All-proportional solid solution versus two-phase coexistence in the Ti–V alloy by first-principles phase field and SQS methods (original) (raw)
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Solid State Communications, 2013
The crystallographic structure and stability of the a 00 phase relative to the a and b phases in Ti-x M (M ¼Ta, Nb, V, Mo) alloys are investigated by using the first-principles exact muffin-tin orbital method in combination with the coherent potential approximation. We show that, with increasing concentration of the alloying elements, the structure of the orthorhombic-a 00 phase evolutes from the hcp-a to the bcc-b phase, i.e., the lattice parameters b/a and c/a as well as the basal shuffle y decreases from those corresponding to the a phase to those of the b phase. The compositional a=a 00 and a 00 =b phase boundaries are determined by comparing the total energies of the phases. The predicted a=a 00 phase boundaries are about 10.2, 10.5, 11.5, 4.5 at% for Ti-V, Ti-Nb, Ti-Ta, and Ti-Mo, respectively, in reasonable agreement with experiments. The a 00 =b phase boundaries are higher than the experimental values, possibly due to the absence of temperature effect in the first-principles calculations. Analyzing the electronic density of states, we propose that the stability of the a 00 phase is controlled by the compromise between the strength of the covalent and metallic bonds.
An empirical theoretical investigation into phase and structural behaviour in Ti–Al alloys
Materials Science and Technology, 2010
According to the average lattice and atom models of the empirical electron theory of solids and molecules (EET), effects of interstitial impurities on valence electron structures and phase transformation of Ti-Al alloys are analysed. Furthermore, the descendant degree of bond energy, melting point, and liquidus temperatures affected by interstitial impurities are calculated based on the bond energy formula of the EET. Moreover, the main controversial experimental results on the phase transformation in Ti-Al alloys are explained well. It is demonstrated that because of the effects of interstitial impurities, atom states increase, bond structures are seriously anisotropic, which results in very complex phase transformations in intermediate Al content. It is also shown that the melting point and liquidus temperatures decrease due to interstitial impurities, and the average decreased degree can be estimated very well using the EET.
Metallurgical and Materials Transactions A, 2002
This article presents the results of a neutron diffraction study of a series of quenched Ti-V alloys and an assessment of the composition dependence of the structural properties in the Ti-V system. Upon quenching to room temperature and atmospheric pressure, three metastable phases occur, viz., the hcp (␣ Ј) phase formed by a martensitic transformation, the omega (⍀) phase formed by a displacive transformation involving the collapse of the (111) planes of the bcc structure, and the untransformed bcc () phase. The lattice parameters (LPs) of the ␣ Ј, , and ⍀ phases are determined as functions of the V content in the composition range 3 Յ at. pct V Յ 70. This information is combined with a detailed analysis of the available experimental data on the ␣ Ј, , and ⍀ phases in pure Ti and Ti-V alloys and the  phase of V. New estimates for the LPs of  and ⍀ Ti and expressions describing the composition dependence of the LPs are presented. Using the assessed values, various open questions are discussed, i.e., the composition range where the hexagonal to trigonal symmetry change is observed in the ⍀ phase, the applicability of an approximation involved in the plane collapse model for the  → ⍀ transformation, and the extent to which the so-called Jamieson correlation for interatomic distances in the ⍀ phase holds for Ti. G. AURELIO, Graduate Student, and A. FERNÁ NDEZ GUILLERMET, Professor, are with CONICET and Centro Atómico Bariloche, 8400 Bari-quenched alloys of the Ti-V system has previously been loche, Argentina, G.J. CUELLO, Scientist, is with the Institut Lauestudied using transmission electron microscopy (TEM) [19,20,21]
Phase field modeling of the growth and dissolution of the alpha phase in near-beta titanium alloys
We have developed a phase field model for studying the growth and dissolution of the ! phase in a multicomponent near-" titanium alloys, during either cooling or heating treatments. The model relies on the formulation of Kim et al. which has been modified to describe the ! phase as stoechiometric, as suggested by some measurements. The growth of a globular structure has been simulated in 2D during isothermal treatments and continuous coolings. The influence of the distribution of the globular precipitates, of the anisotropic interfacial energy as well as of the presence of grain boundaries have been studied. Moreover, we have carried out calculations of the dissolution of a duplex microstructure, composed of globular precipitates and of intragranular plates, during continuous heating treatments. These calculations have been able to explain qualitatively the singular evolution of the ! phase fraction with temperature measured by high energy synchrotron XRD.
First-principles study of ω-phase formation in the Ti 3 Al 2 V system
Journal of Physics: Condensed Matter, 2007
Using first-principles methods, the phase stability of the underlying bodycentered-cubic (bcc) structure of Ti 3 Al 2 V and slightly rearranged atomic structures are investigated. The calculated ground-state energies show an instability in the ternary Ti 3 Al 2 V alloy with respect to the ω structure-type atomic displacement. A Mulliken population analysis shows strong bonding between the transition metals and Al. It is shown that Ti-Al is the strongest bond and that ω-type displacements increase the population overlap for this bond and reduce the energy of the system. The first-principles calculations are extended to finite temperature and various contributions to the free energy are calculated within the quasiharmonic approximation. It is shown that, at high temperatures, the bcc structure is stabilized by the contribution of the low-energy modes to lattice entropy. In agreement with experiment and in contrast to the Ti-Al-Nb system, we find that the metastable B8 2 structure cannot form in this alloy.
On variant distribution and coarsening behavior of the α phase in a metastable β titanium alloy
Acta Materialia, 2016
The stereology, variant distribution and coarsening behavior of semicoherent α(hcp) precipitates in a β(bcc) matrix of a Ti5553 alloy has been analyzed, and a dominant 3-variant cluster has been observed in which the variants are related to each other by an axis-angle pair <11 0> 60 ᴼ. Shape and spatial distribution independent elastic self and interaction energies for all pairwise and triplet combinations of α have been calculated and it is found that the 3-cluster combination that is experimentally observed most frequently has the lowest energy for the semicoherent state. The coarsening behavior of the delta distribution follows LSW kinetics after an initial transient, and has been modeled by phase field methods.
First-principles calculation of phase equilibrium of V-Nb, V-Ta, and Nb-Ta alloys
Physical Review B, 2012
In this paper, we report the calculated phase diagrams of V-Nb, V-Ta, and Nb-Ta alloys computed by combining the total energies of 40-50 configurations for each system (obtained using density functional theory) with the cluster expansion and Monte Carlo techniques. For V-Nb alloys, the phase diagram computed with conventional cluster expansion shows a miscibility gap with consolute temperature T c = 1250 K. Including the constituent strain to the cluster expansion Hamiltonian does not alter the consolute temperature significantly, although it appears to influence the solubility of V-and Nb-rich alloys. The phonon contribution to the free energy lowers T c to 950 K (about 25%). Our calculations thus predicts an appreciable miscibility gap for V-Nb alloys. For bcc V-Ta alloy, this calculation predicts a miscibility gap with T c = 1100 K. For this alloy, both the constituent strain and phonon contributions are found to be significant. The constituent strain increases the miscibility gap while the phonon entropy counteracts the effect of the constituent strain. In V-Ta alloys, an ordering transition occurs at 1583 K from bcc solid solution phase to the V 2 Ta Laves phase due to the dominant chemical interaction associated with the relatively large electronegativity difference. Since the current cluster expansion ignores the V 2 Ta phase, the associated chemical interaction appears to manifest in making the solid solution phase remain stable down to 1100 K. For the size-matched Nb-Ta alloys, our calculation predicts complete miscibility in agreement with experiment.
Phase transformations in TiV alloys
Journal of Materials Science, 1983
The morphology and substructure of the athermal martensite produced byβ-quenching Ti, Ti-5% V and Ti-10% V have been described in detail. The martensitic transformation in the Ti-10% V alloy was found to be incomplete leading to a structure comprised of theμ-,β- andω-phases. The extent ofβ retention increases with the V content of the alloy and the martensitic transformation was completely inhibited on quenching a Ti-20% V alloy to room temperature. This alloy was found to undergo a stress-induced martensitic transformation. The morphology and crystallography of the stress-induced products have been examined in detail.
Microstructural Modeling of the α + β Phase in Ti-6Al-4V: A Diffusion-Based Approach
Metallurgical and Materials Transactions B, 2019
Complex heat treatment operations and advanced manufacturing processes such as laser or electronbeam welding will see the metallic workpiece experience a considerable range of temperatures and heating/cooling rates. These intrinsic conditions will have a significant bearing upon the microstructure of the material, and in turn upon the thermo-mechanical properties. In this work, a diffusion-based approach to model the growth and shrinkage of precipitates in the alpha + beta field of the common titanium alloy Ti-6Al-4V is established. Further, the numerical model is extended using a JMA-type approach to explore the dependency of the beta-transus temperature on extremely high heating rates, whereby dissolution alone is too slow to accurately describe the alpha to beta-phase transformation. Experimental heat treatments at rates of 5, 50, and 500°C/s were performed, and metallographic analysis of the samples was used to validate the numerical modeling framework predictions for lamellar shrinkage, while data from the literature has been used to evaluate the numerical modeling framework for the growth of equiaxed microstructures. The agreement between measurements and numerical predictions was found to be good.
Mixing enthalpies of alloys with dynamical instability: bcc Ti-V system
Acta Materialia, 2020
Enthalpy of mixing is among the key materials parameters to determine phase stability and phase transformations in solid solutions. The possibility to predict it from first principles in the framework of the density functional theory is one of the corner stones of the modern materials modeling and the future datadriven materials design. Here we have considered body-centered cubic (bcc) Ti-V alloys, a system with high potential for aerospace, automotive biomedical and energy applications, which is known to exhibit the dynamical instability of the crystal lattice for Ti-rich alloys at low temperature. We have calculated the mixing enthalpies ΔH of bcc Ti-V alloys in the whole interval of concentration at high temperature using ab initio molecular dynamics (AIMD) simulations. A comparison with state-of-the-art static calculations at temperature 0K shows drastic difference between the two methods: while AIMD predicts positive values of ΔH in the whole range of concentrations, the static zero-temperature simulations result in negative values of ΔH for Ti-rich alloys. We have measured the mixing enthalpy of bcc Ti-V alloys experimentally at 1073 K using an isoperibol high temperature Tian-Calvet calorimeter and found that the enthalpies are positive, in agreement with our finite temperature AIMD calculations. We attribute the failure of the standard static calculations of ΔH to lattice distortions associated with the dynamical instability of bcc Ti-V alloys at zero temperature and argue that the effect should be generally important in theoretical predictions of thermodynamic properties, especially for systems with dynamical instability.