(377d) Modeling of Segregation on Au-Pd (111) Surfaces with Monte Carlo Simulations and Neural Network Atomic Potentials

The simulation of segregation in multi-component alloy surfaces is challenging with atomistic approaches because of the need to model a very large number of possible configurations with a high degree of accuracy. Density functional theory (DFT) is too expensive to use directly, and atomistic potentials are often a compromise between accuracy and computational speed. Neural networks (NN) are a promising alternative to traditional atomistic potential. Using the Behler-Parrinello framework, we were able to create a potential capable of predicting highly-accurate energies for any configuration of a AuPd(111) slab. The fully trained NN spanning all configurations and lattice constants of a AuPd binary alloy is trained from only 3,914 DFT calculations, each with only 7-21 atoms. From these relatively small slabs, Monte-Carlo simulations can be performed on 10 x 10 x 15 atom slabs with average errors under 5 meV/atom.

Mean compositions from the Monte-Carlo simulations were then used to construct segregation profiles spanning bulk compositions between 10 and 90% Au, and at temperatures ranging from 700-1000 K. These simulations result in excellent agreement with available experimental low-energy ion scattering spectroscopy data, which is sensitive only to the composition of the top layer of a metal surface. Site distributions were computed and compared to random distributions, indicating the presence of some short-range ordering favoring the formation of Au-Pd surface bonds. These trends in site distribution are also in excellent agreement with available scanning tunneling microscopy data, further validating our model. These profiles can also be fit to the Langmuir-McLean formulation of the Gibbs-isotherm with a model for the enthalpy of segregation. Based on the trends observed in the calculated enthalpy of segregation across all bulk compositions, it is not clear how one would derive the same trend using more traditional techniques, such as course-grained models based on dilute limit segregation energies alone. The techniques derived in this work are easily implemented, even with limited computational recourses. Due to the flexible nature of the NN, results from this work are also useful in application to more complex systems with adsorbates.