Interference and Radial Distribution Functions of Liquid Copper, Silver, Tin, and Mercury

Abstract

The x-ray scattering from liquid copper, silver, tin, and mercury was measured at temperatures of 1125 °C, 1050 °C, 335 °C, and 28 °C, respectively, from the open surface of horizontal samples using a focusing theta-theta diffractometer, quartz crystal monochromator positioned in the dif fracted beam, scintillation detector, and pulse height discriminator. The effect on the measured intensities of the positioning of the sample with respect to the diffractometer axis and the meniscus of the liquid were considered. Calibration of the primary beam intensity by measurements on liquid mercury provided an alternate check of the standard normalization procedures for copper, silver, and tin. After calculation of the interference functions, atomic and radial distribution functions were evaluated from which interatomic distances and coordination numbers were obtained. The interatomic distances in the liquid were in good agreement with the G o l d s c h m id t diameters of the respective elements.X-ray diffraction is one of the more important methods that may be employed to investigate the liquid state of matter. The arrangement of the atoms determines the angular distribution of the scattered x-rays. This arrangement is usually described by the probability W {r)dv of finding the center of another atom in the volume element dt> at a distance r from a given atom. Then, W (r) = Q (r )/g 0 , where o(r) is the atomic density function and ,o0 the average atomic density in the liquid. It can be shown that, for monatomic liquids, the radial distribution func tion (R D F ) 4 ; r r 2 o(r) is given by1: 4 n r2 Q (r) = 4 n r2 o0 o o + (2 r/ji) f K [ I ( K ) -l]-(sin£r) d K ,(1 ) o where K = 2 ji s = 4 ji sin © //, s = 2 sin G/X, and I( K ) is the interference function:

Atomic-Scale Characterization of Elastic Deformation of Zr-Based Metallic Glass under Tensile Stress

“…The scattering profiles, IðQÞ, were corrected by air scattering, polarization, absorption, and Compton scattering. The profiles were then converted to electron units per atom by the Krogh-Moe-Norman method 13) in order to obtain an interference function, QiðQÞ (¼ QðSðQÞ À 1Þ, SðQÞ: structure factor), estimated from the coherent scattering intensity in absolute units. The RDF was obtained by the Fourier transformation of the QiðQÞ.…”

Effect of Al on Local Structures of Zr–Ni and Zr–Cu Metallic Glasses

“…The observed diffraction profiles were corrected by air scattering, polarization, absorption and Compton scattering, and converted to electron units per atom by the Krogh-Moe-Norman method 14) to obtain an interference function, QiðQÞ estimated from the coherent scattering intensity in absolute units. The ordinary RDF, 2%r 2 &ðrÞ was led by Fourier transformation of the QiðQÞ.…”

The structure of hydrated copper-silicate gels, an analogue compound for natural chrysocolla

“…Mo -Kα radiation (λ = 0.71073 Å) was used so as to obtain the diffraction intensity profile up to Q = 11.5 Å −1 (Q = 4πsinθ/λ) for pair distribution function (PDF) analysis. After the corrections for absorption, polarization, and Compton scattering, the measured intensity patterns were normalized in electron units with the generalized Krogh -Moe -Norman method (Wagner et al, 1965) and PDF was obtained by the Fourier transformation of an interference function Qi(Q) (Waseda, 1980). The measurements of Cu K -edge XAFS spectra were carried out in transmission mode using in -house Xray absorption spectrometer (Rigaku R -XAS looper).…”