Cluster Expansion Approach for Relative Stability among Different Atomic Structures in Alloys: an Approach from a Dilute Limit

Abstract

We demonstrate the ability of our cluster expansion approach (CEA) for cohesive energies of alloys, which allows one to study the chemical trends of the relative stability of different atomic structures of alloys, as an example, X dependence of the atomic structures of Al-rich AlX (X = Sc-Zn) alloys, including ordered structures (L1 2 (Al 3 Sc), DO 22 (Al 3 V)), a Mackay icosahedron (a local structure in the Al 80 Mn 20 quasicrystal), and precipitate shapes in decomposition phases (Al 1Àc Cu c , Al 1Àc Zn c ; c < 0:05). All the terms in the CEA for Al-rich AlX alloy can be determined uniquely and successively from low-order to high-order by using the total energies of isolated Al and X atoms, pure Al and X metals, and X impurities in Al metal. The total energies of impurity systems are calculated accurately by using the all-electron full-potential Korringa-Kohn-Rostoker (FPKKR) Green's function method, combined with the density-functional theory in the generalized-gradient approximation (GGA). We show: (1) the binding energies of X (X = Cu, Zn) impurities in Al are reproduced very well by the CEA including two-and three-body interaction energies of X impurities; (2) the chemical trends of structural stability among ordered structures (L1 2 , DO 22 , DO 23 ) of Al 3 X (X = Sc, Ti, V), being determined by use of the screened-FPKKR and GGA band-structure calculations, are reproduced by the CEA including only two-body (X-X) interaction energies in Al.

Ab initio study for magnetism in Ni2MnAl full-Heusler alloy: A cluster expansion approach for total energy

“…Tel. : +81 53 478 1780; fax: +81 53 478 1781 terms in the present CE, such as the 2-body and 3-body interaction energies (IEs) [6,10,11]. Thus, it is obvious that the present CE is very useful, at least, to study qualitatively the stability of atomic structures and magnetism of ordered and disordered alloys.…”

“…The characteristic feature of the present CE for total energies of A-rich AXY alloys is that all the terms in the present CE are uniquely determined by the combination of total energies at different atomic arrangements of X and Y impurities in A metal with the total energy of A metal (per atom) [10,11,[17][18][19]. The present CE is very different from the Connolly-Williams approach where all the terms in the CE are the adjustable parameters, being determined via the fitting to the total energies of selected ordered alloys [20].…”

“…We have recently proposed the ab initio cluster expansion (CE) approach [10,11] for the total energies of ordered and disordered alloys, and have shown that the relative stability of atomic structures (L1 2 and DO 22 of Al 3 X (X = Sc,Ti,V)) and magnetism (FM and AFM of Ni 2 MnAl) are understood by considering only the low-order * Corresponding author. Tel.…”

Full-Potential Screened KKR Calculations for Magnetism of Co<SUB>2</SUB>MnSi, Ni<SUB>2</SUB>MnAl and Ru<SUB>2</SUB>MnSi, Based on the Generalized Gradient Approximation

“…The definition and accuracy of the cluster expansion from a dilute limit are discussed in Ref. 30). By using these impurity interaction energies, we have already succeeded in understanding the physical mechanism of the NMR experimental results of Mn impurities in NiMn and NiFe alloys.…”

“…They are the 1st-and 2nd-lowest order (one-body and two-body of Mn impurities) terms in the cluster expansion (from a dilute limit) of the internal energies of alloys 30) and may be important to study the characteristic features of magnetism of alloys. The definition and accuracy of the cluster expansion from a dilute limit are discussed in Ref.…”