Ductility deterioration induced by L21-Ni2AlTi precipitates in the aged ferritic alloys was examined systematically by using a combination of scanning transmission electron microscope (STEM), mechanical tests and first-principles thermodynamic calculations. The experimental studies revealed that the strength and hardness of the aged Fe–10Cr–5Ni–1Al–1Ti ferritic alloy containing B2–NiAl and L21-Ni2AlTi precipitates were higher than that of the aged Fe–10Cr–5Ni–1Al ferritic alloy containing NiAl precipitates, whereas the elongation-to-failure decreased dramatically from 9.3% to 0.3% indicating an obvious ductility deterioration due to the formation of L21-Ni2AlTi precipitates. This was also confirmed by the observation of fracture transition mode from dimpled failure to cleavage failure. The first-principles calculations, concerning the precipitate/matrix interface, were carried out to provide a theoretical analysis for the ductile–brittle transition by means of empirical ductility criteria ratios G/B and (C12–C44)/B as well as cleavage energy. The cleavage energy results indicated an intrinsic brittleness of the L21-Ni2AlTi phase and the L21-Ni2AlTi/BCC-Fe interface. Our analysis revealed that the intrinsic brittleness of L21-Ni2AlTi phase and L21-Ni2AlTi/BCC-Fe interface plays a vital role in determining the deformation behavior of the aged Fe–10Cr–5Ni–1Al–1Ti alloy.

Magnetic isotropic and Dzyaloshinskii-Moriya interactions in yttrium iron garnet have been obtained byab initio fully relativistic calculations. The calculated coupling constants are in agreement with availableexperimental data. Using linear spin-wave theory, we are able to reproduce the experimental magnon spectrumincluding the spin-wave gap and stiffness. The way to calculate the exchange coupling constants using theKorringa-Kohn-Rostoker formalism for large magnetic systems such as complex oxides is discussed in detail.

The strengthening by coherent, nano-sized particles of metastable phases (pre-precipitates) continues to be the main design principle for new high-performance aluminium alloys. To describe the formation of such pre-precipitates in Al–Cu, Al–Mg, Al–Zn, and Al–Si alloys, we carry out cluster expansions of ab initio calculated energies for supercell models of the dilute binary Al-rich solid solutions. Effective cluster interactions, including many-body terms and strain-induced contributions due to the lattice relaxations around solute atoms, are thus systematically derived. Monte Carlo and statistical kinetic theory simulations, parameterized with the obtained effective cluster interactions, are then performed to study the early stages of decomposition in the binary Al-based solid solutions. We show that this systematic approach to multi-scale modelling is capable of incorporating the essential physical contributions (usually referred to as atomic size and electronic structure factors) to the free energy, and is therefore able to correctly describe the ordering temperatures, atomic structures, and morphologies of pre-precipitates in the four studied alloy systems.

Atomic interactions and phase stability in Ni-rich Ni-W alloys have been investigated by using first-principles methods and statistical thermodynamic simulations. First-principles methods have been employed to explore lattice expansion, enthalpies of formation, atomic interactions, and ordering energies of ordered as well as random structures in Ni-rich Ni-W alloys with consideration of the corresponding temperature-dependent magnetic states. It is found that atomic interactions in Ni-rich Ni-W alloys depend on alloy composition, atomic volume, and magnetic state. Nevertheless, the magnetic state of Ni greatly affects the formation enthalpies, which leads to a diverse phase separation behavior at finite temperature in Ni-rich Ni-W alloys. By using atomic interactions that reproduce the ordering energies obtained in the direct total energy calculations, our statistical thermodynamic simulations of chemical short-range order results show that fcc-based ordered D1a, D022, and Pt2Mo phases can be observed in Ni-20 at.% W, Ni-25 at.% W, and Ni-33 at.% W alloys, respectively. Moreover, the short-range order diffuse intensity and atomic stacking for aforementioned ordered phases have been analyzed, the order–disorder transition behaviors have been also investigated in detail for the Ni-rich Ni-W alloys up to 35 at.% W with comparison of current experimental results. Both magnetic state and alloy composition have the potential to induce the formation of distinct ordered phases, offering promising avenues for designing Ni-based alloys. The methodologies we used in this study can be applied to investigate the atomic interactions as well as phase stability in other alloy systems.

The distribution of solutes and their interactions play a crucial role in determining the mechanical properties of the γ/γ′ interface in Ni-based single-crystal alloys. In this study, atomic interactions between Re and W and their alloying effects on the inter-phase cohesion of the γ/γ′ interface are investigated by first-principles calculations. Our results show that W atom exhibits a preference for partitioning into the γ phase, while the stability of the γ/γ′ interface can be enhanced due to the partitioning of W to the γ′ phase. Moreover, our results reveal that partitioned W atoms in the γ′ phase contribute to the strengthening of the γ/γ′ interface. Conversely, the dissolution of W atoms in the γ phase weakens the inter-phase cohesion. However, this detrimental effect can be mitigated by introducing of Re into the γ/γ′ interface. Partitioning of Re and W into separate phases yields minimal alterations in interaction energies, resulting in a notable enhancement of inter-phase cohesion when compared to the partitioning of Re and W within γ phase of the γ/γ′ interface. Additionally, the partitioning of solute atoms at the γ/γ′ interface leads to local lattice distortion and interfacial energy reduction, which contribute to the enhancement of inter-phase cohesion of the γ/γ′ interface. As a result, a model is proposed for interpretation of crack propagation at the γ/γ′ interface at the threshold region with the presence of tensile stress in Ni-based single-crystal alloys.

We present a systematic analysis, based on ab initio calculations, of concentrated solute arrangements and precipitate phases in Fe-based alloys. The input data for our analysis are the calculated formation and interaction energies of point defects in the iron matrix, as well as the energies of ordered compounds that represent end-members in the 4-sublattice compound energy model of a multicomponent solid solution of Mg, Al, Si, P, S, Mn, Ni, and Cu elements and also vacancies in bcc Fe. The list of compounds also includes crystal structures obtained by geometric relaxation of the end-member compounds that in the cubic structure show weak mechanical instabilities (negative elastic constants) and also the G-phase Mn₆(Ni,Fe)₁₆(Si,P)₇ having a complex cubic structure. A database of calculated thermodynamic properties (crystal structure, molar volume, enthalpy of formation, and elastic constants) of the most stable late-blooming-phase candidates is thus obtained. The results of this ab initio based theoretical analysis compare well with the recent experimental observations and predictions of thermodynamic calculations employing Calphad methodology.

The article presents ab initio calculated properties (total energies, lattice parameters, and elastic properties) for the complete set of 1540 end-member compounds within a 4-sublattice model of Fe-based solid solutions. The compounds are symmetry-distinct cases of integral site occupancy for superstructure Y (space group #227, type LiMgPdSn) chosen to represent the ordered arrangements of solvent atoms (Fe), solute atoms (Fe, Mg, Al, Si, P, S, Mn, Ni, Cu), and vacancies (Va) on the sites of a body-centered cubic lattice. The model is employed in the research article “Ab-initio based search for late blooming phase compositions in iron alloys” (Hosseinzadeh et al., 2018) [1].

Magnetic exchange interactions determine the magnetic groundstate, as well as magnetic excitations of materials and are thus essential to the emerging and fast evolving fields of spintronics and magnonics. The magnetic force theorem has been used extensively for studying magnetic exchange interactions. However, short-ranged interactions in itinerant magnetic systems are poorly described by this method and numerous strategies have been developed over the years to overcome this deficiency. The present study supplies a fully self-consistent method for systematic investigations of exchange interactions beyond the standard Heisenberg model. In order to better describe finite deviations from the magnetic ground state, an extended Heisenberg model, including multi-spin interactions, is suggested. Using cross-validation analysis, we show that this extended Heisenberg model gives a superior description for non-collinear magnetic configurations. This parameterisation method allows us to describe many different itinerant magnetic systems and can be useful for high-throughput calculations.

Fe-Ga alloys show an unusually large increase in magnetostriction compared to pure Fe and are one of the most interesting Fe-based alloys for this reason. However, the origin of the large magnetostriction and its relation to the chemical ordering on the underlying bcc phase is still under debate. To gain further understanding of the extraordinary magnetoelastic characteristics of this system, we investigate the effect of Ga-concentration and ordering on the spin-wave spectra and stiffness. The magnetic interactions in the Fe-Ga alloys are obtained by ab initio electronic structure calculations and the magnon spectra are modeled using atomistic spin dynamics modeling. Our results agree with available experimental data and show softening of the magnon modes with increasing Ga-concentration and a strong reduction of the spin-wave stiffness due to atomic ordering.

The (CrMnFeNi)_1−xCo_x high-entropy alloy is investigated for 0≤x≤0.2 by density functional theory calculations. All calculations are performed in theparamagnetic fcc-phase. It is shown that the exact muffin-tin orbital formalismcombined with the coherent potential approximation can reproduce experimentalvalues of equilibrium volume and magnetic moment. The thermal expansion isinvestigated using the Debye-Grüneisen model. Experimental results of the thermalexpansion coefficient and lattice parameter are reproduced only when including bothelectronic and magnetic contribution to the free energy. The investigated alloysshow anti-invar behaviour with a large increase in thermal expansion parameter withtemperature. For reduced Co-concentrations, the thermal expansion coefficient andlattice parameter are seen to increase, leading to slightly lower values of the elasticconstants. The stability of the alloys is discussed in terms of stacking fault energy andmixing energy.

This study investigates the thermodynamic and mechanical properties of Y4Zr3O12 and Y2Ti2O7 oxides in ferritic alloys with and without Helium utilizing a systematic first-principles approach. Firstly, the atomic arrangement of Y and Zr atoms at cation 18f sites in δ-(Y–Zr–O) oxide is identified, while it is found that Y4Zr3O12 exhibits a more robust formation tendency than Y2Ti2O7. Furthermore, it is noted that both Y4Zr3O12 and Y2Ti2O7 oxides demonstrate a prior ability to trap Helium compared to the bcc-Fe matrix, which leads to a substantial enhancement on the stiffness of both oxides. The elastic moduli of both Y4Zr3O12 and Y2Ti2O7 oxide exhibit a gradual increase with the growing Helium concentration. As a result, the enhanced shear modulus of oxides and sustained shear modulus of the bcc-Fe matrix collectively contribute to the overall strength of ferritic alloys under Helium environments. The findings in this work propose valuable insights for guiding critical strategies in the design of high-performance oxide-dispersion-strengthened ferritic alloys, particularly for applications in Helium environments.

The solute segregation and its effects on the cohesion of the Fe/Y₂Ti₂O₇ interface in ferritic oxide dispersion strengthened (ODS) alloy have been investigated using first-principles calculations. The computational results indicate that W, Cr, Al, Nb, Zr, and Hf are prone to segregate to the Fe/Y₂Ti₂O₇ interface and enhance the cohesive strength of the Fe/Y₂Ti₂O₇ interface, improving its stability. He atoms exhibit a strong tendency to segregate at the Fe/Y₂Ti₂O₇ interface, leading to embrittlement of the interface. Moreover, in the case of co-existing of W, Cr, Al, Nb, Zr, and Hf with He atoms, it is found that W, Cr, and Al increase the segregation energy of He at the Fe/Y₂Ti₂O₇ interface. This promotes the diffusion of He from the Fe/Y₂Ti₂O₇ interface into the bulk of the Y₂Ti₂O₇, thereby reducing He-induced embrittlement at the Fe/Y₂Ti₂O₇ interface. Finally, the electronic structures of the Fe/Y₂Ti₂O₇ interfaces with and without solute elements, as well as the interaction between metallic solutes and He, have been discussed in detail to reveal the mechanisms of alloying reduction effect on He-segregated embrittlement at the Fe/Y₂Ti₂O₇ interface. The results obtained from this work suggest that adjusting the alloying components in ODS alloys can improve the radiation resistance of the alloy, providing theoretical guidance for the design and optimization of ferritic ODS alloys.

The dependence of stacking fault energy (γ_SFE) on temperature in austenitic Fe–Cr–Ni alloy powders was investigated by in situ high energy synchrotron X-ray diffraction and ab initio calculations in the temperature range from − 45 °C to 450 °C. The X-ray diffraction peak positions were used to determine the stacking fault probability and subsequently the temperature dependence of γ_SFE. The effect of temperature on the diffraction peak positions was found to be mainly reversible; however, recovery of dislocations occurred above about 200 °C, which also gave an irreversible contribution. Two different ab initio-based models were evaluated with respect to the experimental data. The different predictions of the models can be explained by their respective treatment of the magnetic moments for Cr and Ni, which is critical for the alloy compositions investigated. Ab initio calculations, taking longitudinal spin fluctuations (LSF) into consideration within the quasi-classical phenomenological model, predict a temperature dependence of γ_SFE in good agreement with the experimentally evaluated trend of increasing γ_SFE with increasing temperature: | Δ γ_SFE/ Δ T| = 0.05 mJm ^{- 2}/ K. The temperature effect on γSFE is similar for all three investigated alloys: Fe–18Cr–15Ni, Fe–18Cr–17Ni, Fe–21Cr–16Ni (wt pct), while their room temperature γ_SFE are evaluated to be 22, 25, 20 mJ m⁻², respectively.

The short/long-range order formation in Fe_1-x-Co_x (x < 0.3) alloys has been studied by the nuclear magnetic resonance (NMR) technique, as well as ab initio based atomistic simulation. The NMR measurements show up the formation of a certain short-range order (SRO) in dilute limit above the Curie temperature T_C and of the D0₃-type SRO (with the dominance of 3rd Co-Co nearest neighbors) in the concentration range 0.2 < x < 0.3 after quenching and subsequent annealing in the ferromagnetic state. The results of Monte Carlo simulations of binary Fe-Co alloys with ab initio interatomic interactions predict SRO in agreement with the experiment for small concentrations of Co (C_Co< 0.1), while the B2-type ordering is preferable in binary alloy in the ferromagnetic state. We demonstrate that the presence of point defects (vacancies, interstitial) can change essentially the ordering in alloys with the Co content 20-30% and result in the D0₃-type SRO formation in a reasonable agreement with the experiment.

Using methods of statistical kinetic theory parametrized with first-principles interatomic interactions that include chemical and strain contributions, we investigated the kinetics of decomposition and microstructure formation in Al-Cu alloys as a function of temperature and alloy concentration. We show that the decomposition of the solid solution forming platelets of copper, known as Guinier-Preston (GP) zones, includes several stages and that the transition from GP1 to GP2 zones is determined mainly by kinetic factors. With increasing temperature, the model predicts a gradual transition from plateletlike precipitates to equiaxial ones and at intermediate temperatures both precipitate morphologies may coexist.

Statistical alloy theory based on the Master Equation approach with ab initio calculated interatomic interactions is employed to investigate the growth of precipitates at the early stages of solid solution decomposition, as well as the dissolution of small precipitates during the coarsening stage, upon simulated annealing of ternary Al–Sc–Zr alloys. We show, in agreement with previous studies, that the Zr alloying to Al–Sc alloys promotes the formation of core–shell nanoparticles whose structure is found to be very sensitive to the parameters characterizing the solute diffusion rates in the alloy. We demonstrate that the core–shell structure of precipitates slows down the dissolution of small particles, thus hampering the microstructure coarsening at elevated temperatures.

Ni and its alloys are susceptible to hydrogen embrittlement. In this study, we investigate the phenomenon of hydrogen-enhanced decohesion at inter-phase interfaces in precipitation-hardened Ni-based alloys using a systematic first-principles approach. We demonstrate that hydrogen atoms primarily prefer to localize at the Ni3Al phase in the Ni/Ni3Al interface, while they tend to be trapped by Ni in the Ni/Ni3Nb interface. Our findings reveal that hydrogen induces inter-phase embrittlement in both the Ni/Ni3Al and Ni/Ni3Nb interfaces. Moreover, we show that the hydrogen-enhanced decohesion at these interfaces is influenced by various factors such as hydrogen pressure, hydrogen content, temperature, and strain. Finally, we discuss in detail the hydrogen-enhanced decohesion mechanisms at the Ni/Ni3Al and Ni/Ni3Nb interfaces, including their electronic structures, energy landscape of hydrogen at trapping sites, and schematics of crack propagation.

The multicomponent Ti alloys, specifically the β-phase, have experienced a strong growth over the last decades, due to their outstanding properties of ultra-high strength and low Young’s modulus. These properties play a significant role in many aerospace and biomedical applications. Selection and optimization of multicomponent alloys is challenging due to the vast chemical and compositional space. Here we investigate the use of machine learning techniques informed by density functional calculations to guide the selection of Nb- and Zr-based Ti binary alloys. From the cubic structures obtained from high throughput calculations and literature, we identify several structures with Young’s moduli below 40 GPa. The multivariant decision tree methods provide efficient surrogate models to identify structure variables have high influences on the energetic stability and Young’s modulus. We implement a workflow of incorporating DFT provided results and machine learning method to explore the chemical and composition space of other binary and multicomponent alloys, to eventually accelerate the material design via taking advantages of identified key variables.

The critical role of Cr on nanoprecipitates and the mechanical property of Fe-Ni-Al-Mn ferritic steel were systematically studied in this research. The two types of nanoprecipitates in the Cr added alloy were characterized through a combination of aberration-corrected scanning transmission electron microscopy and atom probe tomography techniques. The atomic-scale structure and chemistry analysis reveal that fine globular-shaped precipitates have a B2-structure, while coarse elongated precipitates have B2+L2₁ composite structures. The first-principles calculations reveal that the segregation of Cr at the L2₁/bcc interface reduces the interface and strain energy for the nucleation of the L2₁-type phase. With the increasing precipitate size, the B2 structure is gradually transformed to L2₁ to reduce elastic strain, thereby promoting the formation of B2+L2₁ composite nanoprecipitate. The addition of 10 wt% Cr results in an increase of ∼275 MPa in yield strength without obvious loss of ductility. The effect of Cr on the strength mechanisms were quantitatively analyzed, revealing that the strength of the ferritic alloy mainly improved by the formation of B2+L2₁ composite nanoprecipitate, which is more effective than solid solution strengthening.