Interaction in the Al-CaF2 system, ab-initiocalculations and experimental verification

S. Barzilai(a,b),M. Lomberg(a), N. Froumin(a), M. Aizenshtein(b)D. Fuks(a)and

N. Frage(a)*

(a) Department of Materials Engineering, Ben-GurionUniversity,

P.O.Box 653, Beer-Sheva 84105, Israel

(b) NRC-Negev, P.O.Box 9001, Beer-Sheva84190, Israel

Abstract

Ab initio simulations of the adsorption of Al atoms on CaF2(001) and (111) surfaces have been performed for 7 different atomic configurations, using density functional theory (DFT) with the generalized-gradient approximation (GGA). Each configuration was modeled using a periodic two-dimensional slab,a vacuum separation andAl atom at a distance of 0.9-6Å from the surface. It was found that the character of the adsorption bonding strongly depends on the atomic configuration of the adsorption site.For (111) surfaces, an attractive potential is observed only when the Al atom is placed above F atoms. For the (001) orientation, a significant difference was observed between Ca- and F-terminated surfaces. A comparative analysis indicates that the (001) surfacesare reactive and have a strong Al adatom bonding (chemisorption), especially the F-terminated substrate.The (111) plane may be considered as non-reactive (physisorption), having a weak bonding of the Al adatom at the F site. Those calculation results were verified by experimental observation which indicates that Al mainly react with the (001) planes of the CaF2 compounds.

Keywords: CaF2, ab-initiocalculations, adsorption, slab

* Corresponding author. Tel:+97286461468; fax:+97286479441; E-Mail

1. Introduction

Alkaline and alkaline-earth fluorides are relatively stable compounds, have high formation energies and could be used as containers for reactive melts. Ina previous study (1),it was established that the CaF2/Al system may be considered as a reactive, while the CaF2/Me (Me=Cu, Ge, In and Ga)systems are non-reactive.These conclusions are based on sessile-drop wetting experiments, accompanied by interface examination methods and thermodynamic calculations. Theseapproachesare useful for evaluating the possibility of chemical interactions; however they do not give specificbonding information and interfacecharacterizationat the atomic level. Such information couldbe gained from an ab-initio approach, which can characterize the nature of the interface at the atomic level.Comprehensive theoretical study should include many Al atoms in amorphous (liquid) configurations, above a thick slab of the CaF2 substrate. Such calculations require substantial computing resources, especially in selecting the most appropriate configurations. However, much relevant information can be revealed by studies of the bonding nature with adsorbed metal atoms in cluster or supercell approximations. Significant efforts were applied to study wetting (2) and adsorption of metal atoms on the surfaces of the ionic substrates (3) by different semi-empirical and quantum mechanical methods, including shell model potentials, Hartee-Fock and pseudopotential methods.For instance, the adsorption sites and the nature of the interfacial bondingwere studied for halogen atoms on alkali halide surfaces (4),Ag atoms on thesapphire(0001) surface (5) and Cu atoms on the MgO(001) surface (6). To the best of our knowledge, the adsorption of metal atoms on CaF2has not been studied yet, although Shi et al. (7,8)have performed the calculations of the electronic structure and surface relaxation of clean CaF2surfaces,and Leeuw et al. (9, 10)studied the reactivity of these surfaces and the adsorption energy of water on CaF2 (111).In the present study, ab-initio calculations were made for Al adsorption on (001) and (111) planes of CaF2. TheAl adsorption energy was calculatedfor 7 different sites and for differentadsorption distances. At the equilibrium distance, various properties of the electronic configuration are presented, in order to elucidate the nature of the bonding predicted by the calculation.

2. Methodology

Total energy calculations were preformed for each atomicconfiguration usingDensity Functional Theory (DFT)(11-13).Such calculations utilize a non-interacting reference system, the Kohn-Sham system, which possesses the same electron-density distribution as the full interacting system. The static Coulomb interactions and the exchange-correlation energy are included through a self-consistent procedure.We applied the full potential methodwith the Augmented Plane Waves + local orbitals (APW+lo) formalism, as implemented in the WIEN-2k code (14, 15). Periodic slab calculations were performed for 7adsorption sites of CaF2/Al (Figs.1,2).Each site was modeled using a supercell (periodic boundary conditions) containing3 layers of Ca, the appropriate number of F layers (6 for (111) sites and 3 for (001) sites), a vacuum separation of 10Å and one Al atom above each site. The distance of the Al atom from the surface layer was varied from 0.9 to 6Å. All other atoms were constrained to their bulk configuration.Three of the adsorption sites are associated with theCaF2(111)/Alinterface andfour sites are related to the CaF2(001)/Al interface. All the sites were examined for one mono layer (ML) of Al, i.e., one Al atom per surface Ca ion. In order to assess the sensitivity of the results to the specific configurations chosen, additional calculations were performed, e.g., calculations with varying number of layers.

Figure 1Top view of the considered CaF2 surface sites: F-terminated (001) surface - a,b, Ca-terminated (001) surface - c,d and (111) surface - e,f,g.

Figure 2 The atomic configuration of the studied CaF2/Al interfaces, (a-d) 1 ML of Al on CaF2 (001) and (e-g) the same for (111) planes.

The details of the DFT calculations are as follows.The exchange-correlation potential was treated within the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) (16). It was found that ak-mesh of about 100 points in the first Brillouin zone is enough to reach the accuracy of ~10-3 Ry. For the basis-set size, RmtKmax=7 was used.For the 1ML calculations, the radius of the muffin-tin spheres (Rmt) was 1.8 a.u. for all atoms, while for the 0.5ML calculations the Rmt of the Ca atoms was taken as 2.1 a.u. and for F and Al atoms it was taken equal to 2.0 a.u. (larger values of Rmtrequire less computation time; these changes of Rmt were evaluated for 1ML calculations and hardly affect the results).The energy cutoff, separating core and valence states, was chosen equal to -6.0 Ry.Theconvergenceof the self-consistent calculationswas 10-3Ry in mostcases, and 10-4 Ry for the equilibrium points of each absorption site.

3. Calculation Results

3.1 Adsorption Energy

The total energies of theCaF2/Al systems were calculated for each of the sites from Figs. 1,2, and for distances 0.9 -6Å of the Al atom from the topmost layer.For purposes of interpolation, the calculated adsorption energies were best-fitted to Morse potential forms for attractive potentials, and to exponential forms for the purely repulsive cases.The optimum distance and the minimum adsorption energy for each configuration are defined according to the fitted functions. Figure 3 exhibits the adsorption energy curves for different sites, and Table 1 summarizes the adsorption results.Additional calculations were performed for 1ML of Al on a thinner CaF2(001) slab (2 layers of Ca and 2 layers of F). They exhibit nearly identical adsorption energy for site (a) and about 8% difference for site (b).It worth mentioning that the effect of relaxation on the adsorption and adhesion was studiedpreviously for numerousatomic configurations of Al on VN, VC, WC, Al2O3slabs (17),Cu on TiC, TiN slabs (18) andCo on WC, TiC, TiNslabs (19, 20). In most of these calculations,the relaxation changed the adsorption/adhesion energynot morethan 25%.

The adsorption energy (Eadsorp) was extract according to Eq.1

,(1)

where is the total energy of the slab with Al atoms calculated for each configuration site (shown in Fig. 2), is the total energy of the slab configuration without the Al layer, and refers to the total energy of the Al layer without the slab beneath it.

Figure 3 Adsorption energy for CaF2/Al systems as calculated within WIEN 2k code. (a) CaF2(001)/Al, (b) CaF2(111)/Al.

Table 1Calculated values of the adsorption energy in the CaF2/Al system

Site / Adsorption surface / Al adsorption energy, eV / Adsorption distance, Å
(a) / 001 / 4.1 / 1.4
(b) / 001 / 5.2 / 1.1
(c) / 001 / 1.0 / 3.2
(d) / 001 / 1.4 / 2.1
(e) / 111 / 0.26 / 2.2
(f) / 111 / repulsive / ---
(g) / 111 / repulsive / ---

As can be seen, for the (111) surface, only site (e) displays an attraction, while other sites repulse Al atoms. For the (001) surfaces we can distinguishbetween two types of adsorption patterns. The F-terminated surface (sites a,b) hashigh adsorption energies, while for the Ca-terminated surface (sites c,d) relatively low adsorption energies were observed. In order to clarify these variations in adsorption energies, the electron density distributionwas analyzed.

3.2 Electron Density

The redistribution of valence electrons due to adsorption can provide valuable information about the nature of bonding. Figure4 presents the differential electron densities (the differences between the electron density of the system and the sum of the electron densities of the individual atoms) for the adsorbedAl atoms, for two slab surfacesand for the favorable CaF2(001)/Al and CaF2 (111)/Al sites.

For the CaF2 (111) surface very similar electron density distributions are observed for the F atoms at the surface and for those inside the slab (Fig. 4(i)). Thisdistribution is just slightly affected when the Al is brought to its equilibrium position (Fig. 4(ii)). The situation is quite different forthe CaF2(001) surface. As can be seen in Fig.4(iii), there is a considerable difference between the electron distributions around the surface F atoms and the "bulk" F atoms. This difference may indicate the existence of surface activity. The addition of Alatomssignificantly changes the distribution near the surface atoms (Fig. 4(iv)).

Figure 4 Differential electron density distribution (in e/Ǻ3) for two atomic configuration of the CaF2/Al interfaces; (i) CaF2 (111) slab and "isolated" Al above it, (ii) the preferred configuration for the CaF2 (111)/Al, (iii) CaF2 (001) slab and "isolated" Al above it, (iv) the preferred configuration for the CaF2 (001)/Al.

3.3 Density of States

The DFT calculations also provide access to the detailed study of electronic structure of the Kohn-Sham reference system, including the density of states (DOS), which resembles this characteristic for the interacting system.The DOS for Ca and F atoms on the F-terminated slab surfacesare shown in Fig. 5 the (111) and(001) surfaces. The different reactivity of these surfaces (without Al atoms) is evident. It is reflectedby the presence of a totally filled band for the (111) surface, compared to a partly-filled band for the (001) surface, representing F atoms with dangling bonds.

Figure 5LocalDOS of the Ca and F surface atoms of (i) the CaF2(111) slab, (ii) the same slab in the presence of Al, (iii) the CaF2(001) slab, and the (001) slab in the presence of (iv) 1ML of Al. The calculations refer to the preferred sites for adsorption, at the equilibrium distance.

4. Experimental Verification

In our previous study (1) we reported the results related to chemical interaction of the CaF2 substrate with liquid metals, such as Cu, Au, Sn, In, and Al. It was established that only liquid Al reacts with CaF2, although no evidence of new condensed phases which are formed at the interface was found. The experimental results were well accounted for by the thermodynamic analysis of the CaF2/Me systems. According to this analysis the gaseous Al-fluoride phase may be formed at the metal/substrate interface.

Figure 6 AFM pattern of the CaF2 substrate after exposing to molten Al.

In order to clarify the interaction that takes place on the polycrystalline CaF2 substrate, its surface after contact with liquid Al was characterized using an atomic force microscopy (AFM). It was detected (Fig. 6) that the area, which was not exposed to the molten Al is flat, while beneath the Al drop the substrate is rough with evidence of a preferential chemical interaction.

The CaF2 substrate before wetting experiments and the substrate that was in contact with liquid Al were subjected to XRD analysis.

Figure 7 X-ray diffraction of the CaF2 substrate: before (a) and after (b) contact with molten Al.

In order to compare the two patterns, the diffractograms were normalized in respect to the (111) reflection (Fig.7). It is clearly observed that the intensity of most of the peaks (except (311)) decreases significantly compared to (111). This is in accordance with the results of DFT calculations, which concludes that the (111) planes are more stable than the (001) planes in contact with Al. The relations between the stability of the (111) and other planes have to be further investigated.

4. Summary

Ab-initio calculations were performed in order to evaluate the reactivity of (111) and (001) surfaces of CaF2, and to characterize the bonding nature of Al atoms to these surfaces. For the favorable site of the (001) plane, a significant difference was observed between the electron density distribution of the F topmost layer of the clean slab and these of the "bulk" atoms. For the (111) surface, the electron distribution in the vicinity of the F atoms at the topmost layer of the clean slab is nearly identical to that of the F atoms in the bulk. When Al atoms are placed above the (001) surfaces a significant adsorption energy was calculated and an increase of the electron density is observed in the Al-F bonds. When Al atoms are placed above the (111) surface, the electron distribution is scarcely changed and minor attraction occurs when the Al atoms are placed on top of F atom.Other sites respond to the Al atoms in a repulsive manner. The experiential observations of the CaF2/Al interface confirm the results of the DFT calculations.

Acknowledgements

This work was supported by thegrant N0138-05from the Israeli Council of High Education and the Israeli Atomic Energy Commission.

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