Interdiffusion in the carbides of the Nb-C system

Abstract

Interdiffusion coefficients in Nb₂C and NbC_1−x were measured using bulk diffusion couples in the temperature range from 1400 °C to 1700 °C. Marker experiments were used to show that carbon is the only component undergoing significant diffusion in both carbides. Carbon concentrations were measured by difference using electron probe microanalysis, and interdiffusion coefficients were taken from Boltzmann-Matano analyses of the resulting concentration profiles. This analysis clearly showed that, in NbC_1−x, interdiffusion coefficient varies with carbon concentration, and is expressed by

$$\tilde D\left( {NbC_{1 - x} } \right) = 3.84 \times 10^{ - 9} \exp \left( {23.24x} \right)\exp \left( { - \frac{{28,450 \pm 850}}{T}} \right)m^2 /s$$

where x is the site fraction of vacancies on the carbon sublattice. The interdiffusion coefficient in Nb₂C is given by

$$\tilde D\left( {Nb_2 C} \right) = 2.04 \pm 0.57 \times 10^{ - 4} \exp \left( { - \frac{{35,520 \pm 2190}}{T}} \right)m^2 /s$$

Parabolic layer growth coefficients were estimated from the Nb|C diffusion couples as well. They are given by

$$\begin{gathered} K_p \left( {NbC} \right) = 2.65_{2.41}^{2.90} \times 10^{ - 5} \exp \left( { - \frac{{37,600 \pm 1400}}{T}} \right)m^2 /s \hfill \\ K_p \left( {Nb_2 C} \right) = 1.57_{1.28}^{1.92} \times 10^{ - 5} \exp \left( { - \frac{{36,400 \pm 3100}}{T}} \right)m^2 /s \hfill \\ \end{gathered} $$

The value of $\tilde D$ in NbC_1−x was found to be consistent with literature values for the tracer diffusivity of C in NbC_1−x via the thermodynamic factor, which was determined in two ways.