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Computational Materials Science, Volume 72, May 2013, Pages 146-157.
Flemming J.H. Ehlers, Randi Holmestad.
Dept. of Physics, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway.
Abstract
An ab initio based atomistic model scheme for an approximate determination of the interfacial and strain energies for the entire interface of a fully coherent precipitate in a host lattice is presented. For each given presumed compositionally abrupt interface, the model incorporates the effect of the strain evolution along the interface by use of a sequence of supercells. Each cell in this sequence has been distorted to describe the local interface region in question with the optimal accuracy allowed by periodic boundary conditions. Together, the cells comprise a shell of nm thickness, enclosing the full interface and its strongly affected near vicinity. The computational demands for the scheme are connected with the number of atoms in a given interface region cell, i.e., no scaling with precipitate size occurs – other than the number of cells required. In practice, this allows performing calculations for essentially all precipitate sizes. The scheme has been tested for the case of the main hardening precipitate {Beta}″ in the Al–Mg–Si alloy system and compared quantitatively with presently available alternatives. Implementation in an atomic hybrid model scheme for a full description of the precipitate interface energy should be realistic.
Additional Information:
The work presented in this paper is integral to the MultiModAl project (Jan 2010 – Dec 2013), a collaboration between the educational institution NTNU (Trondheim, Norway), the independent science organisation SINTEF and the aluminium industry Hydro Al. The project aims at gaining new territory in the context of utilizing first principles methods for microstructure modelling in age hardenable Al alloys. More precisely, the target is a determination of the interfacial and strain energies, as obtained with such methods, for the Al–Mg–Si alloy main hardening phase {Beta}”, with the precipitate fully surrounded by Al in the model system. Increased reliance of microstructure model schemes on first principles methods ultimately decreases the dependence on tuning parameters when fitting the experimental data. Such controlled modifications may be instrumental to high predictive power – in particular transferability – in theoretical alloy optimization considerations, and hence should be of significant interest to the integrated computational materials engineering community.
It has long been recognized that hybrid schemes are preferable – and even mandatory, given presently available computational resources – for modelling the atomistic systems of the size in question here. The scheme described in the paper proposes a circumvention of a key obstacle in this context, by highlighting a way to model extended interface regions with density functional theory methods – at very low computational costs (see abstract for details). This in turn promises that a high accuracy in the calculated interface properties may be retained everywhere on the interface, provided that a seamless coupling is established to the surrounding parts of the system.
The scheme may also have application beyond the precipitate-host lattice systems – to certain epitaxially grown films as well as other phase boundaries where full coherency is attained locally, but misfit induced strain plays a significant role on the larger scale.
