Abstract The search for new hard materials is often challenging, but strongly motivated by the vast application potential such materials hold. Ti 3 Au exhibits high hardness values (about four times those of pure Ti and most steel alloys), reduced coefficient of friction and wear rates, and biocompatibility, all of which are optimal traits for orthopedic, dental, and prosthetic applications. In addition, the ability of this compound to adhere to ceramic parts can reduce both the weight and the cost of medical components. The fourfold increase in the hardness of Ti 3 Au compared to other Ti–Au alloys and compounds can be attributed to the elevated valence electron density, the reduced bond length, and the pseudogap formation. Understanding the origin of hardness in this intermetallic compound provides an avenue toward designing superior biocompatible, hard materials.

Keywords

Biocompatible alloys

hardness

metals

titanium alloys

gold alloys

titanium gold alloys

coefficient of friction

elevated electron density

pseudogap

medical applications

INTRODUCTION In addition to numerous applications in the industrial, automotive, and aerospace fields, Ti has been widely used for implant devices that replace patients’ hard tissues (1, 2). A number of in vivo and in vitro experiments with various grades of Ti concluded that commercially pure Ti is a highly biocompatible material due to the spontaneous buildup of an inert and stable oxide layer (1, 3). Additional properties that make Ti suitable for biomedical applications include its high strength-to-weight ratio (4, 5) and low ion formation levels in aqueous environments (1). Moreover, Ti is one of a few materials capable of osseointegration—the mechanical retention of the implant by the host bone tissue—which stabilizes the implant without any soft tissue layers between the two (6). These properties enable the wide use of Ti for devices, such as artificial knee and hip joints, screws and shunts for fracture fixation, bone plates, pacemakers, and cardiac valve prostheses (7, 8). Not surprisingly, the dental applications of Ti are just as common, including implants and their components, such as inlays, crowns, overdentures, and bridges (1, 9–12). However, pure Ti is not strong enough for a number of medical devices (13, 14), thus necessitating the development of superior alloys (15–19). Although hardness can be improved by alloying Ti with another element (1), care must be taken to preserve biocompatibility. Previously, a twofold increase in hardness has been achieved by alloying Ti with Cu or Ag (19–22). The use of an alloying element with the same valence as Cu and Ag, but with higher mass density, should result in a higher valence electron density (VED), which would likely lead to higher bond strength and, consequently, enhanced hardness (23, 24). This finding suggests that Au is a suitable alloying candidate to increase the hardness in Ti binary alloys, given its nearly twofold density increase over Cu or Ag (19–22). The current wide use of Au-based implant devices (25–28) is testament to its biocompatibility and corrosion resistance (10). Biomedical applications of both Ti-rich and Au-rich alloys have been previously explored in detail (19, 25, 29, 30). Although hardness values showed modest increase in both these regimes of the Ti–Au solution [Fig. 1, open circles, reproduced from previous studies (25, 29, 30)], the hardness was comparable to that of Ti–Ag and Ti–Cu alloys (19–22). Here, we present evidence that the hardness varies nonmonotonously in the Ti–Au alloys, and a drastic increase is registered at an intermediate composition, for the cubic compound β-Ti 3 Au (Fig. 1, full circles). Further evidence from wear experiments reveal that this enhanced hardness is associated with a low coefficient of friction (COF). Experimental observations and theoretical calculations point to three main factors that contribute to the high hardness in β-Ti 3 Au: the cubic structure with short Ti–Au bonds, the high VED, and a pseudogap evident in the electronic density of states (DOS). Fig. 1 Hardness of Ti 1−x Au x and other intermetallic alloys and compounds. Hardness as a function of x (top axis) or mass density ρ (bottom axis) in Ti 1−x Au x . Blue squares, medical alloys; green triangles, intermetallic compounds.

CONCLUSIONS The mechanical properties of the intermetallic compound β-Ti 3 Au suggest that this material is well suited for medical applications where Ti is already used, with some examples including replacement parts and components (both permanent and temporary), dental prosthetics, and implants. The fourfold increase in hardness, as compared with pure Ti, renders β-Ti 3 Au as the hardest known biocompatible intermetallic compound. The wear properties of β-Ti 3 Au indicate that this compound has a COF that is four times less than that of Ti, resulting in the reduction of the wear volume by 70%, which will ensure longer component lifetime and less debris accumulation. Moreover, the ability to adhere to a ceramic surface will result in reducing both the cost and the weight of these components. The high hardness in β-Ti 3 Au can be attributed to three main factors: (i) the cubic crystal structure with inherently short Ti–Au bonds and high (14) Ti atomic coordination, (ii) the high VED, and (iii) the pseudogap formation. Between the two cubic Ti 3 Au compounds, the Ti–Au bond length is smaller for the β phase (d Ti–Au = 2.84478 Å) compared to the α phase (d Ti–Au = 2.93237 Å). Together with the more complex crystallographic environments of both Ti and Au in β-Ti 3 Au, this inhibits dislocations and results in high hardness in this particular compound. Understanding the factors that influence the hardness of β-Ti 3 Au provides insights for improving the existing biocompatible alloys and designing new biocompatible materials with superior mechanical properties.

METHODS Alloys of Ti 1−x Au x were prepared by arc melting Ti (Cerac, 99.99%) and Au (Cerac, 99.99%) in stoichiometric ratios, with mass losses of no more than 0.3%. To ensure homogeneity, the samples were remelted several times. Given that Ti alloys are frequently heat-treated to improve both hardness and ductility, annealing studies were carried out for the Ti–Au system. However, the use of different annealing cycles, similar to those used for other Ti-based alloys (65), resulted in minimal changes in the hardness compared to the as-cast samples. This might be caused by variation in microstructure homogeneity, which can mask the true annealing effects. The hardness of the arc-melted samples made it virtually impossible to grind these samples, which rendered powder XRD experiments difficult. Therefore, XRD data were collected at room temperature off the cross section (about 3 mm in diameter) of cut and polished specimens using a custom four-circle Huber diffractometer with a focusing graphite monochromator and analyzer in a nondispersive geometry, coupled to a Rigaku rotating anode source producing CuKα radiation. HV was measured in a Tukon 2100 microhardness tester, equipped with a Vickers diamond pyramid indenter. The microhardness tests were performed on a polished sample surface of about 3 mm in diameter. Multiple tests were conducted for all samples to maintain repeatability, using a 300-g load, with a duration of 10 s. Tribological experiments were conducted using a pin-on-disc tribometer (CSM Instruments) with a total of 40,000 cycles. The diamond-SiC disc was selected for its durability. The ingot samples of Ti 1−x Au x (x = 0.25, 0.3, and 0.50) were used as a pin, with a Ti ingot used as a reference. An example of the Ti 0.75 Au 0.25 sample used for wear tests is shown in the inset of Fig. 4A. To simulate wear during walking, a linear reciprocal motion was used with a sliding speed of 3.15 cm s−1 and an applied load of 2 N. The sliding distance of wear tests was set at 4 mm per stroke, with a total of 40,000 cycles. A synthetic body fluid was used as the test medium. The total wear is presented as volume loss. Details regarding the wear of the diamond-SiC disc have been previously reported (66–68). The MTS assay was used to assess the cytotoxicity of the samples. For the study, 293T cells were cultured in Dulbecco’s modified Eagle’s medium supplemented with 10% fetal bovine serum, penicillin, and streptomycin. Five thousand cells were seeded in a 24-well plate along with the samples. The cells with the samples were incubated at 37°C. After 3 days of incubation, 150 μl per well of MTS reagent was added. It was further incubated for an hour and then the optical density was measured using a microplate reader. The sample of pure titanium had very poor cytocompatibility. The cells were observed to be strained and rounded, whereas the alloys did not show any significant effects. Samples for HRTEM analysis were prepared via grinding and ion milling. The HRTEM image of the x = 0.25 sample was performed using a JEOL 2100 field emission gun transmission electron microscope. The microstructures of the x = 0.33 and x = 0.50 samples were investigated by a probe aberration–corrected JEOL JEM-ARM200cF at 200 kV. Band-structure calculations were performed using the full-potential linearized augmented plane-wave method implemented in the WIEN2k package (69, 70). The Perdew-Burke-Ernzerhof generalized gradient approximation was used as the exchange correlation potential, and a 10 × 10 × 10 grid was used to sample the k-points in the Brillouin zone.

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Funding: The work at Rice University (E.M. and E.S.) and part of the work at the National High Magnetic Field Laboratory (NHMFL) (T.B. and T.S.) were supported by the NSF (DMR-1506704). The work at the NHMFL (T.B., Y.X., K.H., and T.S.) was partially supported by the NSF Cooperative Agreement (DMR-1157490) and the State of Florida. T.B. and T.S. were partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under award DE-SC0008832. Work at the Texas A&M University (H.L. and M.F.O.) was partially sponsored by the Turbomachinery Research Laboratory. The Z-contrast facilities were supported by the Florida State University Research Foundation. Author contributions: E.M. and E.S. designed the study. E.S. prepared the samples and performed the data analysis. E.M. and E.S. wrote the manuscript with contributions from all authors. T.B. and T.S. were responsible for x-ray measurements and structural characterization. C.S.T. and P.M.A. performed HRTEM analysis. M.F.O. and H.L. carried out tribological experiments. S.R. and S.M. evaluated the cytotoxicity of the samples. Y.X. and K.H. performed HV tests. J.K.W. performed band-structure calculations. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper. Additional data related to this paper may be requested from the authors.