Sub-stoichiometry and vacancy structures in V/Nb carbide precipitates by cluster expansion and first-principles calculations

Carbide precipitates, particularly V/Nb carbides, play a vital role in modulating many properties, including strength, hardness, wear resistance and hydrogen embrittlement (HE) susceptibility of steels. Our work presented a comprehensive study employing a cluster expansion (CE) approach combined with first-principles calculations to investigate the sub-stoichiometry induced by C vacancies within V/Nb carbides, an important aspect lacking sufficient understanding. Ground-state sub-stoichiometric V/Nb carbide compounds as the C composition varies were predicted, consistent with experimental observations. The predictions were further supported by the good agreement between the calculated bulk moduli and experimental measurements. The elastic moduli of carbides were shown to monotonically decrease as the C composition decreases, attributed to pd bonds being replaced by dd bonds with the introduction of vacancies. We have demonstrated that C vacancies in the carbides would arrange into particular patterns, with notable preference to form 3NN vacancy pairs and triplets. Such vacancy pattern formation was elucidated to be mainly driven by the elastic interaction between vacancies. The present study provides critical new knowledge regarding sub-stoichiometry and vacancy structures in carbide precipitates in steels. The findings are critical for an accurate understanding of the structures and properties of carbides and offer essential inputs for engineering steels of enhanced performance.