Structure factor and atomic distribution in liquid metals by X‐ray diffraction

Abstract

X-ray diffraction patterns have been obtained from liquid metals (Al, Ga, In, TI, Pb, Sn, Bi) near the melting point. After calculating the structure factor (Fourier analysis), the atomic radial distribution function was evaluated from which interatomic distance and coordination number were obtained. It has been shown that the ratio (K,/K,) of the position of the first peak ( K , ) to that of the second peak (K,) in the structure factor is a very useful parameter to represent the structure of liquid metals.Rontgenbeugungsbilder von flussigen Metallen (Al, Ga, In, T1, Pb, Sn, Bi) wurden in der Nahe dea Schmelzpunktes beobachtet. Durch eine schon mehrfach dargestellte Methode (Fourier-Analyse) wurde der Strnktnrfaktor in eine radiale Atomverteilungsfunktion transformiert, aus der sich der mittlere Abstand nachster Atome und die Koordinationszahl ergeben. Es wurde gezeigt, da13 das Verhaltnis (K2/Kl) der Lage des ersten Maximums (Kl) zii der des zweiten Maximums (&) i m Strnkturfaktor eiu niitzlicher Parameter zur Beschreibung der Struktur von flussigen Metallen ist.

Structure of Molten Mg, Ca, Sr, and Ba by X-ray Diffraction

“…The ratio ($2/(^1) of the positions of the second and first maximum is almost constant (^1.85) (see Table 1) and nearly equal to the value (^ 1.83) found for molten alkali metals. The structure factors of molten alkaline earth metals thus look similar to those of the most simple metals such as the alkali metals, in contrast to molten tin, bismuth, and others, which show a subsidiary maximum on the high angle side of the first peak 5 . It is well known that this general form of the structure factor at temperatures just above the melting point agrees with that of the hard sphere model 13 with packing density r\ -0.45, within the first approximation.…”

“…The experimental arrangement and operating procedure for the X-ray measurements on high-temperature melts have been fully discussed in 5 . All data were obtained with a combination of Mo and Cu radiations.…”

“…The observed intensity was corrected by the usual procedures 4 ' 8 for lost counts, background, absorption and polarization, and analysed as described in the previous papers 4 ' 5 . The distribution of atoms as a function of the distance r from a given reference atom is obtained from the X-ray intensity I(Q) scattered coherently by N atoms with an atomic scattering factor f(Q) by the well-known relations…”

Effect of Screening on Resistivity of Liquid Metals

“…We calculated the resistivity for K, Al, Sn and Bi by using Ziman's formula comsidering both the experimental structure factor α(q) [24,25] and the theoretical value based on a hard sphere model as obtained here. The results with different screeming functions are tabulated in Table I and II (also the values of Ω0, kF, m* and σ are tabulated in Table III).…”

Asymmetrical bonding in liquid Bi disentangled by inelastic X-ray scattering

“…3) [2][3][4], in contrast to a symmetrical profile of simple liquid metals. The origin of the shoulder in S (Q) of liquid Bi was theoretically studied and it was found that an effective pair potential with a ridge in the repulsive component could reproduce the shoulder [5,6].…”