The vacancy-mediated diffusion of transition metal solutes in tungsten: Atomic Kinetic Monte Carlo simulations

The kinetic coupling between vacancy flux and solute flux is crucial for comprehending and forecasting the microstructural evolution of tungsten-based alloys under irradiation. We utilized the Atomic Kinetic Monte Carlo (AKMC) method to systematically explore the vacancy-mediated diffusion of transition metal (TM) solutes in tungsten. The diffusion and transport coefficients of TM solutes were obtained and then used to identify the occurrence of vacancy drag and solute-segregation tendencies. Our findings indicate that TM solutes exhibit faster diffusion rates than tungsten self-diffusion. Ti, V, Nb, Mo, and Ta do not experience vacancy drag, whereas for other TM solutes, vacancy drag is the primary vacancy-mediated diffusion mechanism at low temperatures, transitioning to the inverse Kirkendall mechanism at high temperatures. Moreover, their transition temperatures were determined, showing a parabolic trend in each TM series with peaks observed at Co, Rh, and Pt for the 3d, 4d, and 5d series, respectively. In the temperature range investigated here (600∼3000 K), Ti, Zr, Hf, V, Nb, Ta, and Mo exhibit depletion at vacancy sinks, while other TM solutes enrich at vacancy sinks due to vacancy drag at low temperatures but deplete because of the inverse Kirkendall effect as temperature increases. Additionally, our AKMC results confirmed that, for the solute-vacancy interactions, purely attractive and repulsive interactions lead to the vacancy drag and inverse Kirkendall effect, respectively. While for the complex case, involving both attraction and repulsion, the first-nearest-neighbor (1nn) attraction plays a crucial role in enabling solute diffusion via vacancy drag. Even with a strong 2nn repulsion, the solute can still diffuse through vacancy drag, provided there is a 1nn attraction.