TY - JOUR

T1 - Hardness and fracture toughness enhancement in transition metal diboride multilayer films with structural variations

AU - Vidis, Marek

AU - Fiantok, Tomas

AU - Gocnik, Marek

AU - Svec, Peter Jr

AU - Nagy, Stefan

AU - Truchly, Martin

AU - Izai, Vitalii

AU - Roch, Tomas

AU - Satrapinskyy, Leonid

AU - Sroba, Viktor

AU - Meindlhumer, Michael

AU - Grancic, Branislav

AU - Kus, Peter

AU - Keckes, Jozef

AU - Mikula, Marian

PY - 2024/3/21

Y1 - 2024/3/21

N2 - The simultaneous enhancement of hardness (H) and fracture toughness (KIC) through the formation of superlattice structures challenges the conventional belief that these quantities are mutually exclusive. Here, this approach has been applied to the transition metal diborides, whose inherent brittleness severely restricts their application potential. The mechanical properties of TiB2/TaB2 systems as a function of bi-layer period Λ are investigated, combining theoretical and experimental approaches. Density Functional Theory is used to investigate the structural stability and mechanical properties of stoichiometric hexagonal TiB2/TaB2 superlattices for Λ = 3.9 – 11.9 nm. The calculations predict the highest H = 38 GPa and KIC (100) of 3.3 MPa.m1/2 at the value of Λ = 5.2 nm. Motivated by the theoretical results, multilayer films with Λ = 4–40 nm were prepared by direct current magnetron sputtering. Due to the sputtering effects, the deposited diboride films differ significantly from the view of stoichiometry and structure. A detailed structure investigation reveals TiB2/TaB2 in form of superlattices exhibiting coherent interfaces for Λ = 4 nm. For higher Λ, parts of TaB2 layers transform from the crystalline to the disordered phase. These transformations are reflected in the mechanical properties as measured by nanoindentation and micromechanical bending tests. The evolution of hardness follows Hall-Petch behavior, reaching a maximum of 42 GPa at Λ = 6 nm. Enhancing fracture toughness involves more complex mechanisms resulting in two KIC maxima: 3.8 MPa.m1/2 at Λ = 6 nm and 3.7 MPa.m1/2 at Λ = 40 nm.Graphical abstractImage, graphical abstract Download: Download high-res image (420KB) Download: Download full-size imagePrevious article in issueNext article in issueKeywordsSuperlatticesHard filmsFracture toughnessDFTTiB2/TaB21. IntroductionTransition metal diborides (TMB2), which are classified as Ultra High Temperature Ceramics (UHTC), attract significant attention in demanding industrial applications due to their outstanding characteristics such as high temperature stability, chemical inertness, and excellent mechanical properties [1,2]. Thin films of TMB2 are usually synthesized by means of magnetron sputtering, using a stoichiometric compound target in an inert argon atmosphere. Deposition processes are characterized by two fundamental aspects that determine the resulting structure of these films. The first aspect is the different angular distribution of sputtered species, leading to the growth of overstoichiometric TMB2+x films consisting of hex‑TMB2 nanocolumns surrounded by a thin B-rich tissue phase. A typical representative is TiB2+x film, which exhibits extreme hardness values >40 GPa because of the high cohesive strength between the B-rich tissue phase and the intrinsically hard nanocolumns [3,4]. The second aspect is related to the re-sputtering of light boron atoms from the growing films. This effect results in the formation of understoichiometric TMB2-x films, characterized by the presence of boron vacancies in the lattice or a highly disordered structure. This was observed in films containing heavy transition metals (e.g. TaB2 [5], MoB2 [6], or WB2 [7]), where the achievement of high hardness is attributed to different mechanisms, including boron vacancy induced hardening [8].Unfortunately, the high hardness of TMB2 films is accompanied by typically brittle behavior under mechanical load, which significantly limits their application potential. The low fracture toughness, i.e., tendency for micro-cracks initiation and propagation, stems from the poor plastic deformation ability (low ductility) of crystalline grains, due to strong ionic and covalent bonds as well as a low number of slip systems within the nanocolumns' hexagonal structure. Furthermore, the B-rich tissue phase promotes the growth and propagation of micro-cracks, which damages the films irreversibly [9,10].One potential approach to enhance the fracture mechanical properties of TMB2 films, while maintaining their high hardness is the concept of multilayers or lattice-coherent superlattices (SL) composed of periodically alternating layers with a thickness of several nanometers. This idea was successfully used in TM nitride films, where tens of percent increase in hardness was obtained for the optimal bi-layer period Λ [11], [12], [13], [14]. In addition to hardening, recent studies devoted to TM nitrides films have demonstrated that the differences in lattice parameters and shear moduli at the sharp interfaces between nanolayers, effectively reduce the propagation of micro-cracks and thus enhance the toughness [12,13].Pioneering experimental work in this area was published by Daniel et al. [15] on improving the fracture toughness of multilayer systems based on alternating the crystalline TiN and amorphous SiO2 nanolayers. A significant difference in the elastic moduli and the optimal number of bi-layers are responsible for the 60 % increase in fracture toughness (KIC value) compared to the monolithic constituents. Similarly, in the case of multilayer CrN(100)/Cr(100) system, a significant anisotropy of the elastic moduli of both constituents improved the fracture toughness from 3.6 to 5 MPa.m1/2 in comparison with the monolithic films [15]. Recent research on superlattice films shows that hardness and fracture toughness can be improved simultaneously by coherency strains, shear modulus, lattice mismatch, and chemical and structural modifications of individual nanolayers. In the TiN/CrN superlattice system with a Λ = 6.2 nm, a significant increase in KIC of several tens of percent was observed, together with a slight gain in hardness [12]. Similarly, Gao et al. [16] reported an increase in hardness and KIC values of 11 % and 24 %, respectively, in the SL TiN/MoN system with a Λ = 9.9 nm, when compared to the TiN0.5Mo0.5N0.77 solid-solution. Hahn et al. [13] revealed a comparable improvement in the mechanical properties of the SL MoN/TaN system, with a 9 % increase in hardness and 23 % increase in KIC for Λ = 3 and Λ = 6 nm, respectively. On the other hand, Buchinger et al. [17] found a larger optimal bi-layer period of 10.2 nm for the TiN/WN SL system and observed an increase in KIC by ≈35 % (4.6 MPa.m1/2).Until recently, attention was primarily focused on cubic TM nitrides, and only a small number of studies were devoted to TMB2 films which typically crystallize in a hexagonal AlB2 type structure - P6/mmm, abbreviated as α. A theoretical work by Fiantok et al. [18] identified possible candidates for TMB2 superlattices using ab initio calculations. Considering the energetic stability, restrictions Δa < 4 %, ΔG > 40 GPa, and elastic constants the most promising TM combination were suggested. Although the used superlattice model does not account for the B-tissue phase and different bi-layer periods, this study provides an atomic-scale basis for preparation of films with enhanced toughness.Experimentally, Hahn et al. [19] studied the mechanical properties and fracture toughness of sputtered TMB2/TMB2 superlattice films, where TM = Ti, Zr, and W. A considerable lattice mismatch and a small difference in shear modulus (Δa = 0.14 Å and ΔG = 27 GPa) are characteristic for the TiB2/ZrB2 SL system. On the other hand, the TiB2/WB2 SL system exhibits a small lattice mismatch and a large difference in shear modulus (Δa = 0.01 Å and ΔG = 112 GPa). It has been shown that the increase in hardness is related to the large ΔG differences in the TiB2/WB2 SL system, where the highest hardness of 45 GPa (an increase of 12 % compared to binary constituents) was observed for Λ = 6 nm. In contrast, the optimal thickness of the bi-layer period and the large lattice mismatch between the individual nanolayers in the TiB2/ZrB2 system positively influence the increase in the KIC value. The highest value of KIC = 3.7 MPa.m1/2 was measured for Λ = 6 nm, which is almost 20 % higher than the KIC values for TiB2 and ZrB2, respectively.In the present study, we focus on the structure, mechanical properties, and fracture toughness of TiB2/TaB2 multilayers with bi-layer period thicknesses ranging from 4 nm to 40 nm. This selection meets the theoretical criteria of Δa < 4 %, ΔG > 40 GPa. Moreover, due to the opposite sputter-related effects, the experimentally prepared multilayers combine the B-rich TiB2+x and, B-deficient TaB2-y nanolayers. The results show that the thickness of the bi-layer period Λ has a significant effect on the structural character of the multilayers, which ranges from a coherent superlattice for low Λ values to a combination of crystalline TiB2 and disordered TaB2 nanolayers for higher Λ values. These changes have affected the mechanical properties of TiB2/TaB2 films, which are associated with the formation of coherent or incoherent interfaces. The highest increase in hardness and fracture toughness is observed for the optimal Λ = 6 nm.2. Experimental and computational details2.1. Computational detailsDensity functional theory (DFT) calculations were performed using QUANTUM ESPRESSO version 6.4.1. utilizing the projector-augmented wave [20], the Perdew-Burke-Ernzerhof parametrization of the electronic exchange-correlation functional [21,22] and also pseudopotentials produced using the code ONCVPSP (Optimized Norm-Conserving Vanderbilt PSeudopotential) [23] exhibiting improved convergency for higher bi-layer periods.Superlattices were modeled as α-α TiB2/TaB2 structures with different bi-layer periods of Λ = 3.9–11.7 nm using a combination of 1 × 1 × Y unit cells (where Y = 12–36) of α-type TiB2 and α-type TaB2 unit cells (with a 1:1 ratio). The total energies and structural characteristics of all SLs were assessed by relaxing cell shapes, volumes, and atomic coordinates. A plane wave energy cutoff of 80 Ry and the Brillouin zone's 9 × 9 × 5, 9 × 9 × 3, and 9 × 9 × 1 k-point grids were employed for the SLs. At two consecutive self-consistent steps the difference in total energies and forces was below 10−7 Ry and 10−5 Ry/bohr, respectively. To guarantee a total energy convergence within a few meV/atom, all plane wave energy cutoffs and k-point meshes were thoroughly chosen.The energy of formation Ef(1)was used to evaluate the chemical stability [24], where Etot(SL) is the total energy of SL, N number of atoms of SL, ni number of atoms of type i with corresponding chemical potential µi. In order to assess mechanical stability, elastic constants (Cij) were calculated using the THERMO-PW method [25] implemented in the QUANTUM ESPRESSO. Simultaneously, the satisfaction of necessary and sufficient elastic stability conditions for the elastic constants was also examined [26]. The Voight-Reuss-Hill approach [27] was used to calculate the polycrystalline bulk (B), shear (G), and Young's modulus (E) from the acquired elastic constants. Further, Poisson's ratio was also estimated [27]. Calculated elastic constants were used to obtain in-plane (parallel to the interface) CP|| = C12 – C66 and out-of plane (perpendicular to the interface) CP⊥ = C13 – C44 Cauchy pressures. Vickers hardness was estimated according to equation proposed by Chen et al. [28].To obtain the direction dependent fracture toughness KIC, the Griffith formula [29](2)for specific (hkl) = ((001), (100)) was employed, where is the separation energy between boron and metal planes (at the interface and perpendicular to the interface) andis the directional Young's modulus for 〈001〉 and 〈100〉 directions given as an inverse value of compliance tensor components S33 and S11, respectively.2.2. Deposition parametersThe multilayer TiB2/TaB2 films were prepared by magnetron sputtering on silicon (001) and sapphire (001) substrates 10 × 10 mm2. Before the deposition, substrates were ultrasonically cleaned in acetone, isopropyl alcohol, and distilled water; the chamber was evacuated to a base pressure of 8 × 10−4 Pa at 400 °C; the substrates were in-situ cleaned by Ar ions (800 V, 70 mA) for 5 min; and a ∼450 nm thick Cr buffer layer was sputtered from a 100 mm Cr target (99.95 %). The multilayer films were sputtered from stoichiometric TiB2 (99.5 %) and TaB2 (99.5 %) targets (100 mm in diameter, 6 mm thick) in a 90-degree arrangement. For each layer, a rotatable substrate holder was aligned parallel to the TiB2 or TaB2 target surface, and the layer thickness was controlled by shutter-open time tS1 or tS2, respectively. The deposition of multilayer films started with the TiB2 layer. The reference 1600 nm thick TiB2 film was sputtered at 500 W, which results in a deposition rate of 0.22 nm/s. The reference 1800 nm thick TaB2 film was sputtered at 250 W, which results in a deposition rate of 0.25 nm/s. The deposition time was 120 min at a temperature of 400 °C, Ar pressure of 0.35 Pa, and target-to-sample distance of 150 mm. A series of eight samples with nominal bi-layer periods Λ of 4, 6, 8, 10, 12, 20, 30, and 40 nm (labeled as M-Λ) were prepared with the parameters listed in Table 1.Table 1. Deposition parameters of the monolithic TiB2, TaB2, and multilayer films labeled as M-4 up to M-40 with the nominal (Λnom) and X-ray reflectivity measured (ΛXRR) bi-layer period ranging from 4 to 40 nm. Parameters tS1 and tS2 denote the shutter-open times adjusted according to the deposition rates for TiB2 and TaB2 films, respectively.Empty Cell Empty Cell Empty Cell TiB2 TaB2Sample Λnom [nm] ΛXRR [nm] P [W] U [V] tS1 [s] P [W] U [V] tS2 [s]M-4 4 3.91 500 369 9 250 397 9M-6 6 5.95 500 359 14 250 381 13M-8 8 7.85 500 372 19 250 399 18M-10 10 9.82 500 364 23 250 390 22M-12 12 11.2 500 368 28 250 396 27M-20 20 20.7 500 355 46 250 354 44M-30 30 31.2 500 356 69 250 354 66M-40 40 42.6 500 359 92 250 356 88TiB2 500 364 TaB2 250 391 2.3. Chemical and structural characterizationThe elemental composition was analyzed by energy and wave dispersive spectroscopy (EDS and WDS, Oxford Instruments), calibrated with the stoichiometric TiB2 and TaB2 standards. The reported atomic concentrations are average values from five different regions measured with an accelerating voltage of 10 kV. The crystallographic structure was measured with X-ray diffraction (XRD, PANalytical X'Pert Pro) with Cu Kα radiation (0.15406 nm) in the symmetrical Bragg-Brentano (BB) and grazing incidence (GI) setups. The X-ray reflectivity (XRR) setup was used to verify the formation of sharp interfaces.The microstructure was examined by aberration-corrected scanning transmission electron microscopy (STEM, FEI Titan Themis 300) operated at 200 kV with probe convergence angle set to 17.5 mrad. The detection system was set to 24–95 mrad for the annular dark-field (DF) and 101–200 mrad for the high-angle annular dark-field (HAADF) detector. The acquired micrographs were evaluated and analyzed by CrysTBox software v1.10 [30]. Selected area electron diffraction (SAED) and Fast Fourier Transform (FFT) were used to determine the crystallographic phase and orientation. The inverse FFT (IFFT) technique was used to increase the visibility of lattice defects. Nanoscale elemental EDS mapping (STEM-EDS) was performed by FEI Super-X detector system embedded in the microscope column. The cross-section specimens were prepared by focus ion beam (FIB, Tescan Lyra workstation). The cross-section morphology of the cleaved samples was investigated by the scanning electron microscope (SEM, Thermo Fisher Scientific Apreo 2).2.4. Evaluation of mechanical propertiesThe hardness H, and effective Young's modulus E were obtained by nanoindentation with a standard Berkovich diamond tip (Anton Paar NHT2). The reported values of H and E are average values from 20 indentations calculated via the Oliver and Pharr method [31]. The used Poisson values of 0.11 for TiB2, 0.27 for TaB2, and 0.20 for all multilayer films were extracted from our DFT calculations. The indentation depth was kept below 10 % of the film thickness to minimize the influence of the sapphire substrate.The fracture toughness of the films was evaluated by in-situ micromechanical tests. The cantilever beams with a length l = 8.1–11.5 µm, width b = 2.0 µm, and thickness w = 1.3–2.3 µm (the thickness of the film) were fabricated using FIB (Tescan Lyra workstation) and inserted into SEM (LEO 982, Crossbeam 1540XB, Zeiss) equipped with a nanoindenter (PicoIndenter 85, Hysitron). The cantilevers were loaded by a sphero-conical indenter while recording the applied normal force F and beam deflection δ. The fracture stress σF can be calculated as follows(3)Subsequently, the fracture toughness KIC is calculated using the σF for the cantilever with a notch of depth a as(4)where f(a/w) is a geometry-specific shape factor [15]. The first letter of the subscript in the KIC represents the opening mode (mode I), in which the direction of tensile stress is normal to the fracture plane. In the present paper, the reported experimental and theoretical fracture toughness should be understood as the critical stress intensity factor at which the crack propagates effortlessly and unlimitedly [32].3. Results3.1. Calculation resultsAccording to the ab initio calculations of the α-TiB2/α-TaB2 system, the values of the in-plane lattice misfit Δa (1.7 %), and the difference in shear moduli ΔG (39 %) suggest the TiB2/TaB2 as an appropriate candidate for the superlattice system with improved fracture toughness [18]. The essential calculated parameters are shown in Fig. 1 and Table 2 as a function of the bi-layer period Λ in the range 3.9–11.7 nm. Panel a) shows the formation energy Ef, which monotonically increases with Λ from −0.859 eV/at. (3.9 nm) to −0.851 eV/at. (11.7 nm). That indicates a very small impact of Λ on the chemical stability of the system. After verifying the chemical stability of the SL systems for all bi-layer periods, the elastic constants have been calculated. These parameters represent a linear response of the system to the deformation as the values correspond to the slope of the stress vs. elongation relationship for small elastic stresses. A higher value of Cij indicates greater stiffness in the particular direction in which also a high hardness can be expected. At the same time, the Cij parameters were used to verify the elastic stability criteria [26] of system in the whole range of Λ.Fig 1 Download: Download high-res image (342KB) Download: Download full-size imageFig. 1. (a) Energy of formation Ef, (b) strength indicators Cij, and (c) out-of-plane (100) and in-plane (001) fracture toughness KIC as a function of the bi-layer period Λ of TiB2/TaB2 SLs.Table 2. Elastic properties of TiB2/TaB2 SLs as a function of the bi-layer period Λ. Specifically, E, G, B and G/B denote the polycrystalline elastic modulus, shear modulus, bulk modulus, and Pugh's ratio respectively. Further, ν and H are Poisson's ratio and Vickers hardness. The CP|| and CP⊥ denote directional Cauchy pressure values in the hexagonal (001) and (100) planes, respectively.define the separation energy, andare the directional Young's moduli in relevant directions in the hexagonal system.Λ [nm] E [GPa] G [GPa] B [GPa] G/B ν H [GPa] CP|| [GPa] CP⊥ [GPa] [J/m2] [J/m2] [GPa] [GPa]3.9 490 203 277 0.73 0.21 28 −100 −50 3.03 4.38 319 4995.2 558 239 279 0.86 0.17 38 −139 −112 3.10 4.39 428 5826.5 533 226 279 0.81 0.18 34 −129 −86 3.07 4.38 379 5547.8 498 207 277 0.75 0.20 29 −119 −54 3.04 4.37 309 5069.1 502 210 276 0.76 0.20 30 −126 −57 3.03 4.37 313 51110.4 496 207 277 0.75 0.20 30 −115 −53 3.03 4.40 313 50611.7 508 212 279 0.76 0.20 30 −126 −59 3.03 4.37 331 524TiB2 594 267 255 1.05 0.11 53 −250 −166 3.63 4.69 435 644TaB2 414 163 301 0.54 0.27 16 −55 56 2.91 4.11 227 418Fig. 1b depicts the C11 and C33 elastic constants, which are predicted to correlate with the in-plane and out-of-plane tensile strengths of the SLs, respectively. A considerable difference can be observed between C11 and C33, which exceed 100 GPa. This anisotropy is related to the presence of strong covalent in-plane boron bonds. With increasing Λ, the Cij elastic constants increase, reach a maximum at Λ = 5.2 nm, and decrease for larger Λ. This behavior resembles the Hall-Petch mechanism, except that in this case, interfaces play the role of grain boundaries [33]. The C33 maximum is noticeably larger compared to C11, due to the presence of interfaces in this direction. The changes in the elastic constants also project into the predicted hardness increase shown in Table 2.Fig. 1c depicts the in-plane (001) and out-of-plane (100) fracture toughness KIC. Similar to the case of Cij, a strong anisotropy of the KIC values is observed, which can be attributed to both the presence of interfaces and strong in-plane boron bonds. Nevertheless, in both directions a significant peak at Λ = 5.2 nm arises, which is larger for the (100) planes. Although the calculated KIC increase (about 0.3 MPa.m1/2) seems to be small, we note that these results are for the stoichiometric and crystalline systems with coherent interfaces.According to the Griffith Formula (2), the KIC increase originates from the separation energy Esep and directional Young's modulus E. We can thus examine the individual contribution from both variables listed in Table 2. Looking at the line for Λ = 5.2 nm both the Esep and E reach a maximum for the optimal Λ, yet the major contribution to KIC comes from the directional Young's modulus. This is the case for the 〈100〉 as well as 〈001〉 direction. For other bi-layer periods, the Esep remains almost constant, except for the increasedat Λ = 10.4 nm which is compensated by the decreased E <100>.Table 2 also lists the Poisson's value, Pugh's ratio, and Cauchy pressures. These parameters are suggested as indicators of ductile/brittle behavior, where a higher Poisson's value and lower Pugh's ratio suggest a more ductile response. According to Zeng et al. and Fiantok et al. [18,27], a positive Cauchy pressure (CP) suggests the ability of a material to respond in a more ductile manner when subjected to shear deformation. In particular, the CP|| (C12 – C66) corresponds to the in-plane shear deformation (parallel to interfaces), and the CP⊥(C12 – C44) corresponds to the out-of-plane shear deformation (orthogonal to interfaces).As can be seen in Table 2, all three parameters ν, G/B, and CP suggest a less ductile response for the SL system with Λ = 5.2 nm. A more brittle behavior is indicated for other values of Λ and for the binary TiB2. The obtained values are connected with the presence of strong covalent bonds, which are responsible for the low tendency of the system to deform plastically. An exception is observed in the case of α-TaB2, where significantly higher ν, CP, and lower G/B were obtained, which suggests a more ductile response.Based on these findings, a noticeable improvement in hardness and fracture toughness is predicted for the ideal bi-layer period Λ of 5.2 nm. Nevertheless, this enhancement is more related to the increased stiffness of the material, and according to the Poisson's value, Pugh's ratio, and Cauchy pressure, a lower ductility (an ability of material to deform plastically) is predicted.3.2. Chemical compositionThe sputter-related effects in the case of TMB2 compound targets result in a significant deviation from the boron/metal ratio of the targets. While differences in the angular distribution of Ti and B dominate the growth of highly overstoichiometric TiB3.5 (B/Ti ∼ 3.5), the boron re-sputtering due to reflected Ar neutrals leads to a highly understoichiometric TaB1.2 (B/Ta ∼ 1.2), according to our WDS measurements. Additionally, the EDS shows low oxygen content below 3 ± 1 at. %, for both titanium and tantalum diboride reference films.3.3. Crystalline structureInitial information about the crystalline structure is provided by the XRD results presented in Fig. 2a. The diffraction pattern of binary TiB3.5 film contains peaks corresponding to the diffraction of the (001), (101), and (002) planes of hex‑TiB2 phase. The presence of strong (001) and (002) reflections indicate textural character of the structure. The reflection of the Cr buffer layer also needs to be considered, as it is overlapping with the TiB2 (101) at 2θ ≈ 44° In contrast to the highly oriented TiB3.5, the diffraction pattern of the TaB1.2 film contains only one broad maximum at 2θ ≈ 42° located between the reflections of orthorhombic-TaB (111) and hexagonal-TaB2 (101), which indicates a short-range-ordered structure. Reflections belonging to the Cr buffer layer are not visible, likely due to the stronger scattering of heavy Ta atoms.Fig 2 Download: Download high-res image (1MB) Download: Download full-size imageFig. 2. (a) Symmetrical θ/2θ scans of the monolithic and multilayer films prepared on sapphire substrates. The maxima marked as n, n ± 1 are satellite peaks of the main reflections. The (hkl) indexes (top-to-bottom) mark the reference reflections (left-to-right). (b) Detail of the (101) diffraction of hexagonal TiB2 and TaB2 phases. The bcc-Cr diffraction at 2θ = 44.37° overlaps with the hex‑TiB2 (101). (c) Representative X-ray reflectivity of selected samples M-4, M-10 and M-40.In the case of multilayered TiB2/TaB2 structures M-4 up to M-40, sharp interfaces are formed as indicated by the repeating peaks in the X-ray reflectivity shown in Fig. 2c. The XRD of M-4 film with the smallest bi-layer period of 4 nm shows a strong peak at 2θ ≈ 27° which corresponds to the overlapped (001) reflections of hex‑TiB2 and hex‑TaB2 (see the top pattern in Fig. 1a). This suggests that both nanolayers possess a crystalline structure. Moreover, strong satellite n ± 1 peaks can be identified in M-4, which indicates coherent interfaces between layers. For films with larger Λ, the satellite peaks are less distinct and closer to each other. Nevertheless, the n-1 satellite of (101) reflection is also recognizable in M-10.In addition to the satellite peaks, three main effects are observed with increasing Λ. Firstly, the strong (001) reflection of M-4 diminishes for a larger Λ of 6–40 nm. Secondly, the position of (001) shifts to higher angles. This shift can be attributed to macrostresses and variations in the stoichiometry of the layers. Thirdly, as shown in panel b), the distinguishable (101) diffraction of hex‑TaB2 in M-4 shifts to lower angles and finally becomes the broad maximum at 2θ ≈ 42° (sample M-40), which corresponds to the diffraction pattern of the monolithic TaB1.2 film. Moreover, the increase in FWHM of the TaB2 (101) peak indicates a decreasing volume of the coherent domains, which suggests that the TaB2 layer becomes disordered with increasing Λ. According to these results, the structural character of TiB2/TaB2 films tends to change from a superlattice, where both layers are highly ordered, to a combination of crystalline and disordered structure with increasing thickness of the bi-layer period.3.4. Transmission electron microscopySTEM investigation was conducted on three selected samples with Λ = 4, 10, and 40 nm in order to obtain a deeper understanding of the structure formation of TiB2/TaB2 multilayers during their growth. A representative view of alternating TiB2 and TaB2 layers with Λ = 10 nm, grown on a relatively rough Cr buffer layer, is presented in Fig. 3a. The cross-section STEM-HAADF micrograph shows an apparent distinction in material composition, enabling simple identification of the dark TiB2 and light TaB2 layers. Additionally, it shows the well-defined interfaces achieved through the use of automated shutters during the deposition process. The uniform distribution of sputtered metals throughout each layer is evident in the STEM-EDS map, as depicted in Fig. 3b. The thicknesses of 5 nm and 6 nm estimated from the STEM-HAADF profile correlates with the nominal thicknesses of 5.06 nm and 5.5 nm, calculated from the deposition rate and shutter open-times (listed in Table 1) for the TiB2 and TaB2 layers, respectively.Fig 3 Download: Download high-res image (2MB) Download: Download full-size imageFig. 3. (a) The cross-section STEM-HAADF micrograph of as-deposited multilayer TiB2/TaB2 film with Λ = 10 nm. (b) The STEM-EDS map shows a distinguishable TiB2 and TaB2 layers with sharp interfaces. (c-e) SAED patterns obtained from M-4, M-10, and M-40, indicating structural changes in the multilayer films.The collection of SAED patterns from extensive regions of the samples yields comprehensive insights into the nanostructural differences between TiB2/TaB2 multilayers (Figs. 3c-e). Sharp points are visible in the SAED pattern for M-4 (Fig. 3c), which suggests a crystalline, long-range-ordered structure of hexagonal diboride phases. This is in good agreement with the XRD pattern, which indicates the superlattice character of the M-4 film. However, even from the SAED pattern, it is not possible to distinguish the structure of individual layer constituents. Electron diffraction analysis conducted on the M-10 sample (Fig. 3d) reveals differences in the nanostructure's features. In this case, the intensity of the sharp points is disappearing, and the SAED pattern is rather formed by circles, indicating a slight reduction of the highly ordered structure of the crystalline phases. The SAED pattern associated with the M-40 film (Fig. 3e) displays circles surrounded by a small diffuse region. This fact indicates that both crystalline and disordered diboride phases are formed during the growth of TiB2/TaB2 multilayer films with a large bi-layer period.The degree of crystallinity is demonstrated by the STEM micrographs from larger regions of M-4, M-10, and M-40 films. Even for the sample with the smallest Λ of 4 nm (Fig. 4a and d), we can clearly recognize the sharp interfaces between dark TiB2 and bright TaB2 layers. Large coherent domains, marked as yellow regions, indicate a close-to-epitaxial growth of M-4 film. The long-range ordering observed in Fig. 4a is consistent with the inset FFT pattern with sharp points and the narrow (001) peak in the XRD pattern in Fig. 2a. The selected detail in Fig. 4d and its reconstruction by inverse FFT reveal coherent and defect-free interfaces over 46 atomic planes. In contrast, Fig. 4b shows smaller coherent domains with multiple orientations in M-10. A closer examination of the interfaces in Fig. 4e reveals imperfections in the interatomic arrangement that are probably a consequence of lattice defects. Indeed, the IFFT reconstruction clearly shows stacking faults spreading across the upper TaB2/TiB2 interface. Finally, Fig. 4c shows the films with the largest Λ of 40 nm. Here, the long-range ordering of TaB2 is absent, in accordance with XRD, where the (101) peak of TaB2 is not visible in the diffraction pattern of M-40. However, the detailed STEM-DF micrographs in Fig. 4f reveal small regions with ordered TaB2. These regions are located in the vicinity of the interface (2–4 nm), where the TaB2 layer grows on top of the crystalline TiB2.Fig 4 Download: Download high-res image (2MB) Download: Download full-size imageFig. 4. Cross-section STEM micrographs of multilayers M-4 (a,d), M-10 (b,e), and M-40 (c,f). Dark (bright) regions correspond to the TiB2 (TaB2) layers. Coherent regions with different crystal orientations are marked with yellow loops. (d) Detail of red region in panel (a), which shows coherent and defect-free interfaces for film with Λ = 4 nm. (e) Detail of red region in panel (b) and its IFFT reconstruction which depicts two stacking faults in the 〈001〉 direction spreading across the TaB2/TiB2 interface of film with Λ = 10 nm. (f) Detailed STEM-DF micrographs of film with Λ = 40 nm, which show a disordered TaB2 layer (bottom), a crystalline (nanocolumnar) TiB2 layer in between, and a semi-ordered TaB2 layer deposited subsequently.The atomically resolved HAADF micrograph of the M-4 film (Fig. 5a) provides a more detailed visualization, revealing the existence of perfectly arranged atomic planes within both the TiB2 and TaB2 layers. The presence of hex‑TiB2 and hex‑TaB2 phases in the film was identified using the analysis of FFT patterns obtained from selected regions A and B in Fig. 5a. In addition, it is important to mention that lattice-matched coherent interfaces were observed between individual layers. A comparable situation also occurs during the M-10 film's growth, as seen in Fig. 5b, where the formation of crystalline phases in both layer constituents is visible. The presence of hex‑TiB2 and hex‑TaB2 phases is confirmed by FFT patterns from selected regions A and B. However, the investigation of larger areas (see Fig. 4b) presents multiple regions with different crystalline orientations, which indicates a decrease in the coherence domain size compared to M-4 film. A cross-section STEM-HAADF micrograph of M-40 film with the TiB2 layer (dark), TaB2 layer (bright), and sharp interface between them is displayed in Fig. 5c. More details can be seen in the DF data shown in Fig. 5f. Lattice fringes are visible in the TiB2 layer's selected region A, where the presence of the hex‑TiB2 phase is indicated by sharp points in the FFT pattern. However, the nanostructure of the TaB2 layer varies with respect to the distance from the interface. While the FFT pattern demonstrates that crystalline planes from the hex‑TaB2 phase are present close to the interface (region B), the blurred FFT pattern from region C confirms that the structure becomes disordered a few nanometers (2–4 nm) away from the interface.Fig 5 Download: Download high-res image (2MB) Download: Download full-size imageFig. 5. Cross-sectional STEM analysis of samples M-4 (a,d), M-10 (b,e) and M-40 (c,f) based on HAADF (a-c) and DF (d-f) micrograph. The FFT of regions A and B (marked by squares) show the crystalline structure of hexagonal AlB2-type with the (101) orientation for M-4 and with (001) orientation for M-10, M-40. Panel f) depicts the crystalline/disordered transition between regions B and C in the film M-40 as confirmed by FFT.3.5. Mechanical propertiesThe indentation nanohardness H and effective Young's modulus E are depicted in Fig. 6a. The mechanical properties of multilayer films stem from the H & E of the monolithic constituents, which are 36.1 ± 3.1 GPa & 447 ± 27 GPa for the TiB3.5 layer, and 32.0 ± 2.5 GPa & 396 ± 17 GPa for the TaB1.2 layer, respectively. Both H and E exhibit similar behavior with increasing bi-layer period. For Λ = 4 nm, the hardness and Young's modulus are 38.1 ± 2.5 GPa & 466 ± 27 GPa, respectively. For Λ = 6–12 nm, Hall-Petch hardening occurs, and a maximum H of 42.3 ± 4.4 GPa & E of 505 ± 35 GPa are obtained for the film M-6. In the range Λ = 20–40 nm, a slight increase of H and E is observed, while both quantities lie between the values for the constituent layers.Fig 6 Download: Download high-res image (551KB) Download: Download full-size imageFig. 6. Mechanical properties of TiB3.5, TaB1.2, and multilayer films as function of Λ in the log-scale. (a) Hardness and Young's modulus obtained from the DFT calculations (dashed), and by indentation of the films prepared on sapphire substrate (solid). (b) Fracture toughness obtained from the DFT calculations (dashed), and by micromechanical bending of cantilever prepared from the films on silicon substrates. Reference values for the monolithic TiB3.5 and TaB1.2 films are shown as the last two points.The values of fracture toughness KIC measured by micromechanical bending of cantilevers prepared from selected samples are depicted in Fig. 6b. Similar to hardness, the KIC of multilayer films should stem from the values of monolithic constituents, 2.97 ± 0.53 MPa.m1/2 for TiB3.5 and 3.98 ± 0.43 MPa.m1/2 for TaB1.2, which is the highest observed value in this work. For the multilayer films, which contain both crystalline TiB3.5 and disordered TaB1.2, two trends in the experimentally measured KIC can be recognized. Firstly, the KIC significantly increases with the decreasing bi-layer period and reaches the maximum value of KIC of 3.81 ± 0.25 MPa.m1/2 for Λ = 6 nm. Further decreasing of the bi-layer period to Λ = 4 nm leads to deteriorated fracture toughness with KIC below the value for the TiB3.5 film. Secondly, an increase can be observed in sample M-40 with a larger bi-layer period when compared to the KIC of TiB3.5 and M-12 films.Fig. 6 also contains the theoretical values of H, E, and KIC obtained from the ab initio calculations. For all three parameters, the calculations are in good accordance with the experimentally observed trends. The calculated polycrystalline H, E, and the KIC in the stronger (100) plain (the dashed lines with empty data points) predict the optimal bi-layer period Λ = 5.2 nm, which is very close to the experimentally observed optimal Λ = 6 nm. In addition to the position of extremal values, the calculations also capture the significant decrease for small Λ = 4 nm for all three investigated parameters.In overall, the formation of multilayer films has a positive impact on the mechanical properties of the film, which manifests in the 17 % increase in hardness and 28 % increase in fracture toughness for Λ = 6 nm, when compared to the reference TiB3.5 film. The experimentally observed trends correspond well to the ab initio calculations, which predicts the optimal value of Λ to be 5.2 nm.4. DiscussionIn order to effectively increase the hardness and enhance the fracture toughness of diboride films, we are applying the concept of periodically alternating TM1B2/TM2B2 layers, which have a small lattice mismatch and a large difference in shear moduli. In the case of the stoichiometric, hexagonal α-TiB2 (a = 3.036 Å, c = 3.238 Å) and α-TaB2 (a = 3.098 Å, c = 3.227 Å), the small lattice mismatch Δa = 2 % allows the formation of (semi)coherent interfaces between individual layers and the growth of superlattice films. In addition, different shear moduli (ΔG = 39 %) provide a prerequisite for improving mechanical properties.However, experiments have demonstrated that TiB2 and TaB2 films represent entirely distinct systems in terms of composition and structure. While the highly overstoichiometric TiB3.5 film has a nanocolumnar structure formed by (001)-oriented filaments surrounded by excess boron, the large boron deficit in the TaB1.2 film leads to the formation of a disordered structure.The combination of the non-stoichiometry constituents in a multilayer system brings surprising findings. In contrast to the disordered monolithic TaB1.2 film, the STEM investigation of M-4 and M-10 revealed crystalline TiB2 and TaB2 layers, which were identified as hexagonal α-phases. These observations suggest that excess boron from the boron-rich layer passed into the boron-deficient layer. This compositional matching between TiB2+x and TaB2-y layers enables the formation of highly ordered hex‑TaB2 phase and coherent interfaces. In the case of multilayer M-4 with the smallest Λ, the coherent growth also manifests in the XRD pattern as distinct satellite peaks.A certain similarity can be seen in stoichiometric SiN/TiN [34] and AlN/TiN [35] superlattices. Hultman et al. [34], demonstrated that the SiNx layer, which prefers the disordered a-Si3N4 structure, acquires the crystalline c-SiN phase up to the thickness of 0.5–1.3 nm, when it grows on the surface of the TiN(001) layer. For these systems, the authors assume that the reduction of strain energy is responsible for the epitaxial interface stabilization.In our situation, the local epitaxy (at a maximum distance of 2–4 nm) is also influenced by the changes in boron concentration in the vicinity of the interface. The boron transfer may occur during deposition when the film is bombarded by the Ar ions, Ar neutrals, and heavy Ta atoms. We note that structural analyses of the multilayer films did not reveal the presence of sub-stoichiometric phases, such as orthorhombic Ta3B4 or TaB. Furthermore, the boron enrichment of the TaB2 layer during film growth is supported by theoretical calculations, which predict that the hexagonal alpha phase is preferred only for B/Ta > 1.7 [8,36].Due to the different lattice parameters of TiB2 and TaB2, it is reasonable to expect that lattice defects such as edge dislocations or stacking faults will compensate for the mismatch. Considering a mismatch of 2.0 %, a total of 24 atomic planes are required to create a shift by one half of the interatomic spacing. Nevertheless, in the case of M-4, we observe coherent and defect-free interfaces over 46 and 38 atomic planes (see HR-STEM data in Figs. 4d and 5a). As a result, these coherent interfaces will introduce tensile stress in the TiB2 layer and compressive stress in the TaB2 layer (a(TiB2) < a(TaB2)).A different situation occurs for higher bi-layer periods. In the film M-10 regions with coherent interfaces can still be found. Nevertheless, the STEM data from a larger area (Fig. 4b) reveal the presence of crystallites with different orientations and a lower coherent domain size compared to M-4. Therefore, a higher density of lattice defects can be expected in M-10. Indeed, the IFFT reconstruction from M-10 (see Fig. 4e) reveals the presence of stacking faults. According to [37] this particular defect can be classified as antiphase boundary (APB) of type 1, which does not influence the stoichiometry. However, the presence of other types of APB defects, which may compensate for the boron deficit, cannot be excluded. The observed APB-1 defect is formed at the TiB2/TaB2 interface and continues along the <001> direction through the whole TaB2 layer and across the next TaB2/TiB2 interface.The STEM analysis of the film with the largest thickness of the bi-layer period Λ = 40 nm provides further evidence of the stoichiometry related changes in the structure of TiB2/TaB2 multilayers. As might be expected given the significant excess of boron, the crystalline TiB2 nanolayer is formed by the hex‑TiB2 phase and does not change throughout the thickness. Conversely, the structure of the thick TaB2 layer undergoes significant changes. While the TaB2 layer is crystalline near the interface (Figs. 4f and 5f), where the B-enriched region forms the hex‑TaB2 phase, the subsequent decrease of boron results in the formation of a disordered structure that is structurally and compositionally similar to the monolithic TaB1.2 film.The structure and compositional evolution as a function of Λ has a significant effect on the mechanical properties. Due to the combination of several mechanisms, the hardening effect in the TiB2/TaB2 multilayers is a non-trivial phenomenon to describe. Furthermore, some of the mechanisms are Λ-dependent. Particularly those having the greatest impact on the hardness of our films with Λ from 4 to 40 nm are: i) intrinsic nature of chemical bonds; ii) difference in elastic moduli (Koehler theory) [38]; iii) density of interfaces (primary Hall-Petch); and iv) variation in chemical composition and crystalline structure.DFT calculations predict the peak in hardness at Λ = 5.2 nm. Since the model assumes stoichiometric, defect-free systems without the complex dislocation mechanism, we assume that the hardness increase is related to the nature of the chemical bonds.The influence of the variation in elastic moduli may be demonstrated on the M-4 system. Considering the Koehler theory [38,39], difference in shear moduli of 105 GPa, and the angle between the interface plane and the most available glide plane 20–57° (situation for STEM in Fig. 5a– situation for 〈001〉 growth according to XRD), it is possible to estimate the upper limit of the hardening effect to 6–13 GPa.Since the film thickness remains constant, the density of superlattice interfaces rises with decreasing Λ. According to [33], this increases the number of interfaces that the propagating dislocations must overcome, resulting in a hardening of the film. However, when the Λ decreases below a threshold value of 6 nm, the generation of dislocations is suppressed. At such low Λ, the generation and propagation of dislocations cease to be the dominant deformation mechanism (inverse Hall-Petch).In the case of TMB2, the hardness of monolithic TiB2+x [9,10] and TaB2-y [8] films is strongly dependent on their stoichiometry. This effect is important due to the notable gradient of boron content throughout the TiB2/TaB2 multilayers. According to TEM, the hex‑TaB2 phase is achieved in the 2–4 nm vicinity of the interface. At Λ = 12 nm, the effect of non-stoichiometry becomes considerable since the TaB2 far from the interface is less affected.Other effects that should not be omitted are the size and orientation of coherence domains in each layer (secondary Hall-Petch) and the lower number of slip systems compared to more common multilayers based on TM nitrides.As expected, the superlattice architecture also enhances the fracture toughness KIC, as verified by the micromechanical bending tests. The measured points in Fig. 6b exhibit two distinct trends. The first trend is observed for small Λ = 4–12 nm and is characterized by a peak at Λ = 6 nm. The increase in KIC can be attributed to the crack growth resistance of the film. This resistance originates from coherent stresses and elastic lattice strains due to mismatch at the interfaces and prevents the propagation of microcracks, which are generated during cantilever bending [13]. It is also in accordance with the work of Hahn et al. [19], where the authors show that the lattice mismatch is crucial in order to observe the KIC increase in TM1B2/TM2B2 systems.For other bi-layer periods, lower KIC values are obtained. The drop of KIC for very small Λ (4 nm in our films) was also observed in other SL systems, e.g. TiN/CrN [40]. For this system, the authors report high tensile stress in the layer with a smaller lattice parameter and missing dislocations for very small Λ, which results in the drop of toughness [40]. The decrease in KIC for Λ = 8–12 nm is a consequence of the defective structure. For thicker Λ, the regions with coherent interfaces are smaller (see STEM data for M-10) and the mismatch is compensated by the lattice defects. This causes a relaxation of the interface stresses. Moreover, films with thicker Λ contain fewer interfaces which block the propagation of microcracks. As a result, we observe an almost linear trend of decreasing KIC.Furthermore, the first trend is in agreement with the KIC obtained from DFT. The calculated KIC values stem from the elastic constants and separation energy of the multilayer systems and correctly captures the maximum KIC for Λ = 5.2 nm and steep decreases in both directions from the optimal Λ value. Similarly, to the maximum in hardness, the DFT calculations suggest that the peak in KIC has origin in the fundamental nature of chemical bonds.The second trend (Λ = 12–40 nm) of increasing KIC is related to the TaB2 layers and their structural transition. For thicker Λ, the structure of TaB2 layer changes from the crystalline hex‑TaB2 to disordered a-TaB2-y, as evidenced by the STEM observations (Fig. 5f). This transition is most likely caused by the stoichiometry variations near the interface composed of boron-rich TiB3.5 and boron-deficit TaB1.2. The measured KIC exhibits a rising trend, which ends with the highest overall value of KIC = 4.0 MPa.m1/2 obtained for the monolithic TaB1.2 layer. This second trend is readily understood when taking into account the mechanical properties of a-TaB1.2. Compared to hexagonal TaB2, the disordered TaB1.2 layer is more ductile, as suggested by a relatively low value of the Young's modulus E = 396 GPa (Fig. 6a). This causes the energy of the propagating crack to dissipate. Moreover, the ductile response of TiB1.2 is in good agreement with the work of Grančič et al. [41], who observed a plastic flow of the material after cube corner indentation. Thus, the increase of KIC for large Λ can be explained as a consequence of the increased volume fraction of the more ductile a-TaB2-y phase in the system.5. Summary and conclusionsIn an effort to acquire a deep understanding of the interface-induced strengthening and toughening effects in TMB2-based ceramic superlattices, we conducted theoretical and experimental study on TiB2/TaB2 systems. First principle DFT calculations were used to investigate the (001)-oriented, stoichiometric, hexagonal TiB2/TaB2 superlattices with bi-layer period Λ = 3.9–11.7 nm. Assessing the mechanical properties as a function of Λ reveals a Hall-Petch behavior, with the maximum hardness H = 38 GPa, and fracture toughness KIC(100) = 3.3 MPa.m1/2 at Λ = 5.2 nm. The simplicity of the model suggests that the origin of the peaks in H and KIC is given by the intrinsic nature of chemical bonds. To verify the predicted behavior, we have prepared the monolithic TiB2, TaB2 films, and TiB2/TaB2 multilayers in a wide range of Λ = 4–40 nm. In contrast to the DFT, the prepared TiB3.5 and TaB1.2 films are over- and under-stoichiometric and possess crystalline and disordered structures, respectively. Consequently, the structure of TiB2/TaB2 films changes from a superlattice with coherent interfaces to a combination of crystalline and disordered layers with increasing Λ, as observed by STEM. This transition on the nanoscale strongly influences the mechanical response.In agreement with DFT, the highest H = 42 GPa and KIC = 3.8 MPa.m1/2 of the sputtered TiB2/TaB2 films are obtained at the optimal Λ of 6 nm. In contrast to DFT, the variation in chemical composition and crystalline structure also influences the measured hardness and fracture toughness. The main contributions to the hardness enhancement can be attributed to the differences in shear moduli and the decreasing volume for the generation of dislocations with an increasing number of interfaces.A reliable evaluation of the film's fracture toughness is reached by micromechanical bending tests. The results indicate two fracture toughness maxima of 3.8 MPa.m1/2 at Λ = 6 nm and 3.7 MPa.m1/2 at Λ = 40 nm. The former can be attributed to the interface stresses due to the lattice mismatch. The latter is given by a high volume fraction of a ductile disordered-TaB1.2 phase.Declaration of competing interestThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Data availabilityThe data are available from the authors on reasonable request.AcknowledgementsThe work was supported by Slovak Research and Development Agency (Grant No. APVV-21–0042), Scientific Grant Agency (Grant No. VEGA 1/0381/19), and Operational Program Research and Development (Project No. ITMS 26210120010). P.Š. Jr. acknowledges Slovak Research and Development Agency (Grant No. APVV-19–0369), Scientific Grant Agency (Grant No. VEGA 2/0144/21). 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KúšStoichiometry, structure and mechanical properties of co-sputtered Ti 1-x Ta x B 2±Δ coatingsSurf. Coat. Technol., 367 (2019), pp. 341-348, 10.1016/j.surfcoat.2019.04.017View PDFView articleView in ScopusGoogle ScholarCited by (1) TiB1.8 single layers and epitaxial TiB2-based superlattices by magnetron sputtering using a TiB (Ti:B = 1:1) target 2024, Surface and Coatings Technology Show abstract1 Authors contributed equally.© 2024 The Author(s). Published by Elsevier B.V. on behalf of Acta Materialia Inc.Recommended articles Microstructure and materials properties of understoichiometric TiBx thin films grown by HiPIMS Surface and Coatings Technology, Volume 404, 2020, Article 126537 Jimmy Thörnberg, …, Johanna RosenView PDFAb initio supported development of TiN/MoN superlattice thin films with improved hardness and toughnessActa Materialia, Volume 231, 2022, Article 117871Zecui Gao, …, Paul Heinz MayrhoferView PDFMagnetic properties and structure of short-term annealed FeCuBPSi nanocrystalline alloysJournal of Magnetism and Magnetic Materials, Volume 590, 2024, Article 171662Beata Butvinová, …, Igor Maťko View PDFShow 3 more articlesArticle MetricsCitations Citation Indexes: 1Captures Readers: 5plumX logoView details

AB - The simultaneous enhancement of hardness (H) and fracture toughness (KIC) through the formation of superlattice structures challenges the conventional belief that these quantities are mutually exclusive. Here, this approach has been applied to the transition metal diborides, whose inherent brittleness severely restricts their application potential. The mechanical properties of TiB2/TaB2 systems as a function of bi-layer period Λ are investigated, combining theoretical and experimental approaches. Density Functional Theory is used to investigate the structural stability and mechanical properties of stoichiometric hexagonal TiB2/TaB2 superlattices for Λ = 3.9 – 11.9 nm. The calculations predict the highest H = 38 GPa and KIC (100) of 3.3 MPa.m1/2 at the value of Λ = 5.2 nm. Motivated by the theoretical results, multilayer films with Λ = 4–40 nm were prepared by direct current magnetron sputtering. Due to the sputtering effects, the deposited diboride films differ significantly from the view of stoichiometry and structure. A detailed structure investigation reveals TiB2/TaB2 in form of superlattices exhibiting coherent interfaces for Λ = 4 nm. For higher Λ, parts of TaB2 layers transform from the crystalline to the disordered phase. These transformations are reflected in the mechanical properties as measured by nanoindentation and micromechanical bending tests. The evolution of hardness follows Hall-Petch behavior, reaching a maximum of 42 GPa at Λ = 6 nm. Enhancing fracture toughness involves more complex mechanisms resulting in two KIC maxima: 3.8 MPa.m1/2 at Λ = 6 nm and 3.7 MPa.m1/2 at Λ = 40 nm.Graphical abstractImage, graphical abstract Download: Download high-res image (420KB) Download: Download full-size imagePrevious article in issueNext article in issueKeywordsSuperlatticesHard filmsFracture toughnessDFTTiB2/TaB21. IntroductionTransition metal diborides (TMB2), which are classified as Ultra High Temperature Ceramics (UHTC), attract significant attention in demanding industrial applications due to their outstanding characteristics such as high temperature stability, chemical inertness, and excellent mechanical properties [1,2]. Thin films of TMB2 are usually synthesized by means of magnetron sputtering, using a stoichiometric compound target in an inert argon atmosphere. Deposition processes are characterized by two fundamental aspects that determine the resulting structure of these films. The first aspect is the different angular distribution of sputtered species, leading to the growth of overstoichiometric TMB2+x films consisting of hex‑TMB2 nanocolumns surrounded by a thin B-rich tissue phase. A typical representative is TiB2+x film, which exhibits extreme hardness values >40 GPa because of the high cohesive strength between the B-rich tissue phase and the intrinsically hard nanocolumns [3,4]. The second aspect is related to the re-sputtering of light boron atoms from the growing films. This effect results in the formation of understoichiometric TMB2-x films, characterized by the presence of boron vacancies in the lattice or a highly disordered structure. This was observed in films containing heavy transition metals (e.g. TaB2 [5], MoB2 [6], or WB2 [7]), where the achievement of high hardness is attributed to different mechanisms, including boron vacancy induced hardening [8].Unfortunately, the high hardness of TMB2 films is accompanied by typically brittle behavior under mechanical load, which significantly limits their application potential. The low fracture toughness, i.e., tendency for micro-cracks initiation and propagation, stems from the poor plastic deformation ability (low ductility) of crystalline grains, due to strong ionic and covalent bonds as well as a low number of slip systems within the nanocolumns' hexagonal structure. Furthermore, the B-rich tissue phase promotes the growth and propagation of micro-cracks, which damages the films irreversibly [9,10].One potential approach to enhance the fracture mechanical properties of TMB2 films, while maintaining their high hardness is the concept of multilayers or lattice-coherent superlattices (SL) composed of periodically alternating layers with a thickness of several nanometers. This idea was successfully used in TM nitride films, where tens of percent increase in hardness was obtained for the optimal bi-layer period Λ [11], [12], [13], [14]. In addition to hardening, recent studies devoted to TM nitrides films have demonstrated that the differences in lattice parameters and shear moduli at the sharp interfaces between nanolayers, effectively reduce the propagation of micro-cracks and thus enhance the toughness [12,13].Pioneering experimental work in this area was published by Daniel et al. [15] on improving the fracture toughness of multilayer systems based on alternating the crystalline TiN and amorphous SiO2 nanolayers. A significant difference in the elastic moduli and the optimal number of bi-layers are responsible for the 60 % increase in fracture toughness (KIC value) compared to the monolithic constituents. Similarly, in the case of multilayer CrN(100)/Cr(100) system, a significant anisotropy of the elastic moduli of both constituents improved the fracture toughness from 3.6 to 5 MPa.m1/2 in comparison with the monolithic films [15]. Recent research on superlattice films shows that hardness and fracture toughness can be improved simultaneously by coherency strains, shear modulus, lattice mismatch, and chemical and structural modifications of individual nanolayers. In the TiN/CrN superlattice system with a Λ = 6.2 nm, a significant increase in KIC of several tens of percent was observed, together with a slight gain in hardness [12]. Similarly, Gao et al. [16] reported an increase in hardness and KIC values of 11 % and 24 %, respectively, in the SL TiN/MoN system with a Λ = 9.9 nm, when compared to the TiN0.5Mo0.5N0.77 solid-solution. Hahn et al. [13] revealed a comparable improvement in the mechanical properties of the SL MoN/TaN system, with a 9 % increase in hardness and 23 % increase in KIC for Λ = 3 and Λ = 6 nm, respectively. On the other hand, Buchinger et al. [17] found a larger optimal bi-layer period of 10.2 nm for the TiN/WN SL system and observed an increase in KIC by ≈35 % (4.6 MPa.m1/2).Until recently, attention was primarily focused on cubic TM nitrides, and only a small number of studies were devoted to TMB2 films which typically crystallize in a hexagonal AlB2 type structure - P6/mmm, abbreviated as α. A theoretical work by Fiantok et al. [18] identified possible candidates for TMB2 superlattices using ab initio calculations. Considering the energetic stability, restrictions Δa < 4 %, ΔG > 40 GPa, and elastic constants the most promising TM combination were suggested. Although the used superlattice model does not account for the B-tissue phase and different bi-layer periods, this study provides an atomic-scale basis for preparation of films with enhanced toughness.Experimentally, Hahn et al. [19] studied the mechanical properties and fracture toughness of sputtered TMB2/TMB2 superlattice films, where TM = Ti, Zr, and W. A considerable lattice mismatch and a small difference in shear modulus (Δa = 0.14 Å and ΔG = 27 GPa) are characteristic for the TiB2/ZrB2 SL system. On the other hand, the TiB2/WB2 SL system exhibits a small lattice mismatch and a large difference in shear modulus (Δa = 0.01 Å and ΔG = 112 GPa). It has been shown that the increase in hardness is related to the large ΔG differences in the TiB2/WB2 SL system, where the highest hardness of 45 GPa (an increase of 12 % compared to binary constituents) was observed for Λ = 6 nm. In contrast, the optimal thickness of the bi-layer period and the large lattice mismatch between the individual nanolayers in the TiB2/ZrB2 system positively influence the increase in the KIC value. The highest value of KIC = 3.7 MPa.m1/2 was measured for Λ = 6 nm, which is almost 20 % higher than the KIC values for TiB2 and ZrB2, respectively.In the present study, we focus on the structure, mechanical properties, and fracture toughness of TiB2/TaB2 multilayers with bi-layer period thicknesses ranging from 4 nm to 40 nm. This selection meets the theoretical criteria of Δa < 4 %, ΔG > 40 GPa. Moreover, due to the opposite sputter-related effects, the experimentally prepared multilayers combine the B-rich TiB2+x and, B-deficient TaB2-y nanolayers. The results show that the thickness of the bi-layer period Λ has a significant effect on the structural character of the multilayers, which ranges from a coherent superlattice for low Λ values to a combination of crystalline TiB2 and disordered TaB2 nanolayers for higher Λ values. These changes have affected the mechanical properties of TiB2/TaB2 films, which are associated with the formation of coherent or incoherent interfaces. The highest increase in hardness and fracture toughness is observed for the optimal Λ = 6 nm.2. Experimental and computational details2.1. Computational detailsDensity functional theory (DFT) calculations were performed using QUANTUM ESPRESSO version 6.4.1. utilizing the projector-augmented wave [20], the Perdew-Burke-Ernzerhof parametrization of the electronic exchange-correlation functional [21,22] and also pseudopotentials produced using the code ONCVPSP (Optimized Norm-Conserving Vanderbilt PSeudopotential) [23] exhibiting improved convergency for higher bi-layer periods.Superlattices were modeled as α-α TiB2/TaB2 structures with different bi-layer periods of Λ = 3.9–11.7 nm using a combination of 1 × 1 × Y unit cells (where Y = 12–36) of α-type TiB2 and α-type TaB2 unit cells (with a 1:1 ratio). The total energies and structural characteristics of all SLs were assessed by relaxing cell shapes, volumes, and atomic coordinates. A plane wave energy cutoff of 80 Ry and the Brillouin zone's 9 × 9 × 5, 9 × 9 × 3, and 9 × 9 × 1 k-point grids were employed for the SLs. At two consecutive self-consistent steps the difference in total energies and forces was below 10−7 Ry and 10−5 Ry/bohr, respectively. To guarantee a total energy convergence within a few meV/atom, all plane wave energy cutoffs and k-point meshes were thoroughly chosen.The energy of formation Ef(1)was used to evaluate the chemical stability [24], where Etot(SL) is the total energy of SL, N number of atoms of SL, ni number of atoms of type i with corresponding chemical potential µi. In order to assess mechanical stability, elastic constants (Cij) were calculated using the THERMO-PW method [25] implemented in the QUANTUM ESPRESSO. Simultaneously, the satisfaction of necessary and sufficient elastic stability conditions for the elastic constants was also examined [26]. The Voight-Reuss-Hill approach [27] was used to calculate the polycrystalline bulk (B), shear (G), and Young's modulus (E) from the acquired elastic constants. Further, Poisson's ratio was also estimated [27]. Calculated elastic constants were used to obtain in-plane (parallel to the interface) CP|| = C12 – C66 and out-of plane (perpendicular to the interface) CP⊥ = C13 – C44 Cauchy pressures. Vickers hardness was estimated according to equation proposed by Chen et al. [28].To obtain the direction dependent fracture toughness KIC, the Griffith formula [29](2)for specific (hkl) = ((001), (100)) was employed, where is the separation energy between boron and metal planes (at the interface and perpendicular to the interface) andis the directional Young's modulus for 〈001〉 and 〈100〉 directions given as an inverse value of compliance tensor components S33 and S11, respectively.2.2. Deposition parametersThe multilayer TiB2/TaB2 films were prepared by magnetron sputtering on silicon (001) and sapphire (001) substrates 10 × 10 mm2. Before the deposition, substrates were ultrasonically cleaned in acetone, isopropyl alcohol, and distilled water; the chamber was evacuated to a base pressure of 8 × 10−4 Pa at 400 °C; the substrates were in-situ cleaned by Ar ions (800 V, 70 mA) for 5 min; and a ∼450 nm thick Cr buffer layer was sputtered from a 100 mm Cr target (99.95 %). The multilayer films were sputtered from stoichiometric TiB2 (99.5 %) and TaB2 (99.5 %) targets (100 mm in diameter, 6 mm thick) in a 90-degree arrangement. For each layer, a rotatable substrate holder was aligned parallel to the TiB2 or TaB2 target surface, and the layer thickness was controlled by shutter-open time tS1 or tS2, respectively. The deposition of multilayer films started with the TiB2 layer. The reference 1600 nm thick TiB2 film was sputtered at 500 W, which results in a deposition rate of 0.22 nm/s. The reference 1800 nm thick TaB2 film was sputtered at 250 W, which results in a deposition rate of 0.25 nm/s. The deposition time was 120 min at a temperature of 400 °C, Ar pressure of 0.35 Pa, and target-to-sample distance of 150 mm. A series of eight samples with nominal bi-layer periods Λ of 4, 6, 8, 10, 12, 20, 30, and 40 nm (labeled as M-Λ) were prepared with the parameters listed in Table 1.Table 1. Deposition parameters of the monolithic TiB2, TaB2, and multilayer films labeled as M-4 up to M-40 with the nominal (Λnom) and X-ray reflectivity measured (ΛXRR) bi-layer period ranging from 4 to 40 nm. Parameters tS1 and tS2 denote the shutter-open times adjusted according to the deposition rates for TiB2 and TaB2 films, respectively.Empty Cell Empty Cell Empty Cell TiB2 TaB2Sample Λnom [nm] ΛXRR [nm] P [W] U [V] tS1 [s] P [W] U [V] tS2 [s]M-4 4 3.91 500 369 9 250 397 9M-6 6 5.95 500 359 14 250 381 13M-8 8 7.85 500 372 19 250 399 18M-10 10 9.82 500 364 23 250 390 22M-12 12 11.2 500 368 28 250 396 27M-20 20 20.7 500 355 46 250 354 44M-30 30 31.2 500 356 69 250 354 66M-40 40 42.6 500 359 92 250 356 88TiB2 500 364 TaB2 250 391 2.3. Chemical and structural characterizationThe elemental composition was analyzed by energy and wave dispersive spectroscopy (EDS and WDS, Oxford Instruments), calibrated with the stoichiometric TiB2 and TaB2 standards. The reported atomic concentrations are average values from five different regions measured with an accelerating voltage of 10 kV. The crystallographic structure was measured with X-ray diffraction (XRD, PANalytical X'Pert Pro) with Cu Kα radiation (0.15406 nm) in the symmetrical Bragg-Brentano (BB) and grazing incidence (GI) setups. The X-ray reflectivity (XRR) setup was used to verify the formation of sharp interfaces.The microstructure was examined by aberration-corrected scanning transmission electron microscopy (STEM, FEI Titan Themis 300) operated at 200 kV with probe convergence angle set to 17.5 mrad. The detection system was set to 24–95 mrad for the annular dark-field (DF) and 101–200 mrad for the high-angle annular dark-field (HAADF) detector. The acquired micrographs were evaluated and analyzed by CrysTBox software v1.10 [30]. Selected area electron diffraction (SAED) and Fast Fourier Transform (FFT) were used to determine the crystallographic phase and orientation. The inverse FFT (IFFT) technique was used to increase the visibility of lattice defects. Nanoscale elemental EDS mapping (STEM-EDS) was performed by FEI Super-X detector system embedded in the microscope column. The cross-section specimens were prepared by focus ion beam (FIB, Tescan Lyra workstation). The cross-section morphology of the cleaved samples was investigated by the scanning electron microscope (SEM, Thermo Fisher Scientific Apreo 2).2.4. Evaluation of mechanical propertiesThe hardness H, and effective Young's modulus E were obtained by nanoindentation with a standard Berkovich diamond tip (Anton Paar NHT2). The reported values of H and E are average values from 20 indentations calculated via the Oliver and Pharr method [31]. The used Poisson values of 0.11 for TiB2, 0.27 for TaB2, and 0.20 for all multilayer films were extracted from our DFT calculations. The indentation depth was kept below 10 % of the film thickness to minimize the influence of the sapphire substrate.The fracture toughness of the films was evaluated by in-situ micromechanical tests. The cantilever beams with a length l = 8.1–11.5 µm, width b = 2.0 µm, and thickness w = 1.3–2.3 µm (the thickness of the film) were fabricated using FIB (Tescan Lyra workstation) and inserted into SEM (LEO 982, Crossbeam 1540XB, Zeiss) equipped with a nanoindenter (PicoIndenter 85, Hysitron). The cantilevers were loaded by a sphero-conical indenter while recording the applied normal force F and beam deflection δ. The fracture stress σF can be calculated as follows(3)Subsequently, the fracture toughness KIC is calculated using the σF for the cantilever with a notch of depth a as(4)where f(a/w) is a geometry-specific shape factor [15]. The first letter of the subscript in the KIC represents the opening mode (mode I), in which the direction of tensile stress is normal to the fracture plane. In the present paper, the reported experimental and theoretical fracture toughness should be understood as the critical stress intensity factor at which the crack propagates effortlessly and unlimitedly [32].3. Results3.1. Calculation resultsAccording to the ab initio calculations of the α-TiB2/α-TaB2 system, the values of the in-plane lattice misfit Δa (1.7 %), and the difference in shear moduli ΔG (39 %) suggest the TiB2/TaB2 as an appropriate candidate for the superlattice system with improved fracture toughness [18]. The essential calculated parameters are shown in Fig. 1 and Table 2 as a function of the bi-layer period Λ in the range 3.9–11.7 nm. Panel a) shows the formation energy Ef, which monotonically increases with Λ from −0.859 eV/at. (3.9 nm) to −0.851 eV/at. (11.7 nm). That indicates a very small impact of Λ on the chemical stability of the system. After verifying the chemical stability of the SL systems for all bi-layer periods, the elastic constants have been calculated. These parameters represent a linear response of the system to the deformation as the values correspond to the slope of the stress vs. elongation relationship for small elastic stresses. A higher value of Cij indicates greater stiffness in the particular direction in which also a high hardness can be expected. At the same time, the Cij parameters were used to verify the elastic stability criteria [26] of system in the whole range of Λ.Fig 1 Download: Download high-res image (342KB) Download: Download full-size imageFig. 1. (a) Energy of formation Ef, (b) strength indicators Cij, and (c) out-of-plane (100) and in-plane (001) fracture toughness KIC as a function of the bi-layer period Λ of TiB2/TaB2 SLs.Table 2. Elastic properties of TiB2/TaB2 SLs as a function of the bi-layer period Λ. Specifically, E, G, B and G/B denote the polycrystalline elastic modulus, shear modulus, bulk modulus, and Pugh's ratio respectively. Further, ν and H are Poisson's ratio and Vickers hardness. The CP|| and CP⊥ denote directional Cauchy pressure values in the hexagonal (001) and (100) planes, respectively.define the separation energy, andare the directional Young's moduli in relevant directions in the hexagonal system.Λ [nm] E [GPa] G [GPa] B [GPa] G/B ν H [GPa] CP|| [GPa] CP⊥ [GPa] [J/m2] [J/m2] [GPa] [GPa]3.9 490 203 277 0.73 0.21 28 −100 −50 3.03 4.38 319 4995.2 558 239 279 0.86 0.17 38 −139 −112 3.10 4.39 428 5826.5 533 226 279 0.81 0.18 34 −129 −86 3.07 4.38 379 5547.8 498 207 277 0.75 0.20 29 −119 −54 3.04 4.37 309 5069.1 502 210 276 0.76 0.20 30 −126 −57 3.03 4.37 313 51110.4 496 207 277 0.75 0.20 30 −115 −53 3.03 4.40 313 50611.7 508 212 279 0.76 0.20 30 −126 −59 3.03 4.37 331 524TiB2 594 267 255 1.05 0.11 53 −250 −166 3.63 4.69 435 644TaB2 414 163 301 0.54 0.27 16 −55 56 2.91 4.11 227 418Fig. 1b depicts the C11 and C33 elastic constants, which are predicted to correlate with the in-plane and out-of-plane tensile strengths of the SLs, respectively. A considerable difference can be observed between C11 and C33, which exceed 100 GPa. This anisotropy is related to the presence of strong covalent in-plane boron bonds. With increasing Λ, the Cij elastic constants increase, reach a maximum at Λ = 5.2 nm, and decrease for larger Λ. This behavior resembles the Hall-Petch mechanism, except that in this case, interfaces play the role of grain boundaries [33]. The C33 maximum is noticeably larger compared to C11, due to the presence of interfaces in this direction. The changes in the elastic constants also project into the predicted hardness increase shown in Table 2.Fig. 1c depicts the in-plane (001) and out-of-plane (100) fracture toughness KIC. Similar to the case of Cij, a strong anisotropy of the KIC values is observed, which can be attributed to both the presence of interfaces and strong in-plane boron bonds. Nevertheless, in both directions a significant peak at Λ = 5.2 nm arises, which is larger for the (100) planes. Although the calculated KIC increase (about 0.3 MPa.m1/2) seems to be small, we note that these results are for the stoichiometric and crystalline systems with coherent interfaces.According to the Griffith Formula (2), the KIC increase originates from the separation energy Esep and directional Young's modulus E. We can thus examine the individual contribution from both variables listed in Table 2. Looking at the line for Λ = 5.2 nm both the Esep and E reach a maximum for the optimal Λ, yet the major contribution to KIC comes from the directional Young's modulus. This is the case for the 〈100〉 as well as 〈001〉 direction. For other bi-layer periods, the Esep remains almost constant, except for the increasedat Λ = 10.4 nm which is compensated by the decreased E <100>.Table 2 also lists the Poisson's value, Pugh's ratio, and Cauchy pressures. These parameters are suggested as indicators of ductile/brittle behavior, where a higher Poisson's value and lower Pugh's ratio suggest a more ductile response. According to Zeng et al. and Fiantok et al. [18,27], a positive Cauchy pressure (CP) suggests the ability of a material to respond in a more ductile manner when subjected to shear deformation. In particular, the CP|| (C12 – C66) corresponds to the in-plane shear deformation (parallel to interfaces), and the CP⊥(C12 – C44) corresponds to the out-of-plane shear deformation (orthogonal to interfaces).As can be seen in Table 2, all three parameters ν, G/B, and CP suggest a less ductile response for the SL system with Λ = 5.2 nm. A more brittle behavior is indicated for other values of Λ and for the binary TiB2. The obtained values are connected with the presence of strong covalent bonds, which are responsible for the low tendency of the system to deform plastically. An exception is observed in the case of α-TaB2, where significantly higher ν, CP, and lower G/B were obtained, which suggests a more ductile response.Based on these findings, a noticeable improvement in hardness and fracture toughness is predicted for the ideal bi-layer period Λ of 5.2 nm. Nevertheless, this enhancement is more related to the increased stiffness of the material, and according to the Poisson's value, Pugh's ratio, and Cauchy pressure, a lower ductility (an ability of material to deform plastically) is predicted.3.2. Chemical compositionThe sputter-related effects in the case of TMB2 compound targets result in a significant deviation from the boron/metal ratio of the targets. While differences in the angular distribution of Ti and B dominate the growth of highly overstoichiometric TiB3.5 (B/Ti ∼ 3.5), the boron re-sputtering due to reflected Ar neutrals leads to a highly understoichiometric TaB1.2 (B/Ta ∼ 1.2), according to our WDS measurements. Additionally, the EDS shows low oxygen content below 3 ± 1 at. %, for both titanium and tantalum diboride reference films.3.3. Crystalline structureInitial information about the crystalline structure is provided by the XRD results presented in Fig. 2a. The diffraction pattern of binary TiB3.5 film contains peaks corresponding to the diffraction of the (001), (101), and (002) planes of hex‑TiB2 phase. The presence of strong (001) and (002) reflections indicate textural character of the structure. The reflection of the Cr buffer layer also needs to be considered, as it is overlapping with the TiB2 (101) at 2θ ≈ 44° In contrast to the highly oriented TiB3.5, the diffraction pattern of the TaB1.2 film contains only one broad maximum at 2θ ≈ 42° located between the reflections of orthorhombic-TaB (111) and hexagonal-TaB2 (101), which indicates a short-range-ordered structure. Reflections belonging to the Cr buffer layer are not visible, likely due to the stronger scattering of heavy Ta atoms.Fig 2 Download: Download high-res image (1MB) Download: Download full-size imageFig. 2. (a) Symmetrical θ/2θ scans of the monolithic and multilayer films prepared on sapphire substrates. The maxima marked as n, n ± 1 are satellite peaks of the main reflections. The (hkl) indexes (top-to-bottom) mark the reference reflections (left-to-right). (b) Detail of the (101) diffraction of hexagonal TiB2 and TaB2 phases. The bcc-Cr diffraction at 2θ = 44.37° overlaps with the hex‑TiB2 (101). (c) Representative X-ray reflectivity of selected samples M-4, M-10 and M-40.In the case of multilayered TiB2/TaB2 structures M-4 up to M-40, sharp interfaces are formed as indicated by the repeating peaks in the X-ray reflectivity shown in Fig. 2c. The XRD of M-4 film with the smallest bi-layer period of 4 nm shows a strong peak at 2θ ≈ 27° which corresponds to the overlapped (001) reflections of hex‑TiB2 and hex‑TaB2 (see the top pattern in Fig. 1a). This suggests that both nanolayers possess a crystalline structure. Moreover, strong satellite n ± 1 peaks can be identified in M-4, which indicates coherent interfaces between layers. For films with larger Λ, the satellite peaks are less distinct and closer to each other. Nevertheless, the n-1 satellite of (101) reflection is also recognizable in M-10.In addition to the satellite peaks, three main effects are observed with increasing Λ. Firstly, the strong (001) reflection of M-4 diminishes for a larger Λ of 6–40 nm. Secondly, the position of (001) shifts to higher angles. This shift can be attributed to macrostresses and variations in the stoichiometry of the layers. Thirdly, as shown in panel b), the distinguishable (101) diffraction of hex‑TaB2 in M-4 shifts to lower angles and finally becomes the broad maximum at 2θ ≈ 42° (sample M-40), which corresponds to the diffraction pattern of the monolithic TaB1.2 film. Moreover, the increase in FWHM of the TaB2 (101) peak indicates a decreasing volume of the coherent domains, which suggests that the TaB2 layer becomes disordered with increasing Λ. According to these results, the structural character of TiB2/TaB2 films tends to change from a superlattice, where both layers are highly ordered, to a combination of crystalline and disordered structure with increasing thickness of the bi-layer period.3.4. Transmission electron microscopySTEM investigation was conducted on three selected samples with Λ = 4, 10, and 40 nm in order to obtain a deeper understanding of the structure formation of TiB2/TaB2 multilayers during their growth. A representative view of alternating TiB2 and TaB2 layers with Λ = 10 nm, grown on a relatively rough Cr buffer layer, is presented in Fig. 3a. The cross-section STEM-HAADF micrograph shows an apparent distinction in material composition, enabling simple identification of the dark TiB2 and light TaB2 layers. Additionally, it shows the well-defined interfaces achieved through the use of automated shutters during the deposition process. The uniform distribution of sputtered metals throughout each layer is evident in the STEM-EDS map, as depicted in Fig. 3b. The thicknesses of 5 nm and 6 nm estimated from the STEM-HAADF profile correlates with the nominal thicknesses of 5.06 nm and 5.5 nm, calculated from the deposition rate and shutter open-times (listed in Table 1) for the TiB2 and TaB2 layers, respectively.Fig 3 Download: Download high-res image (2MB) Download: Download full-size imageFig. 3. (a) The cross-section STEM-HAADF micrograph of as-deposited multilayer TiB2/TaB2 film with Λ = 10 nm. (b) The STEM-EDS map shows a distinguishable TiB2 and TaB2 layers with sharp interfaces. (c-e) SAED patterns obtained from M-4, M-10, and M-40, indicating structural changes in the multilayer films.The collection of SAED patterns from extensive regions of the samples yields comprehensive insights into the nanostructural differences between TiB2/TaB2 multilayers (Figs. 3c-e). Sharp points are visible in the SAED pattern for M-4 (Fig. 3c), which suggests a crystalline, long-range-ordered structure of hexagonal diboride phases. This is in good agreement with the XRD pattern, which indicates the superlattice character of the M-4 film. However, even from the SAED pattern, it is not possible to distinguish the structure of individual layer constituents. Electron diffraction analysis conducted on the M-10 sample (Fig. 3d) reveals differences in the nanostructure's features. In this case, the intensity of the sharp points is disappearing, and the SAED pattern is rather formed by circles, indicating a slight reduction of the highly ordered structure of the crystalline phases. The SAED pattern associated with the M-40 film (Fig. 3e) displays circles surrounded by a small diffuse region. This fact indicates that both crystalline and disordered diboride phases are formed during the growth of TiB2/TaB2 multilayer films with a large bi-layer period.The degree of crystallinity is demonstrated by the STEM micrographs from larger regions of M-4, M-10, and M-40 films. Even for the sample with the smallest Λ of 4 nm (Fig. 4a and d), we can clearly recognize the sharp interfaces between dark TiB2 and bright TaB2 layers. Large coherent domains, marked as yellow regions, indicate a close-to-epitaxial growth of M-4 film. The long-range ordering observed in Fig. 4a is consistent with the inset FFT pattern with sharp points and the narrow (001) peak in the XRD pattern in Fig. 2a. The selected detail in Fig. 4d and its reconstruction by inverse FFT reveal coherent and defect-free interfaces over 46 atomic planes. In contrast, Fig. 4b shows smaller coherent domains with multiple orientations in M-10. A closer examination of the interfaces in Fig. 4e reveals imperfections in the interatomic arrangement that are probably a consequence of lattice defects. Indeed, the IFFT reconstruction clearly shows stacking faults spreading across the upper TaB2/TiB2 interface. Finally, Fig. 4c shows the films with the largest Λ of 40 nm. Here, the long-range ordering of TaB2 is absent, in accordance with XRD, where the (101) peak of TaB2 is not visible in the diffraction pattern of M-40. However, the detailed STEM-DF micrographs in Fig. 4f reveal small regions with ordered TaB2. These regions are located in the vicinity of the interface (2–4 nm), where the TaB2 layer grows on top of the crystalline TiB2.Fig 4 Download: Download high-res image (2MB) Download: Download full-size imageFig. 4. Cross-section STEM micrographs of multilayers M-4 (a,d), M-10 (b,e), and M-40 (c,f). Dark (bright) regions correspond to the TiB2 (TaB2) layers. Coherent regions with different crystal orientations are marked with yellow loops. (d) Detail of red region in panel (a), which shows coherent and defect-free interfaces for film with Λ = 4 nm. (e) Detail of red region in panel (b) and its IFFT reconstruction which depicts two stacking faults in the 〈001〉 direction spreading across the TaB2/TiB2 interface of film with Λ = 10 nm. (f) Detailed STEM-DF micrographs of film with Λ = 40 nm, which show a disordered TaB2 layer (bottom), a crystalline (nanocolumnar) TiB2 layer in between, and a semi-ordered TaB2 layer deposited subsequently.The atomically resolved HAADF micrograph of the M-4 film (Fig. 5a) provides a more detailed visualization, revealing the existence of perfectly arranged atomic planes within both the TiB2 and TaB2 layers. The presence of hex‑TiB2 and hex‑TaB2 phases in the film was identified using the analysis of FFT patterns obtained from selected regions A and B in Fig. 5a. In addition, it is important to mention that lattice-matched coherent interfaces were observed between individual layers. A comparable situation also occurs during the M-10 film's growth, as seen in Fig. 5b, where the formation of crystalline phases in both layer constituents is visible. The presence of hex‑TiB2 and hex‑TaB2 phases is confirmed by FFT patterns from selected regions A and B. However, the investigation of larger areas (see Fig. 4b) presents multiple regions with different crystalline orientations, which indicates a decrease in the coherence domain size compared to M-4 film. A cross-section STEM-HAADF micrograph of M-40 film with the TiB2 layer (dark), TaB2 layer (bright), and sharp interface between them is displayed in Fig. 5c. More details can be seen in the DF data shown in Fig. 5f. Lattice fringes are visible in the TiB2 layer's selected region A, where the presence of the hex‑TiB2 phase is indicated by sharp points in the FFT pattern. However, the nanostructure of the TaB2 layer varies with respect to the distance from the interface. While the FFT pattern demonstrates that crystalline planes from the hex‑TaB2 phase are present close to the interface (region B), the blurred FFT pattern from region C confirms that the structure becomes disordered a few nanometers (2–4 nm) away from the interface.Fig 5 Download: Download high-res image (2MB) Download: Download full-size imageFig. 5. Cross-sectional STEM analysis of samples M-4 (a,d), M-10 (b,e) and M-40 (c,f) based on HAADF (a-c) and DF (d-f) micrograph. The FFT of regions A and B (marked by squares) show the crystalline structure of hexagonal AlB2-type with the (101) orientation for M-4 and with (001) orientation for M-10, M-40. Panel f) depicts the crystalline/disordered transition between regions B and C in the film M-40 as confirmed by FFT.3.5. Mechanical propertiesThe indentation nanohardness H and effective Young's modulus E are depicted in Fig. 6a. The mechanical properties of multilayer films stem from the H & E of the monolithic constituents, which are 36.1 ± 3.1 GPa & 447 ± 27 GPa for the TiB3.5 layer, and 32.0 ± 2.5 GPa & 396 ± 17 GPa for the TaB1.2 layer, respectively. Both H and E exhibit similar behavior with increasing bi-layer period. For Λ = 4 nm, the hardness and Young's modulus are 38.1 ± 2.5 GPa & 466 ± 27 GPa, respectively. For Λ = 6–12 nm, Hall-Petch hardening occurs, and a maximum H of 42.3 ± 4.4 GPa & E of 505 ± 35 GPa are obtained for the film M-6. In the range Λ = 20–40 nm, a slight increase of H and E is observed, while both quantities lie between the values for the constituent layers.Fig 6 Download: Download high-res image (551KB) Download: Download full-size imageFig. 6. Mechanical properties of TiB3.5, TaB1.2, and multilayer films as function of Λ in the log-scale. (a) Hardness and Young's modulus obtained from the DFT calculations (dashed), and by indentation of the films prepared on sapphire substrate (solid). (b) Fracture toughness obtained from the DFT calculations (dashed), and by micromechanical bending of cantilever prepared from the films on silicon substrates. Reference values for the monolithic TiB3.5 and TaB1.2 films are shown as the last two points.The values of fracture toughness KIC measured by micromechanical bending of cantilevers prepared from selected samples are depicted in Fig. 6b. Similar to hardness, the KIC of multilayer films should stem from the values of monolithic constituents, 2.97 ± 0.53 MPa.m1/2 for TiB3.5 and 3.98 ± 0.43 MPa.m1/2 for TaB1.2, which is the highest observed value in this work. For the multilayer films, which contain both crystalline TiB3.5 and disordered TaB1.2, two trends in the experimentally measured KIC can be recognized. Firstly, the KIC significantly increases with the decreasing bi-layer period and reaches the maximum value of KIC of 3.81 ± 0.25 MPa.m1/2 for Λ = 6 nm. Further decreasing of the bi-layer period to Λ = 4 nm leads to deteriorated fracture toughness with KIC below the value for the TiB3.5 film. Secondly, an increase can be observed in sample M-40 with a larger bi-layer period when compared to the KIC of TiB3.5 and M-12 films.Fig. 6 also contains the theoretical values of H, E, and KIC obtained from the ab initio calculations. For all three parameters, the calculations are in good accordance with the experimentally observed trends. The calculated polycrystalline H, E, and the KIC in the stronger (100) plain (the dashed lines with empty data points) predict the optimal bi-layer period Λ = 5.2 nm, which is very close to the experimentally observed optimal Λ = 6 nm. In addition to the position of extremal values, the calculations also capture the significant decrease for small Λ = 4 nm for all three investigated parameters.In overall, the formation of multilayer films has a positive impact on the mechanical properties of the film, which manifests in the 17 % increase in hardness and 28 % increase in fracture toughness for Λ = 6 nm, when compared to the reference TiB3.5 film. The experimentally observed trends correspond well to the ab initio calculations, which predicts the optimal value of Λ to be 5.2 nm.4. DiscussionIn order to effectively increase the hardness and enhance the fracture toughness of diboride films, we are applying the concept of periodically alternating TM1B2/TM2B2 layers, which have a small lattice mismatch and a large difference in shear moduli. In the case of the stoichiometric, hexagonal α-TiB2 (a = 3.036 Å, c = 3.238 Å) and α-TaB2 (a = 3.098 Å, c = 3.227 Å), the small lattice mismatch Δa = 2 % allows the formation of (semi)coherent interfaces between individual layers and the growth of superlattice films. In addition, different shear moduli (ΔG = 39 %) provide a prerequisite for improving mechanical properties.However, experiments have demonstrated that TiB2 and TaB2 films represent entirely distinct systems in terms of composition and structure. While the highly overstoichiometric TiB3.5 film has a nanocolumnar structure formed by (001)-oriented filaments surrounded by excess boron, the large boron deficit in the TaB1.2 film leads to the formation of a disordered structure.The combination of the non-stoichiometry constituents in a multilayer system brings surprising findings. In contrast to the disordered monolithic TaB1.2 film, the STEM investigation of M-4 and M-10 revealed crystalline TiB2 and TaB2 layers, which were identified as hexagonal α-phases. These observations suggest that excess boron from the boron-rich layer passed into the boron-deficient layer. This compositional matching between TiB2+x and TaB2-y layers enables the formation of highly ordered hex‑TaB2 phase and coherent interfaces. In the case of multilayer M-4 with the smallest Λ, the coherent growth also manifests in the XRD pattern as distinct satellite peaks.A certain similarity can be seen in stoichiometric SiN/TiN [34] and AlN/TiN [35] superlattices. Hultman et al. [34], demonstrated that the SiNx layer, which prefers the disordered a-Si3N4 structure, acquires the crystalline c-SiN phase up to the thickness of 0.5–1.3 nm, when it grows on the surface of the TiN(001) layer. For these systems, the authors assume that the reduction of strain energy is responsible for the epitaxial interface stabilization.In our situation, the local epitaxy (at a maximum distance of 2–4 nm) is also influenced by the changes in boron concentration in the vicinity of the interface. The boron transfer may occur during deposition when the film is bombarded by the Ar ions, Ar neutrals, and heavy Ta atoms. We note that structural analyses of the multilayer films did not reveal the presence of sub-stoichiometric phases, such as orthorhombic Ta3B4 or TaB. Furthermore, the boron enrichment of the TaB2 layer during film growth is supported by theoretical calculations, which predict that the hexagonal alpha phase is preferred only for B/Ta > 1.7 [8,36].Due to the different lattice parameters of TiB2 and TaB2, it is reasonable to expect that lattice defects such as edge dislocations or stacking faults will compensate for the mismatch. Considering a mismatch of 2.0 %, a total of 24 atomic planes are required to create a shift by one half of the interatomic spacing. Nevertheless, in the case of M-4, we observe coherent and defect-free interfaces over 46 and 38 atomic planes (see HR-STEM data in Figs. 4d and 5a). As a result, these coherent interfaces will introduce tensile stress in the TiB2 layer and compressive stress in the TaB2 layer (a(TiB2) < a(TaB2)).A different situation occurs for higher bi-layer periods. In the film M-10 regions with coherent interfaces can still be found. Nevertheless, the STEM data from a larger area (Fig. 4b) reveal the presence of crystallites with different orientations and a lower coherent domain size compared to M-4. Therefore, a higher density of lattice defects can be expected in M-10. Indeed, the IFFT reconstruction from M-10 (see Fig. 4e) reveals the presence of stacking faults. According to [37] this particular defect can be classified as antiphase boundary (APB) of type 1, which does not influence the stoichiometry. However, the presence of other types of APB defects, which may compensate for the boron deficit, cannot be excluded. The observed APB-1 defect is formed at the TiB2/TaB2 interface and continues along the <001> direction through the whole TaB2 layer and across the next TaB2/TiB2 interface.The STEM analysis of the film with the largest thickness of the bi-layer period Λ = 40 nm provides further evidence of the stoichiometry related changes in the structure of TiB2/TaB2 multilayers. As might be expected given the significant excess of boron, the crystalline TiB2 nanolayer is formed by the hex‑TiB2 phase and does not change throughout the thickness. Conversely, the structure of the thick TaB2 layer undergoes significant changes. While the TaB2 layer is crystalline near the interface (Figs. 4f and 5f), where the B-enriched region forms the hex‑TaB2 phase, the subsequent decrease of boron results in the formation of a disordered structure that is structurally and compositionally similar to the monolithic TaB1.2 film.The structure and compositional evolution as a function of Λ has a significant effect on the mechanical properties. Due to the combination of several mechanisms, the hardening effect in the TiB2/TaB2 multilayers is a non-trivial phenomenon to describe. Furthermore, some of the mechanisms are Λ-dependent. Particularly those having the greatest impact on the hardness of our films with Λ from 4 to 40 nm are: i) intrinsic nature of chemical bonds; ii) difference in elastic moduli (Koehler theory) [38]; iii) density of interfaces (primary Hall-Petch); and iv) variation in chemical composition and crystalline structure.DFT calculations predict the peak in hardness at Λ = 5.2 nm. Since the model assumes stoichiometric, defect-free systems without the complex dislocation mechanism, we assume that the hardness increase is related to the nature of the chemical bonds.The influence of the variation in elastic moduli may be demonstrated on the M-4 system. Considering the Koehler theory [38,39], difference in shear moduli of 105 GPa, and the angle between the interface plane and the most available glide plane 20–57° (situation for STEM in Fig. 5a– situation for 〈001〉 growth according to XRD), it is possible to estimate the upper limit of the hardening effect to 6–13 GPa.Since the film thickness remains constant, the density of superlattice interfaces rises with decreasing Λ. According to [33], this increases the number of interfaces that the propagating dislocations must overcome, resulting in a hardening of the film. However, when the Λ decreases below a threshold value of 6 nm, the generation of dislocations is suppressed. At such low Λ, the generation and propagation of dislocations cease to be the dominant deformation mechanism (inverse Hall-Petch).In the case of TMB2, the hardness of monolithic TiB2+x [9,10] and TaB2-y [8] films is strongly dependent on their stoichiometry. This effect is important due to the notable gradient of boron content throughout the TiB2/TaB2 multilayers. According to TEM, the hex‑TaB2 phase is achieved in the 2–4 nm vicinity of the interface. At Λ = 12 nm, the effect of non-stoichiometry becomes considerable since the TaB2 far from the interface is less affected.Other effects that should not be omitted are the size and orientation of coherence domains in each layer (secondary Hall-Petch) and the lower number of slip systems compared to more common multilayers based on TM nitrides.As expected, the superlattice architecture also enhances the fracture toughness KIC, as verified by the micromechanical bending tests. The measured points in Fig. 6b exhibit two distinct trends. The first trend is observed for small Λ = 4–12 nm and is characterized by a peak at Λ = 6 nm. The increase in KIC can be attributed to the crack growth resistance of the film. This resistance originates from coherent stresses and elastic lattice strains due to mismatch at the interfaces and prevents the propagation of microcracks, which are generated during cantilever bending [13]. It is also in accordance with the work of Hahn et al. [19], where the authors show that the lattice mismatch is crucial in order to observe the KIC increase in TM1B2/TM2B2 systems.For other bi-layer periods, lower KIC values are obtained. The drop of KIC for very small Λ (4 nm in our films) was also observed in other SL systems, e.g. TiN/CrN [40]. For this system, the authors report high tensile stress in the layer with a smaller lattice parameter and missing dislocations for very small Λ, which results in the drop of toughness [40]. The decrease in KIC for Λ = 8–12 nm is a consequence of the defective structure. For thicker Λ, the regions with coherent interfaces are smaller (see STEM data for M-10) and the mismatch is compensated by the lattice defects. This causes a relaxation of the interface stresses. Moreover, films with thicker Λ contain fewer interfaces which block the propagation of microcracks. As a result, we observe an almost linear trend of decreasing KIC.Furthermore, the first trend is in agreement with the KIC obtained from DFT. The calculated KIC values stem from the elastic constants and separation energy of the multilayer systems and correctly captures the maximum KIC for Λ = 5.2 nm and steep decreases in both directions from the optimal Λ value. Similarly, to the maximum in hardness, the DFT calculations suggest that the peak in KIC has origin in the fundamental nature of chemical bonds.The second trend (Λ = 12–40 nm) of increasing KIC is related to the TaB2 layers and their structural transition. For thicker Λ, the structure of TaB2 layer changes from the crystalline hex‑TaB2 to disordered a-TaB2-y, as evidenced by the STEM observations (Fig. 5f). This transition is most likely caused by the stoichiometry variations near the interface composed of boron-rich TiB3.5 and boron-deficit TaB1.2. The measured KIC exhibits a rising trend, which ends with the highest overall value of KIC = 4.0 MPa.m1/2 obtained for the monolithic TaB1.2 layer. This second trend is readily understood when taking into account the mechanical properties of a-TaB1.2. Compared to hexagonal TaB2, the disordered TaB1.2 layer is more ductile, as suggested by a relatively low value of the Young's modulus E = 396 GPa (Fig. 6a). This causes the energy of the propagating crack to dissipate. Moreover, the ductile response of TiB1.2 is in good agreement with the work of Grančič et al. [41], who observed a plastic flow of the material after cube corner indentation. Thus, the increase of KIC for large Λ can be explained as a consequence of the increased volume fraction of the more ductile a-TaB2-y phase in the system.5. Summary and conclusionsIn an effort to acquire a deep understanding of the interface-induced strengthening and toughening effects in TMB2-based ceramic superlattices, we conducted theoretical and experimental study on TiB2/TaB2 systems. First principle DFT calculations were used to investigate the (001)-oriented, stoichiometric, hexagonal TiB2/TaB2 superlattices with bi-layer period Λ = 3.9–11.7 nm. Assessing the mechanical properties as a function of Λ reveals a Hall-Petch behavior, with the maximum hardness H = 38 GPa, and fracture toughness KIC(100) = 3.3 MPa.m1/2 at Λ = 5.2 nm. The simplicity of the model suggests that the origin of the peaks in H and KIC is given by the intrinsic nature of chemical bonds. To verify the predicted behavior, we have prepared the monolithic TiB2, TaB2 films, and TiB2/TaB2 multilayers in a wide range of Λ = 4–40 nm. In contrast to the DFT, the prepared TiB3.5 and TaB1.2 films are over- and under-stoichiometric and possess crystalline and disordered structures, respectively. Consequently, the structure of TiB2/TaB2 films changes from a superlattice with coherent interfaces to a combination of crystalline and disordered layers with increasing Λ, as observed by STEM. This transition on the nanoscale strongly influences the mechanical response.In agreement with DFT, the highest H = 42 GPa and KIC = 3.8 MPa.m1/2 of the sputtered TiB2/TaB2 films are obtained at the optimal Λ of 6 nm. In contrast to DFT, the variation in chemical composition and crystalline structure also influences the measured hardness and fracture toughness. The main contributions to the hardness enhancement can be attributed to the differences in shear moduli and the decreasing volume for the generation of dislocations with an increasing number of interfaces.A reliable evaluation of the film's fracture toughness is reached by micromechanical bending tests. The results indicate two fracture toughness maxima of 3.8 MPa.m1/2 at Λ = 6 nm and 3.7 MPa.m1/2 at Λ = 40 nm. The former can be attributed to the interface stresses due to the lattice mismatch. The latter is given by a high volume fraction of a ductile disordered-TaB1.2 phase.Declaration of competing interestThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Data availabilityThe data are available from the authors on reasonable request.AcknowledgementsThe work was supported by Slovak Research and Development Agency (Grant No. APVV-21–0042), Scientific Grant Agency (Grant No. VEGA 1/0381/19), and Operational Program Research and Development (Project No. ITMS 26210120010). P.Š. Jr. acknowledges Slovak Research and Development Agency (Grant No. APVV-19–0369), Scientific Grant Agency (Grant No. VEGA 2/0144/21). 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KW - Superlattices

KW - Hard films

KW - Fracture toughness

KW - DFT

KW - TiB2/TaB2

U2 - 10.1016/j.mtla.2024.102070

DO - 10.1016/j.mtla.2024.102070

M3 - Article

VL - 34.2024

JO - Materialia

JF - Materialia

SN - 2589-1529

IS - May

M1 - 102070

ER -