Comparison of embedded-atom models and ®rst-principles calculations for Al phase equilibrium John E. Jae a , Richard J. Kurtz a , Maciej Gutowski a,b, * a Materials Sciences Department, Paci®c Northwest National Laboratory, 902 Battelle Blvd., Richland, Washington 99352, USA b Department of Chemistry, University of Gda nsk, 80-952 Gda nsk, Poland Received 17 July 1999; accepted 18 November 1999 Abstract We have performed total energy calculations on Al in the face-centered cubic (fcc), body-centered cubic (bcc), ideal hexagonal close packed (hcp), and simple cubic (sc) crystal structures over a range of unit cell volumes. We employed density functional theory (DFT) in the local density approximation (LDA) and the generalized gradient approximation (GGA) as well as two dierent forms of the embedded-atom method (EAM) empirical atomistic potential with the aim of evaluating the predictive range of the EAM relative to ®rst-principles methods. All four calculations correctly give the fcc structure as the preferred one at zero pressure, with the DFT results in good agreement with the experimental equation of state and the model potentials in exact agreement (by construction). The hcp structure is found to be fairly close in energy to the fcc structure in all cases, and the sc structure is always found to be energetically very unfavorable. However, for the energetics of the bcc phase there is a serious disagreement between ®rst-principles and atomistic calculations: The bulk modulus of bcc Al is much lower as predicted by the model potentials, with the result that its energy approaches that of the fcc phase as the volume is reduced. For the potential of Mishin et al. an fcc ® bcc phase transition is predicted at a pressure of 27.4 GPa, in disagreement with the experimental fact that fcc Al is stable to at least 220 GPa. Our DFT results are consistent with earlier DFT calculations and with experiment in predicting no transition over the density or pressure range considered. Ó 2000 Elsevier Science B.V. All rights reserved. Keywords: Local density approximation; Generalized gradient approximation; Embedded-atom model; Aluminum; High pressure; Phase transition 1. Introduction The embedded-atom method (EAM) [1] is a popular and eective approach for modeling the properties of metallic solids while studying ex- tended defects or other situations in which the size of the required crystalline unit cell is too large for ab initio electronic structure calculations, or when very many time steps would be required in a dy- namic simulation. While the method eliminates electronic degrees of freedom in favor of a purely atomistic description, it includes a many-body po- tential term (the ``glue potential'') that incorporates some eects of the spatially varying electron den- sity described by a ®rst-principles calculation. In practice, EAM potentials are stated in terms of a set of parameters whose values are determined by www.elsevier.com/locate/commatsci Computational Materials Science 18 (2000) 199±204 * Corresponding author. Tel.: +1-509-375-4387; fax: +1-509- 375-2167. E-mail address: maciej.gutowski@pnl.gov (M. Gutowski). 0927-0256/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 0 ) 0 0 0 9 6 - 3