Structural and dynamical properties of liquid Al-Au alloys

We investigate temperature- and composition-dependent structural and dynamical properties of Al-Au melts. Experiments are performed to obtain accurate density and viscosity data. The system shows a strong negative excess volume, similar to other Al-based binary alloys. We develop a molecular-dynamics (MD) model of the melt based on the embedded-atom method (EAM), gauged against the available experimental liquid-state data. A rescaling of previous EAM potentials for solid-state Au and Al improves the quantitative agreement with experimental data in the melt. In the MD simulation, the admixture of Au to Al can be interpreted as causing a local compression of the less dense Al system, driven by less soft Au–Au interactions. This local compression provides a microscopic mechanism explaining the strong negative excess volume of the melt. We further discuss the concentration dependence of self- and interdiffusion and viscosity in the MD model. Al atoms are more mobile than Au, and their increased mobility is linked to a lower viscosity of the melt.

Figure 1

Mass density of liquid Al-Au alloys for various concentrations as indicated, as a function of temperature. Symbols correspond to the experimental results obtained using electromagnetic levitation. Solid lines are linear fits.

Figure 2

Temperature coefficient ${\rho }_T$ of the mass density, cf. Eq. (4), of liquid Al-Au at $T=1400\text{K}$ as a function of Au mole fraction, $x_{\text{Au}}$. Star symbols correspond to experimental results, circles denote the results obtained from MD simulation using our EAM potential.

Figure 3

Molar volume of Al-Au alloys with compositions as labeled, as functions of temperature. Crosses with error bars correspond to the experimental data shown in Fig. 1. Circles are MD simulation results obtained from our EAM potential; squares shown for pure Al and pure Au are obtained from the original EAM potentials of Ref. [37] (for Al) and Ref. [38] (for Au). Lines are guides to the eye.

Figure 4

Molar volume $V_{\text{mol}}$ vs $x_{\text{Au}}$ at $T=1400\text{K}$. Star symbols show experimental data; circles are the results from MD simulations with our modified EAM potential.

Figure 5

Arrhenius plot of the viscosity $\eta \left(T\right)$ for liquid Al (a) and liquid Au (b). Stars are our experimental data; squares denote results from MD simulations using the EAM potentials of Ref. [37] (for the case of Al) and Ref. [38] (for the case of Au). Circles show results obtained using our regauged EAM potentials. Solid lines represent Arrhenius fits with parameters given in Table 2. Dashed lines are experimental data by Gebhardt [44], with dashed dot lines from Dubberstein.

Figure 6

Viscosity of Al-Au alloys at three different compositions as labeled that were selected as representative examples. Star symbols with error bars are our experimental data; circles are MD simulation results.

Figure 7

Isothermal viscosities $\eta$ of Al-Au melts obtained from experiment (filled and semi-filled symbols) and from MD simulations (open symbols), at fixed temperature $(T=1700\text{K},1400\text{K}$, and $1200\text{K}$; bottom to top), as functions of $x_{\text{Au}}$. Semifilled symbols denote values that have been obtained from extrapolating the experimental data using Arrhenius fits. For MD, results for $T=1000\text{K}$ are also shown (topmost curve).

Figure 8

Pair distribution functions for pure Al (top) and pure Au (bottom panel) at $T=1400\text{K}$. Circles are experimental data from Ref. [48]; lines are our MD simulation results. Dashed lines indicate $g\left(r\right)$ obtained from the original EAM potentials of Refs. [37] and [38].

Figure 9

Radial distribution functions (RDF) of liquid Al-Au obtained from MD simulation at $T=1400\text{K}$, at various compositions as labeled. (a) Total RDF $g\left(r\right)$; (b)–(d) Partial RDF $g_{\alpha \beta }\left(r\right)$ for the cases $x_{\text{Au}}\ne 0$ and $x_{\text{Al}}\ne 0$. In (c), the vertical dashed lines correspond to the peak positions, with values $r_{\text{max}}^{\left(1\right)}=2.83\text{Å},1.68r_{\text{max}}^{\left(1\right)}$, and $1.88r_{\text{max}}^{\left(1\right)}$.

Figure 10

Evolution of the first maxima of the partial radial distribution functions $g_{\alpha \beta }\left(r\right)$, with $\alpha ,\beta$ as labeled, and the total RDF $g\left(r\right)$ (labeled “all”), with composition.

Figure 11

Total and partial (Ashcroft-Langreth) static structure factors $S_{\alpha \beta }\left(q\right)$ of liquid Al-Au at $T=1400\text{K}$, from MD simulations using our EAM potential, for various compositions as indicated as a function of wave number $q$.

Figure 12

Bhatia-Thornton concentration–concentration structure factor $S_{cc}\left(q\right)$ corresponding to the static structure factors shown in Fig. 11.

Figure 13

Self-diffusion coefficients $D_{\text{Al}}$ (circles) and $D_{\text{Au}}$ (diamonds) as a function of temperature, obtained from MD simulations for ${\text{Au}}_{\text{20}}{\text{Al}}_{\text{80}}$ and ${\text{Au}}_{\text{80}}{\text{Al}}_{\text{20}}$.

Figure 14

Self-diffusion (circles: Al, and diamonds: Au) and interdiffusion (triangles: $D_{cc})$ coefficients of Al-Au alloys as a function of composition, for temperatures as indicated. Also shown is the kinetic contribution to interdiffusion, the Onsager coefficient $L$ (inverted triangles).

Figure 15

Thermodynamic factor $\mathrm{\Phi }$ for interdiffusion, as a function of composition at fixed temperature as indicated. Symbols are results from MD simulations. A dashed line indicated the estimate from a thermodynamic assessment, Ref. [57] at $T=1000\text{K}$.

Figure 16

Stokes-Einstein effective diameter calculated from $d_{\text{SE}\alpha }=k_{B}T/\left(2\pi \eta D_{\alpha }\right)$, using the self-diffusion coefficient of Au and Al, as labeled, for temperatures $T=1700$, 1400, and $1000\text{K}$ as functions of the composition.