John Moriarty, Lorin Benedict, Randy Hood and Fred Streitz

Predictive large-scale atomistic simulation of materials properties is a forefront scientific and computational challenge that demands an accurate description of interatomic forces. To help meet this challenge, we are developing advanced quantum-based interatomic potentials for metals and alloys, including directionally-bonded d- and f-electron metals. First-principles generalized pseudopotential theory (GPT) provides a fundamental basis for such potentials through rigorous expansions of the electron density and total energy within density-functional quantum mechanics. In real space, the GPT total energy takes the form of a collective volume term plus sums over transferable two-, three-, and higher multi-ion potentials. For systems where directional bonding is negligible, including simple metals, series-end transition metals, and dilute transition-metal aluminides, only the volume and pair-potential terms need be retained. For central d-transition metals, on the other hand, angular-force, three- and four-ion potentials reflect important contributions from partially-filled d bands that also need to be retained. At the same time, however, in the full GPT these potentials are non-analytic, multidimensional functions that cannot be readily tabulated for application purposes. This has led to the development of the model GPT or MGPT for bcc transition metals. Within the MGPT, the multi-ion potentials are systematically approximated, via canonical d bands and other simplifications, to achieve short-ranged, analytic forms that can then be used in large-scale atomistic simulations. To compensate for the approximations introduced into the MGPT, a limited amount of parameterization is allowed in which the coefficients of the modeled potential contributions are constrained by experimental or ab initio theoretical data. In this form, the MGPT does indeed provide a robust framework for performing accurate and predictive atomistic simulations on bulk transition metals. Optimized MGPT potentials have now been obtained for Ta to 1000 GPa and Mo to 400 GPa (see figure). Successful application areas for GPT and MGPT potentials include equation of state, structural phase diagrams, melting, rapid solidification, high-pressure elastic moduli, ideal shear strength, vacancy and self-interstitial formation and migration, grain-boundary atomic structure, and dislocation core structure and mobility. Recent algorithm improvements have allowed more general matrix representations beyond canonical bands, extension to f-electron actinide metals and a factor of six increase in computational speed. We are also developing temperature-dependent GPT and MGPT potentials to subsume important electron-thermal effects at high temperature. Parallel versions of many of our MGPT molecular statics and molecular dynamics simulation codes have also been developed to take advantage of powerful ASC computers at LLNL.

## Selected Publications

- J. A. Moriarty, L. X. Benedict, J. N. Glosli, R. Q. Hood, D. A. Orlikowski, M. V. Patel, P. Söderlind, F. H. Streitz, M. Tang and L. H. Yang, "Robust Quantum-Based Interatomic Potentials for Multiscale Modeling in Transition Metals ," J. Mater. Res.
**21**, 563 (2006). - J. A. Moriarty, J. F. Belak, R. E. Rudd, P. Söderlind, F. H. Streitz, and L. H. Yang, "Quantum-Based Atomistic Simulation of Materials Properties in Transition Metals ," J. Phys.: Condens. Matter
**14**, 2825 (2002). - J. A. Moriarty and M. Widom, "First-Principles Interatomic Potentials for Transition-Metal Aluminides: Theory and Trends across the 3d Series , Phys. Rev. B
**56**, 7905 (1997).

Maintained by metals-alloys-web [at] llnl.gov (Lorin X. Benedict)