Quality Control Metrics to Assess MoS2 Sputtered Films for Tribological Applications

Pure molybdenum disulfide (MoS2) solid lubricant coatings could attain densities comparable to doped films (and the associated benefits to wear rate and environmental stability) through manipulation of the microstructure via deposition parameters. Unfortunately, pure films can exhibit highly variable microstructures and mechanical properties due to processes that are not controlled during deposition (i.e., batch-to-batch variation). This work focuses on developing a relationship between density, hardness, friction, and wear for pure sputtered MoS2 coatings. Results show that dense films (ρ = 4.5 g/cm3) exhibit a 100 × lower wear rate compared to porous coatings (ρ = 3.04–3.55 g/cm3). The tribological performance of high density pure MoS2 coatings is shown to surpass that of established composite coatings, achieving a wear rate 2 × (k = 5.74 × 10–8 mm3/Nm) lower than composite MoS2/Sb2O3/Au in inert environments.


Introduction
Molybdenum disulfide (MoS 2 ) solid lubricants have historically been used as coatings in space applications because of their low friction coefficients (µ < 0.05) and wear rates (k< 1 × 10 -6 mm 3 /Nm) in inert and vacuum environments [1][2][3]. Pure MoS 2 coatings are not commonly used in terrestrial applications due to high wear rates and oxidation when exposed to water and oxygen [4][5][6][7][8][9][10][11]. To mitigate adverse interactions in terrestrial environments, dopants such as C, Sb 2 O 3 , Au, Ni, Ta, and Ti are commonly added to improve the tribological performance and environmental robustness [12][13][14][15][16][17][18][19][20]. While reported mechanisms for performance improvement of composite coatings vary depending on additives, composites such as MoS 2 /Sb 2 O 3 /Au have been shown to help facilitate the expression and retention of MoS 2 at the interface through agglomeration of Au nanoparticles [21]. Other composites such as MoS 2 /C/Sb 2 O 3 have been shown to exhibit extremely low shear strengths. The sliding interface of MoS 2 /C/Sb 2 O 3 changes during sliding depending on the environment, with the surface becoming carbon-rich in humid testing conditions and MoS 2 -rich in dry, inert environments [22].
A common hypothesis for the improved environmental resilience of composite MoS 2 coatings involves densification and hardening imparted by dopants [23][24][25][26][27][28]. Sputtered pure MoS 2 coatings have been shown to exhibit low densities (ρ ~ 3.3-4 g/cm 3 , theoretical = 4.8-5.06 g/cm 3 [29,30]), which varies depending on coating microstructure [31]. Buck [31] observed the density of sputter-deposited amorphous coatings (ρ ~ 3.3 g/cm 3 ) was lower than that of crystalline coatings (ρ ~ 3.95 g/cm 3 for basally oriented coatings) due to the presence of microscopic vacancies and a high degree of disorder. Lince et al. [32] found that a higher oxygen content in MoS 2-x O x coatings led to an increase in film density due to a reduction in crystallite size. Interactions between oxygen molecules and MoS 2 increased the defect density of the coating, thereby forming a disordered microstructure [32]. Techniques such as ion-beam assisted deposition (IBAD) have been shown to improve both the density of pure MoS 2 coatings (ρ ~ 4.4 g/cm 3 ) and wear resistance in humid and dry environments [29].
A prevailing hypothesis for enhanced wear resistance of doped-MoS 2 is that it is linked to improved coating density [23][24][25][26][27][28], though there is little to no direct evidence or a well-developed fundamental understanding of the role of this relationship present in the literature. A major barrier to this understanding lies in the difficulty in depositing fully dense pure films, or even films with consistent density. Variability in coating morphology is one of the main challenges limiting the widespread commercial use of sputtered pure MoS 2 films in engineering applications.
From a research perspective, understanding temperature dependence, environmental resilience, or load-dependent friction behavior becomes even more challenging when coating microstructure varies from one deposition to the next. Relationships between detailed coating structure and deposition parameters such as substrate temperature [33,34], argon partial pressure [31,32], bias voltage [37], and target-substrate distance [8] have been studied for decades. While many parameters are controllable during deposition, there exist other variables and/or by-products that cannot. For instance, Buck [38] studied the effects of water vapor in the plasma on the microstructure and tribological behavior of MoS 2 coatings. By varying the partial pressure of water, he showed that increased water vapor produced low density, less crystalline coatings that exhibited poor wear resistance. A secondary source of water vapor was also found to be a result of substrate heating during deposition via desorption of water from surfaces. The study found this source of contamination also led to less wear resistant coatings. Interestingly, substrate heating is often changed to improve the performance of MoS 2 coatings, yet it can have a negative effect depending on the cleanliness of the system.
From an applied perspective, sputtered MoS 2 films are a preferred solid lubricant coating in inert environments, such as vacuum and space applications. However, despite the best efforts by coatings developers, batch-to-batch variations in film properties, which originate from difficulties in precisely controlling mutually influencing deposition parameters, pose significant challenges for hardware engineers owing to the resulting variability in functional behaviors, including tribological performance. Typically, aerospace hardware manufacturers provide witness coupons for each coating batch and subject them to in-house testing designed to qualify the batch. In recent years, several high-performance MoS 2 based composites have fallen out of favor with hardware engineers due to the inability to reliably achieve the same caliber of tribological performance they once did. While the motivation for more wear resistant, lower friction, and environmentally agnostic materials always remains, there is an applied need to develop metrics to quantify what properties make universally "good" MoS 2 coatings and encourage an understanding of what variables during or prior to deposition may be at play to disrupt this. This information will be invaluable in ensuring the quality and consistency of MoS 2 films, as well as metrics that can enable future materials discovery and optimization of film composition and structure for a range of applications.
Given that even experienced commercial suppliers of sputtered MoS 2 coatings can produce films with varying structure and performance due to uncontrolled deposition parameters, a method is needed to efficiently inspect coatings for critical attributes that will insure adequate tribological performance in the intended application. The purpose of this work is to show that density and hardness can be used as quality control metrics to insure the tribological performance of pure sputtered MoS 2 coatings.

Materials Synthesis
Two manufacturers were asked to provide dense, nanocrystalline, pure MoS 2 coatings in two separate deposition runs. These were requested to understand if (1) comparable coatings (i.e., orientation, porosity, tribological performance) could be made by separate manufacturers and, (2) if the same manufacturer could provide two identical batches of coatings. The samples include a "Low-Density Coating #1" designated here as LD-1, a "Low-Density Coating #2" designated LD-2, and a "High-Density Coating" designated HD-1; sample designations were based on the results of characterization presented later in this manuscript.

Deposition of LD-1
Pure MoS 2 films were deposited in a vacuum deposition system (base pressure 5 × 10 -6 torr) equipped with both radio frequency (RF) and direct current (DC) magnetrons. The substrates were affixed to a rotating stage that was biased at 50 VDC. The RF magnetron was used to sputter MoS 2, and the DC magnetron was used to sputter a 99.99% pure titanium (Ti) target. The Ti target was sputtered first to create a ~ 100 nm thick Ti adhesion layer between the steel substrate followed by a ~ 200 nm gradient layer of Ti/MoS 2 and then a ~ 800 nm thick pure MoS 2 coating. Target powers were kept at 80 and 120 W, respectively.

Deposition of HD-1 and LD-2
Pure MoS 2 coatings (~ 1 μm thick) were deposited on polished 440C steel substrates (~ 20 nm R a roughness) with a 10 nm Cr adhesion layer (using arc evaporation) via DC magnetron sputtering using 1.5 mTorr Ar and a 3″ MoS 2 target at 150 W and 30 V bias for 30 min. Identical processing conditions were used to produce HD-1 and LD-2.

Hardness Measurements
Hardness values of MoS 2 films were determined via nanoindentation on a Hysitron TI980 equipped with a Berkovich tip. Prior to experimental testing, the tip area function and load frame compliance were calibrated over the entire load range of the instrument with fused silica as the reference material. 5 × 5 indent arrays with a 10 µm spacing between indents were performed on each film. The maximum load in the load function was 1 mN. For each indent, a CMX (continuous measurement of X) load function was used, consisting of a constant strain-rate load superimposed with a 220 Hz oscillating load. The strain rate was kept constant at 0.123 s −1 to mitigate strain-rate effects and the oscillating load was employed to provide depth-dependent data. The instantaneous hardness H was calculated by H = F max /A, where F max is the maximum load and A is the contact area at each depth. H values were averaged over indentation depths between 40 and 100 nm to calculate the mean for each indent, as the mechanical properties in this regime were relatively constant. The reported value for each MoS 2 film represents the mean and standard deviation from the 25 indents.

Tribological Testing
Tribological testing was performed on all three coatings simultaneously using a custom-built ball-on-flat high-throughput linear reciprocating tribometer in a controlled environmental chamber. A normal force of 1 N was applied to a 3 mm diameter 440C ball (~ 1 GPa Hertzian stress) on each sample by a load head consisting of a normal load cell connected perpendicular to the friction load cell (phidgets 100 g micro-load cell). The load head is then connected to a compliant titanium flexure driven by a stepper motor stage. The samples were mounted to a bidirectional linear reciprocating stage and tested at a sliding speed of 2 mm/s. Experiments were performed in a dry N2 environment (Mbraun Labstar pro, O 2 < 0.5 ppm, H 2 O < 0.5 ppm) and air environments at 0%, 30% and 60% RH (± 2% RH) in a separate humidity-controlled enclosure.

Focused Ion Beam (FIB)/Transmission Electron Microscopy (TEM)
Cross-sections were prepared for transmission electron microscopy TEM analysis using a focused ion beam (FIB) in a Dualbeam ThermoFisher Helios. A 2 µm thick protective Pt layer was deposited by first the electron beam and then the ion beam to ensure the surface was not damaged by the FIB. The lamella was studied with the TEM at 200 kV (JEOL JEM-ARM200cF, Tokyo, Japan) and images were acquired with a Gatan Ultrascan CCD camera. Scanning TEM (STEM) dark-field and bright-field images were acquired with a probe size of 0.078 nm and the images were processed and analyzed in DigitalMicrograph (Gatan, Pleasaton, CA). TEM of LD-2 cross-sections was performed using an aberration corrected scanning TEM (FEI Titan™ G2 80-200 STEM) operated at 200 kV and high-angle annular dark-field (HAADF) imaging.

X-ray Diffraction (XRD)
A PANalytical Empyrean diffractometer with a Cu X-ray tube at a wavelength of 1.541 Å was used to take the X-ray diffraction (XRD) measurements. A Bragg-Brentano HD mirror with suitable slits were used to shape the incident beam to maximize irradiation on the sample. The diffracted beam was shaped with a 7.5 mm antiscatter slit and a soller slit and detected with a PIXcel3D-Medipix3 1 × 1 area detector in scanning line 1D mode. Symmetric θ-2θ (gonio) scans were taken with a step size of 0.0066° and counting rate of 25 s/step.

Rutherford Backscatter Spectroscopy (RBS)
Rutherford backscatter spectroscopy (RBS) was performed by Infinita Laboratories, Saratoga, CA. A beam of 1.9 MeV 4He + was used for RBS with detection at a 165° scattering angle. An average beam current of 5 nA with integrated charge of 2.0 µC was used. Coating densities were calculated from RBS areal densities (atm/cm 2 ), RBS measured composition, and TEM measured thickness. The spot size of the RBS has a diameter of ~ 10 mm, or ~ 78.5 mm 2 analysis region.

Void Concentration
TEM of the films (Figs. 1a-c) shows the void concentration varying from sample to sample. LD-1 (Fig. 1a) and LD-2 (Fig. 1b) exhibit a high concentration of voids throughout the thickness of the coating while HD-1 appears to have significantly less features that could be interpreted as voids at this magnitude.

Crystallographic Orientation
XRD of the three MoS 2 coatings (Fig. 2a) indicates P6 3 / mmc hexagonal crystal structure (PDF 01-077-1716) with different orientations. LD-1 has little-to-no (0002) oriented lamella (basal orientation, i.e., the basal plane of the hexagonal crystal is preferentially parallel to substrate) and shows a peak at 33.2° indicating that the coating consists of (10 1 0) oriented lamella (edge-oriented) relative to the substrate (i.e., the edge plane is parallel to the substrate). The XRD spectra for LD-2 show no peak at 33.2° yet has a very broad peak at 13.48° likely due to (0002) oriented lamella relative to the substrate (i.e., parallel to the substrate). HD-1 shows three distinct MoS 2 peaks at 12.7°, 33.2° and 59.5° corresponding to (0002), (10 1 0) and (11 2 0) suggesting a more random crystallographic orientation compared to the  100) and (110). The LD-1 coating only has a peak at (100) and LD-2 shows a peak only at (002). B Density measurements of all three coatings measured by RBS with reference to fully dense MoS 2 (4.08-5.06 g/cm 3 [29, 30]) preferred orientation in LD-1 and LD-2. HD-1 has higher intensities than LD-1 or LD-2 suggesting that HD-1 is more crystalline.

Film Density and Stoichiometry
Density derived from RBS of all three coatings is shown in Fig. 2b. The LD-1 and LD-2 films are substantially below the density for bulk crystalline MoS 2 , while HD-1 has density close to the bulk value of 4.8-5.06 g/cm 3 [29,30]. Total oxygen content for all three films was measured by RBS to be at or below 5 at%, a value close to the accuracy of the analytical method (± 3 at.%). The stoichiometry (S:Mo ratio) of the three coatings was calculated from the aerial densities obtained by RBS. HD-1 is closest to stochiometric with a S:Mo ratio of 1.94, followed by LD-2 (S:Mo = 1.87) and LD-1 (S:Mo = 1.6).

Hardness and Modulus
Coating hardness for HD-1 was ~ 2-2.75 × greater than that for both LD-1 and LD-2. LD-1 had a measured hardness of 1.6 ± 0.2 GPa while LD-2 had a measured hardness of 2 ± 0.2 GPa. HD-1 exhibited the highest hardness with a value of 4.4 ± 0.6 GPa (shown in Fig. 3 and Table 1). The storage modulus of all three films was measured and had a similar trend with hardness with HD-1 having the highest storage modulus of 83.6 ± 7.2 GPa followed by LD-2 (E = 67.8 ± 4.5 GPa) and LD-1 (E = 50.4 ± 4.1 GPa).

Friction Behavior in Different Environments
The tribological properties of LD-1, LD-2, and HD-1 in environments consisting of air with varying humidity and dry nitrogen are shown in Figs. 4a-e. Measurements in dry N 2 (Fig. 4a) all show MoS 2 behavior consisting of an initially higher cycle one coefficient of friction with a transition (run-in) to lower steady-state coefficient of friction with increased sliding cycles. While the steady-state friction coefficients were nearly identical after 5000 sliding cycles (µ ~ 0.05), the initial friction behavior varied between samples. LD-2 and HD-1 both exhibited lower friction (µ ~ 0.02) for the first 1000 sliding cycles than LD-1 (µ ~ 0.05), and then increased, possibly due to a wear event. The average coefficient of friction for HD-1 was measured in dry N 2 for 250,000 sliding cycles (Fig. 4e) and shows a gradual and minimal increase in the coefficient of friction over the duration of the test from 0.03 to 0.08 and shows no indication of coating failure.
All three coatings exhibited similarly low friction in dry air with a steady-state coefficient of friction of 0.05 after 2000 sliding cycles (Fig. 4b). LD-2 and HD-1 showed very similar friction behavior for the entire test in dry air and ranin to low friction after 200 cycles. LD-1 showed prolonged run-in, with a friction coefficient above 0.1 for 600 cycles until it achieved its final steady-state friction coefficient of 0.05.
During tests run in 30% RH air (Fig. 4c) for 200 sliding cycles, LD-1 and HD-1 exhibited friction coefficient between 0.1 and 0.13 while LD-2 exhibited higher friction, µ ~ 0.2, before dropping to 0.08 for the last 60 sliding cycles. In 60% RH air (Fig. 4d), the coefficient of friction over 200 cycles for LD-1 and HD-1 was consistently around 0.1. The coefficient of friction for LD-2 started at 0.1, but after 20 cycles the coefficient of friction increased to 0.25, where it varied sporadically suggesting complete failure of the coating.

Wear Behavior in Different Environments
Wear rates are shown in Fig. 5 and are tabulated in Table 1. HD-1 showed 10-100 × lower wear than the lowdensity coatings throughout all environments. In dry N 2 , HD-1 achieved a wear rate of 5.74 × 10 -8 mm 3 /Nm while Fig. 3 Average hardness values with corresponding uncertainty intervals for LD-1, LD-2, and HD-1 coatings. Hardness of each specimen was determined from 25 nanoindentation measurements, and the average and standard deviation in the hardness values was calculated for each sample LD-1 had the second lowest wear rate (7.98 × 10 -7 mm 3 / Nm), followed by LD-2 which had the highest wear rate (1.59 × 10 -6 mm 3 /Nm). The ultra-low wear rate of HD-1 is further highlighted by the low coefficient of friction sustained for 250,000 sliding cycles (Fig. 4e). In dry air, the wear rates for all three coatings increased, yet HD-1 experienced the smallest change in wear rate with an increase of ~ 2 × (1.28 × 10 -7 mm 3 /Nm). The wear rate of LD-1 increased in dry air by almost two orders of magnitude (5.47 × 10 -5 mm 3 /Nm) and LD-2 increased by 7 × in dry air (7.71 × 10 -6 mm 3 /Nm).
In 30% RH air, the wear rate for HD-1 (5.09 × 10 -6 mm 3 / Nm) increased by 40 × over its wear rate in dry air, and nearly two orders of magnitude over its wear rate in dry N 2 . The measured wear rates for LD-1 and LD-2 were comparable in 30% RH air (8.60 × 10 -5 mm 3 /Nm and 8.30 × 10 -5 mm 3 /Nm, respectively), nearly an order of magnitude greater than measurements in dry air.
In 60% RH air, HD-1 had the lowest wear rate of the three coatings tested (2.19 × 10 -5 mm 3 /Nm) and had a lower wear rate than both LD-1 and LD-2 in 30% RH. The wear rates for the LD-1 and LD-2 were highest in 60% RH air  (7.10 × 10 -4 mm 3 /Nm and 9.55 × 10 -5 mm 3 /Nm, respectively), yet the wear rate of LD-2 in 60% RH air was only slightly higher than in 30% RH air. The wear rate of LD-1 in 60% RH air increased by roughly an order of magnitude, more than LD-2.

Discussion
Both the LD-2 and HD-1 coatings were manufactured in the same deposition chamber with nominally the same (controllable) deposition parameters, and by the same technician, albeit on different days. Additionally, the LD-1 coating was manufactured in a different chamber but with similar deposition parameters as LD-1 and HD-1. One of the most striking and quantifiable differences between the coating batches is the density. HD-1 (ρ = 4.5 g/cm 3 ) has a density close to that of bulk MoS 2 (ρ = 4.8-5.06 g/cm 3 ), exceeding the average density of IBAD coatings (ρ = 4.4 g/cm 3 ) [29]. Both LD-1 (ρ = 3.55 g/cm 3 ) and LD-2 (ρ = 3.04 g/cm 3 ) have measured density values that are well below HD-1, likely due to the formation of the voids observed in the TEM (Fig. 1). Differences in density and void formation could be due to variations in crystallite orientation and degree of crystallinity, as indicated by XRD. Buck observed that crystalline pure MoS 2 coatings (ρ ~ 3.8-3.95 g/cm 3 ) are denser than amorphous coatings (ρ ~ 3.3 g/cm 3 ), and that increased basal-orientation improves density due to decreased porosity [31]. Though our results show that LD-1, which is edge-oriented (as indicated by the (10 1 0) peak), is denser than the basally oriented LD-2 coating, both coatings have low peak intensities corresponding to their preferential orientations. Orientation and crystallinity can influence the friction and wear behavior of MoS 2 , with highly crystalline, basally oriented coatings having lower initial friction coefficients and faster run-in to steady-state friction over amorphous microstructures [39,40]. Although nanocrystal-amorphous coatings have been reported to have lower wear rates than nanocrystalline coatings [41], in this study it is challenging to decouple the individual effects of orientation and crystallinity from density on the tribological behavior. The impact of orientation on density and void formation is supported by the growth kinetics of MoS 2 during deposition. Low density, porous coatings are a result of the formation of edgeoriented MoS 2 crystallites providing reactive edge-sites for new deposits leading to a high vertical growth rate and decreased horizontal growth rate. As larger, vertically oriented lamellae form, they cause a shadowing effect, blocking incoming deposits resulting in the formation of voids [42,43]. Void formation can greatly impact hardness. This phenomenon is widely studied in other material systems such as ceramics [44][45][46][47][48][49] where it has been observed that hardness increases as porosity decreases.
Pure MoS 2 coatings deposited by PVD are typically sub-stoichiometric with a deficiency in sulfur [35,50] and can have high levels of oxygen in the bulk (> 10%) [32,51]. Oxygen substituted into the crystal lattice of MoS 2 forms MoS 2-x O x by substituting sulfur and results in a peak shift of the (10 1 0) due to a reduced lattice constant [32]. Though the coefficients of friction observed for oxygen rich films are not as low as pure MoS 2 coatings, films containing high amounts of oxygen have been shown to have increased density from a reduced crystallite size, thereby producing lower wear rates than that of pure MoS 2 coatings [32]. Addition of oxygen, which can be viewed as a dopant, means that "pure" is a misnomer for MoS 2 films without dopants because of the added benefits oxygen can impose. In this work, no statistically significant difference in oxygen content in the coatings under investigation was detected. Notably, the oxygen content was very low and close to the accuracy of the analytical tool. While we do not believe that oxygen is contributing to the improved densification of HD-1, it is not unlikely that sources of contamination during the deposition process could introduce unwanted oxygen or water. Sources such as adsorbed water on the deposition chamber walls due to exposure to lab air during sample changing or transfer and a contaminated sputtering target could be key uncontrolled factors that influence the coatings density and tribological behavior.
For MoS 2 , relationships between coating porosity, hardness, and wear are not well established. Seynstahl et al. [52] varied the sample substrate rotation during deposition and observed that compact pure MoS 2 coatings with little to no porosity were harder (H = 5.69 GPa) and more wear resistant (k ~ 1 × 10 -7 mm 3 /Nm) than softer (H ~ 0.06-0.25 GPa), porous films (k ~ 5 × 10 -6 -2 × 10 −5 mm 3 /Nm). Although the authors did not directly measure density, we observe a similar trend with HD-1 exhibiting a higher hardness (H = 4.4 GPa) and lower wear rate (k = 5.74 × 10 -8 mm 3 /Nm) in dry N 2 than both LD-1 (H = 1.6 GPa, k = 7.98 × 10 -7 mm 3 / Nm) and LD-2 (H = 2 GPa, k = 1.59 × 10 -6 mm 3 /Nm). While density is a major factor contributing to the increased hardness of HD-1, the discrepancy between hardness and density for LD-1 and LD-2 could be due to differences in coating orientation. Though both LD-1 and LD-2 have weak peak intensities indicating nanocrystalline/amorphous microstructures, there is weak preferential vertical orientation of LD-1 (i.e., basal planes parallel to the indentation axis), compared to the more basally oriented LD-2 (basal planes perpendicular to the indentation axis), allowing for deformation to occur between low shear strength basal planes as the coating is deformed. For vertically oriented coatings, the indenter tip can advance further into the coating by pushing the columns apart resulting in a lower measured hardness [44]. The high hardness and density of HD-1 produced a greater wear resistance than that of widely established composite films such as MoS 2 /Sb 2 O 3 /Au (k ~ 1 × 10 -7 mm 3 /Nm [21]) in dry N 2 environments. Improvements in the wear rates imparted by density and hardness are also observed in humid environments (Fig. 5), suggesting that wear performance measured in humid air could be a metric for a quality MoS 2 coatings, which for practical flight hardware, could be a useful metric if inert environments are unavailable or impractical to use.
Density as a driving factor for low wear MoS 2 coatings, and hardness as an indicator of coating density, provides a useful metric for the qualification of MoS 2 coatings to be used in practical applications. The low measured hardness of LD-1 and LD-2 would, for instance, indicate to an engineer that the batch of coatings will not meet specifications and should not be used. By using hardness as a metric, timely tribological testing of coating batches or costly characterization techniques such as RBS can be avoided, and only performed on batches such as HD-1 which meet an adequate hardness threshold. Additional useful metrics such as crystallinity and orientation, measured by XRD, would help provide a fast and accurate indication of a quality film.

Conclusions
Uncontrolled variation in mechanical properties of sputter deposited pure MoS 2 has limited their use in engineering applications. In this work, relationships between the mechanical properties and density of pure MoS 2 coatings were developed to establish deterministic parameters for high-quality coatings. Three batches of pure MoS 2 coatings were deposited using similar parameters, yet the wear rates of the coatings varied by ~ 100 × in dry N 2 . Density of the coatings showed that each coating batch varied in density with the highest density, lowest wear coating (k = 5.74 × 10 -8 mm 3 /Nm, ρ = 4.5 g/cm 3 ) having little to no void formation and achieving a density close to bulk MoS 2 . The other coatings both had low density (ρ = 3.04 and 3.55 g/cm 3 ) and significant void formation throughout the coatings. Nanoindentation showed distinct hardness and modulus differences between dense (H = 4.4 GPa, E = 83.7 GPa) and porous (H = 1.6-2 GPa, E = 50.4-67.8 GPa) coatings, correlating to changes in density and coating orientation. These results suggest that density is one of the dominant factors contributing to low wear rates for MoS 2 coatings and that the hardness of a coating is a key indicator of high-performance coatings. Furthermore, using hardness as a key metric to determine coating batch quality could help in reducing time consuming tribological testing or complex and expensive characterization.
of Florida. G.L.D. was supported by funding from the Center for Surface Engineering and Lubrication Research. F.W.D. was supported by the Center for Integrated Nanotechnologies, a Department of Energy office of Basic Energy Sciences user facility. This work was funded by the Laboratory Directed Research and Development (LDRD) program at Sandia National Laboratories, a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Declarations
Competing interest The authors have no competing interests to disclose.
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