| Material surface is the two-dimensional area where the physical and chemical properties have been changed abruptly. Plenty of important physical and chemical processes occur in the surface at first and so does some broken in the materials. Therefore, surface is the window where the materials connect with the outside environment directly. Through the research of material surface one can make the material properties changed in one's needs. So the research of the atomic structure in the crystal surface has been the central issue in surface science. Kinds of Many modern experimental techniques, as well as a large number of semi-empirical and empirical models for covalent materials have been used to observe and simulate the reconstruction of surface, but the mechanism for the reconstruction forming has not been concluded. In this work, the modified embedded atom method (MEAM) has been used to simulate the possible structures for (110), (211) and (311) surfaces of seven FCC transition metals and (001) surface of three diamond cubic crystals with the computer simulation. We discuss and analyze the mechanism of forming the surface reconstruction from the energy minimization, surface topography and valence electron structure.(1) The energy densities of the ideal (1×1), missing row (MR) (1×2) and missing column (MC) (2×1) (110) surfaces have been calculated for seven FCC transition metals Au, Pt, Ag, Pd, Rh, Cu and Ni. The results from energy minimization, that the MR (1×2) reconstruction can be formed naturally for Au and Pt, but can not be formed naturally on Ag, Pd, Rh, Cu and Ni, are better than EAM calculated results in comparing with experimental results. Because the EAM calculations show the MR (1×2) reconstruction can also be formed naturally on Ag (110) and Pd (110) surfaces. The MC (2×1) reconstruction can not be formed for all metals. In addition to the surface energy explanation, we analysis the relative possibility of forming the MR and MC reconstructions on each metal (110) from the surface topography and valence electron structure.(2) Calculate the change in the surface energy density of (1×2) MR reconstruction from initial (1×1) ideal (211) and (311) surfaces to ascertain MR reconstruction for seven transition metals Au, Pt, Ag, Pd, Rh, Cu and Ni, and comparative analyze the (110), (211) and (311) three MR reconstruction surfaces. The results, that the MR reconstruction can not be formed naturally on (211) surfaces of all transition metals,but can be formed naturally on Pt (311) surface, are good consisitent with experimental results and first principles calculations. Moreover, the possibility of forming the (1×2) MR reconstruction on all three surfaces (110), (211) and (311) decreases oscillatorilly for 5d metals Au and Pt, 4d metals Ag, Pd and Rh, 3d metals Cu and Ni, successively. The results are explained in valence electron structure and surface topography.(3) The energy densities of the ideal (1×1), dimer (2×1) and trimer (3×1) structures on (001) surfaces have been calculated for three diamond cubic crystals C, Si and Ge. From energy minimization, the dimer (2×1) and trimer (3×1) reconstructions can be formed naturally and without any barrier. The dimer corresponding to the lowest energy implies it is the easiest to be formed and the most stable as well. This is consistent with the experimental result and other theoretical prediction. Determined dimer bond length of 2.43(?) for Si drops in the experimental range of 2.20(?)～2.47(?), and of 2.5(?) for Ge is close to the 2.55(?) measured by X-ray diffraction. The trimer, constructed here firstly, has not been observed in the experimental due to its slightly higher energy than dimer. Its bond lengths have been determined to be 1.96(?), 2.64(?) and 2.75(?) for C, Si and Ge respectively. Further experimental testing is needed.
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