An Insight towards the Design of a Ruthenium-Containing Biomaterial

Abstract

Ruthenium (Ru) is one of the platinum group metals (PGMs). These metals belong to the transition metals group of the periodic table. They have excellent properties such as high melting point and are inert with variety of substances, thus also called noble metals. Currently, Ru is the cheapest of the PGMs, thus it is readily available compared to other PGMs. Recently, incorporating PGMs in shape memory alloys (SMAs) has been extensively explored, with titanium-nickel (TiNi) used as a bench-mark material. TiRu is amongst the compounds that are currently explored for various potential applications. This compound has an ordered B2 (CsCl-type) crystal structure. It is hard and brittle, thus some shape memory (SM) properties are difficult to induce in this compound. However, due to Ru possessing some good biomedical properties such as biocompatibility, corrosion resistance, improved radiopacity and ultra-low magnetic susceptibility for MRI diagnostics, the mechanical properties of TiRu must be improved for biomedical applications. Since niobium (Nb) is known to be biocompatible and is usually studied in biomedical alloys, a systematic substitution of Ti with niobium (Nb) was performed in an effort to reduce the stiffness (Young’s modulus). This chapter gives an insight on the structural and mechanical properties of biocompatible Ru-rich alloy compositions.

1. Introduction

The equilibrium phases of the Ti-Ru system are the disordered bcc (βTi) solid solution, the ordered cubic compound (B2) TiRu and the close-packed hexagonal solid solution. Figure 1 shows the experimentally obtained phase diagram of the Ti-Ru system. It can be observed that the β to α transformation temperature decreases from 882°C with an increase in Ru content up to 9 atomic percent (at.%), after which the β phase is stabilized. The maximum solubility of Ru in βTi is about 25 at.% at the peritectic temperature of 1575°C. On the other hand, the B2 TiRu compound is observed at composition range of 43–53 at.% Ru. TiRu congruently melts at 2130°C, below which the B2 phase remains stable to low temperatures [1].

Figure 1.

Ti-Ru system phase diagram [1].

Due to lower cost compared to other PGMs, Ru addition has been explored in different alloy systems (β and B2 type alloys) in order to improve various properties [2, 3, 4, 5]. In βTiNb alloys which hold much promise in the biomedical field because of intrinsic properties such as low modulus, biocompatibility and shape memory properties, such as superelasticity (SE), Ru is expected to increase strength, corrosion resistance, improve radiopacity and decrease magnetic susceptibility. Shape memory effect (SME) typically encompasses the phase transformation between two phases. For β-alloys, the reversion occurs between the high temperature β-phase and low temperature orthorhombic martensite α′′-phase at a critical alloying compositions, whilst for CsCl-type intermetallic compounds-like alloys the reversion is typically between the high-symmetry B2 and low-symmetry B19′/B19/B33/L1₀ phase [6]. It is this phase transformation that governs the functionality of SMAs. SE is important for biomedical applications such as orthodontic arc wires, bone plates and stents because it allows for shape recovery after deformation [4, 7]. However, recoverable strain have been found to be small in βTiNb alloys. Kim and Miyazaki [8] observed that alloys containing more that 25 at.% Nb had a recoverable strain of about 2.5%, which is much lower than that of TiNi alloys, which is ∼8%.

In order to improve SE at room temperature, addition of ternary elements to TiNb has been considered. The shape memory properties of ternary Ti-Nb-X (X = Si, Mo, O, N, Zr, Pd, Al, Ag, Pt, etc.) alloys have been extensively investigated [9, 10, 11, 12, 13, 14, 15, 16, 17, 18].

However, there are only limited studies that considered Ru as a ternary element in TiNb alloys [4, 19]. This remains so despite several improvements that were observed due to addition of Ru in Ti-20Nb-xRu (x = 0, 0.5, 1.0, 1.5 at.%). The yield strength ranged from 560 to 900 MPa and the Young’s modulus ranged from 60 to 100 GPa, with increasing Ru content. Furthermore, it was observed that Ru acted as a β-phase stabilizer and thus showed a potential to promote the existence of SE at room temperature [4]. The occurrence of SE in shape memory alloys is detailed elsewhere [20]. Although, according to authors’ knowledge the SE of Ti-20Nb-xRu (x = 0, 0.5, 1.0, 1.5 at.%) has not been published, it can be deduced that 20 at.% Nb could still yield lower transformation strain as it is reported that this strain can only be improved at Nb content less than 15 at.% [7, 8].

Previous studies [4, 19] have shown that Ru also improves properties such as corrosion resistance and lower magnetic susceptibility. Corrosion resistance is an important characteristic in biomedical alloys because corrosion results in harmful ionic release into the body and poor osseointergration due to metal loss. The effect of Ru addition in TiNb alloys has been reported from investigations of Ti-20Nb-xRu by Biesiekierski et al. [19] and it was revealed that Ru-containing alloys were more corrosion resistant compared to Ru-free alloys. Furthermore, it has been reported that Ru can enhance the corrosion resistance of biomedical Ti-based alloys by several orders of magnitude with even a 0.1 at.% addition in particular alloy systems [19, 21].

Moreover, it has been reported that most conventional metallic biomaterials with high magnetic susceptibility have adverse effects on the Magnetic Resonance Imaging (MRI) and diagnostics as they would become magnetized in the intense magnetic field of the MRI. This causes heat generation in the biomedical materials and therapeutic devices, which leads to displacement of biomaterials and therapeutic devices, and artifacts on the MRI. Such artifacts can distort the authentic bio-imaging of the human organs and tissues around the implant. Materials and devices with an ultra-low magnetic susceptibility are required for surgery and diagnostics performed under MRI. The βZrRu alloys with ultra-low magnetic susceptibility have been developed for biomedical and therapeutic devices. Here, adding Ru to Zr reduced magnetic susceptibility, as shown in Figure 2 [2].

Figure 2.

The magnetic susceptibility of pure Zr and βZrRu alloys [2].

In ordered B2 systems, the effect of Ru addition has been reported in B2 Ti₅₀Ni_50−xRu_x, Ti₅₀Pt_50−xRu_x, Zr₅₀Pd_50−xRu_x potential SMAs [3, 5, 22]. The phase stability, transformation temperature and elastic properties has been studied in the B2 Zr₅₀Pd_50−xRu_x (x = 0, 6.25, 12.50, 18.75) alloy compositions using computational methods [5] . The transformation temperature of Zr₅₀Pd_50−xRu_x alloys was observed to be sensitive to the Ru content, where B2 phase became more stable with Ru addition. This was shown by calculation of total energy difference (ΔE) between the austenite B2 and orthorhombic martensite phase. It was observed that the total ΔE decreased with increasing Ru content as shown in Figure 3, meaning that the transformation temperature of Zr₅₀Pd_50−xRu_x alloys decreased with increasing Ru content.

Figure 3.

The total energy difference (ΔE) between austenite and martensite phases of Zr₅₀Pd_50−xRu_x alloys [5].

Also, a preceding experimental study on similar alloys with even higher Ru contents showed that transformation temperature decreased from about 620°C at x = 0 binary alloy to around 0°C for x = 35 alloy [5, 23], indicating the B2 phase-stabilizing effects of Ru. These findings were similar to work done by Tsuji et al. [3], where systematic substitution of Ni with Ru in TiNi stabilized the B2 phase to the point where martensitic phase transformation completely diminished.

In B2 Ti₅₀Pt_50−xRu_x, the partial substitution (5 at.%) of Pt with Ru decreased the transformation temperature from martensitic finish (M_f) =1285 K for TiPt to M_f = 1129 K for Ti₅₀Pt₄₅Ru₅, further proving the B2-stabilizing effect of Ru. The compressive strength obtained at about 1129 K was slightly improved from ∼500 MPa for TiPt to ∼700 MPa for Ti₅₀Pt₄₅Ru₅. This means that partial substitution of Pt with Ru increased the critical stress for slip deformation. Furthermore, the recovery ratio due to shape memory effect was improved from ∼11% for TiPt to ∼45% for Ti₅₀Pt₄₅Ru₅ [22].

Furthermore, the B2 NbRu and TaRu have been studied as potential SMAs for high temperature applications [24]. Both compounds exhibit a B2 phase at higher temperatures and starts transforming to tetragonal (L1₀) martensitic phase below ∼1158 K for NbRu and ∼1403 K for TaRu. The shape recovery of NbRu and TaRu was reported to be 73% and 80%, respectively [24, 25], which is better than ones for B2 TiPt [22] and TiRu [3] at higher temperatures.

Although Ru is expensive compared to other transition metals considered for biomaterials, it is extremely promising for potential biomedical applications because it exhibits low ionic cytotoxicity in vitro, has excellent biocompatibility in vivo and no evidence of mutagenicity or carcinogenicity [21]. Moreover, it has good osteocompatibility that can exceed that of conventional pure Ti and Ti-based biomaterials [2].

At this point, the advantages of Ru addition in both β and B2-type alloys have been outlined. In view of the biomedical properties improved by Ru, it is worth a while to explore alloys with high Ru content, which means studying B2 alloys that form at high Ru compositions. Thus, the current study starts with B2 TiRu alloy that is stable to below ∼874 K, a factor that often makes it difficult to obtain the SM properties. Since SE is also dependent on the elastic moduli of material, the underlying mechanical properties of B2-type alloys must be improved for consideration in biomedical applications. Specifically, in this case the aim is to improve the mechanical properties of TiRu alloy for biomedical applications. Therefore, this chapter outlines the underlying mechanical properties induced by addition of Nb in TiRu in order to give an insight towards the design of a biomaterial with possible SME. The prediction of elastic properties has been performed for the B2 Ti-Nb-Ru alloys using the DFT method to guide the reader towards the design and development of Ru-rich biomaterials.

2. Computational details

To the authors’ knowledge, there is currently no experimental data available on the alloy system investigated in this chapter. Therefore, the authors have used similar approaches to that employed by other authors [5, 26, 27, 28] in order to have basis for the current research. The calculations in this study were performed on a unit cell and 2 × 2 × 2 supercell of B2-type crystal structure with space group #221(Pm-3m) consisting of 2 and 16 atoms, respectively, using DFT based CASTEP code embedded in Materials Studio 2020 software package [29]. Robust Vanderbilt ultrasoft pseudopotentials [30] were used to describe the ion-electron interaction within the generalized gradient approximation (GGA) [31] of Perdew-Burke-Ernzerhof (PBE) [32]. A plane wave energy cutoff of 700 eV and k-point set of 16x16x16 and 8x8x8 for unit cell and supercell, respectively, were sufficient to converge the total energy of the considered systems [33]. The effect of high Ru content and then substituting Ti atoms with Nb on the structure and elastic properties was determined. The starting composition was a binary Ti₈Ru₈, representing 50 at.% Ru and 0 at.% Nb. Then, the ternary compositions considered were of stoichiometry, Ti₇Nb₁Ru₈, Ti₆Nb₂Ru₈, Ti₅Nb₃Ru₈ and Ti₄Nb₄Ru_8, representing 6.25, 12.50, 18.75 and 25.0 at.% of Nb, as shown in Figure 4. All the ground-state structures were optimized using the Brayden-Fletcher-Goldfarb-Shanno (BFGS) minimization scheme. The convergence criterion of less than 1 × 10⁻⁵ eV/atom, the maximum residual forces of 0.03 eV/Å, maximum residual bulk stress of 0.05 GPa and maximum atomic displacement of 1 × 10⁻³ Å were utilized.

Figure 4.

Crystallographic structures of B2 Ti_(50−x)Nb_xRu₅₀ alloys.

The theoretical lattice parameters for cubic crystals of B2 Ti_(50−x)Nb_xRu₅₀ alloys were calculated and are presented in Table 1. The experimental lattice parameter for Ti₅₀Ru₅₀ is 3.067 Å [1, 3], which agrees with the theoretical value within the percentage error of 0.36%. The experimental values for ternary alloys are not yet available in literature. The atomic radii of Ru, Nb and Ti are 1.34, 1.47 and 1.46 Å, respectively [34]. Given that Nb and Ti have almost similar atomic size, it is noted that lattice constant (a_o) increased with increasing Nb content, owing to high coefficient of thermal expansion of Nb. This has been observed in the work conducted by Bonisch et al. [11] where the lattice parameters showed dependence on Nb content in TiNb. The linear thermal expansion of the Nb-rich orthorhombic martensite phase was found to be larger along the lattice parameter a than lattice parameters b and c. The a expanded at a rate of 163 × 10⁻⁶°C⁻¹ at temperatures below 500 K, indicating the high thermal expansion of 9.2 × 10^–6°C⁻¹ for Nb compared to Ti which is 8.4 × 10^–6°C⁻¹ [35].

Ti50Ru50	3.078
Ti43.75Nb6.25Ru50	3.092
Ti37.50Nb12.50Ru50	3.104
Ti31.50Nb18.50Ru50	3.115
Ti25Nb25Ru50	3.280

Table 1.

Theoretical lattice parameters (Å) of equilibrium cubic crystals (a₀) of B2 Ti_(50−x)Nb_xRu₅₀ alloy compositions.

3. Mechanical properties

3.1 Mechanical stability

The mechanical properties of materials could be estimated to some extent by analyzing the elastic constants. However, very accurate calculation of elastic constants is essential for gaining meaningful insight into the mechanical stability and elastic properties of materials. Elastic constants of a mechanically stable phase should meet the requirements of mechanical stability based on the Born Standard. The elastic behavior of a lattice is described by its matrix of second order elastic constants as shown in Eq. (1) [36].

$$C_{\mathit{ij}}=\frac{1}{V_0}\left(\frac{{\partial }^{2}E}{{\partial }_{{\epsilon }_i}{\partial }_{{\epsilon }_j}}\right)$$E1

Where: E is the energy of the crystal, V₀ is the equilibrium volume and ε is strain. The elastic matrix has a size of 6 × 6 and is symmetric, thus composed of 21 independent components. A crystalline structure is stable in the absence of external load and in the harmonic approximation only if all its phonon modes have positive frequencies for all wave vectors. The elastic energy E is given by Eq. (2), and E₀ is the minimum energy of a relaxed crystal structure. The equation gives the energy of the crystal from the arbitrary deformation by an infinitesimal strain [36].

$$E=E_0+\frac{1}{2}{V}_0{\sum }_{i,j=1}^6{C}_{\mathit{ij}}{\epsilon }_i{\epsilon }_j+O\left({\epsilon }^3\right)$$E2

For cubic crystals, the minimum energy conformation requires about four simulations. The derivation of coefficients requires an additional three or four simulations per independent coefficient. Fifteen energy calculations are required from which three independent constants C₁₁, C₄₄ and C₁₂ are derived for a cubic crystal. The mechanical stability criteria for cubic system is explained in [37] and is given as follows:

$$C_{11}-C_{12}>0;C_{44}>0;C_{11}+2C_{12}>0$$E3

Using the calculated equilibrium lattice constants, the single-crystal elastic constants for B2 Ti_50−xNb_xRu₅₀ lattice structures were calculated in the current study in order to determine the effects of systematically substituting Ti with Nb on the stability and elastic properties of the B2 phase. There is currently no experimental values available for comparison for these ternary alloy compositions, only the Vickers hardness (VH) of TiRu has been found to be around 400 GPa [3]. Based on these three independent single crystal elastic constants of a cubic crystal, the tetragonal shear modulus C′ is determined using the following expression:

$$C^{\prime }=\frac{C_{11}-C_{12}}{2}$$E4

The tetragonal shear modulus has been found to be significant in quantifying the mechanical stability. A positive C′ indicates the mechanical stability of a crystal [38]. Table 2 shows the calculated elastic constants C_ij and C′.

x (at.% Nb)	Elastic constants (GPa)
	C11	C44	C12	C′
0.00	421	88	114	154
6.25	401	86	119	141
12.50	396	87	133	132
18.75	342	84	160	91
25.00	297	84	195	51

Table 2.

Theoretical single-crystal elastic constants of B2 Ti_50−xNb_xRu₅₀ alloys.

The calculated elastic constants are all positive, which indicates that the mechanical stability criteria in Eq. (3) is satisfied. Also the tetragonal shear modulus C′ is positive, which further indicates the stability of B2 phase. Since these calculations are carried out at 0 K temperature, this therefore implies that B2 phase is stable even below room temperature. Figure 5 shows the graphical presentation of the elasticity data, and it can be observed that C′ decreases with increasing Nb concentration (i.e., with decreasing Ti concentration). While elastic constant C₄₄ remains almost constant, the C′ reduces slightly for Nb compositions up to 12.50 at.% (change <15 GPa), mainly due to high mechanical stability of B2 TiRu and its strong bonding character, hence the small increment in Nb does not create a significant change. However, at 18.75 at.% Nb and above, the decrease in C′ starts to be more pronounced. This decrease is attributed to higher content of more ductile Nb in the place of less ductile Ti. As indicated, presence of Nb results in the expansion of the average volume per atom in Ti-Nb-Ru, which means a decrease of the average bond strength and consequently reduces the ability of the alloy to resist the tetragonal shear. Furthermore, the crystal structure theory of transition metals states that solids with increasing d-occupation number increases its metallicity, a factor that is linked to ductility [39].

Figure 5.

Elastic constants of Ti_50-xNb_xRu₅₀ alloys as a function of Nb content.

The stability of B2 TiRu phase has been experimentally studied by Murray [1] as indicated by the phase diagram in Figure 1 in the introductory chapter. It was shown that, the B2 phase undergoes congruent melting at about 2130°C. Below this temperature the B2 phase remains stable to low temperatures for compositional ranges of 45 to 52 at.% Ru. The obvious observation here is that with higher Ru concentration the crystal structure moves from being disordered β to ordered B2. At this point, it was beneficial to study the mechanical properties of the ordered B2 structures in order to further gain an insight on the underlying contribution of Ru. As indicated, the introduction of Nb has proven to reduce the stability of B2 phase as shown by a substantial decrease in C′, thus we also further investigate the impact of Nb addition on other mechanical properties.

3.2 Bulk modulus, B

The bulk modulus is a measure of resistance to volume change or to compression deformation by applied pressure. Based on the three independent single-crystal elastic constants of a cubic crystal, the bulk modulus B is expressed as follows [40]:

$$B=\frac{C_{11}+2C_{12}}{3}$$E5

Figure 6 shows the graph of B for B2 Ti_50−xNb_xRu₅₀ alloys. The B varies with increasing Nb content. Previous studies have suggested that crystals with larger lattice constants possess lower average bond strength and thus can be easily compressed compared to those with smaller lattice constants [39]. As such, an anomalous behavior is observed in this study where in general both lattice parameter and B increase with increase in Nb, despite the surprising decrease in B at 6.25 at.% Nb. This observation can be explained using valence electron density theory. Previous studies have reported that B has a direct relationship with valence electron density, that is, more electrons will correspond to greater repulsions within a structure [41]. The bulk moduli for the first 94 periodic table elements are shown in Figure 7 [43]. It is shown that the B of Ru is amongst the highest values and that of Nb is greater than B of Ti. Also, it can be seen that there are large variations in moduli with atomic number. The maxima is observed when the valence shells of rows one and two are half full electrons and when the transition shells d-orbitals (3d, 4d 5d) are roughly half filled.

Figure 6.

Bulk modulus B of B2 Ti_50−xNb_xRu₅₀ alloys.

Figure 7.

Natural logarithm of bulk modulus as a function of atomic number [42].

3.3 Shear modulus, G

Shear modulus is a measure of resistance against changes in atomic bond length and angle or resistance to shape change. It can be expressed using Eq. (6) [40]. A larger shear modulus means greater ability to resist shearing forces. Figure 8 shows that shear modulus decreases with increasing Nb content. At first, Nb additions below 12.50 at.% show small change less than 5 GPa, then a significant decrease of about 15 GPa is observed as the Nb content is increased beyond that. This demonstrates that Ti₅₀Ru₅₀ has a higher tendency to resist motion of planes within a solid parallel to each other [42]. This is the reason why such an alloy is not desirable for development of superelastic materials because from crystallographic point of view, the transformation from B2 to low temperature phase occurs by Bain strain and lattice-invariant shear. The Bain strain consist of atomic movements needed to produce new structure from the parent phase, while the lattice invariant shear is an accommodation step.

Figure 8.

Shear modulus G of B2 Ti_50−xNb_xRu₅₀ alloys.

The general mechanisms by which this happens is either by slip or twinning. Twinning is unable to accommodate volume changes but, accommodation is achieved by shape change in a reversible way. Therefore, here we observe that the addition of Nb is necessary in order to induce (to a certain degree) shear deformation that is required for phase transformation to occur by twinning.

$$G=\frac{1}{2}\left[\frac{C_{11}-C_{12}+3C_{44}}{5}+\frac{5C_{44}\left(C_{11}-C_{12}\right)}{4C_{44}+3\left(C_{11}-C_{12}\right)}\right]$$E6

3.4 Young’s modulus, E

Young’s modulus (E) is the measure of a material’s ability to withstand changes in length when under tension or compression (material’s stiffness). This mechanical feature is important in biomedical materials for determining the specific implant application. For instance, if an implant has a greater E than the replaced bone, stress shielding occurs. This stress shielding effect prohibit the transfer of needed stress to the adjacent bone, which leads to bone resorption around the implant and consequently cause death of bone cells. Therefore, an ideal biomedical material should have combined properties of modulus closer to that of bone and high strength to sustain a long term service period and reduce revision surgery. Figure 9 shows a typical compressive E of different types of human soft bone [44].

Figure 9.

Young’s modulus E (GPa) of human bone [44].

Apart from transformation strain, it is also well established that SE is dependent on the E of the material. The degree of SE is typically small for alloys with high E compared to ones having low E, as shown in a schematic diagram in Figure 10 (Spring back = SE) [45]. Here, the theoretical elastic constants data have been used to predict the E of B2 Ti_50−xNb_xRu₅₀ at 0 K. Figure 11 shows the E across different compositions. The composition dependence trend is similar to that of shear modulus, with highest value being 372 GPa for Ti₅₀Ru₅₀. Again, further substitution of Ti with Nb reduces the E to less than 150 GPa. Based on the predicted trend, it is anticipated that increasing Nb composition further than considered in this study might result in E closer to 50 GPa which will be closer to that of B2 TiNi and human bone [46, 47]. As a result, the current predicted data is encouraging to pursue this work further.

Figure 10.

The relationship between E and SE [45].

Figure 11.

Young’s modulus E of B2 Ti_50−xNb_xRu₅₀ alloys.

On contrary to what has been believed to be a disadvantage in terms of high E, recently other researchers have found that high E can be of advantage if all other biomedical aspect are taken into consideration. For example, Nakai et al. [45] discussed that surgeons specializing in spinal diseases pointed out that the amount of SE in implant rods must be balanced such that it offers better handling during operation, but also be ductile enough not to create stress shielding for the patient. Moreover, biomaterials with higher E and consequent high yield strength have received much attention lately in the development of alternative porous orthopedic implants via powder metallurgy routes such as additive manufacturing (AM) techniques [48]. The porosity route is viewed as one of the viable means to reduce E and thus overcome stress-shielding health-risk.

Therefore, in order to satisfy both surgeon and patient’s requirements, the E should be adjusted by phase transformations. That is, during deformation, phase transformation occurs such that the new phase introduces high E, while the non-deformed part remains low. That is, in orthopedic operations for treating spinal diseases, the implant rod is bent so that it corresponds to the curvature of the spine. Thus, an alloy with desired superelastic properties can be designed to suit the surgeon’s requirement. Then during operation, while the material is bent, the new deformation-induced phase with high Young’s modulus is formed for surgeon’s requirement and the non-deformed part remains low for patient comfort. The illustration in Figure 12 demonstrates how the Young’s modulus can be adjusted in β alloys [45]. This can similarly be true for B2 alloys, as we have observed that the effect of Ru is the same in both β and B2 alloys, although with B2 alloys, the deformed part may need to have lower E.

Figure 12.

Illustration of self-adjustment of Young’s modulus in implant rod [45].

3.5 Stiffness ratios

The brittle/ductile behavior of materials can be determined using the Pugh’s modulus ratio k = G/B [40]. The k ratio highlights the relationship between the elastic and plastic properties of crystalline materials, where brittle materials have high k values (>0.57) and ductile materials have low ones (<0.57) [41]. It is known that with approximately equal values of shear G and bulk B moduli under applied tensile stress, atomic bonds in local volume tend to dilate and rotate. This occurs instead of the domination of uniform rotation that leads to shear deformation in the plastic stage in crystals whose B is significantly greater than G. This means that atoms in local volume undergo a random movement under applied stress and if strain rate exceeds the rate of atomic relaxation, the amorphous state may result [49].

Moreover, in simple tension or compression tests, a force is applied to a rod parallel to its axis creating a tensile or compression stress. The rod responds by either elongating (tensile) or shortening (compression), leading to change in axial strain (±ε = Δl/l) to a fractional amount. This results in simultaneous decrease (or increase under compression) of its cross-sectional area. The ratio of transverse contraction, −(Δd/d), to the longitudinal extension, (+ε = Δl/l), is the Poisson ratio υ [43].

In order to predict the stiffness ratio of B2 Ti_50−xNb_xRu₅₀ alloy composition, we used both Pugh’s ratio and Poisson ratio. Figure 13 shows the calculated ratios with respect to composition. As expected, the k ratio plot trend shows that B2 Ti₅₀Ru₅₀ is more brittle than presently considered ternary alloy compositions, as indicated by decreasing values. This agrees well with experimental data that was reported by Tsuji et al. [3], where TiRu was measured to have hardness of about 400 GPa and it was deduced that the addition of Ru to TiNi increased hardness and thus, decreasing ductility. Thus we see that high Ru alloys are brittle, leading to the need to introduce Nb at the expense of reducing Ti in order to induce ductility. The Poisson ratio increases with increasing Nb content, further indicating the improved ductility with Nb additions.

Figure 13.

The calculated stiffness ratios of B2 Ti_50−xNb_xRu₅₀ alloys.

3.6 Possible biomedical applications of Ru-rich alloys

The possible applications of Ru-rich alloys in biomedical filed are summarized in Table 3. The investigated alloys showed that the Young’s modulus of about 100 GPa is attainable, which is attributed to high Ru content. The stiffness ratios also indicated that even with high Ru content the alloy can still be mechanically adjusted to fit in the application criteria. For example, an alloy composition with such high Young’s modulus can be beneficial during the spinal fixation operations. Previously, surgeons had to rely on the phase transformation of β-phase to brittle ω-phase precipitates to prevent the occurrence of superelasticity within the limited time of adapting the spinal fixation device to the physiological curvature of the spine [45, 51]. The currently investigated alloys are structurally more ordered due to stabilizing effect of Ru, and thus the phase transformation to brittle ω-phase is suppressed. The result is that the Young’s modulus does not drastically change during deformation. It is only by continuous cyclic loading after the installation of the implant that the transformation of B2 phase to martensite phase can be observed and this is where the patient can receive the benefit of precipitated soft phase to accommodate the surrounding human tissue and prevent stress-shielding effect. Therefore, this means that the correct alloy composition of B2 Ti_50−xNb_xRu₅₀ can be developed for use in the design of spinal fixation devices.

Device type	Ru-effect on properties
Spinal fixation devices	Increased Young’s modulus reduces the spring-back during the operation [45, 50] Ultra-low magnetic susceptibility [2]
Removable internal fixation devices, e.g. bone plates	Inhibition of precipitation of calcium phosphate, thus allowing easy removal of an implant at the end of healing process [51]
Orthopedic implants	Addition of Ru in βTiNb alloys increased tensile and fatigue strength [2, 4] Stability of high temperature phase (β or B2) to low temperatures improves possibility of superelasticity [10, 19, 21, 52]
Vascular stents	Ultra-low magnetic susceptibility [2] Improved corrosion resistance [21]

Table 3.

Possible applications of Ru-rich biomaterials.

Other possible applications of Ru-rich biomaterials is in removable implants such as the internal fixation devices implanted into the bone marrow (e.g. femoral, tibia and humeral marrow), screws used for bone plate fixation and implants used for children. These type of implants may grow into the bone, but it is essential to remove the internal fixation device after surgery, owing to specific local symptoms indications such as palpable hardware, wound exposure of hardware and also the implant may need to be removed in the case where an athlete return to contact sports. Surgeons have experienced difficulties with the removal of these fixation devices because during the assimilation of the device with the bone there is precipitation of calcium phosphate which might cause bone refracture [53].

Thus, in this instance, it is important to prevent the adhesion of the alloys with the bone tissues. This implies that the newly developed alloy must be able to inhibit the precipitation of calcium phosphate. The reactivity of Ru-containing alloys have been found to decrease with increasing Ru-content in tetrazolium salt (MTS) assay, which represents the body fluid [2, 4]. Also Ti has been observed to quickly facilitate the formation of calcium phosphate in order to improve bone adherence. Previously, one had to coat the Ti substrate with the Zr coating which could have resulted in other properties being compromised. Thus for the current alloys with high Ru content, the precipitation of calcium phosphate can be prevented because the Ti content has been reduced and the Ru is non-toxic, allergy-free and has the potency to prevent quick reaction of Ti and consequently reduce deposition of calcium phosphate [53].

Furthermore, in cardiology, the imaging technology can begin with the advent of chest X-ray, in which a topographic image of a heart could be done in different projections. This is often done by multiple projections to help analyze cardiac structures and the location of abnormalities. It has been reported that most conventional metallic biomaterials with high magnetic susceptibility have adverse effect on the MRI and diagnostics. The resulting artifacts can distort the authentic bio-imaging of the human organs and tissues around the implant. Materials and devices with an ultra-low magnetic susceptibility are required for surgery and diagnostics performed under MRI [2]. Addition of Ru can improve/lower magnetic susceptibility as observed in the Zr-Ru alloys where an ultra-low magnetic susceptibility was obtained with increasing Ru content [2].

4. Conclusions

In this study the B2 TiRu alloy has been modified in order to improve the underlying mechanical properties required in biomaterials. The advantages of Ru addition have been outlined, which include biocompatibility, improved corrosion resistance, β-stabilizer and also B2 stabilizer and ultralow magnetic susceptibility. However, high Ru content of about 50 at.% results in a more ordered structure, which has adverse effects on the mechanical properties. Therefore, although it may be beneficial to have a high Ru alloy, it is also crucial to identify the shortfalls arising due to Ru addition. The approach used started with TiRu binary compound, which is known to be hard and brittle. In order to induce beneficial mechanical properties for biomedical applications, the systematic substitution of Ti with Nb was performed.

The results showed that 50 at.% Ru constitute to high stability of B2 phase at 0 K, such that even with increasing Nb content, B2 phase remained highly stable (C′ positive). The bulk modulus showed variation with increasing Nb content, whilst the shear modulus decreased with increasing Nb content. Also, of importance to the design of biomaterials is SE, which is dependent on both the transformation strain and Young’s modulus. The Young’s modulus decreased with increasing Nb content. Therefore, in order to design an alloy with beneficial properties for both surgeons and patients, we propose higher Nb content towards potential high temperature shape memory alloy B2 Nb₅₀Ru₅₀. Current results are encouraging that by increasing Nb content it could be possible to identify ternary B2 Ti_50−xNb_xRu₅₀ composition that has Young’s modulus closer to 50 GPa which will be closer to that of B2 TiNi and human bone. This means that we are able to retain high Ru with said biomedical properties, whilst achieving the desired mechanical properties.

Acknowledgments

The authors acknowledge the Advanced Materials Initiative (AMI) of the Department of Science and Innovation (DSI) through Mintek for their financial support. The authors are also grateful to the National Research Foundation (NRF) South Africa—JSPS GRANT No: 148782. The gratitude is also extended to the Centre for High-Performance Computing (CHPC) in Cape Town for allowing us to carry out the calculations using their remote computing resources.

Conflict of interest

The authors declare no conflict of interest.