Synthesis, chemical bonding, and mechanical properties of Ti–Nb–Hf ternary solid solution MAXs

Abstract

MAX phase ceramics have garnered widespread attention owing to their numerous exceptional functionalities from their emerging new phases. M-site element regulation in MAXs stands as one of the core strategies for new phase exploration and performance optimization. However, challenges lie in the compositional design and kinetic regulation to bypass the multiple intermediate phases in acquiring new MAX phases with high purity for target properties. Herein, two new MAX phases with a Ti, Nb and Hf solid solution in the M-site, namely Ti_1−xNb_1−xHf_2xAlC (2x = 0.2 and 0.4), are synthesized using the spark plasma sintering method. Density functional theory (DFT) simulations are employed to study their electronic structures, bonding status of different M–C and M–A bonds, and the corresponding elastic properties. The calculations indicate that in the solid solution MAX phase, the bond strengths follow the order of Nb–C > Hf–C > Ti–C and Nb–Al > Hf–Al > Ti–Al. The corresponding bulk modulus, shear modulus, and Young's modulus are calculated to be 165.55 GPa, 122.76 GPa, and 295.28 GPa, respectively. The mechanical properties of the as-prepared samples are investigated on microscopic and macroscopic scales as well. Specifically, Ti_0.9Nb_0.9Hf_0.2AlC exhibits leading compressive strength of 1574.77 ± 31.15 MPa and fracture toughness of 7.14 ± 0.05 MPa m^1/2 among the reported MAX phases. This work highlights the superiority of M-site composition regulation in boosting the mechanical properties of MAX phase ceramics.

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Hong Yu

Hong Yu is currently an associate professor in the School of Materials Science and Engineering at Northwestern Polytechnical University. She received her PhD degree in 2016 from the School of Materials Science and Engineering of Nanyang Technological University. She continued her research as a postdoctoral research fellow in Nanyang Technological University prior to joining Northwestern Polytechnical University in 2017. Currently, her research focuses on the design and synthesis of advanced functional materials for energy storage and tribological applications.

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Introduction

The advantages of both ceramics and metals are integrated into an emerging class of transition metal carbide/nitride nanolaminates—the MAX phase ceramics. With excellent electrical/thermal conductivity, oxidation resistance, corrosion resistance, tribological performance and easy machinability, MAX phase ceramics have gained widespread attention and become a hotspot in the scientific community in recent decades.^1–3 Possessing hexagonal crystal structures (P6₃/mmc space group), MAX phase ceramics can be expressed by the general formula M_n+1AX_n (n = 1, 2, 3), where M denotes early transition metals, A represents main group elements, and X is carbon or nitrogen.^4–6 The vast reservoir of composing elements with numerous possible combinations has established a new approach to tailor specific properties of MAX phases. So far, over 300 MAX phases with new compositions have been discovered and synthesized, which have revealed a variety of fascinating composition-dependent properties.^7–9

In particular, composition design for the M-site element of MAX phase ceramics, from single to double and further to multi-elements, has been demonstrated as an effective approach in property regulation. For example, substituting 20 at% Ti with V in Ti₂AlC yielded the (Ti_0.8V_0.2)₂AlC MAX phase, which showed 29%, 36%, and 45% increases in Vickers hardness, flexural strength, and shear strength, respectively.¹⁰ Similar mechanical enhancement was also observed in the Ti/Mo solid solution (Ti_0.8Mo_0.2)₂AlC MAX phase, which exhibited enhanced Vickers hardness, flexural strength, and fracture toughness by 44%, 34%, and 136%, respectively, as compared to its Ti-containing 211 counterpart.¹¹ Not only mechanical properties but also thermoconductivity,¹² corrosion resistance,^13–18 tribological performance^19–22 and thermoelectric properties^23,24 of MAX phase ceramics can be regulated. For example, Du et al. reported an enhancement in high-temperature tribological properties upon Mo incorporation in the Cr₂TiAlC₂ MAX phase via a modified interlayer binding and optimized tribo-oxide film.²⁵ Further addition of V to produce a high entropy (TiVCrMo)₃AlC₂ revealed an increase in hardness and a strong sluggish diffusion effect of elements.²⁶ Thus, M-site solid solution in MAX phase ceramics is an innovative structure correlated property manipulation approach and is imperative for the future design of multifunctional new MAX phases.

On the other hand, the synthesis of the MAX phase with high purity is difficult due to the formation of multiple intermediate phases. Transition metal carbides, metal alloys, and metal oxides commonly occur during the heat treatment process.^27–30 Besides, the formation of hierarchical MAX phases also happens, especially when there are multiple transitional metals in the M-site with a synthetic temperature overlapping. For example, Nb₄AlC₃ 413 impurity was detected in the Nb₂AlC 211 sample by hot-press sintering at 1600 °C; comparatively, sintering at the same temperature (Ti_0.45Nb_0.55)₅AlC₄ 514 impurity was detected in the Ti/Nb solid solution (Ti_0.45Nb_0.55)₂AlC 211 sample.³¹ Therefore, although intriguing properties can be anticipated from exploring new MAX phases with M-site solid solution, the intrinsic thermodynamic instability caused by large atomic differences in M-site candidates and kinetic competition between multiple intermediate phases during synthesis has posed the fabrication of new MAX phases a challenge.

Herein, Ti, Nb and Hf solid solution 211 MAX phase ceramics are synthesized for the first time by a spark plasma sintering (SPS) method. The variation of morphology, structural information and electronic properties along with an increasing Hf concentration are investigated. Density functional theory (DFT) simulations are employed to study the electronic structure, bonding status with respect to different M–A and M–C bonds and corresponding elastic properties. Furthermore, the mechanical properties of M-site solid solution MAXs are investigated microscopically and macroscopically with their failure behaviors elucidated. Specifically, excellent compressive strength of 1574.77 ± 31.15 MPa and fracture toughness of 7.14 ± 0.05 MPa m^1/2 are achieved, implying the superiority of M-site composition regulation in boosting the mechanical properties of MAX phase ceramics.

Experimental section

Preparation of MAX phase ceramics

Graphite flake powder (99.9% purity) was sourced from Alfa Aesar. Ti₂AlC, Nb₂AlC, Al, Ti, Nb and Hf (all 99.9% purity) powders were sourced from Qinghe Benyu Metal Materials Co., Ltd. All powders required no further purification and were used as received. The experiment employed Spark Plasma Sintering (SPS) to fabricate TiNbAlC, Ti_0.9Nb_0.9Hf_0.2AlC, and Ti_0.8Nb_0.8Hf_0.4AlC. The SPS furnace was purchased from FCT Systeme GmbH. Taking TiNbAlC as an example, powders of Ti₂AlC, Nb₂AlC, and Al were blended at a Ti₂AlC : Nb₂AlC : Al molar ratio of 1 : 1 : 0.2. Under an argon atmosphere, the mixture was then subjected to two cycles of ball milling (ball miller of 8000 M Mixer/Mill®), with each cycle lasting for 30 minutes and a half-hour interval between the two cycles. Subsequently, the milled mixture was sintered by SPS at 1500 °C for 15 minutes in a furnace with flowing argon gas. The sintered block was cut into cylindrical specimens with dimensions of Φ5 × 8 mm. Polished sequentially on SiC paper to 1200 grit, all specimens were finished uniformly. For the three Hf-doped MAX ceramics, Hf powder was stoichiometrically added to the initial mixture with all other parameters held constant.

Material characterization

Using an X'Pert PRO diffractometer, all X-ray diffraction (XRD) patterns were collected over a 2θ range of 5–120 with a 0.02° scanning step size. Using Cu target Kα rays (λ = 1.5418 Å) at 0.0001° angular resolution, the test voltage was 40 V and current was 40 mA. Lattice parameters and phase purity were determined for all samples through Rietveld refinement (GSAS II). The surface of the material was analyzed using a PHI 5000 VersaProbe III X-ray photoelectron spectrometer. Measured via the Archimedes method, the sample's density and relative density were averaged from three determinations. The original morphology, cross-section, and fracture morphology of the MAX phase materials were observed using an FEI Helios G4 C FIB scanning electron microscope and a ZEISS Sigma 300 field emission scanning electron microscope. An integrated energy dispersive spectrometer integrated into these systems was employed to analyze the elemental distribution.

Mechanical property testing

After polishing the sample surface with 3000-grit sandpaper to remove impurities, on the cross-section of the specimen parallel to the sintering pressure direction, Vickers hardness and nanoindentation tests were performed. Using a 1 kgf load and 5 s dwell time, Vickers hardness was measured with a diamond indenter. Through 15–20 replicate measurements per specimen, average hardness values were determined by selecting ten concordant values. Nanoindentation tests were performed at 5 mN constant load (5 s loading, 2 s dwelling, and 5 s unloading) using a Bruker Hysitron system. The reduced modulus (E_r) and indentation hardness (H) were derived from fifteen selected measurements out of 16–20 indentations. Compression tests were performed using a CMT5105 computer-controlled electronic universal testing machine with a 100 kN load cell at 0.48 mm min⁻¹ loading speed. For compression performance testing, specimens were selected that were cylindrical with dimensions of Φ5 mm diameter and 8 mm height. Prior to testing, the specimens were progressively polished using SiC sandpaper to a final grit of 1200, and three tests were conducted to obtain the average value. Using the single-edge notched beam (SEPB) methodology, specimens (2 mm × 4 mm × 18 mm) were notched to 0.2 mm diameter and 2 mm depth. Testing was carried out on a Shandong Liangong electronic universal testing machine (50 kN load cell) at 0.05 mm min⁻¹ loading rate, with three replicates performed to calculate the average fracture toughness.

Computational methods and theory

In this study, development of the 211 MAX phase ceramic model was accomplished using a special quasi-random structure (SQS). SQS modeling³² is a method for simulating the microstructure of alloys, which involves first creating a supercell lattice structure and then randomly assigning metal elements to lattice sites to form a disordered model structure with specific short-range order. In this work, the Nb₂AlC structure was used as the initial structure, and a 2 × 2 × 1 special quasi-random structure was generated by randomly substituting Ti and Zr at the M sites of the Nb₂AlC structure using ATAT software. Within the density functional theory (DFT) framework, all calculation results in this paper were obtained through the projected augmented-wave (PAW) method implemented in the Vienna ab initio simulation package (VASP).³³ For description of the exchange–correlation effects, the Perdew–Burke–Ernzerhof (PBE) energy functional was selected under the generalized gradient approximation (GGA) framework.³⁴ The cutoff energy was set at 600 eV during computation of plane wave functions. Employing the conjugate gradient method, structural optimization was performed until the total energy change was diminished to less than 10⁻⁵ eV, and forces on all atoms were constrained below 0.02 eV Å⁻¹, preceding static calculations. For the Brillouin zone, the central gamma scheme was used to select k-points, which were set to 9 × 9 × 2. These parameters have been tested for convergence to ensure the accuracy of the calculations. Utilization of the LOBSTER code was made for computation of the crystal orbital Hamilton population (COHP) to reconstruct the orbital energies of the calculated band structure.^35–37 The stress–energy relationship method was employed for calculation of the materials' elastic constants, while the Voigt–Reuss–Hill approach was utilized to determine the bulk modulus (B), shear modulus (G), Young's modulus (E), and Poisson's ratio (ν).^38–40 The Voigt–Reuss approximations were commonly used methods for calculating these moduli. Hill proposed that the Voigt and approaches represent the modulus's upper and lower bounds, respectively, and suggested that the average of the calculation results of the Voigt model and the Reuss model be taken to obtain more accurate results. Bader charge and density of states (DOS) calculations were also conducted for the materials.

Results and discussion

Fig. 1a illustrates an exclusive 4f (2/3, 1/3, 1/12) Wyckoff position for the transition metal M to accommodate within the M₂X slab for the M₂AX phase.⁴¹ Thus, all three transition metal elements of Ti, Nb, and Hf would be located at the 4f site forming a ternary solid solution in the M₂X slabs. Initial structural characterization was performed on the Ti_1−xNb_1−xHf_2xAlC system (2x = 0, 0.2 and 0.4) through X-ray diffraction (XRD) and Rietveld refinement. As evidenced by Fig. 1b–e, all three as-prepared MAX samples have a dominant Nb₂AlC 211 phase with high purity, which are 92.5 wt%, 92.6 wt% and 85.7 wt% for TiNbAlC, Ti_0.9Nb_0.9Hf_0.2AlC and Ti_0.8Nb_0.8 Hf_0.4AlC, respectively. Moreover, the predominant Al₂O₃ impurity in all three MAX phases is attributed to the addition of excessive Al precursor, which is implemented to offset evaporation during sintering. An insignificant amount of HfO₂ impurity (0.7 wt% and 4.9 wt%, respectively) is also observed in the Ti_0.9Nb_0.9Hf_0.2AlC and Ti_0.8Nb_0.8Hf_0.4AlC samples. The lattice parameters of TiNbAlC, determined as a = b = 3.0790(8) Å and c = 13.8070(9) Å with a volume of V = 113.36(4) ų, are presented in Fig. 1f and Table S1. With increasing Hf concentration, the lattice of the 211 phase expands progressively. Specifically, Ti_0.9Nb_0.9Hf_0.2AlC exhibits a = b = 3.0980(3) Å, c = 13.8439(4) Å and V = 115.06(9) ų, while Ti_0.8Nb_0.8 Hf_0.4AlC shows a = b = 3.1122(5) Å, c = 13.8681(3) Å and V = 116.33(2) ų. This lattice expansion is explained by the larger atomic radius of Hf relative to Ti and Nb, with consistency demonstrated through the highest reported lattice constants for Hf₂AlC (a/b = 3.2757(1) Å, c = 14.3628(4) Å) in previous literature.⁴² Incorporation of Hf induces unit cell expansion, verifying that the Ti–Nb–Hf solid solution has been successfully formed within the M₂X sub-lattice. The calculated c/a ratios for TiNbAlC, Ti_0.9Nb_0.9Hf_0.2AlC and Ti_0.8Nb_0.8 Hf_0.4AlC are 4.48, 4.47, and 4.46, respectively, which fall within the characteristic 3.5–4.6 range of 211 MAX phases.⁴³

Fig. 1 (a) Schematic illustration of Ti_1−xNb_1−xHf_2x solid solution MAX ceramic. XRD data and Rietveld refinement results of (b) TiNbAlC, (c) Ti_0.9Nb_0.9Hf_0.2AlC and (d) Ti_0.8Nb_0.8Hf_0.4AlC. (e) The phase percentage and (f) the unit cell parameters of the 211 phases for the MAX ceramics.

The density of the Ti_1−xNb_1−xHf_2xAlC series was calculated using the Archimedes method. As summarized in Table S2, TiNbAlC reveals a density of 5.21 g cm⁻³, which is 98.65% of its theoretical value. With increasing Hf concentration, the density increases to 5.80 g cm⁻³ Ti_0.9Nb_0.9Hf_0.2AlC and further to 6.23 g cm⁻³ Ti_0.8Nb_0.8Hf_0.4AlC, which are 99.85% and 97.82% of their theoretical value, respectively.

The morphology and structure of the Ti_1−xNb_1−xHf_2xAlC (2x = 0, 0.2 and 0.4) series were characterized using backscattered electron (BSE) detection in scanning electron microscopy (SEM). The BSE image of TiNbAlC (Fig. 2a) reveals a dense and smooth grey matrix with dark micron/submicron size particles embedded in it. At a higher magnification, energy-dispersive spectroscopy (EDS) mapping was employed to distinguish these two phases (Fig. S1). On the grey matrix, Ti, Nb, Al and C are homogeneously distributed, which is assignable to the TiNbAlC MAX phase. Enrichment of Al and O observed on the dark micron/submicron particles is attributed to the Al₂O_x phase, and this assignment corroborated XRD results. With Hf incorporation, besides the grey matrix and dark particles, additional dispersion of bright particles is noticed in both Ti_0.9Nb_0.9Hf_0.2AlC (Fig. 2b) and Ti_0.8Nb_0.8Hf_0.4AlC (Fig. 2c). EDS mapping displays a similar homogeneous distribution of Ti, Nb, Hf, Al and C on the grey matrix and overlapping of Al and O on the dark particles for both MAXs, signifying a similar inclusion of Al₂O_x inside the Ti_0.9Nb_0.9Hf_0.2AlC and Ti_0.8Nb_0.8Hf_0.4AlC matrices (Fig. S2 and S3, respectively). Point analysis was further conducted to determine the composition of the bright particles. As revealed in Fig. S4–S7, a sharp increase in the atomic percentage of both Hf and O is observed in the bright particles as compared to the grey matrix, validating the formation of HfO_x impurity in both Ti_0.9Nb_0.9Hf_0.2AlC and Ti_0.8Nb_0.8Hf_0.4AlC. Fig. S8–S10 depict the surface morphology of etched specimens, where random orientation of slab-like grains is observed for all three samples with grain size varying from 10 μm to 20 μm in length.

Fig. 2 The BSE images of (a) TiNbAlC, (b) Ti_0.9Nb_0.9Hf_0.2AlC and (c) Ti_0.8Nb_0.8Hf_0.4AlC. High-resolution XPS spectra for the three MAX ceramics of (d) Ti 2p, (e) Nb 3d, (f) Al 2p and (g) C 1s orbitals.

The electronic status of each element in Ti_1−xNb_1−xHf_2xAlC (2x = 0, 0.2 and 0.4) series was investigated using X-ray photoelectron spectroscopy (XPS). The high-resolution Ti 2p spectrum of TiNbAlC (Fig. 2d) is deconvoluted into three 2p_3/2/2p_1/2 pairs assigned to Ti–C (454.48 and 459.58 eV), Ti³⁺ (456.36 and 460.93 eV) and Ti⁴⁺ (458.72 and 464.57 eV) species, respectively.^26,29 The high-resolution Nb 3d spectrum of TiNbAlC (Fig. 2e) exhibits three deconvoluted doublets, corresponding to distinct chemical states of Nb–C (203.08 eV and 205.80 eV), Nb⁴⁺ (204.36 eV and 207.08 eV), and Nb⁵⁺ (207.40 eV and 210.12 eV) species, respectively.^44,45 The Al electron core level in TiNbAlC (Fig. 2f) is resolved into two distinct peaks of Al–M (72.51 eV) and Al–O (74.46 eV) bonds, respectively.²⁶ In the C 1s spectrum, the binding energy at 282.75 eV confirms the presence of C–M species. While the other three peaks centered at 284.75, 286.53, and 288.74 eV correspond to the adventitious contaminants²⁹ (Fig. 2g). Similar XPS spectra and deconvoluted doublets of Ti, Nb, Al and C elements in Ti_0.9Nb_0.9Hf_0.2AlC and Ti_0.8Nb_0.8Hf_0.4AlC are observed as compared to TiNbAlC. In the high resolution Hf 4f spectra (Fig. S11), three similar characteristic 4f_5/2/4f_7/2 pairs corresponding to Hf–C, Hf^x+ and Hf⁴⁺ species are noted in both Ti_0.9Nb_0.9Hf_0.2AlC and Ti_0.8Nb_0.8Hf_0.4AlC samples, which is consistent with the coordination environment of the 4f site in the M₂C slab and HfO_x impurities.

Density functional theory (DFT) was employed to examine the electronic structure of the Ti_1−xNb_1−xHf_2xAlC solid solution system. A 2 × 2 × 1 supercell was constructed to simulate the solid solution Ti_1−xNb_1−xHf_2xAlC structure with a special quasi-random structure (SQS) in an alloy theoretical automated toolkit (ATAT). As presented in Fig. 3a, among a total of 16 4f sites, Ti takes 7 sites, Nb takes 7 sites and Hf takes 2 sites. The total and projected densities of states (DOSs) of Ti_1−xNb_1−xHf_2xAlC in Fig. 3b present a continuous pattern with a local minimum at the Fermi level (E_f), indicating the metallic nature and good stability of the Ti_1−xNb_1−xHf_2xAlC structure.⁴⁶ The orbital-resolved DOS reveals the orbital-wise contributions of each element. In the range of −7.5–−2.5 eV, states are mainly contributed by the hybridization of 3d orbitals of transition metal elements (M = Ti, Nb and Hf) and 2p orbitals of C element. While in the range of −2.5 – E_f, states are dominantly contributed by the M 3d–Al 2p hybridization. Furthermore, the bonding status of M–C and M–A bonds is revealed through the crystal orbital Hamilton population (COHP) analysis in Fig. 3c. All paired electrons in Ti–Al, Nb–Al and Hf–Al bonds appear as bonding interactions. Comparatively, in Ti–C, Nb–C and Hf–C bonds, the paired electrons reveal a majority of bonding interactions with some negligible antibonding interactions appearing close to the E_f. A similar antibonding feature in the M–C bond near the E_f was also observed in other 211 MAX phase materials.⁴⁷

Fig. 3 (a) Ti_0.875Nb_0.875Hf_0.25AlC SQS model. (b) The total and projected DOSs and (c) the average –COHP of Ti_0.875Nb_0.875Hf_0.25AlC. (d–i) The average –COHP and –ICOHP for specific bonds: (d) Ti(3)–Al(22, 23, 24) and Ti(6)–Al(18, 19, 20), (e) Nb(12)–Al(17, 19, 20) and Nb(14)–Al(21,22,23), (f) Hf(15)–Al(17,18,19) and Hf(16)–Al(17,18,20), (g) Ti(3)–C(25, 26, 27) and Ti(6)–C(25, 27, 28), (h) Nb(12)–C(30, 31, 32) and Nb(14)–C(26, 27, 28), and (i) Hf(15)–C(29, 30, 32) and Hf(16)–C(25, 26, 27).

The detailed atomic electronic interactions concerning respective coordination environments of Ti_1−xNb_1−xHf_2xAlC with respect to their bond strength were further studied by Bader charge (Fig. S12) and integrated –COHP (–ICOHP) analyses. From the structural point of view, each M₂C layer is interleaved between two Al layers, thus the M–C and M–A bonds are intertwined with each other. As revealed in Fig. 3d–i, the Hf incorporation induces higher electron donation towards the Al layer and a larger interlayer distance between Ti or Nb and the Al layer, which leads to weakened Ti–Al and Nb–Al bonds. For Ti(6) located within the same layer as Hf, the average bond strength for Ti(6)–Al(18, 19, 20) is integrated to be 1.82 eV bond⁻¹. Comparatively, for Ti(3) in a different layer as Hf, the average bond strength of Ti(3)–Al(22, 23, 24) is higher at 1.95 eV bond⁻¹. Similarly, the average bond strength of Nb(12)–Al(17, 19, 20) is 2.26 eV bond⁻¹, which is lower than that of Nb(14)–Al(21, 22, 23) at 2.42 eV bond⁻¹. For Hf, the average bond strength of Hf(16)–Al(17, 18, 20) (2.17 eV per bond) is stronger than that of Hf(15)–Al(17, 18, 19) (2.01 eV bond⁻¹). On the other hand, as Hf, Ti and Nb reveal a decreasing electronegativity difference with C from Hf/C (1.25) to Ti/C (1.01) and further to Nb/C (0.95), the ionic feature of these M–C bond decreases and thus the covalent feature increases in the order of Hf–C bond to the Ti–C bond and further to the Nb–C bond. This change in ionicity of these M–C bonds can be further validated by the electron localization function (ELF) analysis, which provides localization probability information of the same-spin electrons. Fig. S13 displays the plane intercepts of all three types of Ti–C, Nb–C and Hf–C bonds. There is a highly localized electron density around the C atom. Notably, varied electron distributions are observed on the metal atoms. Compared to the almost electron-deficient region around Hf and Ti atoms, electrons with low density are found around the Nb atom, which indicates an increased covalency of the Nb–C bond. Thus, the Hf incorporation would cause varied impacts on the M–C bond strength, which is closely related to the respective distribution of paired electrons and the coordination environment of the M atom. As observed, Ti(6)–C(25, 27, 28) delivers a higher bond strength of 3.97 eV bond⁻¹ compared to that of Ti(3)–C(25, 26, 27) at 3.88 eV bond⁻¹. This increased Ti–C bond strength is possibly ascribed to electron delocalization on the coordinated C atoms from the adjustment of other bonding M-site atoms, as well as a higher electron accumulation at the coordinated Al atoms. An opposite bonding strength trend is observed for the covalent Nb–C bond when electron delocalization on the coordinated C atoms and electron enrichment on the coordinated Al atoms occur. A lower bond strength of 4.62 eV bond⁻¹ is displayed for Nb(12)–C(30, 31, 32) compared to that of 4.77 eV bond⁻¹ for Nb(14)–C(26, 27, 28). As for the Hf–C bond, the trade-off of electron distribution on C and Al gives a slightly stronger Hf(16)–C(25, 26, 27) bond as compared to the Hf(15)–C(29, 30, 32) bond. As summarized in Table S3, the average bond strength of M–C and M–Al in the cell was calculated to be 4.19 eV bond⁻¹ and 2.12 eV bond⁻¹, respectively, with the Ti–C/Ti–Al and Hf–C/Hf–Al bonds locating at the lower strength end and the Nb–C/Nb–Al bond located at the higher strength end. The bond strength ratio of R = M–C/M–A increases in the order of R_Nb (1.958) < R_Hf (1.962) < R_Ti (2.01).

Given the anisotropic bonding properties derived from the solid solution Ti_1−xNb_1−xHf_2xAlC structure, intriguing mechanical properties are expected. Through theoretical calculations, the elastic properties of the Ti_1−xNb_1−xHf_2xAlC structure were first calculated with the second-order elastic constants c_ij, and the values are summarized in Table S4. Satisfying the Born stability criteria for hexagonal crystals: c₄₄ > 0, c₁₁ > |c₁₂|, (c₁₁ + c₁₂)c₃₃ > 2c₁₃²,⁴⁸ the Ti_1−xNb_1−xHf_2xAlC structure reveals good mechanical stability upon applied strain. Similar to the previously reported MAX phase, the Ti_1−xNb_1−xHf_2xAlC structure possesses anisotropic elastic constants.⁴⁶ Specifically, linear deformation resistance along crystallographic directions is characterized by elastic constants: c₁₁ for the a-axis and c₃₃ for the c-axis.⁴⁹ A higher value of c₁₁ than c₃₃ is displayed by Ti_1−xNb_1−xHf_2xAlC, indicating a greater resistance along the a axis. Compared to the 211 phase with a single Ti, Nb, or Hf M-site element, both the c₁₁ and c₃₃ values are higher in the Ti_1−xNb_1−xHf_2xAlC structure, suggesting enhanced elastic resistance in both directions.⁴⁶ c₄₄, a key hardness parameter and shear resistance indicator along the basal plane,⁴⁹ is smaller in Ti_0.875Nb_0.875Hf_0.25AlC than in Ti₂AlC and Nb₂AlC, suggesting lower hardness and shear strength in the solid solution Ti_1−xNb_1−xHf_2xAlC. The corresponding bulk modulus (B), shear modulus (G) and Young's modulus (E) of Ti_1−xNb_1−xHf_2xAlC were approximated by Voigt–Reuss–Hill average, which yielded 165.55, 122.76 and 295.28 GPa for these moduli, respectively (Table S5). Poisson's ratio (ν) was calculated to be 0.20. The brittleness of the structure was reviewed by the B/G ratio, where B/G >1.75 indicates ductility and lower values suggest brittleness.⁵⁰ Although the obtained B/G ratio of 1.35 of Ti_1−xNb_1−xHf_2xAlC does not fall within the ductile region, it is still higher than those of Hf₂AlC,⁵¹ Ti₃AlC₂ (ref. 52) and ZrB₁₂-based high-temperature ceramics.⁵³

The mechanical properties of the as-prepared Ti_1−xNb_1−xHf_2xAlC (2x = 0, 0.2 and 0.4) sample series were further evaluated experimentally. The nanoindentation test was utilized to determine the micromechanical properties with high spatial resolution and minimal interference from the impurity phase. As the indentation size of approximately 0.4 μm² is within one to several grain diameters in all three samples, the mechanical properties measured by the nanoindentation test intrinsically reflect the mechanical properties of these 211 grains. Fig. 4a–c depict the displacement–load curves of the three samples with similar loading, holding, and unloading stages, indicating similar elastoplastic deformation, creep and recovery response to a consistent loading. Specifically, during the loading stage, the displacement–load curves of all three samples almost overlap with each other with low slopes, suggesting low elastic moduli. In the holding stage, displacement increases with time under constant load, indicating creep deformation. Steep initial unloading segments imply high contact stiffness. After unloading, only elastic recovery occurs, leaving displacement changes from both plastic deformation and creep processes. According to the Oliver–Pharr model, the reduced elastic modulus (E) and nanoindentation hardness (H) for the three 211 MAX phase ceramics were calculated (Fig. 4d).⁵⁴ The E and H values for TiNbAlC are 214.28 and 13.40 GPa, respectively. Compared to TiNbAlC, the solid solution Ti_1−xNb_1−xHf_2xAlC (2x = 0.2 and 0.4) samples show slightly reduced E and H.

Fig. 4 Nanoindentation displacement–load curves of (a) TiNbAlC, (b) Ti_0.9Nb_0.9Hf_0.2AlC and (c) Ti_0.8Nb_0.8Hf_0.4AlC. (d) Nanoindentation hardness and converted modulus, (e) compressive strength and (f) fracture toughness of the three MAX ceramics.

Macroscopically, the hardness, compressive stress and fracture toughness of the 211 series were analyzed as well. The Vickers hardness (Fig. S14a) of TiNbAlC, Ti_0.9Nb_0.9Hf_0.2AlC, and Ti_0.8Nb_0.8Hf_0.4AlC were measured to be 5.68, 6.09, and 6.69 GPa, respectively. These values are comparable to the previously reported Ti and Nb containing single and double transition metal 211 MAX phases, i.e. Ti₂AlC at 4.2–5.7 GPa,⁵⁵ Nb₂AlC at 6.1 GPa (ref. 30) and TiNbAlC at 5.8 GPa.⁵⁶ Unlike the conventional ceramics, such as Si₃N₄ (ref. 57) and SiC⁵⁸ with crack propagation upon indentation, the typical indentation morphology of TiNbAlC (Fig. S14b) reveal high toughness without observable cracks, which is similar to MAX phases. As the size of the indention is around 70 μm, the contribution of the grain boundary and oxide impurities to the measured hardness cannot be excluded, which may possibly be the reason for the varied trend in hardness between microscopic and macroscopic scales.

The compressive stress–strain curves of all three MAX phases depict brittle behaviour (Fig. S15). Except for the toe region, the curves of the three 211 MAXs display linear correlation between stress and strain, featuring elastic deformation upon loading. As summarized in Fig. 4e, the compressive strengths of TiNbAlC, Ti_0.9Nb_0.9Hf_0.2AlC, and Ti_0.8Nb_0.8Hf_0.4AlC are 1360.67 ± 19.01, 1574.77 ± 31.15, and 1493.67 ± 35.56 MPa, respectively. A similar trend in the fracture toughness of the three MAXs are observed as well (Fig. 4f). The fracture toughness values of TiNbAlC, Ti_0.9Nb_0.9Hf_0.2AlC, and Ti_0.8Nb_0.8Hf_0.4AlC were measured to be 5.52 ± 0.35, 7.14 ± 0.05 and 6.62 ± 0.22 MPa m^1/2, respectively. These values are much higher than the current reported MAX phase ceramics, including 211, 312 and 413 phases and even the common engineering ceramic Al₂O₃ (Table S6). Except for the intrinsic mechanical property differences among these 211 grains, the presence of Al₂O₃ and HfO₂ impurities would also impact their compressive strength and fracture toughness by revising crack propagation.⁵⁹ For example, Chen et al. revealed improved toughness and compressive strength in Ti₃AlC₂ with 5% Al₂O₃ addition.⁶⁰ Zhu et al. discovered that the compressive strength of Ti₂AlC with 12% Al₂O₃ increased by 248%.⁶¹ Tzenov et al. found that Ti₃AlC₂ containing 4% Al₂O₃ exhibited higher mechanical properties compared to monolithic Ti₃AlC₂.⁶² As for our case, the oxide impurity increases from the 6.9 wt% in TiNbAlC to 7.8 wt% in Ti_0.9Nb_0.9Hf_0.2AlC and further to 14.5 wt% in Ti_0.8Nb_0.8Hf_0.4AlC, where the impact from the high content second phase cannot be ignored. Besides the strengthening effect by the oxide second phase, the existence of possible defects from insufficient density of 211 phase would, on the other hand, compromise the strength and toughness. Thus, the enhanced compressive strengths of the solid solution Ti_1−xNb_1−xHf_2xAlC compared to TiNbAlC is likely due to the synergistic effect of the varied mechanical properties of M-site solid solution and the presence of high strength impurity phases and defects.

To better understand the mechanical behaviour in relation to the structure, the surface morphology of the fractured particles from the three MAXs was examined. Fig. S16 presents SEM images of fractured surfaces from the compressive test. As observed, the lamellar structures in all three MAXs are randomly oriented, which is beneficial for a delayed crack propagation and enhanced strength.⁶³ These lamellar structures have a dimension of 2–5 μm in thickness and 10–20 μm in length, which are similar to their original structures. Two distinct failure modes are identified in the three MAXs, i.e., (i) the delamination of lamellar structure along the a–b plane and (ii) the transgranular fracture along the c axis. The delamination along the ab plane is facilitated by the weak A-layer/MX-layer interfacial bonding under the shear force. The transgranular fracture along the c axis features the breakage of both strong M–C bonds and weak M–A bonds. Furthermore, TiNbAlC displays a sharp cross-section surface on the fractured grains, indicating simultaneous breakage of the M–C and M–A bonds within the grain (Fig. 5a). Comparatively, both Ti_0.9Nb_0.9Hf_0.2AlC and Ti_0.8Nb_0.8Hf_0.4AlC depict irregular ruptured surfaces cross-sectionally along the layers (Fig. 5b and c). This zig-zag propagation of the cracks from layer to layer in Ti_0.9Nb_0.9Hf_0.2AlC and Ti_0.8Nb_0.8Hf_0.4AlC indicates a higher energy absorption, which is consistent with their higher compressive strengths. Similar two distinct failure surfaces as characteristics of two failure modes are observed after the fracture toughness test (Fig S17). Submicron-sized pores are observed in all three MAXs. Notably, under the BSE detector (Fig. 5d–f and S18–S21), the distribution of Al₂O_x and HfO_x in between grains is evident, which may play a role in impeding the crack propagation via deflection or bridging mechanisms.⁶⁴

Fig. 5 SEM images of the fractured surfaces from the compressive test of (a) TiNbAlC, (b) Ti_0.9Nb_0.9Hf_0.2AlC and (c) Ti_0.8Nb_0.8Hf_0.4AlC. The BSE images of the fractured surfaces from the fracture toughness test of (d) TiNbAlC, (e) Ti_0.9Nb_0.9Hf_0.2AlC and (f) Ti_0.8Nb_0.8Hf_0.4AlC.

Conclusions

In this work, three MAX phases, namely TiNbAlC, Ti_0.9Nb_0.9Hf_0.2AlC, and Ti_0.8Nb_0.8Hf_0.4AlC, were synthesized via spark plasma sintering (SPS). The electronic structures, bonding states of different M–C and M–A bonds, and corresponding elastic properties of these MAX phases were investigated through DFT simulations. The calculations reveal that in Ti_0.875Nb_0.875Hf_0.25AlC, the bond strengths follow the order: M–C > M–Al, Nb–C > Hf–C > Ti–C, and Nb–Al > Hf–Al > Ti–Al. The calculated bulk modulus, shear modulus, and Young's modulus of Ti_0.875Nb_0.875Hf_0.25 are 165.55 GPa, 122.76 GPa, and 295.28 GPa, respectively. Upon testing their macroscopic mechanical properties, the nanoindentation hardness and reduced modulus decrease with an increase in the Hf doping content. Among the samples, Ti_0.9Nb_0.9Hf_0.2AlC exhibited the highest compressive strength (1574.77 ± 31.15 MPa) and fracture toughness (7.14 ± 0.05 MPa m^1/2).

Author contributions

Conghui Meng: investigation, data curation, formal analysis, validation, and writing – original draft. Mengfei Xu: simulations. Shiyao Lei: investigation. Yifei Xiao: simulations. Cheng-Feng Du: conceptualization, formal analysis, funding acquisition, writing –review, supervision. Linze Fan: investigation. Weihong Qi: simulations. Hong Yu: conceptualization, formal analysis, writing – review, funding acquisition and supervision.

Conflicts of interest

The authors declare that they have no conflict of interest.

Data availability

The original data can be obtained upon request from the corresponding authors.

The data supporting this article have been included as part of the SI. See DOI: https://doi.org/10.1039/d5ta05278e.

Acknowledgements

This project was supported by the National Natural Science Foundation of China (No. 52275212), Aeronautical Science Foundation of China (2024Z046053001), the “Special Lubrication and Sealing for Aerospace” Shaanxi Provincial Science and Technology Innovation Team (No. 2024RS-CXTD-63), the research fund from Analytical & Testing Center of Northwestern Polytechnical University (2023T012) and State Key Laboratory of Solidification Processing in NPU (Grant No. 2025-TS-09).

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