First-principles study on thermal expansion of W-Re sigma and chi phases

We investigate how the Re content affects the coefficient of thermal expansion (CTE) of the non-stoichiometric W-based sigma and chi phases, forming upon neutron irradiation of W, to explore and quantify its mismatch between precipitates (W-Re) and matrix (W). To this end, we have conducted first-principles calculations using two approaches: the Debye-Grüneisen (DG) model and the quasi-harmonic approximation (QHA). The two approaches yield different results: the QHA, which is deemed to be the most accurate of the two, predicts substantial changes with Re content, while the acoustic-modes based DG model does not. The CTE of the sigma and chi at stable Re contents is compared to experimental values for bcc-W and bcc-W-Re containing 25 at.% Re. Taking bcc-W as a reference, we find a significant mismatch in CTE of up to 37% and 62% for sigma and chi, respectively, which may contribute to thermal stress buildup in the material at elevated temperatures. The mismatch is shown to increase with the temperature and Re content for both phases. The produced data are used to fit a temperature and Re concentration-dependent analytical function of the CTE for both phases, which can be employed as input for continuum mechanical modeling.