Pressure derivatives of the elastic moduli of BCC Ti-V-Cr, Nb-Mo and Ta-W alloys

Ab initio quasi-harmonic thermoelasticity of molybdenum at high temperature and pressure

We present the ab initio thermoelastic properties of body-centered cubic molybdenum under extreme conditions obtained within the quasi-harmonic approximation including both the vibrational and electronic thermal excitation contributions to the free energy. The quasi-harmonic temperature-dependent elastic constants are calculated and compared with existing experiments and with the quasi-static approximation. We find that the quasi-harmonic approximation allows for a much better interpretation of the experimental data, confirming the trend found previously in other metals. Using the Voigt-Reuss-Hill average, we predict the compressional and shear sound velocities of polycrystalline molybdenum as a function of pressure for several temperatures, which might be accessible in experiments.

Pressure and temperature dependentab-initioquasi-harmonic thermoelastic properties of tungsten

We present theab-initiotemperature and pressure dependent thermoelastic properties of body-centered cubic tungsten. The temperature dependent quasi-harmonic elastic constants (ECs) are computed at several reference volumes including both the phonon and the electronic excitations contribution to the free energy and interpolated at different temperatures and pressures. Good agreement with the experimental ECs on a single crystal at ambient pressure is found. The pressure and temperature dependence of the shear sound velocity measured on polycrystalline tungsten by Qiet alis also in agreement with theory. Some discrepancies are found instead for the compressional velocity at high temperature and this is attributed to the temperature derivative of the bulk modulus, higher in theory than in experiment. These conclusions are reached both by PBE and by PBEsol functionals. The two give elastic properties with a similar pressure and temperature dependence although the latter is closer to experiment at 0 K.

Machine-learning interatomic potential for W-Mo alloys

In this work, we develop a machine-learning interatomic potential for W_xMo_1-xrandom alloys. The potential is trained using the Gaussian approximation potential framework and density functional theory data produced by the Viennaab initiosimulation package. The potential focuses on properties such as elastic properties, melting, and point defects for the whole range of W_xMo_1-xcompositions. Moreover, we use all-electron density functional theory data to fit an adjusted Ziegler-Biersack-Littmarck potential for the short-range repulsive interaction. We use the potential to investigate the effect of alloying on the threshold displacement energies and find a significant dependence on the local chemical environment and element of the primary recoiling atom.

Orbital localization error of density functional theory in shear properties of vanadium and niobium

It is believed that the density functional theory (DFT) describes most elements with s, p, and d orbitals very well, except some materials that have strongly localized and correlated valence electrons. In this work, we find that the widely employed exchange-correlation (XC) functionals, including local-density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, underestimate the shear modulus and phase stability of V and Nb greatly. The advanced hybrid functional that is usually better for correlated systems, on the other hand, completely fails in these two simple metals. This striking failure is revealed due to the orbital localization error in GGA, which is further deteriorated by hybrid functionals. This observation is corroborated by a similar failure of DFT+U and van der Waals functionals when applied to V and Nb. To remedy this problem, a semiempirical approach of DFT+J is proposed, which can delocalize electrons by facilitating the on-site exchange. Furthermore, it is observed that including density derivatives slightly improves the performance of the semilocal functionals, with meta-GGA outperforms GGA, and the latter is better than LDA. This discovery indicates the possibility and necessity to include higher-order density derivatives beyond the Laplacian level for the purpose of removing the orbital localization error (mainly from d orbitals) and delocalization error (mainly from s and p orbitals) completely in V and Nb so that a better description of their electronic structures is achieved. The same strategy can be applied to the other d electron system and f electron system.

Nucleation of twins and dislocations in V-Ti alloys under various straining conditions

The features of plasticity nucleation in V-4Ti and V-16Ti crystallites under uniaxial tension and bilateral compression are studied. It is shown that the nucleation of plasticity in crystallites is associated with the formation of twins under uniaxial tension. During the development of plasticity, a screw dislocation cell structure is formed between twin plates. The strain and stress at which plasticity nucleates in the material decreases with increasing Ti concentration. It was found that the distribution pattern of Ti atoms in the initial structure has a significant effect on the elastic limit of the simulated crystallites. The plastic deformation of crystallites with 16% Ti under bilateral compression is realized only by the dislocation mechanism. This behavior of the material is due to the low value of the stress at the elastic limit, which is insufficient for the formation of twins.

Origin of low Young modulus of multicomponent, biomedical Ti alloys - Seeking optimal elastic properties through a first principles investigation

Multicomponent, biomedical β-Ti alloys offer ultra-low Young modulus values that are related to a unique and poorly understood reduction of C₄₄ and C' elastic constants in comparison with binary systems. The elastic properties of such materials are difficult to control due to the large variations occurring even for a small change in chemical composition, which cannot be explained using existing theories. In this article, we investigate the above issues through systematic ab initio elastic constants calculations for a series of binary, ternary and quaternary Ti alloys. Special attention is paid to examining the reliability of the methodology adopted and to clarifying the atomic scale mechanisms that affect the mechanical properties of the systems analysed. It was found that the lower boundary of the polycrystalline Young modulus of Ti-Nb-base β phase is close to 50 GPa, and strongly depends on two specific electronic hybridisations related to niobium and simple metals addition that control C₄₄ and C'. Based on the relationship established between electronic structure and mechanical properties, we propose several quaternary alloys whose directional <100> Young modulus values are equal or similar to that of human bones. Some electronic-based guidelines for designing new multicomponent β-Ti alloys are also formulated.

Origin of ultralow Young׳s modulus in a metastable β-type Ti-33Nb-4Sn alloy

Although there is difficulty in growing a Ti-33Nb-4Sn single crystal due to its ultralow β-phase stability, the single-crystal elastic constants of metastable β-type Ti-33Nb-4Sn (wt%) alloy were extracted successfully from its polycrystal by in-situ synchrotron X-ray diffraction technique, to clarify the origin of the ultralow Young's modulus in its polycrystal. It is indicated that compared to binary TiCr, TiV and TiNb alloys, the Ti-33Nb-4Sn alloy possesses slightly lower β-phase stability with respect to {110}<110>(-)shear (i.e., C׳) but much lower β-phase stability regarding to {001}〈100〉 shear (i.e., C44). An analysis by the Hill approximation suggests that the ultralow isotropic polycrystalline Young׳s modulus (EH) of Ti-33Nb-4Sn alloy originates from the extremely low shear modulus C44 as well as the relatively low C׳. This indicates that in addition to C׳, C44 has a significant contribution to the Young's modulus of polycrystal, which challenges a conventional understanding that the Young's modulus of β-type Ti alloys is predominantly determined by C׳.

"Ideal" engineering alloys

A newly discovered group of alloys, called Gum Metals, approaches ideal strength in bulk form, exhibits significant plastic deformation prior to failure, and shows no indications of conventional-dislocation activity. Two conditions must be met for a material to exhibit this "ideal" behavior: (1) the stress required to trigger conventional-dislocation plasticity in the material must exceed its ideal strength, and (2) the material must be intrinsically ductile when stressed to ideal strength. Gum Metals satisfy both criteria, explaining their remarkable mechanical properties.

Lattice dynamics of molybdenum at high pressure

We have determined the lattice dynamics of molybdenum at high pressure to 37 GPa using high-resolution inelastic x-ray scattering. Over the investigated pressure range, we find a significant decrease in the H-point phonon anomaly. We also present calculations based on density functional theory that accurately predict this pressure dependence. Based on these results, we infer that the likely explanation for the H-point anomaly in molybdenum is strong electron-phonon coupling, which decreases upon compression due to the shift of the Fermi level with respect to the relevant electronic bands.