Microstructure and nanomechanical properties of magnetron sputtered Ti − Nb films

    Microstructure and nanomechanical properties of magnetron sputtered Ti Nb films D. Photiou, N.T. Panagiotopoulos, L. Koutsokeras, G.A. Evangelakis, G. Constantinides PII: DOI: Reference:

S0257-8972(16)30505-9 doi: 10.1016/j.surfcoat.2016.06.014 SCT 21256

To appear in:

Surface & Coatings Technology

Received date: Revised date: Accepted date:

7 March 2016 4 June 2016 7 June 2016

Please cite this article as: D. Photiou, N.T. Panagiotopoulos, L. Koutsokeras, G.A. Evangelakis, G. Constantinides, Microstructure and nanomechanical properties of magnetron sputtered Ti - Nb films, Surface & Coatings Technology (2016), doi: 10.1016/j.surfcoat.2016.06.014

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ACCEPTED MANUSCRIPT Microstructure and nanomechanical properties of magnetron sputtered 𝐓𝐢 − 𝐍𝐛 films

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Constantinidesa,b*

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D. Photioua,b, N.T. Panagiotopoulosc,d,e, L. Koutsokerasa,b, G.A. Evangelakisc, G.

Department of Mechanical Engineering and Materials Science and Engineering,

b

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Cyprus University of Technology, Lemesos, CY Research Unit for Nanostructured Materials Systems, Cyprus University of

Department of Physics, University of Ioannina, Ioannina, 45110, GR d

Univ. Grenoble Alpes, SIMAP, F-38000 Grenoble, France CNRS, SIMAP, F-38000 Grenoble, France

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e

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Technology, Lemesos, CY

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*corresponding author: [email protected] Keywords: titanium alloys; nanoindentation; electron microscopy; X-ray diffraction;

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𝛽 − Ti; poromechanics

Abstract

Titanium niobium (Ti − Nb) films, covering a broad spectrum of compositions, are deposited on silicon substrates using magnetron co-sputtering. The morphological, crystallographic and mechanical characteristics of the films are studied using scanning electron microscopy (SEM), X-ray diffraction (XRD) and nanoindentation, respectively. The Ti − Nb films exhibit a columnar growth and contain porosity at volumetric percentages of 2-14 vol.%. Furthermore, it is observed that the allotropic 𝛽 − Ti phase can be stabilized at room temperature for Nb compositions beyond 20

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ACCEPTED MANUSCRIPT at.%. Phase composition and microstructural details have subsequent implications on the mechanical properties of the films which are studied experimentally and

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micromechanically. Among the tested compositions, Ti85Nb15 exhibits the lowest elastic modulus. The obtained structure-property relations could serve as a tool for

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material optimization. Introduction

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Titanium (Ti) and its alloys currently serve as the materials of choice for biomedicine [1,2], with applications including, but not limited to, cardiovascular/dental/orthopedic

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implants, bone fixation devices, joint replacement parts, surgical instruments, etc. [1,3]. Their applicability is by no means restricted to the biomedical sector but

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extends to the automotive, aerospace, chemical and offshore industries. Their wide exploitation relates to their physical, chemical and mechanical properties: lightweight

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(half the weight of steel), high strength to weight ratio (specific strength), excellent

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corrosion resistance, low modulus of elasticity (compared to other metals), excellent hemo- and bio-compatibility, and thus titanium-alloys outperform other candidate

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materials [1,3–5]. The biomaterials research community has recently directed its efforts towards beta titanium alloys (𝛽 − Ti) which compose the most versatile class of titanium alloys with an excellent combination of strength and toughness and the ability to lower the elastic modulus of the metal in more compatible with the bone values. In fact, the elastic modulus of the implanted material must exhibit similar stiffness as of bone, 20 − 30 GPa, in order to minimize any stress concentrations at the interface and avoid any stress-shielding phenomena [6,7]. This class of materials can be generated through alloying titanium with elements that stabilize the 𝛽 − Ti phase even at room temperature by shifting the β-transus temperature into lower values (even below room temperature), thus promoting the formation of the more 2

ACCEPTED MANUSCRIPT compliant body-centered cubic (bcc) allotropic phase, 𝛽 − Ti. There are several betastabilizing elements that can be used in titanium alloys (e.g. Mo, V, Ta, Nb, Fe, Ni,

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Cr), the most popular of which has been nickel, leading to the well-known nitinol alloy (Ni-Ti) extensively used in biomedical applications. Over the past decade there

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has been an effort to substitute the cytotoxic nickel element from biomaterials and replace it with other biocompatible and hemocompatible elements that are non-toxic and allergy-free. Among the candidates, niobium (Nb) appears as a very promising

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alloying element that satisfies the prerequisites of biocompatibility while retaining the

corrosion resistance [7–12].

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main Ni − Ti characteristics, i.e. shape memory effect, super-elasticity and high

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Preliminary studies on the Ti − Nb system suggest that their elastic moduli depend largely on the chemical composition of the material, mainly due to the complex phase

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transformations that take place. The phase diagram of Ti − Nb system at low

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temperatures suggests the possible existence of 𝛼 phase (hcp), the martensitic 𝛼" (bco), and 𝛽 phase (bcc) with the possible precipitation of 𝜔 phase particles as the Nb

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content increases [13]. While the exact values of the elastic properties of each phase are still a matter of scientific debate there is a consensus on the elastic hierarchy: 𝐸𝜔 > 𝐸𝑎 > 𝐸𝛼" > 𝐸𝛽 [3,7,14,15]. Other important literature results suggest that Ti − Nb alloys exhibit the lowest elastic moduli values as compared with other 𝛽 −based Ti alloys [16], and that niobium increases the fatigue strength of Ti alloys [5]. The majority of 𝛽 −phase Ti −alloys presented in the literature, including the studies on Ti − Nb systems, derive from thermodynamic bulk processes, in order to stabilize the soft metastable 𝛽 −phase at room temperature. There is little information on the possibility of stabilizing the 𝛽 −phase through physical vapor deposition methods in 3

ACCEPTED MANUSCRIPT film geometries. Magnetron sputtering is a well-established industrial scale vapor deposition technique by which a plethora of material systems, including high

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temperature alloys, can be grown at high deposition rates over large areas with good adhesion [17–20]. Moreover, magnetron sputtering involves a series of deposition

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parameters and variables that can be controlled for tailoring the structural and physical properties of the grown coatings [21–23]. The aim of this study is, therefore, to investigate the idea of moving from bulk materials to coated systems using

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magnetron sputtering as the deposition technique [24] while concurrently exploiting

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the microstructural and nanomechanical characteristics, such as to develop structureproperty relations. Through thin film technology, we attempt to stabilize the 𝛽 −phase

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of Ti − Nb alloys and introduce porosity by depositing the alloys at room temperature using relatively low ion energies. The porosity is expected to influence the

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mechanical properties of materials [25,26] while concurrently enhancing the

2.1

Materials and methods Growth of Ti-Nb films

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osseointegration process [27].

Titanium-niobium (Ti − Nb) films spanning a broad spectrum of compositions –from pure titanium to pure niobium– have been deposited on commercial Czochralski grown, 𝑛 −type Si (100) substrates. The films have been grown using a dual confocal unbalanced magnetron sputtering system at room temperature. The base pressure in the high vacuum chamber was set at 𝑃𝑏 = 2 x 10−6 mbar while the working pressure resulting from leaking high purity argon (99.999%), which served as sputtering gas, was 𝑃𝑤 = 4 x 10−2 mbar. A direct current (DC) power gun was set on niobium target and a radio frequency (RF) of 13.56 MHz power gun on titanium target. Ti and Nb 4

ACCEPTED MANUSCRIPT targets were characterized by 99.995% and 99.98% purity, respectively. The angle between the two power guns was 90o with their centers spaced at 9 cm. A rotating

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substrate holder was located at 45o with respect to the titanium and niobium targets at substrate-to-target distances of 5.5 cm and 7 cm, respectively. The composition was

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controlled by changing the power on each gun. The deposition time was kept constant at 40 min for all deposited films, except for pure titanium (23 min) and pure niobium (30 min). Table 1 summarizes the growth conditions and the resulting thicknesses and

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compositions for all Ti − Nb alloy films grown in this study. The substrate

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temperature was held at chamber conditions (room temperature) thus suppressing any

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surface and bulk diffusion processes.

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ACCEPTED MANUSCRIPT Table 1: Growth conditions for 𝐓𝐢 − 𝐍𝐛 films. Thickness values measured through cross-sectional SEM images are reported to the nearest 5 nm. Nb Power

(at.%)

(W)

(W)

Pure Ti

80

Ti85Nb15

80

Ti80Nb20

80

Ti68Nb32

80

Ti62Nb38

100

Ti56Nb44

Pure Nb 2.2

(nm) 415

10

40

590

15

40

735

30

40

970

60

40

1350

80

60

40

1280

50

60

40

1185

40

60

40

1105

20

60

40

890

0

60

30

740

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Ti27Nb73

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Ti37Nb63

(min)

Thickness

0

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Ti43Nb57

Deposition Time

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Ti Power

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Samples

Characterization of 𝐓𝐢 − 𝐍𝐛 films

2.2.1 Microstructural measurements The specimens were imaged in a Quanta 200 (FEI, Hillsboro, Oregon, USA) scanning electron microscope using an acceleration voltage of 30kV and a working distance of 10 to 11mm. The specimens were micro analyzed using the EDVAC Genesis x-ray analysis probe at various sites and spectral patterns, that allow elemental compositions, were generated for each session of analysis. The atomic percentages

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ACCEPTED MANUSCRIPT reported in Table 1 correspond to the experimentally obtained values. Grazing incidence X-ray diffraction (GID) and X-ray reflectivity measurements have been

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performed in a Bruker D8-Advance diffractometer, equipped with a Göbel mirror, using Cu-Ka radiation to obtain information about the crystal structures and the

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densities of the grown films, respectively. The resulting film thicknesses have been

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measured using cross-sectional SEM measurements (Figure 1(b) and (c)).

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(c)

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(a)

(b)

1 μm

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Figure 1: SEM images of grown films. (a) Top view of the fractured interface of

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Ti27Nb73 – the grooves between the grains are evident; (b) cross-sectional view of pure titanium film; (c) cross-sectional view of pure niobium film.

2.2.2 Elastic modulus measurements The Young’s moduli of the films were probed using an instrumented nanoindenter (NanoTest 3, Micromaterials Ltd). In this platform a load-profile (𝑃) is applied in a controlled manner through a diamond indenter on the surface of the sample under investigation and the resulting penetration depth (ℎ) is continuously monitored in the process (𝑃 − ℎ curves). Through an inverse application of advanced models the reduced elastic modulus (𝐸𝑟 ) of the sample can be determined:

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ACCEPTED MANUSCRIPT 𝛦𝑟 =

√𝜋 𝑆 2 √𝐴𝑐

(1)

𝑑𝑃

where 𝑆 is the unloading slope at maximum depth 𝑆 = 𝑑ℎ|

, and 𝐴𝑐 is the

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ℎ=ℎmax

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projected area of contact generated between the indenter and the specimen at maximum load. The elastic modulus of the material can be calculated through Eq. (1) which derives from the analytical solution of a rigid axisymmetric probe being pushed

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on the surface of linear elastic half space [28] and provides a link between the unloading contact stiffness 𝑆 with the reduced elastic modulus of the material 𝐸𝑟 [29].

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𝛦𝑟 is associated with the combined deformation actions of the material and the indenter through:

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(1 − 𝑣𝑖 2 ) (1 − 𝑣𝑠 2 ) 1 = + 𝛦𝑟 𝛦𝑖 𝛦𝑠

(2)

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where 𝛦𝑠 and 𝑣𝑠 , and 𝛦𝑖 and 𝑣𝑖 , correspond to the elastic moduli and Poisson’s ratios

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of the specimen and indenter, respectively. In our experiments a diamond Berkovich indenter is used with 𝐸𝑖 = 1140 GPa and 𝑣𝑖 = 0.07. All quantities included in Eq. (1)

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can be directly extracted from the experimentally obtained 𝑃 − ℎ curves. The projected area of contact 𝐴𝑐 can also be linked to the experimental parameters through the methodology proposed by Oliver and Pharr [30]. The non-ideal geometry of the indenter is included in the analysis through a diamond area calibration process in which the exact shape of the indenter (Diamond Area Function) is quantified by performing multi-depth indentations on a reference material with known mechanical properties (here Quartz). Eq. (1) relies on the homogeneous and isotropic nature of the indented material. In the case of films on substrate geometries the validity of the equation starts to break down

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ACCEPTED MANUSCRIPT as the depth of penetration increases, to a significant percentage of the film thickness; one therefore needs to take into account the possible interaction between the indenter

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and the substrate material. To circumvent this problem and obtain “film-only” properties, it has been proposed to indent at low (less than 10% of the film thickness)

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penetration depths, so that any substrate effects would be negligible [31]. This is, however, an approximation that does not take into account the elastic mismatch between the film and substrate that under certain circumstances can render the 10%

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rule inaccurate [32]. The film geometry has been the subject of many analytical

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[33,34], numerical [35,36] and experimental [37–39] studies and general guidelines for materials extraction have been proposed. The ISO14577-4 [40], recommends the

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collection of data at multiple depths and the use of a linear extrapolation to zero contact depth in order to assess the elastic moduli of the films. In the case of

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soft/ductile films on stiff/hard substrates, the linear plot must be in the region where 𝑎/𝑡 < 1.5 for Berkovich indenter, where 𝑎 stands for the radius of contact and t for

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the film thickness. Moreover, the approach of Oliver and Pharr [41] has to be used in

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order to extract the mechanical properties of the films. Following the ISO guidelines we performed multi-depth indentation (“load-partial unload”) in a range of contact depths and the film properties have been obtained by linearly extrapolating the results to zero contact depths. Only the data that satisfied the 𝑎/𝑡 < 1.5 restriction were included in the analysis. Fifteen contact loads have been used for each specimen and the results have been repeated at 3 different locations. At 90% of every unloading a 60s dwell time was included to measure and correct the experimental data for any thermal drift effects.

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Results and discussion Morphological characteristics

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SEM images of the various Ti − Nb alloy films are presented in Figure 2. Pure

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titanium exhibits elongated features with irregular sizes and shapes, where the observed morphology supports a significant volume of pores. The presence of porosity is consistent with the classical structure-zone model which suggests that low

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normalized substrate-to-melting temperature, 𝑇𝑠 /𝑇𝑚 , in combination with moderate

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inert gas pressure leads to films with fibrous grains and voided boundaries [42,43]. The addition of Nb is associated with a morphological feature size reduction and a change in feature shape, moving from elongated to more rounded geometries. The

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pure Nb film has a microstructure characterized with smaller inter-granular groove

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spaces and morphological feature sizes. These observations are consistent with the data presented in Mardare et al. [44] where they deposited by co-sputtering Ti − Nb

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films on thermally oxidized silicon substrates. The nanogranular and porous nature of

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the deposited films are in close resemblance. The morphological changes observed in scanning electron microscopy with increasing Nb content could be related to the phase transformations that the material undergoes for various compositions and are discussed next.

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Ti85Nb15

Ti68Nb32

Ti62Nb38

Ti56Nb44

Ti43Nb57

Ti37Nb63

Ti27Nb73

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Ti

Nb

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1 μm

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Figure 2: SEM images of 𝐓𝐢 − 𝐍𝐛 films show the distribution of morphological

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feature sizes as a function of the chemical composition. Aiming in obtaining more quantitative information on the morphological feature size

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(𝑑) the SEM images have been analyzed using a public domain program, ImageJ [45]. The images were processed using fast-Fourier transform (FFT) and band-pass filters and average length characteristics have been obtained. Figure 3 shows the average morphological feature size evolution with increasing Nb content. In the 0 to 20 at.% Nb content there is a noticeable morphological feature size reduction and shape transformation where elongated features are converted to more rounded equivalents. The 20 to 40 at.% domain is associated with negligible changes in the morphological feature size and shape while from 40 at.% Nb and until a pure niobium (100%) content is achieved the morphological feature size reduces monotonically until sub-50nm features are obtained. 11

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Crystallographic evolution

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Figure 3: Evolution of average morphological feature size with niobium content.

The x-ray diffraction patterns of the various deposited Ti − Nb films are plotted in

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Figure 4. It is evident that several peaks appear in the spectra which for pure Ti can be

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attributed to the (100), (002) and (101) diffraction angles. The data suggests the polycrystalline nature of the material with a preferred orientation of (002). The

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growth mechanism of Ti films has been studied in the past [38,46] and the orientation mechanisms appear to be a function of growth characteristics like substrate chemistry/temperature/roughness, sample distance, deposition pressure, sputtering power, etc. Our results for pure titanium films are consistent with literature data [38,44,46]. In general, the (002) growth direction is preferred for depositions on Si when the distance between the target and the substrate is large (>70 mm) or for high sputtering powers (>150 Watt). The introduction of Nb into the system tends to suppress the (100) and (101) peaks and slowly transform the (002)α into (111)α” and eventually (110)β. In fact, for 15 at.% Nb content, the hcp pure titanium is converted to an orthorhombic structure which is characterized by martensitic 𝑎′′ − Ti. The 12

ACCEPTED MANUSCRIPT existence of this martensitic phase at Nb concentrations around 15 at.% is supported by several other publications [47,48]. Furthermore, at 20 at.% of Nb content and

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beyond, the 𝛽 − Ti phase (bcc) can be stabilized at room temperature. The kinetic energy provided by magnetron sputtering can generate enough momentum to stabilize

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the 𝛽 −phase at even lower compositions and temperatures, compared with equivalent results on bulk specimens found in the literature. Noteworthy, for high Nb contents (> 77%) the crystal structure of the alloys and of pure niobium is fcc instead of its

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commonly observed bcc structure. The response of Ti − Nb alloys at high niobium

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concentrations is still a matter of scientific investigation and has not yet been elucidated. While for most practical biomedical applications the Nb content rarely

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exceeds compositions of 50 at.%, the topic is nevertheless of great scientific interest, and it serves to clarify the physical mechanisms for the formation of this rare

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allotropic phase.

Figure 4: X-ray diffraction patterns of 𝐓𝐢 − 𝐍𝐛 alloy films.

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ACCEPTED MANUSCRIPT The existence of 𝛽 −phase for niobium concentrations above 20 at. % is further supported by grazing incidence diffractograms (GID) that provide the lattice

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parameters of the samples. Figure 5 shows the experimental results along with the corresponding database values. This trend is in good agreement with all 𝛽 − Ti alloys

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as well as for the grown fcc Nb alloys. At 15 at. % Nb, the orthorhombic martensite 𝑎′′ − Ti is formed with the lattice constants 𝑎 = 3.047, 𝑏 = 4.929, 𝑐 = 4.688 in close agreement with database values 𝑎 = 3.100, 𝑏 = 4.880, 𝑐 = 4.700 [47,48]. The broad

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scattering behavior has also been reported by several authors [13,49].

Figure 5: Experimental and ICSD database lattice constants for various niobium

3.3

contents.

Film porosity

The density of the films was quantified through x-ray reflectivity measurements in which the maximum incidence angle that the x-rays undergo total reflection (critical angle) has been detected and quantified. The densities of the films were extracted by fitting the experimental data with a layer structure model by optimizing the parameter values of thickness, density and roughness until the residual between the measured and calculated reflectivity data is minimized. The reflectivity curves for all films 14

ACCEPTED MANUSCRIPT together with their respective model fittings are shown in Figure 6(a). The experimentally obtained densities (Figure 6(b)) are all lower than the expected

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theoretical densities of bulk equivalent, calculated using a simple rule of mixture. This discrepancy suggests the existence of pores in the system which has been

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promoted by the deposition conditions. In fact, the 𝑇𝑠 /𝑇𝑚 ratio for Ti ((𝑇𝑚 )Ti = 1,668℃ = 1,941K) and Nb ((𝑇𝑚 )Nb = 2,469℃ = 2,742K) used in this study ranges from 0.15 to 0.11 (calculated using Kelvin), respectively, values which according to

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the structure-zone model promote fibrous grains with nanoscale intergranular spaces.

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In such low relative temperatures the surface and bulk diffusion is negligible thus leading to a porous system with high dislocation density and thus brittle in nature. One can quantify the volumetric percentage of pores (𝜑) at each film using the

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experimental (𝜌𝑒𝑥𝑝 ) and theoretical bulk density (𝜌𝑏𝑢𝑙𝑘 ) discrepancy through

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𝜑 = 1 − 𝜌𝑒𝑥𝑝 /𝜌𝑏𝑢𝑙𝑘 (Figure 6(c)) [50–52]. It should be noted, however, that the discrepancy between bulk and experimental density can be potentially attributed to

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several other factors beyond porosity, i.e. vacancies, boundaries and several other

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forms of non-ideal packing. Consequently, the estimation of porosity presented in Figure 6(c) should be considered as an upper bound estimate. With the exemption of pure Nb all other porosities are retained within 2 to 14 vol.%. The significant increase of porosity in pure Nb is consistent with the high melting point of niobium which reduces significantly the 𝑇𝑠 /𝑇𝑚 ratio and thus further suppresses any surface diffusion phenomena. Despite the fact that there are some fluctuations in the 𝜑 vs. Nb at. % relation, the volume of pores remains relatively unaffected by the alloying conditions and it is primarily related to the deposition conditions rather than the chemistry of the material. The presence of pores in the films is expected to influence their mechanical response and this is discussed in relation to the nanoindentation data below. 15

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Figure 6: (a) X-ray reflectivity curves together with their best fit solutions of the

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layer structure model. (b) Experimental and theoretical densities of 𝐓𝐢 − 𝐍𝐛

3.4

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films. (c) Calculated porosities for all 𝐓𝐢 − 𝐍𝐛 films grown in this study. Elastic modulus of 𝐓𝐢 − 𝐍𝐛 films

3.4.1 Nanoindentation results Before proceeding to the presentation and discussion of the mechanical results a comment on the accuracy of the adopted methodology is due. The Oliver and Pharr approach [29] which is used for estimating the area of contact at maximum load and included in Eq. (1) for calculating the elastic modulus of the indented material is known to be accurate provided that no pile-up phenomena are present [53]. Figure 7 depicts SEM images of residual imprints left on the specimen surface after

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Berkovich geometry of the tip used in all tests. The sharp geometry of the probe produces large stresses beneath the tip and subsequently large plastic strains, initiating

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almost at the onset of depth penetration. For small indentation depths the imprint exhibits sink-in effects (Figure 7(a)) while at larger indentation depths, pile-up phenomena kick-in (Figure 7(b)). This observation suggests that the area of contact

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can be reliably estimated with the Oliver and Pharr methodology for small indentation

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depths, while its use at large depths should be treated with caution. The experimental data used in the linear fitting process excludes data for which the area of contact

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exceeded 𝑎/𝑡 > 1.5, the regime where pile-up phenomena appeared, in line with the

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ISO guidelines.

500 nm

(b)

5 μm

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(a)

Figure 7: SEM images show residual imprints left on the film surface after Berkovich indentation. (a) Low load (~10 mN) and (b) high load (~450mN, backscatter electron mode). Pile-up is observed for high penetration depths.

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Figure 8: Depth dependency of indentation modulus for all 𝐓𝐢 − 𝐍𝐛 samples.

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The experimental results on the elastic moduli of all Ti − Nb films studied as a function of the indentation depth are presented in Figure 8. The upward trend is

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related to the stiffer silicon substrate that influences the response for large indentation depths. In fact for large penetration depths compared to the film thickness the properties of the substrate can be recovered. The silicon used as substrate material in this study has been independently measured by nanoindentation which yielded E = 175.6 GPa, in close agreement with literature data [54,55]. The experimental data at each point of Figure 8 represents the composite response of the Ti − Nb/Si system. The properties of the Ti − Nb films can be recovered by linearly extrapolating to zero depth response (𝑎/𝑡 = 0), the intercept with the vertical axis. The extracted elastic moduli of all binary Ti − Nb alloy films are presented in Figure 9. The mechanical fluctuations exhibited in the Ti − Nb alloys result from the 18

ACCEPTED MANUSCRIPT combined action of phase transformations and the volume of pores present at each composition (Nb content). The discrepancy between the experimentally obtained exp

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elastic modulus of pure Ti (𝐸Ti = 76GPa) and the anticipated theoretical value th (𝐸Ti = 115GPa) is purely attributed to the presence of porosity, as it will be

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demonstrated in Section 3.4.2. As the Nb content increases the elastic modulus reduces, in line with the fact that the base-centered orthorhombic structure (martensitic 𝑎′′ − Ti) has lower elastic modulus in comparison with the hcp allotrope

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(𝛼 − Ti). For Nb contents greater than 20 at. %, where 𝛽 −phase occurs, we were

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expecting lower values due to the presence of the “softer” crystal structure. However, as our experimental results show, we didn’t reach similar low values as emerged in

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the Ti85Nb15 sample with our results fluctuating between 68-85 GPa. The observed elastic response is the result of the combined action between relative volume fraction

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of the various phases present in the microstructure, including porosity. A possible explanation of the stiffer than anticipated response in the >20 at.% Nb contents could

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be attributed to the presence of stiff 𝜔 particles which according to previous studies

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commonly occur in Ti-alloys with niobium contents from 15 at. % up to 35 at. % [16,56,57]. The elastic properties of the 𝜔 phase have been calculated/measured at 𝐸 = 130 − 200 GPa [16], so even if present at small proportions would still have a noticeable impact on the composite response. While we have not detected any 𝜔 phases in our XRD analysis, their detection might be impossible if nanosize particles are at stake. Furthermore, one should bear in mind that the 𝛽 − Ti phase undergoes martensitic transformation into 𝛼" − Ti under plastic deformations [47,48]. As indentation entails significant plastic deformations during loading, this phase transformation mechanism could be an additional source of stiffening in ours results.

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titanium alloys. Their calculations are based on two parameters: (a) the bond order 𝐵𝑜 , which is a measure of the covalent bond strength between Ti and an alloying element

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and (b) the metal d-orbital energy level 𝑀𝑑 , which relates to the electronegativity and metallic radius of elements [59]. These values for titanium and niobium are 𝐵𝑜Ti = 2.790, 𝑀𝑑Ti = 2.447 eV and 𝐵𝑜Nb = 3.099, 𝑀𝑑Nb = 2.424 eV, respectively. The phase

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stability of titanium alloys can be assessed on the basis of ̅̅̅ 𝐵𝑜 and ̅̅̅̅ 𝑀𝑑 which are the

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compositional averages of the constituent elements based on their atomic fractions. The elastic modulus of a titanium alloy was found to relate to its average bond

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strength; the higher the ̅̅̅ 𝐵𝑜 of the alloy the higher its elastic modulus. Furthermore, the elastic modulus of an allow was found to relate with its location on the ̅̅̅ 𝐵𝑜 − ̅̅̅̅ 𝑀𝑑

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diagram [58]. More precisely, the moduli of alloys were observed to decrease with

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their proximity to the transus line. These two observations can explain (a) the minimum elastic modulus reported for Ti85Nb15 which is the alloy with the closest

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proximity to the transus line, and (b) the higher elastic moduli reported for higher Nb contents, due to the fact that alloys with higher Nb at.% have higher ̅̅̅ 𝐵𝑜 values and diverge from the transus line on the ̅̅̅ 𝐵𝑜 − ̅̅̅̅ 𝑀𝑑 diagram.

20

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ACCEPTED MANUSCRIPT

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Figure 9: Elastic modulus versus chemical composition of 𝐓𝐢 − 𝐍𝐛 films. For

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each sample, its crystal structure and porosity volume is presented. Figure 10 presents experimental stiffness data of Ti − Nb alloys for different Nb

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contents found in the literature, the majority of which are in the Nb −range of 0 − 50 at.%. The reported data is primarily on bulk specimens (Figure 10(a)) where the

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𝛽 − Ti phase is stabilized by increasing the content of the beta-stabilizing element,

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Nb. Additionally some studies utilize heat processing coupled with furnace cooling or water quenching to maximize the beta phase presence. In general, high cooling rates

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lead to materials with lower elastic moduli [7,60], an example of which is shown in Figure 10(a) through the data of Afonso et al. [60] where the 𝐸 −modulus shifts from 79GPa in the furnace cooled case to 74GPa when water quenched. On the contrary, aging of quenched materials at high temperatures can lead to the precipitation of stiff 𝜔 nanoparticles and increase the elastic material response [15,16]. Figure 10(b) contrasts our experimental results with the only (to the best of our knowledge) available data on Ti − Nb films. In general, the films deposited within this study exhibit lower elasticity values which can be attributed to the incorporation of porosity into the system. Consistent with the data of Achache et al. [61] the 𝛽 − Ti phase can be stabilized at Nb contents greater than 20 at. % resulting in lower 21

ACCEPTED MANUSCRIPT 𝛦 −values than pure, 𝛼 − Ti. In general the two data sets are in reasonable agreement except for pure Ti and Ti85 Nb15, the discrepancies of which can be attributed to the

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variations in porosities (no porosities have been reported/measured in Achache et al. [61]).

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For high percentages of Nb content (>50 at.%) the elastic modulus of the films increases until a pure niobium response is reached (Figure 9). It is interesting to note

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that the fcc niobium grown during magnetron sputtering deposition is not common and its mechanical properties (to the best of our knowledge) have not been reported in

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the literature. In what follows we will extract through micromechanical modeling the contribution of porosity on the composite response such as to extract the mechanical

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properties of compact (porosity-free) materials. The elastic modulus estimates of porosity-free materials (Ti and Nb) will serve as: (a) a benchmark for our

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experimental results in the case of pure Ti, and (b) and experimental first estimate of

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the elastic properties of fcc Nb for the case of pure Nb.

Figure 10: Literature data on elastic modulus vs. Nb content for (a) bulk specimens and (b) films. Data from [7,8,47,61].

22

ACCEPTED MANUSCRIPT 3.4.2 Microporomechanical modeling The porous titanium composite can be conveniently modeled with the self-consistent

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micromechanical scheme developed by Hershey and Kroner (see [62]). The model has been tested on several materials and has been found to show very good predictive

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capabilities. In the case of an isotropic matrix with spherical pore inclusions, the scheme yields the following homogenized response (K, G) [63]: 𝐾 4𝜑 𝐺/𝑔𝑠 = 𝑘𝑠 4 𝐺/𝑔𝑠 + 3(1 − 𝜑)𝑟𝑠

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(3)

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𝐺 1 5 3 = − (1 − 𝜑) − 𝑟 (2 + 𝜑) 𝑔𝑠 2 4 16 𝑠

𝑘

2(1+𝜈 )

(4)

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1 + √144(1 − 𝑟𝑠 ) − 480𝜑 + 400𝜑 2 + 480𝑟𝑠 𝜑 − 120𝑟𝑠 𝜑 2 + 9𝑟𝑠 2 (2 + 𝜑)2 16

where 𝑟𝑠 = 𝑔𝑠 = 3(1−2𝜈𝑠 ) > ∅ and k s , g s are the bulk and shear moduli of the solid 𝑠

𝑠

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phase respectively, 𝐾, 𝐺 are the bulk and shear modulus of the composite porous

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material, 𝜑 is the volume fraction of porosity and 𝑣𝑠 is the Poisson’s ratio of the solid phase material. Finally, the elastic modulus of the porous material can be calculated

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through the classical relation of linear isotropic elasticity: 𝐸=

9𝐾𝐺 3𝐾 + 𝐺

(5)

The self-consistent scheme exhibits a percolation threshold at 𝜑 = 0.5 and it is therefore more suitable for granular or polycrystalline materials. Other composite models, like the differential [64] or the Mori-Tanaka [65] scheme exhibit a smooth gradual evolution of the composite elastic response with porosity that vanishes when 𝜑 = 1. Nevertheless for porosity values below 25% the various models exhibit almost identical responses. Figure 11 presents the composite response of porous titanium as predicted by the self-consistent and differential schemes in comparison with 23

ACCEPTED MANUSCRIPT experimental results collected herein (our nanoindentation data point on pure Ti) and reported in Ref. [25]. It is readily understood that the lower values of pure Ti

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measured experimentally through nanoindentation relates to the presence of pores in our material system. The small deviations from the theoretical models may result

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from either the experimental measurements of the porosity or from the calculations to estimate the elastic modulus of films. The accuracy of the prediction validates the extracted elastic modulus of the porous Ti −alloys presented above and the adopted

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methodology. Furthermore, the micromechanical analysis presented herein suggests

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an alternative route for creating mechanically biocompatible materials, by further increasing the porosity of the material closer to 30-40 vol.%.

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Finally, using Eqs. (3) to (5) and the experimentally obtained porosity for pure niobium film one can back-calculate the elastic modulus of the porosity-free fcc

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niobium, 𝐸 ≈ 185 GPa. The stiffer response of the fcc crystal structure compared to

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the bcc niobium (𝐸 = 105 GPa) is in line with the more compact arrangement of

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atoms in the unit cell.

Figure 11: Experimental data and micromechanical predictions of the elastic response of porous titanium. The graph includes the experimental data from Oh et al [25], the nanoindentation measurement for Ti collected in this study and the micromechanical predictions of the self-consistent and differential schemes. 24

ACCEPTED MANUSCRIPT 4

Concluding remarks

We report on the growth (magnetron sputtering) and characterization of Ti − Nb films

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covering a broad spectrum of compositions. Through this systematic study we provide experimental data on the synthesis-structure-mechanical properties of Ti − Nb alloys

applications. The main observations follow:

Magnetron co-sputtering at moderate deposition energies results in columnar

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

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on the basis of which the material system can be tailored for biomedical or other

growth and porous titanium niobium films with porosities in the 2 − 14 vol. %

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range. In the case of pure Nb the porosity significantly increases to 25 vol.% due to the high melting point of the material that results in very low 𝑇𝑠 /𝑇𝑚

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ratios and subsequently suppresses any surface diffusion phenomena during growth.

With 20 at. % of niobium, the 𝛽 − Ti phase is stabilized as evident by x-ray

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

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measurements and the calculated lattice constants. This result demonstrates the ability of magnetron sputtering to stabilize the 𝛽 −phase of titanium in

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lower temperatures than those of their bulk counterparts due to the ability of the technique to control kinetic and impact energies, instead of thermodynamic processes.



At high niobium concentrations the fcc phase is stabilized. A back-analysis on the composite porous response of the niobium film suggests an elastic modulus of the zero-porosity polycrystalline fcc niobium phase of 𝐸 ≈ 185 GPa.

While we have demonstrated that 𝛽 − Ti alloys can be grown in film geometries with elastic moduli in the ~70-90GPa range their optimization in terms of

25

ACCEPTED MANUSCRIPT mechanical biocompatibility remains a subject of further investigation. Additional reduction in the elastic modulus could potentially be achieved via two routes: (a)

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maximizing the β-phase while suppressing the possible growth of any stiff phases (i.e., 𝜔 particles) through ternary alloying and/or (b) introducing additional

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porosity into the system (see 𝐸 vs. 𝜑 scaling in Figure 11). Acknowledgements

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GC, LK and DP would like to acknowledge the financial support from the Strategic Infrastructure Project NEW INFRASTRUCTURE/STRATH/0308/04 of DESMI

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2008, which is co-financed by the European Regional Development Fund, the European Social Fund, the Cohesion Fund, and the Research Promotion Foundation

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of the Republic of Cyprus. GC would also like to acknowledge the financial support from Cyprus University of Technology, through the start-up grant. NTP and GAE

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would like to acknowledge support from the BioTiNet ITN (No. 264635) FP7 Marie

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Curie project. Finally, the authors would like to acknowledge the reviewers that evaluated our manuscript for their thoughtful and constructive comments that

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contributed to the improvement of this paper.

26

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Highlights

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Magnetron-sputtered Ti−Nb films, in a broad composition range, have been studied 𝛽−Ti has been stabilized for Nb contents greater than 20 at.%

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Low adatom mobility resulting from deposition conditions led to porous Ti− Nb films Biocompatible films can be achieved through soft 𝛽/𝑎"−Ti allotropes and/or porosity

32