Total energies of cubic boron nitride (c-BN͒ ͑001͒ surfaces are systematically studied for various reconstructed configurations by the local density-functional approach with ultrasoft pseudopotentials. Stable phases as a function of nitrogen chemical potential are predicted theoretically. We examine the validity of the electron counting ͑EC͒ rule, which plays an important role for the study of the GaAs surfaces, and obtain supplemental factors to determine stable surface structures. The results of the total-energy minimization calculation demonstrate that the EC rule holds very well within the models that contain at most one layer with defects and no interlayer N-N and B-B bonds, and that next to the EC rule, the electrostatic energy has the most important role in determining stable structures. Furthermore, in the nitrogen-rich region, we found that the EC rule does not hold, because the energy difference between the N-B and N-N bonds is larger than the energy gain from using the EC model. We suggest that the important factors for determining stable structures of the c-BN͑001͒ surface are N-B bond saturation, the EC rule, and electrostatic energy, whose effect decreases in this order. The difference between c-BN and GaAs surfaces is also discussed. ͓S0163-1829͑96͒01723-7͔

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To clarify atomic diffusion in amorphous materials, which is important in novel information and energy devices, theoretical methods having both reliability and computational speed are eagerly anticipated. In the present study, we applied neural network (NN) potentials, a recently developed machine learning technique, to the study of atom diffusion in amorphous materials, using LiPO as a benchmark material. The NN potential was used together with the nudged elastic band, kinetic Monte Carlo, and molecular dynamics methods to characterize Li vacancy diffusion behavior in the amorphous LiPO model. By comparing these results with corresponding DFT calculations, we found that the average error of the NN potential is 0.048 eV in calculating energy barriers of diffusion paths, and 0.041 eV in diffusion activation energy. Moreover, the diffusion coefficients obtained from molecular dynamics are always consistent with those from ab initio molecular dynamics simulation, while the computation speed of the NN potential is 3-4 orders of magnitude faster than DFT. Lastly, the structure of amorphous LiPO and the ion transport properties in it were studied with the NN potential using a large supercell model containing more than 1000 atoms. The formation of PO units was observed, which is consistent with the experimental characterization. The Li diffusion activation energy was estimated to be 0.55 eV, which agrees well with the experimental measurements.