Using density functional theory, we studied the bulk and surface properties of Li and Na electrodes on an atomistic level. To get a better understanding of the initial stages of surface growth phenomena (and thus dendrite formation), various self-diffusion mechanisms were studied. For this purpose, dedicated diffusion pathways on the surfaces of Na and Li were investigated within the terrace-step-kink (TSK) model utilizing nudged elastic band calculations. We were able to prove that the mere investigation of terrace self-diffusion on the respective low-index surfaces does not provide a possible descriptor for dendritic growth. Finally, we provide an initial view of the surface growth behavior of both alkali metals as well as provide a basis for experimental investigations and theoretical long-scale kinetic Monte Carlo simulations.