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Abstract

Topologically close-packed (TCP) phases play an important role in many modern alloys and steels. While particular TCP phases are desirable in precipitate-hardened steels, the precipitation of TCP phases in single-crystal superalloys has a detrimental effect on the mechanical properties. In order to gain a microscopic understanding of TCP phase formation, we investigate the factors that drive their structural stability. In particular, we employ electronic-structure calculations at different levels of coarse-graining, ranging from density-functional theory (DFT) to tight binding to analytic bond-order potentials (BOPs). The analytic BOP depends explicitly on the valence of the transition-metal (TM) elements and accounts for charge transfer and magnetic contributions to the binding energy. By comparison to an empirical structure map, we analyse the interplay of electron count and size-mismatch as dominating factors for the stability of TCP phases. We carry out high-throughput DFT calculations of the TCP phases A15, C14, C15, C36, mu, sigma, and chi in various binary TM alloys relevant to steel and Co-based superalloys. We demonstrate that the role of electron count on the structural trend across the non-magnetic 4d and 5d TM observed in DFT calculations can be clearly identified with coarse-grained electronic structure calculations on the level of BOPs. We briefly discuss the role of entropy and magnetism on structural stability. In a concerted effort with casting experiments and microstructure analysis, we demonstrate that the structure map provides guidance for the identification of TCP precipitates and rationalises the influence of local variations of the chemical composition on TCP phase formation.