Surface property is an important factor that is widely considered in crystal growth and design. It is also found to play a critical role in changing the constitutive law seen in the classical elasticity theory for nanomaterials. Through molecular static simulations, this work presents the calculation of surface properties (surface energy density, surface stress and surface stiffness) of some typical cubic and hexagonal crystals: face-centered-cubic (FCC) pure metals (Cu, Ni, Pd and Ag),

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... tered-cubic (BCC) pure metals (Mo and W), diamond Si, zincblende GaAs and GaN, hexagonal-close-packed (HCP) pure metals (Mg, Zr and Ti), and wurzite GaN. Sound agreements of the bulk and surface properties between this work and the literature are found. New results are first reported for the surface stiffness of BCC pure metals, surface stress and surface stiffness of HCP pure metals, Si, GaAs and GaN. Comparative studies of the surface properties are carried out to uncover trends in their behaviors. The results in this work could be helpful to the investigation of material properties and structure performances of crystals.