reported that {101 0}<112 0> prismatic slip, {101 1}<112 0> first order pyramidal slip and { 112 2} < 1 1 23> second order pyramidal slip are also activated in magnesium at high temperature [1,2]. These slip systems are shown in Figure 1. Additionally, it is interesting that the dominant slip mode is different in HCP metals. For example, slip occurs preferentially on basal plane in Mg, Be, Cd and Zn, but prismatic slip is preferred in Ti, Y, Hf and Zr. {112 2} {101 0} {101 1} {0001} Figure 1: Slip systems in magnesium. In slip deformations, the critical parameter is a property of the generalized stacking fault (GSF) energy which is also called γ-surface [3]. The GSF energy is defined as follows; a crystal is cut into two halves along the slip plane and one half is displaced relative to the other by the vector t. As this vector is varied, the energy changes and traces out the GSF energy γ(t) , which is normally defined as energy differences from bulk crystal. If this vector are varied along with Burgers vector, the GSF energy is identified with the potential energy necessary to ideal slip. So shear strength of real materials should increase as the GSF energy increases. There exists a relationship between the GSF energy and the dislocation density or Peierl's stress [4]. Especially, the stable stacking fault energy which is the minimum of the GSF energy play a major role in the behavior of dislocation core. Legrand [5] calculated the GSF energy on basal and prismatic planes for various HCP metals including Mg using empirical pseudopotential method and tight-binding method. He found good agreements between the observed main slip system of various HCP metals and ratio of basal to prismatic stable stacking fault energy. It can be explained that the stable stacking fault energy is a dominant factor of the splitting width of the dislocation core and it is easy to slip as the energy is smaller. However, their calculations are based on the semi-empirical method and there is hardly quantitative and accurate investigations. Thus, in the present work we employ ab initio pseudopotential method for magnesium to study accurate GSF energy on basal and prismatic plane. METHODS All calculations presented in this paper were performed using Cambridge Serial Total-Energy Package (CASTEP). CASTEP is an ab initio pseudopotential method code for the solution of the electronic ground state of periodic systems with the wavefunctions expanded in plane wave basis using a technique based on density functional theory (DFT) [6,7]. The electronic exchange-correlation energy is given by the generalized gradient approximation (GGA) of Perdew and Wang [8] in the DFT. We use the normconserving pseudopotential of Troullier and Martins [9] in a reciprocal space. The pseudopotential is transformed to a separable form as suggested by Kleinman-Bylander [10]. The partial core correction [11] is also included in this pseudopotential. The electronic ground state is efficiently obtained using the conjugategradient technique [12]. The cutoff energy for the plane-wave basis is 4.36×10-17J (20Ry) which is sufficient for all our purposes. The stable atomic configurations are obtained through relaxation according to the Hellmann-Feynman forces. The supercells containing 10 basal atomic layers and 12 prismatic atomic layers are used for the calculation of the GSF energies on basal and prismatic plane, respectively (see Figure 2). For basal and prismatic supercells, Brillouin zone integration over k points are performed using 12×12×2 and 11×7×3 regular divisions of each axis in reciprocal space, respectively. The slip deformation occurs with dislocations along Burgers vector, but dislocations are dissociated to
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