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The substitutional solute atom induced local lattice distortion (LLD) in dilute metal solid solution was believed to be uniform that may even be modeled by using soap bubble raft. Contrary to this conventional picture, we report in this manuscript that the Mo induced LLD in dilute Ti-Mo solid solution is highly non-uniform as evidenced by our first principles calculations. The non-uniform LLD is ascribed to the Jahn-Teller splitting of the degenerated d states of Mo atom. We propose that the substitutional solid solutions with non-uniform LLD should satisfy two conditions. With which, the solid-solutions suffering from non-uniform LLD are predicted. The non-uniform LLD is expected to result in non-spherical stress field around the solute atom, and, therefore, challenges the application of classical solid solution hardening model to this kind of solid solutions., Comment: 8 pages and 4 figures

Precipitates, including silicides and Ti3Al (α2) phase, and alloying elements distribution in a near α titanium alloy Ti65 (Ti-5.8Al-4.0Sn-3.5Zr-0.5Mo-0.3Nb- 1.0Ta-0.4Si-0.8W-0.05C) after solution treatment and aging process were characterized by using transmission electron microscopy (TEM) and atom probe tomography (APT). Quantitative composition analysis and TEM observation indicate that the silicides fit to (Ti, Zr)6(Si, Sn)3. Zr exhibits a β-stabilizing effect in near α titanium alloys but is weaker than other β stabilizing elements. The enriching tendency of the alloying elements in the retained β phase is in the order of Zr

CdSiP2 (CSP) with outstanding mid-infrared nonlinear optical properties in the 3–5 μm and 8–12 μm windows has always been expected for application requirement, whereas the inadequate of absorption losses cannot be ignored as practical usage. The defect formation energies, electronic structure characteristics, structure distortion and related optical properties of CSP with some traditional and basic dopants M= (Mg, Al, Cu, Fe, and Mn) substituting Cd or Si sites are investigated by employing density functional theory (DFT). The calculations show that the energetically and thermally stable states in CSP crystals are Mg0, Al1+, Cu4+, Fe4+, Mn4+ at Cd sites and FeSi1+ at SiP2 reference states. Fe and Mn dopants at Cd sites bring abundant valences, including 0, +1, +2 and +4 charged states, and result in a mean absorption spectrum increase. New peaks appear in the density of states as the CuCd4+, FeCd4+, and MnCd4+ take shape, and thus affect the absorption spectrum. According to the calculation results, highly localized d orbitals of dopants should be mainly responsible for the absorption aberrance, because they not only lead to a mean absorption spectrum increase, but also bring new absorption peaks affecting the conversion efficiency along X/Y or Z directions.

Atomic-scale simulations are performed to investigate the interaction between prismatic interstitial loops and moving dislocations in nickel. Depending on their relative position, a loop either drags a dislocation elastically or decorates a dislocation with jogs, resulting in a systematic change of the critical stress for subsequent dislocation glide. Loop-decoration significantly reduces the mobility of a dislocation, and the critical shear stress can increase up to ten times larger than the conventional Peierls stress. This work presents the atomic-scale details of loop-dislocation interaction, thus providing reliable information for parameterizing debris-dislocation interaction in meso- or macro-scale simulations.

The volume modeling of the sigma phase is an indispensable complement to the integrated computational material design of technologically important materials, such as high-alloy steels and Ni-based superalloys. The molar volume of the sigma phase is influenced by both the atomic mixing (the volume variation affected by this factor is caused by composition alteration rather than site occupation change) and atomic order (i.e. atomic constituent distribution or site occupancy preference on inequivalent sites of a crystal). In the present work, we developed a new integrated thermodynamic and molar volume model to consider physically both mixing and order factors. The integrated model was built within the compound energy formalism (CEF), enabling the thermodynamic calculations to determine equilibrium site occupancies for the subsequent volume calculations. The model parameters of the CEF were assigned by using the first-principles calculated energies and molar volumes of the complete sets of ordered configurations of the sigma phase, as well as the extrapolated molar volumes of the pure elements in the hypothetic sigma phase structure. Such extrapolation for pure elements is based on the experimental data from the literature and the first-principles calculations. We applied the integrated model to study the binary compounds, e.g. Cr-Co, Cr-Fe, Cr-Mn, Mo-Fe, Mo-Mn, Mo-Re, Re-Cr, Re-Fe, Re-Mn, Nb-Al, Ta-Al, V-Fe, V-Ni, and ternary compounds Cr-Fe-X (X = Co and Ni). The integrated thermodynamic and molar volume databases can predict successfully the molar volume of the binary and ternary sigma compounds. As most experimental volume data were measured at room temperature and atmospheric pressure, and the first-principles calculations were performed at 0 K, the present model parameters are valid at about room temperature and atmospheric pressure.

The ductile-to-brittle transition is commonly observed in metastable β-titanium (Ti) alloys containing ω-precipitates, while the fundamental understanding on ω-embrittlement hitherto remains elusive. In this work, the prototypical Ti-20 wt% Mo metastable β-Ti alloy has been systematically investigated by coupling experiments and first-principles calculation to eliminate this puzzle. It is shown that the structural evolution of ω-phase controls the deformation mechanism transition of twinning-to-slip in Ti Mo alloy, being the origin of ductile-to-brittle transition of this alloy. The initial trigonal ω-structure continuously collapses to hexagonal ω-structure (structural collapse) whilst Mo-atoms are rejected out concurrently (stoichiometric varieties), both leading to hardening of ω-precipitates. This self-hardening of ω-precipitates was further rationalized in terms of the enhanced propensity for a covalent character of the atomic bond demonstrated by the electronic density of states (DOS) from first-principles calculation. Specifically, the self-hardening behavior of ω-precipitates promotes dislocation slip on isolated planes in lieu of correlative slip on successive planes inside ω1-variant, while dislocations are completely blocked ahead ω2/ω3/ω4-variants. This in turn renders the transition from deformation twinning that contributes to great macro-plasticity to ordinary dislocation slip that contributes to localized deformation bands in the present Ti Mo alloy.

ω phase precipitating in a β -Ti alloy is generally detrimental to the ductility and plasticity of the alloy.To understand the influence of ω phase on the mechanical properties of β -Ti alloys, the property of the β/ω interface is demanded.In this regard, we calculate the interface energies ( γ int ), cleavage energies ( γ cl ), and generalized stacking fault energies ( γ ) of the β/ω interfaces with different orientations using a first-principles method.Our calculations predict interface energies of 0.32 J m−2 and 0.03 J m−2 for the ( 1 1 1 ¯ ) β / ( 0 0 0 1 ) ω and ( 1 1 2 ) β / ( 1 0 1 ¯ 0 ) ω interfaces, respectively.The strong anisotropy of the interface energy contributes to the ellipsoid-like morphology of ω phase with its major axis parallel to the 〈 1 1 1 〉 β direction.The influence of the interface on the ductility of the alloy is discussed with the calculated cleavage energies and the unstable stacking fault energies ( γ us ) extracted from the generalized stacking fault energy (GSFE). The γ cl / γ us ratio of the ( 1 1 2 ) β / ( 1 0 1 ¯ 0 ) ω interface is lower than those of the main slip planes of the bulk phases, indicating that this interface is prone to crack initiation and propagation as compared to the bulk and contributes to theω-embrittlement of β -Ti alloys.

Variant selection during solid–solid phase transformation in titanium alloys affects greatly the microstructure and mechanical properties of the alloys. Theoretical investigations of the variant selection were generally performed by using phase field simulation that considers solely the elastic coherency strain energy. In the present work, we develop a model to determine the variant selection directly from first-principles calculations. The source of the variant selection is considered to be the varying free energy gains (including both bulk and interface contributions) induced by the transformation from the parent phase to different variants of the product phase. This model is applied to investigate the effects of shear stress and alloy composition on ω variant selection during athermal β → ω transformation in binary Ti-xMo ( x ≤ 25 at.%) alloys. The random distribution of the atoms in the alloy is described by using virtual crystal approximation (VCA). We show that the tendency of variant selection becomes stronger with increasing shear stress. With increasing Mo concentration, the favorable ω variant transfers from one to another, except for the ω phase with very small particle size (e.g., radius R ≤ 1 nm) where one variant is always selected. The critical Mo concentration for the transfer of the favorable ω variant approaches to 5 at.% with increasing size of the ω phase particles and remains almost unchanged against the shear stress. At the critical Mo concentration, the considered variants have equal free energy gains and there is no variant selection. This finding opens the possibility of controlling the variant selection and the associated microstructure by changing the composition of the alloys.

Phase decomposition influences significantly the mechanical properties of high entropy alloys (HEAs). Prediction of the phase decomposition of HEA is greatly hindered by the hyper-dimensional composition space of the alloys. In the present work, we propose to represent the HEAs as various pseudo-binary alloys of which the temperature dependent free energies as functions of compositions may be readily calculated by using first-principles methods in combination with thermodynamic models. With the calculated free energies, the phase diagrams of the pseudo-binary alloys may be constructed and the phase decomposition can be predicted. This procedure is applied to Hf-Nb-Ta-Ti-Zr alloy with body-centered cubic (BCC) structure. We predict that the equiatomic HfNbTaTiZr HEA suffers from phase decomposition below critical temperature of 1298 K. The HEA decomposes most favorably to BCC NbTa-rich and HfZr-rich phases. The BCC HfZr-rich phase transfers to a hexagonal close-packed structure (HCP) phase at low temperature. The predicted compositions of the decomposed phases are in good agreement with experiment and Thermal-Calc modeling. Furthermore, the effect of the phase decomposition on the strength of the HEA is evaluated by considering the solid-solution and precipitation strengthening mechanisms. The precipitation strengthening effect is stronger than the solid-solution strengthening at the low annealing temperature but becomes weaker at high annealing temperature.

We investigated surface properties of metals by performing first-principles calculations. A systematic database was established for the surface relaxation, surface energy (γ), and surface stress (τ) for metallic elements in the periodic table. The surfaces were modeled by multi-layered slab structures along the direction of low-index surfaces. The surface energy γ of simple metals decreases as the atomic number increases in a given group, while the surface stress τ has its minimum in the middle. The transition metal series show parabolic trends for both γ and τ with a dip in the middle. The dip occurs at half-band filling due to a long-range Friedel oscillation of the surface charge density, which induces a strong stability to the Peierls-like transition. In addition, due to magnetic effects, the dips in the 3d metal series are shallower and deeper for γ and τ, respectively, than those of the 4d and 5d metals. The surface stress of the transition metals is typically positive, only Cr and Mn have a negative τ for the (100) surface facet, indicating that they are under compression. The light actinides have an increasing γ trend according to the atomic number. The present work provides a useful and consistent database for the theoretical modelling of surface phenomena.

International audience; The present work systematically clarifies the influence of the atomic mixing and the atomic order (i.e. atomic constituent distribution or site occupancy preference on inequivalent sites of a crystal) on the molar volume of the binary sigma phase. We calculated the molar volumes of 21 binary sigma compounds with different atomic order by using EMTO-CPA (Exact Muffin-Tin Orbitals - Coherent Potential Approximation) method. The calculation results follow a similar trend as the experimental data. Moreover, the calculated molar volumes with respect to the composition of the sigma phase in disordered states show that the sigma compounds do not comply with the linear volume-composition relationship. This is due to the influence of the atomic mixing and the deviation can be either negative or positive depending on the tendency of electron loss or gain of the two constituent elements. Additionally, we compared the molar volume difference (ΔVm = Vdisorder-Vorder) between the hypothetically disordered and ordered states of the binary sigma compounds. The results indicate that the effect of the atomic order on the molar volume of the sigma phase depends on the size difference and the electron configurations of the two constituent elements

An intricate understanding of the fundamental β→α phase transformation upon the presence of metastable ω phase is vital for tailoring the multiphase microstructures of titanium and titanium alloys for various specific applications. To approach this, the structures and energetics of heterophase interfaces among α, β, and ω in titanium were thoroughly investigated, using the combination of high-resolution transmission electron microscopy and first-principles density functional theory calculations. The results strongly suggest that metastable ω does not necessarily act as the precursor of α but can reduce the energy barrier for α nucleation in β. The ω/β interfaces acts as favorable nucleation sites for α which, once forms, tends to grow favorably into the β matrix. These findings validate the ω-assisted α nucleation mechanism, and adequately rationalize many TEM observations on titanium alloys.

Solute atoms such as Fe, Co, and Ni diffuse abnormally fast in α-Ti, which influences significantly the mechanical properties of the titanium alloys. Various mechanisms (e.g., the interstitial diffusion mechanism and solute-vacancy complex mechanism) have been proposed to account for the fast diffusion of these solutes in α-Ti. To elucidate such diffusion mechanism, a first-principles method is employed to calculate the formation energies, migration energy barriers, and solute-vacancy binding energies of the substitutional and interstitial solute atoms including Al, Si, Sn, V, Mn, Fe, Co, Ni, and Cu in α-Ti. Based on the calculated parameters, the diffusion mechanisms are discussed. Comparing the formation energies of the substitutional and interstitial solutes, we find that all the solute atoms prefer the substitutional configuration to the interstitial one. The interstitial migration energy barriers are quite low for all the solutes. Al and Sn diffuse mainly through normal vacancy mediated mechanism due to the high substitutional to interstitial preferential energy that leads to very low fraction of interstitial solutes (about 10 − 15 ∼ 10 − 16 at 1000 K) at thermal equilibrium state and high interstitial diffusion activation energy. The 3d metal solute atoms, especially Mn, Fe, and Co, are fast diffusers and the diffusion coefficients are dominated by the interstitial mechanism because of their sizable thermal equilibrium interstitial fractions (several percent at 1000 K). The solute-vacancy complex mechanism is not likely to account for the fast diffusions in α-Ti. We show that the direct chemical interaction between the solute and matrix atoms determines the site-occupancy of the solute atoms in α-Ti besides the atomic size effect that was commonly believed to be responsible for the fast diffusions.

Breakdown of Schmid's law is a long-standing problem for exploring the orientation-dependent deformation mechanism in intermetallics. The lack of atomic-level understanding of the selection rules f ...

Brittle ω-precipitates in bcc β-Ti alloys are well known to dramatically degrade material plasticity and even trigger macroscopic premature fracture, posing an obstacle for structural applications. The embrittlement mechanism is intimately related to dislocation pile-up at the ω/β interface that leads to stress concentration and undesirable failure. The underlying physics of improving ductility remains to be further uncovered. Here we report a new finding in β-Ti alloy single crystal micropillar compression that the plasticity can be substantially improved by means of increasing strain rate, while mechanical strength simultaneously exhibits striking “faster is stronger” fashion. The results reveal that the improvement of micropillar plasticity upon higher loading rate can be ascribed to the wider deformation band, in contrast to equivalents under quasi-static mode. The microscopic examination shows that cross slip induced by screw dislocations governs the plasticity improvement, which is further validated by crystallographic analysis and first principle energy landscape calculations. This “dynamic self-toughening” behavior advances our fundamental understanding to the plastic deformation mechanism of ω-precipitate contained bcc β-Ti alloys. Keywords: Ti alloy micropillars, Omega-precipitates, Strain rate, Plasticity, Deformation band, Dislocations

Local chemical ordering influences significantly the mechanical properties of refractory high entropy alloys. In this work, the effects of local chemical ordering on the structural stability and mechanical properties of AlNbVTiZr are investigated by using first-principles simulations. It is shown that the Al Zr bond dominates the chemical ordering for ordered configurations. The local ordering enhances the structural stability, elastic property and ideal strength. By taking into account the effects of temperature and pressure, we found that chemical ordering mediates the thermodynamic properties of the AlNbVTiZr alloy, but it has little effect at high pressure.

Increasing the solubility of Al and inhibiting the growth of Ti3Al precipitates in high temperature titanium alloy improve both the thermal strength and thermal stability of the alloy. In principle, this may be achieved by adding some other alloying atoms which attract Al so as to serve as traps for Al in the alloy. In the present work, the interaction energies between Al and alloying atoms X with X covering all the transition metal (TM) and noble metal (NM) elements in the Chemical Elemental Period Table (CEPT) are calculated by using a first principles method in order to screen the traps for Al. The effects of temperature (taking Mo-Al interaction as an example) as well as the newly found off-center site-occupation of alloying atoms (Acta Mater. 197, 2020, 91) on the interaction energies are considered. We show that the interactions between Al and the TM alloying atoms early in the CEPT are weak. The middle TM alloying atoms attract but the late TM and NM ones repel Al. At finite temperature, the lattice vibration enhances whereas the configurational entropy weakens the Mo-Al attraction. Both effects become stronger with increasing temperature. The physical origins underlying the X-Al interactions are revealed by analyzing the electronic density of states and bonding charge density. Alloying atoms such as Mo, Tc, Ru, W, Re, and Os are identified to benefit the strength and thermal stability of high temperature titanium alloys. This work is helpful to the rational design of high temperature titanium alloys.

Using density-functional theory, we determine the generalized stacking fault energy (GSFE) for the { 1 1 ¯ 2 } 〈 1 ¯ 11 〉 twinning system in ferromagnetic (FM) body-centered cubic Fe and Fe-Cr alloys with molar fraction of Cr ≤ 0.5 . We adopt both reflection and isosceles twinning pathways and reveal the magnetic ordering effects on the GSFE by contrasting the FM results to those obtained for the magnetically disordered paramagnetic (PM) state. The results show that the isosceles twin boundary configuration is energetically preferred in this binary. The loss of long-range magnetic order lowers the GSFE amplitude but increases the twin boundary migration (TBM) energy regardless of the Cr content. The twin boundary formation (TBF) energy and the TBM energy show non-linear dependences on Cr content in the FM and PM states, and the effect of Cr on these properties critically depends on the magnetic state. We discuss our results in regard to the stable twin boundary structure and deformation twinning experimentally observed in homogeneous Fe-50 wt.% Cr alloy up to temperatures slightly above the magnetic ordering temperature.

ω-embrittlement is ubiquitous in metastable β-titanium (Ti) alloys, while the fundamental understanding on the damage-fracture mechanism hitherto remains elusive. In this study, we systematically investigate ω-embrittlement of high misfit Ti-10Cr (wt.%) alloys by coupling experiments and first-principles calculation. It is found that brittle cleavage-like fracture prevails in tensile samples, irrespective of the quenching or subsequent aging states. Microscopically, cracks nucleation and propagation proceed along slip bands, inside which ω-lattices are first disordered and then the localized (β + ω)-amorphous-like structures are developed in the shape of white patches. The underlying mechanism of mechanically-driven localized amorphization is that due to the remarkable covalent character of atomic bonding of ω-precipitates caused by composition partitioning of the Cr element, ω-precipitates impart extremely high energy barrier opposed to dislocation gliding and render dislocations pile-up ahead of ω-precipitates, thus leading to their lattice disordering. It is unveiled that the hydrostatic pressure, serving as the driving force for dislocations pile-up, plays a critical role in this unusual cleavage-like fracture of Ti-10Cr alloys caused by mechanically-driven ω-mediated localized amorphization. Accompanied by the transition from the co-operation of deformation twining and ordinary dislocation slip in the quenched Ti-10Cr alloys to the exclusive ordinary dislocation slip in the long-time aged Ti-10Cr samples, it is unexpected that the resulting tensile fracture strength monotonically decreases to a stress level of ~ 100 MPa. These findings provide new insights into the damage and fracture behavior of high misfit β-titanium alloys, such as Ti-Cr alloys.

Individual solute interstitial atoms in Mg alloys were directly observed through aberration-corrected Z-contrast imaging. The atomic species and local positions of solute interstitials were further determined in combination of density functional theory calculations based on their formation energy. Individual octahedral and tetrahedral interstitials in hexagonal-close-packed Mg are Zn and Y, respectively. Interestingly, there are six positions around the center of each octahedral interstice, which can also accommodate a Zn interstitial, besides the ideal octahedral interstice. Y tetrahedral interstitials evolve to [0001] Y-Mg dumbbells. Moreover, an Y atom can form a crowdion between two neighboring Mg atoms along the 20 2 − 3 > direction. In particular, small clusters consisting of various point defects were observed, providing direct evidence for enthalpy-driven clustering of point defects, which may have implications for atomic-scale understanding of nucleation mechanisms of strengthening precipitates.

In this work, site-preference and elastic properties of TiNi-Nb austenite were investigated for various compositions, by using Exact Muffin-Tin Orbitals method in conjunction with Coherent Potential Approximation (EMTO-CPA). Moreover, composition-dependent elastic constants were calculated and used to explain the relation between composition and martensitic transition temperature. Our calculations suggested that Nb atoms prefer to occupy either Ni sites or Ti sites, depending strongly on composition. Variation of TiNi-Nb compositions is achieved through the formation of four sorts of defects: substituting Ti by Nb, substituting Ni by Nb, Ti anti-sites and Ni anti-sites. Our results suggested that c ′increases when Ni is substituted by Nb, while c 44 increases when Ni is substituted by Nb or Ni anti-sites form. Moreover, the maps of composition-dependent elastic constants were presented. TiNi-Nb with high c ′and c 44 could be obtained in Ni-deficient area. However, in Ni-excess area, only high c 44 could be obtained. Changing of martensitic transition temperature is sensitive to the variation of c 44 , rather than c ′. With the variation of c 44 , we explained the composition-dependent martensitic transition temperature for TiNi-Nb.

A plane wave pseudo-potential method based on density functional theory is employed to calculate the migration energy barrier for the atomic self-diffusion in HCP metals including Mg, Zn, Ti, Zr, and Hf. The influences of some key factors (plane-wave cutoff energy, k-mesh, supercell size, and geometric optimization scheme) on the calculated migration energy barrier and its anisotropy are systematically investigated. We show that the supercell size affects heavily the migration energy barrier and its anisotropy for the metals with valence d electrons (Ti, Zr, and Hf) but not for the ones with only valence s metals (Mg). In general, the anisotropy of the migration energy barrier reduces with increasing size of the supercell especially for Ti, Zr, and Hf. The optimization of the shape and volume of the supercell matters for the migration energy barrier calculated with the small size supercell but not for that calculated with the large supercell. With the calculated migration energy barrier, the self-diffusion coefficients are evaluated based on the transition state theory and compared with other first-principles calculations and the experimental measurements.

The lattice constant, formation enthalpy, and elastic parameters of Cu 1 - x Au x (0 ⩽ x ⩽ 1) alloys in the face centered cubic crystallographic phase are investigated by using the first-principles exact muffin-tin orbitals and plane-wave pseudopotential methods in order to explore the effect of alloying with special focus on the impact of local lattice distortion (LLD) on the above properties. The compositional disorder is treated within the framework of the coherent potential approximation (CPA) and the special quasi-random structure (SQS) scheme. Calculations based on SQS and CPA show that, while LLD lowers significantly the formation enthalpy of Cu 1 - x Au x due to the large size mismatch between Cu and Au atoms, it has negligible influence on the lattice constants and elastic parameters. These findings confirm the reliability of CPA for computing the enthalpy changes upon isotropic and unisotropic lattice distortions in disordered alloys with sizable atomic size differences.

First-principles calculations have been performed to study the effect of C on the stacking fault energy (SFE) of paramagnetic γ -Fe and Fe Cr Ni austenitic steel. In these systems, the local magnetic structure is very sensitive to the volume in both fcc and hcp structures, which emphasizes the importance of the magnetovolume coupling effect on the SFE. The presence of C atom suppresses the local magnetic moments of Fe atoms in the first coordination shell of C. Compared to the hypothetical nonmagnetic case, paramagnetism significantly reduces the effect of C on the SFE. In the scenario of C being depleted from the stacking fault structure or twin boundaries, e.g. , due to elevated temperature, where the chemical effect of C is dissipated, we calculate the C-induced volume expansion effect on the SFE. The volume induced change in the SFE corresponds to more than ∼ 50% of the total C effect on the SFE obtained assuming uniform C distribution.

First-principles method is used to characterize segregation and magnetic properties of alloyed Ti/TiO 2 interface. We calculate the segregation energy of the doped Ti/TiO 2 interface to investigate alloying atom's distribution. The oxidation resistance of Ti/TiO 2 interface is enhanced by elements Fe and Ni but reduced by element Co. Magnetism could be produced by alloying elements such as Co, Fe and Ni in the bulk of titanium and the surface of Ti at Ti/TiO 2 interface. The presence of these alloying elements could transform the non-magnetic titanium alloys into magnetic systems. We have also calculated the temperature dependence of magnetic permeability for the doped and pure Ti/TiO 2 interfaces. Alloying effects on the Curie temperature of the Ti/TiO 2 interface have been elaborated.

The critical resolved shear stress (CRSS) and its related plastic deformation of titanium with hexagonal close packed structure are highly anisotropic, leading to low ductility of the material. Understanding the alloying effect on the CRSS is crucial for the improvement of the mechanical properties through rational composition design. Accurate prediction of the CRSS is not straightforward due to the atomic randomness of the alloy. The generalized stacking fault energies (GSFEs) for the basal and prismatic plane 〈 a 〉 slips of random α-Ti1−xAlx alloys ( 0 ≤ x ≤ 0.1875 ) are calculated by using first-principles methods including exact muffin-tin orbitals (EMTO) and plane-wave psuedopotential (VASP) methods in this work. The random distribution of Al in the alloy is treated by using both coherent potential approximation (CPA) for EMTO and special quasirandom structure (SQS) techniques for VASP. The CRSSs are then evaluated within the frame work of semi-discrete variational Peierls-Nabarro model. The VASP-SQS calculations with atomic relaxation generate reasonably good GSFE and CRSS compared with the EMTO-CPA and VASP-SQS calculations without atomic relaxation. For pure Ti, the unstable stacking fault energy ( γ u s f ) and CRSS ( τ a ) for the basal 〈 a 〉 slip are higher than those for the prismatic 〈 a 〉 slip. With increasing Al concentration x, γ u s f b for the basal 〈 a 〉 slip decreases whereas γ u s f p for the prismatic 〈 a 〉 increases. The CRSSs for the basal 〈 a 〉 slip ( τ a b ) and the prismatic 〈 a 〉 slip ( τ a p ) both increase with x while τ a p increases faster than τ a b such that τ a b approaches to τ a p . The calculated CRSSs explain successfully our recently measured mechanical properties (yield strength, fracture toughness, ultimate strength, and elongation) of the α-Ti1−xAlx alloy against x.

The stacking fault energy (SFE) plays an important role in the deformation mode selection and consequently the mechanical properties of high entropy alloys. In the present work, the SFEs of face-centered cubic (fcc) CoCrFeNi and Al0.57CoCrFeNi HEAs are calculated by using first-principles calculations. The influence of the local lattice distortion (LLD) on the SFE is explored. We show that the addition of Al to CoCrFeNi alloy increases the intrinsic SFE (ISFE, γisf) but decreases the unstable SFE (USFE, γusf) such that the energy barrier (γusf - γisf) for the 〈11 2 ( _ ) 〉(111) slip decreases. The lattice distortion contributes significantly to the ISFE but has limited influence on the USFE, leading to decline of the slip energy barriers of both alloys. The ISFE and slip energy barrier differences between the two alloys are enhanced by the lattice distortion. Based on the calculated ISFE and slip energy barrier, the effects of Al alloying and lattice distortion on the mechanical properties of CoCrNiFe HEA are discussed.

Unlike the general belief that either dislocations cut or by-pass the ω -precipitates contributes to the high strength of Ti alloys, here we uncovered a new strengthening mechanism of lattice disordering of ω -precipitates by investigating the deformation behavior of body-centered-cubic (bcc) single crystalline Ti-10V-2Fe-3Al (Ti1023) alloy micropillars. This unique ω -precipitate disordering strengthening mechanism emerges in-between the precipitate cutting and by-passing mechanisms, because the dislocations pile-up stress reaches the ideal strength of ω -phase. The ω -precipitates with four variants manifest the strong deformation anisotropies, as verified by both the crystallographic orientation analysis and energy landscapes from the first principle calculations. The combination of precipitates cutting of ω 1-variant and precipitates disordering of ω 2/ ω 3/ ω 4-variants leads to the formation of precipitate-free channel in bcc (146) β -oriented Ti1023 alloy micropillars. Due to the presence of ω -precipitates, the bcc Ti1023 alloy micropillars exhibit stable plastic flow, associated with weak-size dependent superior strength. These findings provide fundamental understanding of the deformation characteristic of precipitate-hardening alloys, and have important implications for the design of small-scale materials.

In the present work, a first-principles method is used to calculate the oxidation energies of Al2O3 and TiO2 as well as the formation energy of oxygen vacancy in TiO2 containing various alloying elements, in order to shed some light on the alloying effects on the oxidation resistance of γ-TiAl. Our calculations demonstrate that almost all alloying elements increase the oxidation energies of Al2O3 and TiO2. The alloying elements with number of d electrons from 2 to 5 in the forth and fifth rows of the periodic table (e.g., Zr, Nb, Mo, Hf, Ta, W) increase significantly the oxidation energy difference between Al2O3 and TiO2, i.e., reduce the relative stability of Al2O3 to TiO2. On the other hand, these alloying elements increase the formation energy of oxygen vacancy in TiO2. The effects of other alloying elements are less significant or opposite. Observing the experimental mass gains of TiAl alloys and unalloyed TiAl due to oxidation, we find that the elements reducing the relative stability of Al2O3 to TiO2 and increasing the formation energy of oxygen vacancy enhance the oxidation resistance of TiAl whereas others do not. Such correlations are rationalized by analyzing the alloying effects on the internal oxidation of Al in the γ-TiAl matrix and the diffusion of oxygen in TiO2 surface scale.

The ω-phase transformation in metastable β-titanium (Ti) alloys has attracted great attention in the past decade due to its intrinsic complexity and modifying mechanical properties. Interfacial twin boundary (ITB) ω-phase was reported to appear along {332}β or {112}β twin boundaries in metastable β-Ti alloys. The formation of such ITB ω-phase was proposed to arise from the reverse α″ to β martensitic transformation and subsequent stress relaxation along the twin boundaries. In this study, a new formation mechanism is revealed in Ti-10wt.%Cr alloy containing ω-precipitates in the initial microstructure. It is experimentally found that the formation of ITB ω-phase is closely correlated with the favored pre-existing one ω-variant at the expense of the other three-siblings, i.e., reorientation of ω-variants. The ω-reorientation mechanism is further rationalized by first-principles calculation in terms of the energy barrier of transformation pathway between ω-variants. These findings advance our fundamental understanding to the ω-phase transformation and further plastic deformation behavior of Ti alloys.

The site occupancy, lattice misfit and elastic modulus of Ni-based single crystal superalloys are investigated by combining the first principles exact muffin-tin orbital method and coherent-potential approximation. The site preference of alloying elements in γ′-Ni3Al can be classified into four types: Co, Fe, Ru and Ir occupy Ni site or Cr, Mo, Re, Ti, V occupy Al anti-site (namely alloying elements occupy Al site while the removed Al occupy Ni site). Ti and V are the alloying elements which stabilize the γ′-Ni3Al. The lattice misfit and the difference of elastic properties between γ and γ′ phases are the causes of γ′ rafting, while the alloying elements will improve the differences. The effects of 1 at. % ~5 at. % alloying elements on lattice constant and misfit are studied, because of biggish atomic radius, Ir, Mo, Ti, Re and Ru increase the lattice constant of γ/γ′ phase much faster, and the alloying elements have some impacts on the lattice misfit of γ/γ′ phase. Re is the most remarkable alloying element which improves the elastic modulus of Ni-based superalloys.

Introducing high symmetric cubic disordered β or ordered β 0 phases by alloying β-stabilizers improves the strength and high-temperature deformability of intermetallic γ-TiAl. However, the β phase is prone to decomposition of lower symmetric hexagonal phases such as ω 0 and ω ’ ’ , which are extremely brittle and harmful to the ductility of the alloy. Therefore, understanding the effect of the β-stabilizers on the phase stability of TiAl is crucial for the rational design of TiAl based alloys. In the present work, the equilibrium lattice structures, bulk moduli, and heats of formation of β, β 0 , ω ’ ’ , and ω 0 of TiAl with some typical β stabilizers V, Nb, Ta, Cr, Mo, W, and Mn were calculated by using a first-principles method, with which the relative phase stability were discussed. We showed that the phase stability sequence is β β 0 ω 0 ω ’ ’ for Ti4Al3Nb and Ti4Al3Ta, β ω 0 β 0 ω ’ ’ for Ti4Al3V, Ti4Al3Mo and Ti4Al3W, and β ω 0 ω ’ ’ β 0 for Ti4Al3Cr and Ti4Al3Mn. The β-stabilizing effect of the alloying element X increases from Nb/Ta to V/Mo/W to Cr/Mn. The relative stability of the various phases is roughly in accordance with the trends of the unit volume and bulk modulus against the phases with a few exceptions. The phase diagrams of the alloys associated with these phases were estimated by comparing the free energies against the temperature of various phases, evaluated with the calculated unit volumes and bulk moduli.

Using ab initio alloy theory, we systemically investigate the effect of alloying elements on the elastic properties of body-centered cubic (bcc) Ti1−x−yMoxMy (0.05 ≤ x ≤ 0.2; 0 ≤ y ≤ 0.4; M = Mg, Mn, Ni, Zr, Nb, and W) alloys. The theoretical single-crystal and polycrystalline elastic moduli of Ti1−xMox (0.05 ≤ x ≤ 0.2) agree well with the available experimental values and previous theoretical data. The lattice parameters of Ti-Mo-M ternary alloys significantly increase (decrease) with increasing Mg and Zr (Mn and Ni) contents, while remain almost constant for Nb and W additions. It is found that Mg is a promising alloying element that could decrease the Young’s modulus of bcc Ti-Mo alloys, but its content should be as small as possible since the stability of the β phase decreases with increasing Mg concentration. On the other hand, Mn, Ni, Nb, Zr, and W enhance the Young’s modulus and the stability of the β phase.

We propose an ω-lattice mechanism that is irrelevant to dislocation behaviors for a popular twinning ({1 1 2}〈1 1 1〉-type) system in body-centered-cubic (bcc) metals and alloys. The twinning process is dependent on the reverse transformation of ω (hexagonal) → bcc. The driving force of the twinning is attributed to the instability of a high density of nanoscale metastable ω precursors, and the mechanism has been experimentally and theoretically confirmed in bcc-Ti alloys with the {1 1 2}〈1 1 1〉-type twin formed under conditions free of external stress and internal strain. The ω-lattice mechanism involves bcc lattice shuffling only, thus can be applied to all bcc metals and alloys.

Aluminum addition to ferritic stainless steels was found to effectively suppress the deleterious 475 degrees C embrittlement resulting from the phase decomposition in concentrated Fe-Cr alloys. Wit ...

The crystallographic structure and stability of the alpha" phase relative to the alpha and beta phases in Ti-x M (M=Ta, Nb, V, Mo) alloys are investigated by using the first-principles exact muffin ...

Stacking fault energy (SFE) plays an important role in the plastic deformation of metals. As compared to those of face-centered cubic metals, the SFEs of hexagonal close-packed (hcp) metals are less reported in literature. In this paper, we derive the expressions of four types ( I 1 , I 2 , E and T 2 ) of basal plane SFEs of hcp metals in terms of the interlayer interaction energies within the framework of the Ising model. The SFEs of 14 kinds of hcp metals are then evaluated with the interlayer interaction energies extracted from the total energies of four prototypes calculated by using the first-principles full-potential augmented plane-wave method. We show that the hcp metals can be divided into three types according to their interlayer interaction energies. For all the hcp metals involved in this study, I 1 has the lowest SFE, whereas E has the highest. The metals (Mg, Co, Zn and Cd) with principal slip system (0 0 0 1) [ 1 1 2 ¯ 0 ] generally have low basal plane SFEs. The I 1 and T 2 SFEs increase linearly with the energy difference between double hexagonal close-packed and hcp structures, whereas the I 2 and E SFEs increase linearly with the energy difference between the short-period twin and hcp structures, indicating a trivial contribution of the interaction energy between atomic layers over third nearest neighbors to the SFEs. The SFEs also correlate with the cohesive energy density (cohesive energy of unit volume) with the exception of Be, Co, Tc and Re.

In this paper, the local asymmetrical distortion (measured as the dipole shape factor) induced by interstitial atoms (IAs: C, N, and O) in bcc-metals (V, Nb, and Ta) and the diffusion barriers of the IAs in the matrix are calculated by the use of a first-principles pseudopotential method. The obtained dipole shape factor and diffusion barrier are in reasonable agreement with the experimental values. The trend of the dipole shape factor and diffusion barrier with respect to the IAs and host metals are discussed in terms of the size difference between the IA and the interstice, the chemical and elastic interaction between the IA and the host metals. It is shown that both the size difference and the chemical interaction affect significantly the dipole shape factor, whereas the diffusion barrier is dominated by the chemical interaction.

In this paper, the five-layer modulated (5M) martensitic structures of Ni(2)Mn(Al(x)Ga(1-x)), with x = 0, 0.1 and 0.2, are investigated by the use of the exact muffin-tin orbital method in combination with the coherent potential approximation. The 5M martensite is modeled by varying c/a (shear) and wave-like displacements of the atoms on (1 1 0) plane (shuffle) scaled by eta according to Martynov and Kokorin (J. Phys. III 2, 739 (1992)). For Ni(2)MnGa, we obtain 5M martensite with equilibrium c/a of 0.92 and eta of 0.08, in reasonable agreement with the experiment results (0.94 and 0.06, respectively). c/a and eta are linearly coupled to each other. Al-doping increases c/a and decreases eta, but the linear c/a similar to eta coupling remains. Comparing the total energies of the 5M martensite and L2(1) austenite, we find that the martensite is more stable than the austenite. Al-doping increases the relative stability of the austenite and finally becomes energetically degenerated with the 5M martensite at an Al atomic fraction (x) of about 0.26. The relative phase stability is analyzed based on the calculated density of states. The calculated total magnetic moments mu(0) as a function of c/a exhibit a maximum around the equilibrium c/a. Al-doping reduces mu(0) (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The origin of the superior high temperature strength of Ti-rich gamma-TiAl with addition of Nb is a highly controversial issue. In this paper, we calculated the interaction energies between point defects in these alloys using a first-principles plane-wave pseudopotential method. It is found that, the nearest neighbouring Nb atoms on Al-sublattice (Nb(Al)) repel whereas the next nearest neighbouring Nb(Al) atoms attract each other, indicating that Nb(Al) atoms may form short-range ordered structure. Based on this finding, we propose that the short-range order may be responsible for the high strength of the Ti-rich TiAl-Nb alloys. (C) 2010 Elsevier Ltd. All rights reserved.

The interaction energies between substitutional rare earth (RE) atoms, between RE and interstitial C, N, O, H atoms, as well as between RE and vacancies in alpha-Ti are calculated via first-principles density-functional theory with projector augmented-wave (PAW) pseudopotentials. The results show that the RE-vacancy and RE-RE interactions are attractive due to the weaker RE-Ti bond than the host Ti-Ti bond. All of the RE atoms investigated in this paper are repulsive to C and N, but attractive to H. RE-O interactions are repulsive for the light RE atoms, though the interactions are very weak for the heavy RE atoms. The mechanism underlying the interactions and their possible influence on the properties of Ti alloys are discussed. (C) 2009 Elsevier B.V. All rights reserved.

The composition-dependent elastic properties and electronic structure of off-stoichionietric TiNi with a B2 structure are investigated by using the first-principles exact muffin-tin orbitals method in combination with coherent potential approximation and first-principles plane-wave pseudopotential method (for computing bonding charge densities). The Zener anisotropy, c(44)/c', increases with increasing Ni contents, but is quite small, indicating a strong correlation between the softening Of c(44) and c' with decreasing temperature during martensitic transformation (NIT). For the Ni-rich TiNi, c(44) increasing Ni content whereas c' decreases. On the Ti-rich side, both c(44)and c' are insensitive to the composition. It was observed that larger c(44) corresponds to higher MT temperature, and the composition dependence of elastic modulus is discussed on the basis of the bonding charge densities and electronic density of states. We propose that the strong composition dependence of the elastic modulus of the Ni-rich TiNi can be attributed to the Coulomb static electronic repulsion between the antisite Ni atorns and their surroundings. The insensitivity of the elastic modulus of the Ti-rich TiNi to the composition is due to the absence of such repulsion between the Ti antisites and their nearest neighbors. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

First-principles method based on the electronic structure theory is one of the most promising approaches of computational materials design. Although only a few of mechanical properties (e.g., ideal strength and elastic constants) are accessible directly by first-principles calculations, such methods may predict the complex mechanical properties by extracting appropriate calculable parameters (e.g., the ratio of bulk modulus to shear modulus, the formation energies of and interaction energies between lattice defects) and adopting proper models (e.g., Peierls-Nabarro model for dislocation core). In this paper, we briefly review recent first-principles investigations of mechanical properties of structural materials, covering topics of ideal strength, elastic constants, and lattice defects. Some of the major recent advances, such as the application of coherent potential approximation coupled first-principles methods (accurate enough for the calculating of the elastic constants of random alloys with complex compositions), the appreciation of the importance of low C, I-C, 2 to the,super properties' of BCC-Ti based alloys, and the relationship between solute-vacancy interaction and creep resistance, etc., are highlighted. (c) 2006 Elsevier Ltd. All rights reserved.

A recently developed mean-field model has been combined with first principles calculations of binding energy to investigate the site occupancies of micro-alloying elements and vacancies in NiAl as well as the stability of the micro-alloyed B2 phase with respect to disordering and second-phase formation. The theoretical results suggest that the transition metal elements in the same row of the periodic table increasingly tend to the Ni sublattice with increasing atomic number. Micro-alloying addition tends to decrease the vacancy concentration of NiAl alloys. Alloying with X that substitutes for Ni is predicted to have the sides of its solubility lobe parallel to the Ni-X side of the isotherm, but parallel to the Al-X side if X substitutes for Al. Micro-alloying was shown to raise the ordering temperature of the B2 phase over the corresponding binary alloy, in contrast with the effect of vacancies. Alloying effects on ordering temperature and the formation of point defects appear independent of the site substitution behaviour, and are less significant for 3d than for 4d and 5d transition metal elements. (C) 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.