Computational Design of Corrosion-resistant and Wear-resistant Titanium Alloys for Orthopedic Implants_2

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Computational Design of Corrosion-resistant and

Wear-resistant Titanium Alloys for Orthopedic Implants

Noel Sionya, Long Vuongb, Otgonsuren Lundaajamtsb, Sara Kadkhodaeic,∗

aDepartment of Physics, University of Illinois Chicago, 845 W. Taylor St., Chicago, IL 60607 USA

bMechanical & Industrial Engineering, University of Illinois Chicago, 842 W. Taylor St., Chicago, IL

60607 USA

cCivil, Materials, and Environmental Engineering, University of Illinois Chicago, 2095 Engineering

Research Facility, 842 W. Taylor St., Chicago, IL 60607 USA

Abstract

Titanium alloys are promising candidates for orthopedic implants due to their mechan-

ical resilience and biocompatibility. Current titanium alloys in orthopedic implants

still suffer from low wear and corrosion resistance. Here, we present a computational

method for optimizing the composition of titanium alloys for enhanced corrosion and

wear resistance without compromising on other aspects such as phase stability, bio-

compatibility, and strength. We use the cohesive energy, oxide formation energy, sur-

face work function, and the elastic shear modulus of pure elements as proxy descrip-

tors to guide us towards alloys with enhanced wear and corrosion resistance. For the

best-selected candidates, we then use the CALPHAD approach, as implemented in

the Thermo-Calc software, to calculate the phase diagram, yield strength, hardness,

Pourbaix diagram, and the Pilling-Bedworth (PB) ratio. These calculations are used

to assess the thermodynamic stability, biocompatibility, corrosion resistance, and wear

resistance of the selected alloys. Additionally, we provide insights about the role of

silicon on improving the corrosion and wear resistance of alloys.

1. Introduction

Orthopedic implants have signiﬁcantly improved the quality of life for people who

have irreversibly injured their bones [1–4]. In the past, a signiﬁcant injury to the hip

or knee was recovered by amputating the affected limbs [5]. Initial orthopedic im-

plants were very different from what we use today. More akin to metal casts, early

implants used plates and screws to reinforce damaged bones rather than completely

replace the damaged bone with a new artiﬁcial part. It was not until later that science

had progressed far enough to make the concept of a complete replacement possible for

patients. The ﬁrst knee implants utilized ivory as the primary construction material [6].

The success of the material for an implant depends on several factors: biocompatibility

∗Corresponding author

Email address: sarakad@uic.edu (Sara Kadkhodaei)

Preprint submitted to Elsevier October 4, 2022

arXiv:2210.00845v1 [physics.med-ph] 22 Sep 2022

with the body, the strength of the material, ability to resist wear, and the ability to resist

the corrosive conditions of the body. At the time, ivory was the best material that ﬁt

these criteria as it can withstand compression forces quite well and is naturally resistant

to corrosion inside the body [7]. Additionally, studies done on patients long after they

had been given an ivory implant showed that the bone fused well with the ivory implant

in most areas [7].

Later, ceramic implants were tested because they provided higher wear resistance.

Today, ceramic implants are still used for patients who reject metal implants due to im-

mune reactions. However, the major drawbacks to ceramic implants come from their

brittle nature and inability to take repetitive impacts (dynamic loading) from activities

such as jogging [8]. Ceramic implants bring a higher chance of fracture and, in the

worst cases, the complete shattering of the implant. Today, a commonly used ceramic

is alumina due to its great ability to withstand compression forces and wear. However,

alumina suffers from a weakness to tensile stresses like other ceramics do [9]. Zirco-

nia is a common alternative to alumina as it shares hardness properties comparable to

alumina while having incredible crack resistance. A composite material was developed

composed of zirconia introduced into an alumina matrix called zirconia toughened alu-

mina or ZTA [10]. This composite combines the best features of its base materials

and offers a material that is highly resistant to wear and cracking while maintaining its

high toughness [11]. Though ZTA excels in these categories, it is prone to aging in the

presence of water; a form of deterioration that leads to lowered strength and a higher

risk of fracture [12].

Metal implants became available as the metal industry evolved and more manu-

facturing processes became available and reﬁned [13–18]. Early implementations of

metal implants suffered from a lack of quality control leading to low wear resistance

and fracturing [19]. The low wear resistance lead to more signiﬁcant implant deteriora-

tion and cause free-ﬂoating metal ions to enter the bloodstream. For patients with weak

kidneys, this heightened metal level in the bloodstream could result in metal poisoning

as they cannot ﬁlter out the metal fast enough [19]. To avoid metal poisoning, metal

implants with higher wear resistance are needed. Aside from high wear resistance, the

desired characteristics are high strength, low modulus, and excellent corrosion resis-

tance. The combination of low elastic modulus and high strength of the implant results

in a more uniform distribution of stresses between the bone and the implant [11,20].

Typical metals for orthopedic implants are cobalt-chrome alloys (CoCr), stainless

steel, and titanium alloys. For a long time, CoCr was one of the primary materials used

in the construction of surgical and dental implants due to its ability to resist corrosion

better than stainless steel and ceramics. CoCr utilizes its oxide layer, Cr2O3, to pro-

tect itself from corrosion. Its high corrosion resistance combined with wear resistance,

biocompatibility, and strength, makes CoCr the alloy of choice for implants [21]. Even

though CoCr is one of the most wear-resistant and corrosive-resistant alloys for im-

plants, if the oxide layer does get worn down and cobalt and chromium particles are

exposed to the patient’s bloodstream, it will result in severe immune reactions. While

the effects of low amounts of Co and Cr particles in the body are still mostly unknown,

high amounts of these elements are highly toxic to humans [22,23]. Surgical grade

stainless steel (316L) is mainly used for non-permanent applications such as stabiliz-

ing broken bones to help the body heal. In some cases, these implants are replaced

with a CoCr or titanium-alloy-based implant if the situation demands it. Stainless steel

transient usage is because stainless steel does not resist corrosion and is not as strong

as titanium alloys [11]. Alloying stainless steel with other elements does improve cor-

rosion resistance but it is still outclassed by many other materials.

Titanium alloys have excellent material properties and high corrosion resistance [24–

26]. Like CoCr, titanium naturally forms an oxide when inside the human body that

protects it from corrosion resistance [27]. Grade four commercially pure titanium (CP-

Ti) and Ti-6Al-4V (Ti-64) are the two most commonly used forms of titanium for

medical implants [24,28]. Titanium’s success as an implant comes from its superiority

in corrosion resistance, biocompatibility, and high strength to weight ratio [23,28–33].

However, titanium suffers from lower wear resistance than CoCr and more often results

in wear debris in patients [11]. The debris poses a considerable risk to patients since

vanadium is highly cytotoxic [34]. Many substitutions to vanadium have been made to

create a safer alloy. For example, Ti-6Al-7Nb substituted out the cytotoxic vanadium

for the much safer alternative of niobium which had the added beneﬁt of increasing

corrosion resistance [34]. Ti-5Al-2.5Fe is another alloy created for a similar purpose.

Ti-5Al-2.5Fe is an improvement on Ti-6Al-4V in almost all ﬁelds [35]. Surface modi-

ﬁcation of titanium alloys have also been reported to improve the corrosion resistance,

such as the use of SiO2oxide for coating the Ti6Al7Nb alloy and the CP-Ti titanium

(Grade 4) [36,37]. However, even with all these improvements, all Ti-alloys still suffer

from the same problem that all implants suffer from: the constant friction forces gener-

ate considerable amounts of metal debris inside the body over a long time [35,38], and

new modiﬁcations of the alloy composition to improve wear resistance is desirable.

This report aims to present a computational method for optimizing the compo-

sition of titanium alloys for increased wear and corrosion resistance. The presented

method and alloy optimization results serve a two-fold purpose: 1) To provide a high-

throughput method for down-selecting alloys with improved corrosion and wear resis-

tance, which can be utilized to guide the experimental design of orthopedic implants.

2) To deepen our understanding of the effect of different alloying elements on increas-

ing the mechanical compatibility, wear resistance, and corrosion resistance of alloys.

The presented computational approach is used for assessing the stability, mechanical

biocompatibility, wear resistance, and corrosion resistance of several titanium alloys.

We adopt a two-tier approach: In the ﬁrst tier, we use fundamental atomic and elec-

tronic attributes for a high-throughput selection of alloying elements that increase wear

and corrosion resistance. In the second tier, we use the CALPHAD databases and tools

integrated within the ThermoCalc software to predict the thermodynamic stability, cor-

rosion resistance, wear resistance, and mechanical compatibility of the selected ternary

titanium alloys. We show the improvement of corrosion resistance among the selected

alloy based on their reduced Pilling-Bedworth (PB) ratio, deﬁned as the volume of

formed oxide phase(s) divided by the volume of alloy phase(s) that formed the oxides.

Enhanced wear resistance is assessed based on the increased hardness of the selected

alloys compared to the benchmark system of Ti-6Al-4V (mole%).

In section 2, we elaborate on the methodology used in this work. In section 3,

we utilize the methodology to select ternary titanium alloys with improved wear and

corrosion resistance. We study the stability, biocompatibility, wear resistance, and cor-

rosion resistance of the selected alloys using the CALPHAD approach. In section 4, we

study the role of increased silicon concentration in improving the wear and corrosion

resistance of alloys and suggest a pathway toward the use of silicon alloys for medical

implants. In section 5, we discuss the limitations of the presented method compared to

available studies for the dynamic corrosion behavior and tribocorrosion phenomena in

alloys for orthopedic implants. Additionally, we compare the ﬁndings of this work with

other experimental and clinical studies of the mechanical properties, wear resistance,

and corrosion resistance of Ti-alloys for implants. Finally, in section 6, we present

conclusive remarks about the effect of different alloying elements on improving the

hardness and corrosion resistance of the alloys in our study.

2. Method

We use a two-tier process to design Ti-alloys with enhanced wear and corrosion re-

sistance. The complexity and accuracy of our analysis increase progressively, moving

from tier one to two. In tier one, a rapid screening that covers a wide range of alloying

elements is performed based on simple fundamental parameters as descriptor proxies

for corrosion and wear resistance. To this end, we use available density functional the-

ory (DFT) data for the relevant fundamental parameters, including the cohesive energy,

oxide formation energy, surface work function, and elastic shear modulus. A similar

approach based on cohesive energy and oxide formation energy was initially proposed

by Markus [39] but has only been examined for pure metals. Taylor and coworkers

suggested that an integrative approach that can beneﬁt from these descriptor proxies

should be further developed [40]. Here, we extend Markus’ approach to alloy systems

and add the surface work function as an additional descriptor. Our approach provides

new insights into the suggested integrated computational materials engineering (ICME)

approach by Taylor and co-workers.

In tier two, the corrosion and wear resistance of selected alloys from tier one will be

assessed based on comprehensive thermodynamic data and sophisticated optimization

techniques employed in the Thermo-Calc Software TCTI3 Ti-alloys database [41]. We

use the Equilibrium Calculator for phase diagram and Pourbaix diagram calculations

and the Property Model Calculator for yield strength and hardness calculations.

3. Results

3.1. High-throughput Screening of Ti alloys

We use three different DFT parameters, calculated for transition metals and met-

alloids elements, as proxy descriptors to optimize the alloys for enhanced corrosion

resistance: 1) the cohesive energy, which is the measure of the metal-metal (M-M)

bond strength, as a proxy descriptor of dissolution resistance, 2) the oxide formation

energy, which is the measure of the metal-oxygen (M-O) bond strength, as a proxy

descriptor for oxide scale formation tendency, and 3) the surface work function, which

is the electrostatic work needed to transport the charged electron through the dipole

layer of the metal surface undergoing oxidation. A large surface work function shows

the electrochemical nobility of the metal and favors the galvanic corrosion resistance

of the metal surface. The DFT parameters are collected from the Materials Project

database [42] and are provided in Supplemental Table 1. The oxidation formation en-

ergy is the formation energy per atom for the most stable metal oxide available in the

Materials Project database. The surface work function is the weighted average over

different surface orientations. The cohesive energy is the difference between the bulk

energy and the sum of total DFT energy of isolated atoms in the bulk, obtained from

the Materials Project database.

For increasing the corrosion resistance, our strategy is to select metal components

that combine the oxide scale formation tendency, dissolution resistance, and galvanic

corrosion resistance based on the aforementioned proxy descriptors. In other words, we

optimize the alloy composition through a synergistic operation of alloying elements as

passive (or protective) scale promoters and dissolution blockers. We combine alloying

elements that promote the formation of a passive oxide scale (i.e., selecting elements

with high oxidation formation tendency) with those with a high dissolution resistance

under the human body chemical conditions (i.e., selecting elements with high cohesive

energy and work function). Thereby, we identify scale-forming alloying elements that

can combine the following attributes: high oxidation tendency in the base alloy to form

a stable oxide scale combined with high cohesive energy and work function to mitigate

dissolution and galvanic corrosion.

0123456789

Cohesive energy(eV)

0.5

1.5

2.5

3.5

4.5

Oxide formation (eV)

Mn Mo

Pd Pt

Oxide Scale Promoters

Dissolution Bloackers

a) b)

Figure 1: Fundamental parameters of potential alloying elements (transition metals and metalloids). a)

Oxide formation energy versus the cohesive energy and the weighted surface work function for several

possible alloying elements. The arrows illustrate the increased dissolution blocking and scale formation

capability of different alloying elements. b) Cohesive energy (M-M bond strength) as a proxy descriptor for

metal dissolution resistance versus oxide formation energy (M-O bond strength) as a proxy for oxide scale

formation tendency.

Figure 1(a) shows the oxidation formation energy in terms of the cohesive energy

and surface work function for several possible alloying elements. Increasing the sur-

face work function and cohesive energy favors resistance to corrosive dissolution while

increasing the oxide formation tendency favors oxide scale formation. Figure 1(b) il-

lustrates the oxide formation energy against the cohesive energy. Elements with high

oxide formation energies and relatively low cohesive energies are good oxide scale pro-

moters (see Figure 1(b)). Classical examples are Cr and Al in superalloys that form

protective Cr2O3and Al2O3scales [43]. On the other hand, elements with high cohe-

sive energies and relatively low oxide formation energies are good dissolution blockers

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ComputationalDesignofCorrosion-resistantandWear-resistantTitaniumAlloysforOrthopedicImplantsNoelSionya,LongVuongb,OtgonsurenLundaajamtsb,SaraKadkhodaeic,aDepartmentofPhysics,UniversityofIllinoisChicago,845W.TaylorSt.,Chicago,IL60607USAbMechanical&IndustrialEngineering,UniversityofIllinoisChicago,84...

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