Ceramics International 45 (2019) 6624–6631
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Silicon carbide matrix composites reinforced with two-dimensional titanium carbide – Manufacturing and properties
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Jaroslaw Wozniaka, , Mateusz Petrusa, Tomasz Cygana, Agnieszka Jastrzębskaa, Tomasz Wojciechowskib, Wanda Ziemkowskab, Andrzej Olszynaa a b
Faculty of Material Science and Engineering, Warsaw University of Technology, ul. Wołoska 141, Warsaw 02-507, Poland Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: A: Sintering B: Composites C: SiC
Within this paper, it is explored how two-dimensional Ti2C sheets addition affects silicon carbide matrix composites in terms of the microstructure and mechanical properties. In order to consolidate the powder mixtures, powder metallurgy processing followed by Spark Plasma Sintering was performed to prepare the sinters. According to our knowledge, this is the first attempt to apply delaminated MXene phases as a reinforcing phases of ceramic matrix composites. The delaminated MXene phases were characterized using a high-resolution transmission microscope (HRTEM) and X-ray photoelectron spectroscopy (XPS). Significant improvement of the fracture toughness and hardness for the composites reinforced with 1.5 wt% 2D Ti2C compared to the reference sample were observed. It is expected that the applied reinforcing phase will have an influence on the fracture mechanism, and so this has also been investigated. Two of the main mechanisms of crack propagations (crack deflection and bridging) were observed.
1. Introduction It is well known that, despite many advantages, ceramic materials are characterized by low fracture toughness, thermal conductivity and anisotropy of thermal expansion coefficients [1,2]. To improve these properties, ceramic matrix composites are manufactured [3–5]. However, rapid technological development puts increasingly higher demands on ceramic composites. Therefore, it is necessary to look for new types of reinforcement phases, for such applications as cutting tools, including nanomaterials and 2D materials [6]. Progress in the methods of producing nanomaterials and 2D materials undoubtedly creates an opportunity for the development of composite materials technology. Thanks to introduced innovations, the development of new materials with a two-dimensional structure characterized by unique functional properties is currently one of the fastest developing path in science. Since the discovery of the specific properties of graphene, an avalanche increase in interest in two-dimensional materials (2D crystals) has been observed [7]. So far, the basic properties of such 2D crystals as: hexagonal boron nitride [8], sulphides and selenium of transition metals [9] and oxides and hydroxides of metals with 2D structure [10] as well as the family of graphene materials [11–13] have been recognized. Thiers use in ceramic composite materials is currently known, allow to
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limit the matrix grain growth and improve the hardness and fracture toughness of the composites [6]. Ceramic matrix composites reinforced with titanium carbide with isometric crystal structure (TiC) are also produced. Popular titanium carbide (TiC) is characterized by a combination of properties such as high hardness, high melting point and relatively high electrical and thermal conductivity [14–16]. Mechanical properties of titanium carbide cause that this material is successfully used as a reinforcing phase in ceramic or metallic matrix composites [16]. Most often, titanium carbide is added to the matrix in the form of spherical particles having an isometric crystal structure. In recent years, the MXenes phases, also known as light transition metal carbides, are getting more and more popular. They are obtained from the MAX phases [17]. A big difference in the strength of the M-X and M-A bonds allows the latter to be ruptured by chemical methods, removing the metal A in the form of salt and thus obtaining separated pores with expanded layers with the composition Mn+1Xn [18,19]. They constitute a new and only pre-tested group of materials that most probably have intermediate properties between metals and ceramic materials. Recently, the first method of delamination of MXenes into single crystals with 2D structure was also developed. It is a method of sonication in a liquid containing organic solvents or bases [20,21]. In the case of composite materials, in general terms, there are
Corresponding author. E-mail address:
[email protected] (J. Wozniak).
https://doi.org/10.1016/j.ceramint.2018.12.149 Received 25 October 2018; Received in revised form 10 December 2018; Accepted 20 December 2018 Available online 21 December 2018 0272-8842/ © 2018 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
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in planetary mill for 10 h in isopropyl alcohol suspension. After blending, the dried mixtures were consolidated using the Spark Plasma Sintering (SPS) method. The sintering parameters were as follows: temperature 1900 °C, heating rate 50 °C/min, dwell time 30 min, applied pressure 50 MPa and a vacuum atmosphere. Moreover, an unreinforced silicon carbide sample was sintered as a reference specimen. Fundamental properties of the obtained materials, such as density (Ultrapycnometer 1000 helium pycnometer Quantachrome Instruments), Vickers hardness and fracture toughness (indentation method), with a Vickers Hardness Tester (FV-700e) under the load of 49 N, were measured. Fracture toughness studies consisted of the cracks length measurement, propagating from the corners of the indentation, resulting from pressing into the composite surface the Vickers indenter. The measurements of hardness and fracture toughness were made on at least 5 samples for each composition. The microstructure observations of composites, as well as substrates, were performed on the scanning electron microscope (SEM Hitachi 5500 and Zeiss LEO 1530) and the transmission electron microscope (FEI Tecnai G2). The phase compositions of the Ti2AlC MAX phase, was carried out using Bruker D8 ADVANCE X-ray diffractometer (XRD) with radiation Cu Kα (λ = 0.154056 nm). The surface chemistry of the 2D sheets of Ti2C MXene was analyzed using PHI 5000 VersaProbe (ULVAC-PHI) X-ray photoelectron spectrometer with monochromatic Al Kα radiation (hν = 1486.6 eV). The hemispherical analyzer was used for collecting the high-resolution (HR) XPS spectra at the pass energy of 117.4, and the energy step size of 0.1 eV.
literature reports on the production of polymer matrix composites reinforced with MXenes phases [22]. These composites were used as filtration membranes. Apart from few papers on the polymer matrix composites manufacturing, there is only one publication describing the use of MXenes phases as a reinforcing phase the Al2O3 matrix composites [23]. However, in this work, the used MXenes phases were not subjected to delamination. It should be noted that, so far, no ceramic composite with Ti2C titanium carbide, with 2D structure (subjected to delamination) as reinforcing phase, has been produced. Therefore, there are no known ceramic composites with titanium carbides characterized by a completely different crystal structure (stoichiometry) in comparison to the previously known representative of the family of carbide materials - a popular TiC with an isometric structure. In this studies, silicon carbide matrix composites reinforced with different weight fractions of Ti2C with 2D structure have been produced. Final consolidation of the powder mixtures was carried out with the use of the SPS (Spark Plasma Sintering) method. The microstructure and mechanical properties were studied and compared with unreinforced SiC. 2. Materials and methods In this study SiC-x of Ti2C, (x – 0.2; 0.5; 0.7; 1; 1.5; 2; 2.5 and 3 wt %) composites were fabricated by a powder metallurgy route. As a matrix, commercially available β-SiC powder (Alfa Aesar, 99.8% chemical purity, 0.42 µm average particles size) was used. Additionally, amorphous boron powder (International Enzymes Limited, 96% chemical purity) and synthetic graphite (Sigma Aldrich, 99% chemical purity), with amount of 0.3 and 1 wt% respectively, were applied as SiC sintering activators. The amount of sintering activators was chosen based on our previous work as providing the most optimal properties of sinters [1]. Ti2C was used as the reinforcing phase, the method of its preparation was as follows. The 211 MAX phase (Ti2AlC) was acquired from Kanthal (Sandvik, Sweden). The material contained 5–10 wt% of carbon, 20–25 wt% of aluminium and balanced wt% of titanium. The protocol for the synthesis of Ti2C MXene was presented by us elsewhere [24]. Briefly, the MAX phase powder was added to 48% hydrofluoric acid (Sigma-Aldrich) in a proportion of 1 g of MAX phase to 10 mL of HF. The reaction was carried out for 24 h at room temperature. The resulting suspension was washed in 4 repetitions with both DI water and technical grade ethanol. The Ti2C MXene was then decanted and dried in room temperature for 24 h. The delamination process was carried out in two steps using ultrasound probe sonication (Vibra Cell VCX750, 20 kHz, Sonics & Materials Inc.) in an inert gas (argon) bubbling. In the first step, hexane was used as dispersing medium. The Ti2C MXene was dispersed in ratio of 50 cm3/1 g. The delamination process was carried out with 520 W power of ultrasounds for 2 h (total i.e. only 30 min in a working mode) in an ice bath with the periodical mode (1 s on/3 s off). Subsequently, the dispersion was decanted and dried. In the next step of the process, dry isopropanol was used as a dispersing medium (50 cm3/1 g dispersion was also prepared). The parameters of sonication process was repeated as previously, but the duration of the process was shorter (total of 1 h i.e. only 15 min in a working mode). Such obtained mixed solution was centrifuged at 2500 rpm for 2 min. It should be noted, that typically, 5 min and 3500 rpm is used [25]. However, this approach is suitable for water-based nano-colloids. Isopropanol is much less polar (in comparison to water) which result in weak stabilization of 2D flakes. At the same time, we observed that 2D flakes can be more easily separated from MXene residue using mild conditions for centrifugation. This solvent can additionally improve 2D flakes stability since is aprotic as suggested by Gogotsi et al. [25]. Using this approach, the 73.7% of delamination was achieved. The supernatant of 2D sheets of Ti2C in dry isopropanol was then collected and stored in 5 °C under argon for further use. At the next technological step powder mixtures were homogenized
3. Results and discussion Fig. 1 shows the phase analysis of the Ti2AlC MAX phases powder. The analysis showed the presence of two phases: Ti2AlC and Ti3AlC2, with Ti2AlC being dominant. Due to the presence of the Ti2AlC phase, the powders were given to selective etching and delamination. After these processes, the MXenes and obtained 2D crystals were subjected to observations on a scanning electron microscope. Fig. 2a and b shows the morphology of Ti2C MXenes and Ti2C 2D crystals, respectively. Powders after the etching in hydrofluoric acid have a layer structure similar to those observed in multilayered graphene [26]. The use of the delamination process allowed to obtain Ti2C in the form of 2D crystals (Fig. 2b). In addition, on the surface of the Ti2C flakes, the presence of fine particles, not observed for the MXene powders, was noticed. In order to identify the fine particles observed on the 2D Ti2C flakes surface, the powders were subjected to observations on a high-resolution transmission electron microscope (Fig. 3a-d). The diffraction analysis of the powder after delamination confirm the presence of hexagonal Ti2C. In addition, precipitation on the flakes surface were identified as TiO2 passivating surface of powders. Chemical analysis also showed the presence of fluorine which is a residue after etching the metal layer from the MAX phases. Observation of the sheets at higher magnification shown the multilayered structure of the obtained flakes. In order to verify the obtained results, the powders after delamination were subjected to XPS analyses. The chemical composition of the surface of the 2D sheets of Ti2C were analyzed using ESCA-XPS (X-ray photoelectron spectroscopy for chemical analysis). It is well known that apart from surface morphology the actual surface chemistry of the nanomaterial defines its properties and is also an important factor in understanding the stability of the nanomaterial [27]. These aspects were deeply investigated in this study in relation to the application of 2D sheets of Ti2C MXene phase in ceramic matrix composites. The obtained survey XPS spectrum of the Ti2C was presented in Fig. 4. It was subsequently used for quantitative analysis of the type and nature of chemical species present on the surface of the analyzed 2D sheets. The survey XPS spectrum showed the typical chemical composition of the MXene material, also confirmed by other studies [28]. The solved XPS spectra for Ti2p, C1s, O1s and F1s, obtained for the delaminated 2D sheets of Ti2C MXenes were presented in Fig. 5. When considering the data after 6625
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Fig. 1. The XRD pattern obtained for Ti2AlC MAX phase.
the so called background. However, their presence can be related to impurities coming from the parent MAX phase or as a result of etching with HF. Peaks present at 454.7 eV for Ti2C, with a concentration of 7.2 at%, were identified as being related to a Ti-C species as was also indicated by other studies [28]. The presence of Ti-C connections is also confirmed by C1s signal located at 281.7 eV with a concentration of 0.7 at%. Such lowering of carbon content together with increase of oxygen in the chemical composition of the surface of 2D MXene crystals was previously observed by other groups [31]. These differences in atomic concentrations of atoms present on the surface in relation to theoretical Ti:C corresponds to the fact that XPS collects data only from the surface of the sample (i.e. with a thickness up to 10 nm). It should be also noted that the surface Ti atoms react with water and/or oxygen to form the passivation layer which is typical for MXenes [30]. This is related to Ti nature to spontaneously form on its surface the dense barrier-type titanium dioxide (TiO2). The formed TiO2 is chemically stable and increases greatly by e.g. anodic oxidation [32,33]. The passive behavior of Ti in HF solution has also been previously determined by a number of other studies [34], and the increased film thickness was revealed to incorporate fluoride anions. Our results thus confirmed the presence of a Ti-O layer within the Ti2p signals located at c.a. 455 and 459 eV. It can be noticed that the first signal relates to the amorphous TiO whereas second one is derived from crystalline TiO2. Their presence is typical for MXenes which has a tendency to surface oxidation. Additionally, the presence of C-OH groups on the surface of 2D crystals of Ti2C was confirmed by C1s peaks present at c.a. 286 eV. Also, the carboxyl O˭C-OH species were identified by the C1s signal at 289.4 eV. A signals related to either the C˭O (ketone group) or C-O-C (ether group) were also observed in the 2D crystals of Ti2C at 287.1 eV. We have also identified the presence of Al-F bonds in concentrations of 5.9 at% which is also characteristic for 2D MXenes [35]. It should be noted that the ESCA-XPS analysis clearly confirmed that in contrary to other methods of MXenes delamination to 2D sheets the new method enables obtaining a truly pristine surface possible i.e. without any heteroatoms containing sulfur or ammonium salts derivatives. In our delamination method no additives are present that may change the chemical composition of the obtained 2D MXenes. Fig. 6 shows the influence of 2D-Ti2C sheets weight content on relative density of SiC matrix composites. From the presented results, it can be seen that even a small amount of 2D crystals increases the relative density of composites compared to unreinforced SiC sinters. A further increase of reinforcing phase content increases the relative density. Its highest value was achieved for composites containing 1 wt% of Ti2C. After exceeding 1 wt% a slow decrease in the density of composites is observed. However, even for composites with the lowest density
Fig. 2. SEM micrographs of the expanded Ti2C MXene a) and 2D sheets of the Ti2C b).
deconvolution, the mentioned signals can be observed in a varied intensities. The obtained deconvolutions can be described as similar to Ti3C2 which surface, apart from different stoichiometry of the interior of 2D crystal, is also characterized by the presence of passivation TiO2 layer [29]. The results from the ESCA-XPS analyses were presented in Table 1. It can be clearly seen that the surface of 2D sheets of Ti2C is composed of titanium, and carbon. Additionally, oxygen and fluorine are present as the surface functional groups [30]. Moreover, nitrogen and silicon were detected in amounts in quantities practically within 6626
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Fig. 3. TEM analysis of the 2D sheets of the Ti2C MXene presenting: bright field TEM image a), electron diffraction showing presence of reflections related to hexagonalTi2C lattice as well as surface TiO2 passivation layer b), HREM multilayered structure of the single 2D sheet c), and results of EDX analysis obtained from the surface of 2D sheets d).
Fig. 4. Survey XPS spectrum obtained for 2D sheets of the Ti2C MXene. 6627
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Fig. 5. Solved XPS spectrum related to Ti2p (a), C1s (b), O1s (c) and F1s (d), obtained for 2D sheets of the Ti2C MXene. Table 1 Quantitative results of ESCA-XPS analysis obtained for 2D sheets of the Ti2C MXene. Signal indication
Band position [eV]
Concentration [at %]
Chemical species indication
Ti 2p 3/2 a Ti 2p 1/2 a Ti 2p 3/2 Ti 2p 1/2 b Ti 2p 3/2c Ti 2p 1/2c Ti total N1s N1s N total C 1s a C 1s b C 1s c
454.7 460.3 457.9 463.5 459.4 465.2 – 401.9 396.2 – 284.8 285.8 287.1
7.2 3.6 0.8 0.4 26.3 11.8 50.0 0.6 0.1 0.7 3.0 2.0 0.9
Ti-C (carbide)
C 1s d C 1s e C total O 1s a
289.4 281.7 – 530.7
1.3 0.7 7.8 24.2
O 1s b O 1s c O 1s d O F 1s F total Si2p Si total
531.7 532.6 533.7 – 685.1 – 102.6 –
4.6 3.7 1.8 34.4 5.9 5.9 1.2 1.2
Ti-O (amorphous) Ti-O (TiO2)
N-H N-Ti (nitride)
Fig. 6. Influence of 2D sheets of the Ti2C MXene weight content on relative density of composites.
C-C C-OH (hydroxyl) C˭O (ketone group) or C-O-C (ether group) O˭C-OH (carboxyl) Ti-C (carbide)
(3 wt% of Ti2C), the values are higher than 98%. The increase in the density of composites can be caused by the influence of Ti2C on the SiC matrix sintering process. As can be seen from the literature, in the case of sintering SiC, various oxides and carbides (Al2O3, B4C, Al4C3) [36–38] are used as sintering additives. The presence of Ti2C can improve mass transport during the sintering process and thus improve the density of the resulting composites. The addition of 2D MXene on density and sintering temperature was confirmed by other authors [39]. The addition of Ti3C2 to ZnO resulted in a significant reduction of the sintering temperature to 300 °C while maintaining high density. The similar character of the changes, as for the relative density results, were observed for Vickers hardness measurements (Fig. 7). The increase of
O-Ti (amorphous or crystallite) C-O C˭O C-O Al-F (AlF3) Si-O (silicate)
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Fig. 7. Influence of 2D sheets of the Ti2C MXene weight content on Vickers hardness of composites.
Fig. 8. Influence of 2D sheets of the Ti2C MXene weight content on average grain size of SiC.
Fig. 10. Crack propagation of non-delaminated Ti2C MXene a) and 2D sheet of the Ti2C Mxene b), SiC matrix composites reinforced with 3 wt% of 2D Ti2C.
Ti2C crystals weight content (which is surprising due to the fact that higher hardness should result in a decrease in KIC). The KIC value reaches plateau from 1 wt% of Ti2C and only slightly decreases for composites reinforced with 3 wt% of 2D sheets. It should also be emphasized that significant increase in the value of KIC from 3 to almost 5 MPa*m0.5, respectively, for the unmodified sinters and SiC composite containing 1.5 wt% of 2D Ti2C was achieved. In order to determine the fracture mechanisms of produced materials, the crack propagation was analyzed. Fig. 10 shows the crack propagation for composites reinforced with 3 wt% of 2D flakes in which MXene Ti2C particle (Fig. 10a) and the delaminated 2D Ti2C crystals were found, (Fig. 10b). In the first case, the crack propagates in a similar way to those observed for multilayer graphene [5]. The crack reaches the particle and then propagates along the MXene - ceramic matrix interface. This causes energy dissipation to change of the crack propagation direction and breaking the interface. In the case of delaminated particles, apart from cracking after the phase boundary, the occurrence of bridging was observed Fig. 10b. The presented photographs show that the particles have very strong bond with the ceramic matrix and limit the crack propagation. The presence of non-delaminated MXene phases may explain the decrease in relative density and hardness for composites reinforced with higher amount of Ti2C. Higher amount of the reinforcement results a higher content of non-delaminated particles. The nondelaminated Ti2C caused a decrease in density which is associated with the presence of pores between the individual layers. This, in turn, affects the decrease in the mechanical properties of the manufactured composites. Moreover, lack of a significant change in the KIC values for composites with different reinforcement phases content is related with the overlapping of several factors. In case of lower Ti2C content, the composites exhibit high density and hardness values which contributes
Fig. 9. Influence of 2D sheets of the Ti2C MXene weight content on fracture toughness of composites.
reinforcement phase content cause to increase of the composites hardness. The hardness peak is observed for composites containing 2 wt % of Ti2C and is 25 GPa. A further increase in the 2D sheets weight content causes a slight decrease in hardness (which is consistent with the results of density measurements). However, taking into account the standard deviation values, it can be stated that for composites from 1.5 wt% of 2D crystals hardness value is similar. The increase in the composites hardness with increasement of reinforcement phase content can be explained by the improvement of the materials density as well as SiC matrix grain size. Fig. 8 shows the influence of Ti2C content on the average SiC grain size. The obtained result shows a decrease in grain size with the increasement of reinforcing phase content. The smallest grains were observed for composites with the highest hardness. This indicates that Ti2C flakes block the SiC grain growth during the sintering process. Also in the case of the fracture toughness (Fig. 9), an increase of this values were observed together with an increase of 2D 6629
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Fig. 11. Crack propagation scheme for non-delaminated MXenes a) and 2D sheets b).
to fracture toughness. For higher reinforcement content, a significant effect on the KIC value has bridging as a factor improving fracture toughness of composites. For the highest content of Ti2C, the decrease in density and the increase amount of non-delaminated particles are observed, which translates into a decrease in the KIC values. Fig. 11a and b schematically show the crack propagation for both observed cases. Considering the same volume of the reinforcing phase, the dissipation cracking energy is higher for particles subjected to the delamination process. A larger number of particles causes that cracking path is more deflected and enlarge the interface boundary required to fracture. Moreover, there is an additional mechanism to increase the fracture toughness which is crack bridging. In addition, the presence of not delaminated particles increases the porosity associated with the occurrence of gaps between the individual layers, which further reduces the mechanical properties of the manufactured composites. As was mentioned above, toughening mechanisms of 2D MXene reinforced composites are similar to Gn/GO-reinforced composites. According to literature data the main mechanisms are graphene necking and crack bridging, crack deflection and graphene sheet pull-out [40,41]. Our research has shown the occurrence of crack deflection and bridging on 2D MXene composites, which confirms literature reports. 4. Conclusions Based on the presented results, it can be concluded that it is possible to manufacture silicon carbide matrix composites reinforced with twodimensional Ti2C crystals which exhibit strong interfacial bonding. The obtained composites are characterized by high relative density and higher mechanical properties in comparison to the unreinforced SiC sinters. It was also found that two-dimensional structure of Ti2C particles is more favorable than the not delaminated form of Ti2C (MXene). Two-dimensional crystals block the crack propagation much more effectively, causing the need to deliver higher energy to composite failure. In addition, for the composites containing 2D titanium carbide crystals, an additional mechanism of blocking the crack propagation (crack bridging) was observed. Acknowledgement The study was accomplished thanks to the funds allotted be the National Science Centre within the framework of the research project ‘OPUS 13’ no. UMO-2017/25/B/ST8/01205. References [1] M. Petrus, J. Wozniak, A. Jastrzębska, M. Kostecki, T. Cygan, A. Olszyna, The effect of the morphology of carbon used as a sintering aid on the sinterability of silicon carbide, Ceram. Int. 44 (2018) 7020–7025. [2] M. Petrus, J. Wozniak, T. Cygan, B. Adamczyk-Cieslak, M. Kostecki, A. Olszyna, Sintering behaviour of silicon carbide matrix composites reinforced with multilayer graphene, Ceram. Int. 43 (2017) 5007–5013. [3] K. Broniszewski, J. Wozniak, K. Czechowski, L. Jaworska, A. Olszyna, Al2O3-Mo cutting tools for machining hardened stainless steel, Wear 303 (2013) 87–91. [4] K. Broniszewski, J. Wozniak, M. Kostecki, K. Czechowski, L. Jaworskac, A. Olszyna, Al2O3–V cutting tools for machining hardened stainless steel, Ceram. Int. 41 (2015) 14190–14196. [5] J. Wozniak, A. Jastrzębska, T. Cygan, A. Olszyna, Surface modification of graphene oxide nanoplatelets and its influence on mechanical properties of alumina matrix
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nano-SiC Ceramics: densification by SPS and mechanical characterization, J. Eur. Ceram. Soc. 32 (2012) 633–641. [38] S. Hayun, V. Paris, R. Mitrani, S. Kalabukhov, M.P. Dariel, E. Zaretsky, N. Frage, Microstructure and mechanical properties of silicon carbide processed by spark plasma sintering (SPS), Ceram. Int. 38 (2012) 6335–6340. [39] J. Guo, B. Legum, B. Anasori, K. Wang, P. Lelyukh, Y. Gogotsi, C.A. Randall, Sintered ceramic nanocomposites of 2D MXene and zinc oxide, Adv. Mater. 30 (2018) 1801846.
[40] J. Liu, H. Yan, M.J. Reece, K. Jiang, Toughening of zirconia/alumina composites by the addition of graphene platelets, J. Eur. Ceram. Soc. 32 (2012) 4185–4193. [41] L. Kvetkova, A. Duszova, P. Hvizdos, J. Dusza, P. Kun, C. Balazsi, Fracture toughness and toughening mechanisms in graphene platelet reinforced Si3N4 composites, Scr. Mater. 66 (2012) 793–796.
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