A neural-network based framework of developing cross interaction in alloy embedded-atom method potentials: Application to Zr-Nb alloy

Interaction potentials are critical to molecular dynamics simulations on fundamental mechanisms at atomic scales. Combination of well-developed single-element empirical potentials via cross interaction (CI) is an important and effective way to develop alloy embedded-atom method (EAM) potentials. In this work, based on neural-network (NN) models, firstly we proposed a framework to construct CI potential functions via utilizing single-element potentials. The framework contained four steps: (1) extracting characteristic points from single-element potential functions, (2) constructing CI functions by cubic spline interpolation, (3) evaluating the accuracy of CI functions by referring to first-principle (FP) data, and (4) searching for reasonable CI functions via NN models. Then with this framework, we developed a Zr-Nb alloy CI potential utilizing the MA-III (pure Zr potential developed by Mendelev and Ackland in 2007) and the Fellinger, Park and Wilkins (FPW) (pure Nb potential developed by FPW in 2010) potentials as single-element parts. The calculated results with this Zr-Nb alloy potential showed that: (1) the newly developed CI potential functions could simultaneously present the potential-function features of Zr and Nb; (2) the normalized energy-volume curves of L12 Zr3Nb, B2 ZrNb and L12 ZrNb3 calculated by this CI potential reasonably agreed with FP results; (3) the referred MA-III Zr and FPW Nb potentials can satisfactorily reproduce the priority of prismatic slip in Zr and the tension-compression asymmetry of 111{112} slip in Nb, while other ab initio developed Zr-Nb alloy potentials cannot. Our study indicates that, this NN based framework can take full advantage of single-element potentials, and is very convenient to develop EAM potentials of alloys; moreover, the new-developed Zr-Nb alloy EAM potential can reasonably describe the complicated deformation behaviors in Zr-Nb systems.