### Extending the Reach of First-Principles Methods to Model the Effect of Alloying Elements on Zirconium

In 1929 Paul Dirac, recognizing the difficulties of the deceptively simple equations of quantum mechanics, wrote '...It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.' P.A.M. Dirac, Proc. R. Soc. Lond. A6, 714-733, (1929)

Now in 2014, much computation can be performed, and quantum mechanical descriptions of matter are more accessible than ever before, yet Dirac's comment above remains penetratingly relevant. Quantum mechanical methods cannot extend to the scale and time periods needed to understand many physical phenomena. However, rather than forego the benefits of understanding afforded by atomistic models, quantum mechanical methods can be the foundation upon which more approximate yet practical methods are based.

A recent illustration of this has been provided by

http://www.sciencedirect.com/science/article/pii/S0022311513011902 Christensen et al.1 employing first-principles density functional theory (DFT) and embedded atom model (EAM) calculations to probe the influence of alloying elements on the behavior of zirconium alloys.

Zirconium alloys are tremendously important materials. They are the key structural material in light water reactors, for example. Although, they contain a preponderance of zirconium, their properties are governed by micro-structure, the inclusion of precipitates, and ultimately the details of the elements dissolved within the metallic lattice. Hence, composition exerts a controlling influence on the behavior of zirconium alloys, and an understanding of the atomic basis of such control enables rational design and modification strategies.

The nucleation of an interstitial dislocation loop in zirconium taken from an embedded atom model (EAM) molecular dynamics simulation of 12,670 atoms. The position of an Nb atom is highlighted in purple. Such EAM forcefield simulations, based on first-principles density functional theory (DFT) calculations, describe the effect of heteroatoms on the properties of metallic zirconium.

Christensen and coworkers employed the MedeA environment, and its model building, simulation, and analysis capabilities to obtain a detailed library of information on the intrinsic properties of zirconium and its interactions with a range of typical alloying elements. In addition to structural and energetic information, this library of computed properties (which compares well with experimental knowledge), includes mechanical, thermophysical, and dynamical information. Now first-principles methods alone are limited in system size and the number of configurations which may be simulated. Hence, in order to study the associations and rearrangements representative of the true metal lattice, and the evolution of atomic configurations over nano-seconds, EAM descriptions were employed.

EAM descriptions were obtained systematically and efficiently, using well defined and simple functional forms for the EAM, and fitting to first-principles molecular dynamic trajectories to obtain parameter sets for each element, capable of reproducing with high fidelity the first-principles information for a given impurity.

The resulting description, based on first-principles quantum physics, and EAM methods, provides an understanding of the behavior of alloying elements, and their interaction with hydrogen, in the zirconium lattice. The description which emerges is detailed. The effect of Nb on self diffusion of Zr atoms in zirconium is made apparent for the first time, for example. The origin of its effect is subtle, just the right balance of electronic (or chemical) and mechanical (or size) effects allows the Nb atom to capture passing Zr atoms. As well as Nb, the alloying behavior effects of Fe, Cr, and Sn were studied, using the combined first-principles and EAM approach, and the varied and detailed effects of these alloying elements on diffusion, self-diffusion, and hydrogen uptake analyzed.

The work not only details insights into the underlying causes of the physical phenomena which determine industrial performance but also illustrates the utility of multiscale modeling. A first-principles foundation provides the platform on which a forcefield description is constructed. The forcefield enables the simulation of length and timescales inaccessible to quantum mechanics alone.

The Materials Design, Inc. MedeA environment provides the necessary linkages between first-principles (MedeA-VASP) and EAM forcefield (MedeA-LAMMPS) simulations upon which multiscale simulations can be based. Approximate and practical EAM simulations extend the reach of first-principles methods, providing explanations for what have formerly been simply empirical observations. Increasingly such methods will make it possible to assess the main features of possible modifications and novel systems, confirming Dirac's far reaching prescience. Dirac had an intrinsic appreciation of the numerical complexity of the equations that he originally formulated and recognized that applications to real problems would require recourse to practical approximation, just like that made accessible by the MedeA environment.

If you are interested in learning more about first-principles DFT simulation using MedeA-VASP and EAM simulation using MedeA-LAMMPS, please drop us a line at

M. Christensen, W. Wolf, C.M. Freeman, E. Wimmer, R.B. Adamson, L. Hallstadius, P.E. Cantonwine, E.V. Mader J. Nucl. Mat. 445, 2014, 241â€“250