A tight-binding atomistic approach for point defects and surfaces applied to the o-Al13Co4 quasicrystalline approximant

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Highlights

  • A tight-binding N-body potential for Al–Co interactions is implemented.

  • We model the o-Al13Co4 quasicrystalline approximant in the presence of atomic vacancies and surfaces.

  • The importance of stress relaxation in vacancies formation in bulk o-Al13Co4 is highlighted thanks to an atomic stress mapping.

  • A good agreement between DFT and semi-empirical calculations is obtained for surface structures and relative surface energies.

Abstract

We implemented an N-body potential for the Al–Co interactions and applied it to the o-Al13Co4 quasicrystalline approximant. We show its ability to model this complex compound in the presence of point and extended defects (atomic vacancies and surfaces). The importance of stress relaxation in vacancy formation is highlighted through the mapping of local pressures in the bulk compound. Thanks to the many body character of the potential, the surfaces could be investigated which was not done before in atomistic studies of this complex phase. Our classical simulations point up the competition between preserving the cohesion by minimizing the number of broken bonds and avoiding the presence of Co atoms at the surface. This study opens the way to large scale simulations of phenomena involving complex metallic alloys in particular at their surfaces.

Introduction

The Al13Co4 intermetallic compound has recently attracted the attention of many research groups due to its unusual physical and chemical properties. A few examples include its strongly anisotropic magnetic and electronic transport behavior [1], its interesting catalytic performances towards hydrogenation reactions [2], [3], as well as its unexpected wetting properties [4]. To understand these fascinating features, the determination of structure–properties relationships is crucial. This task is however challenging, since defects play a non negligible role in this compound. For instance, the lack of quantitative agreement between the ab initio-calculated theoretical transport coefficients and the experiments have been attributed, at least in part, to the presence of disorder in the samples [1]. More recently, emphasis was raised on the fact that experimental phonon lifetimes and temperature-independent lattice thermal conductivity in Al13Co4 can only be fully described by properly taking into account the disorder [5].

The orthorhombic o-Al13Co4 crystal structure was primarily refined in the Pmn21 space group using X-ray diffraction (XRD) experiments [6]. Early identified as a quasicrystal approximant [7], o-Al13Co4 presents all structural features characteristic of a Complex Metallic Alloy (CMA) [8], including a crystal cell containing more than 100 atoms, arranged in well-defined bipentagonal polyhedra, and the occurrence of inherent disorder, probed by the large atomic displacement parameters of several aluminum positions. Recently, high-resolution single-crystal XRD with spherical aberration corrected HRTEM and HRSTEM (High Resolution Transmission and Scanning Transmission Electron Microscopy) has revealed multiple split and partially occupied crystallographic sites [9].

Accurate and reliable modeling of o-Al13Co4 where structural complexity and local disorder are at play, requires large computational cells. Thus, in this case, computational limitations prevent Density Functional Theory calculations from being applied to perform atomistic simulations. Alternative methods based on interatomic potentials are more suitable for this purpose. Such approaches have already been successfully used to model bulk o-Al13Co4 characteristics, like thermodynamic [10], [11] and vibrational [5], [12] properties, based on oscillating pair potentials derived from force or/and energy matching to ab initio calculations [13]. However, the transferability of the previous potentials built for bulk systems, to other properties related to the presence of surfaces, is not trivial. Indeed, pair potentials are insensitive to changes in coordination and thus, are not a priori suited to catch the increased bond strength of atoms at or near surfaces due to their strongly reduced average coordination. Because of the strong practical interests on Al13Co4 surfaces, like chemical reactivity [14], wetting [4], oxidation resistance [15], the question of the transferability of Al–Co pair potentials to surface properties is of interest. As far as we know, the few parameterized potentials built for bulk Al–Co alloys [16], [17], [18], [19] are not evaluated against surface properties. On the other hand, studies involving metallic surfaces mainly relate to experimental observations combined with DFT. The latter is used to quantify the relative stability between different configurations [14], [20], [21], [22].

We therefore propose here to move a step forward towards the modeling at the atomic scale of complex intermetallics including their surfaces by developing a new parameter set for Al–Co alloys using a simple many body interatomic potential. This potential based on the tight-binding formalism is founded on the fitting to ab initio data calculated for pure Co, pure Al and several Al–Co alloy phases including o-Al13Co4. The new parameter set is applied to the study of the formation of Al bulk vacancies and the o-Al13Co4(100) surface which are two archetypes of respectively point and extended defects.

Section snippets

Tight-binding potentials

The bonding in (Al, Co) based systems was modeled by using a tight-binding (TB) N-body potential based on the second moment approximation of the density of states in the Tight-Binding formalism (TB-SMA) [23], [24]. It is derived from a simplified but realistic description of the electronic structure and has been widely used for a large set of metals and alloys, mostly of the transition series [24], [25]. It was also extended with success to metals having a free-electron-like character [26], [27]

Parameterization of the interatomic potential

The parameters (A,ξ,p,q) for each type of bonds – Al–Al, Co–Co and Al–Co (12 parameters in total) – are mainly determined by least square mean fittings to DFT quantities like lattice parameters and cohesion or alloy formation energies. The homoatomic parameters are fitted to the cohesion energy curves of fcc Al and Co calculated with DFT as a function of the lattice parameter. For the fitting of mixed interactions, we use the formation energies of the experimentally observed ordered B2 and

Conclusion

We have parameterized an N-body potential based on the tight-binding second moment approximation to describe atomic interactions in o-Al13Co4. This potential has been implemented in classical quenched molecular dynamics simulations for structural studies of the realistic complex compound in the presence of defects, either point (vacancies) or extended (surfaces). Considering the inherent qualitative nature of such studies compared to DFT, most of the physics of the complex o-Al13Co4 compound

CRediT authorship contribution statement

O. Bindech: Methodology, Software, Validation, Investigation, Formal analysis, Visualization. C. Goyhenex: Conceptualization, Methodology, Software, Validation, Investigation, Formal analysis, Visualization, Supervision, Funding acquisition, Writing – original draft. É. Gaudry: Conceptualization, Methodology, Software, Validation, Investigation, Formal analysis, Supervision, Resources, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was funded by the French National Research Agency (ANR) through the Programme d’Investissement d’Avenir under contract ANR-11-LABX-0058 NIE within the Investissement d’Avenir program ANR-10-IDEX-0002-02. It is also supported by the European Integrated Center for the Development of New Metallic Alloys and Compounds. Some of us acknowledge financial support through the COMETE project (COnception in silico de Matériaux pour l’EnvironnemenT et l’Énergie) co-funded by the European Union

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    Present address: Laboratoire de Chimie Quantique, Institut de Chimie Strasbourg, UMR7177 CNRS/Université de Strasbourg 4 rue Blaise Pascal BP296, F-67008 Strasbourg, France.

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