An atom size effect in tracer diffusion

Published diffusion data permit an extensive comparison to be made between tracer diffusion coefficients, D, in Pb and in α-Zr, at 0.6 Tsub(m), where Tsub(m)(K) is the melting temperature of the host metal. For these metals, a striking correlation is found between D and the metallic radius, r, of the corresponding tracer element; except for the smallest r values, the correlation may be expressed in the general form: 1g D = A + exp(- br + c), where A, b and c are individual constants for each host metal. There is, for tracer diffusion in Pb, sufficient experimental data to permit the evaluation of an additional relationship between the pre-exponential factor Dsub(O), and the activation enthalpy, ΔH, in the usual expression D = D0 exp(- ΔH/RT), describing the temperature dependence of D. A combination of these relationships allows the evaluation of expressions for D0 and ΔH in which r is the only variable. Derived relations between D0 and ΔH, and ΔH and ΔH and r, are, respectively, D0 = 2.0 x 10-4 exp (0.345 ΔH)cm2s-1, and ΔH = 30.8 - exp (8.65 - 4.04 r), in which the units of ΔH and r are kcal mol-1 and A respectively. In order to compare tracer diffusion in these 'open' metals (i.e. metals with a relatively large metallic/ionic radius ratio) with tracer diffusion in a 'full' metal, values of D at 0.6 Tsub(m) have been calculated from published data for diffusion in Cu. Again it is found that 1g D tends to display an exponential dependence on r; in contrast to the results for the 'open' metals, however, 1g D is found to increase with r. Expressions derived for D0 and ΔH for diffusion in Cu, corresponding to those given above for Pb, are: D0 = 5.2 x 10-4 exp(0.152 ΔH)cm2s-1 and ΔH 43.1 + exp(17.40 - 11.94 r), in which the units of ΔH and r are as given for Pb. (author)