Diffusion chimique et effet kirkendall dans la phase cubique centree du systeme plutonium zirconium

Abstract

Soluté diffusion and thé Kirkendall effect were studied in the εβ body centred cubic phase of the Pu-Zr system, with the technique of welded couples. The concentration/penetration curves obtained by electron probe microanalysis, using the Lα 1 wavelength of plutonium, use of which leads directly to true concentrations, were interpreted by the methods of Hall and Matano. The chemical diffusion coefficients measured from 650 to 900 °C increase with plutonium concentration and obey Arrhenius' law. Activation energies range from 44 to 18 kcal/mole as the concentration ranges from 20 to 60 at% plutonium. They vary, therefore, in the same sense as the melting point of the εβ phase (melting point of plutonium 660 °C; melting point of zirconium 1853 °C). The existence of a Kirkendall effect in the Pu-Zr system has been shown by the displacement of inert wires, initially placed in the welding plane, towards the element which diffuses more rapidly. Each of the elements which constitutes the diffusion couple is therefore characterised by its own intrinsic diffusion coefficient D Pu or d zr . The variation of the intrinsic diffusion coefficients, of the flux j pu and J Zr of the two species and of the mean “lattice velocity” V as a function of concentration, was studied by the technique of “incremental couples”. These couples were made from a pellet of pure zirconium attached to a pellet of Pu-Zr alloy of different compositions in the various samples. Two methods are possible for measuring D Pu and d zr . The first makes use of the two equations of Darken: D ̃ = N PuD Zr + N ZrD Pu (1) ( D Pu − D Zr )( ∂N Pu / ∂x) (2) where V is the speed of displacement of the Kirkendall plane measured micrographically, D ̃ is the chemical diffusion coefficient calculated from the composition of the Kirkendall plane. The second method uses eq. (1) together with Heumann's relation: D Pu / D Zr = J' Pu / J' Zr (3) where J' Pu and j' zr are the integrated fluxes during the diffusion anneal across the marked plane. J' Pu and J' Zr are determined micrographically from concentration/penetration curve when, by micrography, one knows the position of the plane of the wires. A statistical error calculation shows that the second method, which is in any case experimentally simpler, is more exact than the first method, but it presupposes that the Kirkendall plane is displaced as the square root of time. In the range of concentrations studied (15 to 16 at% plutonium) it is plutonium which diffuses the more rapidly. The ratio D Pu / D Zr increases with plutonium concentration, and ranges from 1.5 to 6. The flux j pu and the mean atomic velocity have their largest value near the Kirkendall plane, while on the other hand J Pu and J Zr do not appear to reach extreme values simultaneously. This study has shown that the equations of Darken and Heumann are well able to interpret the phenomenon we have studied, within the limits of our experimental errors. On the other hand, the Kirkendall effect observed in the Pu-Zr system shows in an unambiguous manner that diffusion in this system takes place by a mechanism which involves the nonconservative migration of defects (vacancies or interstitials).