Tribological Response of δ-Bi₂O₃ Coatings Deposited by RF Magnetron Sputtering

Abstract

Bismuth oxide (Bi₂O₃) coatings and composite coatings containing this oxide have been studied due to their potential applications in gas sensing, optoelectronics, photocatalysis, and even tribology. Two parametric models based on chemical features have been proposed with the aim of predicting the lubricity response of oxides. However, such models predict contradictory values of the coefficient of friction (COF) for Bi₂O₃. In this study, we deposited Bi₂O₃ coatings, via magnetron sputtering, on AISI D2 steel substrates to evaluate the tribological responses of the coatings and determine which parametric model describes them better. Experimentally, only coatings presenting the cubic defective fluorite-like δ-Bi₂O₃ phase could be evaluated. We performed pin-on-disk tests at room temperature and progressively increasing temperatures up to 300 °C using alumina and steel counter-bodies. Low wear and COFs (0.05 to 0.15) indicated that the δ-phase behaves as a lubricious solid, favoring the validity of one of the models. An alternative explanation is proposed for the low COF of the defective fluorite-like structure since it is well known that it contains 25% of anionic vacancies that can be ordered to form low shear-strength planes, similar to the Magnéli phases. Two challenges for future potential applications were observed: one was the low adhesion strength to the substrate, and the other was the thermal stability of this phase.

1. Introduction

The development of coatings to function as solid lubricants for either boundary lubrication conditions or elevated temperatures (above 400 °C) is of special interest to a wide range of industries [1], such as high-speed or dry-cutting machine tools. In boundary lubrication conditions, wear and friction are determined by the interaction between the solid bodies, and heat generation can lead to oxidation. Similarly, most metallic sliding surfaces will oxidize at elevated temperatures [2,3]. Therefore, the oxide films dominate the friction and wear behavior of the interfaces. The most intelligent solution to take advantage of the heating instead of fighting against it is the design of oxide-based lubricant coatings [3,4,5,6]. A material qualifies as a solid lubricant when its friction coefficient is less than 0.2, since, at higher COF, the interfaces are largely deformed [7]. A classification of the different solid lubricants is shown in Figure 1 [1,4], where it can be observed that lubrication in high-temperature (HT) applications relies on the use of intrinsic solid lubricants, such as oxides (V₂O₅, AgMo₂O₇), fluorides (CaF₂, BaF₂, CeF₃), hexagonal boron nitride (h-BN) or soft metals (Ag, Cu, Au, Pb, In). The latter are only stable up to 600 °C [1].

Different mechanisms to explain the tribological response of the oxide-based solid lubricants have been envisioned [1], but only the crystal-chemical approaches offered by Erdemir [8] or Prakash and Celis [9] proposed a predictive model to select lubricant oxide surfaces. Among the binary metal oxides, those developing Magnéli phases are particularly ideal for lubrication at high temperatures [10]. The Magnéli phases are characterized by the organization of oxygen vacancies in such a way that the interlayer distance is increased, leading to the formation of easy shear or crystallographic shear planes [11].

There is an interest in finding predictors to select lubricious metal oxides since the metallic elements could be added into technological hard coatings (AlCrN, TiSiN, TiAlN), expecting that at high temperatures, the scale is dominated by the lubricious oxide [6], while other mechanical properties are provided by the hard coating. Quantum chemical models have proposed correlations between the lubricity and fundamental properties of the material, such as electronegativity, ionic potential, or chemical hardness [12]. This is so because it has been recognized that the tribochemical or mechanochemical processes during the sliding of two surfaces are initiated and facilitated by the exchange of electrons [13]. Such concepts have been used to explain superlubricity in carbon coatings with and without lubrication [14], but no predictive models have been proposed.

Erdemir [8] showed, using empirical data, an inverse linear correlation between the ionic potential and the coefficient of friction at high temperatures (cf. Figure 2a). The ionic potential (IP = Z/r) is defined as the ratio between the cationic charge (Z) and the radius of the cation (r). The IP is a measure of the screening of the cations by the surrounding anions (oxygen ions). The higher IP indicates that the cations interact strongly with their anions, and there is little interaction with other cations. The reduced cation–cation interaction led to soft oxides, which can shear easily, explaining the trend toward low COF observed in Figure 2a. Nevertheless, Prakash and Celis [9] raised some doubts about the usefulness of the ionic potential, explaining that very ionic oxides, such as BaO, PbO or Bi₂O₃, were not included in Erdemir’s plot [8,12]. These oxides exhibited low COF (<0.25) and low IP values (1.5, 2, and 2.88 Å⁻¹, respectively), contradicting Erdemir’s model. According to Prakash and Celis [9], the degree of bonding ionicity is not considered in the IP definition. Alternatively, the authors proposed another marker to consider the interaction between the cation and anion during sliding: the interaction parameter (named A) or Yamashita–Kurosawa’s interaction parameter [15]. The interaction parameter of an oxide with stoichiometry M_pO_q is a complex function of the polarizability of both the cations and anions (free and bonded) [9].

The interaction parameter, A, is defined as

$$A=\frac{\left[({\alpha }_f^{-}-{\alpha }_{O^{2-}})\right]}{2({\alpha }_c+{\alpha }_f^{-})\left({\alpha }_c+{\alpha }_{O^{2-}}\right)}$$

(1)

${\alpha }_f^{-}$ is the polarizability of the anion in the free state, taken as 3.921${Å}^{-3}$ for oxygen based on Pauling values.

${\alpha }_{O^{2-}}$ is the polarizability of the anion in the crystal, which, based on Dimitrov and Komatsu calculations [16] for an oxide of stoichiometry M_pO_q (for Bi₂O₃, p = 2, q = 3), can be expressed in terms of the optical bandgap (E_g) as

$${\alpha }_{O^{2-}}=\left[\frac{molar volume}{2.52}\left(1-\sqrt{\frac{E_g}{20}}\right)-p{\alpha }_c\right]q^{-1}$$

(2)

${\alpha }_c$ is the cation polarizability, equal to 1.508 ${Å}^{-3}$ for Bi³⁺ [17].

Using estimated A values for different oxides [16] and empirical COFs measured at different temperature ranges (Figure 2b shows the COFs measured at T/T_m intervals between 0.3–1, where T_m is the melting temperature of the oxide), Prakash and Celis [9] predicted that lubricious oxides have COF below 0.2 when their interaction parameter is close to zero, independently of the T/T_m range considered.

Despite the significant differences observed between these two models, not much effort has been made to investigate which chemical parameter could be more appropriate to describe lubricious oxides. The work of Erdemir [8] clearly postulated Re₂O₇ and V₂O₅ as candidates for low-friction coatings and afterwards, much work was performed to add V into hard coatings to reduce the COF at high temperatures due to the formation of a V₂O₅ layer [17,18,19]. On the other hand, following Prakash and Celis’ [9] proposal, some works have evaluated the tribological response of Bi₂O₃ added as lubricant nanoparticles [20,21] or into NiAl composite coatings [22].

Bismuth sesquioxide (Bi₂O₃) is a very interesting and challenging material that in this context could be used to elucidate the most influencing chemical parameter to predict the lubricious properties of binary oxides, since it has a low ionic potential (2.88 Å⁻¹); therefore, a high COF at temperatures close to the melting temperature (T_m) is expected according to Erdemir’s model [8]. Meanwhile, the empirical model proposed by Prakash and Celis predicts a low COF, since the interaction parameter of Bi₂O₃ estimated by Dimitrov and Komatsu [16] at T/T_m = 0.99 is very low (0.008 Å⁻³), in agreement with the measured value reported in [9].

However, such models do not consider the dynamic polymorphism of the Bi₂O₃ material that presents two thermodynamically stable and many metastable phases [23]. One is the monoclinic (α) phase, stable from room temperature (RT) to 730 °C, and the other is the defect-fluorite cubic (δ) phase, which is stable above 730 °C and up to the melting point of the material (830 °C). Two metastable phases (β-tetragonal and γ-bcc) are formed during the cooling process, and the transformation temperature depends on the cooling rate, ambient atmosphere (vacuum or air), and oxygen concentration. Finally, another two metastable phases have been observed, under very specific conditions (ω and ε). The α-, β-, γ- and δ-Bi₂O₃ phases have been extensively studied as either bulk materials, nanostructures, or thin films. Thin-film deposition and nanostructure synthesis have resulted in interesting approaches to obtain metastable phases [24], and even the high-temperature δ-phase can be stabilized and retained at ambient conditions, a phenomenon that has been explained as due to the nanometric size of crystals, the film–substrate epitaxial relationship, or the non-equilibrium conditions during the atomic aggregation deposition using sputtering [25,26,27,28].

Knowledge about the Bi₂O₃ polymorphism is very important, since the data compiled by Prakash and Celis show that Bi₂O₃ has a low COF at T/T_m = 0.99. At this temperature, the material has already suffered a phase transition into the δ-Bi₂O₃ phase, and although the crystallographic phase is not mentioned, the reported COF must be related to the δ-Bi₂O₃ phase. Moreover, the estimation of the interaction parameter, A, in Figure 2b for the Bi₂O₃ was performed assuming the optical bandgap of the α-phase [16], which is larger than that corresponding to the δ-phase. The implications of these differences are further discussed later.

In this work, we deposited δ-Bi₂O₃ coatings (labelled hereafter as δ-BO) by magnetron sputtering to determine their tribological response, which was analyzed in terms of the physico-chemical properties of the bismuth oxide coatings and the lubricious oxide models.

2. Materials and Methods

Bismuth oxide coatings were deposited on AISI D2 steel discs using a magnetron sputtering system from an α-Bi₂O₃ phase target. According to our previous studies [28,29], we knew that obtention of single-phase Bi₂O₃ coatings was only possible for the cubic fluorite-type Bi₂O₃ phase, known as the δ phase: radio frequency (RF) power 90 W, substrate temperature 110 °C and deposition time 20 min. The α-Bi₂O₃ phase could be obtained after annealing (400 °C for 4 h) of the coatings deposited at 160 W and 200 °C, but as shown later, the phase composition was not uniform. The substrate surfaces were ground using emery papers with different SiC grain sizes and polished to a mirror finish with alumina suspension. This finish promotes a low roughness. Prior to deposition, the substrates were ultrasonically cleaned with isopropanol and dried using hot air.

Coating thickness was confirmed using a Veeco Dektak 150 stylus profilometer. The morphology of the coatings was characterized by field-emission gun scanning electron microscopy (FESEM) using a JEOL 7600F operated at 10 kV. The topography of the samples was measured using a Sensofar S-Neox 090 microscope and a Zygo Nexview TM optical profilometer, and the images were analyzed through Mx TM version 6.4.0.21 software. The film structure was characterized using a Rigaku Ultima IV X-ray diffractometer (Cu Kα radiation, parallel beam optics, measurement mode 2Theta/Omega, step 0.2°, speed 1°/min, measured area 1 cm × 1 cm) and an En-spectra R532 spectrometer for micro-Raman spectroscopy (wavelength 532 nm, magnification 60× and 28.2 mW).

The tribological behavior was studied using two pin-on-disk tribometers from CSM and Microtest (heatable) under different conditions: load (1N or 2N), linear speed (1 cm/s), alumina or steel balls (6- and 10-mm radius) at room temperature and under heating up to 300 °C. Raman measurements of the initial coatings and contact areas after tribological testing were carried out with a LabRAM Horiba Jobin Yvon spectrometer equipped with a charge-coupled device (CCD) detector and a diode-pumped solid-state laser (532 nm) at 5 mW.

3. Results

3.1. Structural Characterization

The average thickness of the coatings was 1093 ± 34 nm, obtained using the values measured for five different samples deposited under the same conditions.

The coatings presented a uniform globular microstructure with an average grain size of 79 ± 2 nm, as presented in Figure 3a.

The δ-BO coatings were uniform even at a larger scale, as can be observed in Figure 3b, corresponding to the optical profilometry image. The average roughness estimated from 10 measurements was 14.7 ± 0.8 nm, small enough to ensure that the tribological response would not be largely affected. The surface smoothness inherent to the sputtering technique, as observed in the globular surface microstructure, helped to prevent the detachment of debris from protruding particles on the coating, which could act as a third body in the system.

The XRD patterns (Figure 4a) measured in different samples presented the cubic phase with the characteristic five peaks of the δ phase. The peak intensity was similar to that reported in the database for a powder sample, i.e., the coatings were polycrystalline without a crystallographic texture. This polycrystallinity agreed with the SEM image (Figure 3a). The additional peak, located at 44.55°, corresponded to that of the steel substrate, which was detected due to the measurement mode used. This is because the penetration depth of the X-rays was longer than the thickness of the coatings. Meanwhile, the micro-Raman spectra (obtained in different spots and samples) showed a single broad symmetric band around 623 cm⁻¹, confirming the disorder-like structure of the δ-Bi₂O₃ phase (Figure 4b) as described previously [30].

3.2. Tribological Characterization

Figure 5a shows the room temperature coefficients of friction (COFs) obtained for the δ-BO coatings under different loads, counter-bodies and tribometer equipment. It can be observed that steady-state conditions were quickly obtained for both Al₂O₃ and steel balls during the first 20 cycles. The COF values obtained using the Microtest© equipment varied between 0.08 for the steel balls and 0.15 for the Al₂O₃ balls. The inset shows the trend of decreasing friction below 0.1 for a longer test (10,000 cycles) under 1 N load using Al₂O₃ counter-face and the CSM© equipment.

When shear forces were applied to the surfaces, the δ-BO coatings showed a tendency to delaminate as a result of a mechanical mismatch, film stresses and/or insufficient chemical bonding. This was manifested by occasionally spontaneous flaking or local spallation inside the wear track (Figure S1 in Supplementary Material). This phenomenon was particularly more pronounced when load was increased (i.e., 2 N instead of 1 N) and observed as a reduction in the number of cycles for which the coefficient of friction remained low (even at RT). The effect of local heating during the RT pin-on-disk tests and the structural stability of the δ-Bi₂O₃ phase could not be ruled out, since it has been reported that the δ-BO coatings initiate phase transformation into the tetragonal β-phase at relatively low temperatures (250 °C) [30,31]. The transformation is accompanied by local distortions due to the volume differences among both phases (Figure S2), which might negatively affect the tribological response.

Further tribological analysis to understand the friction mechanism was carried out by studying the wear track for coatings that retained the low COF up to 1000 cycles. Figure 5b exhibits a very smooth wear track, and the Raman spectra obtained inside and outside of the wear track confirm the stability of the δ-Bi₂O₃ phase. Figure 5c depicts the 3D topographic image and associated cross-section profile of the wear track obtained after 10,000 cycles (inset Figure 5a), confirming the low wear rate in the steady-state regime at room temperature. No transfer of film to the Al₂O₃ ball was observed while the low-friction conditions were retained. Such results support the adhesive failure explanation, which could be improved using adequate bonding layers between the AISI D2 steel substrate and the coating.

The effect of substrate heating on the COF during the pin-on-disk test is presented in Figure 6. As the temperature increased continuously from room temperature to 225 °C, the COF steadily decreased, from 0.15 to 0.05, but above 225 °C, a drastic increase was observed, suggesting a severe modification (Figure 6 and Figure S3).

Figure 7 depicts a representative set of wear track pictures corresponding to different friction regimes and temperatures. The inner circular track was obtained after a friction test run at room temperature, with low signs of wear corresponding to the low COF attained (0.09). The following track corresponds to a friction test where the temperature was increasing monotonously from RT to 300 °C, showing clear signs of flaking at different locations, and the friction rose to 0.3 accordingly. The last two wear tracks were obtained from tests carried out after heating the coatings at 300 °C at two different COF values of 0.3 and 0.6, respectively. As noted previously, the coatings tended to break and delaminate easily as the shear and/or temperature increased.

4. Discussion

Different tribological systems and conditions were used to evaluate the tribological response of δ-BO coatings deposited on hard AISI D2 steel substrate. The results indicate that the bismuth oxide coatings presenting the δ-Bi₂O₃ phase can be considered as a lubricious oxide surface, but for a technological application, much work will be required to achieve adequate coating–substrate adhesion.

The results reported in Figure 5 and Figure 6 clearly demonstrate that the δ-BO coatings present COFs below 0.1, which can be considered of interest for solid lubrication. However, the stability of the cubic-Bi₂O₃ phase was limited to about 225 °C, where a phase transition was observed. Figure 6 and Figure S3, corresponding to the pin-on-disk test performed increasing the temperature from RT to 300 °C, show that there is an initial decrease in the COF, which is probably related to a recrystallization of the δ-phase. However, in both measurements, above 225 °C, a sudden COF increase was observed that might be related to the δ-β phase transformation [31]. Raman spectra obtained from the material transferred to the ball after the experiment confirmed the presence of the characteristic peak of the β-Bi₂O₃ phase (Figure S3).

The RT tests showed coating–substrate adhesion problems, but when the testing temperature increased over 225 °C, the coating failure was also promoted by the structural transformation associated with the phase change. A similar situation was obtained when coatings annealed after deposition were tested. Annealing was performed with the aim of evaluating the tribological response of Bi₂O₃ coatings presenting other crystallographic phases. Deposition and annealing conditions were selected from the structural composition map reported previously [31]. Figure S4 shows the pin-on-disk results for a film presenting predominantly the α-phase. The COF during the first laps was about 0.2 but could not be retained after 20 laps, increasing to values of about 0.6, associated with the film failure. However, the tribological response cannot be assigned univocally to any phase due to the structural inhomogeneity of the annealed coatings (Figures S5 and S6). Moreover, the significant change induced on the surface morphology, affecting the roughness, during the annealing is also evidenced in Figure S7, which could contribute to the increase in the COF.

In terms of the controversy stated at the introduction, the low COFs measured at RT for the δ-BO coatings are close to the COF reported for Bi₂O₃ by Prakash and Celis at T_H = 0.99 [9], suggesting that the interaction parameter (A defined in terms of the polarizability of both cations and anions in Equation (1)) is the best predictor for the selection of lubricious oxides based on fundamental chemical properties. Nevertheless, the value of the interaction parameter reported by Prakash and Celis corresponds to an estimation for the α-Bi₂O₃ phase, since the optical band gap used was 2.8 eV [16]. This is in accordance with measurements and calculations but does not correspond to the high-temperature stable phase of Bi₂O₃, i.e., the δ-Bi₂O₃ phase. Using an intermediate value of 1.7 eV for the optical bandgap of the δ-phase (reported values vary between 1.5 and 1.8 eV) [28,32], and Equations (1) and (2), we estimated an interaction parameter of A = 0.003 Å⁻³ for the δ-phase (details shown in the supplementary file). The lower interaction parameter obtained for the δ-Bi₂O₃ phase indicates that under the Prakash–Celis model, the COF could be slightly lower than for the α-Bi₂O₃ phase, which agrees with the values of ≈ 0.1 observed for the δ-BO coatings in this work. Moreover, the fact that both interaction parameters fell below 0.2 suggest that Bi₂O₃ will present low COFs independently of the crystallographic phase.

The definition of the ionic potential (IP) includes only information about the cation; therefore, parameters related to the structure are not taken into consideration. Accordingly, the IPs of the α- and δ-Bi₂O₃ phases are the same: 2.88 Å⁻¹. Making a linear regression for the upper COF values in Erdemir’s plot (cf. Figure 2a), an estimated value of 0.52 is expected for Bi₂O₃ at temperatures close to the melting point, where the α-δ transition should have already occurred [33]. Such a value is much higher than that obtained in this work for the different samples evaluated. However, recent results by Gonzalez–Rodriguez et al. [21], who evaluated the tribological response of different bismuth compounds as lubricants, reported a COF for Bi₂O₃ powders (α-phase) around 0.45 in the temperature range of RT to 600 °C against steel, close to Erdemir’s prediction. Kato and Komai [20] reported that the addition of Bi₂O₃ nanoparticles as lubricants lead to a severe-to-mild wear transition when rubbing steel surfaces. Such transition was associated with the formation of a tribofilm promoted by a high oxygen diffusion rate in Bi₂O₃, but friction coefficients were not reported.

On the other hand, Sun et al. [22] observed a linear reduction in the COF of Ni-5 wt%Al-XBi₂O₃ composite coatings as the temperature was increased, reaching values between 0.1 to 0.2 at 800 °C when the Bi₂O₃ content was increased to a 33 wt.%. They explained the COF reduction in terms of the out-diffusion of the Bi₂O₃ to the interphase. Moreover, the lowest COF was related to the δ-Bi₂O₃ phase, as demonstrated by thermal analysis. The COF reduction was in accordance with Prakash and Celis’ prediction [9].

Direct comparison of those references with our results is difficult due to the completely different tribological systems used, but there seems to be a trend to observe low COFs when the measurements are performed at high temperatures, i.e., where the δ-Bi₂O₃ phase predominates.

An important characteristic of the δ-phase is that Bi cations are organized in an fcc sublattice, and the O anions are placed in a simple cubic sublattice. The charge stability demands that two O ions are missing per unit cell, and so the structure contains oxygen vacancies that are responsible for the high ionic conductivity of this phase. Various theoretical and experimental studies have been performed to understand the distribution of the vacancies in the O-sublattice [34,35,36]. Some of these models predict metallic or semi-metallic character for the δ-Bi₂O₃ phase, which is not consistent with the experimental data that reported optical gaps around 1.7 eV. An exception is the model proposed by Matsumoto et al. [35], who assumed that the vacancies are ordered along crystallographic directions (<100>, <111> or <110>), predicting optical gaps between 1.75 and 2.6 eV, in better agreement with experimental observations. Therefore, we wondered if the low COF of Bi₂O₃ at temperatures above the α-δ transition might be related to the presence and ordering of the O vacancies, as explained by Gardos et al.: “shear strength (friction) is controlled by anion vacancies” [10].

An alternative explanation related to the tribological response of Bi₂O₃ is that the low COF obtained for some samples at high temperatures is related to the presence and aggregation of vacancies to form crystallographic shear planes. Since low COFs are reported at T close to T_m, where the δ-Bi₂O₃ phase is the thermodynamically stable phase, the high density of vacancies present in the cubic-fluorite structure might play an important role, like in the Magnéli phases.

Magnéli [11], and later others [10,19,37,38,39,40,41], showed that sub-stoichiometric oxides of certain elements (Mo, W, Ti, Re, V) form homologous series of compounds that contain crystallographic shear planes, due to ordering of the oxygen vacancies, with reduced binding strength and, therefore, reduced COF. Bismuth oxides are not catalogued as Magnéli phases, but a recent study by Klinkova et al. [33] concluded that δ-Bi₂O₃ is probably the homologous series of Bi₂O_3-x phases, whose members have similar structure and differ in their oxygen proportions and the ordering of the oxygen vacancies. Klinkova et al. [33] evaluated, by XRD and electron diffraction experiments, the thermal stability of Bi₂O₃ materials under cooling, heating, and different atmospheres to conclude that the distinct phases of Bi₂O₃ are oxygen-deficient phases of Bi₂O_3-x, where x changes according to the temperature range. Such definition is very close to that given to the TiO_2-x Magnéli phases [10].

Further studies might be required to demonstrate that Bi₂O₃ is a Magnéli oxide, but clearly, the presence of low-shear planes due to the ordering of the anion vacancies could explain the measured low COF and the no-applicability of Erdemir’s ionic potential model to the δ-BO coatings. In previous works, we demonstrated the high ionic conductivity of the δ-BO coatings due to the presence of anion vacancies [29]. On the other hand, the polarizability model of Prakash and Celis proposed that oxides with low interaction parameters have low activation energy for the formation of vacancies at the surface. Therefore, increasing the temperature led to an increase in the mobility of the ions due to vacancies that might be the cause of the low COF during sliding. Unfortunately, for the δ-BO coatings, raising the temperature led also to the phase transformation, with the related structural variations that negatively affect the tribological response.

A parallel outcome of this work confirming the lubricity of δ-BO coatings is that it might be interesting to study the addition of small fractions of Bi into well-adhered hard coatings and determine if, during sliding at temperatures close to 730 °C, the δ-Bi₂O₃ phase can be formed, reducing the COF, as has been observed with V addition into AlCrN or TiSiN [42,43,44]. Moreover, metallic Bi could provide lubricity at low temperatures [21,45], and Bi₂O₃ at elevated temperatures, to the extent that oxidation occurs.

5. Conclusions

The potential use of bismuth oxide coatings deposited on steel substrates presenting the δ-Bi₂O₃ cubic phase for solid lubrication has been demonstrated. The as-deposited coatings on mirror-polished AISI D2 steel presented a uniform crystallographic structure and smooth topography, which led to COFs against Al₂O₃ or steel balls of about 0.1. Moreover, only a minimal amount of material was transferred to the counter-bodies. However, more work is required to optimize the film–substrate adhesion, since after running at 1 N or 2 N and up to 10,000 cycles, localized spallation areas were observed. Nevertheless, the low friction of the δ-BO coatings was lost when the coating was heated above 225 °C, since, at such temperatures, the structural δ-β phase transition initiates with an associated increase in roughness and surface heterogeneity that led to coating failure.

The results presented here suggest that the ionic potential proposed by Erdemir cannot predict the tribological performance of the Bi₂O₃ oxides, probably due to the strong polarizability of the Bi-O bonds, or because the existence of oxygen vacancies in the structure has not been considered. The interaction parameter, proposed by Prakash and Celis, appeared as the best predictor of the friction coefficient for Bi₂O₃, since it predicts low COFs in accordance with the reported data for the δ-BO coatings. Moreover, the polarizability model is also in agreement with the alternative explanation given for the low COF of Bi₂O₃ materials based on the ordering of the intrinsic vacancies to form crystallographic shear planes as observed for the Magnéli-type structures.