Antiphase Boundary Energy Research Articles

Modeling antiphase boundary energies of Ni3Al-based alloys using automated density functional theory and machine learning

Antiphase boundaries (APBs) are planar defects that play a critical role in strengthening Ni-based superalloys, and their sensitivity to alloy composition offers a flexible tuning parameter for alloy design. Here, we report a computational workflow to enable the development of sufficient data to train machine-learning (ML) models to automate the study of the effect of composition on the (111) APB energy in Ni3Al-based alloys. We employ ML to leverage this wealth of data and identify several physical properties that are used to build predictive models for the APB energy that achieve a cross-validation error of 0.033 J m−2. We demonstrate the transferability of these models by predicting APB energies in commercial superalloys. Moreover, our use of physically motivated features such as the ordering energy and stoichiometry-based features opens the way to using existing materials properties databases to guide superalloy design strategies to maximize the APB energy.

Enhanced strength-ductility synergy via novel bifunctional nano-precipitates in a high-entropy alloy

High-entropy alloys (HEAs) with a single-phased face-centered-cubic structure possess excellent plasticity but generally low strength. Precipitation strengthening is one of the most promising methods to improve the strength of alloys. However, plagued by a nerve-wracking fact that strength-ductility trade-off frequently limits the improvement of alloy properties. To overcome this problem, a new Ni35(CoFe)55V5Nb5 HEA with an excellent strength and ductility synergy was developed by introducing a novel bifunctional L12-Ni3Nb nano-precipitate. This HEA exhibits a high yield strength of 855 MPa, ultimate tensile strength of 1,302 MPa and marvelous elongation of ∼ 50%. First-principles calculations show that the (Ni24Co18Fe6)3(Nb10V4Fe2) nano-precipitate with a L12 structure possesses lower formation energy than that with D022 structure. The novel nano-precipitates provide two-fold functions. On the one hand, L12-(Ni24Co18Fe6)3(Nb10V4Fe2) nano-precipitates have a high anti-phase boundary energy, contributing to a significant increment in the yield strength through precipitation strengthening. More importantly, the precipitation of the precipitates lowers the stacking fault energy (SFE) of the alloy matrix, contributing to the excellent work-hardening ability and large plasticity through activating the continuous formation of SF networks and Lomer-Cottrell locks during deformation. The strategy to introduce the novel bifunctional nano-precipitates paves a new way to enhance the strength-ductility synergy of alloys.

Modeling the competition between solid solution and precipitate strengthening of alloys in a 3D space

Until now, the nature of the competitive and cooperative correlation between solid solution strengthening and precipitate hardening is still uncovered, and then brings great challenges in designing the high-performance alloys. Here, a unified model has been developed to establish the quantitative relationships among the aging process, microstructure, and yielding strength for a model nickel-based superalloy in a three-dimensional (3D) space, which agglomerates the three independent variables of aging temperature, cooling time, and matrix composition, and these variables dominated the size and volume fraction of precipitates, and anti-phase boundary (APB) energy. Our experiments clearly suggest the competitive and cooperative correlation of solid solution and precipitate hardening exits in a 3D space. The size and volume fraction of precipitates, and the composition of matrix after the aging process can be predicted, and then integrated into the physical model to obtain the yielding strength of alloys. On average, the deviation of the yielding strength is 4%, which is far better than 15% with the existing strength model without considering the heat treatment, significantly reducing the development cycle. The size and volume fraction of precipitates decrease with the increased cooling rate, leading to that the precipitate strengthening firstly increases and then decreases. Meanwhile, this trend would result in enhancing solid solution strengthening monotonously. Especially, the critical cooling rate coordinates the relationship between the competition and cooperation owing to the obvious change of the APB energy together with the matrix composition, and a maximum yielding strength occurs at 166 ℃/min. The present work can provide a key theoretical guidance for designing advanced alloys with the excellent performance in a 3D space.

Ordered structure and solute-suppressed atomic ordering in iron-cobalt alloys

The slowly cooled Fe-25 wt% Co alloys generally suffer from poor ductility due to the atomic ordering. Combining DFT calculations and experiments, ordered L60-Fe3Co structure was first demonstrated to crystallize in the slowly cooled ∼ 25 wt% Co alloys and lead to brittleness. The stable existence of L60-Fe3Co structure is of great significance to further understand the binary Fe-Co phase diagram. Metal elements (e.g. V and Nb) are generally added into FeCo alloy to improve ductility and workable ability. The toughening mechanism of these solutes is mainly realized by suppressing atomic ordering. The reduced antisite defect energies by V and Nb additions lowers the maximum degree of order and antiphase boundary (APB) energies. The key to suppress atomic ordering is reducing antisite defect energy or site-exchange energy. A comprehensive theoretical understanding on the mechanism of suppressing atomic ordering is helpful to further find alloying elements which simultaneously improve mechanical and magnetic properties for Fe3Co or other ordered alloys.

Phase stability, mechanical, thermal, electronic properties, anisotropy, lattice dynamics and APB -energies of Ti2AlX intermetallics in α2, B2, and O phases: A first principle study

The ternary titanium aluminide based alloys have been lucrative for high-temperature applications in next-generation aerospace vehicles. Present work systematically investigates phase stability, structural and elastic properties of Ti2AlX (XMo, W, Ta, Nb, Zr, Hf) in α2, B2 and, O phases, calculated using density functional theory (DFT) within generalized gradient approximation (GGA). The Pugh’s ratio, Poisson’s ratio, Cauchy pressures, Vicker’s hardness, machinability index, anisotropies, Debye temperature, thermal conductivity, melting temperature, and Peierls stress, derived from the elastic constants are also presented. Phonon calculations reveal that Ti2AlX (XMo, W) in their α2 phase are dynamically unstable. The dominant slip systems are predicted from antiphase boundary (APB) energy calculations which indicate that dominance and mobility of the slip systems are largely affected by the ternary element ‘X′ and explains its ductile-brittle behavior. The bonding behavior is also investigated using the electronic density of states plots. The increased Ti-X bonding enhances while increased Ti-Al bonding degrades the ductility in Ti2AlX intermetallics.

The Impact of Vibrational Entropy on the Segregation of Cu to Antiphase Boundaries in Fe3Al

We performed a quantum mechanical study of segregation of Cu atoms toward antiphase boundaries (APBs) in Fe3Al. The computed concentration of Cu atoms was 3.125 at %. The APBs have been characterized by a shift of the lattice along the ⟨001⟩ crystallographic direction. The APB energy turns out to be lower for Cu atoms located directly at the APB interfaces and we found that it is equal to 84 mJ/m2. Both Cu atoms (as point defects) and APBs (as extended defects) have their specific impact on local magnetic moments of Fe atoms (mostly reduction of the magnitude). Their combined impact was found to be not just a simple sum of the effects of each of the defect types. The Cu atoms are predicted to segregate toward the studied APBs, but the related energy gain is very small and amounts to only 4 meV per Cu atom. We have also performed phonon calculations and found all studied states with different atomic configurations mechanically stable without any soft phonon modes. The band gap in phonon frequencies of Fe3Al is barely affected by Cu substituents but reduced by APBs. The phonon contributions to segregation-related energy changes are significant, ranging from a decrease by 16% at T = 0 K to an increase by 17% at T = 400 K (changes with respect to the segregation-related energy difference between static lattices). Importantly, we have also examined the differences in the phonon entropy and phonon energy induced by the Cu segregation and showed their strongly nonlinear trends.

Improved ductility by coupled motion of grain boundaries in nanocrystalline B2-FeCo alloys

Embedded-atom method (EAM) potential for the FeCo binary systems has been improved to reproduce the antiphase boundary (APB) energies, crucial to the mechanical properties for ordered alloys. Using the improved potential, we further carried out tensile simulations on nanocrystalline FeCo models to investigate the effect of disordered grain boundaries (GBs) on the intergranular fracture. We found that the large concentrated stress at GBs ascribed to the poor dislocation behavior and plastic-deformation compatibility caused the occurrence of microcracks. As the degree of order at GBs was reduced, the GB motion can be enhanced contributed to the smaller GB migration energy barrier. The GB-dominant plasticity can improve the plastic-deformation compatibility and release the concentrated stress at GBs to prevent the generation of microcracks and intergranular fracture. Collectively, the enhancement of coupled GB motion by disordered GBs opens more pathways to improve the mechanical properties for both nanostructured and conventional polycrystalline alloys with ordered superlattice structures.

First-principles study of the effect of Al and Hf impurities on Co[formula omitted]W antiphase boundary energies

The effects of Al and Hf impurities on the (111) antiphase boundary (APB) energy of metastable FCC Co3W are investigated via ab initio calculations. Cluster expansions are used to predict the total energies of supercells containing non-dilute concentrations of impurities using Monte Carlo simulations at relevant temperatures, giving APB energies as a function of impurity concentration and temperature for each ternary system. The cluster expansions are validated by comparing with direct energy calculations of supercells of pure L12 Co3W and the effects of each impurity are compared. Two sets of compositions are explored for each system — constant ratio (constant ratio between Co and W) and sacrificial W (constant Co). It is found that sacrificial W compositions stabilize the L12 structure over a wider range of compositions than constant ratio compositions (given the restriction to the FCC lattice) in both systems and should be preferred. In sacrificial W compositions, Hf increases the APB energy far more than Al, particularly at higher concentrations of the impurity, and both systems exhibit little variation with respect to temperature. It is further shown that at higher concentrations of Hf, and most noticeably for Co3(W0.5Hf0.5), Hf and W tend to segregate into alternating planes, unlike the corresponding Co3(W0.5Al0.5), which explains the different impacts of the two impurities on the APB energy. Finally, the ratio of (111) to (100) APB energies is studied for sacrificial W compositions to understand cross slip behavior in both ternary systems.

Investigation of physical properties and superdislocation characters of Ni3Al under uniaxial tension/compression normal to slip plane

The <110>{111} superdislocations play a key role in the mechanical behaviors of L12 Ni3Al. Through the combination of density functional theory (DFT) calculations and Peierls-Nabarro (P–N) model, the physical properties of Ni3Al and the characters of superdislocations are systematically investigated under different uniaxial tensile/compressive loads normal to {111} slip planes. The influence of applied loads on ideal stress-strain relation, ideal strength, shear modulus along slip direction, anti-phase boundary (APB) energy, γ surface, splitting width of superdislocation (i.e., APB width), core width of super partial dislocations and Peierls stress is thoroughly discussed. The results show that the effects of uniaxial normal tensile/compressive loads on above properties are remarkable for both nonmagnetic (NM) and ferromagnetic (FM) states. The compressive loads along the <111> direction tend to expand the splitting width of superdislocations and the core width of super partial dislocations, which further induce higher Peierls stress and yield strength of Ni3Al, while the tensile loads lead to opposite effects. In addition, it is found that the stability zone of Ni3Al is in the normal applied strain range of −0.14–0.14 rather than −0.18–0.22 as suggested by previous works. For the case free of applied strain (i.e. ε = 0), both the predicted APB width and Peierls stress of the NM state are about 10% percent larger than those of the FM state. Obviously, since the physical properties of Ni3Al and characters of superdislocations are asymmetric under tensile/compressive normal loads, the tension/compression asymmetry of the mechanical behaviors for Ni3Al is inherent.

Micropillar compression deformation of single crystals of Fe3Ge with the L12 structure

The plastic deformation behavior of single crystals of Fe3Ge with the L12 structure has been investigated at room temperature as a function of crystal orientation by micropillar compression tests. In addition to slip on (010), slip on (111) is observed to occur in Fe3Ge for the first time. The CRSS (critical resolved shear stress) for (111)[101¯] slip, estimated by extrapolating the size-dependent strength variation to the ‘bulk’ size, is ~240 MPa, which is almost 6 times that (~40 MPa) for (010)[101¯] slip similarly estimated. The dissociation scheme for the superlattice dislocation with b=[101¯] is confirmed to be of the APB (anti-phase boundary)-type both on (010) and on (111), in contrast to the previous prediction for the SISF (superlattice intrinsic stacking fault) scheme on (111) because of the expected APB instability. While superlattice dislocations do not have any preferential directions to align when gliding on (010) (indicative of low frictional stress at room temperature), the alignment of superlattice dislocations along their screw orientation is observed when gliding on (111). This is proved to be due to thermally-activated cross-slip to form Kear-Wilsdorf locks, indicative of the occurrence of yield stress anomaly that is observed in many other L12 compounds such as Ni3Al. Some important deformation characteristics expected to occur in Fe3Ge (such as the absence of SISF-couple dissociation and the occurrence of yield stress anomaly) will be discussed in the light of the experimental results obtained (APB energies on (111) and (010) and CRSS values for slip on (111) and (010)).

Modeling APB energies in multicomponent Ni-base superalloys

An environment dependent nearest neighbor bond (EDNNB) model was developed to estimate the antiphase boundary (APB) energies in γ′ precipitates (L12 structure) in commercial Ni-base superalloys. In this approach, the most frequent combination of nearest neighbor violations across an APB on the {111} planes in the Al-sublattice were identified. Further, the effect of alloying elements such as Ta, Ti, Nb, W, Mo, Ni, and Cr on seven unique combinations of violations on the APB(111) energies (ΓXYNiNi, X, YAl, Ta, Ti, and Cr in the Al-sublattices) was systematically studied. First-principles calculations were employed to evaluate Γ by substituting Al atoms in the supercells by alloying elements on planes adjacent to the APB(111). The effect of alloying and interaction with a unique violation on APB(111) is captured through an environment strength coefficient, η. Interestingly, Ta and Nb have similar effects on the APB energies. Similarly, the effects are equivalent when the substitution is W or Mo irrespective of the combination of violation on the APB(111). The alloying effect is dramatic when the substitutions are within the vicinity of the APB(111). Ni substitution leads to a reduction of APB energy when the violations are of type Al–Al across the APB(111). All alloying additions increase the APB energy when the violation is Ti–Ti across the APB. Additionally, the magnitude of the strength coefficients is significantly higher than the other type of violations considered in this study. The strength coefficients are negative when the APB(111) has Ti–Cr violations, suggesting a driving force for segregation to APB(111). In conclusion, the creation of more Ti–Ti and Al–Ti violations is beneficial to increase the strength of the precipitate. APB energies in many disk and blade alloys were predicted using strength coefficients. The trends in APB energies are in good agreement with the trends in yield strength within the subsets of blade and disk alloys. The development of the EDNNB model opens avenues for predicting planar fault energies in novel multi-principal element compositions strengthened by L12 were discussed.

On short-range order strengthening and its role in high-entropy alloys

Short-range order (SRO) strengthening is one of the major strengthening mechanisms in alloys. Generally it is attributed to the increased resistance to dislocation slip caused by breaking favorable bonds. This contribution may be strong for the first dislocation slipping in a slip plane, but it is certainly less strong for the following next dislocations. Present work discusses SRO strengthening with a different optic: with the focus on the dissipated energy due to the formation of a diffuse antiphase boundary (APB). In this sense, SRO strengthening becomes important to define the friction stress on gliding dislocations. Cluster Variation Method calculations of APB energies are used to estimate the strengthening effect in BCC alloys. The results are illustrated using VNbTaMoW and VNbTaWAl high-entropy alloys, with ab-initio derived parameters. The results show that the strengthening is intense in the range of concentrated solid solutions, and also, that this effect is strongly composition-dependent.

Computational simulation of al-based alloy surface structure dislocation: the first-principles calculation and atomic pair-potential lattice dynamics calculation

In this paper, the first-principles calculation methods are used to obtain the generalized stacking fault (GSF) energy of Al and Al alloy surface structures. At the same time, after obtaining the atomic pair potential, GSF energy is calculated by the means of atomic simulation simultaneously. By comparison, the calculation of GSF energy at different scales is consistent and the study of GSF energy from different scale level with an acceptable accuracy is realized. For the study of surface structure dislocation defects, the calculation of antiphase boundary (APB) energy is pretty significant. By means of the atomic pair potential, we calculate the APB energy of surface structure of the NiAl, FeAl and CoAl binary Al-based alloys. Therefore, in this paper, the surface structural dislocation of Al-base binary alloys was studied on different scales.

First-Principles Study of the Effect of Al and Hf Impurities on Co &lt;sub&gt;3&lt;/sub&gt;W Antiphase Boundary Energies

The effects of Al and Hf impurities on the (111) antiphase boundary (APB) energy of metastable FCC Co 3 W are investigated via ab initio calculations. Cluster expansions are used to predict the total energies of supercells containing non-dilute concentrations of impurities using Monte Carlo simulations at relevant temperatures, giving APB energies as a function of impurity concentration and temperature for each ternary system. The cluster expansions are validated by comparing with direct energy calculations of supercells of pure L1 2 Co 3 W and the effects of each impurity are compared. Two sets of compositions are explored for each system — constant ratio (constant ratio between Co and W) and sacrificial W (constant Co). It is found that sacrificial W compositions are far more stable than constant ratio compositions in both systems and should be preferred. In sacrificial W compositions, Hf increases the APB energy far more than Al, particularly at higher concentrations of the impurity, and both systems exhibit little variation with respect to temperature. It is further shown that at higher concentrations of Hf, and most noticeably for Co 3 (W 0.5 Hf 0.5 ), Hf and W tend to segregate into alternating planes, unlike the corresponding Co 3 (W 0.5 Al 0.5 ), which explains the different impacts of the two impurities on the APB energy. Finally, the ratio of (111) to (100) APB energies is studied for sacrificial W compositions to understand cross slip behavior in both ternary systems.

Micropillar Compression Deformation of Single Crystals of Fe &lt;sub&gt;3&lt;/sub&gt;Ge with the L1 &lt;sub&gt;2&lt;/sub&gt; Structure

The plastic deformation behavior of single crystals of Fe3Ge with the L12 structure has been investigated at room temperature as a function of crystal orientation by micropillar compression tests. In addition to slip on (010), slip on (111) is observed to occur in Fe3Ge for the first time. The CRSS (critical resolved shear stress) for (111)[10‾1] slip, estimated by extrapolating the size-dependent strength variation to the ‘bulk’ size, is ~240 MPa, which is almost 6 times that (~40 MPa) for (010)[101] slip similarly estimated. The dissociation scheme for the superlattice dislocation with b=[10‾1] is confirmed to be of the APB (anti-phase boundary)-type both on (010) and on (111), in contrast to the previous prediction for the SISF (superlattice intrinsic stacking fault) scheme on (111) because of the expected APB instability. While superlattice dislocations do not have any preferential directions to align when gliding on (010) (indicative of low frictional stress at room temperature), the alignment of superlattice dislocations along their screw orientation is observed when gliding on (111). This is proved to be due to thermally-activated cross-slip to form Kear-Wilsdorf locks, indicative of the occurrence of yield stress anomaly that is observed in many other L12 compounds such as Ni3Al. Some important deformation characteristics expected to occur in Fe3Ge (such as the absence of SISF-couple dissociation and the occurrence of yield stress anomaly) will be discussed in the light of the experimental results obtained (APB energies on (111) and (010) and CRSS values for slip on (111) and (010)).

Anti-phase boundary energy of β series precipitates in Mg-Y-Nd system

Anti-phase boundary energy (APBE) is a vital contributing factor for the dislocation shearing mechanism which operates in Mg-RE alloys. To clarify the structure and composition dependence of APBE and provide the guidance for strength improvement of Mg alloys, the formation energy, misfit strain, and APBE of β series precipitates in Mg-Y-Nd system are investigated by first-principles calculations. The atomic occupations of ternary precipitates are determined based on misfit strains. The APBEs of βp″′ phases are higher than that of βs′, and precipitates in Mg-Nd system possess higher APBEs than their counterparts in Mg-Y system. The higher APBEs enable larger strength increments of precipitates in Mg-Nd system than Mg-Y system when the amount of Y and Nd are the same. However, when both elements reach their solubility limit, the large amount of Y makes up the low APBE and achieves superior strength increment than the precipitates in Mg-Nd system.

On Short-Range Order Strengthening and its Role in High-Entropy Alloys

Short-range order (SRO) strengthening is one of the major strengthening mechanisms in alloys. Generally it is attributed to the the increased resistance to dislocation slip caused by breaking favorable bonds. This contribution may be strong for the first dislocation slipping in a slip plane, but it is certainly less strong for the following next dislocations. Present work discusses SRO strengthening with a different optic: with the focus on the dissipated energy due to the formation of a diffuse antiphase boundary (APB). In this sense, SRO strengthening becomes important to define the friction stress on gliding dislocations. Cluster Variation Method calculations of APB energies are used to estimate the strengthening effect in BCC alloys. The results are illustrated using VNbTaMoW and VNbTaWAl high-entropy alloys, with ab-initio derived parameters. The results show that the strengthening is intense in the range of concentrated solid solutions, and also, that this effect is strongly composition-dependent.

Dislocation networks in gamma/gamma’-microstructures formed during selective laser melting of a Ni-base superalloy

A dislocation network which formed during selective laser melting (SLM) of a Ni-base superalloy was analyzed using scanning transmission electron microscopy (STEM). This network traverses an ordered Gamma'-phase domain, in between two adjacent Gamma-solid solution regions. The Gamma’-phase region has formed when two Gamma’-phase particles have started to coalesce, trapping the dislocation network in this ordered region so that it formed two dislocation families with pairs of anti-phase boundary (APB) coupled super partial dislocations. The network features are presented and unusual features (twist character and low APB energies), not previously reported, are discussed.

Reactive elements dependence of elastic properties and stacking fault energies of γ-Ni, γ′-Ni3Al and β-NiAl

Abstract The reactive element effects (REEs) have been proven to improve the thermal oxidation resistance of β-NiAl. However, their effects on mechanical properties, which are significant implications for the Ni-based superalloys substrate and β-NiAl bond coat of thermal barrier coatings (TBCs), have not been well understood so far. In this work, the basic elastic properties, ideal strengths, and stacking fault energies of reactive elements (REs: Hf, Zr, Dy, Y, La) doping γ-Ni, γ′-Ni3Al, β-NiAl systems have been calculated using the first-principles method. The elastic properties results suggest that all five REs can enhance the ductilities of γ-Ni, β-NiAl, and γ′-Ni3Al, of which La performs best. More interesting, the complicated stacking fault (CSF) and anti-phase boundary (APB) energies of γ-Ni and β-NiAl decrease with the addition of REs in order of La > Y(Dy)>Zr > Hf, showing a totally opposite trend to that of commonly accepted the REEs on oxidation. The significant charge density redistributions could explain the physical origin of the improvement of plastic deformation ability for β-NiAl. This work gives insight into the mechanism of RE effects on the ductility and strength of γ-Ni, γ′-Ni3Al, β-NiAl materials, providing theoretical guidance for Ni-based superalloys design via a combinational analysis of bond topology and electronic structure.

Effects of Cr on the properties of multicomponent cobalt-based superalloys with ultra high γ’ volume fraction

Abstract Chromium is known to confer oxidation resistance on Co-based superalloys. Herein we studied the influence of Cr concentration on the properties of a Co-based superalloy, Co–30Ni–11Al–2Ti-5.5W-2.5Ta-0.1B (at.%), with high γ ’ -volume fractions (up to 98%). Additions of 4, 8, or 12 at.% Cr decreased the γ ’ -solvus temperature and the γ ’ -volume fraction, while also reducing the mean radius of γ ’ -particles. Synchrotron X-ray diffraction and atom-probe tomography confirmed that Cr reduces the lattice parameter misfit by altering the partitioning behavior of W between the γ- and γ ’ -phases. Concomitantly, an increase in Cr content significantly improved the oxidation resistance of the alloy. The results indicate that 4 at.% Cr is sufficient to decrease the oxidation rate by two orders of magnitude. A creep study at 850 ∘C revealed that Cr does not affect adversely the creep performance in high γ ’ -volume fraction Co-based superalloys, but the tendency toward γ ’ rafting changes with Cr concentration. Compared to Ni3Al intermetallic compounds, the alloys with high γ ’ -volume fraction studied exhibited a significantly higher creep resistance. This may be attributed to the increase in antiphase boundary energy caused by the addition of Cr, Ti, or Ta, and significant solid-solution hardening in the Co-based intermetallic γ ’ -phase.