**Preface to "Ti-Based Biomaterials"**

Dear Readers,

Recently, great attention has been paid to biomaterials that can be safely used in the human body to prepare parts that replace failed bone structures. Of all materials, Ti-based materials are the most desirable, because they provide an optimum combination of mechanical, chemical, and biological properties. Ti and its compounds are one of the most-investigated biomaterials, and, thus, this book has been proposed as a means to present recent developments in the field of Ti-based biomaterials and is a compilation of 20 articles included in this Special Issue of the MDPI journal Materials, entitled "Ti-Based Biomaterials: Synthesis, Properties and Applications" (https://www.mdpi.com/ journal/materials/special issues/Ti Based Biomaterials). The articles included in this Special Issue demonstrate the top results of scientists working in Australia, Brazil, China, Czech Republic, Egypt, Germany, Italy, Japan, Poland, Romania, Slovenia, South Africa, South Korea, Sweden, and Taiwan. Most of the articles are the results of international cooperation. The included articles mainly focus on β-type Ti alloys, shape memory alloys, nanostructure formation, additive manufacturing, and surface treatment. Microstructure, mechanical properties, and biocompatibility were reported.

The goal of this Special Issue is to provide comprehensive and broad knowledge about Ti-based biomaterials. The content of the book can be useful for students, engineers, researchers, academics, and other specialists whose interests are focused on Ti-based biomaterials development, manufacturing, and application.

I express my appreciation to all of the authors for their contribution.

**Jarosław Jakubowicz** *Special Issue Editor*

### *Editorial* **Special Issue: Ti-Based Biomaterials: Synthesis, Properties and Applications**

#### **Jarosław Jakubowicz**

Poznan University of Technology, Institute of Materials Engineering, Jana Pawla II no 24, 61-138 Pozna ´n, Poland; jaroslaw.jakubowicz@put.poznan.pl; Tel.: +48-061-665-3571

Received: 2 April 2020; Accepted: 3 April 2020; Published: 5 April 2020

**Abstract:** In the last half century, great attention has been paid to materials that can be used in the human body to prepare parts that replace failed bone structures. Of all materials, Ti-based materials are the most desirable, because they provide an optimum combination of mechanical, chemical and biological properties. The successful application of Ti biomaterials has been confirmed mainly in dentistry, orthopedics and traumatology. The Ti biomaterials provide high strength and a relatively low Young's modulus. Titanium biocompatibility is practically the highest of all metallic biomaterials, however new solutions are being sought to continuous improve their biocompatibility and osseointegration. Thus, the chemical modification of Ti results in the formation of new alloys or composites, which provide new perspectives for Ti biomaterials applications. Great attention has also been paid to the formation of nanostructures in Ti-based biomaterials, which has leads to extremely good mechanical properties and very good biocompatibility. Additionally, the surface treatment applied to Ti-based biomaterials provides faster osseointegration and improve in many cases mechanical properties. The special issue "Ti-Based Biomaterials: Synthesis, Properties and Applications" has been proposed as a means to present recent developments in the field. The articles included in the special issue cover broad aspects of Ti-based biomaterials formation with respect to design theirs structure, mechanical and biological properties, as highlighted in this editorial.

**Keywords:** titanium; biomaterials; biofunctionalization

Biomaterials, especially metal ones, are currently one of the most developed and used groups of materials. Titanium is the basic and one from the best biomaterial elements used in the pure form or as the main component in the biocompatible alloys or composites. Very good properties of titanium and its alloys are not able to cover up a few defects, which include for example chemical reactivity with atmospheric gases. Pure Ti, Ti alloys and Ti matrix composites are widely used in different fields. The titanium materials classification is based on structure at equilibrium state. Alloys of α, α + β and β structure are used in biomedical applications. The last one seems to be the most perspective, because theirs high biocompatibility and lowest among Ti alloys Young's modulus, close to that of human bone, causes reduce stress shielding. Careful choice of chemical composition and processing parameters allow to design titanium biomaterials for most biomedical applications. The properties of Ti-based biomaterials should be as close as possible into the properties of the body element that the implant replaces. Hence the Young's modulus is a key factor in biomaterials selection, preferring the titanium for hard tissue implants. Despite the very good properties of titanium and its alloys or composites, some properties are inadequate for biomedical device requirements. For example, wear resistance is poor and requires surface treatment. Deposition of more biocompatible surface layers provides safer used of implants. The nanocrystalline materials are a new group with interesting properties and a growing importance among of titanium biomaterials.

The special issue Ti-Based Biomaterials: Synthesis, Properties and Applications has been proposed to shows recent developments in the field of most extensively investigated and promising metallic biomaterials, and for this reason the nineteen articles included many different, however related aspects of Ti-based biomaterials. All the articles published in the special issue show the most important achievements in Ti-based biomaterials, useful for broader applications. A significant part of the articles included in the special issue focus on β-type Ti alloys, which are the most interesting among Ti alloys family. The β-type Ti alloys shows low modulus of elasticity and high biocompatibility, pointing the perspective and successful applications in hard tissue surgery. In the article by Bai et al. [1], the perspective β-type Ti-Mo alloys modified with Zr were presented. In the Ti-Mo-Zr system the diffusion coefficients were assessed to develop a self-consistent atomic mobility database of bcc phase. The calculated diffusion coefficients were compared with the experimental results showing good agreement. Sandu et al. [2] presents new β-type Ti-Mo alloys modified by Si, Zr and Ta, which shows very low Young's modulus with perspective dental and orthopedic implant applications. Kuroda et al. [3] focus on the β-type Ti-Ta-Zr ternary alloys. The article shows combination of different processing routes (hot-rolling, annealing and solution treatment) for design of alloys of different mechanical properties (hardness and Young's modulus). Fowler et al. [4] modified Ti-Nb-Ta-Zr alloy by addition of antibacterial Cu. As the effect of microstructural changes, the few % of Cu addition results in significant increase of alloys hardness. Consequently, in work [5], Fowler et al. continue study of Cu effect on antibacterial properties of Ti-Cu alloys. Generally, the Ti alloys had good antibacterial rates above 5 wt.% Cu content, however, the un-aged Ti-10 wt.% Cu alloy provide a good antibacterial effect, with superior hardness and corrosion protection. In addition to bulk β alloys, its porous form is very attractive for implant application. Formation of β-type Ti-Ta foams of 60%–76% porosity in the dealloying process was presented by Adamek et al. [6]. The nanocrystalline Ti-Ta-Mg powder mixture was prepared by mechanical alloying. Cold pressing followed by sintering at temperature above boiling point of Mg lead to its removal from the alloy matrix leaving the pores. The foams show mechanical and biological properties respective for hard tissue implant application.

Shape memory alloys are the second group of Ti-based materials with growing research interest in biomedical industry. Lee et al. [7] shows mechanical stability of the elastic nails made of the Nitinol shape memory alloy and compare them to titanium and stainless steel nails in the fixation of diaphyseal long bone fractures. The titanium nails have been recommended as C-shaped ones for diaphyseal long bone fractures when the end cap is not used. For Nitinol and stainless steel nails, use of the end cap prevent the nail from dropping out and provide bone fracture stabilization [7]. The Finite Element Method (FEM) model was compared with experimental results. The Nitinol was studied by Feng et al. [8], with respect to surface properties. The surface was modified using magnetic field-assisted Electrical Discharge Machining (EDM). Under the careful control of discharge conditions is generated a porous surface of different morphology and roughness, which finally effect on surface wettability. The main problem related with most commonly used Nitinols as shape memory alloys in medical industry is Ni as carcinogen. Nagoshi et al. [9] shows shape memory Ni-free β-type Ti-Nb alloys. The mechanical behavior of single crystalline micropillars was investigated in the microscale at various temperatures and crystal orientations to shows anisotropic deformation behavior and shape memory effect. The shape memory parts can work in biomedical microelectromechanical systems (Bio-MEMS).

Another group of Ti-based materials was presented by Miklaszewski and Jurczyk [10]. The Ti-TiB Metal Matrix Composites (MMC) were made using mechanical alloying of elemental Ti and B powders and pulse plasma sintering (PPS) for bulk sample generation. The Ti matrix is reinforced by TiB phase, which crystallizes during powders sintering in the PPS process. The processing conditions strongly effect on the structure and high mechanical properties of the ultrafine grains Ti-TiB composite.

New manufacturing methods are as often investigated as the Ti-based biomaterials themselves. In the work by Wei et al. [11], the Laser Additive Method (LAM) for the production of β-type Ti-Nb alloy has been shown. They used mixture of the elemental powders, which was directly melted under the laser beam. The additive technology in formation of alloy by melting of the powders mixture has many advantages over the melting prealloyed powders. The further annealing plays a key role for structure

optimization and tailoring the mechanical properties. In the work by Bassoli and Denti [12], they focus on additive manufacturing (Laser Powder Bed Fusion—L-PBF) applied for synthesis Ti-6Al-4V for dental applications. The mechanical and structural properties were investigated, correlated and compared to those obtained for Co-Cr-Mo alloys. They found absence of secondary anisotropy in the L-PBF prepared specimens. Hsu et al. [13] applied Selective Electron Beam Additive Manufacturing (SEBAM) for the formation of Ti-6Al-4V under gradient energy density carried out on a specimen from the bottom to the top. This implies structural changes affecting the mechanical behavior.

According to Hall-Petch relation, the grain refinement leads to increase of materials strength. This relationship is used in Ti and its compounds. Different methods, based on severe plastic deformation (SPD) processes provide nano- or ultrafine structure of high strength and additionally good biocompatibility. Palán et al. [14] show properties of pure Ti after SPD processes (conform SPD and rotary swaging). They produced wires with ultrafine grains for medical implants. The process can be used in the large scale with low cost and the final products have ultimate strength around 1 GPa for Grade 2 cp-Ti.

Titanium shows good biocompatibility, however in some cases not sufficient for many applications. For the better osseointegration a different surface treatment is used for Ti parts surface modification. In the work by Elsayed et al. [15], the sphene (Titanite—CaTiSiO5) bioactive coatings were deposited on Ti substrate by airbrush spray technology using preceramic polymer with nano-sized precursors. The room temperature process deposition with subsequent heating results in crack-free coatings. The sphene coatings have good chemical stability, support hADSCs attachment, proliferation and differentiation in vitro. Authors point a potential for use of sphene bioactive coatings on orthopedic and dental implants. The surface treatment was undertaken by Benˇcina et al. [16] to generate TiO2 nanotubes on Ti substrate. The work describes crystallization process of the electrochemically made amorphous TiO2 nanotubes under a low pressure non-thermal oxygen plasma conditions. The surface can be potentially used for blood contacting devices because no platelet adhesion or activation on surfaces was observed. The biocompatibility improvement of the titanium maxillofacial plates treated with amine plasma-polymerization has been presented by Jeong et al. [17]. The Ti surface treatment undergoes through formation of polyallylamine ultra-thin film, which improved the hydrophilicity and biocompatibility confirmed in both in vitro and in vivo tests. The process applied for Ti surfaces can lead to shorten the time required for osseointegration and bone regeneration. In addition to the Ti surface modification, the Ti coatings can be deposited on different substrates for improvement their biocompatibility. In the work [18], Wypych et al. shows the Titanium Plasma Spraying (TPS) applied to polymer substrates. The Ti coatings exhibit a typical for TPS multilayer morphology of low porosity and good adhesion to polyethylene and glass fiber-reinforced polyamide. The Ti coatings did not fall off the substrate after its significant bending deformation. The TPS coatings have significantly greater hardness and Young's modulus in comparison to the properties of the polymer substrates.

Finally, having materials and technology, it is possible to produce a biodevice. In this case, the numerical simulations including FEM can be helpful and are one of the steps for successful biodevice implementations. Gruenwald et al. [19] pointed that Ti electrical conductivity presents a challenge for the electromagnetic transmission of data and power. In article [19], the authors proposed a fast and practical method to determine the necessary transmission parameters for titanium encapsulated implants with inductive transmission, for example implanted infusion pump (with an external controlling device).

Summarizing, the special issue Ti-Based Biomaterials: Synthesis, Properties and Applications shows current achievements in Ti-based materials, pointing future research trends in this field of interest.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**

1. Bai, W.; Xu, G.; Tan, M.; Yang, Z.; Zeng, L.; Wu, D.; Liu, L.; Zhang, L. Diffusivities and Atomic Mobilities in bcc Ti-Mo-Zr Alloys. *Materials* **2018**, *11*, 1909. [CrossRef] [PubMed]


© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Diffusivities and Atomic Mobilities in bcc Ti-Mo-Zr Alloys**

**Weimin Bai 1, Guanglong Xu 2, Mingyue Tan 1, Zhijie Yang 1, Lijun Zeng 1, Di Wu 1, Libin Liu 1,\* and Ligang Zhang 1,\***


Received: 18 September 2018; Accepted: 5 October 2018; Published: 8 October 2018

**Abstract:** β-type (with bcc structure) titanium alloys have been widely used as artificial implants in the medical field due to their favorable properties. Among them, Ti-Mo alloy attracted numerous interests as metallic biomaterials. Understanding of kinetic characteristics of Ti alloys is critical to understand and manipulate the phase transformation and microstructure evolution during homogenization and precipitation. In this work, diffusion couple technique was employed to investigate the diffusion behaviors in bcc Ti-Mo-Zr alloys. The diffusion couples were prepared and annealed at 1373 K for 72 h and 1473 K for 48 h, respectively. The composition-distance profiles were obtained via electron probe micro-analysis (EPMA). The chemical diffusion coefficients and impurity diffusion coefficients were extracted via the Whittle-Green method and Hall method. The obtained diffusion coefficients were assessed to develop a self-consistent atomic mobility database of bcc phase in Ti-Mo-Zr system. The calculated diffusion coefficients were compared with the experimental results. They showed good agreement. Simulations were implemented by Dictra Module in Thermo-Calc software. The predicted composition-distance profiles, inter-diffusion flux, and diffusion paths are consistent with experimental data, confirming the accuracy of the database.

**Keywords:** bcc Ti-Mo-Zr alloys; Inter-diffusion coefficient; Impurity coefficient; Atomic mobility; CALPHAD modeling

#### **1. Introduction**

Due to their biocompatibility, low modulus, high specific strength, and high corrosion resistance, β-type (with bcc structure) and near β titanium alloys have been widely used as surgery implants [1–4]. Previous studies have verified that Nb, Zr, Mo, Hf, and Ta are effective alloying elements leading to low elastic modulus, nontoxic, and non-allergic β-Ti alloys [4–6]. Moreover, Zr can increase hardenability and corrosion resistance for the alloy [7,8]. Mo is a strong β-phase stabilizing element for titanium alloys and the Ti-Mo based alloys exhibit adequate mechanical compatibility and good cyto-compatibility [9–12]. Therefore, the Ti-Mo-Zr system, which showed good performances and magnificent prospects in biomaterial application, has been intensively studied [3,6,10–13]. Several alloys related to the Ti-Mo-Zr system have been investigated recently, for example, Ti-12Mo-6Zr-2Fe [14], Ti-15Mo-5Zr-3Al [15], and Ti-8Mo-4Nb-2Zr [6].

Inter-diffusion in alloys plays an important role in materials processing. Understanding diffusion kinetics of Ti alloys is critical to manipulate phase transformation and microstructure evolution during homogenization and precipitation [16–18]. The reliable inter-diffusion coefficients are the essential input parameters in various quantitative modeling of phase transformation [17,19,20]. It is also valuable to determine thermodynamic stability under long-term service conditions.

Inspired by the CALPHAD (CALculation of PHAse Diagram) method, Andersson and Ågren [21] developed a phenomenological kinetic technique which present the atomic mobilities of individual species using Redlick-Kister polynomials. This technique assesses the discrete diffusion coefficients that were extracted experimentally and then employs a set of parameters to describe composition dependent mobilities and diffusivities. Combined with thermodynamic information, diffusion simulation can be implemented in DICTRA module embedded in Thermo\_Calc software [22,23].

Various of measurements of self- and impurity diffusion coefficients in bcc Ti, Zr, and Mo have been conducted [24] as well as inter-diffusion coefficients in bcc Ti-Mo [25–27], Ti-Zr [28–31] and Mo-Zr alloys [32]. Based these diffusion coefficients, Liu et al. [33,34] assessed the atomic mobilities in bcc Ti-Mo, Ti-Zr, and Mo-Zr alloys with the CALPHAD method. Simulations of concentration profiles and Kirkendall movement using these mobility parameters show good agreement with the experimental results from literatures. However, the ternary diffusion coefficients and mobilities in bcc Ti-Mo-Zr alloys is still open to be evaluated and barely reported. The purpose of this work is to study the diffusion behavior of Mo and Zr in β-Ti alloys and establish a CALPHAD-type atomic mobility database of bcc phase in Ti-Mo-Zr system.

#### **2. Model**

#### *2.1. Extraction of Inter-Diffusion Coefficients and Impurity Diffusion Coefficients*

According to Kirkaldy [35], in one dimension, the inter-diffusion flux of component *i* with concentration *ci* in a ternary system can be expressed as:

$$\hat{f}\_i = \frac{1}{2t} \int\_{c\_i^-}^{c\_i} (z\_i - z\_0) dc\_i = -\sum\_{j=1}^2 \hat{D}\_{ij}^k \frac{\partial c\_j}{\partial z},\tag{1}$$

where *Dk ij* are the inter-diffusion coefficients;*ci*, *cj* are the concentration of species *i* and *j*; *c*<sup>−</sup> *<sup>i</sup>* is the concentration of *i* at the left end of the diffusion couple; *z* is the distance; *z*<sup>0</sup> is the Matano plane for the diffusion couple; and, *t* is the diffusion time.

In a ternary system, it involves four independent diffusion coefficients, *D*-3 <sup>11</sup>, *D*-3 <sup>22</sup>, *D*-3 <sup>12</sup> and *D*-3 21. However only two composition-distance profiles for independent elements 1 and 2 can be derived from one diffusion couple. Hence, two diffusion couples result in two diffusion paths which intersect at one point, are needed to obtain four profiles. Then, the diffusion coefficients at this point can be solved mathematically. The old-fashioned Boltzmann-Matano had to position the Matano planes of four profiles, which is time-consuming and might lead to unnecessary inaccuracy. To avoid this drawback, Whittle and Green [36] introduced a normalized concentration variable:

$$Y\_i = \frac{c\_i - c\_i^-}{c\_i^+ - c\_i^-} \,\prime \tag{2}$$

where *c*− *<sup>i</sup>* and *<sup>c</sup>*<sup>+</sup> *<sup>i</sup>* are concentrations of two elements in the left and right end of the diffusion couple.

With the variable *Y*, the inter-diffusion flux of element *i* is no longer referred to a fixed laboratory coordinate and can be transformed into:

$$\widetilde{\chi}\_{i} = \frac{\left(\mathbf{c}\_{i}^{+} - \mathbf{c}\_{i}^{-}\right)}{2t} \left[ (1 - \mathbf{Y}\_{i}) \int\_{-\infty}^{z} \mathbf{Y}\_{i} dz + \mathbf{Y}\_{i} \int\_{-\infty}^{z} (1 - \mathbf{Y}\_{i}) dz \right]. \tag{3}$$

Reformulating the right-hand side of Equations (1) and (3) lead to:

$$\frac{1}{2t} \left( \frac{dz}{d\varUpsilon\_i} \right) \left[ (1 - \varUpsilon\_i) \int\_{-\infty}^z \varUpsilon\_i dz + \varUpsilon\_i \int\_{-\infty}^z (1 - \varUpsilon\_i) dz \right] = \tilde{D}\_{ii}^k + \tilde{D}\_{ij}^k \frac{d\kappa\_j}{d\kappa\_i} (i = 1, 2). \tag{4}$$

By solving a set of four equations from one pair of diffusion couples, the diffusion coefficients *D*-*Ti MoMo*, *D*-*Ti ZrZr*, *D*-*Ti MoZr* and *D*-*Ti ZrMo* at the intersecting composition can be extracted. Note that the molar volume was taken to be constant for the lack of reliable data on the composition-dependent molar volume in bcc Ti-Mo-Zr alloys. Errors that are introduced by this approximate treatment are believed to be within the accuracy of the results obtained via the Whittle-Green method [36].

By applying a generalized Hall method [37,38], the impurity diffusion coefficients of Zr in Ti-Mo alloys and Mo in Ti-Zr at the terminal compositions of the diffusion couples can be obtained. The profiles were transformed to a plot of *μ vs λ*, in which erf*μ* = 2*Y* − 1 and *λ* = *z*/ <sup>√</sup>*t*. By fitting the plot with a linear equation *μ* = *hλ* + *k*, the *h*1, *k*<sup>1</sup> for the left terminal, and *h*2, *k*<sup>2</sup> for the right terminal of the diffusion couples can be obtained and the impurity diffusion coefficients can be derived via the following formulas:

$$\tilde{D}(z') = \frac{1}{4h\_1^2} \left[ 1 + \frac{2k\_1}{\sqrt{\pi}} \exp\left(\mu^2\right) \times Y(z') \right],\tag{5}$$

$$\check{D}\left(z'\right) = \frac{1}{4h\_2^2} \left[1 - \frac{2k\_2}{\sqrt{\pi}} \exp\left(\mu^2\right) \times \left[1 - \chi\left(z'\right)\right]\right],\tag{6}$$

where *ci* represents the content of *i* in binary alloys and *c*<sup>0</sup> is the content of *i* at the other end of the diffusion couple.

#### *2.2. Atomic Mobility and Diffusivity*

As initiated by Andersson and Ågren [21] and later modified by Jönsson [39], the atomic mobility *Mi* of species *i* can be expressed as:

$$M\_i = M\_i^0 \exp\left(\frac{-Q\_i}{RT}\right) \frac{1}{RT} \times^{\text{reg}} \Omega = \exp\left(\frac{RT \ln M\_i^0 - Q\_i}{RT}\right) \frac{1}{RT} \times^{\text{reg}} \Omega,\tag{7}$$

where *R* is the gas constant; *T* is the temperature; *M*<sup>0</sup> *<sup>i</sup>* is the frequency factor; *Qi* is the activation energy; and, *mg*Ω is the ferromagnetic contribution. Since there is no ferromagnetic transition reported in Ti-Mo-Zr alloys, *mg*Ω can be taken as 1. Provided Δ*G<sup>φ</sup> <sup>i</sup>* = *RT* ln *<sup>M</sup>*<sup>0</sup> *<sup>i</sup>* − *Qi*, Equation (7) can be written as [21]:

$$M\_i = \exp\left(\frac{\Delta G\_i^{\phi}}{RT}\right) \frac{1}{RT'} \tag{8}$$

the parameter Δ*G<sup>φ</sup> <sup>i</sup>* is composition dependent and is expressed in the Redlich-Kister polynomial form as:

$$\begin{aligned} \Delta G\_{i}^{\Phi} &= \sum\_{p} \mathbf{x}\_{p} \Delta G\_{i}^{p} + \sum\_{p} \sum\_{q>p} \mathbf{x}\_{p} \mathbf{x}\_{q} \Bigg[ \sum\_{r=0,1,2,\dots} \Delta^{(r)} G\_{i}^{p,q} \left( \mathbf{x}\_{p} - \mathbf{x}\_{q} \right)^{r} \Bigg] \\ &+ \sum\_{p} \sum\_{q>p} \sum\_{v>p} \mathbf{x}\_{p} \mathbf{x}\_{q} \mathbf{x}\_{v} \Bigg\{ \sum\_{s=p,q,\mathcal{D}} \left[ \mathbf{x}\_{s} + \left( 1 - \mathbf{x}\_{p} - \mathbf{x}\_{q} - \mathbf{x}\_{v} \right) / 3 \right] \Delta^{(s)} G\_{i}^{p,q,\mathcal{D}} \Bigg\} \end{aligned} \tag{9}$$

where *<sup>φ</sup>* denotes the solid solution phase; *xp* is the mole fraction of species *<sup>p</sup>*; <sup>Δ</sup>*G<sup>p</sup> <sup>i</sup>* is the value <sup>Δ</sup>*Gi* of species *<sup>i</sup>* in pure species *<sup>p</sup>*; and, <sup>Δ</sup>(*r*)*Gp*,*<sup>q</sup> <sup>i</sup>* and <sup>Δ</sup>(*s*)*Gp*,*q*,*<sup>v</sup> <sup>i</sup>* are the binary and ternary interaction parameters.

Assuming the mono-vacancy exchange is the dominant diffusion mechanism, and neglecting correlation factors, the tracer diffusion coefficients *D*∗ *<sup>i</sup>* of species *i* is directly related to the mobility *Mi* by means of the Einstein relation:

$$D\_i^\* = RTM\_{i\nu} \tag{10}$$

For a substitutional solution phase, the inter-diffusion coefficients in terms of the volume-fixed reference frame is given by the following general expression:

$$
\delta \hat{D}\_{ij}^n = \sum\_k^n (\delta\_{ki} - \mathbf{x}\_i) \mathbf{x}\_k M\_k \left( \frac{\partial \mu\_k}{\partial \mathbf{x}\_j} - \frac{\partial \mu\_k}{\partial \mathbf{x}\_n} \right), \tag{11}
$$

where *δki* is the Kronecker delta (*δki* = 1 when *i=k*, and 0 otherwise).

Then, the inter-diffusion flux of species *i*, -*Ji* can be calculated via Equation (1), and the concentration evolution of component *i* in ternary systems can be solved by the mass conservation law:

$$\frac{\partial c\_i}{\partial t} + \frac{\partial \widetilde{\jmath}\_i}{\partial z} = 0.\tag{12}$$

What calls for special attention in the formula derivation is that the transformation of concentration of species *i*, *ci*, and the mole fraction *xi*:

$$c\_i = \frac{\chi\_i}{V\_m},\tag{13}$$

where *Vm* is the molar volume of a phase that was taken to be constant in this work.

#### **3. Experiment**

Pure Ti, binary Ti-Mo and Ti-Zr alloys, and ternary Ti-Mo-Zr alloys were prepared from pure Ti (99.99 wt %), Mo (99.99 wt %), and Zr (99.99 wt %) by arc melting in electric arc furnace under an argon atmosphere. All of the alloys compositions were designed in the bcc phase region according the binary phase diagram of Ti-Mo [40], Ti-Zr [41], and Zr-Mo [42] systems and ternary phase diagram of Ti-Mo-Zr system at 1473 K [43] (shown in Figure 1). The compositions of all alloys were listed in Table 1. The ingots were re-melted for six times to attain homogeneity and then annealed at 1473 K for 24 h to obtain microstructure with large grain size above millimeters, such that the effect of grain boundary diffusion can be ignored.

The annealed ingots were cut into blocks with a size of 10 × 10 × 5 mm using wire-electrode cutting. After one surface of the blocks polished to mirror-like quality, the well-contacted diffusion couples were assembled with appropriate pairs of blocks in Table 1 under vacuum at 1173 K for 4 h. The diffusion couples were sealed into quartz capsules that were filled with pure argon. The M1-M8 diffusion couples were annealed at 1373 K for 72 h and N1-N8 diffusion couples were annealed 1473 K for 48 h, followed by quenching in ice water.

After the annealing process, the diffusion couples were then cut into halves parallel to the ends using wire-electrode cutting, and then mounted, ground, and polished by standard metallographic techniques. The composition-distance profiles of 16 diffusion couples were determined using electron probe micro-analysis (EPMA, JEOL, JXA-8230, Tokyo, Japan, 15 kV, 20 nA) with 15 kV voltage, 20 nA current, and a 40◦ take-off angle. The accuracy of the EPMA test is >98% (mass percent).

**Figure 1.** Phase diagram of (**a**) Ti-Mo [40], (**b**) Ti-Zr [41], (**c**) Zr-Mo [42], and (**d**) Ti-Mo-Zr [43] systems.


**Table 1.** Compositions of diffusion couples.

#### **4. Results and Discussions**

*4.1. Inter-Diffusion and Impurity Diffusion Coefficients At 1373 K and 1473 K*

All of the diffusion couples show single bcc phase microstructure. The SEM backscattered electron image (BSE) of diffusion zone of the diffusion couple M1 is taken as an example and is presented in Figure 2a. There is no Kirkendal void existing in the diffusion zone and no microstructure is evident, revealing that the alloys were annealed in single bcc phase. After being annealed at high temperature and quenched, the martensite transformation may present in the samples. However, because martensite transformation is a diffusionless phase transformation, the composition profile will not change. We can still extract the diffusion coefficients from the composition profile that was obtained in this sample.

The composition-distance profiles that were determined from couple M2 is shown in Figure 2b. It is worth mentioning that, to avoid the errors from fitting or smoothing, a robust error function expansion (ERFEX) was put forward to represent the experimental profiles in an accurate analytical form [37,44]:

$$X(r) = \sum\_{i} [a\_i \text{erf}(b\_i z + c\_i) + d\_i]\_\prime \tag{14}$$

where *X*(*r*) is the effective alloying element content at location *z*; *a*, *b*, *c*, and *d* are the fitting parameters.

It could be evidenced by practice that the profiles smoothed using ERFEX method exhibits higher accuracy than using traditional method, such as moving average smoothing, Savitzky-Golay smoothing method, and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation, and it can present the details of the composition profiles. For example, the Mo pill-up at the right end of couple M6 (shown in Figure 2c). The ERFEX method also has its advantages in fitting asymmetrical curves when the diffusivities of the elements in one end of the diffusion couple are much larger than that of the other end. The couple M6 is compared with M8, for instance. The left-hand side of M6 is pure titanium and the other end has a high Mo concentration. The slop of profile M6 is steep at the right end of diffusion (Figure 2c). It is because the diffusivity of Mo in Ti alloys is much lower than that of Ti. In comparison, it is appropriately smooth and it shows the conventional S-shape (Figure 2d) in M8. The steep slope will introduce a larger error when calculating the diffusion coefficients at the concentration on it. That means that the accuracy of the calculated diffusion coefficients at the component close to Ti-Mo boundary will be lower.

**Figure 2.** (**a**) Microstructure (BSE) of the diffusion couple M1 annealed at 1373 K for 72 h and the robust error function expansion (ERFEX) representation of the composition-distance profiles of the different couples annealed in 1373 K for 72 h: (**b**) for M2; (**c**) for M6; (**d**) for M8.

The diffusion paths of all diffusion couples after annealing process are presented in Figure 3. According to the Whittle-Green method, the inter-diffusion coefficients at the intersecting compositions can be extracted. The impurity diffusion of Zr in Ti-Mo alloys and Mo in Ti-Zr alloys can be obtained via the Hall method at the ends of couple M1-M5 and N1-N5.

**Figure 3.** Diffusion paths of diffusion couples determined using electron probe micro-analysis (EPMA) after annealing process.

The determined inter-diffusion coefficients are summarized in Table 2 and graphically presented with three-dimensional plots in Figure 4. The standard deviations were determined from four independent calculations upon two independent measurements. All of the results can satisfactorily fulfill the thermodynamic constrains derived by Kirkaldy [45]:

$$
\tilde{D}\_{\rm ZrZr}^{\rm T\overline{\rm T}} + \tilde{D}\_{\rm NbNb}^{\rm T\overline{\rm T}} > 0,\tag{15}
$$

$$
\hat{D}\_{\rm ZrZr}^{\rm Ti} \times \hat{D}\_{\rm NbNb}^{\rm Ti} - \hat{D}\_{\rm ZrNb}^{\rm Ti} \times \hat{D}\_{\rm NbZr}^{\rm Ti} > 0,\tag{16}
$$

$$4\left(\tilde{D}\_{ZrZr}^{\text{Ti}} + \tilde{D}\_{\text{NbNb}}^{\text{Ti}}\right)^2 - 4\left(\tilde{D}\_{ZrZr}^{\text{Ti}} \times \tilde{D}\_{\text{NbNb}}^{\text{Ti}} - \tilde{D}\_{ZrNb}^{\text{Ti}} \times \tilde{D}\_{\text{NbZr}}^{\text{Ti}}\right) \ge 0. \tag{17}$$



**Table 2.** *Cont.*

The impurity diffusion coefficients that were obtained by Hall methods are listed in Table 3, and also illustrated in Figure 4, along with the inter-diffusion coefficients. In Figure 4a,b, the main inter-diffusion coefficients coincide with the impurity diffusion coefficients when the concentration of diffusion elements tends to 0.

Scrutinizing the map of the diffusion coefficients in Figure 4, it can also be observed that, when the concentration of the gradient elements *j* tends to 0, the limit of main inter-diffusion coefficients *Dk ii* will match the binary diffusion coefficients from literature [33] well, and when the concentration of the diffusion elements *i* tend to 0, the limits of cross inter-diffusion coefficients *Dk ij* will be 0. The main diffusion coefficients are larger than the cross ones and they showed less fluctuation than cross ones. Values of *D*-*Ti MoZr* are negative, which means that the element Zr has a negative effect on the diffusion of Mo in Ti-based alloys.

The variation of *D*-*Ti MoMo* and *D*-*Ti ZrZr* with the composition of Mo and Zr at 1373 K are presented in Figure 5. It can be found that *D*-*Ti MoMo* decrease with the increase concentration of Mo in Figure 5a. In Figure 5b, *D*-*Ti MoMo* also decrease with the increase concentration of Zr. However, the decreasing rate varies with different diffusion Mo contents (the three colors correspond to inter-diffusion coefficients extracted from three different diffusion couples, M6, M7, and M8). In general, a great ratio of x(Zr)/x(Mo) slows down the process of decrease. As to *D*-*Ti ZrZr*, as is shown in Figure 5c,d, show similar trends, like *D*-*Ti MoMo*, when it varies with the concentration of Mo and Zr. From these phenomena, we can infer that the influence of element Mo on the variations of *D*-*Ti MoMo* and *D*-*Ti ZrZr* is much larger than Zr.

When extent to boundary, the impurity diffusion coefficients of Mo in Ti-Zr alloys, *D*∗ *Mo*(*Ti*−*Zr*) show an increasing trend with the increase of Zr concentration. The impurity diffusion coefficients of Zr in Ti-Mo alloys *D*∗ *Zr*(*Ti*−*Mo*) show a decreasing trend with the increase of Mo concentration.

Figure 6 presents the three-dimensional (3D) plot of diffusion coefficients in the bcc Ti-Mo-Zr alloys and the variations of *D*-*Ti MoMo* and *D*-*Ti ZrZr* with of the concentration of Mo and Zr at 1473 K. They showed similar trends as those at 1373 K.

**Figure 4.** Three-dimensional (3D) plot of the ternary inter-diffusion coefficients (**a**) *D*-*Ti MoMo*, (**b**) *D*-*Ti ZrZr*, (**c**) *D*-*Ti MoZr* and (**d**) *D*-*Ti ZrMo* in the bcc Ti-Mo-Zr alloys at 1373 K, together with the impurity diffusion coefficients *D*∗ *Mo*(*Ti*−*Zr*) and *<sup>D</sup>*<sup>∗</sup> *Zr*(*Ti*−*Mo*) , and binary diffusion coefficients obtained from the literature [33].

**Figure 5.** The variation of ternary inter-diffusion coefficients with the compositions: (**a**) *D*-*Ti MoMo* with Mo, (**b**) *D*-*Ti MoMo* with Zr, (**c**) *D*-*Ti ZrZr* with Mo and (**d**) *D*-*Ti ZrZr* with Zr at 1373 K.

**Figure 6.** The 3D plot of the ternary inter-diffusion coefficients (**a**) *D*-*Ti MoMo*, (**b**) *D*-*Ti ZrZr*, (**c**) *D*-*Ti MoZr*, and (**d**) *D*-*Ti ZrMo* in the bcc Ti-Mo-Zr alloys and the variation of ternary inter-diffusion coefficients with the compositions: (**e**) *D*-*Ti MoMo* with Mo, (**f**) *D*-*Ti MoMo* with Zr, (**g**) *D*-*Ti ZrZr* with Mo, and (**h**) *D*-*Ti ZrZr* with Zr at 1473 K.


**Table 3.** Impurity diffusion coefficients of Zr in Ti-Mo and Mo in Ti-Zr alloys at 1373 K and 1473 K.

#### *4.2. Atomic Mobilities in bcc Ti-Zr-Mo System*

The DICTRA module that was embedded in ThermoCalc software [21,22] was employed to obtain the atomic mobility parameters for the Ti-Mo-Zr ternary bcc alloys. Mobility parameters of boundary binary systems were taken from Liu's work [33,34]. Thermodynamic description of boundary binary systems were also the same as Liu's work [40–42]. Thermodynamic modeling of bcc phase in the ternary system can be carried out by simply extrapolation based on three binary systems. By assessing the experimental diffusion coefficients in this work, a set of self-consistent atomic mobility parameters were obtained, as listed in Table 4.

Using these parameters and DICTRA software, the inter-diffusion coefficients at the intersection composition at 1373 K and 1473 K were calculated and compared with the experimental results, as shown in Figure 7. The calculated results agree with the main inter-diffusion coefficients well, within the error allowed. In contrast, the cross coefficients show certain fluctuation with a large error range. Since the calculated and experimental cross coefficients show values in the same order of magnitude, and a same variation tendency with compositions, the accessed mobilities are feasible to represent the cross coefficients.

Figure 8 shows the comparison of the calculated impurity diffusion coefficients and the experimental results. The calculated impurity diffusion coefficients also agree well with the experimental results.

In order to further verify the atomic mobility parameters that were obtained in the present work, the simulation of several diffusion couples were implemented. The diffusion simulation was set up to model the semi-infinite ternary diffusion couples in experiment. It was conducted using the same initial conditions and heat treatment processes in the experiment. The predict composition-distance profiles show good agreement with the experimental profiles. For instance, the predicted composition-distance profiles and fluxes of couple M3 and N8 compared with experimental data are exhibited in Figures 9 and 10 presented the simulated diffusion paths of 16 diffusion couples annealed at 1373 K and 1473 K. The calculated results show good agreement with the experimental results.


**Table 4.** Atomic mobility parameters for the bcc phase of the Ti-Mo-Zr ternary system.

**Figure 7.** Calculated inter-diffusion coefficients of the ternary Ti-Mo-Zr system compared with the experimental measurements (in brackets) in this work: (**a**) *D*-*Ti MoMo*, (**b**) *D*-*Ti ZrZr*, (**c**) *D*-*Ti MoZr* and (**d**) *D*-*Ti ZrMo* at 1373 K and (**e**) *D*-*Ti MoMo*, (**f**) *D*-*Ti ZrZr*, (**g**) *D*-*Ti MoZr* and (**h**) *D*-*Ti ZrMo* at 1473 K.

**Figure 8.** Calculated impurity diffusion coefficients (**a**) *D*∗ *Zr*(*Ti*−*Mo*) and (**b**) *<sup>D</sup>*<sup>∗</sup> *Mo*(*Ti*−*Zr*) as compared with the experimental data.

**Figure 9.** Predicted composition-distance profiles and inter-diffusion fluxes of M3 and N8 as compared with experimental data.

**Figure 10.** Simulated diffusion paths for diffusion couples compared with the experimental measurements: (**a**) 1373 K and (**b**) 1473 K.

#### **5. Conclusions**

In this work, two set of diffusion couples of bcc Ti-Mo-Zr alloys were made and annealed at 1373 K for 72 h and 1473 K for 48 h, respectively. The composition-distance profiles of these diffusion couples were determined using EPMA. The ternary inter-diffusion coefficients and impurity diffusion coefficients were extracted using the Whittle-Green and Hall method. Based on the experimental results and thermodynamic descriptions, as well as atomic mobility parameters of the sub-binary systems of Ti-Mo-Zr system, an atomic mobility database for the bcc phase in the Ti-Mo-Zr ternary system was developed. Inter-diffusion coefficients at the intersection points of diffusion couples and impurity diffusion coefficients were calculated using the database and compared with the data extracted directly from the composition-distance profiles. In addition, simulations of the diffusion couples with the same initial conditions and heat treatment processes of the experiment were proceeded. The composition-distance profiles and diffusion paths were compared with the experimental results. All of the calculated results show good agreement with experimental data.

**Author Contributions:** W.B., G.X., L.L. and L.Z. (Ligang Zhang) designed the study. W.B., M.T., L.Z. (Lijun Zeng), D.W and Z.Y. conducted the experiments; W.B., L.Z. (Lijun Zeng) and G.X. analyzed the results. W.B., G.X., L.L, M.T. and L.Z. (Ligang Zhang) contributed to preparation of the manuscript.

**Funding:** The work was funded by Aof the National Nature Science Foundation of China (Grant No. 51671218), the National Key Research and Development Program of China (Grant No. 2016YFB0701301) and the National Key Basic Research Program of China (973Program) (Grant No. 2014CB644000).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Characterization and Mechanical Proprieties of New TiMo Alloys Used for Medical Applications**

#### **Andrei Victor Sandu 1,2,\*, Madalina Simona Baltatu 1, Marcin Nabialek 3, Adriana Savin <sup>4</sup> and Petrica Vizureanu 1,\***


Received: 27 August 2019; Accepted: 11 September 2019; Published: 13 September 2019

**Abstract:** Ti-based alloys are accessible for use in the human body due to their good mechanical properties, corrosion resistance, and biocompatibilities. These main properties of alloys are important criteria for choosing biomedical implants for human bones or for other kinds of applications in general medicine. This paper presents a comparison of four new Ti-based alloys desired to satisfy various requirements for biomedical implants. The materials were prepared with recipes for two new system alloys, TiMoZrTa (TMZT) and TiMoSi (TMS), alloys with nontoxic elements. The presented research contains microstructure images, indentation tests, Vickers hardness, XRD, and corrosion resistance, showing better characteristics than most commercial products used as implants (Young's modulus closer to the human bone).

**Keywords:** titanium alloy; biomaterial; TiMoZrTa; TiMoSi; mechanical properties; low elasticity modulus; corrosion

#### **1. Introduction**

At present, the market request for biomaterials is very high. The uses of biomaterials in medical applications includes several areas: Orthopedics, cardiovascular surgery, ophthalmology, dentistry, urology, aesthetic surgery, neurology, suture material for wound healing, and controlled release drug delivery systems. Due to this, it is very important to develop new materials with enhanced properties, biocompatibility, and long-term viability as an implant material. Fundamental requirements are that an implant should have biomechanical properties (stiffness, strength, fracture toughness, wear resistance, fatigue strength, corrosion resistance) and biomedical properties (toxicity, surface state, osseointegration) [1–3].

The usual materials currently found in medical applications are classical metallic alloys: Titanium alloys (TiAlV), cobalt alloys (CoCrMo), and stainless steels.

The microstructure, as well as the properties of the titanium alloys, differs depending on the amount of α or β stabilizing elements added to the titanium alloys. Ti-based are grouped into α-type, (α + β)-type, and β-type alloys. Alloying the pure titanium with β-elements leads to the widening of the β-phase domain, as well as the improvement of the mechanical properties proven in the literature [4–7].

Mo, V, Nb, and Ta are β-stabilizers elements that decrease the temperature of allotropic transformation and neutrals, such as Zr. Commercial pure titanium and Ti6Al4V alloy were the first titanium-based materials for commercial use. In recent years, further studies have indicated that vanadium, used to stabilize the α-phase, may produce harmful oxides for the human body [8,9].

The authors of [10,11] concluded that Ti, B, Mg, Si, P, Ca, Sr, Zr, Nb, Mo, Pd, In, Sn, Ta, Pt, and Au are biocompatible elements, while harmful elements include Be, Al, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, and Ag [10,11].

One of the most important features of an implant is that it comes in contact with the living tissues of the body, thus creating an interface between them. The phenomena that occur at this interface are of great interest because they ultimately determine the success or failure of the implant, both in terms of immediate reaction and long-term response. The biological response between the implant and the host tissue is largely dependent on the place of implantation and the surface properties of the implant. The role of biomaterials is to come into contact with a biological system. When a biomaterial is placed in the human body in the form of a medical device, human tissues react to its implantation in different ways, depending on the type of biomaterial used. The mechanism of cell attachment to the implant depends on the tissue response to the surface of the alloy.

Most recently, researchers have aimed to improve properties by introducing nontoxic elements, for enhancing surface characteristics, mechanical properties, corrosion resistance, biocompatibility and developing alloys with low modulus β or near β Ti alloys, such as Ti–Mo systems, Ti–36Nb–2Ta–3Zr, Ti–24Nb–4Zr–7.8Sn [2,12], etc.

Titanium is a nontoxic element, even in larger quantities; some studies have demonstrated the influence of ingestion by humans of up to 0.8 mg of titanium daily, proving that titanium was eliminated without being digested/assimilated. Its uses in medical applications were due to good interaction with the host bone, the titanium implants not being rejected by the body, and having a high corrosion resistance [13–15].

Molybdenum is an element with a lower degree of toxicity compared to Co, Ni, and Cr, and moreover, is a β-stabilizing element. Field studies have highlighted that titanium alloyed with molybdenum in varying percentages between 15%–20% can decrease the modulus of elasticity leading to adequate mechanical properties.

Silicon reduces ductility, improves creep and high-temperature resistance, and increases corrosion resistance.

Zirconium is used in medical applications due to its low modulus of elasticity, high corrosion resistance, and high biocompatibility with human tissue [13–15].

Tantalum is considered biocompatible, being a β-stabilizing element that influences the value of the modulus of elasticity [13–15].

Silicon is an element found in the human bone and is considered biocompatible. It is also a β-stabilizing element that influences the decrease of the modulus of elasticity.

Despite these facts, Mo, Zr, Ta, and Si were selected for designing a new ß-type of Ti-based alloys (Table 1), systems like TMZT (TiMoZrTa) and TMS (TiMoSi) with lower elastic modulus, corrosion resistance, and good biocompatibility.



This article presents new recipes for Ti-Mo system alloys, with good characteristics and using nontoxic elements, which can be used in medical applications.

#### **2. Experimental**

#### *Materials and Preparation*

In order to obtain titanium alloys, it was chosen to use a vacuum arc melting plant, produced in house by Institute of Physics, Faculty of Production Engineering and Materials Technology, Czestochowa University of Technology, Poland, and we used raw materials with a high purity: Ti—99.8%, Mo—99.7%, Zr—99.2%, Ta—99.5%, and Si—99.2%.

The advantages of this equipment are as follows: High melting temperatures, the use of vacuum or protective environment, uniform composition by repetitive melting, and the possibility of melting elements at different melting points (Figure 1).

**Figure 1.** Stages of development of the alloys: (**a**) weighing of raw materials and gravimetric dosing; (**b**,**c**) loading of the raw material; (**d**,**e**) TiMoZrTa (TMZT) semi-products obtained after solidification.

The chemical composition of the alloys was analyzed using a scanning electron microscope (SEM) VEGA II LSH manufactured by the TESCAN Co., Brno, the Czech Republic, coupled with an EDX QUANTAX QX2 detector manufactured by the BRUKER/ROENTEC Co., Berlin, Germany. The chemical analyses (EDX) of the alloys studied were performed at many different points for a precise determination, with a uniform distribution of elements and a homogeneous alloy. The chemical composition is shown in Table 1.

The phase analysis was carried out using a Panalytical X'Pert Pro MPD diffractometer, by Malvern Panalytical a Spectris company, Almelo, The Netherlands. The parameters used for sample analysis were: Range of angle θ–2θ between 20◦ and 80◦; continuous scanning. In order to determine the constituent phases, by X-ray diffraction, from the Ti-based alloys developed, samples with size of 10 mm × 10 mm × 5 mm were cut and used after they had been polished.

A Wilson Wolpert universal hardness tester 751 N model, by Wilson Instruments an Instron Company, Heerlen, The Netherlands, was used for the Vickers hardness measurements, with a load of 9807 N during 12 s. The hardness measurements were performed on samples obtained from Ti-based alloys with dimensions 10 mm × 10 mm × 3 mm, the surface of the samples being prepared by grinding on abrasive paper. Experimental tests consisted of three determinations in different areas on the surface of each sample, using a 9.81 N pressure force and a 12 second measurement time.

Elastic modulus was measured using a CETR UMT-2 Tribometer, by Bruker, Campbell CA, USA. For micro-scratch analysis, a constant load method was used with a load of 5N on a distance of 4 mm,

for a single determination. For indentation tests, samples of Ti-based alloys obtained were cut with a dimension of 17 mm × 5 mm × 5 mm, and the surface of the samples was prepared by grinding with high-grain silicon carbide abrasive paper and polished with alumina suspension until obtaining metallic gloss and removal of surface roughness. The investigated samples were fixed to a flat surface of the test device with screws and clamps. Testing was carried out under dry conditions. A Rockwell diamond-type penetrator was used, having an incisor cone with an angle of 120◦, applying a force of 5 N.

To determine the elastic modulus as accurately as possible, three determinations were performed for each alloy. From the mean values, using UMT 2 software, provided with the CETR UMT-2 Tribometer, the indentation curves (depth vs. force) of TiMoSi alloys were plotted using the ViEWER program.

In order to obtain the electrochemical parameters for characterizing the corrosion resistance of elaborated Ti-based alloys, the electrochemical tests of linear polarization were used. This method can directly and quantitatively determine the corrosion rate. To determine the corrosion potential of Ti-based alloys developed, samples of 5 mm × 5 mm × 5 mm were used. Prior to being subjected to the corrosion potential determination, the samples were cut and ground to remove impurities and the Ti oxide film that formed on the surface of the alloy, then they were embedded in Teflon.

The electrical component of an electrochemical cell consists of a voltmeter, measuring the potential of the product. A reference electrode was a saturated calomel electrode in a potassium chloride solution whose potential is reproducible and has a value of 242 mV at a temperature of 25 ◦C. Additionally, a platinum electrode was used as an auxiliary electrode. Data processing was done with the Volta Master 4 -Electrochemical Software, by Radiometer Analytical SAS, Villeurbanne, France, then imported and processed using experimental data processing software.

#### **3. Results and Discussions**

Figure 2 shows the structure of Ti-based alloys with titanium alloy grain specifics. Images obtained by optical microscopy for titanium alloys have a dendrite structure for TiMoZrTa alloy systems. TiMoSi alloy systems highlight the formation of β-type equiaxed grains, having different dimensions. The acicular and coarse structures are specific to β-alloys. With TiMoSi, a β structure of cube with a centered volume is visible.

The variation of the α, α + β, and β phases consists in the differences in the chemical composition of the constituents. The high percentage of β (Mo, Ta, and Si) stabilizing elements led to the formation of a β-type structure, highlighted very well in the Ti-based alloys obtained. Zirconium contribution in concentrations below 10% contributes to the refining of the microstructure, thus allowing the formation of a homogeneous and uniformly distributed structure. Therefore, elements with percentages of tantalum (5%–15%), combined with a molybdenum concentration of 15%, contribute to the formation of phase β.

Optical microscopy (Figure 2) reveals a uniform biphasic structure, consisting of a high proportion of solid β solutions, in which the dendrite lamellar structures of the orthorhombic martensite α" are present. Orthorhombic martensite occurs frequently in titanium alloys containing β-stabilizers of the transition metals category, including molybdenum and tantalum. In the present case, the presence of the α" phase is due to the decomposition of the β phase during the cooling. Regarding the Ti15Mo0.5Si, the small dark spots are due to pitting corrosion after the chemical etching of the polished surface and do not represent any inclusion or other phases.

The hardness measurements highlight the resistance to the penetration action of an external body and provide information on the behavior of the studied materials. In this way, we can analyze the Ti-based alloys developed for the purpose of fitting them into the specific medical application. The hardness measurements made on the titanium alloys, developed by the Vickers method, are a general method for determining the hardness of metallic materials, commonly used in biomaterial testing.

**Figure 2.** Optical microstructure images of titanium alloys Ti15Mo7Zr5Ta, Ti15Mo7Zr15Ta, Ti15Mo0.5Si, and Ti15Mo1Si at various magnifications: (**a**) 50×, (**b**) 100×.

Some of the mechanical properties of Ti-based alloys developed are presented in Table 2 (hardness and Young's modulus), compared with two other samples: Commercial pure titanium and Ti6Al4V. The values of the elasticity modulus of the titanium alloys developed, resulting from the indentation test, are highlighted in same table.



According to the literature [15–19], classical biomaterial alloys like stainless steel and CoCrMo alloys have hardness values between 155 HV and 601 HV. The titanium alloys obtained comprise values ranging from 188.52 to 390.88. Titanium alloys have values approximate to the Ti6Al4V alloy (349 HV), which is mostly used in implantology [15–19].

The elasticity module is a very important criterion underlying the choice of metallic materials used in orthopedics and should be as close as possible to human bone (17–30 GPa) to avoid the stress-shielding effect [1–3].

The Ti-based alloys obtained have values ranging from 19.82–69.02 GPa for the modulus of elasticity, measured by indentation tests. The lowest value is the Ti15Mo0.5Si alloy (19.82 GPa), and the highest value are the Ti15Mo7Zr5Ta alloys (69.02 GPa). The low elasticity modulus of the investigated alloys is due to the presence of β-stabilizing elements such as Mo, Ta, and Si. According to Table 2, it can be seen that adding elements like Zr and Ta can increase values of modulus of elasticity with approximately 40 GPa. On the other hand, increasing the percentage of Ta from 5% to 15% contributed to a decrease in the modulus of elasticity for TMZT alloys.

As we can see from the data in Table 2, the highest Young's modulus (69 GPa) is visible in the Ti15Mo7Zr5Ta systems, due to the presence of α" phase (martensite). Ti15Mo0.5Si presents the lowest Young's modulus (20 GPa), where on the microstructure, the β boundaries are clearly visible (Figure 2b). These are confirmed also by the literature, that the β phase presents better mechanical properties. Taking into consideration other metallic biomaterials—CoCrMo alloys (210–253 GPa) and stainless steels (190–210 GPa)—the investigated Ti-based alloys exhibited much lower values and closer values to that of the human bone (17–30 GPa). The alloys developed showed a significant improvement for mechanical properties even for titanium alloys: Ti6Al4V (100–114 GPa) and C.P. Ti (102–104 GPa).

From the point of view of elasticity, these alloys fulfilled the most important requirement criteria of metallic biomaterials, the values of the modulus of elasticity being close to that of the human bone.

Figure 3 shows the response of alloys during indentation tests in the form of force– depth dependencies.

**Figure 3.** The strength-depth curve of the indentation test for Ti-based alloys developed: (**a**) Ti15Mo7Zr5Ta, (**b**) Ti15Mo7Zr15Ta, (**c**) Ti15Mo0.5Si, and (**d**) Ti15Mo1Si.

The diffractograms obtained (Figure 4) show the β-type structures identified by optical microscopy, taking into account that titanium is an allotropic element, presenting it in different forms: Up to

a temperature of 882 ◦C, having a α-Ti compact hexagonal structure and above 882 ◦C, β–Ti, having a centered cube structure. In the composition of the investigated alloys, there is a major phase β with a centered cube structure and a secondary phase α" with an orthorhombic structure (martensite), present only for Ti15Mo7Zr5Ta systems.

Phase β, having a centered cubic structure, is fixed by alloying the titanium with transition elements (Mo, Ta, and Si) crystallized in the orthorhombic system and is formed when the content of stabilizing elements phase β decomposed during cooling [20–23].

**Figure 4.** The XRD diffraction patterns of titanium samples: (**a**) Ti15Mo7Zr5Ta, (**b**) Ti15Mo7Zr15Ta, (**c**) Ti15Mo0.5Si, and (**d**) Ti15Mo1Si.

The corrosion of biomaterials is determined by the aggressive corrosive nature of the elements present in body fluids. In order to determine the corrosion potential of titanium alloys developed, it was necessary to investigate them through potentially dynamic and potentiostatic tests in simulated biological environments.

The simplest method of measuring the corrosion rate of a metal involves putting it in contact with the test medium and measuring the amount of material lost by the sample depending on the exposure time.

The polarization resistance method was used to assess the corrosion rate for the Ti-based alloys developed. This method serves to determine the corrosion current and the corrosion potential of the metal or alloy, from the linear polarization curve obtained from relatively small voltages. The corrosion current determined by this method is therefore the current that occurs at the metal/corrosive environment interface when the metal is immersed in the solution and represents the instantaneous corrosion current.

The specific titanium developed samples were introduced into the electrochemical cell, and the selected corrosion medium was Ringer's solution with the composition: NaCl: 8.6 g/L, KCl: 0.3 g/L, CaCl2: 0.48 g/L, in order to investigate their use as potential biomaterials. Measurements were made at 20 ◦C in naturally aerated solutions. The anodic polarization curves were recorded at a potential sweep rate of 0.5 mV/s over a potential range of ± 200 mV versus the open circuit potential. Corrosion potential (Ecorr = E (I = 0)), Tafel slopes (βa and βc), polarization resistance (Rp), instantaneous corrosion density (corrosion), and corrosion rate were evaluated using the VoltaMaster 4 software.

Figure 5 shows the linear polarization curves in semilogarithmic coordinates for the samples studied in the Ringer solution, and in Table 3, we present the instantaneous corrosion parameters in the same physiological environment.

Corrosion potential, Ecorr, measured relative to the potential of the saturated calomel electrode, is the potential at which the oxidation–reduction reactions on the alloy surface are at equilibrium; the rate of the oxidation reaction is equal to the rate of the reduction reaction, and the total current intensity is zero. Increasing the potential to more positive values increases the rate of the oxidation reaction, while the potential shift to negative values is reduced by the oxidation process, and the metal passes. It can be seen that the presence of silicon appears to produce an increase in the corrosion rate.


**Table 3.** The main parameters of the Ringer solution corrosion process.

**Figure 5.** Diagrams of the investigated alloys by corrosion testing in Ringer's solution of the samples: (**a**) Ti15Mo7Zr5Ta, (**b**) Ti15Mo7Zr15Ta, (**c**) Ti15Mo0.5Si, and (**d**) Ti15Mo1Si.

Polarization resistors have high values, which is reflected in very low corrosion rates. The "corrosive" product of these alloys is mainly titanium oxide, TiO2, which is insoluble and adherent to the surface of the alloy. The oxide layer on the surface protects the alloy against the aggressive action of electrolytic media. Considering this, it can be concluded that in the physiological environment, titanium-based alloys are not corroded but actually suffer a passivation process. Under these conditions, the variable corrosion rate is actually passivation velocity.

Particular attention should be given to the Ti15Mo1Si alloy; in these cases, the polarization resistances were small and the corrosion rates were higher than that for the other alloys (almost double).

The value of molybdenum and tantalum concentrations in the studied alloys are important for corrosion studies. The higher the percentage of tantalum, the better the characteristics of corrosion resistance. Molybdenum has a great influence on the corrosion parameters; thus, for a percentage of 15%, the corrosion resistance is very good [24–27].

#### **4. Conclusions**

At the global level, there is continuous concern for the research and development of alloys for medical and biomedical applications. Thus, it is desired to improve both the classic technologies of obtaining implants and the technologies of synthesis of the biomaterials from which they are executed, having as the final aim the promotion of a new generation of multifunctional implants with long-term performance.

Biomaterials are synthetic materials used to replace a part of a living system, or to function in close connection with a living tissue, which is why they must have properties as close to that of the human bone. Young's modulus of the Ti-based alloys obtained values ranging from 19.82 to 69.02 GPa, which is recommended for alloys used in implantology.

For most of the samples, the process that takes place on the surface is the oxidation of the titanium with the formation of an oxide adherent to the surface, which in fact produces the passive alloy. The corrosion rates (in fact passivation rates) are of the same order of magnitude, relatively small (20–30 m/year), for all alloys with uniform composition.

This paper presents the effect of tantalum addition that is beneficial in decreasing the modulus of elasticity as well as the corrosion rate. The addition of silicon has shown that it can present good properties only in a percentage of less than 0.5.

In conclusion, we can state that the characteristics of titanium alloys depend on the alloying elements, influencing the mechanical properties, and the biocompatibility. Elements like molybdenum, zirconium, tantalum, and silicon alloyed with titanium show good properties; in the future, they can be introduced in different medical applications such as dental and orthopedic implants.

**Author Contributions:** A.V.S. did the formal analysis, writing—reviewing and editing and final validation of results; M.S.B. did the investigation and wrote the original draft; M.N. did the alloys casting and contributed with resources and methodology; A.S. validated upon methodology the results; P.V. supervised the research and did the conceptualization.

**Funding:** This work was supported by a grant of the Romanian Ministry of Research and Innovation, CCCDI–UEFISCDI, project number PN-III-P1-1.2-PCCDI-2017-0239/ Contract no. 60/2018, within PNCDI III.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
