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Ab initio calculations, based on the exact muffin-tin orbitals method are used to determine the elastic properties of Cu-Au alloys with Au/Cu ratio 1/3. The compositional disorder is treated within the coherent potential approximation. The lattice parameters and single-crystal elastic constants are calculated for different partially ordered structures ranging from the fully ordered L1(2) to the random face centered cubic lattice. It is shown that the theoretical elastic constants follow a clear trend with the degree of chemical order: namely, C(11) and C(12) decrease, whereas C(44) remains nearly constant with increasing disorder. The present results are in line with the experimental findings that the impact of the chemical ordering on the fundamental elastic parameters is close to the resolution of the available experimental and theoretical tools.

Precipitation strengthening of silicides plays an important role in improving the creep resistance of high‐temperature titanium alloys. The oversize and concentrated silicides remarkably reduce the ductility of the alloys, which shorten the serving life of the key components in aerospace engines and gas turbines. To investigate the alloying effect on the stability of Ti5Si3, the enthalpy of solution for IIIB–VIB and IIIA–IVA elements in Ti5Si3, α matrix, and β phase are calculated and compared. It is proposed that Zr and Hf stabilize Ti5Si3 and promote the nucleation and refinement of silicide particles. The β stabilizers and simple metals destabilize Ti5Si3 and would suppress the precipitation of Ti5Si3. [ABSTRACT FROM AUTHOR]

The authors comment on a study that presents a physics-informed machine-learning approach for screening alloys with low thermal expansion coefficient within the iron-cobalt-nickel-chromium and iron-cobalt-nickel-chromium-copper composition space. They discuss a methodology developed by the researchers for training a machine-learning algorithm and used it to search for Invar materials, which have a very low coefficient of thermal expansion, among high-entropy alloys (HEA).

Materials with high hardness are technologically important for cutting and forming tools, engine components, valves, seals, gears, many types of wear resistant coatings, etc. The search for harder materials has a long history and remains one of the most active areas in materials science. Predictive tools for hardness will make this effort more efficient. In the past ten years, several hardness models based on electronic structure theory for perfect elemental materials/binary covalent and ionic compounds have been put forward. However, most of the engineering materials are alloys (solid solutions) and inevitably contain some impurities or defects such as vacancies. Theoretical predictions of the hardness of this kind of materials have rarely been touched. We have presented a hardness formula for multi-component covalent solid solutions. Here the composition dependence of the hardness of some covalent/ionic solid solutions, predicted with this formula, taking the parameters from our first-principles calculations, will be reported in comparison with experimental results. Furthermore, the electronic structure origin of the composition dependence of the hardness will be discussed. We will show that the band-filling effect proposed in literature to account for the composition dependence of the hardness of e.g. TiCxN1-x fails for some of the systems. Instead, we suggest that the composition dependence is controlled by the competition between the band-filling effect and the strength of electronic states hybridization. [ABSTRACT FROM AUTHOR]

By using first principles in combination with atomistic spin dynamics calculational methods, we determine the temperature-dependent free energies of the L21-and L10-Ni2(Mn1-xFex) Ga (0 ≤ x ≤ 1), including phonon vibrational and magnetic energies. The x-dependent martensitic phase transformation (MPT) temperature (TM) and the Curie temperature (TC) are well represented. It is found that, the abnormal nonmonotonic behavior of TM similar to x mainly originates from the phonon vibrational free energy. The magnetic energy, which does not change the trend of TM ~ x but decreases the driving force of the MPT, is indispensable as well to get reasonable TM values. This insight provides a good understanding of the physical mechanisms driving the MPT of Ni2(Mn1-xFex)Ga, and promotes the improvement of their magnetic shape memory properties. [ABSTRACT FROM AUTHOR]

Abstract: 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 11–C 12 to the ‘super properties’ of BCC-Ti based alloys, and the relationship between solute–vacancy interaction and creep resistance, etc., are highlighted. [Copyright &y& Elsevier]

The alloying effects of Nb, Zr, and/or Sn on the phase stability and elastic properties of Ti are investigated by using a first-principles method. Our calculation results indicate that a carefully designed Ti–Nb–Zr–Sn system can be a good candidate for low modulus biomedical materials. We find that the well-known correlation between the e/a ratio and both elastic and phase stabilities for Ti alloyed with transition metal elements breaks down for the Ti–Sn alloy. [ABSTRACT FROM AUTHOR]

Quantifying the local lattice distortion (LLD) and exploring its correlation with material properties are of fundamental importance for the design of high entropy alloys (HEAs). In the present work, we expressed the LLD as the standard deviation of the bond lengths (SDBL). With which, we calculated the LLDs of the face-centered cubic (fcc) alloys, including the dilute and equiatomic binary TM-Co and TM-Ni (TM = transition metal) alloys and the equiatomic CrMnCoNiFe family HEAs by using a first-principles method. For the binary TM-Co and TM-Ni alloys with TM in the same period of the Chemical Element Periodic Table, the LLD and the number of valence electrons of TM exhibit roughly a parabolic relationship with a minimum in the middle of the period. For the HEAs involved in the present work, the composition-LLD-mechanical property relationship was constructed. It is found that the experimental yield strengths increase monotonically with the calculated LLDs, and to pursue a high LLD in the CoNi-based CrMnCoNiFe family alloys, one should increase Cr to an appropriate content and avoid introducing Fe. Furthermore, the influences of the atomic radius, electronegativity, and magnetism on the LLD were elucidated. The present work provides a comprehensive understanding of the LLD in both dilute and equiatomic FCC alloys. [Display omitted] • The LLD was expressed as the standard deviation of the bond length proposed based on the characteristics of FCC structure. • The composition-LLD-mechanical property relationship was constructed. • The influences of the atomic radius, electronegativity, and magnetism on the LLD were elucidated. • The electronegativity of the transition metals was quantified according to the first-principles calculations. • The valence electron concentration can be employed to roughly judge the magnetic state of Fe in HEAs. [ABSTRACT FROM AUTHOR]

The temperature dependence of the elastic properties of Ni2+xMn1-xGa and Ni2Mn(Ga1-xAlx) (x = 0.0,0.1. and 0.2) random alloys are investigated by using the first-principles exact muffin-tin orbitals method. At 0 K, the calculated equilibrium parameters in both cubic L21 and nonmodulated tetragonal β"'-Ni2MnGa are in good agreement with the available experimental data and other theoretical results. Separating the thermal effects into single electron excitation, volume expansion, phonon smearing, and magnetic terms, we find that phonon smearing gives the dominating positive tetragonal elastic constant (C') versus temperature (T) slope for the cubic phase. For Ni2+xMn1-xGa, the competition between the negative alloying effect (∂C'/∂x < 0) and the positive temperature effect (∂C'/∂T > 0) leads to nearly constant C'[x, TM(x)] at the martensitic transition temperature TM(x). For Ni2Mn(Ga1-xAlx), where both ∂C'/∂x and ∂C'/∂T are positive, however, due to the significantly decrease of TM(x), the critical C'[x, TM(x)] slightly decreases with Al doping. Furthermore, it is demonstrated that both the composition and the temperature dependence of C' are indispensable to get a reasonable theoretical TM(x). [ABSTRACT FROM AUTHOR]

The site preference and elastic properties of Fe-, Co-, and Cu-doped Ni2MnGa alloys are investigated by using the first-principles exact muffin-tin orbital method in combination with coherent-potential approximation. It is shown that Fe atom prefers to occupy the Mn and Ni sublattices even in Ga-deficient alloys; Co has strong tendency to occupy the Ni sublattice in all types of alloys; Cu atoms always occupy the sublattice of the host elements in deficiency. For most of the alloys with stable site occupations, both the electron density n and the shear modulus C' can be considered as predictors of the composition dependence of the martensitic transition temperature TM of the alloys. The physics underlying the composition-dependent C' are discussed based on the calculated density of states. [ABSTRACT FROM AUTHOR]

First-principles alloy theory, formulated within the exact muffin-tin orbital method in combination with the coherent-potential approximation, is used to study the mechanical properties of ferromagnetic body-centered cubic (bcc) Fe1-xMx alloys (M = Mn or Ni, 0≤x≤0.1). We consider several physical parameters accessible from ab initio calculations and their combinations in various phenomenological models to compare the effect of Mn and Ni on the properties of Fe. Alloying is found to slightly alter the lattice parameters and produce noticeable influence on elastic moduli. Both Mn and Ni decrease the surface energy and the unstable stacking fault energy associated with the {110} surface facet and the {110}{111} slip system, respectively. Nickel is found to produce larger effect on the planar fault energies than Mn. The semiempirical ductility criteria by Rice and Pugh consistently predict that Ni enhances the ductility of Fe but give contradictory results in the case of Mn doping. The origin of the discrepancy between the two criteria is discussed and an alternative measure of the ductile-brittle behavior based on the theoretical cleavage strength and single-crystal shear modulus G{110}{111} is proposed. [ABSTRACT FROM AUTHOR]

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. [Display omitted]. [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]

[Display omitted] • X-Al interaction energy is proposed as an index for screening alloying element X in high temperature Ti alloys. • Effects of temperature and off-center occupation of alloying atom on interaction energy are considered. • Mo, Tc, Ru, W, Re, and Os are identifed to benifit both strength and thermal stability of high temperature Ti alloys. Increasing the solubility of Al and inhibiting the growth of Ti 3 Al 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. [ABSTRACT FROM AUTHOR]

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. [Display omitted] [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]

Ab initio calculations on the single-crystal elastic constants (C ij), Zener anisotropy ratio (C 44 / C ′), and single-crystal Young's moduli (E [hkl]) for bcc Ti-Mo- M (M = Mg, Mn, Ni, Zr, Nb, and W) ternary solid solutions as a function of Mo and M contents. • The theoretical elastic moduli of Ti-Mo agree with the available calculated and experimental data. • Complex alloying effects are found in the lattice constants and elastic properties. • Mn, Ni, Nb, Zr, and W enhance both the Young's modulus and the stability of the β phase. • The single crystal Young's moduli of the Ti-Mo - based alloys show a strong elastic anisotropy. Using ab initio alloy theory, we systemically investigate the effect of alloying elements on the elastic properties of body-centered cubic (bcc) Ti 1− x − y Mo x M y (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 Ti 1− x Mo x (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. [ABSTRACT FROM AUTHOR]