High-entropy alloy inspired development of compositionally complex superhard (Hf,Ta,Ti,V,Zr)-B-N coatings

Phase stability and mechanical properties of multimetal-boronnitride (Hf,Ta,Ti,V,Zr)-B-N is investigated by ab initio computations and experimental methods. (Hf,Ta,Ti,V,Zr)-B-N shows a strong energetic preference for the fcc NaCl-type structure over other structures up to a B:N ratio of 3.5


Introduction
By leaving the paradigm of having a major constituent or solvent, which dominates the properties, high-entropy materials have opened up a vast field of interesting properties to material scientists [1,2].The basic premise of high-entropy materials is the distribution of five or more atoms on a crystal lattice in equiatomic or near-equiatomic concentration to form a distorted random solid solution.This condition leads to a high configurational entropy S config !1:5 Á R, with R being the gas constant, that stabilizes the solid solution thermodynamically, although the magnitude of this stabilization has been overestimated in the past [3].High-entropy materials are commonly characterized by 4 core-effects: High configurational entropy, severe lattice distortion, sluggish diffusion, and the so-called cocktail effect [4].Invented for metallic alloys, the high-entropy concept has also been applied to ceramic materials with great success.Instead of constituent metals, these ceramics are composed of at least 5 binary ceramics such as nitrides, oxides, carbides, or borides [5].Since, usually, only the metalsublattice of these phases is disordered, the threshold S config !1:5 Á R is usually only reached per formula unit and not per atom as was intended for metallic alloys.To reflect this in their notation, such materials have also been named high-entropy metal-sublattice ceramics (HESC) [6].
In the pursuit of high-entropy materials, the formal criteria of such a definition are often not met in real materials.Still, interesting properties do not adhere strictly to arbitrary definitions such as S config !1:5 Á R. To reflect a broader horizon of materials, terms such as multi-principal element alloys, compositionally complex alloys, or complex concentrated alloys (CCA) have been coined [7].There is no consensus yet for a definition of CCAs, but commonly named attributes (as demarcation to high-entropy materials) are: possible multi-phase structures, lower requirements for the number of composing elements (even down to 3) [8,9], or that no component represents a base element (all concentrations < 35at%) [10].Sometimes, a precise definition is even omitted, instead multiprincipal element compositions with ''significant concentrations" of the components are deemed sufficiently accurate [11,12].CCAs represent hence not a rigorous classification, but can be understood from the perspective of material development.The common trait of CCAs is a significant disorder on the atomic level (to what magnitude is not always defined), while not fulfilling the strict criteria of a high-entropy material.In any case, these classifications should serve only as a guide for materials design and not obstruct our advances.
Despite the comparably low entropy, multi-principal element ceramics possess compelling properties for protective thin films, usually synthesized by physical vapor deposition (PVD).Easy to deposit in a face-centered-cubic (fcc) solid solution with reactive magnetron sputtering, nitrides have received the most attention so far among the different ceramic classes [13].Nitride thin films with good thermal stability [6], mechanical properties [14,15], low diffusivity [16,17], and high oxidation resistance [18][19][20] have been reported.But among thin films, only two high-entropy sublattice borides with excellent high-temperature stability have been investigated so far, that outperform their lower-entropy counterparts [5,21].These investigations all focus on the metalsublattice, whereas the non-metal sublattice is often neglected.Although deliberate introduction of disorder on the non-metal sublattice could open the door to outstanding material properties, so far, such investigations of mixed ceramic classes are rare.
Since S config increases logarithmically with the number of elements [4], the first additional elements in a random solid solution offer the largest returns.Changing the non-metal sublattice from a perfectly ordered nitride into an equimolar boronnitride would increase the configurational entropy of the non-metal sublattice from 0 to 0:69 Á R, which is a much larger gain than could be obtained by tweaking a metal-sublattice that contains high S config already.So far, high-entropy metal sublattice carbonitride [22,23] oxynitride [24], and carboride [25,26] thin films have been reported, but no high-entropy metal sublattice boronnitrides, even though Ti-B-N prototypes have been investigated in the past [27,28].A possible reason for this lack of attention could be the incongruence of the fcc-nitride and the hexagonal diboride structures that leads to nanocomposite structures in Ti-B-N instead of single-phase solid solutions, which are the prerequisite of highentropy materials.
In this work, we explore the alloying possibilities and mechanical properties of equi-metal-atomic (Hf,Ta,Ti,V,Zr)-B-N -having a high-entropy metal-sublattice -with density functional theory calculations.Based on these results, we deposited (Hf,Ta,Ti,V,Zr)-B-N films with reactive and non-reactive magnetron sputtering (recently we showed that using reactive or non-reactive sputtering has a large influence on the coating properties in Ti-B-N [29]) possessing excellent mechanical properties and thermal stability.

Density functional theory simulations
Ab-initio investigations were conducted using the Vienna Abinitio Simulation Package (VASP) [30,31] with projector augmented plane wave (PAW) pseudo-potentials under the generalized gradient approximation [32].This approach allows the study of electronic, thermodynamic, and mechanical properties of (Hf, Ta,Ti,V,Zr)-B-N with equiatomic metal-sublattice and different B: N occupations on the non-metal sublattice in four different structures: the fcc NaCl-type structure (space group 225), vacancyfree and with 50% non-metal vacancies (equally distributed between B and N), the hexagonal AlB 2 -type structure (space group 191, abbreviated with a [33], to differentiate this structure from the other typical structure for diborides -the WB 2 -structure, space group 194, which is abbreviated with x), and the orthorhombic FeB-type structure (space group 62).Representative visualizations of the unrelaxed cells of each structure type with B:N = 50:50 are shown in the supplemental material.The cutoff energy was set to 500 eV and the stopping criterion for ionic relaxation to %E-4 eV/ at, using a C-centered Monkhorst-Pack k-mesh [34].To simulate the random distribution of elements on their respective sublattices, Special quasi-random structure (SQS) supercells were constructed [35], in which the metals were distributed on the metalsublattice, and B and N on the non-metal sublattice, see Table 1 for the respective supercell sizes and k-meshes.Since for the chosen cubic and hexagonal supercells the number of metal sites is not divisible by 5, the equiatomic occupation of the metal-sublattice was realized by averaging over 10 cells, in which the metal occupations were permuted on the 6 + 6+6 + 7+7 or 5 + 5+5 + 6+6 sites for the fcc and a structures, respectively.The cells were then relaxed regarding size, shape, and atomic positions towards equilibrium.The phase stability of the different structures was calculated with their formation energies E f , where E tot is the total energy of the solid solution cell, and n i and l i are the number of atoms and chemical potential of the ith component.The chemical potential was calculated as the total energy per atom of the metals and of B in their ground state structures (hexagonal close packed for Hf, Ti, and Zr, body centered cubic for Ta and V, phase prototype with space group 166 for B), and of the N 2 molecule.The contributions of vibrational and configurational entropy to phase stability have been calculated using the quasiharmonic Debye model [36], and the sublattice model [7], respectively, for the vacancy-free fcc and the a phase for temperatures up to 1000 K.
Mechanical properties were calculated from the relaxed cells with the stress-strain method [37].The resulting elastic constants were projected onto cubic or hexagonal symmetry with the method of Moakher and Norris [38].The bulk and shear moduli B and G are averaged from the Reuss and Voigt estimates described in [39].The directional Young's moduli of certain crystallographic orientations [40] were calculated in addition to the polycrystalline Young's modulus E and the effective Cauchy pressure Cp, expressed as where C ij refers to the respective matrix element of the elastic constants.
The projected density of states (pDOS) was calculated with an energy resolution of 0.05 eV À1 in the region between À10 and +5 eV around the Fermi-level to discuss individual bonding contributions of the constituents.

Depositions
All coatings were deposited on mirror-polished substrates, (1 0 0)-oriented Si (20 Â 7 Â 0:38mm 3 ), austenitic steel platelets (20 Â 7 Â 1mm 3 ), and (1 1 0 2)-oriented sapphire (10 Â 10 Â 0:53mm 3 ), heated to 440°C, by magnetron sputtering in a modified Leybold Heraeus Z400 deposition facility.Reactive depositions were performed in mixed Ar + N 2 discharges (with an Ar:N 2 flow rate ratio of 18:22 sccm at 0.44 Pa) using an equiatomic, metallic, 3"-diameter Hf 0.2 Ta 0.2 Ti 0.2 V 0.2 Zr 0.2 target (Plansee Composite Materials GmbH).Placing an increasing number of the combined set of HfB 2 , TaB 2 , TiB 2 , VB 2 , and ZrB 2 pieces (all from Plansee Composite Materials GmbH, roughly 4 mm in diameter) on the target racetrack allowed us to prepare (Hf,Ta,Ti,V,Zr)-B-N coatings in addition to the (Hf,Ta,Ti,V,Zr) N. Details on the preparation of the latter can also be found in [6].The non-reactive depositions were performed in Ar discharges (with an Ar flow of 30 sccm at 0.36 Pa) using a 3"-diameter ZrN target (Plansee Composite Materials GmbH) with a surprisingly high C content of 10at%, which was discovered only after the depositions.Also here, we added an increasing number of the combined set of HfB 2 , TaB 2 , TiB 2 , and VB 2 pieces, each, on the target racetrack to prepare not just ZrN but also (Hf,Ta,Ti,V,Zr)-B-N coatings with different metal and B:N ratios, all with additional high C content.
The substrates were ultra-sonically cleaned with Acetone and Ethanol for 10 min and mounted face-to-face at a distance of 4 cm to the target.After waiting for a base pressure of 0.3 mPa, the substrates were heated to a temperature of 440°C by resistance heating and Ar-ion etched at a pressure of 1.3 Pa for 15 min by applying a negative pulsed DC bias of À150 V to the substrates with a pulse frequency of 150 kHz and pulse duration of 2496 ns.During all depositions, a DC bias voltage of À50 V was applied.The depositions were performed supplying a constant current of 0.5 A to the ZrN target, and 1.0 A to the metallic target.The deposition time was adjusted between 30 and 50 min to ensure that the coatings are between 2 and 3 lm thick.

Sample analysis
Cross-sections of the coatings on Si substrates were analyzed with a FEI Quanta 250 scanning electron microscope (SEM)equipped with a field emission gun (FEG) and operated at 5 kVto investigate growth morphology and deposition rates.Since the Si substrates in the non-reactive depositions broke during or after depositions, coatings on steel substrates were cut, embedded and polished to determine the growth rates from the polished crosssections.Additional fracture cross-sections of selected nonreactively deposited coatings on sapphire substrates were recorded before and after annealing with a Zeiss Sigma 500 SEM.Transmission electron microscopy (TEM) was performed with a FEI TECNAI F20, equipped with a FEG, operated at 200 kV, on as-deposited samples.
Chemical compositions of reactively deposited coatings were analyzed by energy dispersive X-ray spectroscopy (EDS), the nonreactively deposited samples warranted a detailed analysis by time-of-flight elastic recoil detection analysis (ToF-ERDA) with a recoil detection angle of 45°using a primary beam of 36 MeV I 8+ ions.Experimental details, data analysis as well as potential systematic uncertainties are described in Refs.[41][42][43].Phase analysis was conducted with X-ray-diffraction (XRD) using a PANanlytical XPert Pro MPD (h À h diffractometer) equipped with a Cu-Ka source (k ¼ 0:15408nm, 45 kV and 40 mA) in Bragg-Brentano geometry.Coatings on sapphire substrates were vacuum annealed in a Centorr LF22-2000 vacuum furnace at T a = 800, 900, 1000, 1100, and 1200°C for 10 min, the heating rate was 20 K/min, and the passive cooling rate at least 50 K/min down to 200°C.Indentation hardness, H, and modulus, E I , were measured on polished coated sapphire substrates with an UMIS II nanoindenter, equipped with a Berkovich tip, following the procedure by Oliver and Pharr [44], assuming a Poisson's ratio of 0.25 to analyze the load-displacement curves.40 data points were recorded per sample with a maximum force of 30 mN and a 0.5 mN decrement between points, down to 10.5 mN.Only data points where the plastic zone was sufficiently developed were used for the evaluation.Raw data is provided in the supplementary material.

Density functional calculations
The energies of formation of the different structures presented in Fig. 1a) for different B:N ratios show a clear preference of the vacancy-free fcc structure over a wide composition range from the pure nitride up to % 78at% of B on the non-metal sublattice.In this structure, E f increases linearly from %-1.7 eV/at to % À0:7eV=at at 90 at.%N on the non-metal sublattice.The fcc structure with 50% non-metal vacancies (equally distributed between B and N) shows a constant offset of % 0:4eV=at in comparison.The orthorhombic FeB structure features slightly lessnegative E f values than the fcc structure.At 25at% B on the nonmetal sublattice, the E f is very close to the vacancy-free fcc structure, a detailed inspection of the corresponding relaxed cell reveals that the original atomic coordination transforms from the layered arrangement of the FeB structure into a more cubic coordination (6 nearest neighbors with %90°angles) upon relaxation.Only in a narrow window between 78 and 91at% B is this structure preferred energetically, but since the difference to the higher-symmetry fcc and a phases is very small, this structure might not be observable in PVD experiments.It is therefore excluded from further considerations together with the fcc structure with vacancies.The a structure follows a non-linear trend as well and is preferred only in the pure boride phase and down to a B content of 90 or 84at% on the non-metal sublattice, depending on which competing phase is considered.A similar behavior is also visible in the constituting binary phases (see the supplementary material).
To study the influence of temperature on the phase stability, the vibrational entropy has been calculated with the quasi-harmonic Debye model in addition to the configurational entropy for the two main competing phases, the vacancy-free fcc structure, and the a structure.The electronic entropy was not considered, as this term is usually vanishingly small and often similar between different phases [36,45].The sum of the entropy contributions together with the total energy is plotted in Fig. 1b) for all investigated B contents at 100 K intervals up to 1000 K.The validity of the quasiharmonic approach is limited by the anharmonic behavior at higher temperatures, but for ceramics with high melting points, insights can be gained within a reasonable range.In general, the configurational entropy is much smaller here than the vibrational term.At 750 K, roughly corresponding to the deposition temperature of our coatings, the maximum stabilization by configurational entropy amounts to À0.06 eV/at in both structures, while the vibrational entropy makes up between À0:16 and À0.18 eV/at in the cubic phase and between À0:09 and À0.28 eV/at in the hexagonal phase.This is another sign that the impact of configurational entropy is often overestimated in HESC [3], but since the Debye model is only a very rough approximation due to its limitations, these numbers should be treated with care.We will instead refer to the relative trends of the free energy curves in Fig. 1b), which all show similar behavior.The free energy curves increase slightly in the range of 100-200 K due to numerical inaccuracies at low values of T, stemming from the Debye model [36].These inaccuracies decrease in impact at higher temperatures.Only the a structured phase with 25at% B on the non-metal sublattice (orange open circles) shows a slightly steeper slope.This is due to a larger vibrational term in this phase, but the large difference in energy to the corresponding cubic phase makes this still negligible.The differences in entropy are minuscule between the phases, hence the entropic contributions do not cause an additional cross-over between the stability curves of the fcc and the a phase.We can therefore state that the phase-fields shown in Fig. 1a) also hold at temperatures above 0 K.The compatibility of B and N incorporation in the fcc and a structure is also noticeable in the cell parameters.In Fig. 2a), the average and standard deviation of the lattice distances and angles of the 10 individual calculated cells are shown for the fcc and a structures.In all cubic structures, the angle of 90°is adhered to with only little deviation (due to random occupation of differently sized metal atoms).At the same time the lattice spacing increases linearly with increasing B content from 4.42 to 4.62 Å at 90at% B (on the non-metal sublattice).Contrary, in the a structured cells with increasing N content, large deviations between individual cells are evident for both lattice angles a and c, as well as the cell parameters a and c.At high N concentrations the a/c ratio is even reversed.The deviation of lattice parameters and angles means that while the B incorporation on the non-metal sublattice of the fcc structure poses no problem, the N incorporation in the hexagonal phase perturbs the structure strongly.This property is also showcased in Fig. 2b), which depict representative fcc and hexagonal cells with 50:50 B:N ratio in [001] direction after structural relaxation.Clearly, the cubic symmetry is basically unaffected by the B atoms, while the non-metal-hexagon network of the a structure is broken by the N incorporation.
The polycrystalline bulk, shear, and Young's modulus, B; G, and E, change only slightly for the fcc structure with B incorporation (Fig. 3).From 0 to 90at% B (on the non-metal sublattice), B; G, and E decrease by 24, 18, and 19%, respectively.In the a structure, going from 0 to 75at% N on the non-metal sublattice, B; G, and E decline by 45, 85, and 82%, respectively in contrast, showing a massive deterioration of mechanical properties by the N incorporation.Since the used formula for the Young's modulus is only strictly valid for isotropic systems, this representation could skew the comparison between the cubic and hexagonal cell, but different directional Young's moduli calculated for both phases yield the same trends.
A direct comparison of our values to literature is not possible due to a lack of studied similar compositions, but can be approximated with linear combinations of reported values of the constituting binary ceramics.The calculated properties of the pure boride phase agree well with such aggregated values for binary transition metal diborides from [33].For the pure nitride phase, the C 11 ¼ 485GPa value falls short roughly 100 GPa compared to such a linear combination from literature values [46,47], while the C 12 ¼ 149GPa and C 44 ¼ 110GPa are more comparable (see the supplementary material).This implies slightly lower values of the Young's modulus compared to the linear combination of the binary nitrides, but also a more isotropic behavior of the directional Young's modulus of our HESBN.
The G=B ratio and C p are useful criteria to study the inherent lattice ductility of materials.In Fig. 4, all the fcc structured cells are grouped around the ductile/brittle threshold, while the pure a structured boride is very brittle.This is expected since borides are known to form strong covalent bonds that lend a brittle fracture behavior [33].The a structured cells quickly change to ductile behavior when N is added to the non-metal sublattice, this can be explained with the broken chemical bond network (Fig. 2c) and thereby resulting low values of G (Fig. 3).
To further understand this behavior, the projected density of states -summing up all metal contributions as well as summing  Fig. 4. Intrinsic ductility criteria G=B versus Cauchy pressure (C12 À C44 for the fcc and for the a-structure) for the two most-likely structures (based on E f calculations, Fig. 1) fcc (NaCl-prototype, with 1:1 ratio between metal and non-metal) and a (AlB 2 -prototype).Clearly, the a-structured diboride (xB = 1) is the most brittle one.
With increasing N substituting for B on the non-metal sublattice, the G=B ratio quickly reduces below 0.57 and the Cauchy pressure to positive values, entering the ductile regime according to these two ductility criteria.Except for the fcc-nitride (xB = 0), which is situated in the ductile region, all other B-containing fcc-structured materials are positioned around the brittle-ductile thresholds.
up over all individual atoms and averaged over the 10 individual structures -was mapped for the different compositions in fcc and a structure, which can be seen in Fig. 5.In the pure cubic nitride, a strong interaction of N p and metal d states at around À5 eV is evident, which indicates sp 3 d 2 hybridization and thus strong covalent bonds [48,49], while the core-near N s states do not contribute to bonding in any of the considered cases.In all investigated compositions, the region close below the Fermi-level is populated -mostly by metal d, but also by B p states -indicating additional metallic bonding character in all compositions.When gradually replacing N with B in the fcc structure, the B p -metal d states hybridize, form a peak at À2.5 eV, and thus supplant the N.At the same time, B s states also hybridize with the metal d states around À6 to À7eV.
In the N-free a structured boride (bottom row), the interaction between B p and metal d states around À4 eV is visible.When N is added to this structure, the N p states gather around À6 eV, while the metal d states shift towards the Fermi level, indicating less intense bonding between the metals and non-metals.Unlike in the fcc structure, the N and B states overlap partially on the energy scale, which is due to the bonding to each other within the hexagon planes.At the same time, the N and B states are spread over a large range on the energy scale, indicating also a wider spread of the electronic states in real space and thus less pronounced covalent character.This delocalization explains the drastically decreased mechanical properties of the N-alloyed a structure.
Please note that the total DOS does not have to align with the summed pDOS contributions, which themselves lack the contributions from the interstitial regions.Also, the presented pDOS are given per atom, so that low concentrations of an element lead to high contribution in the pDOS but only minor contributions in the total DOS.

Chemical analysis
The chemical compositions of the reactively deposited coatings measured by EDS are listed in Table 2.In all coatings, the heavier elements Hf and Ta are more abundant, which is common in sputtered coatings due to different poisoning states of the individual target grains [50] or preferential resputtering of the lighter elements [51,52].This effect is even more pronounced in the boronnitride coatings, since the HfB 2 and TaB 2 pieces show a higher sputter rate compared to the lighter elements.The B content increases from 0 up to $18at% with increasing number of metal diboride pieces on the target.The N concentration is largest in the B-free coating with 48at% N, with B addition, the N-content decreases at first, but then increases together with the B content, which is a sign of BN formation.The maximum B:N ratio obtained is 0.44.
The chemical compositions of the non-reactively sputtered coatings, analyzed by ERDA, are presented in Table 2.The depth profiling with ERDA yielded constant concentrations across the scanned depth, see the exemplary depth profile of the coating with the highest B content in Fig. 6.The only exception is a changed B:C ratio at larger depths, which is due to the inability of the technique to distinguish B and C at larger depths [53].To also avoid influence of surface contamination, the depth between 1000 and 2000 Â 10 15 at/cm 2 was therefore averaged for quantification in all samples, and the given uncertainties are the statistical errors of measurement from averaging over this region.The coatings prepared from the Zr(N,C) target contain 15.0at% C, which decreases to 7-9at% when placing additional diboride pieces (that contain no measureable C content) on the racetrack.All non-reactively sputtered multi-element boronnitride coatings contain around 30at% Zr, while the sum of the other metals increases from 9.3 to 11.8at% with increasing number of diboride pieces on the racetrack.The oxygen content stays around 2at%, except in the coating with 23.6at% B, where 7.1at% of oxygen have amassed.Since we used broken diboride pieces with irregular shapes, the surface contamination with oxygen on these pieces could be significant.This contamination was taken care of by pre-sputtering behind the closed shutter, but, for this sample, the procedure was apparently insufficient.The B and N contents are both close to 25at%, so that their sum is between 48 and 50at% in all coatings.The B:N ratio changes from 0.76 to 1.12 with increasing B content of the (Hf,Ta,Ti,V,Zr)-B-N coatings, Table 2.The configurational entropy S config , calculated with the sublattice model [7], for the reactively sputtered nitride is 1:62 Á R on the metal sublattice, while the small number of N-vacancies on the non-metal sublattice contribute only a negligible amount of configurational entropy, see Table 2.This coating is therefore a highentropy sublattice nitride.The combined S config across both sublattices amounts to 0:83 Á R (per atom), which is expected of a typical fcc high-entropy sublattice nitride.In the reactively sputtered boronnitride coatings, the metal sublattice contributes between 1.43 and 1:52 Á R to S config , while the contribution from the nonmetal sublattice lies between 0.61 and 0:71 Á R. In combination (considering both sublattices), these coatings exhibit S config values between 1.02 and 1:12 Á R (per atom).But these values are overestimated and provide only a rough guideline, since the reactively sputtered coatings all exhibited an additional BN phase to varying degrees, as will be shown by XRD data.The individual configurational entropy data for these reactively prepared coatings indicate that only (Hf,Ta,Ti,V,Zr) N fulfills the condition of S config !1:5 Á R for one sublattice and single-phase solid solution and can thus be named high-entropy sublattice nitride (HESN), see Table 2.The reactively sputtered (Hf,Ta,Ti,V,Zr)-B-N coatings, on the other hand, are multi-phase coatings and can therefore be called compositionally complex boronnitrides (CCBN).
For the non-reactively sputtered coatings, the calculation of S config is complicated by the carbon content, but using different assumptions, we estimated a value.Due to the high Zr content in all these non-reactively prepared coatings, the threshold of S config !1:5 Á R is missed even for the metal sublattice, which provides a maximum of only 0:89 Á R, Table 2.But with the addition of B, C, and O, the configurational entropy of the non-metal sublattice could be massively increased in the non-reactively prepared coatings.If C and O reside on the non-metal sublattice, which is reasonable when considering studies about Ti-C-N [54,55] and Ti-O-N [56], then S config of the non-metal sublattice increases from 0.71 (when considering only B and N) to 1:30 Á R. Together with the contribution of the metal sublattice this amounts to a maximum of 1:08 Á R (per atom), a higher value than in the reactively sputtered high-entropy sublattice nitride.Still, no sublattice reaches the criterion for a HESC, so that these coatings should be called singlephase CCBNs.
The compositions of our calculated and deposited systems are outlined in the ternary metal-B-N phase diagram in Fig. 7, and, also, here we considered C (as well as O) to substitute for N in the non-reactively prepared coatings.Our calculations traced out the phase field between the compositions MeN, MeB, and MeB 2 as most likely for beneficial properties.The reactively deposited coatings start in this region, but at the highest B concentration (and B:N ratio) take a turn towards the BN phase.In Ti-B-N, it was shown that reactive depositions follow the MeN-BN line even at very low B concentrations [29], while our reactively sputtered coatings show this trend only at higher B concentrations, which can be due to different sputtering conditions and N 2 partial pressure.The non-reactively deposited coatings, on the other hand, sustain much higher B concentrations (and B:N ratios) and would still lie in the MeN-MeB-MeB 2 triangle, if we discount the shift by the additional C and O.The one non-reactively sputtered sample that sticks out towards the BN phase does so because of its high O content.

Structure and mechanical properties
The difference between the reactively and non-reactively sputtered coatings manifests even more in the XRD patterns, see the reactively as-deposited coatings on Si in Fig. 8a).The reactively prepared HESN shows a single phase fcc structure, but with B addition the contribution of an amorphous structure clearly increases, see the increased background between 25 and %35°.Furthermore, Table 2 Chemical compositions of the reactively sputtered coatings on Si substrates were analyzed with EDS.Standard errors of 3 respective measurements are 1at% for all coatings and elements.Chemical compositions of the non-reactively sputtered coatings on sapphire substrates were obtained with ERDA.The signal from 1000 to 2000 Â 10 15 at/cm 2 was averaged for all samples, the standard error from this region is given as statistical uncertainty.Configurational entropies have been calculated with the sublattice model [7] and are shown for the metal sublattice M, the non-metal sublattice NM, and their combination R. Fig. 6.ERDA depth profile of the non-reactively sputtered coating with the highest B content.The element ratios are constant across the measured depth, with the exception of B and C, which become indistinguishable at high depths [53].The depth between 1000 and 2000 Â 10 15 at/cm 2 was used for quantification in all samples.
the crystalline (111), (200), and (220) peaks widen with increasing B content (and B:N ratio) tremendously.A similar behavior could not be identified for the non-reactively sputtered coatings, which essentially only exhibit XRD features that point towards a single crystalline phase in as-deposited state, independent of the B content (and B:N ratio), see Fig. 8b).The B content in the single-phase fcc-structured non-reactively prepared coatings is also significantly higher (maximum of 25.5at%) than the maximum reported for a single-phase fcc-structured Ti-B-N of 17.4at% [57].This suggests that the higher elemental complexity allows to solute more B into the fcc transition-metal-nitridebased lattice.Contrary to the reactively prepared coatings, the XRD patterns for the non-reactively prepared coatings are obtained from coated sapphire substrates, since the Si substrates always broke during or after deposition, indicating higher residual compressive stresses.Generally, the peak positions of the Zr(N,C) coating are shifted significantly towards lower diffraction angles (pointing towards a larger lattice parameter of 4.65 Å compared to ZrN).This is likely due to the high compressive stresses and the high C content, ZrC is also fcc structured with a larger lattice constant of 4.69 Å (ICDD 00-035-0784 [58]) compared to ZrN with 4.58 Å (ICDD 00-035-0753 [59]).With the addition of B, the preferred orientation changes from a (200) towards a (111)-oriented growth.All of our coatings have lattice parameters varying between 4.62 and 4.67 Å without a clear trend, which is considerably more than the reference value for ZrN, and also more than the predicted lattice parameter of 4.53 Å for the 50:50 B:N system (see Fig. 2).For the latter case, this is due to the very high Zr content in our coatings, whereas the calculations use equimolar distribution of the metals.In addition, our coatings are highly stressed, which can cause a shift of the XRD positions (macro-stresses) and also significant peak broadening (micro-stresses).In none of our samples could we detect any sign of an a phase, in good agreement with calculations.
The phase composition influences the mechanical properties heavily, see Fig. 8c) for the indentation hardness H and modulus E I of the as-deposited reactively sputtered coatings.The HESN has H and E I of 32.5 and 450 GPa, respectively, with B addition, both these values decrease immediately.The decline is pronounced, especially for E I when increasing the B content beyond 12at%, which is a clear proof for the formation of amorphous BN, as suggested by XRD (Fig. 8).The deterioration of the mechanical properties by BN formation was studied in reactively sputtered Ti-B-N films, where too high N partial pressures quickly lead to reduced hardness due to the formation of an amorphous BN phase [60][61][62][63][64]. Therefore, all reactively sputtered boronnitride coatings in this study possess much lower hardness values than HESN and established nitride coatings [65], let alone borides for which superhardness (H above 40 GPa [66]) is often reported [5,21,[67][68][69].Whether depositions at lower N 2 partial pressures would lead to favorable properties remains to be seen.Due to the reduced mechanical properties in the reactively sputtered coatings, only the non-reactively sputtered coatings were studied further for their thermal stability (the HESN coating is presented in [6]).
The non-reactively sputtered coatings can clearly be classified as superhard, see Fig. 8d) for their H and E I values in the asdeposited state.The Zr(N,C) coating features a hardness of 36.3GPa and an indentation modulus of 460 GPa.Both values peak with the addition of B, where highest H values of 46.3 and 45.7 GPa and highest E I values of 518 and 511GPa are obtained for 21.8at% B (B: N = 0.83) and 23.6at% B (B:N = 1.03), respectively.This is especially remarkable for the coating with 23.6at% B, which also contains %7at% oxygen, where we would expect significant softening due to the increasingly ionic bonding character caused by the electronegative oxygen.
The indentation moduli lie significantly above our calculated values for the Young's modulus of fcc structured boronnitrides.The correlation with the hardness implies that the discrepancy is owed to microstructural differences between of the coatings, which cannot be reflected in ab initio calculations.The surface and strain energy can also have a significant influence on the phase stability, but since our thin films are roughly 2lm thick, they behave more like bulk materials in this regard.
The cross-section TEM micrograph of the coating with 23.6at% B shows a dense micro-columnar coating, see the bright-field image in Fig. 9a) but especially its dark-field variation in Fig. 9b).No amorphous-like structure could be identified at the column or grain boundaries, not even for this coating despite having the highest oxygen content.Therefore, our previous made assumption that oxygen is incorporated in the lattice seems to be plausible.SAED patterns recorded from regions I (close to the substrate) and II (close to the surface) confirm the single-phase fcc structure throughout the whole thin film.The lattice parameter calculated from the SAEDs is 4.73AE0.05Å for region I and 4.77AE0.06Å for region II, in reasonable agreement with XRD measurements.The grain morphology of this coating is strongly different from nonreactively prepared Ti-B-N coatings with similar B contents and B:N ratios, that are usually nanocomposites of TiN and TiB 2 with a disordered encapsulation phase [28,70].The coating with the highest B content (25.5at%) and also highest B:N ratio of 1.12 shows identical cross-section TEM images and SAED patterns as this one presented in Fig. 9 (therefore, not shown here).Additional SEM fracture cross-section micrographs of the coatings with the lowest and highest B content in as-deposited state and after annealing at 1200°C are shown in the supplementary material.vacuum annealing up to 1200°C.Exemplarily, Fig. 10a) and b) show the XRD patterns of Zr(N,C) and the non-reactively prepared multielement boronnitride coating having 25.5at% B. To minimize any substrate interference, the annealing studies were conducted with coatings grown on sapphire.All coatings still exhibit a singlecrystalline fcc structure even when annealed at 1200°C.The most notable change upon the annealing is the rather strong formation of ZrO 2 even when annealed only at 800°C, due to the high oxygen affinity of Zr, for which even the relatively small amount of residual O 2 in the vacuum furnace is sufficient for oxide generation.Basically, several Zr-oxide phases are present, but we have exemplarily marked only the positions of cubic ZrO 2 (ICDD 00-049-1642 [71]).Before the nanoindentation tests, the coatings were polished to remove these oxides.
The other noticeable change is the shift of the peak positions to higher diffraction angles, corresponding to smaller lattice parameters.This is well presented by the lattice parameter evolution with the annealing temperature T a , Fig. 10c).All non-reactively prepared coatings show the same behavior.For Zr(N,C), for example, the lattice parameter decreases from 4.66 to 4.60Å upon increasing T a to 1200°C.The reference value for stress-free ZrN powder is 4.57 Å (ICDD 00-0311493).The single-phase fcc-CCBN coatings follow the same pattern, starting at up to 4.70 Å.
All CCBN coatings exhibit much broader peaks than Zr(N,C), which is also nicely shown by the evolution of the full width at half maximum (FWHM) of the (111) peak with annealing temperature, as shown in Fig. 10d).Although the lattice parameters are steadily decreased with increasing annealing temperature -that is indicative for reduced macrostresses -the FWHM essentially does not change even upon annealing at 1200°C.This observation indicates that the microstresses basically remain, pointing towards reduced recovery rates (during which crystal defects would arrange to lower energy sites).
The slow recovery rate in further consequence explains their much better thermal stability of mechanical properties, where even after vacuum annealing to 1200°C, Fig. 11a), the hardness does not change too much.The Zr(N,C) possesses H = 36.3GPa in its as-deposited state and still 35.1 GPa when annealed at T a ¼ 900 C.After annealing at T a ¼ 1200 C the hardness decreases to 30.2 GPa.Since this coating contains some C, its hardness decreases much slower than in a typical binary nitride (compare for example the softening in TiN to < 30GPa when annealed at T a ¼ 600 C [72]).Since ZrC itself is rather hard [73] the hardness of our Zr(N,C) coating is also significantly higher than that reported for ZrN thin films so far [74][75][76].
Even after annealing to 1200°C, the CCBN coating with 23.6at% B (B:N = 1.03) loses only %2 GPa in hardness, while the coating with 25.5at% B (B:N = 1.12) does not lose any hardness within the error of measurement.This performance is similar to highentropy sublattice diboride coatings [5,21], but vastly superior to Ti-B-N coatings, which lose hardness above annealing temperatures of 900°C due to evaporation of B from the disordered encap- ).For all B contents investigated only a single-phase fcc structure is detected without an indication of an X-ray amorphous contribution.Indentation hardness H and indentation modulus EI of c) reactively sputtered and d) non-reactively sputtered coatings in their as-deposited state (on sapphire substrate).While H and EI drop for the reactively-sputtered coatings with B-contents above 10at%, the non-reactively sputtered coatings are superhard, peaking with 46.3 GPa for a B-content of 23.6at%.Please also note the much higher B:N ratio for the non-reactively prepared coatings.
sulation region [28].We attribute the hardness retention of our coatings to the stable crystalline fcc solid solution up to 1200°C, which is mirrored also by the rather stable FWHM values up to this temperature.
Also, the indentation modulus, E I , shows little dependence (within the error of measurement) on the annealing temperature, see Fig. 11b), but here also Zr(N,C) provides rather stable values.

Conclusions
Ab-initio calculations show that the system (Hf,Ta,Ti,V,Zr)-B-N strongly prefers the fcc structure in a wide compositional range, supporting up to 78at% B on the non-metal sublattice.The B is well incorporated into the cubic structure, as seen by the small variation of the lattice parameters of individual cells and the projected density of states.The elastic properties of such a boronnitride are also stable in a wide compositional range, with only slowly varying bulk, shear, and Young's moduli.The ductility criteria G=B and Cauchy pressure indicate that such boronnitride coatings should be significantly less brittle than an a structured boride.
The a-structure, on the other hand, is only preferred for very high B contents, and the hexagonal lattice does not tolerate N incorporation well.The local atomic symmetry is perturbed gravely, leading to rapidly decreasing elastic constants with increasing N content.Therefore, we expected the formation of fcc structured high-entropy sublattice boronnitride thin films in our experiments.
Reactive sputtering from a Hf 0.2 Ta 0.2 Ti 0.2 V 0.2 Zr 0.2 target with corresponding metal-diboride pieces on the racetrack leads to formation of amorphous BN next to the fcc multimetal-boronnitride, which is accompanied by a significant hardness drop from 32.5 GPa (no B) to 16.7 GPa at 18at% B (B:N = 0.44).This is similar to the behavior in reactively sputtered Ti-B-N.
On the other hand, the non-reactively sputtered coatings, deposited from a Zr(N,C) target with metal-diboride pieces on the racetrack, lead to single phase fcc structures with no amorphous phase and can be assigned as single-phase compositionally complex boronnitride (CCBN) coatings.These coatings all contain a high C content and B contents between 20.0 and 25.5at% (B:N ratios between 0.76 and 1.12) are superhard (H P 40GPa) and possess excellent thermal stability.Our results suggest that the compositional complexity allows to incorporate much more B in the fcc structure than Ti-B-N for example.With increasing B:N ratio the hardness peaks between 46.3 and 45.7 GPa at B:N ratios between 0.83 and 1.03, respectively.Even after vacuum annealing to 1200°C, a hardness of 43.7 GPa is retained, which makes the   Indentation hardness H and indentation modulus EI of non-reactively sputtered coatings with 0, 23.6, and 25.5at% B (on sapphire substrates) after vacuum annealing up to 1200°C for 10 min.Even after vacuum annealing to 1200°C, a hardness of 42.9 and 43.7 GPa is retained in both multi-element boronnitride coatings, while the Zr(N,C) coating gradually loses about 6 GPa (from the % 36GPa in its as-deposited state).

Fig. 1 .
Fig. 1. a) Energy of formation E f for four different structures as function of their B concentration on the non-metal sublattice xB : a (hcp AlB 2 -prototype), fcc 1:1 and 2:1 (NaClprototype without vacancies and with 50% vacancies on the non-metal sublattice), thus the Me: (N,B) ratio is 1:1 or 2:1), and FeB (orthorhombic).The fcc 1:1 structure is preferred for xB 6 78at%, whereas the a-structure is preferred for xB P 91at%.Between xB=78 and 91at%, the FeB-structure also provides a competitively low energy.b) The free energy, expressed by the total energy at 0 K, the vibrational entropy (by the quasi-harmonic Debye model), and the configurational entropy, shows similar trends in the fcc 1:1 (filled symbols) and the a phase (open symbols) for all investigated B contents xB (distinguished by colors and symbols) up to a temperature of 1000 K.The differences in entropy between the two phases are therefore small and do not change the phase fields in a) significantly.

Fig. 2 .
Fig. 2. a) Unit cell angles and lattice parameters of the fcc-structure (NaCl-prototype, with 1:1 ratio between metal and non-metal) and the a-structure (AlB 2 -prototype).Each data point is based on the evaluation of 10 cells.The fcc structure clearly shows no perturbation of cell angle and lattice parameter.The latter increases linearly from 4.43 to 4.62 Å with increasing B-content on the non-metal sublattice from xB = 0 to 91at%.The a-structure on the other hand shows fluctuations for the cell angles and lattice parameters (therefore the error bars).The decreasing error-bar size with increasing B content (hence, decreasing N content) clearly indicates that this a-structure is better compatible with B than N. b) fcc-structured and c) a-structured supercell with xB = 50at% after the relaxation.The N and B atoms are the small greyish and green balls (labelled in c).The structural relaxation caused almost no change to the fcc-structure but a remarkable change to the a-structure, leading to the breaking of the hexagonal layers (which are equally populated by B and N for xB = 50at%).

Fig. 3 .
Fig. 3. Bulk (B), shear (G), and Young's modulus (E) of the two most-likely structures (based on E f calculations, Fig. 1) fcc (NaCl-prototype, with 1:1 ratio between metal and non-metal) and a (AlB 2 -prototype).Compared with the astructure the elastic moduli only mildly change for the fcc structure with varying the B content on the non-metal sublattice xB.The high G and E values of the astructure for xB = 1, decline sharply when N substitutes for B at the non-metalsublattice.

Fig. 5 .
Fig. 5. Projected and total density of states of N, B, and the summarized metals for the relaxed fcc (left-column) and a (right column) structured cells for various Bcontents on the non-metal sublattice (xB, increasing from top to bottom rows).In the fcc nitride (top left), the chemical bonds are formed by interaction of N p with Metal d states, while the core-near N s states do not participate in any case.With increasing xB, the bonding N p states are gradually replaced by B p and s states.The overlapping states shift from À5 eV to À2.5 eV.In the a-structured diboride (bottom right, xB = 1), the chemical bonds are formed between the B p and Metal d states.With the addition of N, the peak at E À E f ¼ À4eV (for xB = 1, with contributions mainly from B p states) is flattened into a broad feature, with contributions of the N p, B p, and B s states.

3. 4 .
Thermal stability XRD investigations indicate that the non-reactively sputtered coatings experience only a marginal change of their structure upon

Fig. 7 .
Fig. 7. Ternary phase diagram of B, N, and summed metals (Me) showing the relative positions of the calculated and deposited compositions with filled and empty symbols.The non-reactively sputtered coatings lie along the MeN-MeB 2 line, while reactive sputtering leads to BN formation especially for the higher B containing films.For simplicity reasons, we counted possible O and C incorporation as N.

Fig. 8 .
Fig. 8. a) XRD patterns of as-deposited reactively sputtered coatings on Si substrates (sharp XRD reflexes and the XRD peak at 2h % 70 ).Next to the fcc reflexes, X-ray amorphous features (at 2h % 30 ) develop with increasing B content in the coating.b) XRD patterns of as-deposited non-reactively sputtered coatings on sapphire substrates (sharp XRD reflexes and the XRD peaks at 2h % 25, 53, and 83°).For all B contents investigated only a single-phase fcc structure is detected without an indication of an X-ray amorphous contribution.Indentation hardness H and indentation modulus EI of c) reactively sputtered and d) non-reactively sputtered coatings in their as-deposited state (on sapphire substrate).While H and EI drop for the reactively-sputtered coatings with B-contents above 10at%, the non-reactively sputtered coatings are superhard, peaking with 46.3 GPa for a B-content of 23.6at%.Please also note the much higher B:N ratio for the non-reactively prepared coatings.

Fig. 9 .
Fig. 9. Cross-sectional TEM micrographs of the as-deposited non-reactively prepared coating with 23.6at% B. Bright-field a) and dark-field b) investigations show a very finegrained micro-structure.Selected Area Electron Diffraction patterns from regions I and II confirm the single-phase fcc structure (reference circles shown for a = 4.75 Å).Please note the different aperture size used for region I and II, therefore a more ring-like pattern is obtained for region II, although there the overall column size is even slightly larger than in region I.

Fig. 10 .
Fig. 10.XRD patterns of non-reactively sputtered a) Zr(N,C) and b) multi-element boronnitride with 25.5at% B, in their as-deposited state and after vacuum annealing at up to 1200°C for 10 min.The multi-element coating retains its single-phase fcc structure even after annealing to 1200°C.Only the formation of surface oxides (reference positions for c-ZrO 2 are shown) by residual O 2 are visible.The only other notable change is a slight decrease of the lattice parameter, shown in c), calculated from the shift of the (111) XRD reflex.The B-alloying leads to highly strained lattices and broad peaks, visible from the FWHM of the (111) reflex in d).The peak width is basically independent of the thermal treatment.

Fig. 11 .
Fig.11.Indentation hardness H and indentation modulus EI of non-reactively sputtered coatings with 0, 23.6, and 25.5at% B (on sapphire substrates) after vacuum annealing up to 1200°C for 10 min.Even after vacuum annealing to 1200°C, a hardness of 42.9 and 43.7 GPa is retained in both multi-element boronnitride coatings, while the Zr(N,C) coating gradually loses about 6 GPa (from the % 36GPa in its as-deposited state).