Tracer diffusion of titanium in α-iron

Abstract

The tracer diffusion coefficient of 44Ti in a-Fe is determined by the serial sectioning method in the temperature range of 948 to 1174 K. In paramagnetic a-Fe the diffusion coefficient of Ti shows a linear Arrhenius relationship from the a-y transformation temperature to about 30 K above the Curie temperature T, = 1043 K. Below 1076 K, the temperature dcpendence of the diffusion coefficient deviates from the linear Arrhenius relationship due to the magnetic spin ordering. The temperature dependence of the diffusion coefficient D in the whole temperature range of a-Fe can be expressed by (293.2 f 8.8) kJ mol-' R T DTi(T) = (0.21?::;3 exp (1 + 0.079M2(T))) mz s -' ,where M is the magnetic long-range order parameter. The frequency factor Do = (0.21 T ! , ; ; ) m2 s -' and the activation enthalpy Q = (293.2 f 8.8) kJ mol-' describe Ti diffusion in paramagnetic a-Fe and correspond to a normal vacancy diffusion mechanism. Ti diffusion is faster by a factor of about 5 when compared to Fe self-diffusion. This can be understood by a vacancy-solute binding due t o the larger atomic radius of Ti. A comparison with the diffusion behaviour of other transition elements in x-Fe confirms thc correlation between diffusion velocity and solute atomic radius.

Diffusion of niobium in α-iron

“…The activation energies for diffusion of niobium and molybdenum in the paramagnetic -iron are larger than that for self-diffusion. Figure 4 shows a plot of the activation energy Q p for self-diffusion, 5) solute diffusion of transition metals of molybdenum, 8) chromium, 19) cobalt, 20) titanium, 22) nickel, 23) vanadium 24) and niobium obtained by the present work in the paramagnetic -iron against (r s À r Fe Þ=r Fe , where r s and r Fe are the radii of the solute atom for the coordination number 8 and of the iron matrix lattice. 9) A linear relationship is observed in Fig.…”

“…This Gibbs free enthalpy of binding between a vacancy and a solute atom leads to a decrease in the vacancy formation enthalpy and thus to an increase in diffusion. 22) Table 3 summarizes the Arrhenius parameters for the self-diffusion 5) and the solute diffusion of molybdenum, 8) chromium, 19) cobalt 20) and niobium obtained by our research group using the radioactive tracer method with serial sputter-microsectioning techniques. The activation energies for diffusion of niobium and molybdenum in the paramagnetic -iron are larger than that for self-diffusion.…”

First-principles analysis of solute diffusion in dilute bcc Fe- X alloys

“…A simple analysis of Eq. (18) shows that the numerator is dominated by the largest terms; either 3 , 3 , or 3 . If the largest in the numerator is larger than 2 in the denominator, f will be approximately unity almost independent of temperature.…”

“…When fitting within the temperature range between 600 and 1200 K and accounting for the negative terms in the numerator and denominator in Eq. (18), it is found that a minor rescaling is required which gives…”

Effect of Ti on Evolution of Microstructure and Hardness of Martensitic Fe–C–Mn Steel during Tempering

“…In the second and the third model, the growth rate is assumed to be controlled by a combination of volume diffusion and diffusion along dislocations. We use the tracer diffusivity of 44 Ti, as measured in large single Fe crystals, 38) as the lattice diffusivity of Ti in martensite, for all three models. The diffusivity data of Ti in α-iron, as measured by Moll and Ogilvie 39) is not used for the calculations as this data is derived from polycrystalline materials, which is believed to overestimate the lattice diffusivity.…”