Ab initio study of the effect of solute atoms on the stacking fault energy in aluminum Yue Qi* and Raja K. Mishra GM R&D Center, MC:480-106-224, 30500 Mound Road, Warren, Michigan 48090-9055, USA Received 11 December 2006; revised manuscript received 16 February 2007; published 6 June 2007 The stacking fault energy SFE in binary and ternary alloys of Al with common alloying elements was studied using density functional theory. Among these alloying elements, Fe further increases the SFE and Ge reduces the SFE of Al. The alloying elements increase the SFE by increasing the directional inhomogeneity in the electronic charge distribution of Al. The maximum value of charge difference on the fault plane, Max, is used to characterize how many electrons have been redistributed due to the stacking fault formation, and the SFE increases with Max. DOI: 10.1103/PhysRevB.75.224105 PACS numbers: 61.72.Nn, 62.20.Fe, 71.15.Nc I. INTRODUCTION Plastic deformation in metals is mediated by dislocation generation, movement, and interaction. The overall ductility is a microstructure-sensitive property, 1 governed by interac- tions between dislocations with solutes, vacancies, other dis- locations, grain boundaries, and secondary phases. Funda- mental studies of dislocation energetics and their generation, multiplication, and annihilation processes could provide guidelines for alloy or process modifications to optimize mi- crostructure for ductility enhancement. In Al alloys, forest dislocation networks on nonintersecting slip planes contrib- ute to nonhomogeneous slip distribution, easy shear localiza- tion, and premature failure. One approach to distribute slip homogeneously is to fundamentally alter the slip behavior by lowering the stacking fault energy SFE of Al alloys so that easy glide of dislocations is replaced by entanglement of partial dislocations and formation of stacking fault tetrahedra. 2 The effect of SFE on dislocation slip in fcc metals is well known. 3 Dislocations in metals and alloys reduce their elastic energy by separating into two partial dislocations which are joined by a band of faulted structure in the slip plane, called a stacking fault. The equilibrium width of such an extended dislocation depends on the characteristic SFE of the material. To allow a dislocation to cross-slip onto a new slip plane, the partial dislocations must be forced together followed by a resplit on the new slip plane. Thus, lower SFE corresponds to larger partial separation and more difficult cross slip for the partials, favoring a three-dimensional network of sessile and glissile dislocations. Such a network formation delays shear band formation and premature localization as seen in Cu, Ag, etc. In contrast, higher SFE leads to narrower dislocation separation or undissociated dislocations in Al, which tends to form forest dislocation networks without appreciable sessile dislocations pinned by jogs and kinks. 1,4 Easy glide results in easy slip band formation. These bands act as soft zones for dislocations to move as deformation proceeds, which local- izes the deformation in these bands in single grains and ac- celerates shear band formation in an aggregate of grains, leading to failure. The differences in SFE of fcc metals like Al, Cu, and Ag arise from the differences in their electronic structures. Al has 2s 2 2p 1 valence electrons, but Cu has a fully occupied 3d orbital and 4s 1 electron. Using density functional theory cal- culations, Ogata et al. 5 have shown that while the charge density distribution is nearly spherical in fcc metals like Cu and Ag, the pocket of charge density at the octahedral inter- stice in Al has a cubic symmetry and is angular in shape due to the slight covalent and directional nature of bonding. 6 When an intrinsic stacking fault is created by shearing the close-packed plane along 112, the electrons can redistribute well in the nondirectionally bonded metals like Cu and Ag without a large energy penalty. However, the electrons do not readapt so readily in Al due to the directionality of the bonds, resulting in large SFE. Experimentally it is known that the SFE in Al is much larger than that in Cu, Ag, or even Ni which shows bond directionality due to magnetic spin contributions. 6 If alloying can change the SFE and favor dislocation dis- sociation in Al alloys, new mechanisms of slip evolution can improve their ductility. Previous searches for alloying addi- tion to reduce the SFE of Al have not been very successful. Reported experimental values of SFE are unreliable because of inaccuracies in measuring small differences in the separa- tion distance between partial dislocations in electron micro- scope images. Theoretical values of SFE in Al and Al alloys vary widely in the literature, partly because of inaccuracies in modeling electronic interactions between atoms using an empirical potential EP, 7 such as the embedded atom poten- tial EAM potential, 8 glue potential, 9 or phenomenological n-body potential. 10 This report presents a first-principles simulation of alloying effects on the SFE to provide limiting case values that can serve as a guide to future experimental search for alloy design to lower the SFE and distribute slip homogeneously. One of the greatest advantages of first- principles electronic structure methods over those utilizing an empirical potential is the incorporation of electronic ex- change and correlation effects which account for the interac- tion of electrons in condensed matter. More importantly, for many alloying elements in our calculation, the empirical po- tential is simply not available. The aim of this paper is to investigate the effect of small additions of alloying elements that could alter the anisotropic electron distribution around Al atoms towards spherical sym- metry, consequently reducing the SFE and altering the slip mechanism. Even though quantitative experimental data on Al SFE are scarce, 11,12 indirect evidence of lower SFE in Al alloys has been reported for Cr and Mg additions. 13,14 In this investigation, first-principles calculations of changes to the electron distribution and SFE with the addition of common alloying elements in binary and ternary Al alloys have been PHYSICAL REVIEW B 75, 224105 2007 1098-0121/2007/7522/2241055 ©2007 The American Physical Society 224105-1