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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. [ABSTRACT FROM AUTHOR]

The formation of the sigma phase in technologically important materials influences greatly their mechanical properties. Fundamental knowledge on the sigma phase is demanded to understand the phase stability and reasonably control its precipitation. The present work clarifies the atomic bonding characteristics of the binary sigma phase including A -Al (A = Nb, Ta) and transition metal systems (TM-TM) based on the electronic density of states (DOS) and electron localization function (ELF) calculated by using first-principles methods. We show that the atomic bonds of the binary sigma phase exhibit both metallic and covalent characters. The completely ordered A 66.7 Al 33.3 (A = Nb, Ta) sigma compounds bear higher stability than their counterparts with atomic disordering. Besides, for a TM-TM sigma compound, the constituent atom with more electron shells or less valence electrons presents stronger electronic stability. When increasing its atomic occupancy on a specific site, the atomic bonding on the site becomes stronger. • Atomic bonds of the sigma phase exhibit both metallic and covalent characters. • Ordered A 66.7 Al 33.3 (A = Nb, Ta) sigma compoundsbear higher stability than their counterparts with atomic disordering. • For a transition metal sigma system, constituent atom with more electron shells or less valence electrons bonds more strongly. [ABSTRACT FROM AUTHOR]

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. • A method is proposed to extrapolate molar volume of pure elements in hypothetic σ structure. • Integrated thermodynamic and molar volume model was successfully established. • Integrated model physically considers influencing factors of both atomic mixing and atomic order on molar volume. • Integrated model can reliably predict molar volume of binary and ternary σ phase. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• Al-Zr bond dominates chemical ordering in ordered AlNbVTiZr alloy. • Ordered configurations with lower total energies significantly increase elastic constant of C 11. • (AlV)-(NbZrTi) configuration with lower total energy has a larger tensile strength than disordered configuration. • Chemical ordering mediates thermodynamic properties of AlNbVTiZr, but has little effects at high pressure. 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. [ABSTRACT FROM AUTHOR]

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-Ti 1− x Al x 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-Ti 1− x Al x alloy against x. • The article calculated GSFEs and CRSSs for basal and prismatic plane (a) slips of random α-Ti 1-x Al x alloys (0 ≤ x ≤ 0.1875). • The local lattice distortion influences significantly on the GSFEs and CRSSs. • Strength and fracture toughness of α-Ti 1-x Al x should increase whereas the plasticity reduces with increasing x. • Basal and prismatic plane slips may be activated during plastic deformation with increasing x. • The unstable stacking fault energy alone does not always work for the description of the mobility of some slip system. [ABSTRACT FROM AUTHOR]

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 Al 0.57 CoCrFeNi 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, γ isf) but decreases the unstable SFE (USFE, γ usf) such that the energy barrier (γ usf - γ isf) 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. • Addition of Al to CoCrFeNi decreases energy barrier for ⟨11 2 - ⟩(111) slip. • Lattice distortion decreases slip energy barriers of CoCrFeNi and Al 0.57 CoCrFeNi. • Contribution of lattice distortion to stacking fault energy against lattice distortion is independent of composition. • Lattice distortion amplifies mechanical property differences between CoCrFeNi and Al 0.57 CoCrFeNi. [ABSTRACT FROM AUTHOR]

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 Ti 4 Al 3 Nb and Ti 4 Al 3 Ta, β < ω 0 < β 0 < ω ' ' for Ti 4 Al 3 V, Ti 4 Al 3 Mo and Ti 4 Al 3 W, and β < ω 0 < ω ' ' < β 0 for Ti 4 Al 3 Cr and Ti 4 Al 3 Mn. 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. • Phase stability of TiAl alloying with transition metal elements is determined. • Phase stability is roughly in accordance with the unit volume and bulk modulus. • Strategy for the composition design of TiAl based alloys is presented. [ABSTRACT FROM AUTHOR]