Temperature Dependence of the Structure of Liquid Indium

The x-ray diffraction pattern of liquid indium were measured at 170, 280, 390, 500, and 650^∘{}C. For comparison, liquid mercury was measured at room temperature. All data were taken with a θ-θ diffractometer from the open surface of the melt between values of K=4πsinθλ=1.5 and 15 ^-1. Absolute intensity data Ie.u.ᶜᵒʰ were obtained by scaling the measured intensity of In to that of liquid mercury (coh=coherent, e.u. =electron units). The values of Ie.u.ᶜᵒʰ for $K>12$ did not show extensive modulation and were in good agreement with the square of the dispersion-corrected scattering factor f of In. The interference function $I(K)$ was calculated by dividing the Ie.u.ᶜᵒʰ values by the theoretical f² values. Fourier transform of $I(K)$ yielded the radial distribution function RDF=4πr²ρ(r) and pair probability function g(r)=ρ(r)ρ₀, where ρ₀ is the atomic density. The RDF curve of Hg is completely free of ripples below $r<D$, where D is the hard-sphere diameter, indicating that Ie.u.ᶜᵒʰ and f² were determined accurately. In the case of In, ripples were found below the first peak in the RDF. We conclude that these ripples are a consequence of the use of inappropriate f² values rather than errors in Ie.u.ᶜᵒʰ, since Hg and In were measured under identical conditions. Fourier transform of the ripple-free RDF yielded an $I(K)$ curve which was about 10% higher in the region of the first peak. Dividing Ie.u.ᶜᵒʰ by the corrected $I(K)$ leads to values of the scattering factor which are 5% lower in the range of K=1.5 to 8 ^-1 than the Dirac-Slater scattering factors. The distribution of the atoms in liquid In can be approximately described by the hard-sphere model with a packing density of 0.45 compared to 0.74 in the solid. This density corresponds to a hard-sphere diameter $D=2.86$ {}, which is the first value of r in the RDF where ρ(r)=ρ₀. The interatomic distances r₁ taken as the position of the first peak maximum in the RDF and the coordination number CN decrease with increasing temperature. Both variations are a consequence of the excess or free volume created in the liquid. The electrical resistivity ρR and thermoelectric power Q of liquid In were calculated from the measured I(K) and the theoretical values of the Fourier transform $U(K)$ of the pseudopotential for different temperatures. The predicted values of ρR are about 50% lower than those observed experimentally. The theory also under-estimates the temperature dependence of the resistivity by about a factor of 3.