Interplay Between Local Environment Effect and Electronic Structure Properties in Close Packed Structures

Abstract

Within a tight binding framework, the interplay between local atomic arrangement, orbital directionality and phase stability properties is discussed for a series of tetrahedrally close packed (tcp) structures. The common features which characterize the local densities of states of tcp phases can be explained by a moment analysis up to fourth order terms. On the contrary, it is shown that structural energy differences between simple and tcp crystalline structures requires the knowledge of at least the fifth order moments, a fact which has been underestimated in the past. Finally, the relative stability of various representative geometries, including the ones of simple crystalline structures is examined as a function of the number of valence electrons. INTRODUCTION and METHODOLOGY

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

“…By taking into account the contribution of six moments to the DOS, the analytic BOP reproduces the structural trend from hcp to bcc to hcp to f cc across the nonmagnetic 4d and 5d transition metal series. This level of approximation is also sufficient to resolve the structural energy differences of tcp phases [2]. In this work we apply the analytic BOP to the structural stability of transition metals in the tcp structures A15, C14, C15, C36, σ, and µ.…”

“…In particular, we used canonical nearest-neighbour bond integrals [21] ddσ : ddπ : ddδ = −6 : 4 : −1 (6) with a decay ∝ 1/R 5 and band-widths as obtained from tight-binding calculations. The second moment µ (2) was chosen identical for all structures to guarantee that the structural energy differences are to first order given by the differences in bonding energy [8]. The resulting valencedependent bond energies shown in Fig.…”

“…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].…”

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

“…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].…”

“…In this manner, the moments subsume the detailed information of the positions and the local environment of the individual atoms. This has been used in the past to analyze trends of structural stability, see, e.g., [12,13,26,27,40,45,46].…”