Title: LAMMPS Simulation in the Investigation of Dimensional Changes in Zirconium in the Presence of Alloying Elements and Hydrogen

Presenter: Clive Freeman

Authors: C.M. Freeman, E. Wimmer, M. Christensen, W. Wolf, D. Rigby, and P. Saxe

Affiliation: Materials Design, Inc., Santa Fe, NM, USA

Abstract: Boiling water reactors are widely employed in the generation of electrical power and considerable effort has been dedicated to the analysis of the materials properties which affect their operation. For example, the bowing of zirconium alloy fuel channels during operation presents a significant practical challenge; and the underlying processes which govern this distortion phenomenon are not completely understood. An appreciation of the origin of the distortion of such reactor components would facilitate improved operational economics, and reduce the environmental impact of component replacement, providing a clear incentive for detailed research.

However, the processes which underlie channel distortion are complex: channel systems operate at high temperatures, in the presence of water, and the channels are constructed from engineering grade metals containing defined concentrations of alloying elements which impart modified properties to the material. Understanding the behavior of hydrogen and alloying elements in metallic zirconium, and their role in modifying the transport of zirconium atoms under reactor conditions requires a combination of theoretical and experimental methodologies. First-principles (VASP) and forcefield based (LAMMPS) calculations, within the MedeA® environment, have been employed 1 to address several questions concerning the details of the atomic interactions which underlie channel bowing.

The LAMMPS simulations, based on a library of first-principles simulations employing VASP, provide detailed information on the role of hydrogen and alloying element atoms in modifying zirconium self diffusion behavior in hexagonally closed packed zirconium systems. The simulations address hydrogen solubility and hydride formation in the metal, the location and behavior of alloying elements within the lattice, and the self diffusion of zirconium in the presence of hydrogen and alloying metals. The LAMMPS calculations draw upon an existing Embedded Atom Method (EAM) formulation for Zr 2, with custom extensions based on first-principles methods for additional elements.

The simulations show that Nb and Sn influence the mobility of Zr self-interstitial atoms (SIA’s) 3. Nb suppresses the diffusion of SIA’s, reducing the rate of formation of interstitial a-loops. Sn atoms, on substitutional sites, have a similar, but smaller effect. If SIA’s approach substitutional Fe, Cr, and Ni atoms, the LAMMPS simulations indicate a spontaneous swap is favored, promoting the smaller transition metal atom into an interstitial site. Such mechanisms allow diffusion of impurities, with a preference for c-direction motion, facilitating segregation to energetically favorable sites such as vacancies, vacancy c-loops, grain boundaries, surfaces, and intermetallic precipitates.

This study illustrates the interplay of first-principles and forcefield methods, the efficiency of LAMMPS in the analysis of a wide range of possible diffusion mechanism, and the use of atomistic simulation in the analysis of materials problems.

References

1 M. Christensen, W. Wolf, C. M. Freeman, E. Wimmer, R. B. Adamson, L. Hallstadius, P. E. Cantonwine, E. V. Mader, ASTM Conference, Feb 6 2013, Hyderabad, India

2 M.I. Mendelev, G.J. Ackland, Phil, Mag. Lett. 87, 2007, 349–359

3 M. Christensen, W. Wolf, C. M. Freeman, E. Wimmer, R. B. Adamson, L. Hallstadiusc, P. E. Cantonwined, E. V. Mader, ‘Effect of alloying elements on the zirconium-hydrogen system’, Submitted for publication, 2013