PHYSICAL REVIEW B 93, 224106 (2016) Effect of composition on antiphase boundary energy in Ni 3 Al based alloys: Ab initio calculations O. I. Gorbatov, 1, 2, 3 I. L. Lomaev, 1, 4, 5 Yu. N. Gornostyrev, 1, 4, 5 A. V. Ruban, 2, 6 D. Furrer, 7 V. Venkatesh, 7 D. L. Novikov, 8 and S. F. Burlatsky 8 1 Institute of Quantum Materials Science, Ekaterinburg 620107, Russia 2 Department of Materials Science and Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden 3 Nosov Magnitogorsk State Technical University, Magnitogorsk 455000, Russia 4 Science for Technology LLC, Leninskiy pr-t 95, 119313 Moscow, Russia 5 Institute of Metal Physics, Ural Division RAS, Ekaterinburg 620219, Russia 6 Materials Center Leoben Forschung GmbH, A-8700 Leoben, Austria 7 Pratt & Whitney, 400 Main Street, East Hartford, Connecticut 06108, USA 8 United Technologies Research Center, 411 Silver Lane, East Hartford, Connecticut 06108, USA (Received 3 June 2015; revised manuscript received 23 May 2016; published 20 June 2016) The effect of composition on the antiphase boundary (APB) energy of Ni-based L1 2 -ordered alloys is investigated by ab initio calculations employing the coherent potential approximation. The calculated APB energies for the {111} and {001} planes reproduce experimental values of the APB energy. The APB energies for the nonstoichiometric γ  phase increase with Al concentration and are in line with the experiment. The magnitude of the alloying effect on the APB energy correlates with the variation of the ordering energy of the alloy according to the alloying element’s position in the 3d row. The elements from the left side of the 3d row increase the APB energy of the Ni-based L1 2 -ordered alloys, while the elements from the right side slightly affect it except Ni. The way to predict the effect of an addition on the {111} APB energy in a multicomponent alloy is discussed. DOI: 10.1103/PhysRevB.93.224106 I. INTRODUCTION Nickel-based superalloys represent an important class of materials which have outstanding high-temperature strength and oxidation resistance [1,2]. They are widely used in aircraft and power-generation turbines and rocket engines, which work in high-temperature environments. Due to their high technological importance, these alloys have been attracting researchers’ interest for several decades [2,3]. The strength of Ni-based superalloys originates from the presence of the ordered γ  (Ni 3 Al-type structure) phase, which is distributed within the disordered fcc γ matrix [2,3]. High resistance to the plastic deformation of two phase γ /γ  alloys is caused by the need of the antiphase boundary (APB) ribbon formation when a single γ -phase 1/2110 dislocation cuts a γ  particle in two-phase γ /γ  alloys. Thus, the APB energy is one of the most important parameters that determines the superdislocation structure [1,2,4,5], the mechanical behavior of the γ  phase, and the strength of the γ /γ  alloys. Unfortunately, it is not possible to measure the APB energy directly. The most promising experimental technique is based on the measurement of the dissociation splitting distance of superpartial dislocations within the γ  phase followed by the estimate of the APB energy on the basis of the theoretical dislocation description (e.g., continual elasticity or Peierls-Nabarro model) [6–10]. For the measurement of the splitting distance, the weak-beam transmission electron microscopy is commonly used. It is, however, somewhat difficult to determine the exact orientation of superpartial dislocations within the lattice, which results in a significant spread in experimental values of APB energies. The first theoretical estimation of the APB energy based on the simple central pair interatomic interactions model was proposed in Ref. [11]. This model was further developed in Refs. [12–15] in which an attempt was made to establish the relation between the APB energy and thermodynamic parameters of alloys such as mixing and ordering enthalpies (or ordering temperature). This approach reveals general trends in the family of Ni 3 Al-type alloys. However, it does not provide a reliable value of the APB energy due to well-known limitations of the nearest-neighbor pair potential approximation in metallic alloys. Atomistic calculations of APB energies were performed using various techniques. It was found that results of molecular dynamic simulations (see Ref. [16] and references therein) are very sensitive to details of approximations for interatomic potentials and contain uncontrollable errors. At the same time, theoretical methods based on first-principles calculations using density functional theory (DFT) are now becoming an efficient and accurate research tool permitting wide possibilities for modeling defects. The {111} and {001} APB energies of ordered L1 2 alloys were calculated using full potential methods [6,17,18] and Green’s-function technique within the linear muffin-tin orbital method [19]. It was revealed that first- principles calculations predict APB energies in agreement with experiments when atomic relaxations near APB planes are taken into account [20]. However, previous ab initio calcu- lations of the APB energy in Ni-based L1 2 alloys [6,17–21] have been performed for ferromagnetic or nonmagnetic states, while they are paramagnetic for all temperatures of interest (T Curie = 41.5 K for Ni 3 Al). Various experiments show that the APB energy is very sensitive to the alloy composition (stoichiometry deviation, alloying addition, etc.) [7,8,22,23]. According to Dimiduk et al. [24], the {001} APB energy increases with Al content, but results by Yu et al. [25] show the opposite trend. Meanwhile, a study by Kruml et al. [8] confirms the results of Ref. [24] 2469-9950/2016/93(22)/224106(8) 224106-1 ©2016 American Physical Society