Migration velocities of intergranular He gas bubbles under thermal gradients in Fe by phase-field modeling

We compute the migration velocity of intergranular He bubbles in Fe under thermal gradients using phase-field (PF) modeling. Grain boundaries (GBs) with energies in the range of 0.88 - 1.6 J/m2 are considered. To develop a suitable PF model, the influences of the PF parameterization strategy, thermal conductivity in grain boundaries, and GB diffusion coefficients on intergranular He bubble geometry are addressed. Good agreement between our simulations and a theoretical model are found for the contact angle at the junction of the bubble and GB. Under the application of a thermal gradient, we find that intergranular He bubbles migrate slower than He bubbles in an Fe matrix. We show that this is a result of the smaller temperature gradient at the bubble/GB junction when the bubble is at the GB, than when the bubble is in the matrix. A linear relationship between bubble migration velocity and temperature gradient is observed for intergranular He bubbles for all GB energies studied in this work, consistent with predictions from a theoretical model. Intergranular bubble migration velocity is also found to depend linearly on the inverse of bubble size. However, we find the shape of the bubble influences intergranular bubble migration velocity. An analytical model for bubble migration velocity that considers the shape of an intergranular bubble is proposed and shown to capture the computed PF data for He bubbles.

Automated summary

In this study, we use phase-field modeling to calculate the migration velocity of intergranular He bubbles in Fe under thermal gradients. Grain boundaries with energies ranging from 0.88 to 1.6 J/m2 are considered. We address the influences of the phase-field parameterization strategy, thermal conductivity in grain boundaries, and GB diffusion coefficients on the geometry of intergranular He bubbles. Our simulations show good agreement with a theoretical model for the contact angle at the bubble/GB junction. We find that intergranular He bubbles migrate slower than He bubbles in the Fe matrix due to smaller temperature gradients at the bubble/GB junction. We observe a linear relationship between bubble migration velocity and temperature gradient for intergranular He bubbles, consistent with theoretical predictions.