Isotope Effect for Diffusion of Iron in Vanadium

The diffusion coefficients of iron, using ${\mathrm{Fe}}^{59}$ as the radioactive tracer, and the isotope-effect parameter, using ${\mathrm{Fe}}^{55}$ and ${\mathrm{Fe}}^{59}$ as tracers, have been measured in vanadium over a temperature range of more than 800°C by standard sectioning and counting techniques. The diffusion of ${\mathrm{Fe}}^{59}$ in vanadium exhibits the anomalous behavior of having not one but two straight lines in a plot of $\ln D$ versus $\frac{1}{T}$, with a change of slope occurring near 1350°C. The data have been analyzed into the sum of two exponentials: $D=2280\mathrm{}$ $\exp (-\frac{101500}{\mathrm{RT}})$ at high temperatures, and $D=0.0936\mathrm{}$ $\exp (-\frac{67600}{\mathrm{RT}})$ at low temperatures. The values of the isotope-effect parameter for the ${\mathrm{Fe}}^{59}$ and ${\mathrm{Fe}}^{55}$ isotopes are approximately constant near 0.7 at low temperatures, but decrease rapidly with increasing temperature above 1350°C. The measurements are interpreted to indicate that two mechanisms of diffusion operate in vanadium. The mechanism predominant at low temperatures is identified as motion of a single vacancy; that at high temperatures is probably motion of divacancies.