Ab initio simulations of the surface free energy of TiN(001)

Axel Forslund, Xi Zhang, Blazej Grabowski, Alexander V. Shapeev, Andrei V. Ruban

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4 Citations (Scopus)


The 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 78meVÅ-2 at 0 K to 73meVÅ-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.

Original languageEnglish
Article number195428
JournalPhysical Review B
Issue number19
Publication statusPublished - 20 May 2021


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