Thermal mass transport mechanism of an adatom on a crystalline surface

The diffusion of particles on surfaces subjected to a thermal gradient driven by phonons is numerically and theoretically investigated. Performing molecular dynamics (MD) simulations, we show that the thermal gradient induces a drift velocity of the adatom toward the cold regions. Beyond the bare study of the adatom trajectories for various thermal gradients, we propose to use a Massieu function as a thermodynamic potential that drives the adatom motion. We generalize the thermodynamic integration method to this out-of-equilibrium system to compute this thermodynamic potential. The thermal-gradient-induced effect is decorrelated from the stochastic diffusion from the analysis of the thermodynamic potential. Based on these results, we propose a model to evaluate the drift velocity and trajectory of an adatom that compares with a good agreement with trajectories provided by MD.