The calculation of the surface energy of high-index surfaces in metals at zero temperature

We used the molecular dynamics simulation with interatomic potentials of the embedded atom method to calculate the high-index surface energies of the surfaces containing the 〈0 0 1〉 axis or 〈−1 1 0〉 axis in f.c.c. metal Al, Cu and Ni at zero temperature. We generalized an empirical formula based on structural unit model for high-index surfaces and present some new formulas that can be used to estimate the surface energy and structural feature of high-index surfaces very well. The results show that the closest surfaces have the lowest surface energy and the surface energies of the closest (1 1 1) surface and the next closest (1 1 0), (1 0 0) surfaces are the extremum on the curve of surface energy versus orientation angle. We also calculated the b.c.c. metal Fe and obtained a similar result. The difference is that in the b.c.c. metal the surface energies of the closest (1 1 0) surface and the next closest (1 0 0), (1 1 2) surfaces are the extremum on the curve of surface energy versus orientation angle. The results of theoretical simulation and the empirical formula consist well with the experiment data.