Wavelength Dependence of Liquid-Vapor Interfacial Tension of Ga

The wave-vector dependence of the liquid-vapor interfacial tension of Ga, $\gamma (q)$, has been determined from diffuse x-ray scattering measurements. The ratio $\gamma (q)/\gamma (0)=1$ for $q<0.05{\AA }^{-1}$ decreases to 0.5 near $q=0.22{\AA }^{-1}$, and increases strongly for larger $q$. The observed form for $\gamma (q)/\gamma (0)$ is consistent with the prediction from the Mecke-Dietrich theory when the known stratified liquid-vapor interfacial density profile of Ga and a pseudopotential based pair interaction with appropriate asymptotic ($r\to \infty$) behavior are used. The detailed behavior of $\gamma (q)/\gamma (0)$ depends on the particular forms of both the interfacial density profile and the asymptotic falloff of the atomic pair interaction.

Figure 1

Diffuse scattering from the liquid-vapor interface of Ga at 35 °C. The measured intensity of diffuse scattering is shown for three pickoff angles: 1°, 1.5°, and 3°. For clarity, the intensity data for 1° and 1.5° have been displaced by multiplication by 0.1 and 0.01, respectively. Different vertical slit sizes were used at the different pickoff angles. The three solid lines show the $q^{-2}$ dependence predicted by the capillary wave theory.

Figure 2

Normalized $q$-dependent surface tension calculated from the diffuse scattering intensity data displayed in Fig. 1. For clarity, the inferred values of $\gamma (q)/\gamma (0)$ for pickoff angles of 1.5° and 3° have been multiplied by 10 and 100, respectively.

Figure 3

Comparison of the normalized $q$-dependent surface tension of Ga determined experimentally with that calculated using the Mecke-Dietrich formalism with several model potentials and a stratified intrinsic interfacial density profile. The interfacial density profile used was obtained from a fit to the x-ray reflectivity from the Ga liquid-vapor interface as a function of angle of incidence. The inset compares the effective atom-atom interactions derived from the EIMP pseudopotential and the so-called individual local pseudopotential.