Diffusion in uranium alloys with zirconium. Analysis of the concentration behavior of the activation energy

Abstract

Uranium metal and alloys based on it are of interest as materials for fast-reactor fuel. A comprehensive investigation of the thermodynamic and diffusion properties of uranium alloys with zirconium permits drawing several fundamental conclusions that could be valid not only for this system but for other alloys as well. Thermodynamic data on the -),-phase alloys of the uranium-zirconium system are presented in [1]. These data were obtained by calculations based on data on the mutual diffusion and diffusion of the components (the calculations were performed on the basis of Darken's formula). It was shown that the computed concentration dependence of the free energy agrees with the value measured by Knudsen's method [2] (Fig. 1). It was also established that the composition dependences of the activity and integrated free energy [3] cannot be described on the basis of models of regular and subregular solutions. The cluster-variation model is an acceptable model that describes the sign-changing behavior of the activity of one of the components.An analysis of the diffusion data (both on interdiffusion and diffusion of individual components), our own data, and the published data was made in [4]. It was shown that the concentration dependences of the interdiffusion coefficients in uranium-zirconium and uranium-titanium systems do not agree with the melting point of the alloys of these systems (Fig. 2). This disagreement is due to the strong influence of thermodynamics (strong concentration dependence of the thermodynamic factor g(c) appearing in Darken's formula for the interdiffusion coefficient). The lowest values of/~(c) are characteristic for alloys with a low thermodynamic stability d2F/dc 2 --* 0, g(c) .-., O. Thermodynamic instability of the alloys results in, on the one hand, phase transformations in the system and, on the other, a decrease of the interdiffusion coefficient, activation energy of interdiffusion, and curvature of the temperature dependence of the interdiffusion coefficients. The decrease in the interdiffusion coefficients follows directly from Darken's formula/9 = (Dl*C 2 + D2*Cl)g(c), where Di*, c i (i = 1, 2) are, respectively, the diffusion coefficient of the components and the concentration; g(c) is a thermodynamic factor, whereac ! F m is the free energy of mixing, R is the universal gas constant, and T is the absolute temperature. The character of the variation of the activation energy as a function of composition and the interdiffusion coefficients as a function of the temperature require analysis. The experimental data presented in [5][6][7] attest to the fact that the interdiffusion activation energy also decreases substantially in the concentration range corresponding to low thermodynamic stability (Fig. 3). Recalling [8], the convex composition dependence of Q [9] was explained by the fact that at a lower temperature intermetallic compounds with a strong interatomic bond are formed, and the value of 0 was regarded as a heat-resistance criterion for the materials.A theoretical analysi...

Computational study of atomic mobility for the bcc phase of the U–Pu–Zr ternary system

“…As shown in Fig. 1, the data by Pavlinov [17], Adda and Philibert [18] and Shevchuk [19] agree favorably over the entire temperature range, and therefore were given the highest weight during the optimizing process. Ogata et al [16] detected the existence of the miscibility gap, however, the derived diffusion rate was given relatively low weight because it lacked collaboration Table 2 Assessed atomic mobilities for the bcc phase of the U-Pu-Zr ternary system (all in SI units).…”

“…A remarkable drop of the interdiffusion coefficients was detected at 1023 and 1073 K due to the demixing of the species in (or close to) the miscibility gap. Among other studies on the U-Zr system include those by Pavlinov [17] at 1223-1723 K, by Adda and Philibert [18] at 1223-1348 K, by Shevchuk [19] in a composition range of 10-90 at.% Zr at 1223-1358 K, and by Akabori [20] with 68-78 at.% Zr at 923-1023 K, respectively. As shown in Fig.…”

“…Mole Fraction of Zr [17]; (c) Shevchuk [19] and (d) Adda and Philibert [18]. from the others and its poor purity of starting materials.…”

“…There is some experimental diffusion data available for the U-Pu-Zr bcc alloys, including tracer, impurity, and interdiffusion coefficients [6,7,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. In the subsections that follow, the data is evaluated system by system.…”

“…The experimental diffusion data for the bcc U-Zr alloys [10][11][12][13][14][15][16][17][18][19][20] are summarized in Table 1. The self-diffusivity of bcc-U was determined by Adda and Kirianenko [10] by using the lathe sectioning technique and by Bochvar et al [11] by a thin-layer sectioning technique.…”