<figure><img src="image_1.png" /></figure>

# Laser assisted fabrication of mechanochemically robust Ti3Au intermetallic at Au-Ti interface

Oktawian Bialas<sup>a,*</sup>, Augustine N.S. Appiah<sup>a</sup>, Marta Wala<sup>b</sup>, Anil Kunwar<sup>a</sup>, Anna Woźniak<sup>a</sup>, Paweł M. Nuckowski<sup>a</sup>, Wojciech Simka<sup>b</sup>, Peter Råback<sup>c</sup>, Marcin Adamiak<sup>a</sup>

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

**Article history:**

Received 20 November 2022

Revised 20 March 2023

Accepted 10 April 2023

Available online 21 April 2023

**Keywords:**

Laser microalloying

Electrodeposition

βTi3Au

Finite element method

Nanoindentation

Corrosion tests

## ABSTRACT

Intermetallics such as Ti3Au are characterised by improved mechanical properties and reduced susceptibility to corrosion. This study extensively blends the techniques of process simulation by finite element analysis, light microscopy, scanning electron microscopy, energy dispersive spectroscopy and structural roentgenography analysis to investigate the interfacial intermetallics (IMC) in Au-Ti system. Ti was electrochemically coated with a micrometric layer of gold and then laser-treated in a wide range of parameters. Variability included both the laser beam power and the beam feed rate. The experimental results confirm that the formation of an intermetallic Ti3Au phase is possible. Finite element method was employed to numerically estimate the transient temperature values at the Au-Ti interface during laser treatment. At laser power 100 W and scan speed of 1.5 mm/s, the interfacial temperature reached a magnitude larger than the melting point of Ti for a duration less than 5.0 ms. The decrease of scan speed to 1.0 mm/s for constant P, increased this duration up to 97.0 ms where both provided sufficient energy for convection-based reaction at the interface. Through nanoscale molecular dynamics simulation, it has been revealed that during nanoindentation, Ti and Au atoms of Ti3Au IMC exert a larger resistance force to the indenter as compared to the atoms of pure Ti material. The IMC material not only offers a more robust mechanical response during indentation but also exhibits superiority over pure Ti material in a corrosion test.

© 2023 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

## 1. Introduction

Cardiovascular diseases are still the main causes of death worldwide, according to recent who data [1], accounting for around 30% of global mortality. Despite the passage of years, this condition is not improving satisfactorily, hence there is a need for continuous intensive development of methods and treatments of chronic cardiovascular diseases. The instruments primarily designed to enhance the heart's pumping capacity in the event of a malfunction are ventricular assist devices (VADs) (pulsative and rotating blood pumps) and total artificial heart (TAH) devices. In addition to the above applications, the use of highly biocompatible materials is also necessary in other medical fields such as otolaryngology (middle ear prostheses) or neurosurgery (clipping of brain aneurysms) [2–4]. Patients with devices implanted into the bloodstream after the first few days are exposed primarily to thrombo-

sis. The resulting clots break off into smaller blood vessels and block the light of their flow, causing ischemic strokes. The formation of thrombosis can be explained by Virchow's triad: stasis, endothelial damage and hypercoagulation. Foreign bodies in relation to natural ones, being a part of the blood system, are thrombogenic and activate the clotting system through factor XII which leads to platelets deposition. It has been shown that platelet deposition on the Dacron rings of the valves typically occurs in the first 24 h after the implantation. The non-physiological blood flow, characterised by the presence of areas with high shear stress or low velocity/stagnation, favours platelet activation and thrombosis. Each individual design of a prosthetic mechanical device has a characteristic blood flow pattern [5–8].

The main metallic materials that have been used for such kinds of medical devices for a long period of time are titanium and its alloys, but due to the unstable formation of a passive layer on titanium and its low mechanical properties, many surface treatment solutions have been applied [9–12]. Among the numerous materials that significantly improve the usability of titanium in biomed-

<footnote><sup>a</sup>Silesian University of Technology, Faculty of Mechanical Engineering, Konarskiego Str. 18A, 44-100 Gliwice, Poland</footnote>

<footnote><sup>b</sup>Silesian University of Technology, Faculty of Chemistry, B. Krzywoustego Str. 6, 44-100 Gliwice, Poland</footnote>

<footnote><sup>c</sup>CSC-IT Center for Science, Keilaranta 14, P.O. Box 405, FIN-02101 Espoo, Finland</footnote>

<footnote>* Corresponding author.
E-mail address: oktawian.bialas@polsl.pl (O. Bialas).</footnote>
ical applications, gold as a precious metal appears to be a very good choice that has the potential to expand its use even further. This is possible due to the gold's characteristics that ensure biocompatibility, antibactericity, non-toxicity, non-immunogenicity, and high tolerance without slowing down cellular functionality. In addition to this, the use of gold nanoparticles can take advantage of its antioxidant effect, leading to internalisation in cell nucleus [13–15]. From the viewpoint of prosthetic application and performance, the biggest disadvantage of gold is its high-density $d_{au} = 19.3$ g/cm³, and consequently its weight, and low hardness. Moreover, the young's modulus of gold (approx. 81 GPa) is lower than that of titanium (approx. 102 GPa). To modify the mechanical properties of gold, other metals have been into pure gold as alloying additives [16]. Popular additives in gold alloys over the years have been and still are palladium Pd and platinum Pt, which increase the solidus temperature, as well as such non-precious elements such as indium, or tin, added to improve hardness and to adjust the coefficient of thermal expansion of the ceramic components of the prosthesis.

Ti-based intermetallics have gained increased importance in biomedical device applications [17–19]. Among this class of Ti-based intermetallics, the intermetallic compounds (IMCs) corresponding to the binary Ti-Au system are of particular interests when it comes to the study of mechanical properties [18]. Besides the mechanical properties, there is a need not only to assess the corrosion properties of such IMCS but also to design the feasible route of their fabrication. Owing to the benefits such as contactless method, precision manufacturing and localized application of energy offered by laser-based devices [20,21], laser processing has been considered as an immensely popular manufacturing technique. The possibility of the laser treated local surface to reach an extremely high temperature enables this manufacturing technique to be employed in systems that employ materials having high melting point such as Ti (melting temperature = 1941 K). Olejnik et al. [21] have implemented laser dewetting technique to fabricate Au-Ti glucose sensing electrodes. The purpose of the laser processing in their work is to insert au nanoparticles (diameter = 60–90 nm) in the nano-sized cavities of Ti foil. In context of their work, for a given energy fluence in the range 30–120 mJ/cm², the Ti does not undergo melting, and there is no mention of Ti-Au intermetallic formation at the interface between au nanoparticles and Ti substrate. To the best of our knowledge, there has not been any work published in the topic of laser-based fabrication of Ti-Au intermetallics for a system consisting of au film deposited over Ti substrate. Any such work associated with laser treatment of Au/Ti system in such a way that both au film and Ti film undergo melting at the vicinity of interface, can ensure the accelerated growth of interfacial intermetallic compounds.

For laser processing of Ti-Au system, convection plays a major role and can be controlled by choosing the specific parameter kit (power, beam speed and defocusing of the laser source) which influence the kinetics of phase formation [22]. That finding indicate the huge potential in Ti-Au system that is still undiscovered. Previous studies conducted by Sundgren et al. [23] indicated that there is a significant difference between protein adsorption on hydrophilic titanium and hydrophobic gold surfaces. The main difference is that gold surfaces tend to form a thin, dense protein layer, that is constant in time, while on titanium surfaces the extended loosely packed protein layer is formed, with a tendency to change with time. This phenomenon is enhanced, inter alia, by the unstable oxide layer of the passivating titanium [24]. The use of the TiAu intermetallics may enable the possibility of controlling the protein layer and thus influencing the clotting system minimalizing the blood-flow pattern and artificial material influence [23,25]. Furthermore, Kodama et al. Research indicates that the use of inter-

metallic compounds (IMCs) composed of a diamagnetic element (e.g. Au) and a paramagnetic element (e.g. Pt) reduces artefacts resulting from a disturbed magnetic field near the imaging target due to the difference in magnetic susceptibility between the metal and the surrounding living tissue [26]. Since the Au-Ti pair is also a diamagnetic and paramagnetic pair (like Au-Pt), surface application of coatings containing these elements may be a cheaper alternative for applications requiring high magnetic field. Currently, a standard for magnetic resonance imaging (MRI) in conventional usage is from 1.5 to 3.0 T of magnetic induction value, for precise imaging of small anatomical structures a magnetic induction value of >3.0 T is necessary [3,27]. Knowing the magnetic induction of living tissues to be in the range of -11 to -7 ppm, Kodama et al [26]. Obtained an approach (in Ti-Pt alloy) to a value of -9 ppm, which (apart from the tissue toxicity of copper) does not occur for any other known metallic material. This allowed for significantly fewer artefacts during MRI, especially in the case of high magnetic excitation. Given that the Ti-Au pair is also diamagnetic-paramagnetic, it can be assumed that the coatings we produce, will also present similar properties, at a reduced material cost. The Ti-Au pair also meets all other material requirements for implants, especially - no toxicity, high corrosion resistance, high electric conductivity.

The above literature reports led us to the decision to perform laser-assisted fabrication of novel TiAu intermetallic multilayers for biomedical and anti-corrosion applications. Our proposed coatings have the potential to replace currently existing coatings due to better control of the passive layer compared to titanium, good mechanical properties described in the literature and still relatively good economic ratio (thin gold layer, not platinum). An analysis of the potential advantages of the synergistic use of materials and processes in relation to the main disadvantages of the presented solution is presented in Fig. 1. The following research aims to establish the feasibility of producing a laser-assisted TiAu coating on a Ti base material. An electrochemically deposited au coating on titanium was subjected to laser processing in a wide range of parameters to produce intermetallic phases as a result of applying sufficient energy to excite the Ti and Au interfacial interface as a consequence of convective motions. An initial determination of the required temperature reached during the process was calculated by finite element analysis (FEA). Subsequently, the simulation results achieved allowed the start of an empirical evaluation of the results obtained in a range of process parameters for laser beam processing. After an initial evaluation by light microscopy (outer section) and scanning electron microscopy (SEM) (on cross-sections), the production of the target coating (line-by-line laser scanning with an overlap covering the not effectively melted zone) was carried out, and the resulting phases were evaluated by energy dispersive spectroscopy (EDS) and structural roentgenography XRD. The corrosion resistance was evaluated during using open circuit potential measurements ($E_{ocp}$) and potentiodynamic tests in ringer's solution. The primary goal of testing sample in similarly behaving to natural physiological liquids environment is to faithfully reproduce a substance's in vivo behavior inside a pertinent biological compartment, and this goal will vary depending on the method of exposure, administration, or translocation of biological individuum which makes the whole process complex and forces researchers to perform in-depth analysis through different methodology for checking the biological response of a material in an organism. The results obtained in the course of the following study allowed the production, identification of the β-Ti3Au phase, and pre-testing of the obtained material, which allows further selection of process parameters towards its optimisation and testing the coating in the series of utility properties tests.
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Experimental methodology with applications resulting from improved properties, (a) original Ti sample, (b) electrodeposited sample (DC current), and (c) laser processed sample.</figcaption></figure>

## 2. Materials and methods

### 2.1. Material preparation

Samples from commercial pure titanium - grade II (cp Ti), were delivered as ø 30 mm rods (Wolften, Wrocław, Poland), and were cut in slices by cutting on a lathe. The material is characterized by the ASTM b348/b348m standard, with the chemical composition presented in Table 1.

The rod was cut into 7 mm thick slices and prepared for coating application. Each sliced sample was prepared according to metallographic procedure: grinding with sic paper grain size gradation sequentially: 220, 800, 1200 in time t = 4 min per each gradient and mechanical polishing using 0.04 µm colloidal silica. The process was performed using the grinding-polishing machine tergamin-30 (Struers, Willich, Germany). The general steps of methodology are presented in Fig. 1.

### 2.2. Gold layer electrodeposition

Titanium samples were washed and degreased, which was followed by their etching in boiling solution of hydrochloric acid (HCl). For the electrodeposition process, samples were polarized cathodically using the Kikusui PWR 800H (Kikusui, Yokohama, Japan) power source in a galvanostatic mode with current density of 0.3 a/dm². A platinum mesh served as an anode. A commercial electrolytic bath for gold plating was provided by the Kiesow Polska company, Zabrze, Poland. The process was adjusted so that the final thickness of the gold layer was ~2 µm which is the result of a

compromise between the use of a noble coating, the desired material roughness (not exceeding 1 µm) and an effective material thickness that will cover the native material with satisfactory efficiency, while still having enough of it to effectively form a Ti3Au layer.

### 2.3. Simulation

The laser processing of electrodeposited samples is associated with the spatial and temporal variation of the temperature. The interdiffusion and interfacial phase formation kinetics are largely dependent on the temperature of the domain. Hence it is necessary to understand the temperature evolution at the Ti-Au interface during laser processing. Fig. 2(a) shows the gold coated Ti specimen. As illustrated in schematic sketch of Fig. 2(b), the thin Au film (approximate thickness of 2 µm) is coated on top of Ti cylinder (base diameter = 30 mm and height = 7 mm). The Ti-Au interface is the region of interest for numerical analysis, and thus the representative volume element (RVE) shown in Fig. 2(a) will be considered as the computational domain for the finite element analysis. The Ti base metal will be represented by a cuboid of size 300 × 300 × 50 µm³, and a thin film of Au of thickness 2 µm is computationally placed over the Ti cuboid.

During laser heating of the Ti-Au samples, portions of the samples phases may undergo melting, and thus the computational domain will simultaneously have solid and liquid regions. The present work implements the apparent or effective heat capacity-based enthalpy method to enable the melting simulation in Ti-Au sample. The enthalpy of a material i (pure Au or pure Ti or Ti-Au

<table><caption>**Table 1**

Chemical composition of grade ii titanium used in experiment [28,29].</caption><thead><tr><th>Ti</th><th>Fe</th><th>O</th><th>C</th><th>N</th><th>H</th></tr></thead><tbody><tr><td>99.65</td><td>0.02</td><td>0.18</td><td>0.10</td><td>0.0096</td><td>0.0290</td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** The image in (a) corresponds to the experimental laser process Au-Ti sample. The schematic sketch of the laser processing in this sample is illustrated in (b). Since the domain of interest for microstructural analysis is the interfacial region, the sketch shown in (c) can be the representative volume element (RVE) of the sample during the finite element analysis. For enabling proper visualization of the coated thin film, the schematic sketches (b)-(c) are not according to scale and the vertical length is exaggerated much more than the horizontal length in these sketches.</figcaption></figure>

alloy) at a given temperature (t) is defined by the following expression [30]:

$$H_i(T) = \int_0^T \left( \rho_i C_{p,i} + \rho_i L_{f,i} \frac{\partial f}{\partial \tau} \right) dT \quad (1)$$

In Eq. (1), the symbols $\rho_i$, $c_{p,i}$ and $l_{f,i}$ are respectively the density, specific heat capacity, and latent heat of fusion of the material.

## 2.4. Laser microalloying

Samples were subjected to laser treatment in the form of lines in parameters presented in Table 2. The experiment was accomplished using Triumph Trudisk 3302 (Triumph, Ditzingen, Germany) based on 1030 nm wavelength continuous laser. The system provides energy that allows remelting of the material. The maximum energy for the laser acquired is 3.3 kw.

## 2.5. Microscopic analysis

Preliminary assessment of the effects of laser micromachining was carried out on an outer section by a metallographic light microscope axio observer (Zeiss, Oberkochen, Germany). The phase distribution of Ti-Au intermetallics present at the cross-section was determined using SEM EVO MA10 (Zeiss, Oberkochen, Germany) fitted with EDS spectrum analyser which enabled the determination of the surface texture and chemical composition.

<table><caption>**Table 2**
Laser parameters applied for the experiment.</caption><thead><tr><td>Laser power (P)</td><td>Scan velocity (Vs)</td><td>Focal defocusing</td></tr></thead><tbody><tr><td>100w</td><td rowspan="3">1 mm/s</td><td rowspan="3">+ 10 mm</td></tr><tr><td>150w</td></tr><tr><td>200w</td></tr><tr><td>100w</td><td rowspan="3">1.5 mm/s</td><td rowspan="3"></td></tr><tr><td>150w</td></tr><tr><td>200w</td></tr></tbody></table>

## 2.6. X-ray diffraction

Phase analysis was performed using an X'pert pro X-ray diffractometer (Panalytical, Almelo, the Netherlands) equipped with a cobalt lamp X-ray source (XRD). The lamp was set to 40 KV and the current, 30 mA was used. The X-ray phase diffraction measurement was carried out according to the Bragg-Brentano geometry. In order to precisely determine the phase composition of the remelted layer and compensate for the influence on the base material, grazing incidence diffraction (GID) geometry was applied. The obtained diffractograms were analysed by means of the X'pert high score plus software (v. 3.0e) with a dedicated inorganic crystal structure database - ICSD (Fiz, Karlsruhe, Germany).

## 2.7. Electrochemical study

The corrosion resistance of the tested samples was investigated using the Tafel method. The test was performed using test stand comprised of autolab 302n potentiostat (Metrohm AG, Herisau, Switzerland), controlled by the nova software (v. 1.1) and three-electrode system (Pt wire - auxiliary electrode, saturated calomel electrode SCE - reference electrode, tested samples - working electrode) in the cell with water jacket. Firstly, the open circuit potential ($E_{ocp}$) was measured in time 60 min for each sample, after which the potentiodynamic test was started from initial potential ($E_{int} = E_{ocp} - 100$ mV) to 278 mV. The test was carried out 3 times for each variant tested. The polarization rate was equal to 1 mV/s. All the electrochemical tests were performed in 250 ml of ringer's solution (NaCl - 8.6 g/cm³, KCl - 0.3 g/cm³, $CaCl_2 \cdot 2H_2O$ - 0.33 g/cm³) at 37 ± 1 °C and pH 7.4.

# 3. Results

## 3.1. Morphological analysis of the experimental samples

In the images from light microscopy (Fig. 3), laser transitions are observed, causing the coating to melt together with the substrate material in varying proportions. In the case of the processing variant p = 100, vs = 1 mm/s, a dendritic structure was observed in
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Light microscopy images of the outer section of the experimental sample parameters.</figcaption></figure>

the centre of the melt, which indicates high kinetics of the material heating and cooling cycle. In addition, for all machining variants with $p = 150$ W and 200 W, a granular structure is revealed, indicating a large grain size distribution.

The nature of the remelting revealed in the cross-sections of samples under the SEM presented in the Fig. 4, indicates overly deep remelting in variants involving laser powers of $p = 150$ w

and $p = 200$ w. Overly deep remelting results in too low concentration of gold in the titanium matrix, which does not allow crystallisation of the ti3au phase. The elemental concentration as a function of distance from the surface for laser powers $P = 150$ W and $P = 100$ W is presented in Fig. 5a–d). These results show that even at $P = 150$ W, there is too low concentration to form desired phases inside the coating.

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Cross-sectional SEM images for laser processed samples. The length of the vertical depth for the bright colored region increases with the increase in laser power (for a given scan speed), and decreases with scan speed (for a given power).</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Results of EDS microanalysis of the cross section of the laser-treated samples; (a) Sample P = 150 W, Vs = 1.5 mm/s Image of microanalytical area showing area of interests with atomic content of elements results, (b) scattered X-ray dispersion energy (EDS) diagram of measured point (a)-1, (c) sample P = 100 W, Vs = 1.5 mm/s image of microanalytical area showing area of interests with atomic content of elements results, (d) scattered X-ray dispersion energy (EDS) diagram of measured point (c)-1.</figcaption></figure>

The obtained results presented in Fig. 4 allow us to conclude that the useful laser power for the obtained coating surface conditions is 100 W. In addition, due to the fact that SEM imaging was carried out using the backscattered diffraction (BSE) technique - the brighter the image, the higher the molecular weight of the compound and it can be concluded that in the case of the variants P = 100 W Vs = 1 mm/s and P = 100 W Vs = 1.5 mm/s we can distinguish at least 2 phases differing significantly in the concentration of the heavier element (Au) from each other. In addition, it should be noted that the mutual contribution of the phases is most uniform for the parameter P = 100 W Vs = 1.5 mm/s. Moreover, this parameter is characterised by the greatest homogeneity of the structure in outer section (Fig. 3).

Fig. 5 shows the differences in atomic content of the elements in each area. The variant shown in Fig. 5a in the near-surface area presents only 2.5% Au atomically, confirming too much convective mixing and too little gold to titanium. For variants higher than 150 W, it was therefore not possible to produce a coating capable of significantly improving biomaterial properties. The situation is completely different from Fig. 5c, where EDS analysis showed a reciprocal ratio of Au to Ti of about 1:3, which may suggest at this stage the formation of a Ti3Au phase in area 1. In area 2, on the other hand, we observe a drastic drop in gold concentration to 11%. In view of the above results, it was decided to carry out XRD studies for the variant P = 100 W Vs = 1.5 mm/s.

To confirm the presence of the assumed phase, X-ray diffraction qualitative analysis was conducted. In the Fig. 6 XRD measurements in a) 2Θ Bragg-Brentano and b) Grazing Incidence Diffraction (GID). Measurement performed at ambient temperature confirmed the presence of a gold solid solution, as well as α-Ti, titanium (II) oxide, titanium(IV) oxide, and β-Ti3Au intermetallic phase crystalized in a cubic crystal system, and two-space groups Pm-3m and Pm-3n. The results from GID method (Fig. 6b) didn't reveal Pm-3m phase variant due to the limited penetration of the X-ray radiation. This means that the Ti3Au Pm-3n variant crystal-

lizes from the gold side and is therefore identified. The Pm-3m variant, due to being crystallized on the titanium side, is located deeper and was not identified in the GID.

## 3.2. Temperature distribution in the laser processed samples – numerical analysis

A constant laser power of 100 W is used, and two values of scan speed (Vs = 1.0 mm/s and 1.5 mm/s) are employed for the laser system directed onto the electrodeposited Au surface of the Au-Ti system. Computation of the temperature variable in the AuTi representative volume element (RVE) is accomplished using finite element analysis. The mesh of the materials system is shown in Fig. 8(a). While the entire mesh is illustrated in Fig. 8(a)(i), the inset image i.e. Fig. 8(a)(ii) highlights the meshing performed at the interface region between the Au thin film and the base Ti material. The tetrahedral mesh elements are used to represent the 3D mesh in the computational domain. Sub-meshes are introduced in the geometrical region corresponding to the volume of the thin Au film, so that the interface region is characterized by a finer mesh. The mesh consists of 169,505 mesh elements, and 29,402 nodes. The initial temperature of Au-Ti system is considered as 298 K (both Au rich top film and Ti base in the slab are in solid phase). Upon exposing the top layer of the materials system to a laser beam of spot diameter 245 µm, the gold film mainly absorbs the incident heat flux and heat transfer takes place. As will be shown mathematically, conduction and convection are the major modes of heat transfer in the system.

The thermodynamic CALPHAD database of Ti-Au alloy is obtained from Xiong et al. [31], and the enthalpies of Au (pure) and Ti (pure) are computed as a function of temperature using OpenCalphad software [32]. The calculated values of H (T) for Au and Ti are presented in Fig. 7. At the melting point of a metal or alloy (1337 K for Au, and 1941 K for Ti), the enthalpy curves appear as vertical lines in the figure. The jump in the enthalpy magnitude
<figure><img src="image_8.png" /><figcaption>Fig. 6. XRD analysis results of sample P = 100 W, Vs = 1.5 mm/s: (a) 2Θ Bragg-Brentano angle, (b) Grazing Incidence Diffraction (GID) (c) elemental unit cells models characterised in XRD made using VESTA software.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Enthalpies of (a) gold and (b) titanium are expressed as a function of temperature. The projections of the vertical lines of the enthalpy curves on the T axis are the melting regime of these materials.</figcaption></figure>

as indicated by the length of the vertical line at the melting regime of the H-T curve is the latent heat of fusion (Lf). The part of the curve at the left side of the vertical line corresponds to the solid phase whereas the potion at the right side is the liquid phase.

The partial differential equation (PDE) for heat transfer process in the AuTi computational domain (Fig. 8(a)) undergoing laser processing is given as follow [30]:

$$ \rho_i C_{app,i} \left( \frac{\partial T}{\partial t} + \vec{u} \cdot \nabla T \right) = k_i \nabla^2 T + Q_{laser} \quad (2) $$

where i = Au, Ti. In above equation, T is temperature variable, t is time. The density and thermal conductivity of the material i are respectively denoted as $\rho_i$ and $k_i$.

The apparent/effective heat capacity ($C_{app,i}$) of the material is a function of its enthalpy ($\partial H_i$) defined by the following expression:
<figure><img src="image_10.png" /><figcaption>Fig. 8. As illustrated in (a), the entire computational domain (volume = 300 µm × 300 µm × 52 µm) with tetrahedral mesh elements is shown in (a)(i), and the inset in (a)(ii) is an enlarged image of the portion of the domain. As revealed in (b) the 50 µm thick Ti base has coarse mesh whereas the Au thin film (2 µm) has a relatively finer mesh. The heat from the laser will enter the medium from the top Au surface. Average magnitude of velocity in the computational domain at t = 0.04 s for laser with P = 100 W, and Vs = 1.0 mm/s is shown in (b). At this stage, only the portion of Au film is molten, and the Ti beneath the Au is still in solid state. The influence of scan speeds of the laser at a given power of 100 W on the temporal evolution pattern of T at the interface point 2 µm below the surface (located at starting point of the laser beam) is depicted in (c). The images in (d) reveal the thermal distribution profiles on the 3D computational domain at different time for heating by the 100 W laser source moving with a scan speed of (d) (i) Vs = 1.0 mm/s, and (d)(ii) Vs = 1.5 mm/s. It is obvious that surface and interface of the Au-Ti system reaches higher temperature, and that too for a longer duration when the scan speed is lower.</figcaption></figure>

$$ \rho C_{\text{eff}} = \frac{\partial H_i}{\partial T} \frac{\partial t}{\partial t} \qquad (3) $$

In the current work, the term $Q_{\text{laser}}$ is represented by flat top heat source [33] and is defined by the following expression:

$$ Q_{\text{laser}} = \frac{2 \propto P \phi}{\pi r_0^2} U^* e^{(-\alpha \delta_z)} \qquad (4) $$

In Eq. (4), $\propto$ is the absorption coefficient of Au, and as mentioned in Zhu et al. [34], its value is assumed equal to 8.5E+07 m⁻¹ for the current experiment using particular wavelength of laser. P is the laser power, and for the current model, its value is 100 W. $\phi$ is a function of excitation beam wavelength and fluorescence quantum efficiency. The quantity $r_0$ is the beam spot radius and is equal to 122.5 µm. The radial distance of a point (x, y) from the center (x(t), y0) of a moving beam is the initial position of the beam center. The scan speed (Vs) of the laser is defined as $V_s = \frac{dx}{dt} = \frac{\chi(t)-\chi_0}{t}$. In the current model, two scan speed values (1 mm/s and 1.5 mm/s) are employed. The quantity $U^* = U|r_0 - r|$ will be 0 if $|r_0 - r|$ has a negative value, and 1 if it is positive. $\delta_z$ in the expression is the length in the vertical (z direction) On obtaining adequate heat ($Q_{\text{laser}}$) from the laser, the surface material at the vicinity of the laser beam spot can melt and subsequently flow with a flow velocity ($\vec{u}$) in the melt pool. As depicted in Eq. (2), the two major modes of heat transfer in Au-Ti medium heated by laser beam are the conduction and convection modes. For laser with large power or small scan speeds, the molten regime can expand to a depth quite beneath the surface.

The dynamics of fluid flow in the melt pool is described by the incompressible Navier-Stokes equations:

$$ \nabla \cdot \vec{u} = 0 \qquad (5) $$

$$ \rho_i \frac{\partial \vec{u}}{\partial t} + \rho \left( \vec{u} \cdot \nabla \right) \vec{u} = \nabla \cdot \left[ -pI + v_i \left( \nabla \vec{u} + \left( \nabla \vec{u} \right)^T \right) \right] + F_i \qquad (6) $$

In the momentum equation (Eq. (6)), $v_i$ is the viscosity of liquid material. The expression for Boussinesq approximation is utilized within the $F_i$ term to enable the variation of liquid density only in the vertical direction and thereby ensure the incompressible nature of flow in the melt pool. The simulation figure illustrating the numerically computed average velocity magnitude in the computational domain treated by laser of P = 100 W and Vs = 1.0 mm/s is presented in Fig. 8(b). It is noteworthy to mention that the temperature of the computational domain has spatial and temporal variation during the laser irradiation procedure. The properties such as density, thermal conductivity, specific heat capacity and viscosity vary with variation of temperature. The temperature dependence of heat capacity can be represented by the enthalpy-temperature curves (Eq. (3)). Viscosities of liquid Au and liquid Ti have been assumed to be equal to that of other molten metal alloys such as Sn-0.7Cu solder, and the temperature dependence of viscosities of liquid and semi-liquid Au and Ti materials is considered in the model. For liquid phase Au or Ti, the Arrhenius equation is utilized to represent the dynamic viscosity [35]. However, for mushy zone, the apparent viscosity is approximated to be equal to the asymptotic viscosity [35]. Solid Au film or solid Ti block
are assumed as materials of very large viscosities, and this consid-
eration will enable these solid regions to have zero velocities in a
multi-phase system.

The fitted data of density of Au and Ti at both solid and liquid states are plotted graphically against temperature in Fig. 9. The densities of solid Au presented are derived from the report by Ricci et al. [36]. The values of liquid Au densities as shown in Fig. 9 are obtained from the work of Paradis et al. [37]. The values for temperature dependent density of solid Ti are obtained from the work of Zhang et al. [38] whereas the densities of liquid Ti are obtained from the report by Wang et al. [39]. It can be inferred from the curves that the absolute density of Au is several times larger than that of Ti for both solid and liquid states. For example, at T = 700 K, both Au and Ti are in solid state. From the images, it can be observed that: $\rho_{Au(700K)} = 18817.6 \text{ kg/m}^3$ and $\rho_{Ti(700K)} = 4433.22 \text{ kg/m}^3$. At 1950 K, both Au and Ti are in liquid state, and from (b) and (d), it is possible to find that $\rho_{Au(1950K)} = 16517.28 \text{ kg/m}^3$ and $\rho_{Ti(1950K)} = 4127.93 \text{ kg/m}^3$. The density of Au decreases linearly with temperature at both solid and liquid states. The density of solid Ti however decreases parabolically with temperature whereas that of liquid Ti decreases linearly.

The thermal conductivity data of Au for solid state are obtained from the work of Cook and Van der Meer [40], and the data for liquid state are derived from the work of Petrov et al. [41]. The report by Zhang et al. [38] is utilized to derive data for thermal conductivity of solid Ti. The thermal conductivity of liquid Ti is derived from the work of Watanabe et al. [42]. The k data were fitted against temperature, and graphically presented in Fig. 10. kAu decreases with temperature in solid state, whereas increase for liquid state. On the other hand, as revealed in Fig. 10, the kTi increases both for solid and liquid states. The curve of kTi is non-linear in solid state, whereas it is linearly increasing with T in liquid state. The kTi is quite smaller in magnitude than the kAu for a given temperature. In the solid state, the thermal conductivity of Au is more than

<figure><img src="image_11.png" /><figcaption>**Fig. 10.** Temperature dependence of thermal conductivities of Au and Ti in solid (s) state and in the liquid (l) state.</figcaption></figure>

10 times larger than that of Ti. For an example, at 700 K, it can be observed from Fig. 10 that $k_{Au(700K)} = 290.40 \frac{W}{mk}$ and $k_{Ti(700K)} = 17.33 \frac{W}{mk}$. On the other hand, in the liquid state, the k values of Au is only 3–5 times larger than those of Ti. Fig. 11 also shows that $k_{Au(1950K)} = 153.42 \frac{W}{mk}$ and $k_{Ti(1950K)} = 34.12 \frac{W}{mk}$.

The results of finite element analysis are presented in Fig. 8(d)
(i). For a given laser heating power of 100 W. Fig. 8(d) mainly high-

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Temperature dependence of densities of Au and Ti in solid (s) state and in the liquid (l) states. While the densities of solid Au (s), liquid Au(l) and liquid Ti(l) decrease linearly with temperature, the density of solid Ti(s) is observed to decrease parabolically with temperature.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Fig. 11.** The schematic sketch of the MD simulation setup for nanoindentation test is shown in image (a). The radius (R) of the spherical indenter is 3 nm (=30 Å). The dimensions of the slab corresponding to initial configuration is indicated as $I_x \times I_y \times I_z$. For Ti supercell (constructed in an orthogonal mode for a unit cell of HCP structure), $I_x = 120.28$ Å, $I_z = 121.96$ Å, and $I_z = 79.17$ Å. On the other hand, the dimensions for Ti₃Au supercell (built from simple cubic unit cell) are $I_x = I_y = 122.72$ Å, and $I_z = 81.81$ Å. In both of these nanostructures, the atoms within the vertical length of $d_{fx} = 40$ Å from the slab base are kept fixed during the entire simulation. The simulation results for (b) Ti, and (c) Ti₃Au nanostructures are presented corresponding to the timestep when the indenter traverses a depth of 2.5 nm (= 25 Å). It is to be understood in these images that Ti atoms are represented by gray colored spheres whereas gold atoms are represented by yellow colored spheres. The curves in (d) reveal the variation of the resultant indentation force with the vertical displacement of the indenter.</figcaption></figure>

lights the spatial-temporal evolution pattern of T in the dimensional computational domain at two Vs values. At the final simulation time of t = 0.2 s, the laser focal point is still somewhere within the computational domain for Vs = 1.0 mm/s, whereas this point already reaches the end length of the Au-Ti computation domain at Vs = 1.50 mm/s. The intensity distribution of irradiation decreases exponentially with the radial distance from the focal point, and thus the Au surface is exposed to relatively larger amount of irradiance when the scan speed is less for a given power value. Hence the surface and interface temperature at vicinity of laser beam focal point reaches a relatively higher value in Fig. 11(d)(i) than as compared to Fig. 8(d)(ii). The temporal evolution of T at the interface point located 2 µm below the starting corner of the domain is graphically plotted for the two scan speeds in Fig. 10.

For P = 100 W, Vs = 1.0 mm/s, the peak temperature is 2133 K whereas the maximum temperature obtained by this interface for laser with P = 100 W, Vs = 1.50 mm/s, is about 1969 K. It must be highlighted that for a total laser heating duration of 0.2 s, the interface point in the computational domain irradiated by 100 W, 1.0 mm/s remains at a temperature above the melting point of Ti (Tm,Ti) for a total duration of 97 ms. However, when using the laser of same power but larger scan speed of 1.5 mm/s, the interface point remains at T > Tm,Ti for duration less than 5 ms. Thus, heating the medium with laser at lower scan speed of 1.0 mm/s accounts for larger convection effects during the interfacial reaction and melt pool evolution. In order to numerically obtain the temperature profile in the Au-Ti materials system undergoing laser heating, the coupled set of partial differential equations corresponding to heat transfer and fluid flow is solved using finite element method in Elmer multiphysicsics software [30,43].

### 3.3. Numerical simulation of indentation test for understanding the mechanical response of Ti and Ti3Au slabs at nanoscale

In this study, the atomistic simulations for the nanoindentation process of the Ti and Ti3Au nanostructures were performed using Molecular Dynamics (MD) methods. The simulation set up with nanoslab of dimensions $I_x \times I_y \times I_z$ is shown in Fig. 11(a). The supercells of Ti and Ti3Au were constructed using Atomsk software [44]. In context of Ti material, a unit cell of hexagonal closed pack (HCP) structure is first built, and then it is replicated in all directions to form a supercell consisting of 66,912 atoms. An operation is implemented during replication to construct it as an orthogonal supercell of $I_x = 120.28$ Å, $I_y = 121.96$ Å, and $I_z = 79.17$ Å. In context of IMC Ti3Au, a unit cell of simple cubic structure is replicated in X, Y and Z directions to form a supercell of dimensions $I_x = I_y = 122.72$ Å, and $I_z = 81.81$ Å. The nanoslab of Ti3Au IMC consists of a total of 73,728 atoms (55296 Ti atoms and 18,432 Au atoms). In this simulation set up, the X, Y and Z axes are respectively along the [100], [010] and [001] crystallographic directions. As revealed in Fig. 11(a), the nanoindentation simulation domain consists of two regions: the top active region (that is being indented) and the bottom fixed region. In the bottom fixed region, the atoms do not move during the entire simulation time, and thus it provides the rigid support for the nanoindentation process. The fixed region spans from the base of the slab to the upward length $d_{fx} = 40$ Å, and the length of the active nanoindentation region = $I_z - d_{fx}$. The indenter is a virtual one, and is represented by a non-atomic rigid and repulsive sphere of radius (R) = 30 Å. The indenter is initially positioned at a location in such a way that the distance from its center to the top surface of the slab is more than R by an amount a fraction of 1 Å.
The dimensions of the slab corresponding to initial configuration is indicated as $l_x \times l_y \times l_z$. For Ti supercell (constructed in an orthogonal mode for a unit cell of HCP structure), $l_x = 120.28$ Å, $l_y = 121.96$ Å, and $l_z = 79.17$ Å. On the other hand, the dimensions for Ti3Au supercell (built from simple cubic unit cell) are $l_x = l_y = 122.72$ Å, and $l_z = 81.81$ Å. In both of these nanostructures, the atoms within the vertical length of $d_{fx} = 40$ Å from the slab base are kept fixed during the entire simulation. The simulation results for (b) Ti, and (c) Ti3Au nanostructures are presented corresponding to the timestep when the indenter traverses a depth of 2.5 nm (=25 Å). It is to be understood in these images that Ti atoms are represented by gray colored spheres whereas gold atoms are represented by yellow colored spheres. The curves in (d) reveal the variation of the resultant indentation force with the vertical displacement of the indenter.

The indenter upon contact with the atoms of the nanoslabs of Ti or Ti3Au, exerts the following repulsive force $F(r)$:

$$F(r) = \begin{cases} -K_c(r-R)^2; & r<R \\ 0; & r \ge R \end{cases} \qquad (7)$$

In Eq. (7), $K_c$ is the specified force constant of value 1300 $eV/Å^3$, and $r$ is the distance from the atom to the indenter's center.

In order to model the Ti-Ti atomic interactions in the pure Ti slab, Embedded Atom Method (EAM) potential developed by Zhou et al. [45] is utilized. In context of intermetallic Ti3Au, the interactions for Ti-Ti pairs and Au-Au pairs is modeled using the EAM interatomic potentials [45]. The interactions between Ti and Au atoms have been described with the help of Morse potentials.

The MD simulations were performed using the LAMMPS software [46]. Identical boundary conditions, timestep size and loading rate (for indentation motion) were applied to both of Ti and IMC materials. The timestep of iteration is taken as 1 fs. Periodic boundary conditions (PBC) are implemented in the X and Y directions whereas non-periodic and shrink-wrapped boundary conditions are applied along the Z direction. The use of PBC along X- and Y-directions will ensure the periodicity in the plane parallel to the indented surfaces [47]. The indenter loading rate of 0.5 Å/ps is utilized in the models. The visualization of the nanoslabs were done with OVITO software [48].

The results of the MD simulations are presented in Fig. 11(b)-(d). The images in Fig. 11(b) and Fig. 11(c) respectively portray the Ti and IMC Ti3Au indented nanostructures at the time when the indenter traverses the depth of 2.5 nm from its initial position. As expected, the indentation shape is clearly visible from the top side in context of both structures. Besides the indentation shape it is important to consider the presence of dislocations in the indented nanostructures. While the dislocations corresponding to the HCP structured Ti slab (Fig. 11(b)) are centred homogeneously around the periphery of the indentation shape, those of Ti3Au (Fig. 11(c)) seem to occur more heterogeneously throughout the active regions. The presence of two different types of atoms - Ti (gray) and Au (yellow), and their initial arrangement in simple cubic structure is accountable for the generation of heterogeneous dislocation during the processing. The set up of the trajectories of dislocation motion and its response to the applied force will definitely influence the mechanical behavior of the treated material structure. Of particular interest is the tendency of a continuum scale material to achieve dislocation exhaustion [49] upon loading, as this can have pronounced influence on properties such as hardness.

Fig. 11(d) shows the load-displacement curves for Ti and IMC material during the nanoindentation test. The maximum magnitude of the indentation depth (horizontal axis) is 3 nm (=30 Å), thus the results are captured for the timespan during which the indenter has still not completed the whole of the active region.

The range of values of indenter force (in µN) as obtained in this work for pure Ti are in good agreement with those presented in the research by Verkhovtsev et al. [50]. While their work uses empirical Finnis-Sinclair-type potential, this works utilizes EAM potential to model the Ti-Ti interaction, and this can account for the minor deviations in the results. Moreover, different type of potential is utilized in their work to discuss the interaction between the indenter and the Ti atoms. The indentation force values for pure Ti slab of this work being in similar magnitudes to those of their work, validates the correctness of our model. From the force-distance curves of Fig. 11(d), it can be understood that the atoms of IMC Ti3Au exert a larger amount of force to the indenter as compared to those of pure Ti. For an example, at a given indentation depth is 25 Å, the indenter penetrating the pure Ti slab experiences a force of 0.36 µN from the adjacent Ti atoms whereas the indenter surrounded by Ti + Au atoms of IMC slab is associated with a force of 0.82 µN. With the help of these curves, an estimation can be made about the hardness of these two materials. For a nanoindentation procedure, the hardness can be understood as the ratio of maximum indentation force to the contact area [51]. For the given simulation set up with an identical indentator, the contact area for the two systems at the critical indentation depth will not be so different and from these curves it can be assumed that the IMC Ti3Au will have a larger hardness value. It has been experimentally reported in the work of Svanidze et al. [18] that the hardness value of β-Ti3Au is about 4 times larger than that of pure Ti. This fact thus validates our assumption. The interaction between the Ti and Au atoms, and the probable dislocation exhaustion in the IMC material owing to the reconfiguration of the Au atoms within the majority atoms during initial phase of indentation procedure, certainly provides a large resistance force to the indenter thereby accounting to its elevated hardness. In addition to the elevation in hardness, the better wear properties of the intermetallics are also reported in the work of Svanidze et al. [18] and this can also be justified by the enhanced cohesion of the surface atoms, and certainly the presence of two types of atoms in the IMC has a role in it. Such behavior of IMC makes it a potentially favourable candidate in the design of harder and super biocompatible materials.

### 3.4. Electrochemical test

For the Ti samples, the open circuit potential values tend to shift toward more electropositive values without stabilization over the test time. Similar progress of the $E_{OCP}$ curves was observed for the TiAu 1.5 mm/s samples. While, for the Au and TiAu 1 mm/s samples the $E_{OCP}$ values begin to decrease and then gradually stabilize (Fig. 12a). More noble $E_{OCP}$ values were obtained for the Au samples - recorded values were more than 7 times higher than those obtained for Ti samples, which suggested better corrosion resistance for samples with Au, and is associated with the noble nature of the Au. The highest values of the $E_{OCP}$ values were obtained for the both TiAu samples group. In order to investigate the effect of Au content on corrosion resistance, the Tafel test was made. Obtained values of corrosion potential ($E_{corr}$) confirm the $E_{OCP}$ behavior (Fig. 12(b) and Table 3). The recorded values of the current density for Au samples were lower than those recorded for uncoated titanium samples, which confirms that the corrosion resistance of the Au samples was better. Meanwhile, the lowest values in $i_{corr}$ were observed for TiAu 1 mm/s and TiAu 1.5 mm/s samples group, which indicated the best corrosion resistance in the tested group. For the TiAu 1 mm/s and TiAu 1.5 mm/s samples, the $i_{corr}$ decreased from 0.44 (Au) to 0.096 and 0.046 µA/cm², respectively. Admittedly, the TiAu samples exhibit the Ti3Au phase, which is prone to preferential dissolution in corrosion environments [52,53]. In turn, gold is one of the least reactive elements
<figure><img src="image_14.png" /><figcaption>**Fig. 12.** Results of electrochemical test: a) EOCP, b) potentiodynamic curves.</figcaption></figure>

<table><caption>**Table 3**
Results of electrochemical test.</caption><thead><tr><th></th><th>E<sub>OCP</sub> [mV]</th><th>E<sub>corr</sub> [mV]</th><th>i<sub>corr</sub> [µA/cm<sup>2</sup>]</th></tr></thead><tbody><tr><td>Ti</td><td>-141</td><td>-134</td><td>0.639</td></tr><tr><td>TiAu 1 mm/s</td><td>10</td><td>-12</td><td>0.096</td></tr><tr><td>TiAu 1.5 mm/s</td><td>40</td><td>44</td><td>0.046</td></tr><tr><td>Au</td><td>-26</td><td>-79</td><td>0.440</td></tr></tbody></table>

on the Periodic and in effect it never corrodes. However, the thickness of the Au layer deposited on titanium substrate material is approximately 2 µm, which was smaller than the deep of remelting of TiAu samples. Additionally, deposited gold layer may be not efficiently dense. In effect, the corrosion solution may penetrate the gold layers defect and the substrate material can corrode.

## 4. Discussion

Fischer et al. [54] stated in his publication concerning binary alloy Ti-Au that, where Ti acted as an alloying additive in the cast alloy with a content of 8% and more Ti, the alloy was too brittle to be used in prosthetics. However, 16 years later, Svanidze et al. [18] described high mechanical properties in a biocompatible intermetallic β-Ti3Au composition, which make it very desirable. That state results from 3 reasons:

1. formation of pseudogaps. Between the two cubic Ti3Au compounds, the Ti-Au bond length is smaller for the β-phase (dTi-Au = 2.84478 Å) compared to the α-phase (dTi-Au = 2.93237 Å). Combined with the more complex crystallographic environments of Ti and Au in β-Ti3Au, this inhibits dislocation formation and results in high hardness of this compound. This 4-fold increase in hardness allows β-Ti3Au to be described as the hardest biocompatible material known [18].

2. Cubic crystal structure with naturally short Ti-Au bonds and high (14) coordination of Ti atoms

3. High valence electron density causes larger Burgers vectors, restricted cross slips, limited number of easy slip systems, and finally, its inability to transfer slips across grain boundaries [55]. The cubic structure of the β-Ti3Au phase discussed above and modelled in Fig. 6c was identified during XRD analysis (Fig. 6) in the coatings produced as a result of the experiment, which suggests that these coatings should perform superior mechanical properties in future application studies.

In order for the material to fulfil its expected properties in the tissue environment, the layer directly in contact with the tissue environment is the most important one. Given the desire to produce a thin film with a strictly desired chemical composition in the course of this study, we chose laser processing of pure titanium with an electrochemically applied layer of gold (with preparation suited to avoid oxide presence between titanium and gold). Based on the analysis of the elemental properties, the authors hypothesise that the presence of near-surface Ti-Au structures will reduce the magnetic induction value in magnetic resonance imaging. It was however not the main aim of this article, and this value will be determined precisely in future application studies according to Stracukova et al. methodology [56,57].

During the planning of the experiment, laser processing was planned in a series of parameters. In order to perform tests which will ensure homogeneous penetration to a sufficiently small depth (up to 15 µm) and at the same time provide adequate melting (with melting of both materials Ti = 1941 K, Au 1337 K) it was planned to use a defocused beam as suggested by the research conducted by T. Kunimine [58]. Finite element method has confirmed that transient temperature values at the Au-Ti interface during laser heating at laser power (P) of 100 W scan speed of 1.5 mm/s, can reach a magnitude larger than the melting point of Ti for a duration less than 5.0 ms. However, the decrease of scan speed to 1.0 mm/s for constant P, increases this duration up to 97.0 ms thereby providing sufficient energy for convection-based reaction at the interface which results in clearly smaller amount of concentration of gold as has been shown in SEM cross-sections. This finding makes it a thesis that, in order to generate the Ti3Au phase, it is necessary to supply sufficient energy to bring the whole system into a liquid state within a very short time window. Otherwise, the contribution of the Ti3Au phase to the other phases decreases rapidly. In that case, the laser power density affects the microstructure and kinetics of the transition (phase formation) through a different increase in heat. Defocusing makes the sample heat up slower, over a larger area and does not penetrate as deeply as if it were in focus. The use of the variant that delivers the same amount of energy but with the beam in focus (applying lower beam power at a higher photon source feed rate) will lead to deeper melting (decrease in near-surface gold concentration) and will affect phase formation by increasing the process speed and thus the kinetics of phase formation. For laser processing of TiAu, convection plays a major role (due to the high speed of the process, mass exchange is not possible through e.g. diffusion). Convection is the most important factor affecting the pool geometry, including its shape, undercutting, and rippling, and can cause defects such as variable penetration, porosity and lack of fusion. Following laser power activation, surface morphology images (Fig. 3) demonstrate distinct changes in grain size, shape, and even presence of a dendritic structure. Convection is also the main factor responsible for mixing and hence affects the composition of the weld pool [22]. The fact that convection in crystalline solids characterised by compact space filling is impeded and occurs exclusively in the remelting pool, it will allow the formation of an Au phases at the desired depth (controlled by parameters and defocusing of the beam as
shown by tendency of Power- remelting depth in Fig. 4), where at the contact surface with body fluids (blood) the film composition will tend to have higher Au concentration and as one penetrates into the core of the material the Ti concentration will increase gradiently. The formation of a multi-phase coating with a gradient change in concentration (as in Fig. 5c) where the top (Ti3Au layer) will be the hardest, is of additional importance for the durability of the coating during load transfer, wear resistance and fatigue (endoprostheses - walking, running, dental implants - chewing function,) the stresses received by the surfaces will be taken over by the less hard substrate (subsequent layers of the coating up to the base material) [59,60]. Corrosion tests showed a positive response of the Au modified samples in similar to natural tissue environment, indicating the usefulness of the obtained coatings for biomedical applications [52,53].

Some researchers have shown that the eutectoid structure of Ti-Au alloy could improve the corrosion resistance of titanium and its alloy [61,62]. From the E<sub>OCP</sub> and Tafel curves, it was seen that the addition of Au reduced corrosion tendency compared with Ti. However, the addition of Au can lead to catalyse TiO<sub>2</sub> oxide layer formation due to galvanic corrosion. Additionally, the Au layer deposited on titanium substrate material may doesn't guarantee enough corrosion protection because of their possible defects and no full density. It can be concluded that TiAu samples are characterized by lower values of corrosion current densities compared to the Au samples. Tok et al. [63] suggested that the reduced size of the Ti-Au phase in samples microstructure, would provide a reduction in the galvanic strength between the second phase and the matrix, and slow down the corrosion rate [64], which was also presented in our article.

The parameters determined during the present study will certainly allow the fabrication of a complete coating with a uniform remelting effect and maximisation of the Ti3Au phase characterised in the course of the research. As laser source is used in this work to produce a thin film of Ti3Au IMC over the bult Ti material, this helps in designing materials with optimal hardness properties. The Ti + Au atoms in the thin film of super hard and wear resistant IMC, can provide a larger resistance to scratching and wear force in biological medium; and can provide better cover to the internal Ti core.

## 5. Conclusions

Investigations of the laser processing of the Ti-Au system for the formation of intermetallic compounds and simulation of the process in a finite element method environment have led to the following conclusions:

The fabrication of a multilayer TiAu coating with given experimental parameters is possible and leads to a series of layers with different concentrations of the enriching element Au.

During treatment of α-Ti and Au, it was possible to produce a coating containing the β-Ti3Au phase, showing improved anticorrosion properties compared to the base material (Ti).

The results from finite element analysis have enabled the mechanical exploration of the role of heat flow dynamics in the phase formation in a Ti-Au system interacting with a laser beam.

During corrosion testing, the recorded current density values of the TiAu samples were lower than those recorded for the titanium samples, indicating that the corrosion resistance of the TiAu samples is higher. A positive response of the material in the corrosion tests allows further *in-vitro* testing.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

This work was supported by the National Science Centre, Poland (PRELUDIUM grant, UMO-2022/45/N/ST8/01004 and SONATA BIS grant, UMO-2021/42/E/ST5/00339). This work was also supported by the European Union through the European Social Fund (grant POWR.03.05.00-00-Z305). The Authors would like to express gratitude to Arkadiusz Ptak - Kiesow Polska Sp. z o.o. Zabrze, Poland, Pawliczka 25 street for the sharing of the gold application bath.

## Data availability statement

The tabular data and user defined functions for temperature dependent material properties – enthalpy, viscosity, thermal conductivity and density, used in the numerical simulation are available online at https://github.com/anilkunwar/temperature-dependent_material_properties. The nature of laser heat source is the main cause necessitating the use of T-dependent materials properties, and the user defined function for numerically representing this laser heat source is also made available at the same repository.

## References

[1] https://www.who.int/healthinfo/statistics/en/ (25.05.2020), (n.d.).

[2] S. Kumar, D. Sahana, G. Menon, Optimal use of temporary clip application during aneurysm surgery – In search of the holy grail, Asian J. Neurosurg. 16 (2021) 237, https://doi.org/10.4103/ajns.AJNS_465_20.

[3] D.S. Thylur, R.E. Jacobs, J.L. Go, A.W. Toga, J.K. Niparko, Ultra-high-field magnetic resonance imaging of the human inner ear at 11.7 Tesla, Otol. Neurotol. 38 (2017) 133–138, https://doi.org/10.1097/MAO.00000000000001242.

[4] A. Ahmed, X. Wang, M. Yang, Biocompatible materials of pulsatile and rotary blood pumps: A brief review, Rev. Adv. Mater. Sci. 59 (2020) 322–339, https://doi.org/10.1515/rams-2020-0009.

[5] W.Y. Lim, G. Lloyd, S. Bhattacharyya, Mechanical and surgical bioprosthetic valve thrombosis, Heart (2017), https://doi.org/10.1136/heartjnl-2017-311856.

[6] G.D. Dangas, J.I. Weitz, G. Giustino, R. Makkar, R. Mehran, Prosthetic Heart Valve Thrombosis, J. Am. Coll. Cardiol. 68 (2016) 2670–2689, https://doi.org/10.1016/j.jacc.2016.09.958.

[7] A.P. Yoganathan, Z. He, S. Casey Jones, Fluid mechanics of heart valves, Annu. Rev. Biomed. Eng. 6 (2004) 331–362, https://doi.org/10.1146/annurev.bioeng.6.040803.140111.

[8] O. Bialas, J. Žmudzki, FEA of displacements and stresses of aortic heart valve leaflets during the opening phase, J. Achieve. Mater. Manuf. Eng. 92 (2019), https://doi.org/10.5604/01.3001.0013.3185.

[9] Z. Chen, Y. Wang, L. Zhuo, S. Chen, L. Zhao, X. Luan, H. Wang, G. Jia, Effect of titanium dioxide nanoparticles on the cardiovascular system after oral administration, Toxicol. Lett. 239 (2015) 123–130, https://doi.org/10.1016/j.toxlet.2015.09.013.

[10] A. Woźniak, M. Adamiak, G. Chladek, M. Bonek, W. Walke, O. Bialas, The influence of hybrid surface modification on the selected properties of CP titanium grade II manufactured by selective laser melting, Materials 13 (2020) 2829, https://doi.org/10.3390/ma13122829.

[11] J.C.B. Alcázar, R.M.J. Lemos, M.C.M. Conde, L.A. Chisini, M.M.S. Salas, B.S. Noremberg, F.V. da Motta, F.F. Demarco, S.B.C. Tarquinio, N.L.V. Carreño, Preparation, characterization, and biocompatibility of different metal oxide/PEG-based hybrid coating synthesized by sol-gel dip coating method for surface modification of titanium, Prog. Org. Coat. 130 (2019) 206–213, https://doi.org/10.1016/j.porgcoat.2019.02.007.

[12] A. Woźniak, M. Staszuk, Ł. Reimann, O. Bialas, Z. Brytan, S. Voinarovych, O. Kyslysia, S. Kaliuzhnyi, M. Basiaga, M. Admiak, The influence of plasma-sprayed coatings on surface properties and corrosion resistance of 316L stainless steel for possible implant application, Archiv. Civ. Mech. Eng. 21 (2021) 148, https://doi.org/10.1007/s43452-021-00297-1.

[13] R. Shukla, V. Bansal, M. Chaudhary, A. Basu, R.R. Bhonde, M. Sastry, Biocompatibility of gold nanoparticles and their endocytotic fate inside the cellular compartment: A microscopic overview, Langmuir 21 (2005) 10644–10654, https://doi.org/10.1021/la0513712.

[14] O. Bialas, T. Poloczek, M. Lis, A. Skowronek, J. Górka, M. Adamiak, Laser assisted size reduction of gold (Au) particles onto a titanium (Ti) substrate surface, Appl. Sci. 11 (2021) 8755, https://doi.org/10.3390/app11188755.

[15] O. Bialas, M. Lis, A. Woźniak, M. Adamiak, Laser superficial fusion of gold nanoparticles with PEEK polymer for cardiovascular application, Materials 14 (2021) 971, https://doi.org/10.3390/ma14040971.
[16] Y. Luo, L. Yang, M. Tian, Application of biomedical-grade titanium alloys in trabecular bone and artificial joints, in, Biomater. Med. Tribol., Elsevier (2013) 181–216, https://doi.org/10.1533/9780857092205.181.

[17] W.-T. Chiu, K. Fuchiwaki, A. Umise, M. Tahara, T. Inamura, H. Hosoda, Investigations of effects of intermetallic compound on the mechanical properties and shape memory effect of Ti-Au-Ta biomaterials, Materials, 14 (2021) 5810, https://doi.org/10.3390/ma14195810.

[18] E. Svanidze, T. Besara, M.F. Ozaydin, C.S. Tiwary, J.K. Wang, S. Radhakrishnan, S. Mani, Y. Xin, K. Han, H. Liang, T. Siegrist, P.M. Ajayan, E. Morosan, High hardness in the biocompatible intermetallic compound β-Ti₃ Au, Sci. Adv. 2 (2016) e1600319.

[19] C. Lopes, C. Gabor, D. Cristea, R. Costa, R.P. Domingues, M.S. Rodrigues, J. Borges, E. Alves, N.P. Barradas, D. Munteanu, F. Vaz, Evolution of the mechanical properties of Ti-based intermetallic thin films doped with different metals to be used as biomedical devices, Appl. Surf. Sci. 505 (2020), https://doi.org/10.1016/j.apsusc.2019.144617 144617.

[20] A. Kunwar, S. Shang, P. Ráback, Y. Wang, J. Givernaud, J. Chen, H. Ma, X. Song, N. Zhao, Heat and mass transfer effects of laser soldering on growth behavior of interfacial intermetallic compounds in Sn/Cu and Sn-3.5Ag0.5/Cu joints, Microelectron. Reliab. 80 (2018) 55–67, https://doi.org/10.1016/j. microrel.2017.11.016.

[21] A. Olejnik, G. Śliwiński, J. Karczewski, J. Ryl, K. Siuzdak, K. Grochowska, Laser-assisted approach for improved performance of Au-Ti based glucose sensing electrodes, Appl. Surf. Sci. 543 (2021), https://doi.org/10.1016/j. apsusc.2020.148788 148788.

[22] C. Chan, J. Mazumder, M.M. Chen, A two-dimensional transient model for convection in melted pool, MTA 15 (1984) 2175–2184, https://doi.org/ 10.1007/BF02647100.

[23] J.-E. Sundgren, P. Bodó, B. Ivarsson, I. Lundström, Adsorption of fibrinogen on titanium and gold surfaces studied by ESCA and ellipsometry, J. Colloid Interface Sci. 113 (1986) 530–543, https://doi.org/10.1016/S0021-9797(86) 00446-7.

[24] A. Asserghine, D. Pilotós, L. Nagy, R.M. Souto, G. Nagy, Do titanium biomaterials get immediately and entirely reperfused? A perspective, NPJ Mater. Degrad. 6 (2022) 57, https://doi.org/10.1038/s41529-022-00270-0.

[25] T. Hanawa, Transition to surface modification of titanium for medical and dental use, in: Titanium in Medical and Dental Applications, Elsevier, 2018: pp. 95–113. 10.1016/B978-0-12-812456-7.00005-6.

[26] T. Kodama, R. Nakai, K. Goto, K. Shima, H. Iwata, Preparation of an Au-Pt alloy free from artifacts in magnetic resonance imaging, Magn. Reson. Imaging 44 (2017) 38–45, https://doi.org/10.1016/j.mri.2017.07.006.

[27] M.A. van der Jagt, W.M. Brink, M.J. Versluis, S.C.A. Steens, J.J. Briaire, A.G. Webb, J.H.M. Frijns, B.M. Verbist, Visualization of human inner ear anatomy with high-resolution MR imaging at 7T: Initial clinical assessment, AJNR Am J. Neuroradiol. 36 (2015) 378–383, https://doi.org/10.3174/ajnr.A4084.

[28] C.C. Camilo, E.C. de Souza, P.L. Di Lorenzo, J.M.D. de A. Rollo, Measurement of the grain boundary energy of commercially-pure grade 2 titanium at high temperature, RBBE.27 (2011) 175–181, https://doi.org/10.4322/rbeb.2011.014.

[29] ASTM B348/B348M, 2019, (n.d.).

[30] A. Kunwar, L. An, J. Liu, S. Shang, P. Ráback, H. Ma, X. Song, A data-driven framework to predict the morphology of interfacial Cu6Sn5 IMC in SAC/Cu system during laser soldering, J. Mater. Sci. Technol. 50 (2020) 115–127, https://doi.org/10.1016/j.jmst.2019.12.036.

[31] W.-H. Xiong, W. Liu, M.-M. Dai, J.-Q. Liu, X.-G. Lu, Assessments of molar volumes of Co-, Ni- and Ti- related BCC and FCC phases, Calphad 66 (2019), https://doi.org/10.1016/j.calphad.2019.101629 101629.

[32] B. Sundman, U.R. Kattner, M. Palumbo, S.G. Fries, OpenCalphad - a free thermodynamic software, Integr. Mater. Manuf. Innov. 4 (2015) 1–15, https:// doi.org/10.1186/s40192-014-0029-1.

[33] N.G.C. Astrath, F.B.G. Astrath, J. Shen, J. Zhou, C.E. Gu, L.C. Malacarne, P.R.B. Pedreira, A.C. Bento, M.L. Baesso, Top-hat cw laser induced thermal mirror: a complete model for material characterization, Appl. Phys. B 94 (2009) 473– 481, https://doi.org/10.1007/s00340-008-3310-1.

[34] S. Zhu, T.P. Chen, Z.H. Cen, E.S.M. Goh, S.F. Yu, Y.C. Liu, Y. Liu, Split of surface plasmon resonance of gold nanoparticles on silicon substrate: a study of dielectric functions, Opt. Express 18 (2010) 21926, https://doi.org/10.1364/ OE.18.021926.

[35] A. Kunwar, J. Givernaud, H. Ma, Z. Meng, S. Shang, Y. Wang, H. Ma, Modelling the melting of Sn0.7Cu solder using the enthalpy method, in: 2016 17th International Conference on Electronic Packaging Technology (ICEPT), IEEE, Wuhan, China, 2016, pp. 166–169, https://doi.org/10.1109/ICEPT.2016.7583112.

[36] E. Ricci, R. Novakovic, Wetting and surface tension measurements on gold alloys, Gold Bull. 34 (2001) 41–49, https://doi.org/10.1007/BF03214811.

[37] P. Paradisa, T. Ishikawaa, N. Koikeb, Density of liquid gold measured by a non-contact technique, Gold Bull. 41 (2008) 242–245, https://doi.org/10.1007/ BF03214876.

[38] X.-P. Zhang, G. Chen, S.-M. Xiong, Q.-Y. Xu, Computer simulation of the solidification of cast titanium dental prostheses, J. Mater. Sci. 40 (2005) 4911– 4916, https://doi.org/10.1007/s10853-005-0418-0.

[39] H. Wang, S. Yang, B. Wei, Density and structure of undercooled liquid titanium, Chin. Sci. Bull. 57 (2012) 719–723, https://doi.org/10.1007/s11434-011-4945-6.

[40] J.G. Cook, M.P. van der Meer, The thermal conductivity and electrical resistivity of gold from 80 to 340 K, Can. J. Phys. 48 (1970) 254–263, https://doi.org/ 10.1139/p70-035.

[41] Y.V. Petrov, N.A. Inogamov, S.I. Anisimov, K.P. Migdal, V.A. Khokhlov, K.V. Khishchenko, Thermal conductivity of condensed gold in states with the

strongly excited electron subsystem, J. Phys. Conf. Ser. 653 (2015), https://doi.org/10.1088/1742-6596/653/1/012087 012087.

[42] M. Watanabe, M. Adachi, H. Fukuyama, Heat capacities and thermal conductivities of palladium and titanium melts and correlation between thermal diffusivity and density of states for transition metals in a liquid state, J. Mol. Liq. 324 (2021), https://doi.org/10.1016/j.molliq.2020.115138 115138.

[43] K. Schüller, J. Kowalski, P. Ráback, Curvilinear melting – A preliminary experimental and numerical study, Int. J. Heat Mass Transf. 92 (2016) 884– 892, https://doi.org/10.1016/j.ijheatmasstransfer.2015.09.046.

[44] P. Hirel, Atomsk: A tool for manipulating and converting atomic data files, Comput. Phys. Commun. 197 (2015) 212–219, https://doi.org/10.1016/j. cpc.2015.07.012.

[45] X.W. Zhou, R.A. Johnson, H.N.G. Wadley, Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers, Phys. Rev. B 69 (2004), https://doi.org/10.1103/PhysRevB.69.144113 144113.

[46] S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J. Comput. Phys. 117 (1995) 1–19, https://doi.org/10.1006/jcph.1995.1039.

[47] R.-G. Xu, H. Song, Y. Leng, S. Papanikolaou, A Molecular Dynamics Simulations Study of the Influence of Prestrain on the Pop-in Behavior and Indentation Size Effect in Cu Single Crystals, MATERIALS SCIENCE, 2021. 10.20944/ preprints202108.0151v1.

[48] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool, Modelling Simul. Mater. Sci. Eng. 18 (2010), https://doi.org/10.1088/0965-0393/18/1/015012 015012.

[49] S. Wu, Z. Kou, Q. Lai, S. Lan, S.S. Katnagallu, H. Hahn, S. Taheriniya, G. Wilde, H. Gleiter, T. Feng, Dislocation exhaustion and ultra-hardening of nanograined metals by phase transformation at grain boundaries, Nat. Commun. 13 (2022) 5468, https://doi.org/10.1038/s41467-022-33257-1.

[50] A.V. Verkhovtsev, A.V. Yakubovich, G.B. Sushko, M. Hanauske, A.V. Solov'yov, Molecular dynamics simulations of the nanoindentation process of titanium crystal, Comput. Mater. Sci. 76 (2013) 20–26, https://doi.org/10.1016/ j.commatsci.2013.02.015.

[51] S. Amaya-Roncancio, E. Restrepo-Parra, D.M. Devia-Narvaez, D.F. Arias- Mateus, M.M. Gómez-Hermida, Al nuclear dynamics simulation of nanoindentation in Cr, Al layers and Al/Cr bilayers, using a hard spherical nanoindenter, 81 (2014) 102–107.

[52] Y.-R. Lee, M.-K. Han, M.-K. Kim, W.-J. Moon, H.-J. Song, Y.-J. Park, Effect of gold addition on the microstructure, mechanical properties and corrosion behavior of Ti alloys, Gold Bull. 47 (2014) 153–160, https://doi.org/10.1007/s13404- 014-0138-9.

[53] M. Takahashi, M. Kikuchi, Y. Takada, O. Okuno, T. Okabe, Corrosion behavior and microstructures of experimental Ti-Au alloys, Dent. Mater. J. 23 (2004) 109–116, https://doi.org/10.4012/dmj.23.109.

[54] J. Fischer, Mechanical, thermal, and chemical analyses of the binary system Au-Ti in the development of a dental alloy, J. Biomed. Mater. Res. 54 (2000) 678–686, https://doi.org/10.1002/1097-4636(20001215)52:4<678::aid-jbm12>3.0.co;2-p.

[55] C.C. Lukose, I. Anestopoulos, T. Mantso, L. Bowen, M.I. Panayiotidis, M. Birkett, Thermal activation of Ti(1-x)Au(x) thin films with enhanced hardness and biocompatibility, Bioact. Mater. 15 (2022) 426–445, https://doi.org/10.1016/j. bioactmat.2022.02.027.

[56] J. Starčuková, Z. Starčuk, H. Hubálková, I. Linetskiy, Magnetic susceptibility and electrical conductivity of metallic dental materials and their impact on MR imaging artifacts, Dent. Mater. 24 (2008) 715–723, https://doi.org/10.1016/ j.dental.2007.07.002.

[57] S. Puvanasanthararajah, D. Fontanarosa, M. Wille, S.M. Camps, The application of metal artifact reduction methods on computed tomography scans for radiotherapy applications: A literature review, J. Appl. Clin. Med. Phys. 22 (2021) 198–223, https://doi.org/10.1002/acm.13255.

[58] T. Kunimine, R. Miyazaki, Y. Yamashita, Y. Funada, Effects of laser-beam defocus on microstructural features of compositionally graded WC/Co-alloy composites additively manufactured by multi-beam laser directed energy deposition, Sci. Rep. 10 (2020) 8975, https://doi.org/10.1038/s41598-020-65429-8.

[59] M.R. Loos, J. Yang, D.L. Feke, I. Manas-Zloczower, S. Unal, U. Younes, Enhancement of fatigue life of polyurethane composites containing carbon nanotubes, Compos. B Eng. 44 (2013) 740–744, https://doi.org/10.1016/ j.compositesb.2012.01.038.

[60] G.M. Bernacca, T.G. Mackay, R. Wilkinson, D.J. Wheatley, Polyurethane heart valves: fatigue failure, calcification, and polyurethane structure, J. Biomed. Mater. Res. 34 (1997) 371–379.

[61] J.-M. Hwang, E.-J. Park, W.-J. Moon, H.-J. Song, Y.-J. Park, Characterization of passive layers formed on Ti–10 wt% (Ag, Au, Pd, or Pt) binary alloys and their effects on galvanic corrosion, Corros. Sci. 96 (2015) 152–159, https://doi.org/ 10.1016/j.corsci.2015.04.007.

[62] S. Fu, X. Zhao, L. Yang, G. Qin, E. Zhang, A novel Ti-Au alloy with strong antibacterial properties and excellent biocompatibility for biomedical application, Biomater. Adv. 133 (2022), https://doi.org/10.1016/j. msec.2022.112653 112653.

[63] H.Y. Tok, E. Hamzah, H.R. Bakhsheshi-Rad, The role of bismuth on the microstructure and corrosion behavior of ternary Mg-1.2Ca-xBi alloys for biomedical applications, J. Alloy. Compd. 640 (2015) 335–346, https://doi.org/ 10.1016/j.jallcom.2015.03.217.

[64] R. Zeng, K.U. Kainer, C. Blawert, W. Dietzel, Corrosion of an extruded magnesium alloy ZK60 component–The role of microstructural features, J. Alloy. Compd. 509 (2011) 4462–4469, https://doi.org/10.1016/ j.jallcom.2011.01.116.