Structure and dynamics of NiAl(110) studied by high-resolution ion scattering combined with density functional calculations

Abstract

The surface relaxation and the rumpling of the top layer and the second layer together with the mean thermal vibration amplitudes of NiAl(110) are determined by high-resolution medium energy ion scattering (MEIS) with an excellent depth resolution of typically $\ifmmode\pm\else\textpm\fi{}0.01\text{ }\text{\AA{}}$. We also perform classical molecular-dynamics (MD) simulations employing the embedded atom method and the first-principles calculations using the VASP (Vienna ab initio simulation package) code. The results obtained by MEIS are compared with the theoretical predictions and experimental analysis reported so far. Interestingly, the present MEIS analysis observes slightly expanded relaxation $\ensuremath{\Delta}{\ensuremath{\epsilon}}_{12}$, which is supported by the present MD and VASP calculations and by x-ray diffraction analysis whereas other experimental and theoretical analyses give contracted relaxation. The root-mean-square thermal vibration amplitude of the bulk Ni atoms is determined to be $0.10\ifmmode\pm\else\textpm\fi{}0.005\text{ }\text{\AA{}}$, which agrees well with the value of $0.097\text{ }\text{\AA{}}$ derived from the phonon-dispersion relation calculated from VASP. A slightly enhanced thermal vibration amplitude of the top-layer Ni in the surface-normal direction observed is consistent with the MD simulation.