Multi-Scale Study of the Static Structure of Liquid Li 70-Bi 30 Alloy

A multi-scale approach is applied to study the static structure of Li70-Bi30 liquid alloy. In order to describe the interatomic interactions in this non-simple metal, we make a set of three empirical pair potentials fit ab-initio computations of the forces and energy in this system. Large scale classical simulations are performed using these fitted potentials from which the partial and total structures are computed. These results are validated by comparison with new experimental neutron data. The partial structure clearly indicates heterocoordination, which is consistent with a marked ionic nature of the bonding, in agreement with earlier electrical resistivity measurements. a Corresponding author: wax@univ-metz.fr


Introduction
Molecular dynamics (MD) simulations have demonstrated how helpful they can be for the study of alloys, leading easily to the knowledge of partial structures and chemical order [1,2]. However, non simple metals and alloys are difficult to describe using pair potentials.
Although ab-initio methods are accurate, they are limited as far as the number of particles is concerned. Thus, multi-scale approaches, modelling the interactions from ab-initio computations and using these models on a larger space-scale (namely in classical MD) are required.
In this study, we apply a method developed by Mihalkovic et al. [3] to the case of liquid Li 70 -Bi 30 alloy, a composition close to the Li 3 Bi compound forming one. The temperature is 1073 K and the corresponding density, =4.73 g/cm 3 . Under these conditions, this alloy is far from being a simple metal (i.e. nearly-free electronlike) as shown by its electrical resistivity [4]. Indeed, it is suspected to lie on the borderline between a metallic and an ionic liquid.
In order to illustrate the interest of this method, which we will shortly describe in section 2, we will focus on the static structure of this alloy. The corresponding results will be displayed and discussed in section 3.

Description
In a first step, ab-initio MD simulations are performed which provide us with configurations from which energies and forces are obtained; these are considered as reference data. We used VASP code and applied it to a box filled with 200 particles over a 30 ps simulated time, under the desired thermodynamic conditions. In a second step, an analytical expression is fitted in order to reproduce the ab-initio energies and forces. The parameter values thus obtained are displayed in Table 1.
Then, in a final step, these fitted potentials are used to perform classical MD simulations. We considered 13 500 particles over 10 ps in order to obtain the structural functions of interest. From the partial pair distribution EPJ Web of Conferences functions, g ij (r), Ashcroft-Langreth and Bathia-Thornton partial structure factors were computed and then the total one for neutrons (see Refs. 1 and 2 for more details).
Nevertheless, some checks are necessary and the fitting procedure can be tested by comparing ab-initio and classical MD predictions for the partial structures. Besides, the realism of the model of interactions can be ascertained by comparing simulation and experimental results.

Pair potentials
As can be observed from the data in Table 1, u LiLi (r) is purely repulsive: this feature is consistent with ionic-like behaviour. Moreover, considering the curves of these potentials ( Fig. 1), Bi-Bi core-repulsion is wider than both others while Li-Bi interaction is strongly attractive: all these features are promoting hetero coordination tendencies. 3 Structure of the alloy

Partial pair distribution functions
This hetero coordination is clearly displayed considering the partial pair distribution functions (Fig. 2). Indeed, g LiBi (r) has the highest first peak, indicating that Li atoms are mostly surrounded by Bi atoms, and vice-versa. Besides, considering the particular shape of g BiBi (r), its very low first peak indicates that the first neighbour of a Bi atom is rarely of the same kind and that most of the Bi atoms are pushed back into the second neighbour shell. Thus, this is consistent with the existence of loosely bound Li 3 -Bi compounds and with the increase of the ionic character of the bonding [4,5]. Comparing now classical and ab-initio MD results, even if there is not a perfect quantitative agreement, the main features are recovered, namely (i) the peak positions, (ii) the hierarchy between peak heights, and even (iii) the peculiar first peak of g BiBi (r). Therefore, we can consider that the fitted pair potentials correctly reproduce the interactions from ab-initio MD.

Neutron structure factor
In order to check the realism of the fitted potentials, it is necessary to consider experimental measurements. Therefore, we examine now the total structure factor as measured in neutron diffusion experiments. These data were obtained by integrating over energy the dynamic structure factor, S(q,), as obtained from inelastic scattering experiments [6]. These were performed at ILL's hot source. We thus obtained S(q) for several scattering vectors between 0.5 and 2 Å -1 . They are displayed in figure 3 with the results that we obtained by combining the partial pair structure factors using the appropriate diffusion lengths.
As can be seen, the agreement is excellent, which indicates that our fitted potentials describe the interactions in a realistic way.

Bhatia-Thornton structure factors
From the partial structure factors, we can also easily compute the so-called Bathia-Thornton structure factors (Fig. 4). These are useful to consider topological and chemical orders. It can be seen that S NN (q) is rather common, demonstrating that there is no particular topological order.
On the other hand, S CC (q) is remarkable. Its low-q limit S CC (0) ≈ 0.011 which is really less than 0.21, the value for an ideal mixture of same composition: this clearly demonstrates strong hetero coordination tendencies which could lead to compound formation. It also exhibits a marked peak at about half the position of the main peak of S NN (q). This indicates composition anomalies on a space-range equal to about twice the interatomic distance. All these features are consistent with the existence of loosely bound Li 3 Bi compounds. This interpretation is corroborated by the phase diagram [7] which displays an intermetallic Li 3 Bi compound. Electrical resistivity measurements [8]

Conclusion
We applied a multi-scale approach developed by Mihalkovic et al. to study the static structure of liquid Li 70 -Bi 30 alloy. This is far from a simple metal (inter metallic compound in the phase diagram, peaked dependence of the resistivity versus composition) and is thus very difficult to describe. Indeed, it is not freeelectron like and usual methods are unable to predict the effective pair interactions.
Nevertheless, Mihalkovic et al. approach succeeds in predicting the structure qualitatively and even quantitatively. Our computations agree remarkably well with neutron experiments. They confirm the structural particularities of the mixture, namely a strong hetero coordination and a peculiar partial Bi-Bi structure. These observations are consistent with the persistence of loosely bound Li 3 Bi compounds into the liquid state.
In order to refine our understanding of this alloy, as well as to confirm this hypothesis, an extension of this study to other compositions, as well as to dynamic properties such as diffusion and collective excitations is in progress.