Structural evolution of Ag nanoparticles during electron driven synthesis of Ag filaments on Ag$_{2}$WO$_{4}$: \textit{In situ} observation and theoretical supporting evidence*

$\alpha -$Ag$_{2}$WO$_{4}$ crystals irradiated by an electron beam from an electron microscope under high \textit{vacuum}, nucleate metallic Ag, and form Ag metallic nanowires on the $\alpha $ crystals surface. In order to understand this interesting and complex behavior of the formation and growth of Ag nanowires on $\alpha $-Ag$_{2}$WO$_{4}$ we investigated by detailed in situ transmission electron microscopy (TEM), field emission scanning electron microscopy (FE-SEM) studies, density functional theory calculations and \textit{ab initio} molecular dynamics (MD) simulations. First principle calculations point out that Ag-3 and Ag-4 atoms, located on the (100) surface, are the most energetically favorable to undergo the diffusion process to form metallic Ag. \textit{Ab initio} MD simulations and nudged elastic band (NEB) method were used to investigate the minimum energy pathways for diffusion of Ag atoms to outward sites on the (100) surface. The results point out that the injection of electrons decreases the activation barrier for this diffusion step and this unusual behavior results from the presence of a lower energy barrier process.