Incoherent interfaces are ubiquitous in materials, yet their interfacial properties remain poorly understood. Due to the high computational cost, density functional theory (DFT) studies are typically restricted to coherent or semicoherent interfaces. In this work, we propose a novel approach to estimate incoherent interfacial energies within a DFT-accessible supercell size. Based on the so-called “incoherent γ-surface” concept, we first develop a classical-model-potential-based framework to capture the evolution of the one-dimensional (1D) incoherent γ-surface with increasing cell size. The method is then extended to the Ni/Ni3Nb interface in a quasi-1D configuration, and further to a fully two-dimensional case of the Cu–Nb incoherent interface possessing very different lattice mismatches along the two in-plane directions. All investigated systems exhibit a consistent smoothing behavior of the γ-surface with increasing cell size. Moreover, the average value of the incoherent γ-surface is demonstrated to be a robust estimator for the incoherent interfacial energy, which is shown to converge rapidly even at small cell sizes. This work extends the applicability of first-principles methods to ideal incoherent interfaces and deepens the understanding of the coherent versus incoherent γ-surface concepts.

In this study, novel non-equiatomic CoCrFeMnNi-based medium- and high-entropy alloys (M/HEAs) were designed to activate distinct deformation mechanisms, including twinning-induced plasticity (TWIP) and/or transformation-induced plasticity (TRIP). Tensile tests were performed at 298 and 173 K. A variety of ex-situ multiscale characterization techniques, strengthening modeling, thermodynamic modeling (CALPHAD method), and ab initio density functional theory (DFT) calculations were employed to investigate the structural and microstructural evolution, enabling accurate identification of the strengthening and active deformation mechanisms operating in the M/HEAs. Strengthening modeling revealed that grain boundary strengthening was the primary contributor to yield strength at both temperatures. A key finding of this study is that a controlled FCC→HCP martensitic transformation, associated with TRIP, enhances the strength-ductility balance even when the resulting HCP phase reaches ∼50% volume fraction. This demonstrates that TRIP-enabled metastability engineering is a promising strategy for designing high-performance M/HEAs for next-generation structural applications in energy, aerospace, and defense.

Gold (Au) segregation at Pt grain boundaries (GBs) plays an important role in the properties of Pt-based alloys. It was reported that close-packed GBs and open GBs exhibit different segregation behaviors, and their origin is still unclear. Based on the density functional theory as implemented in the exact muffin-tin orbitals method and the full charge density technique, we investigate the impact of bulk composition and temperature on the segregation behaviors of the Σ 3 ( 111 ) [ 1 1 ¯ 0 ] , Σ5(310)[001], and Σ 9 ( 221 ) [ 1 1 ¯ 0 ] symmetric tilt GBs in Pt-Au alloys. It is revealed that the segregation driving forces are correlated with the large local volume near the GB and the miscibility gap in Pt-Au alloys. At finite temperatures when the configurational entropy is considered, a competition between the chemical driving force and the configurational entropy is responsible for the segregation anisotropy in Pt-Au alloys. The bulk composition has a small effect on the segregation energy but strongly impacts the equilibrium concentration profiles at finite temperatures. The present study provides a theoretical analysis for the segregation anisotropy, and the methodology utilized in this work can be generalized to other binary or multi-component dilute or concentrated alloys while the composition variation is involved.

The formation energy of the coherent interface between the primary strengthening phase γ ′ ′ and γ matrix in Inconel 718 alloy is investigated using ab initio calculations. We begin by examining the interface energy of the ordered Ni/Ni 3 Nb system. A negligible interface energy (1 mJ/m 2 ) is obtained for the nonmagnetic state, which is explained by a nearest-neighbor layer interaction model. Allowing for spin polarization within both face-centered cubic (FCC) and D0<inf>22</inf> structures increases the interface energy to 181 mJ/m 2 . The strong magnetic dependence of the formation energy of the ordered Ni/Ni 3 Nb interface arises primarily from the different magnetic behavior of Ni in FCC and D0<inf>22</inf> phases. A detailed analysis of the site preference of minor elements in the γ ′ ′ phase shows that Fe and Cr occupy the Ni-site, while Al, Mo, and Ti tend to occupy the Nb-site. The coherent interface energy of the γ / γ ′ ′ interface is predicted to be 257 mJ/m 2 for the paramagnetic state and 255 mJ/m 2 for the ferromagnetic state. The closeness of these formation energies reflects a similar magnetic response from both phases. The sensitivity of the γ / γ ′ ′ interface energy to variations in the γ and γ ′ ′ compositions is also investigated. Only small variations are revealed for the reported composition intervals. Our predictions serve as input for further theoretical simulations and as a reference for experimental investigations.

Using an efficient first-principles computational approach, we investigate the influence of the thermal longitudinal spin fluctuations (LSFs) within the nickel sublattices on the thermoelastic properties of Ni3Nb with D022 structure. Leveraging the mean magnetic moment values to represent the spin-fluctuation state at respective temperatures and incorporating the lattice vibration contributions via the Debye model, the equilibrium bulk parameters and elastic constants are derived. We find that, although the volume expansion remains the primary mechanism behind the softening of the elastic constants with increasing temperature, the LSFs effect contributes significantly to the temperature dependence of c11 and c33. Our analysis reveals that including the LSFs makes the theoretical thermal-expansion coefficient highly anisotropic, in line with the experiments. Quantitative agreement between theory and experiment is obtained for the thermal expansion along the c axis at temperatures up to 500 K, whereas the measured thermal expansion along the a axis is underestimated by theory. The present results provide theoretical thermoelastic data for free-standing Ni3Nb precipitates with D022 structure, which can be used to estimate the lattice strains around such precipitates in Ni-based superalloys.

First-principles calculations were performed to investigate the elastic and thermodynamic properties for multi-component Co-based superalloy systems and explored the effect of alloying on stabilizing the γ′ phase. First, the comparisons were carried out for the γ′ phase in Co3(Al,TM) (TM being transition metals) and Ni3Al systems between the present computational results using the EMTO-CPA method and other available DFT calculations as well as experimental data. The lattice parameters, elastic constants, and Debye temperatures are consistent with experimental results and other calculations. The predicted thermodynamic properties, e.g., the Gibbs free energy, excess entropy, and linear thermal expansion coefficient, agree well with CALPHAD results, experimental results, and other available first-principles calculations. A combination of EMTO-CPA method and Debye–Grüneisen model is utilized in this work to ensure that the alloying effect on the stability of the γ′ phase in a multi-component Co-based system is captured efficiently. This could open the path for designing novel multi-component Co-based alloys based on first-principles calculation. To demonstrate this, predictions for the properties of multicomponent systems were undertaken. Our results show that Ni aids in the stabilization of the (CoNi)3(Al, Mo, Nb) phase. Graphical Abstract: [Figure not available: see fulltext.]

Refractory high-entropy alloys (RHEAs) are of growing interest due to their potentially superior mechanical performances at elevated temperatures. Inherent lattice distortions are believed to be a major contributor to strength in solid solution phases of RHEAs. Here, we investigate the NbMoTaWHfx alloy series (x = 0, 0.27, 0.57, 0.92, 1.33, 1.82) using first-principles simulations, thermodynamic modeling, and experimental techniques. The first-principles results suggest that Hf alloying is an effective means to enhance atomic-scale lattice distortions in BCC NbMoTaWHfx solid solutions. X-ray diffraction on prepared as-cast samples shows that the alloys with Hf content x <= 0.92 are single phase BCC alloys, whereas a dual BCC phase microstructure is observed for x = 1.33 and 1.82. Elemental mappings from scanning electron microscopy for the dual-phase alloys are checked with predictions from thermodynamic modeling for equilibrium and non-equilibrium solidifications. Room-temperature compressive mechanical tests reveal that yield and ultimate strengths increase strongly with the addition of Hf and saturate for x > 0.92, whereas the compressive plasticity is slightly improved by Hf but remains limited. We predict the compositional effects on poly-crystal elastic moduli for the constituent BCC phases and the dual-phase composites and find a linear behavior between modulus-normalized yield strength and lattice distortion on average.

Stacking fault energy and twinning stress are thought to be closely correlated. All currently available models predict a monotonous decrease in twinning stress with decreasing stacking fault energy and depart from the assumption that the intrinsic stacking fault energy has a positive value. Opposite to this prediction, for mediumand high-entropy alloys the twinning stress was shown to increase with decreasing SFE. Additionally, for metastable materials, first principles methods predict negative intrinsic stacking fault energy values, whilst experimentally determined values are always positive. In the present communication, it is postulated that the twinning stress scaled by the Burgers vector bridges the difference between intrinsic and experimentally measured stacking fault energy. The assumption is tested for Cu-Al alloys, for pure metals and for medium- and high-entropy alloys and, for the first time, provides a consistent quantitative interpretation of data for both alloys with positive and negative stacking fault energy.

Stacking fault energy (SFE) plays an important role in deformation mechanisms and mechanical properties of face-centered cubic (fcc) metals and alloys. In many concentrated fcc alloys, the SFEs determined from density functional theory (DFT) calculations and experimental methods are found having opposite signs. Here, we show that the negative SFE by DFT reflects the thermodynamic instability of the fcc phase relative to the hexagonal close-packed one; while the experimentally determined SFEs are restricted to be positive by the models behind the indirect measurements. We argue that the common models underlying the experimental measurements of SFE fail in metastable alloys. In various concentrated solid solutions, we demonstrate that the SFEs obtained by DFT calculations correlate well with the primary deformation mechanisms observed experimentally, showing a better resolution than the experimentally measured SFEs. Furthermore, we believe that the negative SFE is important for understanding the abnormal behaviors of partial dislocations in metastable alloys under deformation. The present work advances the fundamental understanding of SFE and its relation to plastic deformations, and sheds light on future alloy design by physical metallurgy. 

The authors regret that in producing Figs. 1 and 2, and Table S1 in our article an inadvertent error was made when calculating the bulk reference energy using an incorrect lattice setting. The bulk reference energy was recalculated using the correct lattice setting. Correction of the error results in a systematic shift in the grain boundary (GB) energies towards higher energies; see the corrected figures and table below. The change weakens the effect of Cr on the GB energy of chemically homogenous Fe1-xCrx alloys as shown in Fig. 1 (squares, red line), but doesn't influence the trends for chemically inhomogeneous Fe1-xCrx alloys as shown in Fig. 2 and Table S1. The correction has no effect on the analysis of the results and the conclusions presented in the original paper. The authors would like to apologise for any inconvenience caused.