Topologically close-packed phases in binary transition-metal compounds: matching high-throughputab initiocalculations to an empirical structure map

Abstract

In steels and single-crystal superalloys the control of the formation of topologically close-packed (TCP) phases is critical for the performance of the material. The structural stability of TCP phases in multi-component transition-metal alloys may be rationalised in terms of the average valence-electron count N and the compositiondependent relative volume-difference ∆V /V . We elucidate the interplay of these factors by comparing density-functional theory calculations to an empirical structure map based on experimental data. In particular, we calculate the heat of formation for the TCP phases A15, C14, C15, C36, χ, µ, and σ for all possible binary occupations of the Wyckoff positions. We discuss the isovalent systems V/Nb-Ta to highlight the role of atomic-size difference and observe the expected stabilisation of C14/C15/C36/µ by ∆V /V at ∆N = 0 in V-Ta. In the systems V/Nb-Re, we focus on the well-known trend of A15→ σ → χ stability with increasing N and show that the influence of ∆V /V is too weak to stabilise C14/C15/C36/µ in Nb-Re. As an example for a significant influence of both N and ∆V /V , we also consider the systems Cr/Mo-Co. Here the sequence A15→ σ → χ is observed in both systems but in Mo-Co the large size-mismatch stabilises C14/C15/C36/µ. We also include V/Nb-Co that cover the entire valence range of TCP stability and also show the stabilisation of C14/C15/C36/µ. Moreover, the combination of a large volume difference with a large mismatch in valence-electron count reduces the stability of the A15/σ/χ phases in Nb-Co as compared to V-Co. By comparison to non-magnetic calculations we also find that magnetism is of minor importance for the structural stability of TCP phases in Cr/Mo-Co and in V/Nb-Co.

Microsegregation and precipitates of an as-cast Co-based superalloy—microstructural characterization and phase stability modelling

“…The influence of N on the relative structural stability of TCP phases is well known from the calculations with density functional theory (DFT) [18,19] and approximate electronic structure methods [20][21][22][23]. The interplay of N and DV=V was discussed in DFT calculations for various binary systems [22][23][24][25].…”

Crystal-Structure Analysis with Moments of the Density-of-States: Application to Intermetallic Topologically Close-Packed Phases

“…More values than sublattices, e.g., C14 at x = 0.5, arise if the same composition can be represented by different sublattice occupations. The similarity of the moments of C14 for x = 0, 1/3, 2/3, and 1 indicates weak internal relaxations for both, the stable C14-V 2 Ta and the energetically unfavourable [24] C14-VTa 2 phase.…”

“…The moments analysis is performed for unit cells of TCP phases in 4d/5d unaries [29], in V-Ta [24], and in Fe-Nb [51] that were fully relaxed by density-functional theory (DFT) calculations. In all cases, we included all permutations of the occupations of Wyckoff positions with different elements.…”

“…The considerable difference of the atomic volume of V and Ta leads to a stabilization of V-Ta Laves and µ phases, in contrast, e.g., to the Nb-Ta system with negligible size difference [24]. We computed the moments for the unit cells of V-Ta TCP phases as obtained by full relaxation with DFT calculations [24].…”

“…This has been investigated in detail for the χ phase [7], the Laves phases [8][9][10], the A15 phase [11][12][13][14], and the σ phase [15]. The theoretical analysis of TCP phases is mostly based on density-functional theory (DFT) calculations [16][17][18][19][20][21][22][23][24][25] and approximate electronic structure methods [12,13,[26][27][28][29].…”