Low modulus Ti-rich biocompatible TiNbZrTaHf concentrated alloys with exceptional plasticity

This study investigates the evolutions of microstructure and performance of TiNbZrTaHf-based alloys from equiatomic high-entropy alloys to Ti-rich dilute alloys. A novel biocompatible alloy, Ti50Nb12.5Zr12.5Ta12.5Hf12.5, was developed with a high yield strength of 839 ± 12 MPa, low modulus of 61.5 GPa, low magnetic susceptibility of ∼1.99 × 10−6 cm3g−1, and unprecedented tensile plasticity of 28.7 ± 2.2%. The study discusses the underlying mechanisms responsible for these superior performances, attributing the exceptional plasticity to the activation of cross-slip dislocations, enhanced dynamic recovery and high resistance to crack propagation. The findings provide new insights into the development of biomedical titanium alloys. GRAPHICAL ABSTRACT IMPACT STATEMENT This study introduces a novel biocompatible concentrated alloy with high strength, low modulus and unprecedented ductility, providing new insights for developing high-performance biomedical titanium alloys.


Introduction
In recent years, there has been significant progress in the development of beta-type titanium alloys for biomedical applications, with a focus on non-toxic and allergy-free alloys [1][2][3]. Among them, Ti-35Nb-7Zr-5Ta (TNZT) is considered one of the most promising candidates for the next generation of implant materials due to its extremely low elastic modulus of about 55 GPa [4]. However, the newly developed beta-type titanium alloys, including TNZT, have relatively low yield strength (400-800 MPa) and medium tensile plasticity ( < 15%) [4,5]. To address this issue, many alloy strengthening and toughening strategies have to be taken into account in processes [5,6]. Recently, a new alloy design concept, termed high-entropy alloys (HEAs) or concentrated alloys, has been presented [7][8][9]. Among the newly developed alloys, many body-centered cubic (BCC) HEAs containing refractory metal elements have demonstrated excellent biocompatibility [10,11], but their high elastic modulus and relatively low plasticity always limit their use in biomedical applications [8,9]. Recently, high strength and toughness TiNbZrTa-based HEAs were reported [12][13][14]. Unlike conventional alloys, such as TNZT, these biocompatible HEAs are typically composed of multiple principal alloying elements or have (near) equiatomic concentrations [7][8][9], thus have relatively high density. Despite having a crystalline order similar to traditional metals, the HEAs are compositionally disordered and always exhibit local chemical shortrange order (CSRO) [15][16][17][18][19][20]. The experimental investigation on the TiNbZrTa-based HEAs showed that CSRO or local chemical fluctuation contributes to the increment in both strength and ductility due to strongly promoted local double cross-slips of dislocations [13], which is different from the deformation mechanism of traditional homogeneous beta-type titanium alloys, such as TRIP (Transformation-Induced Plasticity) and TWIP (Twinning-Induced Plasticity) effect [21]. Therefore, it would be of great engineering and academic value to develop heterogeneous TiNbZrTa-based HEAs into TNZT-like single-principal biocompatible titanium alloys with improved performance by introducing similar structure and deformation mechanism with parent HEAs.
Motivated by this idea, we studied TiNbZrTaHf-based HEA alloys with increasing Ti content. We discovered that a novel Ti-rich biocompatible Ti 50 Nb 12.5 Zr 12.5 Ta 12.5 Hf 12.5 concentrated alloy, with a composition between equiatomic HEAs and commercial TNZT alloys, possesses a unique combination of high plasticity, high yield strength, low modulus, and low magnetic susceptibility, making it a promising material for use in next-generation medical implants.

Materials and methods
Alloy ingots with nominal compositions of Ti x (NbTaHf Zr) 100−x (at. %, x = 20, 30, 40, 50 and 60) (referred to as Ti20, Ti30, Ti40, Ti50 and Ti60) were prepared by arc-melting a mixture of pure metals (purity > 99.9%). The alloy ingots were re-melted at least five times to ensure compositional homogeneity. The as-cast ingots were hot-rolled into a sheet with a thickness of 8 mm (thickness reduction of approximately 30%) at 1223 K and then cold-rolled to a final thickness of 1 mm. The rolled sheets were then subjected to recrystallisation annealing at 1073 K for 4 h in a vacuum sintering furnace, followed by furnace cooling. The phase constitution of the samples was characterized by X-ray diffraction (XRD) (X'pert Powder, PANalytical, Netherlands). The microstructure was investigated by A transmission electron microscope (TEM, FEI Talos F200X, America) and scanning electron microscopy (SEM, Carl Zeiss Gemini 300 microscope) equipped with an Oxford Symmetry S2 electron backscatter diffraction (EBSD) detector. To evaluate the mechanical properties, uniaxial tensile tests were performed along the rolling direction and on dog-boneshaped samples with a gauge section 4 mm in width, 1 mm in thickness, and 14 mm in length at a strain rate of 5 × 10 −4 s −1 using a universal testing machine (Instron 8860, USA). Strain values were measured using an electronic extensometer. The detailed methodology for the first-principles calculations of TiNbZrTaHf-based alloys is available in the supplementary materials.

Results and discussion
The XRD patterns of cool-rolled and annealed TiNbZr TaHf-based alloys with varying Ti contents are shown in Figure 1a. Samples with Ti contents not exceeding 50 at.% primarily exhibit a single-phase BCC structure. However, when the Ti content increases to 60 at.%, a trace of HCP α-Ti phase is detected, indicating that higher Ti content induces phase instability in the TiNbZrTaHf-based alloys. Notably, unlike the cast TiN-bZrTaHf HEA [14,22], the major peak of the deformed and annealed samples shifted from the (110) plane to the (211) plane. EBSD analyses reveal this is mainly due to formation of weak textures.  Figure 1i-k). The average size of completely recrystallised grains for the Ti30, Ti40,Ti50 and Ti60 is determined to be 15.2 ± 2.3 μm, 20.6 ± 3.0 μm, 24.4 ± 4.2 μm and 28.4 ± 3.3 μm, respectively. The increasing grain size with increase of Ti content is primarily ascribed to higher diffusion coefficient of Ti element at 1073 K comparing with other elements [27], as well as decreasing recrystallisation temperature. Furthermore, SEM-energy dispersive X-ray (EDX), highangle annular dark-field (HAADF) images and corresponding elemental distribution maps reveal homogeneous composition distribution in all crystallized samples (Figure 1l-q and Fig.S2). The selected area electron diffraction (SAED) pattern along the [110] direction confirms that the alloy Ti30 is a single-phase BCC solid solution without the precipitation of second phases or phase separation (Figure 1l). Figure 2a shows the room-temperature tensile engineering stress-strain curves of the TiNbZrTaHf-based alloys with different Ti contents. The equiatomic TiN-bZrTaHf HEA (Ti20) demonstrates an ultrahigh yield strength but limited tensile plasticity due to highdensity dislocation and internal stress in the unrecrystallized sample. As the Ti content increases from 20% to 50%, the yield strength decreases from 1378 ± 20 MPa to 839 ± 12 MPa, while the corresponding elongation increases from 2.1 ± 0.2% to 28.7 ± 2.2%, respectively. In the case of Ti60 alloy, the formation of a minor HCP phase results in decreased plasticity and increased yield strength. Notably, the Ti50 alloy exhibits a remarkable combination of strength and plasticity. Figure 2b presents a comparison of the newly developed alloys with conventional TNZT beta-Ti alloy and BCC HEAs. Evidently, the newly developed alloys (Ti30, Ti40 and Ti50) achieve unprecedented levels of strength and ductility. In particular, the plasticity of the Ti50 alloy surpasses that of commercial TNZT alloys [4,5,[23][24][25][26][27][28][29][30][31][32][33][34][35] and most BCC refractory HEAs [12,13,[36][37][38][39][40][41].
To prevent the stress-shielding effect in biomaterials, a low elastic modulus is necessary. In this study, the Young's elastic modulus is derived from stress-strain curves. The results indicate that the Young's elastic modulus decreases from 127.86 GPa to 61.54 GPa as the Ti content increases from 20 at.% to 50 at.%, but sharply increases to 87.21 GPa when the Ti60 alloy forms an HCP phase. The Young's elastic modulus is an intrinsic property of materials, closely related to their crystal structure. For example, BCC-structured Ti generally has a lower Young's elastic modulus than HCP-structured Ti [42]. The increase in the Young's elastic modulus in the Ti60 alloy is due to the formation of the HCP phase. Valence electron concentration (VEC) is an important factor used to determine the phase structure and stability of metals, such as Ti alloys [43] and some HEAs [7][8][9]. VEC for a multi-component alloy can be estimated by equation: VEC = n i=1 c i (VEC) i , where (VEC) i is the valence electron concentration of the ith element [12].
However, it is still necessary to further verify whether VEC can be used to determine the phase stability of Tirich BCC HEAs and establish its correlation with Young's elastic modulus. In this study, the VEC values for Ti20, Ti30, Ti40, Ti50, and Ti60 are determined to be 4. 40, 4.35, 4.30, 4.25, and 4.20, respectively. According to the XRD results (Figure 1a), it can be concluded that the TiNbZrTaHf based alloys retained a single BCC structure when VEC ≥ 4.25. The critical VEC of 4.25 for the transition between the HCP and BCC structures is close to the previously reported value of 4.18 [12]. The results confirmed that VEC can be used to predict the structure of Ti-rich HEAs. In this regime with VEC ≥ 4.25, Young's elastic modulus decreased monotonically with decreasing VEC. This trend can be explained by the fact that the Young's modulus in the < 100 > direction of BCC crystals is typically lowered by reducing c11-c12 [12,42], which generally decreases with decreasing d + s valence electrons (i.e. VEC) for transitional metals with BCC structure [44]. Therefore, the low elastic modulus achieved in Ti-50 alloy is mainly due to its small VEC while simultaneously maintaining the BCC structure.
To ensure accurate magnetic resonance imaging (MRI) measurements, it is important for implants to have a low magnetic susceptibility. Figure 2c illustrates the magnetic variation of TiNbZrTaHf-based alloys with respect to the applied magnetic field. Linear fitting of this data shows that the magnetic susceptibilities of these alloys monotonically increase from 1.4517-2.2526 × 10 −6 cm 3 g −1 as the Ti content increases (as shown in the inset of Figure 2c). Figure 2d compares the Young's elastic modulus and magnetic susceptibility of sample Ti50 with those of several representative biomechanical materials, including Co-Cr-Mo, CP-Ti, Ti-6Al-4 V, Ti-6Al-7Nb alloys and typical BCC HEAs [12,[45][46][47]. The results show that the elastic modulus of Ti50 ( ∼ 61.54 GPa) and its magnetic susceptibility (1.99 × 10 −6 cm 3 g −1 ) are lower than those of the aforementioned alloys [12,[45][46][47]. The low elastic modulus, low magnetic susceptibility, high yield strength, and exceptional plasticity of the developed Ti50 alloy make it highly suitable for use in next-generation medical implantations.
While most refractory HEAs with a BCC structure are recognized for their high strength and limited ductility [9], the Ti50 alloy developed in this study demonstrates exceptional plasticity. To understand the source of this plasticity, the deformation mechanism of the Ti50 alloy was examined. When a tensile strain of 6% was applied to the sample, straight slip traces with uniform spacing of about 20.1 μm were formed uniformly in the entire deformed region, indicating the dominance of planar slips of dislocations in the early stage of plastic deformation, as shown in Figure 3a-1. Moreover, cross-slipped bands were occasionally observed in some regions (Figure 3a-2), indicating the activation of multiple slip systems [13,48]. As the tensile strain reached 24%, necking occurred (Figure 3b-1), and closer inspection revealed wavy slips with spacing of approximately 0.8 μm dominating the middle and final stages of plastic deformation (Figure 3b-2, Figure 3b-3, and Figure 3b-4). When the sample broke, on the fracture surface shown in Figure 3c, numerous cross-slip bands were observed at the tips of the cracks (Figure 3c-1 and Figure 3c-2). Additionally, high-density flat-shaped dimples with a diameter of about 5.1 μm covered most of the fracture surface (Figure 3c-3), resembling the Taylor meniscus instability pattern [49]. This type of pattern is often found in amorphous materials such as metallic glasses [50], polymers [51], and liquid interfaces [52]. More recently, these patterns were also observed on the fracture surfaces of highstrength and toughness metastable Ti-Mo alloys [53]. The presence of Taylor patterns suggests a significant temperature rise in the slip bands or cracks, resulting in the formation of a viscous layer [49]. The conversion of mechanical energy to heat, adiabatic heating, and frictional heating are the possible reasons for the localized temperature increase.
Based on above deformation mechanism, the exceptional plasticity of Ti50 alloy can be rationalized. When stress is applied to Ti50, dislocations of the primary slip system may begin to operate first, forming straight slip bands (Figure 3a). For further deformation, a secondary slip system is activated, resulting in cross or wavy slip bands, which form cross-links (Figure 3b-4) [48]. Because of the cross-links of slip bands and possible CSRO [15][16][17]54], dislocation motion would be impeded. For further deformation, dislocation cross slips may occur, transferring the planar slips of the dislocation into various atomic planes (Figure 3d). Cross-slips of dislocations decrease the dislocation density on a certain atomic plane, thus effectively avoiding the dislocation tangles and stress concentration of planar slips [13]. Therefore, a slight stress increase was observed in the stress-strain curve during the plastic deformation stage (Figure 2a). Another possible mechanism is that such secondary slip or cross-slip dislocations may be easily annihilated, that is, dynamic recovery may occur significantly, thus resulting in a consistently low dislocation density during deformation. With increase of deformation, the dynamic recovery may be more significant because of the decreasing space for dislocation motion by forming high-density cross-links and the temperature rise in the slip bands [55]. Both the enhanced dynamic recovery and cross-slips of dislocations would suppress dislocation pile-up, leading to the release of local concentrated stress, which delays the formation of cracks.
The Ti50 alloy showed remarkable plasticity, but microcracks were unexpectedly observed at the grain boundary in samples with a tensile strain of only 6% (Figure 3a-3 and Figure 3a-4). Generally, the formation of cracks during deformation indicates that the material is approaching failure [56]. However, the Ti50 alloys demonstrated an ultimate plastic strain of 28.7 ± 2.2%, which is at least four times the strain of the initial crack formation ( < 6%). The fact that microcracks formed long before the material fractured suggests that the Ti50 alloy has an exceptionally high resistance to crack propagation. The resistance to crack propagation in solid solution alloys depends on the competition between dislocation emissions and the propagation of cleavage near the crack tip [44,57]. The cleavage propagation and dislocation emissions near the crack tip closely relate to the surface energies (γ surf ) of cleavage planes and unstable stacking fault energies (γ usf ) of specific slip systems, respectively [58]. Approximately, an alloy with a higher ratio of γ surf /γ usf can be considered to have a higher likelihood of being intrinsically ductile [58,59]. For BCC-structured materials, 110 < 111 > is one of the most common slip systems during plastic deformation [9,59]. In order to determine the surface energies and unstable stacking fault (γ surf and γ usf ) of a TiNbZrTaHfbased alloy with varying Ti compositions, density functional theory (DFT) calculations were conducted using the VASP code [58]. The resulting values for γ usf of the (110) < 11(−)1 > slip systems and γ surf of (110) plane are presented in Figure 4a. The data shows that γ usf decreases from 0.411 J/m 2 to 0.367 J/m 2 with an increase in Ti content from 20 at. % to 60 at. % in the TiNbZrTaHf alloy, while γ surf remains relatively constant at a value of 1.55 ± 0.55 J/m 2 for all alloy compositions ( Figure  4a). The ratio between the two types of stress intensity factors, γ surf /γ usf, is displayed in Figure 4b, which indicates an increasing trend with increasing Ti content. The Ti50 alloy has a high γ surf /γ usf of 3.95, which is located in the ductility zone compared with previous studies and larger than most of the quaternary alloys screened in the 10-component compositional space [58]. The trend of γ surf /γ usf suggests that increasing the Ti content in TiNbZrTaHf based alloy improves dislocation mobility but has little effect on cleavage fracture propagation. When the dislocations at the crack tip are easily activated or have high mobility, they blunt the cracks and delay extension (Figure 4c). Although EBSD and XRD tests revealed some degree of texture in the samples, the Schmid factors of samples with varying titanium contents showed no significant change as the titanium content increased (Fig.S3). In other words, the weak texture in this study does not play a decisive role in the plasticity. The increased plasticity for the TiNbZrTaHfbased alloy with increasing Ti content results from the increasing resistance to crack propagation. This explains why the Ti50 alloy exhibits higher tensile plasticity than cast or completely recrystallized equiatomic TiNbZrTaHf HEA (28.7% vs. 18.5% [22]). These results offer valuable insights into the underlying mechanisms governing the mechanical properties of TiNbZrTaHf-based alloys, and suggest potential avenues for optimizing their performance in various applications.

Conclusions
In this study, a novel biocompatible Ti 50 Nb 12.5 Zr 12.5 Ta 12.5 Hf 12.5 concentrated alloy with a high yield strength of 839 ± 12 MPa, low modulus of 61.5 GPa, low magnetic susceptibility of ∼ 1.99 × 10 −6 cm 3 g −1 and unprecedented tensile plasticity of 28.7 ± 2.2% was developed by tuning the Ti content of equal-atomic-ratio TiN-bZrTaHf high-entropy alloys. The high plasticity of the Ti 50 Nb 12.5 Zr 12.5 Ta 12.5 Hf 12.5 alloy may originate from the enhanced dynamic recovery, cross-slips of dislocations and high resistance to crack propagation. The newly developed alloy has enormous potential to be the next generation of biological implant materials.