Energy dispersive x-ray diffraction and reverse Monte Carlo structural study of liquid gallium under pressure

The structure of liquid gallium has been studied along the melting curve from 0.64 to 5.6 GPa by the energy dispersive x-ray diffraction technique, followed by modeling of the experimental data by the reverse Monte Carlo (RMC) method. The RMC models were constrained by the experimentally obtained equation of states of liquid Ga and in good accordance with experimental data. Analysis of the structure factor $S\left(Q\right)$ and the radial distribution function $g\left(r\right)$ shows that the anisotropic local structure of liquid Ga deviates from that of a simple hard-sphere-like liquid metal structure. Whereas the third and fourth coordination shell positions and position of the first maximum of $S\left(Q\right)$ demonstrate pressure dependencies close to a uniform compression scaled by the ${(V/V_0)}^{1/3}$ volume relation, the positions of the first (especially) and second coordination spheres have more flat pressure dependencies. At the same time, the first and second coordination numbers increase: The first coordination number starts from 10 to 10.5 and increases by $\sim$5$\%$ in the studied pressure interval. This indicates that liquid gallium contraction is nonuniform, and the local structure changes with increasing pressure. Analysis of the radial distribution function $g\left(r\right)$ by a distorted-crystalline model shows that at lower pressures liquid consists of two species similar to the solid Ga I and Ga II structures. The fraction of the Ga I-like part is about $0.2\pm 0.05$ at 0.64 GPa, and it gradually decreases under pressure to zero at approximately $7.5\pm 0.5$ GPa.

Figure 1

The density approximation for liquid gallium under pressure compared with previous results. The data from the ultrasonic measurements at 285 K (black circles) show the melting of solid Ga I at 1 GPa under compression. The inset shows the selected experimental points on a phase diagram.

Figure 2

(a) Structure factors $S\left(Q\right)$ and (b) radial distribution functions $g\left(r\right)$ of liquid gallium from experiments (thick red lines) and from RMC models (thin black lines) at selected $p-T$ conditions.

Figure 3

Pressure dependencies of ratios of the position of the second peak to that of the first peak in the structure factor (circles) and radial distribution function (our data: solid triangles; data from Ref. 16: open triangles).

Figure 4

The comparison of density dependence of the first four neighbor distances $r_i/r_i\left(0\right)$ with the relation ${(V/V_0)}^{1/3}$.

Figure 5

The first coordination number calculated by different methods. Our data $N$${}_{\min }$ (solid triangles), $N$${}_{\text{RMC}}$ (solid squares), $N$${}_{\text{sym}}$ (solid circles) is compared with previous results from Ref. 12 as open diamonds, Ref. 17 as open triangles, Ref. 16 as open circles, Ref. 23 as open stars, and Ref. 34 as open reverse triangles.

Figure 6

Structural details of RMC models at selected experimental $p-T$ points: (a) $N$ distributions for neighbors within 2.35–3.55 Å  from the lowest (0.64 GPa at 300 K, black squares) to the highest (5.6 GPa at 393 K, bright red diamonds); (b) partial radial distribution functions $G_i\left(r\right)$, where $i$ is the index of the neighbor at 0.64 GPa at 300 K and 5.6 GPa at 393 K (shifted along the $y$ axis for clarity).

Figure 7

The triplet correlation function for liquid gallium calculated from the RMC models at selected $p-T$ conditions, compared with data from Refs. 15 and 35.

Figure 8

Power-law scaling of the first peak $Q_1$ vs atomic volume $v_a$. Both $Q_1$ and $v_a$ are on a logarithmic scale. The straight dashed lines are given as guides to the eye.

Figure 9

Comparison of $g\left(r\right)$ measured for the gallium melt (thick gray lines) at 0.64 GPa at 300 K and at 4.2 GPa at 340 K, with those simulated for several solid structures with the same number density.

Figure 10

(a) Experimental and simulated $g\left(r\right)$ for liquid Ga; (b) comparison of the goodness of fit parameter $R$ for different combinations of local structures used in simulations. Curves for low pressure (0.64 GPa, 300 K, open symbols) and high pressure (4.20 GPa, 340 K, solid symbols) are given. (c) Pressure-induced change of component fractions for the best fit combinations.