Is There Icosahedral Ordering in Liquid and Undercooled Metals?

The local structure of simple liquids is significantly different from that of corresponding crystalline systems. Signatures of fivefold local ordering have been previously found, but current knowledge is limited to pair distribution, leaving considerable uncertainty in the determination of the geometrical structure. New x-ray absorption experimental results on liquid and undercooled liquid copper, interpreted using an advanced data-analysis method based on multiple-scattering simulations, are shown to contain direct information on triplet correlations making feasible a reliable determination of the bond-angle distribution and fraction of nearly icosahedral configurations in liquids.

Figure 1

XAS experimental data of liquid Cu at 1398 K ($l\mathrm{\text{−}}\mathrm{C}\mathrm{u}$) compared with the two-body component of the RMC multiple-scattering simulation (upper panel). The residual lower curve shows that the higher order terms have to be included to simulate the whole XAS spectrum. The inset shows the pair correlation function associated with the RMC simulation and previous determinations using neutron diffraction (ND) and x-ray (XRD) diffraction. The difference spectrum is compared in the lower panel with a XAS three-body signal calculated using a Gaussian three-body distribution for equilateral triangles. The full bond-angle $N(\theta )$ distribution resulting from the RMC simulation is compared with that of the equilateral triangles.

Figure 2

XAS data of liquid and undercooled Cu at various temperatures compared with RMC MS simulations including three-body contributions (upper panel). The decomposition into two-body (${\gamma }^{(2)}$) and three-body (${\gamma }^{(3)}$) terms for each liquid is shown in the middle panel. XAS data after removal of the two-body contributions are compared with three-body MS simulations on the enhanced scale of the lower panel.

Figure 3

Bond-angle distribution $N(\theta )$ as determined by RMC simulations reproducing XAS data of liquid and undercooled Cu. The distribution shows a clear peak around $60°$ and another broad maximum at about $110°$. The $N(\theta )$ corresponding to the uncorrelated limit is also shown (dashed line) for comparison. The number of nearly equilateral triangles increases lowering the temperature in the undercooling regime (see inset). The pair correlation functions of liquid and undercooled Cu measured by XAS are compared with previous ND and XRD diffraction determinations (see top-right figure).

Figure 4

Histogram of the frequency density of the ${\widehat{W}}_6$ cubic invariant monitoring the local geometry around each atom in undercooled liquid Cu. The histogram related to the fcc solid Cu, limited to a very narrow region around $-0.013161$ (value for a “perfect” fcc 13-atom cluster), is shown for comparison (scaled by a factor of 100). The ${\widehat{W}}_6$ distribution is found to be very broad and includes a region (shaded area under the histogram) corresponding to distorted nearly icosahedral configurations as indicated by the typical angular distribution with peaks at $60°$ and $110°$ and a minimum at $90°$ (see the left inset).