Atomic distributions in liquid copper-tin alloys

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Abstract
Molten copper-tin alloys have been studied by X-ray diffraction, using a focusing theta-theta diffraetometer and Mo-Kα radiation (monochromator in the diffracted beam). Five alloys with 20, 35, 45, 55 and 78 atomic percent Sn, and pure Cu and Sn were measured at temperatures about 20 °C above the liquidus, and at 1100 °C. The total interference functions I(K), where K = 4π sin θ/δ, were obtained from the observed scattered intensities Ia(K) per atom and the theoretical atomic scattering factors. Splitting of the first peak in I(K) has been observed in the Cu-55 at% Sn alloy at the liquidus temperature. The partial interference functions Itj(K) at the liquidus temperature and at 1100°C were evaluated (assuming that they are independent of atomic concentration) using the five total I(K) of the alloys. The functions Iij(K) are in reasonable agreement with those obtained by Enderby, North and Egelstaff from neutron diffraction data of a Cu-45 at % Sn alloy. The reduced partial distribution functions Gij(r) = 4πρ0 r{gij(r) − 1} and the probability functions gij(r) = ρ ij(r)/cj ρ0, where ρ ij(r) is the number of j-type atoms per unit volume at the distance r from an i-type atom, cj is the atomic fraction of j-type atoms and ρ0 is the average atomic density, have been evaluated by Fourier transformation of {Iij(K) − 1} K. The electrical resistivities ρ R of the alloys, calculated with the Faber-Ziman equation using the measured Iij(K) and Animalu-Heine pseudo-potential elements Ui(K), are in good agreement with the experimental values of Roll and Motz. Assuming that Ui (2k F) is independent of the values of the Fermi diameter 2k F of the alloys, the concentration dependence of (3 - X)ρR, where X is the thermoelectric parameter measured by Enderby and Howe, is well reproduced when using the X-ray values of Iij (2k F).

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