulating relevant battery operating conditions. The atomistic potential dependent DFT results were upscaled using kMC simulations allowing to extract mesoscopic behavior at various operating potentials. The results of these calculations demonstrate the effect of potential on both the energetics and the dynamics of diffusion at the electrode-electrolyte interface. In particular, the equilibrium morphology of the metal electrode is strongly modified by the potential, leading to the stabilization of different surface orientations with potential. We show that the applied potential impacts atomic diffusion barriers leading to different surface mesoscopic relaxation times in the overall kinetics. The obtained results provide not only potential dependent information about systems morphology evolution, but also demonstrate the importance of using a suitable potential range (i.e. coherent with the experimental conditions): an unrealistic potential could lead to a very different behavior of the system on atomic and on meso scale. Image 1 • Influence of potential on crystal shapes of lithium and magnesium. • Influence of potential and time on energetics and kinetics of the system. • Descriptors for distinction between smooth growth/dendrite growth. • Widely applicable and transferable potential dependent multiscale methodology. [ABSTRACT FROM AUTHOR]