Phase-field microstructure-based effective thermal conductivity calculations in tungsten

Abstract

Using a phase-field approach with the heat conduction equation, we predict the grain growth behaviors in tungsten (W) and their effects on the effective thermal conductivity. Results show that the simulated grain growth kinetics is basically consistent with the experimental observations. An empirical correlation describing the averaged grain area as a function of the temperature and time is derived. Further, we study the effect of the grain growth, columnar crystal structure, and the recrystallization on the effective thermal conductivity of W. It is found that the effective thermal conductivity non-linearly increases with increasing the grain size, and a simple correlation of converting two-dimension into three-dimension effective thermal conductivity is obtained. Interestingly, the effective thermal conductivity of the columnar crystal is relatively high along the elongated direction and higher than that of the isometric crystal. Nevertheless, the effective thermal conductivity decreases with the occurrence of the recrystallization due to the increased grain boundary density. Our results reveal that grain growth and grain structure can affect the capacity of the heat transfer at high temperatures, which could be considered in the transient event of the long-time service of W materials in fusion devices.

The Effective Diffusion Coefficient of Hydrogen in Tungsten: Effects of Microstructures From Phase-Field Simulations

“…To solve the steady-state diffusion equation shown in Eq. 16, a spectral iterative method is adopted, which has been used to solve the heat conduction equation in previous work (Wang et al, 2016;Li et al, 2022). In order to facilitate the reader's understanding, we present the details of the solution process here.…”

“…In this work, σ gb 2.32 J m −2 is determined by averaging the grain boundary energies of 408 grain boundaries of W (Ratanaphan et al, 2017), and l gb is assumed to be 4.0 nm to ensure there are sufficient grid points across the diffused interface. The grain boundary migration energy E a is 0.6 eV based on the annealing experiment of the grain growth in W (Guo et al, 2018), and L 0 is 8.33 × 10 −6 m 3 J −1 s −1 obtained by fitting the annealing experimental results of the grain growth (Guo et al, 2018;Li et al, 2022).…”

“…Grain structures and irradiated voids are considered as the main defect microstructures generated by using phase-field simulations, although other defect microstructures such as dislocations, precipitates, and gas bubbles can also be easily incorporated in the model. A spectral iterative algorithm (Wang et al, 2016;Li et al, 2022) is used to solve the stationary diffusion equation based on the phase-field microstructures to obtain the effective diffusion coefficient. The current method is only applied at high temperature or there is no interaction between the diffusion component and microstructure, where H atoms can be eventually desorbed from grain boundaries and voids consisting with the thermal desorption experimental observations (Eleveld and Veen, 1994;Hodille et al, 2014).…”