Numerical modeling of the diffusional transport of nitrogen in multi-phase solid titanium and its application to determine diffusion coefficients

Abstract

As part of a program to understand the dissolution of nitrogen-rich titanium solids in liquid titanium, this manuscript presents a numerical study of nitrogen transport in titanium at elevated temperatures. A Landau transformation was applied to the equations governing mass transport which were used as the basis for the numerical model. The numerical model was used initially to simulate nitrogen transport in a planar geometry and the predicted nitrogen concentration profiles and displacement of Ti–N phase boundaries showed good agreement with analytically derived solutions. The numerical model was then used to simulate nitrogen transport in commercially pure titanium cylinders. The model results were shown to be sensitive to the diffusion coefficients of Ti–N phases present in the system. Based on the sensitivity analysis, diffusion coefficients at 1650 °C of 4.3×10−11m2s−1,1.6×10−11m2s−1 and 1.7×10−12m2s−1 for β-Ti, α-Ti and TiN phases, respectively, were back calculated using the model. The model predictions, using the new diffusion coefficients, showed good agreement with previously published data in terms of both the nitrogen concentration profiles and displacements of Ti–N phase boundaries under the conditions examined in the study. The comparison indicates the presented model is capable of accurately approximating the transport of nitrogen in titanium at elevated temperatures.

Keywords

• Titanium
• Nitrogen
• Diffusion
• Landau transformation
• Numerical method