Ab-initio and experimental study of phase stability of Ti-Nb alloys

Highlights

• α′, α″, β and ω-phases in Ti-Nb are studied by ab-initio and experimental methods.

• The Ti-Nb favoured stability is related to its lowest total energy.

• The electronic lowest occupation/energy values link to the favoured phase.

• At high Nb content, antibonding Nb p – Ti d hybridizations destabilize α′ and ω.

• Directional strong bonding between Ti d - Nb d stabilize the β-phase.

Abstract

A systematic theoretical and experimental study concerning the crystallographic structure and electronic properties of Ti-xNb (x < 50 at%) alloys is presented, aiming to enlighten the electronic origins of the β-phase stability which is of high interest for the development of novel β stabilized Ti-based alloys for biomedical applications. Both quantum-mechanical calculations and X-ray diffraction found several structural phases depending on Nb concentration. The ab-initio total energy results reveal that at low Nb contents the α′ and ω phases are favoured while at Nb content >18.75 at% the β-phase is favoured against all other crystallographic structures in line with the experimental results. Interestingly, at high Nb content the α′ and ω hexagonal phases become unstable due to the electronic band filling close to the Fermi level E_F, which is mainly due to Nb-p and Ti-d antibonding hybridizations. On the contrary, in the cubic β-Ti-25Nb (at%) the depletion of the occupied electronic states at the E_F occurs mainly due to Nb-d and Ti-d bonding interactions, resulting in a stable β-TiNb structure. These data could enlighten the electronic origin of the Ti-Nb phase stability, thus, may contribute to the design of β stabilized low moduli Ti-based alloys suitable for load-bearing biomedical applications.

Introduction

Ti-based alloys are dominating as metallic biomaterials and in this role are central to the well-being and quality of life of a large part of the human population. Since the 1950s Ti-6Al-4V (wt.%) is the most conventional alloy for medical bone-replacing and supporting use due to its good workability, heat treatability and large strength compared to steels or Co-Cr alloys [1], [2]. However, compatibility concerns in terms of biological safety of V and Al [3], [4] and mechanical properties [5], [6] have motivated extensive efforts since the 90ies to develop β-stabilized Ti-based alloys without harmful elements and reduced Young's modulus. Due to these efforts this class of alloys and in particular Ti-Nb-based, Ti-Ta-based and Ti-Zr-based alloys are emerging as promising materials for load-bearing as well as for functional biomedical implant components [1], [2], [5].

The strongest attention was and is still given to β-phase Ti-Nb-based alloys [1], [7], [8]. The high attractiveness of Ti-Nb alloys is based on their superior combination of low elastic moduli [9], [10], high corrosion resistance [11], [12] and minimal cytoxicity [13], [14], together with their superelastic and shape memory features [8], [15], [16]. Several phases (including α, β, α′′ and ω) may coexist in Ti-Nb alloys, depending on the Nb concentration, which decisively influence their mechanical and functional properties, as has been suggested in previous works [5], [9]. Nb is a β-stabilizer and, therefore, the body centered cubic (bcc) β-phase is retained at room temperature (RT) by quenching for compositions above about Ti-22.5Nb (at%). For Nb-leaner compositions, the phase transition pathway from the hcp α-phase to into the bcc β-phase gives rise to the α″ orthorhombic phase [17], [18]. The suitability of Ti-Nb alloys for some task heavily depends on the composition, microstructural design and processing. Appropriate selection of composition and thermo(mechanical) processing allows tailoring of the mechanical and functional properties for biomedical applications [4], [5], [19], [20], [21].

This behavior is directly related to the instability of pure β-Ti at ambient conditions, which is correlated with its elastic instability (negative values of the tetragonal shear modulus C′) [22], [23]. For cubic d transition metals and alloys, C′ is associated with the energy difference between the face centered cubic (fcc) and bcc phases, while the stability of the fcc, hexagonal close packed (hcp) and bcc structures is linked to the electronic band filling and the number of d-electrons and the shape of their electronic density of states (EDOS) [22]. In particular, the stability of the β-Ti phase is attributed to the increase of the number of d-electrons due to charge transfer from the s and p electrons upon pressure [24], [25] or upon alloying with V, Nb, Ta, Mo, and W [26], [27] where a critical number of 4.24 valence electrons per atom (e/a) was introduced [26] as a convenient predictive criterion. Tailoring C′ and e/a allows obtaining a unique combination of very low elastic modulus and large elastic strain together with high mechanical strength and large deformability as demonstrated by the “Gum metal” alloy family [26].

In addition, due to the d-electrons, the β-phase elements may exhibit strong directional covalent bonds [28]. Covalent bonding was also suggested in the ω–phase of Ti, Zr, Hf [23]. Further theoretical studies introduced the Bond order (Bo) as a measure of the strength of the covalent bonding, while another theoretical model combines the Bo with the highest occupied molecular orbital centered upon the alloying atom and the resulting absolute-energy value as a measure of the ionization potential of this atom in the corresponding system [29]. Both methodologies try to correlate the electronic properties of the Ti-based alloy with the experimentally observed low elastic modulus and shape memory characteristic and provided guidelines for the design of new alloys.

Although during the last years there has been a lot of attention on the Ti-Nb alloys, investigations concerning the whole set of experimentally observed phases (α′, β, α′′ and ω) are rare. Most of the studies, especially the theoretical ones, have been focused mainly on the electronic properties and the stability of one or two of the four phases, or on selected alloy compositions. A detailed study of the crystallographic structures and electronic characteristics, combining theoretical calculations with experiments, is lacking.

In this work, we present results from a systematic study of several Ti-Nb alloys covering a large Nb concentration range from 0 at% to 50 at%, combining both experimental and theoretical data. The α′, β, α′′ and ω phases observed in our experimental Ti-Nb samples (in both bulk and thin film forms) were studied by ab-initio calculations seeking for the electronic origin of their formation, as well as their stabilities. The lattice parameters and the EDOS were obtained for all phases and Nb concentrations, in order to uncover their influence in the resulting poly-crystalline alloys.