An Assessment of TiN Formation on NiTi Alloy and the Corrosion Resistance of TiN/NiTi Alloy Using First-Principles Calculation

Abstract

In this paper, the interfacial bonding properties between (110)_NiTi and (200)_TiN interfaces, as well as the adsorption capacity of Cl⁻ on the surfaces of (110)_NiTi and (200)_TiN, were investigated using the first-principles computational method based on density functional theory (DFT). Four types of interfacial models between (110)_NiTi and (200)_TiN were developed. It was found that the interfacial bonding energies of the four interface models are greater than zero, indicating stable interface bonding between (110)_NiTi and (200)_TiN. For comparison, model III (N of (200)_TiN is located at the bridge size between Ti and Ni in (110)_NiTi) has the largest Wad value of 9.773 J/m², which is attributed to stronger N-Ti bonding at the interface. Based on interface model III, an interfacial model of Cl⁻ at three different adsorption locations (top, bridge, and hole) on the (110)_NiTi and (200)_TiN surfaces, respectively, was constructed. The results reveal that the adsorption energies of Cl⁻ on the surface of (110)_NiTi are significantly less than those of the Cl⁻ on the surface of (200)_TiN. This suggests that (110)_NiTi is more likely to react with Cl⁻. Hence, the introduction of a TiN layer on the surface of NiTi alloy can effectively improve its corrosion resistance.

1. Introduction

NiTi shape memory alloys (SMAs) are widely used in automotive, aerospace, and biomedical fields due to their unique functional properties such as shape memory effect, superelasticity, and good biocompatibility [1,2,3,4,5,6]. However, their soft texture and poor microstructural stability severely limit their application in precision machinery and load-bearing fields [7]. To date, researchers have conducted extensive measures to optimize the performances of NiTi alloys, especially by adopting surface treatments [8]. Currently, surface treatment techniques mainly consist of magnetron sputtering [9], ion plating [10], surface oxidation [11], laser shock [12], etc., aiming to improve the hardness, biocompatibility and wear resistance, as well as the corrosion properties, of NiTi alloys.

In recent years, it has become possible to introduce a TiN ceramic phase into the surface of titanium alloy by ion nitriding, which can be utilized to improve its elevated hardness, wear and corrosion resistance. Czarnowska et al. [13] investigated the microstructure and corrosion resistance of an NiTi alloy modified with a TiN ceramic layer. It was found that the nanocrystalline-structured thin layer, composed of titanium nitride (TiN), was successfully synthesized at the surface of the NiTi alloy through glow discharge nitriding at a temperature of 290 °C. The corrosion current density significantly decreased proportionally from 0.035 μA/cm² to 0.011 μA/cm², while the corrosion potential increased from −340 mV to 85 mV, indicating a significant improvement in the corrosion resistance of the NiTi alloy after nitriding treatment. In addition, Li et al. [14] studied the microstructural features and functional properties of TC4 alloy processed by hollow-cathode plasma nitriding at 500 °C. The results revealed that a complex multi-layer structure including TiN, Ti₂N and nitrogen-stabilized α(N)–Ti phases was present in the nitrided TC4 alloy. Meanwhile, the corrosion resistance of the studied nitrided TC4 alloy improved significantly: the corrosion current density decreased from 1.4592 A·cm⁻⁶ to 7.4103 A·cm⁻⁹, while the corrosion potential shifted from −0.4698 V to −0.1476 V. This means that nitriding treatment, serving as an important surface treatment, is an effective method to enhance the mechanical properties, wear properties and corrosion resistance.

The interfacial bonding strength between the TiN ceramic layer and the NiTi substrate plays an important role in improving the mechanical properties, wear and corrosion resistance of an NiTi alloy. However, it is difficult to evaluate the comprehensive performance of a thin TiN ceramic layer on the surface of titanium alloys through experimental methods. In contrast, the first-principles method is an effective way to evaluate the interface electronic structure and bonding performance. To date, a number of scholars have investigated the interface electronic structure and bonding properties between the NiTi alloy and surface coatings through first-principles calculations. For instance, Li et al. [15] investigated the interface structural stability in NiTi/Nb metal nanowires. Their results revealed that the interface between (211)_NiTi and (220)_Nb in NiTi/Nb metal nanowires demonstrated exceptional structural stability and featured minimal cohesive energy, fracture energy, and distinctive electronic structural characteristics. Liu et al. [16] explored the optimal interface structure and ideal adhesion energy of the interface between (110)_β-Ti and (111)_TiN. The results demonstrate that the optimal structure is the FCC site at the N-terminal interface, which has an adhesion energy of 7.16 J/m². This can be attributed to the continuation of the ceramic phase structure to the metal phase structure. In the present study, the optimal crystal orientation preference for the interface combination between the NiTi alloy and TiN ceramic layer was also investigated. Nevertheless, the bonding force between (110)_NiTi and (200)_TiN has not been explored systematically. Meanwhile, the adsorption capacity of the interface between Cl⁻ and NiTi/TiN is an important parameter for evaluating the corrosion performance of an NiTi alloy and NiTi alloy modified with a TiN ceramic layer.

The present study systematically investigated the stability and electronic structure of the interface between (110)_NiTi and (200)_TiN, including adhesion work (Wad), electron density difference (CDD), and density of states (DOS). Four types of interface models between (110)_NiTi and (200)_TiN were constructed by using first-principles calculations based on density functional theory (DFT). While previous studies have primarily focused on the experimental fabrication and macroscopic properties of TiN-coated NiTi alloys [13,14,17], a systematic theoretical investigation into the atomic-scale interfacial bonding mechanisms and their direct impact on corrosion resistance remains lacking. Furthermore, the adsorption behavior of corrosive species such as chloride ions (Cl⁻) at these interfaces, which is crucial for understanding the initial stage of corrosion, has not yet been explored from a first-principles perspective. Therefore, the stability of Cl⁻ at varying locations on the surface of (110)_NiTi and (200)_TiN was assessed by providing a barrier with a lower tendency to react with chloride ions.

2. Calculation Model and Methods

The construction of the TiN/NiTi interface model was carried out as follows: Firstly, the geometric structures of B2-NiTi and TiN were optimized, as shown in

Table 1. Calculated and experimental values of the lattice constats of B2-NiTi and TiN, adapted from Refs. [18,19,20].

Structure	Methods or References		a (Å)	b (Å)	c (Å)
B2-NiTi	Current study	GGA-PBE	3.031	3.031	3.031
	Other calculations	GGA-PBE	3.005	3.005	3.005
	Experiment	Strutt et al.	2.998	2.998	2.998
TiN	Current study	GGA-PBE	4.261	4.261	4.261
	Other calculations	GGA-PBE	4.270	4.270	4.270
	Experiment	Kutschej et al.	4.240	4.240	4.240

[17,18,19]. In the subsequent stage of the process, the surfaces of B2-NiTi₍₁₁₀₎ and TiN₍₂₀₀₎ were cut following the optimization stage. The (110) surface of B2-NiTi was selected as it is the most stable and densely packed plane [18], while the (200) surface is one of the most commonly observed and stable orientations in experimentally deposited TiN coatings [20], which is highly relevant to practical applications. In order to obtain a stable surface structure, convergence tests were conducted on (110)_NiTi and (200)_TiN. The construction of an interface model was finally achieved by utilizing the optimized (110)_NiTi and (200)_TiN, with the incorporation of a 15 Å vacuum layer at the interface. This approach was implemented to eradicate interactions between the plates, thereby ensuring the efficacy of the model. Furthermore, when disparate surfaces were amalgamated, the lattice mismatch at the interface was guaranteed to be less than 5% through surface recombination or supercell formation. The optimized mismatch was achieved by constructing a supercell, where the larger TiN lattice was kept fixed. Moreover, a minimal isotropic strain was applied to the NiTi slab to ensure the formation of a coherent interface, which is a common approach in simulating metal–ceramic interfaces [16]. It was evident that the presence of disparate terminal atoms gave rise to the manifestation of discrete interface structures within the interface. Consequently, the present article proposes the construction of all possible interface structures. Concurrently, in order to facilitate to compare the corrosion properties of NiTi and TiN, the interface models of NiTi(Cl⁻) and TiN(Cl⁻) were also constructed. In order to enhance computational efficiency, Cl⁻ ions were positioned at a distance of 3 Å from the designated interface position.

In this study, the CASTEMP program, founded upon DFT (density functional theory), was utilized for first-principles calculations in order to investigate the interaction energy between B2-NiTi and TiN, in addition to the energy changes, structure, and electronic properties of chlorine adsorption by B2-NiTi and TiN, whichwere performed using Materials Studio 2017 R2 (version 17.1.0.48). The electron exchange-correlation energy was described within the generalized-gradient approximation (GGA) using the Perdew–Burke–Ernzerhof (PBE) functional under the assumption of a uniform electron gas and with spin-polarization effects neglected [21,22,23]. The ultra-soft pseudopotential (USPP) [24] was utilized to delineate the interaction between electrons and ions. The electronic wave function adopts a vector group of plane basis vectors. The results of the convergence test of the total energy of the unit cell indicate that the energy cutoff of the plane wave was set to 400 eV, and the value of the Brillouin zone K point was 4 × 4 × 1. During the geometric optimization process, the convergence accuracy was set to 2.0 × 10⁻⁶ eV/atom, the maximum force was fixed as <0.01 eV/Å, the maximum displacement was smaller than 5 × 10⁻⁴ Å, and the maximum stress was less than 0.02 GPa.

3. Results and Discussion

3.1. Study of the Interfacial Properties of the Nitride Layer

The bonding strength between the TiN and 60 NiTi alloy was evaluated. To this purpose, a nitrogen-infiltrated structure was created at the interface between (110)_NiTi and (200)_TiN. The optimized (110)_NiTi and (200)_TiN were sliced, supercelled, and an interface model was constructed, as shown in Figure 1. The mismatch degree of the interface model between (110)_NiTi and (200)_TiN was found to be less than 5%. To ensure the reliability of the slab models, convergence tests with respect to both vacuum layer thickness and the number of atomic layers were rigorously performed. The total energy of the system was chosen as the convergence criterion. For the vacuum layer, thicknesses ranging from 10 to 20 Å were tested. A thickness of 15 Å was found to be sufficient to eliminate any spurious interactions between periodic images, as the energy change was less than 0.001 eV/atom. Meanwhile, a number of layers of (110)_NiTi and (200)_TiN, varying from four to eight and from five to nine, respectively, were tested to determine the optimized slab thickness. The results revealed that when six layers for NiTi and seven layers for TiN were employed, the calculated surface energy can be converged within 0.01 J/m², indicating that the central layers exhibit bulk-like properties. These converged parameters were subsequently employed in all interface and adsorption models. It is evident that the distinct atomic arrangements presented at the surface of (110)_NiTi and (200)_TiN give rise to four varieties of interface models. These four models are predicted on the basis of the arrangement of atomic layers at the interface between (110)_NiTi and (200)_TiN. The characteristics of these four interface models were established as follows: the N atom of (200)_TiN is located at the top of Ti and Ni in (110)_NiTi, the Ti atom of (200)_TiN is located at the top of Ti and Ni in (110)_NiTi, the N atom of (200)_TiN is located at the bridge between Ti and Ni in (110)_NiTi, and the Ti atom of (200)_TiN is located at the bridge between Ti and Ni in (110)_NiTi. As illustrated in Figure 1, these four interface models are designated Module I, Module II, Module III, and Module IV.

In the process of combining (110)_NiTi with (200)_TiN to form the stable interface structure, the universal binding energy relationship (UBER) is adopted to ascertain the appropriate interplanar spacing d₀. The fundamental principle of UBER is to initially establish the Wad-d₀ relationship curve. The Wad-d₀ relationship curve denotes the relationships between the interfacial adhesion work (Wad) and the interplanar spacing (d₀). It is evident that Wad can be calculated without optimization of the geometric structure of the interface model. The interface stability can be evaluated by means of adhesion work. The adhesion work of interfaces between (110)_NiTi and (200)_TiN can be obtained by the following formula [25]:

$$W_{ad}=(E_A+E_B-E_{A+B})/S$$

(1)

In the formula, E_A+B denotes the total energy after interface model relaxation, E_A signifies the total energy after interface model component A relaxation, E_B denotes the total energy after component B relaxation, and S represents the interface area.

The Wad-d₀ curves of four distinct interface models are presented in Figure 2. d₀ is designated as the minimum point of adhesion energy at the initial spacing when the interface is constructed. As demonstrated in Figure 2, the d₀ values of the four various interface models are 1.72 Å, 2.54 Å, 1.28 Å, and 2.26 Å, respectively. Subsequently, the geometric structure of the interface was optimized and constructed. Subsequently, the optimal interplanar spacing d and Wad of the interface between (110)_NiTi and (200)_TiN were calculated, and the relevant calculated results are displayed in

Table 2. The energy and binding energy of four interface models between (110)_NiTi and (200)_TiN.

	ETiN (eV)	ENiTi (eV)	ETiN+NiTi (eV)	Area (Å)	d (Å)	Wad (J/m2)
Module I	−11,796.72	−14,787.35	−26,592.03	4.75 × 3.02	1.72	8.873
Module II	14,466.10	−14,787.35	−29,257.93	4.75 × 3.02	2.54	4.988
Module III	−11,796.73	−14,787.35	−26,592.84	4.75 × 3.02	1.28	9.773
Module IV	−14,466.12	−14,787.42	−29,258.44	4.75 × 3.02	2.26	5.457

.

As demonstrated in Figure 2, the total energy of the four types of interface models between (110)_NiTi and (200)_TiN is −26,592.038 eV, −29,257.933 eV, −26,592.845 eV, and −29,258.442 eV, respectively. By employing Formula (1), the adhesion energies of these four interface models are calculated to be 8.873 J/m², 4.988 J/m², 9.773 J/m², and 5.457 J/m², respectively. It can be observed that the interfacial adhesion energy values of the four models are greater than 0. It is well accepted that an adhesion energy value greater than 0 is indicative of a stable interface. That is to say, the TiN ceramic phase layer formed by nitriding is in a stable state thermodynamically, and a stable TiN ceramic phase can be formed by nitriding. Remarkably, Model III demonstrated the highest Wad value of 9.773 J/m², which is attributed to the formation of strong N-Ti bonds at the bridge site configuration. This superior interfacial strength is paramount for ensuring the mechanical integrity and delamination resistance of the TiN coating under severe conditions.

The bonding of interface atoms is determined by their electronic structure and bonding properties [26]. To facilitate a more comprehensive understanding of the electronic interactions at the interface, a comparative analysis of the electron density differences among the four models is shown in Figure 3. It is widely acknowledged that a positive density difference indicates that the electron density is more significant than that of the electron density obtained by overlapping the original atomic density. Conversely, negative density differences exhibit an opposing trend. It is evident that all four models show distinct orientation characteristics surrounding Ti atoms at the interface, which is characterized by a negative density difference. In contrast, a significant positive density difference is observed around N atoms. The bonding contour around Ni elements displays a butterfly shape, indicating the formation of strong Ti-N bonds and demonstrating the extremely strong bonding stability at the interface. In particular, they exhibit the more pronounced orientation features at the interfaces of Model I, Model III and Model IV. It is evident that the Ti atoms in NiTi of Model II also exhibit sharp orientation characteristics. However, no significant bonding between Ti atoms and the surrounding N atoms was observed due to inherent issues in the model design, which is mostly consistent with the calculated results of adhesion energy.

In Figure 4, the partial average density of states (PDOS) of the four models are displayed, mainly focusing on the atoms located at the interface. The stability of the crystal structure is closely related to the electronic state of the Fermi level. It is evident that PDOS provides a comprehensive representation of the distribution of electronic states in the vicinity of the Fermi level, thus facilitating a deeper understanding of the chemical bonds and electronic interactions at interfaces. Consequently, the electrons at the Fermi level are imperative. It was found that in all the interface models, Ti-d orbitals in (110)_NiTi and N-p orbitals in (200)_TiN overlap with each other at approximately −3 eV, thereby indicating that orbital hybridization and enhanced electronic conductivity, as well as charge transfer efficiency, are evident at the interface. The enhancement of electronic conductivity is advantageous for the optimized electrical contact at the interface, while the improvement of charge transfer efficiency facilitates electron transfer and delocalisation during deformation, thereby forming Ti-N bonds [27]. The formation of Ti-N bonds is of crucial importance in improving the stability of the interface between the NiTi alloy and TiN ceramic layer.

3.2. Corrosion Resistance

The energy changes, structural features and electronic properties of adsorbed Cl⁻ at the surface of B2-NiTi and TiN were calculated by using first-principles calculations. First of all, the geometric structures of B2-NiTi and TiN were optimized to obtain the most stable geometric configuration. Moreover, B2-(110)_NiTi and (200)_TiN were cut from the optimized B2-NiTi and TiN unit cells, respectively. Interface models were constructed for the adsorption of Cl⁻ on the surface of (110)_NiTi and (200)_TiN. In addition, three different adsorption sites (top, bridge, and hole sites) were considered, as shown in Figure 5. In order to ensure the convergence of calculations and the reliability of results, it is necessary to allow only two layers of atoms at the surface of (110)_NiTi and (200)_TiN to undergo free relaxation during the interface optimization process. The positions of the remaining atoms can be fixed.

To better understand the Cl⁻ adsorption characteristics at the surface of (110)_NiTi and (200)_TiN, the adsorption energies of Cl⁻ at the three different ideal sites of (110)_NiTi and (200)_TiN were calculated by the following formula:

$$E_{\mathrm{int}}=E_{slab-inos}-(E_{slab}+E_{inos})$$

(2)

E_slab-inos represents the total energy after optimizing the structure. E_slab represents the energy of (110)_NiTi and (200)_TiN after structural optimization, while E_inos represents the energy of Cl⁻.

Table 3. The final chemisorption energies of Cl⁻ and (110)_NiTi and (200)_TiN after relaxation was optimized.

Structure	Eint (eV)
(110)NiTi-Top	0.618518267
(110)NiTi-Bridge	0.618599997
(110)NiTi-Hole	0.618399257
(200)TiN-Top	0.688416877
(200)TiN-Bridge	1.128183357
(200)TiN-Hole	1.362865157

illustrates the chemical adsorption energies between Cl⁻ and (110)_NiTi/(200)_TiN. As presented in Table 3, the interface adsorption energies are ranked as follows: (200)_TiN-Hole > (200)_TiN-Bridge > (200)_TiN-Top > (110)_NiTi-Bridge > (110)_NiTi-Top > (110)_NiTi-Hole. Nevertheless, it is evident that all adsorption energies are positive, indicating that both NiTi and TiN are stable during the adsorption process. In comparison with (110)_NiTi, (200)_TiN exhibits higher adsorption energy at the top, bridge, and hole sites, suggesting that the TiN layer can slow down the corrosion process to some extent. For (110)_NiTi and (200)_TiN, it was demonstrated that the top and bridge position is more conducive to the adsorption of Cl⁻.

To better comprehend the electronic interactions during the adsorption process, the electron density between Cl⁻ and (110)_NiTi as well as (200)_TiN is displayed in Figure 6. It is well accepted that a positive density difference indicates the electron density is more significant than the density obtained by superimposing the original atomic density. Conversely, a negative density difference exhibits an opposing trend [28]. The charge density distribution of chlorine adsorption on the surfaces of (110)_NiTi and (200)_TiN is significantly different.

It is noteworthy that both NiTi and TiN demonstrate substantial charge accumulation on the Cl⁻-side, as evidenced by butterfly-shaped profiles surrounding the Ti and Cl⁻, in addition to discernible directional characteristics. This indicates that a significant amount of electronic exchange occurs, which contributes to the interfacial stability. The strong adsorption properties can be attributed to these covalent bonds. A comparison of the electron density difference between (110)_NiTi and Cl⁻, as well as between (200)_TiN and Cl⁻, reveals that the former exhibits a more compact electron cloud distribution around Cl⁻, accompanied by increased charge accumulation. This suggests that (110)_NiTi forms stronger bonds between titanium (Ti) and Cl⁻ than (200)_TiN. Furthermore, the charge distribution characteristics exhibit slight variations at different stacking positions. The top sites and the bright sites exhibit a substantially higher charge transfer compared to the hole sites, suggesting a heightened probability of binding and more conducive conditions for chlorine adsorption. These results are clearly consistent with the calculated adsorption energy.

To further elucidate the bonding properties between (110)NiTi/(200)TiN and Cl⁻, the partial density of states (PDOS) for three different conditions are shown in Figure 7. Only atoms in the interfacial layer are considered. It is well known that the stability of the crystal structure is mainly influenced by the electrons in the Fermi energy level. Hence, it is crucial to analyze the PDOS near the Fermi level. In all the adsorption models, it can be observed that the Ti-d and Cl-s orbitals overlap at the adsorption interface at around −2.5 eV, indicating that orbital hybridization occurs. This hybridization peak is characterized by the sharp peaks of the neighboring atomic orbitals in PDOS, implying a bonding process between neighboring atoms and the formation of Ti-Cl bonds. For comparison, in the adsorption structure between (110)NiTi and Cl⁻, a wider pseudo-energy gap can be found at the Fermi energy level, regardless of the position. Generally speaking, a pseudo-energy gap near the Fermi level reflects the covalent nature and bonding strength between neighboring atoms [29]. In addition, wider pseudo-energy gaps correspond to stronger covalent properties and atomic bonding. Hence, the electronic structure features between (110)NiTi and Cl⁻ further confirm that (110)NiTi is more likely to form a more stable adsorption interface. In contrast, the narrow pseudo-energy gap at the Fermi level means that it is difficult to form stable chlorine adsorption interfaces. This suggested that (110)NiTi has a stronger tendency to react with Cl⁻, which could initiate the corrosion process. Hence, the introduction of a TiN layer on the surface of the NiTi alloy is predicted to effectively improve its corrosion resistance by mitigating this initial adsorption step.

4. Conclusions

The findings of the present study provide valuable atomic-scale insights for guiding the experimental design of nitriding processes for NiTi alloys. The high interfacial adhesion energy predicts that stable and adherent TiN coatings can be achieved in NiTi alloy, which is crucial for its long-term performance. Furthermore, the lower adsorption energy of Cl⁻ on the TiN surface suggests that the introduction of a dense and continuous (200)-oriented TiN layer could significantly enhance the corrosion resistance of 60 NiTi alloy. It should be noted that the present model was established as an idealized system under vacuum conditions. The actual corrosion process involves more complex factors, such as the presence of water molecules, solvation effects, pH, potential, and the possible formation of oxide films. These factors are beyond the scope of this current thermodynamic-based DFT study. The specific conclusions are as follows.

(1)

Four kinds of interface models between (110)_NiTi and (200)_TiN with different atomic layer arrangements were constructed. In addition, all four interface models had a positive work of adhesion (Wad), indicating stable interface bonds between (110)_NiTi and (200)_TiN. In contrast, Model III had the highest Wad of 9.773 J/m², attributed to the strong N-Ti bonds formed at the interface after relaxation.

(2)

A significant negative density difference around Ti atoms and a significant positive density difference around N atoms were observed at the interface between (110)_NiTi and (200)_TiN, indicating strong interface bonding stability between (110)NiTi and (200)_TiN. The Ti-d orbitals of (110)_NiTi and the N-p orbitals of (200)_TiN overlapped at approximately −3 eV, indicating orbital hybridization and bonding formation of Ti-N.

(3)

The adsorption capacities of Cl⁻ on the surface of (110)NiTi and (200)TiN were investigated. The adsorption energies of Cl⁻ on the surface of (110)NiTi are lower than that of (200)TiN, regardless of the Cl⁻ adsorption sites. This suggested that (110)NiTi was more prone to reacting and forming bonds with Cl⁻, indicating a higher thermodynamic driving force for corrosion initiation. Therefore, the introduction of a TiN layer on the surface of NiTi alloy can effectively enhance its corrosion resistance properties by acting as a more inert barrier layer.