Forslund, AxelZhang, XiGrabowski, BlazejShapeev, Alexander V.Ruban, Andrei V.2022-08-222022-08-2220212469-99691815186496http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-123144http://elib.uni-stuttgart.de/handle/11682/12314http://dx.doi.org/10.18419/opus-12297The temperature dependence of the surface free energy of the industrially important TiN(001) system has been investigated by means of an extended two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD) methodology, to include the fully anharmonic vibrational contribution, as obtained from ab initio molecular dynamics (AIMD). Inclusion of the fully anharmonic behavior is crucial, since the standard low-temperature quasiharmonic approximation exhibits a severe divergence in the surface free energy due to a high-temperature dynamical instability. The anharmonic vibrations compensate for the quasiharmonic divergence and lead to a modest overall temperature effect on the TiN(001) surface free energy, changing it from around 78 meV Å-2 at 0 K to 73 meV Å-2 at 3000 K. The statistical convergence of the molecular dynamics is facilitated by the use of machine-learning potentials, specifically moment tensor potentials, fitted for TiN(001) at finite temperature. The surface free energy obtained directly from the fitted machine-learning potentials is close to that obtained from the full AIMD simulations.eninfo:eu-repo/semantics/openAccess530article