Introduction

Thin ceramic films deposited using physical vapor deposition (PVD), i.e. transition metal borides, carbides, nitrides, and oxides, are used as protective coatings in the cutting and forming tool industry1,2. They prolong the lifetime of their underlying tool, e.g. WC–Co or hot working steel, by up to some 100%. Their beneficial properties like high hardness, high Young’s modulus, chemical stability, thermal stability, and oxidation resistance provide an ideal basis for application in harsh environments3,4,5. However, the constant endeavor in industrial processes for increased throughput in cutting and forming processes without suffering restrictions in reliability leads to a demand for even better coatings. A weak point is typically their low fracture toughness KIC, which is a material property difficult to quantify for hard coatings and thus has yet to be comprehensively researched. However, recent advances in micromechanical testing methods—applying in situ secondary electron microscope testing (SEM) using focused ion beam (FIB) shaped geometries—established the possibility to do so6,7,8,9. Since low KIC values can lead to premature failure of the coating and thus to lack of performance in industrial processes, especially when mechanical loads dominate the wear behavior, fracture toughness is technologically highly relevant2. Not only the fracture toughness—a property describing the resistance of a material against crack propagation—but also the damage tolerance, a term including strength and fracture toughness, is important to prevent early failure.

Known mechanisms to increase the fracture toughness of ceramic materials are based on either intrinsic or extrinsic mechanisms10. While extrinsic mechanisms are often based on a reduction of the stress intensity at the crack tip, intrinsic effects draw upon increasing necessary maximum stress intensities for crack propagation as well as crack initiation. Examples for extrinsic strategies commercially used in hard coatings are for instance ductile phase toughening, toughening through nanostructural design, and toughening through multi- (nano-) layered structures11,12,13,14,15,16,17. Unlike that, intrinsic mechanisms are not easily accessible; however, Sangiovanni et al. calculated increased Poisson’s ratio (ν), Cauchy pressure (CP = c12–c44), and decreased G/B ratio (all of the latter are indicating a more ductile behavior) for Mo, W, Nb, and Ta alloyed nitrides18. The authors propose that a toughness increase primarily originates from increased valence electron concentration (VEC) and the associated change in bonding states.

In this work, we combine two of the theoretically ductile nitrides, MoN and TaN, in a form of the superlattice architecture, i.e. alternating coherent MoN and TaN nanolayers. As indicated by our previous ab initio calculations, MoN/TaN superlattices outperform their monolithic MoN and TaN components in terms of B/G and Poisson’s ratio. Consequently, even greater ductility than that of MoN and TaN (predicted by Sangiovanni18 and by us19) can be achieved for MoN/TaN via the superlattice architecture. We envision—and confirm later in the manuscript—that additional advantage of the superlattice architecture is the improved fracture toughness, which can be enhanced up to 2.99 MPa m1/2 by tuning the bilayer period. Our previous modeling and experimental results (XRD, EDX, nanoindentation) further suggest that only ~50% of N sites in MoN layers of MoN/TaN superlattices are occupied and that TaN is stabilized in a form of a tetragonally distorted zeta-phase19 due to the template effect from MoN0.5. This is a somewhat surprising finding which can not be simply deduced based on the knowledge of the monolithic MoN and TaN coatings. Vacancies play a critical role in a stabilization of the cubic (fcc, Fm\({\bar{\mathrm{3}}}\)m) phase. While MoN favors nitrogen vacancies (their specific content depends on the applied N2 partial pressure and can reach up to 50%), TaN is stabilized by metal vacancies as Ta0.75N or by Schottky defects20.

We identified MoN/TaN as a promising material system, however, it did not make any link between mechanical properties and the most important tuning parameter known for SL architectures: the bilayer period. The purpose of the present work is to investigate the fracture properties of MoN0.5/TaN SL coatings with different bilayer periods. We expect that the combination of very similar shear modulus (124 GPa for the cubic MoN0.5 and 127 GPa for cubic, defect-free TaN, and 159 GPa for ζ-TaN) but notably different structural parameters could lead to a strong superlattice effect mirrored by significant enhancement of fracture properties. Furthermore, this would enable us to provide new insight on the relevant mechanism behind the fracture toughness enhancement observed for superlattice films apart from the well-known hardness increase21.

We demonstrate the structure–property relation of the MoN/TaN coating system by applying in situ micromechanical experiments, X-ray diffraction, scanning electron microscopy, transmission electron microscopy investigations and synchrotron nanodiffraction experiments. The latter experiments were performed to possibly verify the presence of ζ-TaN by probing small volumes, as well as to review the XRD data and perform residual stress measurements. The results are corroborated and supplemented using ab initio calculations together with a continuum mechanics model.

Results

Ab initio calculations

To estimate the relative tendency for brittle/ductile behavior of the monolithic as well as SL coatings, first-principles calculations on elastic constants were carried out. The structures in question were rs-MoN0.5, rs-TaN, MoN0.5/TaN SL with (001) interface, and Λ = 1.7 and 3.5 nm, as well as rs-AlN, rs-TiN, and AlN/TiN SL with (001) interface and Λ = 1.7 nm for comparison. The polycrystalline bulk, B, shear, G, and Young’s moduli, E, together with the Poisson ratio, ν, and Cauchy pressure, CP, were evaluated using the calculated elastic constants. Subsequently, the brittleness/ductility map was constructed by plotting ν and CP/E, respectively, against the G/B ratio. Figure 1 clearly shows that all our data points fall onto the decreasing hyperbolic line connecting CP/E over B/G values of cubic and hexagonal structures. Unlike the rs-AlN, rs-TiN, and AlN/TiN SL, the rs-MoN0.5, rs-TaN, MoN0.5/TaN SL are found within the ductile region. The rs-TaN is predicted to slightly outperform its monolithic rs-MoN0.5 counterpart in terms of ductility, whereas the behavior of MoN0.5/TaN SL seems to be largely influenced by the bilayer period. Specifically, the SL with Λ = 1.7 nm is less ductile than its single-phase components, unlike the Λ = 3.5 nm variant, which leads to the highest ductility out of all the here considered structures.

Fig. 1: Density functional theory studies describing the ductility.
figure 1

The Poisson’s ratio (according to the Frantsevich’s criterion: ν > 0.26 for ductile materials62) as a function of the G/B ratio (according to Pugh’s criterion, G/B > 0.571 for ductile materials63) is indicated by orange pentagons. The G/B dependence of the Cauchy pressure over the polycrystalline Young’s modulus (CP/E > 0 for tough materials64) is indicated with blue stars, gray triangles for literature data of cubic structures and blue circles for literature data of hexagonal structures. Our calculations are labeled using dotted–dashed lines. The ductile region is located at the left top corner (orange background), the brittle region at the bottom right corner (blue background). The dashed lines mark the various toughness criteria (the scale was chosen in a way that Frantsevich’s criterion and the criterion by Niu et al.64 are on the same height). Exact values for literature data are given in Supplementary Table 1.

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The literature data presented in Fig. 1 show a hyperbolic relationship between the G/B and the CP/E ratio. The relation is described by ref. 22 as a universal criterion for cubic materials regarding their strength and ductility. Deviations from this relation mostly belong to metastable structures, i.e. rs-AlN or rs-TaN. Also, the data for hexagonal diborides (light gray stars in Fig. 1) fall on a hyperbola, located ~0.3 CP/E under that of cubic materials. This in turn would tell us that diborides, in general, tend to be stronger but less ductile in comparison with their cubic counterparts. Also, in this case, deviations from the hyperbola mostly belong to metastable structures.

Motivated by the ab initio predicted promising toughness and ductility of the MoN/TaN system, we proceeded with experimental investigations. As a first step, we employed electron microscopy and diffraction methods to study the morphology of the deposited MoNx/TaN multilayered coatings.

Structure and morphology

Our coatings have a dense morphology, visible in the SEM cross section pictures (Fig. 2a–c). We can further state that there was no interrupted growth as the columns are not re-nucleating between the single layers (inset in Fig. 2c), indicating a coherent growth.

Fig. 2: Cross-sectional SEM studies.
figure 2

The SEM-micrographs in (a–c) show cross sections of our MoN–TaN coatings with nominal bilayer periods of 1.5, 5.2, and 43.3 nm, respectively. The dashed lines sign the interface between the coating and Si (100) substrate. The inset in (c) shows an enlarged view visualizing the layered structure of this coating. The scale bars in (a) to (c) are 1 µm, the scale bar in the inset has a length of 200 nm.

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This is also shown in Fig. 3a, c depicting TEM cross sections of the coatings with Λ = 9.0 and 3.0 nm, respectively. Additionally, we observe the desired layered structure; the bilayer periods of these samples were measured to be ~ 8.5 and 2.9 nm (by averaging 10 bilayers, not shown here). The white square in Fig. 3c shows the region chosen for Fast Fourier Transformation (FFT), Fig. 3f. We do not observe any sign of other phases than cubic structures in the [110] orientation.

Fig. 3: TEM studies describing the microstructure.
figure 3

The HR-TEM micrographs (a) and (c) show a cross section of coatings with a nominal bilayer period of 9.0 and 3.0 nm, respectively. The white marked area in (c) was used to generate the FFT pattern in (f) calculated by Gatan Digital Micrograph. The TEM top view in (d) was taken from the sample with Λ = 1.5 nm, the column width was calculated using the linear intercept method. (b) and (e) show a SAED pattern of the region in (a) and (d), respectively, including an integration of the pattern. The scale bars in (a) and (c) are 10 nm, in (b) and (e) 5 nm−1, in (d) 200 nm, and in (f) 10 nm−1.

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A typical plan view TEM image is given in Fig. 3d (Λ = 1.5 nm). The in-plane grain size, i.e. the column width, of our coatings is D|| ~ 46 nm as obtained by applying the linear intercept method23. The selected area electron diffraction (SAED) pattern of our TEM samples, Fig. 3b, e, shows no signs of other phases than cubic structured nitride (the main detectable orientations are labeled). To enhance the visibility of the structures present, we also integrated the SAED pattern using the PASAD plugin24 of Gatan Digital Micrograph and subtracted the underground (inserted).

X-ray diffraction experiments show cubic structures in the measured out-of-plane direction (Bragg–Brentano). We do not observe any signs of the hexagonal TaN phase; also, Mo–N is present in its cubic MoN0.5 structure following the accordance of measured, calculated, and literature-based lattice constants (2.101 Å and 2.090 Å for calculated and literature-based values, respectively) (Fig. 4a)25,26. The coatings with Λ = 1.5 and 3.0 nm show the main Bragg reflections (111) and (200) in between the calculated peak positions for ζ-TaN and MoN0.5 (35.1° & 37.0°, and 40.7° & 43.0°, respectively). With an increasing bilayer period, these peaks split into two separate peaks each, staying at a similar position for larger Λ (Fig. 4a). Additionally, one can deduct from the XRD measurements a pronounced layered structure due to positive and negative satellite peaks (indicated with m ± 1). The intensity of these satellites relative to the main peaks increases with increasing bilayer period (1.5–9.0 nm), suggesting an improving layer quality (definiteness) when assuming a constant inter-diffused zone (due to similar deposition conditions). The peaks in between both Bragg reflections for the sample with 9 nm bilayer period as well as those in between the peaks of Λ = 15 nm are assumed to be superlattice reflections. To confirm our adjusted nominal bilayer period, we evaluated the bilayer period using the following equation:

$${\rm{sin}}\theta _ \pm = {\rm{sin}}\theta _B \pm \frac{{m \cdot \lambda }}{{2 \cdot {\Lambda}}},$$
(1)

where θ± donates the diffraction angle of the satellite peak (positive or negative), θB the angle of the Bragg peak for the solid solution, m the order of the satellite peak, λ the wavelength of the used X-ray source and Λ the bilayer period. The results of these calculations given in Table 1 correlate well with the nominal bilayer periods (also with those calculated by dividing the film thickness with the total number of bilayers).

Fig. 4: X-ray diffraction analysis.
figure 4

X-ray diffraction patterns in (a) of our superlattice thin films. The labeling (m+1) and (m-1) mark the satellite peaks stemming from the layered structure of our coatings. The bilayer periods quoted on the right side of a are the nominal ones. The intensity plot in (b) shows a quarter of a Debye–Scherrer pattern recorded in transmission geometry (sample thickness in beam direction was ~50 μm) at the nanofocus endstation at the beamline P03 of PETRAIII at Deutsches Elektronen-Synchrotron (DESY). The gray marked area was integrated in φ direction and plotted in (c). The plot in (d) shows derived lattice parameters over sin2(φ) and the corresponding linear fit.

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Table 1 Nominal and measured bilayer periods.
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Figure 4b shows a quarter of the Debye–Scherrer pattern of a MoN0.5–TaN superlattice coating with a bilayer period of 5.2 nm grown on austenitic steel. The growth direction of this sample is towards φ = 0°. Therefore, the textured (200) nature of this sample can be identified, also indicated in the Bragg–Brentano high definition (BBHD) laboratory XRD measurements, Fig. 4a. In order to calculate the corresponding lattice constants in out-of-plane and in-plane directions, we integrated the intensity in the φ direction (Fig. 4c) and fitted these data (using Lorentz-peak shapes, see Fig. 4d). The corresponding lattice parameters vs. sin2(φ) are linearly fitted and extrapolated to φ = 0° and 90°. The coefficient of determination was R2 = 0.976. We found a tetragonally distorted unit cell with a c/a ratio of 1.013. This distortion mostly originates from residual stresses, which are calculated to be −3.8 ± 0.2 GPa using the sin2(φ) method; however, we also calculated a slight unit cell distortion (c/a ratio of 1.00022 for Λ = 1.72 nm) in our ab initio simulations stemming from the superlattice structure and its intrinsic residual stresses on the atomic scale.

These values, as well as the constants derived from nanodiffraction experiments and our BBHD measurements, are illustrated in Fig. 5a. Figure 5b shows the unit cell (disordered vacancies) of MoN0.5/ζ-TaN with Λ = 1.72 nm. In Fig. 5a, it is visible that the lattice constants move towards the calculated constituent values with increasing bilayer period (5.2 nm). For larger bilayer periods we observe decreasing lattice constants, well coinciding with our calculations for different phases allowing for following bilayer-period-depending phase-evolution interpretation: with increasing bilayer period an epitaxial stabilization of ζ-TaN on MoN0.5 becomes energetically less favorable. We propose that a different structural variant of TaN starts to form in TaN layers at the expense of ζ-TaN when the bilayer period exceeds some critical level. The possible candidates, Ta0.75N and Ta0.875N0.875, contain vacancies and Schottky defects (i.e. the same amount of vacancies on both Ta and N sublattice), respectively, and are the most stable variants of the cubic TaN. Importantly, both Ta0.75N and Ta0.875N0.875 exhibit a lattice parameter that results in a d200 value closely overlapping with the experimental one (2.1716 Å and 2.1950 Å for Ta0.75N and Ta0.875N0.875, respectively). Also, the parameters derived from the nanodiffraction experiments are consistent with our ab initio calculations.

Fig. 5: Development of lattice parameter with increasing bilayer period.
figure 5

Diamond symbols in (a) show the obtained lattice plane distances from the XRD patterns of our superlattices on Si (100), Fig. 4a. The out-of-plane d200 lattice planes for ζ-TaN, Ta0.75N, MoN0.5, MoN0.5/ ζ-TaN, and MoN0.5/Ta0.75N are indicated with horizontal lines in (a). The results for the coating with Λ = 13.1 nm are obtained from films grown on MgO, as their the 200 XRD peak was more distinct (compare Fig. 4 and Supplementary Fig. S1). Data points in stars are obtained by calculating the average. The right side of a shows in-plane and out-of-plane lattice plane distances obtained from our synchrotron experiments. In (b) the unit cell of the superlattice with Λ = 1.72 nm is shown.

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Mechanical properties

The hardness and Young’s modulus of our coatings are plotted in Fig. 6a, b. The indentation hardness is comparable to that of typical physical vapor deposited Ti1−xAlxN (~ 28–32 GPa27,28) and shows no significant increase. This is due to the similar shear moduli of MoN0.5 (ab initio calculated value of 124 GPa), ζ-TaN (159 GPa), and rs-TaN (127 GPa), as the hardness enhancement in superlattices is usually obtained by the hindrance of dislocation movement over the interface due to those differences29. The shear moduli of the defect-containing TaN depends on the defect type and concentration and is calculated to be 191 and 121 GPa for Ta0.75N (metal vacancies) and Ta0.875N0.875(Schottky defects), respectively.

Fig. 6: The mechanical properties of MoN–TaN superlattice thin films.
figure 6

The hardness as a function of the bilayer period is shown in (a). The vertical dashed line indicates the bilayer period where we assume the formation of a second phase in the TaN layer. Young’s modulus over Λ is shown in (b). Here, besides the computational Young’s modulus (Grimsditch and Nizzoli) including a second phase in TaN, we also plotted the one without it. The sketch in (c) shows the proposed coating architecture. The SEM micrograph (d) shows a cantilever before micromechanical testing in a 10° inclined view including the dimensions of the lever arm l, cantilever width b, cantilever height w, the initial notch, and the point of application of force. The fracture cross sections in (e) (1.5 nm) and (f) (8.3 nm) show the depth of the initial notch a; exemplary marked are the thin bridges necessary for our micromechanical tests. The plots (g) and (h) show the derived fracture toughness KIC and the empirical H/E toughness criteria, respectively. All mechanical properties were determined on sample deposited on Si (100), additionally, Young’s modulus was cross-checked by performing nanoindentation experiments also on MgO (100), sapphire, and austenitic steel. All error bars represent standard deviation. The scale bar in (d) is 5 µm long, in (e), and (f) the scale bar is 1 µm long.

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A relatively large scatter of indentation moduli, from about 375 up to 430 GPa, is measured depending on the bilayer period. While the experimental records for the indentation moduli of the superlattices with bilayer periods above ~6 nm slowly saturate from 380 to about 400 GPa (the coating with Λ ~ 45 nm), they show an increase up to ~430 GPa when approaching Λ = 1.7 nm. To take a closer look at this peculiar dependence of our indentation data on the bilayer period, we applied the linear elasticity continuum model by Grimsditch and Nizzoli (cf. Methodology section). Our generalized version of this model allows us to calculate the overall elasticity of a SL containing material A and B based on the elastic contributions from the A/B interface layer and the bulk-like regions of the A and B layers. Furthermore, both A and B bulk-like layers can contain several sublayers with different concentrations of the respective material to consider, e.g., compositional fluctuations within one material. The bilayer period dependence enters via varying the volume ratio between the interface (of a certain thickness) and the bulk-like layers. Applied to our SL system, the MoN0.5/TaN SL with Λ = 1.7 nm was used to model the interface layer, while the two bulk-like layers were approximated by rs-MoN0.5 and tetragonally distorted ζ-TaN. Figure 6b reveals that under such assumptions, the indentation data for the samples with Λ in the 1.7–5 nm range can be very closely reproduced. However, the model deviates from the experimental records noticeably when the bilayer period exceeds 5 nm, hence suggesting possible structural transformations in one type of the layers (or both). Based on the dependence of the d200 spacings on the bilayer period, we proposed a hypothesis that the defect-containing rs-Ta0.75N or rs-Ta0.875N0.875 could form when the TaN layers become too thick to retain the defect-free ζ-TaN. Consequently, the material suspicious from structural transformations was the TaN, well known for its strong driving force for vacancies/Schottky defects. Specifically, the rs-Ta0.75N with 25% of ordered metal vacancies (illustrated as comic in Fig. 6c) is the energetically most favorable variant of the cubic TaN26. The TaN bulk-like layer of the SL in our Grimsditch–Nizzoli model was therefore divided into two sublayers containing ζ-TaN and (a) Schottky-defected Ta0.875N0.875 or (b) rs-Ta0.75N. When the rs-Ta0.75N was implemented in the simulation, we obtained a close overlap between the indentation data and the calculated Young’s moduli. Considerations of elastic response thus helped to differentiate between (energetically and structurally close) rs-Ta0.75N and rs-Ta0.875N0.875: we conclude that the presence of the former one in the SL is more likely. Therefore, the decrease of the indentation modulus was ascribed to the decreasing interface density as well as to the increasing volume fraction of ζ-TaN in the TaN layers. As the elasticity of the bulk-like region predominantly contributes to the overall elasticity of the SL at higher bilayer periods (i.e. the interface effects are largely diminished), this leads to the saturation of the indentation modulus towards the average polycrystalline Young’s modulus of rs-MoN0.5 and rs-Ta0.75N.

The micromechanical testing setup with necessary dimensions used to calculate the fracture toughness is exemplarily shown in Fig. 6d. We gave special attention to the positioning of the spherical indenter tip to avoid deviations from mode I load conditions. Figure 6e, f shows fracture cross sections of cantilevers after testing. The thin material bridges are visible, as well as the initial notch depth a. The spherical indenter tip accompanies with a reduction of the lever arm l during the micromechanical test. The resulting overall error due to this uncertainty is calculated to be less than 2% (calculated in the framework of Euler–Bernoulli beam theory, also accounting for uncertainties coming with a blunted tip) and is already included in the experimental error. This is justified since a sharp indenter (i.e. Berkovich or cube corner) could lead to unwanted plastic deformation in the contact area, falsifying the outcome by incorrect displacement data, as well as by violations in mode I conditions due to forces in the lateral direction (inducing yield stresses in the cross section).

The derived fracture toughness KIC of our MoN/TaN superlattice coatings (Fig. 6g) reaches a maximum value of 2.97 ± 0.21 MPa m½ at a bilayer period of Λ = 5.2 nm. Compared to TiN/CrN superlattices, we observe higher fracture toughness values (there the maximum was 2.01 ± 0.18 MPa m½ at a bilayer period of ~6.2 nm)17. The Ti–Si–N system reaches a maximum fracture toughness of ~ 3.0 ± 0.2 MPa m½15, and also for Ti–Al–N a KIC of ~ 3.0 MPa m½ can be achieved after annealing at 900 °C12.

With increasing bilayer period, we observe a decrease in fracture toughness to 2.32 ± 0.23 MPa m½ for 8.3 nm, when Λ is further increased, KIC stays constant at ~ 2.5 MPa m½. For decreasing bilayer periods (Λ = 1.5 nm) we see a decrease to 2.30 ± 0.13 MPa m½. Although this behavior (superlattice effect on KIC) has been reported in previous works on superlattices, the here presented KIC peak for a certain bilayer period is observed without significant differences in the shear moduli of the constituents and hence, with no substantial hardness increase.

The H/E ratio (Fig. 6h), an empirical indication used to describe the toughness of hard coatings also shows an increase for bilayer periods between 3 and 6 nm. However, it has to be noted that the error bars are overlapping, thus these differences are not significant30.

To provide an insight into the KIC dependence on the bilayer period, we performed ab initio calculations quantifying cleavage properties of MoN0.5/TaN SL as well as of the monolithic rs-MoN0.5, ζ-TaN, and rs-Ta0.75N, which were predicted to form in the bulk-like layers of the SL. Specifically, we determined cleavage energy, Ec, which represents the energy to separate a solid material into two blocks, and critical stress, σc, which corresponds to the maximum tensile stress perpendicular to the cleavage plane before cleavage happens31. In accordance with the experimental procedure, our SLs were cleaved perpendicularly to the interfaces. Subsequently, theoretical KIC* values were estimated using a simple formula

$$K_{{\rm{IC}}}^ \ast = \sqrt {c \cdot E_{hkl} \cdot E_{\rm{C}}},$$
(2)

where Ehkl and Ec are the directional Young’s modulus and the cleavage energy, respectively, and c is a scaling factor, conventionally set to 432. Table 2 shows that the E100 value of the MoN0.5/TaN SL, i.e. Young’s modulus perpendicular to the interface, is 618 GPa, which is close to the 645 and 671 GPa of ζ-TaN and rs-TaN0.75, respectively, but way above the ~389 GPa for rs-MoN0.5. The cleavage stresses as well as cleavage energies vary quite significantly between 32.6 GPa (SL) and 44.4 GPa (ζ-TaN) and 3.6 J/m2 (SL) and 5.4 J/m2 (ζ-TaN), respectively. According to the predicted KIC* values, crack propagation is the easiest in MoN0.5 yielding KIC* ~2.59 MPa m½. The KIC* of ~2.99 MPa m½ for the 1.72 nm MoN0.5/TaN SL suggests more for a rule-of-mixture-like behavior, as the KIC* values of ζ-TaN and rs-Ta0.75N are much higher with 3.72 and 3.25 MPa m½, Table 2. Consequently, based on these DFT calculations the ζ-TaN phase provides the highest cleavage stresses and energies as well as highest KIC*.

Table 2 Elastic properties and cleavage properties of the constituents of our superlattices as well as of the superlattice with a bilayer period of 1.72 nm.
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Discussion

Using ab initio calculations to predict material properties has been proven to serve as a powerful tool in materials science. The theoretically calculated indicators for ductility (G/B, CP, and ν) and their comparison with literature values clearly indicate a trend towards increased ductility for MoN0.5/TaN superlattice coatings. This also holds true compared to its constituents (Fig. 1). Furthermore, we identified ζ-TaN, Ta0.75N, and rs-MoN0.5 as the strongest constituents within our MoN–TaN superlattice system, in terms of cleavage stress and energy. Among these constituents, the calculated KIC* is with 3.72 MPa m1/2 significantly higher for ζ-TaN than for any other phase or the MoN0.5/TaN SL studied here. As we have recently proposed, this ζ-TaN phase, however, is only accessible for certain bilayer periods in the MoN–TaN SL system19. Therefore, we developed various MoN0.5/TaN superlattice coatings with different bilayer periods. By comparing our experimentally obtained data (from detailed XRD and TEM studies) with calculated lattice constants and elastic constants as well as energy-of-formation studies of various MoN/TaN superlattices19, we were able to draw the most realistic scenario of layer and phase arrangements, Fig. 6c, where an epitaxially (to MoN0.5) stabilized tetragonal distorted ζ-TaN layer (up to ~2.5 nm layer thickness) leads the formation of an rs-Ta0.75N layer.

We do not observe strong intermixing—conceivable through diffusion processes—at the interfaces of our superlattice constituents. This is recognizable by the multiple satellite reflections in their XRD patterns, even for a nominal bilayer period of only 1.5 nm. Besides this, our TEM micrographs show curved interfaces stemming from kinetic limitations during the growth, as described in refs. 33,34. The lattice parameters of the Mo–N-layers best match those calculated for MoN0.5, d200 for the Ta-N layers gradually decrease from the value for ζ-TaN to Ta0.75N with increasing bilayer period (from ~ 5.2 nm to 45 nm) as shown in Fig. 5a. For superlattices with Λ = 1.5 and 3.0 nm, we observed just one XRD main peak in the out-of-plane direction, suggesting for strained unit cells due to lattice mismatch.

Typically, such conditions are the prerequisites for achieving high hardness-peaks, being easily above the hardness of the constituting materials. However, due to the relatively similar shear moduli of the two materials (MoN0.5 and ζ-TaN), we do not observe a significant hardness-peak. Importantly though, we observe a clear peak in fracture toughness. Consequently, there need to be additional mechanisms active. In ref. 17, we studied the fracture toughness as well as the hardness of TiN/CrN SL films and found a pronounced dependence of both properties (KIC and H) as a function of the bilayer period, having their peak-values at comparable bilayer periods. We proposed several mechanisms like (1) coherency strains, (2) misfit dislocation arrays at the interfaces, (3) spatially oscillating elastic moduli, and (4) average grain size, that can explain this behavior.

The MoN/TaN SL system studied here is an interesting model system as it essentially allows us to study the effect of largely different lattice parameters at comparably similar shear moduli (the difference in G is below 32 GPa). For comparison, ∆G for other well-studied SL systems is easily between ~50 and 90 GPa17,35,36,37. The average grain size of our MoN/TaN superlattices also shows no strong dependence on the bilayer period, contrary to other material combinations. The lattice mismatch of ~5% can result in residual stresses being comparably high to growth-related or thermal expansion related stresses. The lattice parameter difference of Δa = 0.225 Å (between MoN0.5 and ζ-TaN), and an interface width of one unit cell (4 planes of each, nitrogen and metal, and thus five transitions with a change in lattice parameter) a total difference of 0.045 Å, results in coherency strains εc of ~1%. This gives residual stresses of ~3.3 GPa, both tensile and compressive surrounding the interfaces between MoN0.5 and ζ-TaN. These stresses have to be overcome during cleavage, thus they effectively enhance the measured fracture toughness. This mechanism is illustrated in Fig. 7. Thereby, also the hardness slightly peaks as reported by Shinn and Barnett38 and obtained for our samples. An additional mechanism increasing the fracture toughness without significantly influencing the hardness (as obtained for our samples) is suggested in our DFT calculations.

Fig. 7: Illustration of a fracture process in superlattice thin films.
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Schematics of the coherency strains and their consequential stresses influencing crack propagation across the interface. Here, the compressive residual stresses, pictured by arrows in the fracture process zone, impede crack growth across the interface.

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The peak of the experimental KIC at a bilayer period of about 5 nm can partially be interpreted via compositional and structural changes within the TaN layers, being triggered by the superlattice arrangement with rs-MoN0.5. The calculated KIC* value has a maximum of ~3.72 MPa m½ for ζ-TaN. Hence, these superlattices that allow for the highest volume fraction of ζ-TaN will also provide a high KIC. As the ζ-TaN phase is stabilized by the coherency strains to MoN0.519 and from a certain TaN layer thickness onwards, the rs-structure will form, there is a close relationship with the bilayer period. This can also explain the decline of KIC for bilayer periods above ~5 nm, as thereby the volume fraction of ζ-TaN decreases at the expense of the rs-TaNx phase. The latter has a lower KIC*, e.g., we calculated ~3.25 MPa m½ for rs-TaN0.75. The real picture, of course, is much more complex, meaning that the ζ-phase formation is only one possible contributing factor to the observed KIC evolution besides the bilayer period-depending coherency stresses.

To conclude, the concept of enhanced mechanical properties due to superlattice architectures has been shown in multiple studies. Together with increased hardness, the fracture toughness of protective coatings is of particular importance. We deposited MoN/TaN superlattice coatings, characterized them using density functional theory calculations, X-ray diffraction, and mechanical testing, coming to the following conclusion: the constituents of the MoN/TaN superlattice system are—when deposited by physical vapor deposition—present in the MoN0.5 and ζ-TaN, Ta0.75N, phases. The latter depends on individual layer thickness: we observe a change at a layer thickness of ~2.5 nm TaN. This was observed by two different methods: first, our XRD measurements confirm this trend as the peak position of the TaN layer shifts to higher 2θ angles with increasing bilayer periods as a result of increasing Ta0.75N proportion. Second, the progression of Young’s modulus follows a calculation including the Ta0.75N phases after an initial growth of ~2.5 nm ζ-TaN instead of the calculation without it. We calculated an intrinsic higher fracture toughness for ζ-TaN compared to Ta0.75N as a part of an increase in KIC. Another mechanism active in this superlattice coatings is coherency stresses which have to be overcome. This increase in KIC was also observed in micromechanical experiments.

Methods

Coating deposition

Our coatings were deposited using a lab-scale AJA Orion 5 sputtering system. Two confocal 2-inch cathodes, equipped with an unbalanced magnetron system were powered in current-controlled mode at a maximum current density of 19.7 mA/cm2. Our targets had a purity of 99.6% (Plansee Composite Materials GmbH). The nanolayer architectures were realized using a computer-controlled shutter system. The base pressure of our coating system was lower than 10−4 Pa. Prior to deposition, the substrates were ultrasonically cleaned in acetone and ethanol for five minutes each, heated to deposition temperature (380 °C at the substrate), thermally cleaned for 20 min and plasma etched in Ar plasma (6 Pa). We used a gas mixture of Ar and N2, 7 and 3 sccm, respectively, at a total pressure of 0.4 Pa to deposit our thin films on the rotating substrates (Si (100), MgO (100), Al2O3 (1\(\bar 1\)02)). Austenitic steel was used as it has a polycrystalline nature and hence avoids an overexposing of synchrotron radiation on the detector. The nominal bilayer periods were set to 1.5, 3.0, 6.0, 9.0, 15.0, and 45.0 nm. Additionally—to achieve a dense coating morphology—we applied a negative bias voltage of −40 V.

Computational details

To carry out DFT calculations, we used the Vienna Ab-initio Simulation Package (VASP)39,40 together with the projector augmented plane wave (PAW) pseudopotentials. The exchange-correlation effects were incorporated employing the generalized gradient approximation (GGA)41 using a Perdew–Burke–Ernzerhof (PBE) exchange and correlation functional42. The plane-wave cut-off energy was always set to 600 eV, while the k-vector sampling (25000 k-points) of the Brillouin zone provided a total energy accuracy of about 10−3 eV/at.

The models for MoN/TaN superlattices were based on the cubic rock salt (Fm\(\bar 3\)m) structure. Various bilayer periods were constructed by stacking the desired number of cubic cells in the (100) direction. Various defected states (vacancies or Schottky defects) were generated in an ordered or disordered manner employing the SQS method43. In the latter case, a sufficiently large supercell (containing 64 and 128 atoms for the bulk and the SL systems, respectively) was produced. Lattice parameters of the defect-free structures were optimized by fitting the energy vs. volume data with the Birch–Murnaghan equation of state44, while all structure optimizations in the vacancy-containing supercells were performed by relaxing the volume, shape, and atomic positions.

To provide an insight into the elastic behavior of selected systems, a tensor of elastic constants was derived from Hooke’s law by applying the stress-strain method45,46,47. Subsequently, we used the Voigt’s notation to transform this fourth-order elastic tensor to a 6 × 6 matrix, which was further projected onto a desirable (cubic or tetragonal) symmetry48. The polycrystalline bulk, B, and shear, G, moduli were determined by averaging the Reuss’s and Voigt’s estimates49,50, while the polycrystalline Young’s modulus, E, was evaluated as

$$E = \frac{{9 \cdot BG}}{{3 \cdot B + G}}$$
(3)

Following formulae in ref. 51, we computed Young’s modulus values in the prominent crystallographic directions. The tendency for brittle/ductile behavior was estimated by plotting the G/B ratio vs. Poisson’s ratio, ν=(3B-2G)/(6B+2G), or Cauchy pressure/E, c12–c44/E. Considering the defected SLs—which do not exhibit overall cubic but tetragonal symmetry— as well as the hexagonal boride systems, effective Cauchy pressure value was estimated as 1/3(c12–c66 + c13–c55+ c23–c44). Since bilayer-period-dependent trends in mechanical properties are very costly to obtain from first-principles (especially when it comes to defected systems), the increasing demands on CPU time and/or memory motivated us to estimate elastic properties of SLs with higher bilayer periods using a computationally cheaper approach by Grimsditch and Nizzoli52. In the original formulation, this linear elasticity continuum model allows us to calculate effective elastic constants of a system composed of two layers having arbitrary symmetry requiring elastic constants of the two-layer materials together with their volume ratio. The model, however, disregards any heterogeneity introduced by interfaces. In particular, the input elastic constants correspond to the equilibrium lattice parameters of each individual phase, which do not properly represent the stress state of the material in the SL. To provide a more realistic picture of the interface, the original formalism was extended to a generally n layers forming the SL in question35. The interface effects were modeled by setting the elastic constants of one of the n layer materials to those of a chosen superlattice with a small bilayer period. By varying the volume ratio of the interface layer (of a certain thickness) and the remaining bulk-like layers, we managed to predict elastic data depending on the desired bilayer period, which would not have been possible using the original Grimsditch–Nizzoli formalism. Furthermore, to corroborate our fracture experiments, the tensile strength in terms of cleavage energy and stress for brittle cleavage was estimated using the rigid-block displacement method53,54.

Structural characterization

Transmission electron microscopy (TEM) investigations were performed on an FEI Tecnai F20 equipped with a field emission gun. All our TEM samples were produced using a dual beam FIB and applying the lift-out method55. To reduce the Ga+ ion damage, we reduced the milling current down to 0.1 nA and sputter-cleaned our sample using a Technoorg Linda Gentlemill. X-ray diffraction patterns were recorded using a Panalytical XPert Pro MPD θ–θ diffractometer in Bragg–Brentano configuration. The x-ray source was a Cu-Kα source (λ = 1.5418 Å). Nanodiffraction experiments were conducted at the nanofocus endstation of Beamline P03 at PETRAIII located at synchrotron facility DESY (Hamburg), the used monochromatic X-ray radiation had a wavelength of λ = 0.80533 Å (15.0 keV beam energy). The sample was placed in transmission geometry, to collect Debye Scherrer patterns using a cross-sectional approach56.

Mechanical properties

Hardness measurements were performed in compliance with guidelines given by ref. 57, and evaluated using the method after Oliver and Pharr with a Fischer Cripps Laboratories ultra-micro indentation system (UMIS) equipped with a Berkovich diamond tip58. To eliminate possible substrate effects, we calculated Young’s modulus of our coatings by extrapolating E vs. h to zero indentation depth for different substrates following59.

We conducted micromechanical experiments to calculate the fracture toughness of our thin films. Hereby, we first dissolved the substrate (Si (100)) in aqueous KOH (with a concentration of 40 wt.% KOH and a temperature of 70 °C) to obtain free-standing thin film material. We FIB machined microcantilevers (FEI Quanta 200 3D DBFIB) according to regulations given by60. The initial current used for milling with our Ga+ ion source was 1.0 nA, subsequently reduced to 0.5 nA to prevent unwanted damage. The initial notch was machined with a current of 50 pA. These cantilevers were then loaded with a Hysitron PI-85 Scanning electron microscope (SEM) PicoIndenter equipped with a spherical diamond tip (diameter of 1 μm) inside an FEI Quanta 200 FEGSEM. We performed these tests in displacement-controlled mode (5 nm s−1) to obtain the maximum force before failure. This also enabled us to monitor possible mode I violations and assure linear elastic behavior of our beams. The fracture toughness was then calculated according to Matoy et al.61:

$$K_{{\rm{IC}}} = \frac{{P_{{\rm{max}}} \cdot l}}{{b \cdot w^{\frac{3}{2}}}} \cdot f\left( {\frac{a}{w}} \right)$$
(4)

with

$$f\left( {\frac{a}{w}} \right) = 1.46 + 24.36 \cdot \left( {\frac{a}{w}} \right) - 47.21 \cdot \left( {\frac{a}{w}} \right)^2 + 75.18 \cdot \left( {\frac{a}{w}} \right)^3,$$
(5)

where Pmax is the maximum force before fracture, a the depth of the initial notch, b the cantilever width, and w the cantilever thickness (film thickness in this case). We performed seven fracture tests for each system with a total success rate of 87%.