Full Length ArticleDensity functional theory study of Al/NbB2 heterogeneous nucleation interface
Graphical abstract
Introduction
It is known that the achievement of fine grain structure is beneficial to the soundness and mechanical properties of Al alloy castings [1], [2]. Although there are several ways to obtain excellent grain refining performance, adding master alloys into aluminum melts has been recognized as most economical and practical method to achieve engineered designed heterogeneous nuclei for refinement [3], [4], [5]. In recent years, the focus of attention is on grain refining efficiency of Al-Ti-B and Al-Ti-C master alloys since the master alloys are the most frequently used in the foundry. Computer simulation and experiment results have illustrate the potency of Al3Ti and TiB2 as the heterogeneous substrate for enhanced α-Al nucleation in Al alloys [6], [7], [8]. However, the master alloys are not very effective on refining Al-Si alloys. AlB2, which is the potential heterogeneous nucleation of α-Al phase in Al-Si alloys, cannot effectively refine the grain size of purity aluminum from thermo-dynamically considerations [9]. The heterogeneous nucleation of α-Al on the NbB2 substrates is difficult to achieve.
The two most common Nb-based master alloys, niobium borides and niobium aluminides, have the characteristics of high melting point and good lattice match with Al nucleating phase [10]. The structure and lattice parameters of NbB2 is not only similar to the respective Ti-based compounds, but more importantly the phenomenon of Si poisoning seldom occur. For Ti-based master alloys, Ti has higher affinity with Si than Al, which leads to the formation of Ti silicide, and the aluminum melt gradually is depleted of Ti, reducing TiB2 and AlTi3 substrates potency at pouring temperature of Al-Si alloy [11]. However, formation kinetics of niobium silicide is very low at same temperature [12]. So, NbB2 can be considered as potential heterogeneous substrate for purity aluminum and Al-Si alloys.
The atom configuration, interfacial adhesion and interfacial bonding nature play an important role in the analysis of nucleation potency of a heterogeneous substrate. The first-principle calculation with density functional theory (DFT) can provide fundamental information for theoretical research of solid–solid interface at atom or even electron levels. So, it is an ideal and realistic method to study theoretically nucleation potency of a heterogeneous substrate [13]. However, Up to now, Al(1 1 1)/NbB2(0 0 0 1) interfacial feature is rarely discussed. The aim of this work is to study Al/NbB2 surface and interfaces by using density functional theory based on the first-principles method, and discuss potential of NbB2 as heterogeneous nucleation substrates for α-Al grains based on the calculations. It can provide theoretical guidance for the related experiments. Based on metal solidification theory, the interfacial energy between nucleating substrates and matrix crystal provide direct basis for determining the potency of a heterogeneous substrate. In general, good matching between crystal structure of matrix crystal and nucleating substrates contributes to formation of low interfacial energy, which is conducive to the heterogeneous nucleation. Because The crystal structure of Al and NbB2 is the face-centered cubic (FCC) and close-packed hexagonal (HCP) lattice respectively, Al(1 1 1)/NbB2(0 0 0 1) interface is chosen to study. According to the equation of Bramfitt, the lattice mismatch of Al(1 1 1)/NbB2(0 0 0 1) is only 7.6%.
Section snippets
Computational methodology
Interfacial properties of Al(1 1 1)/NbB2(0 0 0 1), such as interfacial adhesion and interfacial bonding, are obtained using CASTEP package of materials studio [14], [15]. Generalized gradient approximation (GGA) with PW91 functional was used for the exchange correlation between electrons in this work [16]. Ultrasoft pseudopotentials, which allow the calculation to be performed at a lower energy cutoff, was used [15], [16], [17]. Kohn–Sham equation was solved with self-consistent field (SCF) and
Bulk properties of Al and NbB2
The calculations of lattice constants for NbB2 bulk and Al bulk were performed first for obtaining the reliable results. Some important parameters such as k-point sampling grids, cut-off energy were identified after several tests to control fluctuation margin of the calculated results within an acceptable range. The accuracy can be obtained by comparison of calculation value and experimental value. The space group symmetry of , which is hexagonal structure similar to , is P6/mm [18].
Interface model of Al/NbB2
Based on the convergence tests results, a 7-layer Al (1 1 1) slabs is stacked on the substrate of 9-layer NbB2 (0 0 0 1) slabs to form the model of the Al (1 1 1)/NbB2 (0 0 0 1) interface. The coherent interface approximation is adopted to keep the periodic boundary conditions in the super-cell calculation [26], [27]. The softer Al (1 1 1) slabs are stretched to be equal to NbB2 (0 0 0 1) slabs. To determine the optimal interface, Three possible stacking sites (top-site, hollow-site and
Analysis on NbB2 as heterogeneous nucleation of Al
Although interfacial property of Al/NbB2, such as interfacial adhesion and interfacial bonding, are obtained using CASTEP at 0 K, the calculated results closely match experimental results of solid–solid and solid–liquid interface at high temperature [41], [42]. The interfacial energy between efficient heterogeneous nucleation NbB2 particles and the α-Al have to be lower than that between the α-Al/Al melt (0.15 J/m2) from the viewpoint of thermodynamic [9]. B-terminated-hollow-sited interfacial
Conclusion
In this paper, surface energy, the work of adhesion, charge density differences, and PDOS of Al (1 1 1)/NbB2 (0 0 0 1) interfaces have been calculated by first-principles calculations. Six different models were compared to discuss heterogeneous nucleation potency of NbB2 as substrates for α-Al grains from thermodynamic considerations. The main conclusions of this paper are as follow:
- (1)
Compared with Nb-terminated interface with same stacking sequences, B-terminated one have larger work of
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