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Dmytro Demirskyi, Kyosuke Yoshimi, [Tohru S. Suzuki](https://orcid.org/0000-0001-9458-6863), [Oleg O. Vasylkiv](https://orcid.org/0000-0002-5041-6130)

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This is the peer reviewed version of the following article: Preparation of high‐strength (Ta,W)C solid‐solutions by spark plasma sintering, which has been published in final form at https://doi.org/10.1111/ijac.14438. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Preparation of high‐strength (Ta,W)C solid‐solutions by spark plasma sintering](https://mdr.nims.go.jp/datasets/e564eb7e-d3b8-4391-bc0d-b4213405cf43)

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Preparation of high-strength (Ta,W)C solid-solutions by spark plasma sinteringD. Demirskyi (a,b,c)†, K. Yoshimi (b), T.S. Suzuki(c), and O. Vasylkiv (c)†.(a) WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 Japan (b) Department of Materials Science and Engineering, Tohoku University, 6-6-02 Aramaki Aza Aoba, Sendai, 980-8579, Japan(c) National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanAbstract (Ta,W)C bulks were prepared by spark plasma sintering. Densification kinetics and solid-solution formation kinetics were performed on the powder mixtures using TaC and W powders. The as-received tungsten powder had a spherical shape and rather coarse size. By using the crushed and as-received powder, it can be suggested that sintering at 2000 °C limits the reaction volume to 3–6 μm and hence allows forming a complete solid-solution using finer powders. The lattice parameter, hardness, toughness and strength were investigated as a function of the TaC content. The flexural strength of the (Ta,W)C ceramic bulks was investigated up to 2000 °C and it was found that the maximum strength was for the 60 mol.% TaC composition. Strength as a function of the temperature tended to increase up to 1200 °C followed by a gradual decrease to 2000 °C. When the TaC was reinformed by coarse W spheres, the flexural strength monotonically decreased from 570 MPa at room temperature to 220 MPa at 2000 °C.1 IntroductionRecent interest in multicomponent solid-solution carbides has spurred long-lasting research on the correlation between the synthesis, structure and properties of ultra-high-temperature ceramics (UHTC). Among the UHTC family, the TaC, ZrC and NbC carbides have received considerable attention due to their high-hardness and high elastic moduli due to a mixed ionic, covalent and metallic bonds inside a rock-salt type crystal cell. This combination of mixed bonding inside a crystal cell defines a high melting point for these carbides, which exceeds 3400 °C [1,2].In order to promote densification or in order to obtain a peculiar set of physical, chemical and mechanical properties, these carbides are often doped with other elements. Nevertheless, it is solid-solutions between these carbides that may result in a considerable increase in hardness, strength or high-temperature creep resistance. The solid-solution of tantalum carbide with TiC [1], ZrC [3], NbC [4], and HfC [5] showed that processing and composition determine the high-temperature properties. Yang et al. [6] have reported that the addition of TaC may lead to a higher toughness of WC compared to the bulk binderless WC [7]. However, macroscopic properties, such as Youngs’ modulus and strength, are scarce for this binary carbide system. Considering the potential use of these solid solutions as neutron reflectors and in industrial machinery and deep mining components, further investigation of properties such as strength over a wide temperature range is vital. Moreover, due to the development of the various WC-based alloys it is a relatively small addition of TaC that may add an extra functionality to the complex WC-Co composite [8]. Holleck et al. [9] showed that adding up to 30 mol.% of W to TaC will (i) lead to a linear increase in the hardness and (ii) improves the high-temperature hardness by 40 % up to 1000 °C. Regarding the solid-solution hardening, in the case of Holleck et al. [9], the carbon deficiency had a considerable effect on the hardness. Carbon in (Ta,W)Cx prepared by hot-pressing at 2700 °C varied from 0.73 to 0.89.Another aspect to consider is the solubility between carbides. Since the original review by Swarkopf and Kieffer [8], it is widely known that WC will have a limited solubility in typical UHTC carbides. Brun and Stubican [10] showed that the solubility of WC in TiC or ZrC greatly depends on the temperature, and processing at a temperature exceeding 2500 °C is required to achieve solid-solutions containing W [10]. Recently, reports of the processing of high-entropy carbides indicated that based on the processing and phase ratio, one can obtain a full solubility of W or WC in rock-salt-type lattice [11,12], otherwise precipitates or secondary phases rich in W will form during consolidation or on the cooling stage. For the high-entropy carbide with five principal metal atoms, 10 mol.% W is being used. In the case of the ZrC–WC system, a processing temperature of lower than 1800 °C is required [10]. This raises a question about the solubility of W/WC in UHTC carbides in general and in TaC in particular. The effect of the solid-solution formation on other macroscopic properties in the TaC–WC system, such as toughness or strength, was not previously reported.Hence, this study focused on accomplishing the following goals: (a) produce dense TaC-WC solid-solution bulks, (b) investigate the densification mechanism controlling the densification process, and (c) use a W powder with a distinct spherical phase to verify how the size of the powder directly affects the solid-solution formation. Finally, using bulk (Ta,W)C ceramics, we performed high-temperature flexural strength tests up to 2000 °C to understand the extent of the potential applications of these binary carbides. For this task we selected ceramics with 60 mol.% TaC.2 Materials and MethodsCommercially-available TaC (Lot #LKP4101) by Wako Pure Chemical Industries and gas-atomized W by MicronMetals were used as the starting materials. TaC had the median size of 1.2±0.2 mm, and the main impurity was Nb up to 500 ppm.W had a specific spherical shape and particle size that ranged from 40 to 80 μm. Thus, in order to evaluate the densification and reaction kinetics in the TaC–W system, we used the as-received tungsten powder and a crushed one. Crushing was done in ethanol using a agate mortar. As a rule, powders with an irregular shape and particle size of between 2 and 6 μm were thus produced.Mixing of the powder mixtures was performed using the Intelli-Mixer RM-2M (ELMI, Latvia) mixer. This procedure excludes using solvents or grinding the materials. The mixing process and partial crushing of the ceramic particles occur due to fast vibrations in a relatively small volume (50 ml). In the case of the as-received W powder, the powder mixture consisted of coarse powders covered with a fine layer of TaC (greyish in color). After the mixing step, the powder mixtures were kept in a dry desiccant box under a vacuum before the spark plasma sintering (SPS) step. A summary of the powder mixtures used in this study is provided in Table 1.Table 1. Composition, physical and mechanical properties of bulks in the TaC–WC system ID TaC/(TaC+W), using mol.% Lattice parameter, Å X-ray density, g/cm3 Bulk density, g/cm3 Median grain size, μm Hardness, GPa Toughness(3), MPa·m1/2 Strength, σRT, MPa 09T 0.9 4.433 14.73 14.47(4) 8.2±0.6 15.2±0.2 4.2/4.5 480±22 08T 0.8 4.425 14.83 14.58(5) 11.4±1.6 15.3±0.1 4.5/4.9 385±17 06T 0.6 4.395 15.19 15.14(5) 9.8±2.6 16.0±0.3 4.2/4.9 350±25 05T4 0.5 4.380 15.26 15.25(6) 9.5±3.3 15.7±0.3 4.2/4.6 320±17 05TS1 0.5 4.360 2 15.58 15.42(6) 60±20 15.4±0.3 6.4/7.8 430±26(1) – as received W spheres were used(2) – lattice parameter of the (Ta,W)C solid-solution after SPS at 2300°C, 0 min, 45 MPa.(3) – 25 °C / 1600 °C.(4) – single-phase solid-solution was detected by XRD after SPS at 2300°C, 10 min, 45 MPa.During the SPS procedure the untreated powders were placed in the SPS graphite die using an inner graphite foil to separate the die from the powder mixture. The SPS experiments were conducted using the ‘Dr. Sinter’ 1050 (Sumitomo, Japan) unit with a 30-mm die.The schedule for the specimens used for the high-temperature flexure had these major steps: (1) heating to 800 °C in four minutes followed by (2) heating to the densification temperature of between 1800 °C and 2000 °C using a fixed rate of 100°C/min. At the sintering temperature (3) a dwell of 0 to 10 min was used as a homogenizing step. (4) cooling to 1800 °C in 5 min was then performed, followed by cooling to 600 °C in 40 minutes. A pressure of 45 MPa was maintained during the heating, consolidation and cooling stages. Argon gas at the flow rate of 2 L/min was used.After coarse grinding, the sintered specimens were polished with diamond disks with a particle size of up to 0.5 µm. This was followed by fine polishing using a 0.1 µm alumina suspension. The density of the samples was then measured by Archimedes method using water or ethanol as the medium in accordance with ASTM B 963–08.An X-ray diffraction (XRD) analysis (D8 Advance, Bruker, Karlsruhe, Germany) was performed on the polished surfaces of the bars after the flexural tests using Cu-Kα radiation. The intensity data were collected over the 2θ range of 30°–130° in steps of 0.02° using a sampling time of 5 s for each step. The software used for the refinement was Profex [13]. Instrumental broadening was determined using a NIST 660b LaB6 standard run under the same conditions for each sample.The structural characteristics of the carbide ceramics were studied by scanning electron microscopy (SEM, JCM-6000, JEOL) with secondary (SE) or backscattered electrons (BSE mode). Energy Dispersive X-ray Spectroscopy (EDS) was performed using a JEOL DX200s unit. We used a 1k resolution and a dwell of 2 μs for acquiring the element maps. For the analysis of the EDS data, we used NIST DTSA-II software [14].The grain size was analyzed using a custom MATLAB code (The MathWorks, Inc., Natick, MA, US) that employed an intercept technique to calculate the grain size. The grain boundaries were automatically detected with a high level of accuracy using a self-learning algorithm.The hardness was determined by a Vickers hardness tester (Akashi, AVK-A, Japan) using loads of 49, 98 and 196 N with a dwell time of 15 s following the standard procedure (ASTM C 1327–15).The three-point flexural strength was determined using rectangular blocks (1.5×2×25 mm, ASTM C1211−13, configuration B) and the strength testing equipment that was previously described in detail [15]. A span of 16 mm was used. The flexural strength data were averaged based on three tests at the elevated temperature and by five tests at room temperature. In the case of the properties-screening procedure only two tests were performed at room temperature and at 2000 °CThe toughness was measured using two 3×4×25 mm bars (ASTM C1211−13, configuration A). An indentation was made on the 3-mm side using a Vickers hardness tester and a load of 98 N, following ASTM C1421–10. The toughness at elevated temperature was measured at 1600 °C. The heating, cooling and testing conditions for the high-temperature tests were identical for the toughness and strength tests and these are fully described in [15]. 3 Results and Discussion3.1 Densification kinetics of (Ta,W)C ceramicsTwo sizes of the W were used in this study as we were attempting to promote a reaction during the SPS for the crushed powder. In the case of the reaction, the consolidation process can be described by a model proposed by Di Rupo et al. [16] (Figure 1). As can be seen in this case, the grain-boundary area where the reaction is being localized should be different when one of the ingredients is coarser than the other. Furthermore, because there is a difference in the grain size of W, one can recheck if the rule for Coble creep [17] or Nabarro–Herring creep [18] is applicable for the SPS.Figure 1. Composite microstructure associated with the model proposed by Di Rupo et al. [16]. The reacting grains are spheres, and the material diffuses from the intergrain regions, through the boundary phase, to the grain surfaces adjacent to the pores. (b) shows the situation when there is an 8-fold difference in the grain size between TaC and W. In this case, the grain-boundary phase includes only TaC particles at the beginning of the SPS process as the solid solution phase will not be formed without exposure of the initial powder mixture to high temperatures.The shrinkage data during the sintering process can be used to identify the dominant consolidation mechanism. In the case of hot-pressing or spark plasma sintering one can analyze the consolidation of powders similar to the creep of the bulk. A model proposed by Bernard-Granger and Guizard [19] can be used for such an analysis. This model is based on the creep deformation process of bulk ceramics which should satisfy the following equation 1:(1)where  is the creep rate, A – constant, D – diffusion coefficient, G0 – shear modulus, b – the Burgers vector, k – Boltzmann’s constant, T – absolute temperature, d – grain size,  macroscopic applied stress, p – inverse grain size exponent, and n is the stress exponent, while t is the time.Using a fixed densification rate, one can identify the stress exponent n by presenting the SPS shrinkage data in the  vs  coordinates. The bulk density  and densification rate  are retrieved from the SPS data.Within this study, we also applied this approach, while the key parameters for (eq. 1) were a green density of 60% for the theoretical density (TD), G0 = 185 GPa [2], Poisson’s ratio = 0.22 [2, (https://doi.org/10.1016/0022-5088(71)90046-4)] and = 45 MPa.The typical shrinkage data obtained during the SPS are presented in Figure 2. This is being done for the 08T specimen. One can note a peculiarity that the majority of the shrinkage will occur below the homogenizing dwell. Another observation can be made during the cooling as the sample will show the signs of expansion and shrinkage during cooling. This may lead to the accumulation of additional stresses inside the ceramic bulk. In this case, a change in the cooling rate did not change the shrinkage behavior for the (Ta,W)C bulks during the cooling stage.Figure 2. Shrinkage behavior of the powder compacts at the heating rate of 100 °C/min and the constant pressure of 34 kN. (b) shows the relative shrinkage as a function of the dwell at 1920 °C.Figure 3. Analysis of the SPS of (Ta,W)C at 1920 °C using a densification rate of 0.014 s-1, and (b) Arrhenius plot for the evaluation of the apparent activation energy for the densification process during SPS at 1600–2000 °C.Figure 3 shows the data obtained during the SPS for the fixed shrinkage rate of 0.014 s-1. One can see that there is an excellent fit for the stress exponent n of 0.74. As a rule, for the diffusional creep processes, such as the Coble creep or Nabarro–Herring creep, this exponent should be unity or close to unity. Other processes, such as power-law creep or grain-boundary sliding, should lead to the n of 3–5 or 2, respectively.Figure 4. Grain size dependence of the densification rate of the (Ta,W)C ceramics prepared using crushed and non-crushed W spheres.Other specimens in this study showed an n value between 0.7 and 0.85, hence one can assume that such a behavior is due to the diffusional creep. The activation energy for densification can also be estimated using the SPS data of 510±14 kJ/mol. The diffusion or creep data for TaC or WC are summarized in Table 2 [1,2,20–23]. One can attempt to verify the diffusion mechanism governing the densification process by plotting the normalized densification rate as a function of the grain size (Figure 4). Table 2. Activation energies for diffusion and creep in TaC and WC Diffusing species Type of the diffusion Temperature range, °C Type of the experiment (n, value for creep) Qa (kJ/mol) Reference 185W Self 2000–2550 Polycrystalline TaC 502±33 [2] 185W Self 2130–2300 Polycrystalline WC 577±79 [2] 14C Self 1965–2370 Polycrystalline WC 368 [2] 14C Self 2360–2960 Polycrystalline TaC 496±50 [20] 14C Self 1965–2370 Polycrystalline WC 366 [21] - Lattice diffusion 1200–1500 Compressive creep, WC, n = 1 215 [22] - Lattice diffusion 2350–2700 Compressive creep, TaC, n = 1 610–630 [1] - Lattice diffusion 2500–3000 Creep in flexure, TaC, n = 1 610 [23] - Lattice diffusion 1800–2000 SPS, polycrystalline (Ta,W)C, n = 0.8, densification 510±14* This study* the data may vary as much as 530 kJ/mol or as low as 495 kJ/mol for selected compositions. Nevertheless, the activation energy obtained in Fig. 3 provides a general agreement for all data obtained within this study.The fixed composition data for the densification using the crushed and non-crushed W spheres indicates that the grain size exponent p is equal to –1.4. The Nabarro–Herring creep and Coble creep are being controlled by the p of –2 and –3, respectively. One can thus assume that considering n = 0.8 and p = –1.4, the Nabarro–Herring creep is the most likely process to govern the densification process in TaC or (Ta,W)C. This type of creep results from the diffusion of vacancies from regions of high chemical potential at the grain boundaries subjected to normal tensile stresses to regions of lower chemical potential where the average tensile stresses across the grain boundaries are zero. Hence, it is highly likely that the activation energy obtained during such an analysis should correspond to the bulk diffusion of C in Ta, Ta in TaC or W in TaC. The data in Table 2 indicate a similarity of the activation energy to that observed in ref. [2] for diffusion of W in TaC or for the creep of TaC [23].3.2 Reaction kinetics of (Ta,W)C ceramics Because the resulting carbides are solid-solutions, the reaction aspect of the SPS processing can also be discussed. The XRD data (Fig. 5) showed that (1) the solid solution formation is a multi-stage process, and (2) in some instances, intermediate specimens will have two (Ta,W)C solid-solutions. The latter observation can be explained by the temperature gradient during the SPS [24].Figure 5. X-ray diffraction trace of the solid-solution product while using the different sizes of the W particles for the 50 mol.% TaC specimens. The specimens were subjected to the identical SPS conditions (1920 °C, 0 min dwell). Top figure obtained using W spheres (05TS), while the bottom one using the crushed W spheres (05T). Figure 6. Time dependence of the conversion of W to the TaC–WC solid solution for the composite containing 80 mol.% TaC. Each point represents an individual SPS held at the stated temperature, for the specified time. (a) shows data on the W content, (b) shows linear dependence of log(ɑ) vs time for TaC–WC composite. (c) Arrhenius plot of values of K derived from data in (b) using dɑ/dt = –K·ɑ.Nevertheless, one of the peculiar parameters here is the amount of W that can be easily identified by XRD. As such, one can treat the solid-solution reaction as a first order reaction that can be described as dɑ/dt = –K·ɑ [25], where ɑ is the amount of the reacting agent, while the K is the rate of the reaction.We performed an analysis of the 08T ceramic (80 mol.% TaC), and the results are presented in Fig. 6. The estimated activation energy for the reaction is 91±12 kJ/mol, which is at least five times lower than the activation energy for the densification. Although the activation energy cannot be directly compared with the data in Table 2, the merit for estimation lies in the development of the solid-solutions. First, this value is for the crushed W spheres, meaning a comparable size between reagents (Fig. 1 (a)). Second, because the activation energy is sufficiently lower than that for the densification, the reaction process will be predominant or more favorable. Finally, in terms of the formation of the complex solid-solutions such as medium or high-entropy carbides, it is thus essential to have a comparable particles size. (See subsection 3.4 for details).3.3 Lattice parameter of (Ta,W)C ceramics Figure 7 shows the relation between XRD of the raw powder and 50 mol.% TaC when the final product is a solid-solution without traces of the W or W2C. As expected, other solid-solutions will have a shift towards the higher diffraction angle with an increase in the contribution of W in (Ta,W)C. Figure 8 illustrates such a shift for the (422) peak, while Figure 9 summarizes the data for the lattice parameters for the cubic (Ta,W)C solid-solution reported in this study and in refs. [9,26–29]. One can see the variation in the lattice parameters with an increase in the W addition follows the quasi-linear Vegards’ law. Compositions above 50 mol.% TaC in (Ta,W)C were not attempted as data for the TiC–WC or ZrC–WC systems indicate that there is a solubility around this area [10].Figure 7. X-ray diffraction patterns for the raw powders and the SPSed 50 mol.% TaC ceramic.Figure 8. Effect of composition on the position of the (422) peak for the various (Ta,W)C bulks.Figure 9. The lattice parameter of the Fm-3m TaC–WC solid-solution as a function of the WC content. Data of Hachisuka [26], Rudy et al. [27], and Panov and Meerson [28] are shown as references. Panov and Meerson [28] reported the decomposition of the solid solution after a 48-h dwell at 1450 °C. Rudy et al. [29] reported the lattice parameter for the cubic solid-solution after a dwell at 1700°C for stoichiometric and carbon deficient tungsten carbides. Data of Sara [29] is for the cubic tungsten carbide with the WC0.82 composition.3.4 Effect of coarse W source on solid-solution formationFigure 10 shows an EDS map and overlay for the specimen consolidated using the as-received W spheres. It is clear that in this case the solid-solution area is limited only to a layer region. EDS analysis suggested that W and Ta were the main peaks (Fig. 11). Ti originated from the raw TaC powder and was a minor impurity (~0.2 mol%). Another observation can be made in Figure 12. First, because this figure was taken from the polished cross-section of the flexure bar, one can see that that the cracks originated during fracture will terminate at the W/(W,Ta)C boundary. Second, inset in (b) shows an irregular shape of the reaction interface, suggesting that one of the atom fluxes of W into TaC and Ta into W are not identical (see Suppl S1 for details). Third, the area between two-spheres or three-spheres has a significant number of pores. This is a characteristic feature of the vacancy sink for the initial stage sintering. The voids in the neck area may be a place for the annihilation of vacancies [30], hence, the necking is intentionally underlined as seen in Fig. 1 (b). Alternatively, the formation of pores is due to the grain growth rate of the TaC ‘matrix’. As a rule, if the grain boundary movement slowly occurs, the pores on the grain boundaries can be annihilated. However, if the grain growth process occurs rapidly, there is no time for pore annihilation by the specimen shrinkage, so the relatively large pores are formed by the coalescence of the smaller pores. Such processes are characteristic for the pure and doped alumina ceramics [31].Figure 10. Typical EDS maps for polished (Ta,W)C ceramic after flexural test at 1800 °C. (a) shows an overlay of Ta (red) and W (blue) maps on the SEM image. (b) overlay maps of Ta and W. An inset in (b) highlights the presence of the intermediate layer (violet) between the W and TaC. Black areas in (a) are pores and pull-out areas.Figure 11. Typical EDS data from polished (Ta,W)C ceramic. Vertical dashed lines indicate position of the main peaks for metals and C. The aluminum peak originates from the sample holder. The data were analyzed and corrected with NIST DTSA–II [14].Figure 12. Polished cross-section of the flexure bar after testing at 2000 °C. Cracks propagated from right to left. It is clear that a majority of the cracks terminate at the W particles. Insets show (a) general area used for probing and (b) apparent irregular outward diffusion. In (a) the excessive contrast was used in the BSE mode to show the difference between the W grains and TaC ‘matrix’. Note the presence of the secondary phases and pores between the binary and triple W grains which indicate that these places are most likely to be sources for the vacancy sink during the sintering process.Furthermore, it is important to underline the fact that the rate for formation of the solid-solution in the case of the large spheres should be slower that that presented in Fig. 6. However, the lattice parameter for the solid-solution formed at the interface between W and TaC was similar to that determined for the crushed spheres (Fig. 9). Importantly, the thickness of the newly-formed layer on the coarse W spheres averages 3–6 μm, which is comparable with the size with grain size for the 05T specimen.Hence, similar to the scaling law in sintering kinetics [32], one may require a 4–8-fold increase in the processing time in order to dissolve the 50 μm compared to the 5 μm one. Such experiments lay outside this study, and, obviously, the time estimation here is a preliminary one. Nevertheless, in the case of longer processing at 2000 °С, one should tackle the issue of the ongoing grain growth which should result in a decreased mechanical behavior [33].3.6 Mechanical propertiesHardness for the (W,Ta)C ceramics was between 15.3±1.2 GPa at 49 or 98 N loads. A further increase of the load resulted in a slight decrease in the hardness as the 196 N load hardness was within 14.5±0.7 GPa. These results are comparable to that reported for tantalum carbide [34–36]. The hardness of cubic WC was not previously reported. The hardness for the binderless tungsten carbide depends on the consolidation method or applied load within 17–27 GPa [6,7,37,38]. For instance, Gubernat et al. [7] using a 30 N load reported the hardness of 26±0.5 GPa. The results in Table 1 for the (W,Ta)C ceramics indicated that there is a slight increase in hardness with an increase in the W content with a maximum for the 06T composition. Such an increase in hardness can be explained due to formation of a solid-solution [2,8].The toughness at room temperature remained at the same level with the exception of the 05TS ceramic which used the as-received W spheres. In this case, the toughness of 6.4 MPa·m1/2 can be explained due to the presence of ductile particles as ductile phase toughening was initiated. This toughening mechanism presumes that the cracks will stop at the ductile phase, which was often observed (see Fig. 12). With an increase in temperature to 1600 °C, there was a slight increase in toughness for all compositions suggesting that the toughness increase should be directly related to a reheating procedure [39]. This indicated that (i) the solid-solution phase becomes more ductile or (ii) there are microcracks formed in the solid-solution upon reheating thus providing an additional shielding for the cracks.The strength at room temperature showed a general decrease with an increase in the W content. Because the strength is a parameter that depends on a number of parameters including the porosity and grain size, it is fair to compare the (W,Ta)C ceramics to the bulk TaC. As a rule, the strength of the monolithic tantalum carbide is higher than 550 MPa [40,41], suggesting that formation of the solid-solution does not result in the solid-solution strengthening or this effect is being neglected by other factors such as the grain size or porosity. For reference, the flexural strength of the hexagonal binderless tungsten carbide was reported in [7] as 720 MPa.3.6.1 High-temperature flexural strength and fracture peculiaritiesFigure 13 summarizes the screening results for the flexural strength at 25 °C and at 2000 °C. One can see that for the tests at 2000 °C, there is a monotonic increase in strength, suggesting that the higher ductility (or lower brittle to ductile transition temperature) of the solid-solution phases. For the equimolar composition, the strength is on the same level as for the bulk TaC in [40] (i.e., ~200 MPa). For the in-depth temperature dependence of the strength, we selected the 06T ceramic (60 mol.% TaC) that showed the highest strength during the screening procedure.Figure 13. Effect of the TaC content on the flexural strength at room temperature and at 2000°C. The strength data are based on two tests per temperature. The data for the WC from Gubernat et al. [7] for the specimen prepared by hot-pressing without additives. The data for the monolithic tantalum carbide using the data of Demirskyi et al. [40].Figure 14. Temperature dependence of the flexural strength of the bulk TaC [40– 45] and (Ta,W)C ceramics. (b) shows the effect of the W source in the (Ta,W)C ceramic for the strength of the 50 mol.% TaC ceramic. *in (a) data for the 06T composition.Figure 14 provides a summary of the data for the flexural strength of the bulk TaC and (Ta,W)C ceramics [40–45]. In this study, the flexural strength increases with an increase in temperature, then after a peak at 1200 °C, there is a gradual increase in the strength. As a rule [33], one should expect a partial decrease in the strength upon reheating to 1000–1400 °C. Such a decrease in strength is due to the partial relaxation of the thermal stresses upon reheating. This means that the increase in strength depicted in Fig. 14 is due to generation of new stresses upon reheating. At 1600 °C or above, such stresses will be relaxed and the strength decreases. Above 1600 °C, microplastic zones formed inside the carbide specimen may cause both the decrease or increase in strength [24]. The strength should abruptly fall near the brittle to ductile transition temperature as a macroscopic plastic deformation will be dominant [1].Figure 14 (b) also provides an insight into the 50 mol.% TaC ceramics. For the 05T ceramic one can see that there is a 35% increase in strength at 1600 °C followed by a 200 MPa strength at 2000 °C. This behavior can be explained by the same processes as for the 06T ceramic (Fig. 14 (a)). When using large W spheres, the trend is different; the strength gradually decreases from 25 °C to 2000 °C. This behavior is thought to be due to the presence of the ductile phase in the composite at the elevated temperatures. The brittle to ductile transition temperature for the polycrystalline tungsten is 200-800°C [46–48]. Figure 12 showed that during the test at 2000 °C a majority of the cracks or microcracks will terminate at the W particles, which is consistent with the toughening mechanism previously described. For the 05TS specimen, the plasticity on the loading curves was noticed at 1600 °C, while it is fully plastic at 1800 °C or 2000 °C (Fig. 15).Figure 15. Representative loading curves for (Ta,W)C ceramics prepared using large W spheres. For a better visualization of the curve at 2000 °C, it is shifted in the abscissa. The solid-black line is for the test at room temperature (25 °C).For these temperatures, the fracture is mainly intergranular (Fig. 16). The fracture surfaces collected in the BSE mode had almost no contrast, so please refer to Fig. 12 to understand that the W spheres were lighter in color (W has a higher atomic number than Ta). Another noticeable difference between the polished cross-section and fractured one is that the fracture contained cracked W spheres. The presence of the grain facets in the vicinity of the W sphere (Fig. 16 (b)) is highly noticeable (see also Suppl S2). These indicated that (i) the fracture is intergranular for the TaC and (ii) argon etching allows observing fine sub-grains which are not always visible during the examination of the polished specimens.Fracture of the specimens prepared using crushed spheres was mainly intergranular above 1200 °C (Fig. 17). The observation in the BSE mode showed that there was a high homogeneity in the chemical composition, suggesting that a full solid-solution was formed. One can also note that in the case of the Fig. 17 (b) porosity, it is more profound and a majority of the pores are located in the vicinity of the triple points or at the grain boundaries.Figure 16. High-temperature fracture peculiarities for (Ta,W)C ceramics at (a,b) 1800 °C and (c,d) 2000 °C. Fracture was observed in the center of the fracture surface of the bar. The compression goes from top to bottom, while the crack propagates from bottom to top. (a,c) are acquired using the BSE mode.Figure 17. Fracture peculiarities for (Ta,W)C ceramics at 2000 °C. (a,b) is 50 mol.% TaC ceramic, while (c,d) is the 60 mol.% TaC ceramic. (d) is acquired using the BSE mode.The process of formation of the solid-solution between WC and TiC or ZrC [10] is quite sensitive not only to the composition but also to the temperature. As a rule, the higher the temperature, higher the solubility. That being said, temperatures near 2600 °C were reported for the 60 mol.% ZrC for the formation of the solid-solution by Brun and Stubican [10]. Applied to the Ta-W-C system, these temperatures most likely can cause an excessive grain growth (~10 μm at 2000 °C, see Table 1), which at the same time should lead to a reduction in the room-temperature strength. Due to the relatively low activation energy for the solid-solution formation when compared to the activation energy for the densification, i.e., 91±12 kJ/mol vs 510±14 kJ/mol, the former process should dominate over densification. Thus, is not surprising that use of the WC as a milling media during the preparation of various UHTCs will facilitate the formation of the W-containing phases [49–51]. As result, one can also expect that any medium-entropy or high-entropy carbide should not have problems with the W solubility when processing at 2000 °C. In order to reconfirm the findings of this study, experiments using the Mo/TaC system are being currently performed.Summary and concluding remarks In this study the densification, solid-solution formation and mechanical properties of the TaC–WC system were determined. As a tungsten source, we used crushed and as-received W powders which were mixed with TaC powders and subjected to spark plasma sintering.The grain size dependence of the densification rate of TaC–WC ceramics prepared using crushed and non-crushed W spheres indicated that the rate dependence follows the m –1.4 law instead of the classical –2 exponents for the grain size (Nabarro–Herring creep). The densification was analyzed using an approach proposed by Bernard-Granger and Guizard [19] and it was found that the stress exponent (n ~ 0.9) suggests that densification is being controlled by diffusional creep. The activation energy for the densification was estimated to be 510±14 kJ/mol.The solid-solution formation reaction was also estimated using the XRD data for the 80 mol.% TaC specimens in the temperature range of 1600–2000 °C. The solid-solution formation reaction is a first-order reaction with the apparent activation energy of 91±12 kJ/mol. A model experiment using the W spheres suggested that using the ~50 μm spheres restricts the reaction, and W will remain unreacted even at 2000 °C. The decrease in the size of the W particles to ~5 μm will result in the formation of the complete solid-solution.The lattice parameter for the TaC-WC ceramics monotonically decreased with an increase in the WC content. This satisfies Vegards’ law for the binary solid-solutions. The homogeneous solid-solution was formed up to 50 mol.% TaC, suggesting that a solubility limit for this binary system lies above this value. This agrees with the results of Brun and Stubican [10] for the ZrC–WC or TiC–WC systems.Importantly, ceramics prepared using as-received W spheres showed a gradual decrease in flexural strength from room temperature (~520 MPa) to 2000 °C (~220 MPa). Furthermore, in this case, the polished cross-section of the specimen fractured at 2000 °C showed a considerable number of cracks. These findings are most likely due to a micro-stress field around a ductile phase and may provide an additional strength unless both phases become ductile and a plastic-strain-stress curve is being observed.AcknowledgementsDD was supported by World Premier International Research Center Initiative (WPI), MEXT (Japan), and Core Research Cluster for Materials Science, Tohoku University (Japan)References[1] Zubarev PV. High-temperature strength of the interstitial phases. Moscow: Metallurgiya; 1985. (in Russian).[2] Andrievski RA, Spivak II. Strength of Refractory Compounds. Chelyabinsk: Metallurgiya; 1989. (in Russian).[3] Kats SM, Ordan’yan SS. Extreme character of concentration dependence of creep rate of solid solutions of ceramics in the MIV–MVC system. Izd Akad Nauk SSSR, Neorg Mat. 1983;19[2]:196–201.[4] Kats SM, Ordan’yan SS. Creep in sintered polycrystalline niobium carbide and niobium carbide-based solid solutions. 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Composite microstructure associated with the model proposed by Di Rupo et al. [16]. The reacting grains are spheres, and the material diffuses from the intergrain regions, through the boundary phase, to the grain surfaces adjacent to the pores. (b) shows the situation when there is an 8-fold difference in the grain size between TaC and W. In this case, the grain-boundary phase includes only TaC particles at the beginning of the SPS process as the solid solution phase will not be formed without exposure of the initial powder mixture to high temperatures.Figure 2. Shrinkage behavior of the powder compacts at the heating rate of 100 °C/min and the constant pressure of 34 kN. (b) shows the relative shrinkage as a function of the dwell at 1920 °C.Figure 3. Analysis of the SPS of (Ta,W)C at 1920 °C using a densification rate of 0.014 s-1, and (b) Arrhenius plot for the evaluation of the apparent activation energy for the densification process during SPS at 1600–2000 °C.Figure 4. Grain size dependence of the densification rate of the (Ta,W)C ceramics prepared using crushed and non-crushed W spheres.Figure 5. X-ray diffraction trace of the solid-solution product while using the different sizes of the W particles for the 50 mol.% TaC specimens. The specimens were subjected to the identical SPS conditions (1920 °C, 0 min dwell). Top figure obtained using W spheres (05TS), while the bottom one using the crushed W spheres (05T).Figure 6. Time dependence of the conversion of W to the TaC–WC solid solution for the composite containing 80 mol.% TaC. Each point represents an individual SPS held at the stated temperature, for the specified time. (a) shows data on the W content, (b) shows linear dependence of log(ɑ) vs time for TaC–WC composite. (c) Arrhenius plot of values of K derived from data in (b) using dɑ/dt = –K·ɑ.Figure 7. X-ray diffraction patterns for the raw powders and the SPSed 50 mol.% TaC ceramic.Figure 8. Effect of composition on the position of the (422) peak for the various (Ta,W)C bulks.Figure 9. The lattice parameter of the Fm-3m TaC–WC solid-solution as a function of the WC content. Data of Hachisuka [26], Rudy et al. [27], and Panov and Meerson [28] are shown as references. Panov and Meerson [28] reported the decomposition of the solid solution after a 48-h dwell at 1450 °C. Rudy et al. [29] reported the lattice parameter for the cubic solid-solution after a dwell at 1700°C for stoichiometric and carbon deficient tungsten carbides. Data of Sara [29] is for the cubic tungsten carbide with the WC0.82 composition.Figure 10. Typical EDS maps for polished (Ta,W)C ceramic after flexural test at 1800 °C. (a) shows an overlay of Ta (red) and W (blue) maps on the SEM image. (b) overlay maps of Ta and W. An inset in (b) highlights the presence of the intermediate layer (violet) between the W and TaC. Black areas in (a) are pores and pull-out areas.Figure 11. Typical EDS data from polished (Ta,W)C ceramic. Vertical dashed lines indicate position of the main peaks for metals and C. The aluminum peak originates from the sample holder. The data were analyzed and corrected with NIST DTSA–II [14].Figure 12. Polished cross-section of the flexure bar after testing at 2000 °C. Cracks propagated from right to left. It is clear that a majority of the cracks terminate at the W particles. Insets show (a) general area used for probing and (b) apparent irregular outward diffusion. In (a) the excessive contrast was used in the BSE mode to show the difference between the W grains and TaC ‘matrix’. Note the presence of the secondary phases and pores between the binary and triple W grains which indicate that these places are most likely to be sources for the vacancy sink during the sintering process.Figure 13. Effect of the TaC content on the flexural strength at room temperature and at 2000°C. The strength data are based on two tests per temperature. The data for the WC from Gubernat et al. [7] for the specimen prepared by hot-pressing without additives. The data for the monolithic tantalum carbide using the data of Demirskyi et al. [40].Figure 14. Temperature dependence of the flexural strength of the bulk TaC [40– 45] and (Ta,W)C ceramics. (b) shows the effect of the W source in the (Ta,W)C ceramic for the strength of the 50 mol.% TaC ceramic. *in (a) data for the 06T composition.Figure 15. Representative loading curves for (Ta,W)C ceramics prepared using large W spheres. For a better visualization of the curve at 2000 °C, it is shifted in the abscissa. The solid-black line is for the test at room temperature (25 °C).Figure 16. High-temperature fracture peculiarities for (Ta,W)C ceramics at (a,b) 1800 °C and (c,d) 2000 °C. Fracture was observed in the center of the fracture surface of the bar. The compression goes from top to bottom, while the crack propagates from bottom to top. (a,c) are acquired using the BSE mode.Figure 17. Fracture peculiarities for (Ta,W)C ceramics at 2000 °C. (a,b) is 50 mol.% TaC ceramic, while (c,d) is the 60 mol.% TaC ceramic. (d) is acquired using the BSE mode.† Authors to whom correspondence should be addressed, Dmytro Demirskyi, demirskyi.dmytro.e2@tohoku.ac.jp, Oleg Vasylkiv oleg.vasylkiv@nims.go.jp1image3.emfn = 0.74(Ta,W)Cdensifi�cation rate 0.014 s-1ln(1/Geff) (1/ρ)(dρ/dt))−30.15−30.10−30.05−30.00−29.95ln(σeff/Geff)−7.9 −7.8 −7.7(TaW)C, 45 MPa510±14 kJ/mol (R2 0.97)ln(T/Geff) (1/ρ)(dρ/dt)(Geff/σeff)n−20−18−16−14−121/T, K-15.0×10−4 5.5×10−4 6.0×10−4(a) (b)image4.emfslope –1.4W spheressolid solution grains1600°C1800°C2000°CTemperaturelog (densifi�cation rate [g /(cm3  s)])−5−4−3−2log (grain size [μm])1.5 2.0 2.5 3.0 3.5 4.0image5.emfimage6.emf1600°C1800°C2000°C% W remaining via XRD102030Time, s0 2000 4000log(% W)0.81.01.21.4Time, s0 2000 4000Qa = 91.0±12.7 kJ/mol (R2 0.93)Qa = 91.0±12.7 kJ/mol (R2 0.93)ln(K), (s-1)−10.0−9.5−9.01/T, K-14.5×10−4 5.0×10−4(b)(a) (c)image7.emf50 mol.% TaCWTaC(111)(111)(110) (200) (211) (220) (310)(200)(200)(220)(220)(311)(311)(222)(222)(400)(400)(331)(331)(420)(420)Intensity, countsDiffraction angle, 2theta,°30 40 50 60 70 80 90 100 110image8.emf90 mol.% TaC80 mol.% TaC50 mol.% TaC60 mol.% TaCIntensity, a.u.Difraction angle, 2 theta, (°)114 115 116 117 118 119 120 121 122image9.emf(Ta,W)C by SPS, this studyHachisuka [26]Panov and Meerson [28]Rudy et al. (WC) [27]Rudy et al. (WC1-x) [27]Sara [29]Holleck et al. [9]WC0.82WC0.82TaC phase after 48 h at 1450°C [30]using W spheres(Ta,W)C0.89-0.73(Ta,W)C lattice parameter, Å4.204.254.304.354.404.45TaC/(TaC+W) mol.%0 0.2 0.4 0.6 0.8 1.0image10.jpegimage11.emfCKɑTi L*/LβAl KɑW/Ta M*Mɑ/MβMγTi MɑLɑMγLβTa LγTiTaWCountsEnergy, keV0 0.5 1.0 1.5 2.0 2.5 8 9 10 11image12.tiffimage13.emf25°C2000°C[Demirskyi et al.][Gubernat et al.]Strength, MPa0200400600800TaC/(TaC+W), mol.%1 0.9 0.8 0.6 0.5 0image14.emf(b)(a)spherescrushed spheresStrength, MPa0200400600Temperature, °C25 1600 2000TaC [41]TaC [45]TaC [44]TaC [43]TaC [40]TaC [42](Ta,W)C* [this study]Flexural strength, MPa0200400600800Temperature, °C0 500 1000 1500 2000image15.emfRT1600°C2000°C1000°C1200°C1800°CStress, MPa0200400600Strain, mm/mm0 0.001 0.002 0.003image16.tiffimage17.jpegimage1.emfimage2.emfCoolingHeatingDwell (1920±5°C)Relative shrinakge, %−18−16−14−12−10−8−6Temperature, °C1750 1800 1850 1900Relative shrinakge, %−11−10−9Dwell at 1920°C, s0 100 200 300 400 500 600(a) (b)