Simulations of friction force microscopy on the KBr(001) surface based onab initiocalculated tip-sample forces

We report on ab initio-based simulations of friction-force microscopy on the KBr(001) surface at zero and nonzero temperature. To simulate sliding friction, we employ an extended three-dimensional (3D) Prandtl-Tomlinson model. The microscopic part of the tip is modeled by ${\mathrm{K}}^{+}$- or Br${}^{\ensuremath{-}}$-terminated tips. We use a tip-surface interaction potential, which is calculated within local-density approximation of density-functional theory and supplemented by a long-range van der Waals interaction resulting from the macroscopic part of the tip. Thermal fluctuations are included via random white noise. The loading force acting on the tip enters the Langevin equation of motion separately from all other forces so that it can be changed at will. We analyze friction as a function of loading force, temperature, and mass of the tip and identify regions of these parameters where distinct stick-slip behavior or ultra-low friction occurs. A comparison of our 3D ab initioresults with those obtained using sinusoidal tip-surface forces (1D model) is very revealing. By and large, both approaches yield results in good agreement at $T$ = 0 K. At higher temperatures, however, distinct differences occur. For example, at $T$ = 295 K, the 1D model calculations overestimate the friction hysteresis and energy dissipation, and for positive loading forces they even can yield a different periodicity in the friction-force profile.