First-principles calculations of structural, elastic and electronic properties of second phases and solid solutions in Ti–Al–V alloys

• The β phase is a metastable phase with the better mechanical properties than α phase.

• The structural and elastic properties of α and β phase demonstrate that β phase is metastable phase with better mechanical properties than α phase.

• Based on the contents of β phase, the four solid solutions, Ti32Al4V2, Ti31Al5V2, Ti35Al5V2 and Ti30Al4V2, are selected to further reveal the solution strengthening mechanism.

• The calculated results indicate that Ti₃₀Al₄V₂ has the strongest resist deformation capacity. Ti₃₅Al₅V₂ has the best plasticity. Ti₃₁Al₅V₂ has the largest stiffness. And these four solid solutions are all ductile.

Abstract

The mechanical and electronic characters of the second phases and solid solutions in Ti-xAl-yV (x = 5.0–7.0 wt %; y = 3.5–6.0 wt %) alloys were investigated in detail via first-principles calculations based on density functional theory (DFT). Firstly, the contents of α(AlTi₃) and β(Ti–V) phase in goal alloys were calculated. Furthermore, their structural and elastic properties were calculated. Besides, the supercell models of the four solid solutions (Ti₃₂Al₄V₂, Ti₃₁Al₅V₂, Ti₃₅Al₅V₂, and Ti₃₀Al₄V₂) were established based on the content of β phase in the selected alloys, and then their corresponding structural, elastic and electronic properties were calculated. The computational results for the solid solutions showed that Ti₃₀Al₄V₂ might present the strongest resist deformation capacity and Ti₃₁Al₅V₂ might own the largest stiffness. These four solid solutions are all ductile and the directional covalent bonding leads to better stability of Ti₃₅Al₅V₂ and Ti₃₀Al₄V₂.

Introduction

Ti–Al–V series titanium alloys, α/β dual-phase titanium alloys, are widely used in the biomedical, aerospace, automotive, space, and other major industries due to their low density, high strength and excellent corrosion resistance specifications [1,2]. The mechanical properties of Ti–Al–V alloys could be improved through heat treatment procedures [3]. Many studies have demonstrated that favorable heat treatment would be in favor of advantageous microstructures of Ti–Al–V alloys, further to gain excellent mechanical properties [[4], [5], [6]]. In particular, a better understanding of the structure and morphology of precipitate can further improve the strength of alloys, which are important to control the nucleation and growth of precipitates [[7], [8], [9]].

The precipitates usually refer to the second phase that formed in a matrix, resulting in the strong performance of metallic materials [10]. This hardening method is usually named second phase strengthening. It could increase the yield strength by dispersing second phase particles to hinder dislocation movement [11]. However, the effect of each second phase on mechanical properties is different. Therefore, it is necessary to analyze the intrinsic characteristics of each second phase and its effect on the overall mechanical properties of the material. For instance, Huang et al. [12] calculated the intrinsic characteristics, including cohesive energy (E_coh), formation enthalpy (ΔH), elastic constants and band structure, to characterize the structural stability, elastic properties and electronic properties of Mg₂Si, Mg₁₇Al₁₂ and Al₂Y phases. Their calculated results indicated that Al₂Y had the strongest alloying ability and structural stability. Besides, the solid solution strengthening, which is another important material strengthening mechanism, means that solute atoms are soluble into the matrix to create a lattice distortion. The lattice distortion increases the resistance of the dislocation motion and causes the slip difficult to proceed, thereby improving the strength and hardness of alloys [13].

In recent years, computational material science based on density functional theory (DFT) has emerged as an effective method to investigate materials characteristics [14]. The first-principles calculation method, ab initio, has been applied in the fields of chemistry, physics, life sciences, and materials science. Its basic idea is to treat a system composed of multiple atoms as a system composed of multiple electrons and nuclei, and to maximize the “non-empirical” treatment of the problem. Only five basic constants are needed, which is magnetics constant (μ₀), electric charge (e), Planck constant (h), light velocity (c) and Boltzmann constant (k), to investigate the physical properties of the energy and electronic structure of the system [14]. Therefore, the physical properties calculated by the first-principles calculation are closer to the real results, and the calculated results can be used to guide the design of materials and conduct deeper results analysis [11].

Karre et al. [15] predicted the alloy compositions of Ti–Nb and Ti–Nb–Zr alloy systems with stable β-phase via first-principles calculation. The theoretical results suggested that the stability of the β-phase increased with the addition of Nb in Ti and Zr in Ti–Nb. It was found that the stability of the β phase in the Ti–Nb alloy began to be completely stabilized when the content of Nb at 22 at.%. The structural, elastic, thermodynamic and electronic properties of the Ti_15-xMo_xSn compounds were systematically investigated by Chen et al. [16] via first-principles calculations based on DFT. It was found that the structural stability of the Ti_15−xMo_xSn compounds increased significantly with the increase of Mo content. And the calculation of the bulk modulus B, shear modulus G, Young's modulus E and Poisson's ratio ν of polycrystalline aggregates indicated that among these Ti_15−xMo_xSn compounds, the stiffness of Ti₄Mo₁₁Sn is largest while the ductility of Ti₁₂Mo₃Sn is greatest. The lower elastic Young's modulus of the compounds Ti1₂Mo₃Sn and Ti₁₁Mo₄Sn are 61.01 GPa and 65.59 GPa, respectively, rendering them to be promising metal biomaterials for implant applications.

TC4(Ti–6Al–4V) and TC10(Ti–6Al–6V) have great potential applications in aerospace and additive manufacturing industries [17]. The composition of TC4 is Ti-xAl-yV (x = 5.5–6.8 wt%; y = 3.5–4.5 wt%), and that of TC6 is Ti-xAl-yV (x = 5.0–6.0 wt%; y = 5.0–6.0 wt%). It can be clearly seen that whether it is TC4 or TC10, they all refer to the range of alloying element, rather than a specific composition. Alloying is one of the most basic measures to regulate the mechanical properties of metallic materials. A subtle difference in the content of alloying element may cause a significant change in performance. Therefore, when considering the specific application of the alloys, it is necessary to carefully investigate the mechanical properties of the alloys with more accurate alloying element content.

In the present work, 36 Ti-xAl-yV (x = 5.0–7.0 wt %; y = 3.5–6.0 wt %) alloys compositions were designed based on the compositions of TC4 and TC10. The type of second phases in 36 Ti-xAl-yV (x = 5.0–7.0 wt %; y = 3.5–6.0 wt %) alloys were determined based on the room temperature equilibrium phase diagram of Ti–Al–V alloys [18]. Afterwards, the types and corresponding content of second phases in each alloy were assessed according to the phase diagram. The formation enthalpy, cohesive energy and the elastic constants of second phases were calculated to characterize their intrinsic characteristics. Besides, four solid solutions systems were selected based on the content of the strengthening phase and then constructed their supercell structures by applying special quasi-random structure (SQS) method. Furthermore, the elastic and electronic properties of the solid solution systems were calculated, which was utilized to assess solid solution strengthening effect. The results can provide theoretical guidance on the design and composition selection of Ti–Al–V alloys.