Crystalline surface phases of the liquid Au-Si eutectic alloy

A two-dimensional crystalline layer is found at the surface of the liquid eutectic ${\mathrm{Au}}_{82}{\mathrm{Si}}_{18}$ alloy above its melting point $T_M=359°\mathrm{C}$. Underlying this crystalline layer, we find a layered structure, 6–7 atomic layers thick. This surface layer undergoes a first-order solid-solid phase transition occurring at $371°\mathrm{C}$. The crystalline phase observed for $T>371°\mathrm{C}$ is stable up to at least $430°\mathrm{C}$. Grazing-incidence x-ray diffraction data at $T>371°\mathrm{C}$ imply lateral order comprising two coexisting phases of different oblique unit cells, in stark contrast with the single phase with a rectangular unit cell found for low-temperature crystalline phase, $359°\mathrm{C}<T<371°\mathrm{C}$.

Figure 1

(Color online) Measured x-ray reflectivity data for $T<371°\mathrm{C}$ and $T>371°\mathrm{C}$ along with their corresponding model fits (lines) discussed in the text. The reflectivity expected for a standard 3–4 surface layers, observed in all other metallic liquids, is shown in a dashed line. The solid thin line shows the Fresnel reflectivity curve, expected for an ideally flat and smooth liquid AuSi alloy’s surface.

Figure 2

(Color online) Fresnel-normalized reflectivity $R∕R_F\left(q_z\right)$ from the liquid AuSi surface for different temperatures. Notation as in Fig. 2. Note the logarithmic $R∕R_F$ scale.

Figure 3

(Color online) Density profiles for a standard layering model (dashed line, upper panel) and for the low-temperature (thin line) and high-temperature (thick black line) phases of the liquid AuSi surface (lower panel). The three density profiles shown here were obtained from the fits of the x-ray reflectivity curves shown in the same-color lines in Figs. 1, 2.

Figure 4

(Color online) Grazing-incidence diffraction patterns for low-temperature and high-temperature surface phases. The sharp peaks indicate the presence of a crystalline surface phase. The broad underlying peak is the liquid bulk scattering peak.

Figure 5

(Color online) Grazing-incidence x-ray diffraction patterns with liquid bulklike contribution subtracted. The plots show the experimental data (circles), the theoretical fits (lines), and the difference (lower panels) for the (A) low-$T$ and (B) high-$T$ phases. Insets show the unit cells of the two-dimensional crystalline phases corresponding to the fits, with larger circles representing Au and smaller representing Si. The high-$T$ diffraction patterns could only be fitted by a combination of phases A and B.

Figure 6

(Color online) Line shapes of the (23), (31), and (04) GIXD peaks of the low-$T$ phase measured with high-resolution Bonse-Hart Si (220) double-bounce crystal analyzer setup (circles). Fits with Gaussian function (lines) yield resolution-limited full width at half maximum of $\Delta q_{xy}\approx 0.0005–0.0007{\mathrm{\AA }}^{-1}$. Peaks (23) and (31) appear as a single peak with the low-resolution Soller slit setup but are well resolved in the pattern measured with the crystal analyzer.

Figure 7

(Color online) Bragg rod trajectory for (23) and (31) GIXD peaks centered at $q_{xy}=2.653{\mathrm{\AA }}^{-1}$, collected with Soller slits. Bragg rod is oriented along surface-normal direction $q_z$, indicative of a two-dimensional powder of crystallites aligned flat against the liquid surface. A dashed line shows theoretically expected trajectory for a three-dimensional powder cone $(q_{xy}^2+q_z^2=\mathrm{const})$.

Figure 8

Bragg rod intensity as a function of $q_z$, for the combined (23) and (31) GIXD peaks centered at $q_{xy}=2.653{\mathrm{\AA }}^{-1}$, measured with the low-resolution Soller slits setup.