Modeling Topologically Close-Packed Phases in Superalloys: Valence-Dependent Bond-Order Potentials Based on Ab-Initio Calculations

Abstract

Refractory elements are used in Ni-based superalloys to increase creep resistance (Mo, Re, W) and to retard the coarsening of the γ' phase (Re). At high concentrations of refractory elements precipitation of topologically closepacked (tcp) phases [1] is detrimental to the creep properties of the alloys. A more detailed understanding of the formation kinetics and thermodynamic stability of tcp phases will therefore be beneficial for the design of the next generation superalloys. Atomistic modeling of tcp stability with interatomic potentials requires to go beyond the second-moment approximation to the electronic density of states by including up to at least the sixth moment [2]. We have developed an analytic bond-order potential (BOP) that systematically takes into account higher moment contributions to the density of states and depends explicitly on the valence of the transition-metal elements [3]. For the parameterization of the new BOP, we performed extensive density functional theory (DFT) calculations of elemental and binary compound phases of Ni, the technologically important alloying element Cr, and the refractory metals Mo, Re, and W. We will discuss the structural trends of the DFT calculations, compare to the predictions of the analytic BOP and report on our progress on the parameterization of the analytic BOP for the Re-W system. This work is part of the EPSRC-funded collaborative multi-scale project 'Alloys by Design'.

Structural Stability of Topologically Close-packed Phases: Understanding Experimental Trends in Terms of the Electronic Structure

“…Recently developed material-specific TB models [17] are employed in first molecular-dynamic simulations of interfaces between cubic phases and TCP phases. The tight-binding and bond-order potential calculations presented in this work were carried out with the BOPfox code [18].…”

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

“…Knowledge of the moments allows for the construction of the electronic DOS that yields the bond energy by integration to the Fermi level as described in the framework of BOPs in various previous works [41][42][43][44]. This leads to close relations between the moments and the trends of structural stability with band filling, see e.g., [27][28][29]40,42,47,48].…”

“…This approach has been used before in the analysis of trends of TCP phase stability across the transition metal (TM) series [28,29]. The observations reported for TCP phases are equivalent to results using an alternative canonical TB model for d-d bonding [26,27].…”

“…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].…”

Closing the Gap Between Nano- and Macroscale: Atomic Interactions vs. Macroscopic Materials Behavior

“…The bond energy can be taken analytically to an arbitrary number of moments. Therefore the BOPs provide an effective interatomic interaction scheme that converges systematically to the exact solution of the TB HAMILTONIAN.T h e number of moments required in practice depends on the investigated quantity and is approximately six for identifying qualitative features of structural stability in transition metals (Hammerschmidt et al, 2008) to nine for reproducing quantitative features of defects and transformation paths (Mrovec et al, 2004).…”