# Design, synthesis, structure, and stability of novel multi-principal element (Ti,Zr,Hf,W)C ceramic with a miscibility gap

Ahmet Bahadir Yildiz, Hu Yixuan, R. Prasath Babu, Thomas C. Hansen, Mirva Eriksson, Kolan Madhav Reddy, Peter Hedström

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Ahmet Bahadir Yildiz, Hu Yixuan, R. Prasath Babu, Thomas C. Hansen, Mirva Eriksson, et al. Design, synthesis, structure, and stability of novel multi-principal element (Ti,Zr,Hf,W)C ceramic with a miscibility gap. Journal of the European Ceramic Society, 2022, 42 (11), pp.4429-4435. 10.1016/j.jeurceramsoc.2022.04.029. hal-05442041

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# Design, synthesis, structure, and stability of novel multi-principal element (Ti,Zr,Hf,W)C ceramic with a miscibility gap

Ahmet Bahadir Yildiz<sup>a, *</sup>, Hu Yixuan<sup>b</sup>, R. Prasath Babu<sup>a</sup>, Thomas C. Hansen<sup>c</sup>, Mirva Eriksson<sup>d</sup>, Kolan Madhav Reddy<sup>b</sup>, Peter Hedström<sup>a</sup>

## ARTICLE INFO

### Keywords:

Multi-principal element

Carbide

Miscibility gap

Computational thermodynamics

Mechanical properties

## ABSTRACT

Here we design a novel multi-principal element carbide system (Ti,Zr,Hf,W)C with a miscibility gap using computational tools and report on the formation of a single-phase (Ti,Zr,Hf,W)C after spark plasma sintering. The (Ti,Zr,Hf,W)C shows high nanohardness (32.7 GPa) and fracture toughness (5 MPa·m<sup>1/2</sup>). Aging studies at 1350 °C for 100 h show that the single-phase carbide solid solution is quite stable even though this temperature is within the predicted miscibility gap of the system. Detailed electron microscopy characterization shows that phase separation has initiated with minor decomposition after aging by forming rock-salt (Ti,W)C- and (Zr,Hf)C-rich phases as well as hexagonal WC precipitates. We show that the (Ti,W)C- and (Zr,Hf)C-rich phases form a lamellar structure upon aging and the interlamellar spacing is considerably coarser than what has been previously found for the binary (Ti,Zr)C system. The decomposition kinetics, on the other hand, is sluggish due to the reduced driving force for phase decomposition.

## 1. Introduction

Transition metal carbides, carbides constituting elements from group four to six in the periodic table, offer an excellent combination of high hardness, resistance to wear, and high melting temperature together with high-temperature strength and chemical inertness [1]. Since their discovery, they have been the choice of material when structural stability at high temperatures is sought, e.g. in metal cutting and rock excavation tools (hard metals), which are the most widespread commercial applications [2,3]. The need for lighter and stronger structural materials for applications in extreme service environments including high-speed machining of complex components and leading edges in hypersonic aerospace vehicles increases the demand for further development of novel carbides [4].

Early attempts led to the development of binary transition metal carbide mixtures with superior properties. It was shown that these carbide systems have higher hardness [3,5], oxidation resistance [6], and fracture toughness [7] compared to that of the unary carbides. Recent developments in high-entropy alloys (HEA), also known as

multi-principal element alloys, have also fostered the design of high entropy carbide (HEC) systems [8–16]. The “high entropy” effect refers to stabilization of the single-phase solid solution through the configurational entropy as it increases with the number of equimolar alloying elements $N$ by $\Delta S_{mix} = \sum R\ln N$, where R is the gas constant [17]. The number of equimolar alloying elements, i.e. principal elements, is thus key for increasing the $\Delta S_{mix}$ and accordingly the high-entropy effect. The definition of high-entropy materials is controversial: the classification has been made through e.g. the number and amount of elements and value of the configurational entropy [17,18]. Whilst alloys with a minimum of five principal elements ($\Delta S_{mix} > 1.6$ R) are considered in the high-entropy class, several carbide systems comprising four equimolar transition metals, e.g. (Ti,Zr,Hf,Nb)C [9] and (Ti,Zr,Nb,V)C [10], are also classified as high-entropy materials. Sarker et al. [11] have suggested an entropy forming ability term describing the single-phase solid solution formation tendency of carbide systems. They have shown that having five equimolar transition metals, i.e. complying with the high-entropy criteria, does not necessarily result in a single-phase carbide solid solution e.g. in (Hf,Mo,Ti,W,Zr)C. Previous research has

<footnote><sup>a</sup> Department of Materials Science and Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden</footnote>

<footnote><sup>b</sup> School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China</footnote>

<footnote><sup>c</sup> Institut Laue-Langevin, 71 Avenue des Martyrs, CS 20156, 38042 Grenoble Cedex 9, France</footnote>

<footnote><sup>d</sup> Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University, SE-106 91 Stockholm, Sweden</footnote>

<footnote>* Correspondence to: Department of Materials Science and Engineering, KTH Royal Institute of Technology, Sweden.
E-mail address: abyildiz@kth.se (A.B. Yildiz).</footnote>
revealed that carbide systems with multiple principal elements can result in enhanced hardness [9], fracture toughness; and reduced thermal diffusivity and conductivity [10], making them possible material candidates for future high-temperature applications.

The stability of the carbides is key since it can both lead to deterioration of the mechanical properties of the single-phase material but possibly also enable in-situ hardening during service at elevated temperatures. The in-situ hardening hypothesis has stimulated interest for binary carbide systems with miscibility gaps [19–21], since aging within the miscibility gap can result in phase separation through spinodal decomposition or discontinuous precipitation. Spinodal decomposition takes place spontaneously since there is no energy barrier for nucleation [22,23] and several reports have shown that it can enhance the hardness of alloys [24] and ceramics [21] during service at elevated temperatures and result in improved performance. This hardening effect has been explained by the coherency strain resulting from the generation of local compositional changes [22]. Discontinuous precipitation, on the other hand, proceeds through nucleation and growth; and, the effect on mechanical properties in carbides is unclear at present. The decomposition to a lamellar nanostructure may restrict dislocation motion, but could instead deteriorate the solid solution hardening effect and degrade the mechanical properties.

We design and synthesize here a novel multi-principal element carbide, (Ti,Zr,Hf,W)C, with a miscibility gap and study how aging for 100 h at 1350 °C within the immiscibility region affects the carbide structure and mechanical properties. Whilst the carbide system is designed by CALPHAD (CALculation of PHAse Diagrams) methodology, the micro- and nanostructures have been investigated by neutron diffraction and scanning- and transmission electron microscopy (SEM and TEM) related techniques.

## 2. Materials and methods

### 2.1. Synthesis

Equilibrium thermodynamics calculations were performed by CALPHAD methodology using Thermo-Calc Software [25] and TCHEA3 High Entropy Alloy database [26] in order to predict the equilibrium phase diagram and phase compositions.

Multi-principal element (Ti,Zr,Hf,W)C with equimolar TiC, ZrC, HfC, and WC content was synthesized. 6 cm³ powder mixture of equimolar TiC (~2 µm), ZrC (~325 mesh, i.e. <44 µm), HfC (~2 µm), and WC (<1 µm) powders of 99.5% purity (Alfa Aesar) were fed into a Teflon jar (50 ml volume) with 30 ml (107 g) Y-stabilized Zr₂O₃ balls (5 mm diameter) together with 16 ml ethyl alcohol (>97% purity). This was followed by ball milling at 350 rpm for 3 h in a Retsch PM 100 planetary ball mill. The rotation direction of the mill was changed every 10 min. The milled powder slurry was pan-dried. The dried powder was sieved by a 250 µm mesh and filled in a graphite die with 12 mm diameter in 23 g batches for producing consolidated samples with around 20 mm height. Spark plasma sintering (SPS) of powder mixtures was performed by a Dr Sinter SPS-825 apparatus at 2200 °C for 10 min. The heating rate to the holding temperature was 100 °C/min. A uniaxial pressure of 30 MPa was applied during the heating and isothermal holding at the sintering temperature. The process was performed in a vacuum up to 1000 °C, thereafter, Ar atmosphere was used to avoid the sublimation of the graphite punches. The relative density of samples was measured by the Archimedes' principle using the theoretical densities calculated by the Rietveld analysis of the neutron diffraction patterns.

### 2.2. Materials characterization

The nanostructural investigations were performed by two transmission electron microscopes (JEOL ARM 200 F), one is equipped with a cold field emission gun and an aberration corrector for the probing lens system to obtain the atomic resolution scanning

transmission electron microscopy (STEM) images, the other one is equipped with an aberration corrector for the objective lens system to obtain high-resolution transmission electron microscopy (HRTEM) images. Both TEM equipment was operated at 200 kV. High-angle annular dark-field STEM (HAADF-STEM) images were recorded using an annular-type detector with a collection semi-angle of ~100–269 mrad. STEM energy dispersive X-ray spectroscopy (EDX) elemental maps were also acquired to reveal the phase distribution and chemical composition. To prepare the samples for TEM observations, the bulk samples of (Ti,Zr, Hf,W)C were firstly cut into thin pieces by a low-speed saw with a diamond disc (TECHCUT 4™) and then polished with diamond slurry to reduce the thickness to 80–100 µm. An ultrasonic hole drill (Gatan-601) was used to cut out 3 mm diameter TEM specimens. Thereafter, the specimens were dimpled to a thickness of 30–40 µm using a dimple grinder (Gatan-656), and finally, it was placed in an ion-beam milling machine (Gatan-PIPSII-695) to create a hole in the specimen center with an electron transparent edge of the hole, suitable for TEM observations.

A dual-beam FIB-SEM (FEI Nova600 workstation) equipped with EDX was used for microstructural investigations. 10 kV accelerating voltage was employed during the investigations.

Neutron powder diffraction experiments were performed on the instrument D20 at the Institut Laue-Langevin (ILL), France [27,28] using a neutron wavelength of 1.54 Å to examine the crystal structure and phase evolution after synthesis and aging. The neutron wavelength was obtained using (115) reflection of the Germanium monochromator at a take-off angle of 90°. Rietveld [29] and single-peak analysis of the diffraction patterns were performed using GSAS-II [30] software.

Vickers microhardness measurements were performed using a microhardness tester XHVT-1000Z (SCTMC, China) for a series of loads (0.5, 1, 2, and 3 kg) and 15 s dwell time. Nanohardness and elastic modulus were measured by depth-sensitive nanoindentation (Hysitron-Ti950) with a load of 10 mN, a holding duration of 2 s, and at a loading rate of 0.1 mN/s. Reported average nanohardness and elastic modulus values and their uncertainties were calculated as an average of 12 indents. Indentation fracture toughness was calculated by measuring the crack lengths emanating from the corners of the diagonal of the indents created by the Vickers microhardness test. These measurements were carried out using a field emission SEM (FEI Versa 3D). Antis formula [31] was used to calculate the fracture toughness:

$$K_{IC} = 0.016 \left( \frac{E}{H} \right)^{1/2} \frac{P}{C^{3/2}} \quad (1)$$

where KIC is the fracture toughness (MPa·m¹/²), E is Young's modulus (GPa), H is the hardness (GPa), C is the crack length (m) and P is the load (N). Reported Vickers microhardness, indentation fracture toughness, and associated uncertainty values are the average result of measurements on 8–10 indents.

## 3. Results

### 3.1. Computational materials design

Fig. 1 shows the phase diagram of (Ti,Zr,Hf,W)C system. The synthesis and aging temperature are marked in the figure. As can be seen, the stability range of single-phase (Ti,Zr,Hf,W)C solid solution is predicted to span between 1640 and 2910 °C, i.e. it is metastable at room temperature. Below 1640 °C, the carbide solid solution is predicted to decompose into (Zr,Hf)C-rich and (Ti,W)C-rich phases with rock-salt crystal structures. Upon reaching temperatures below 1400 °C, a WC phase with hexagonal crystal structure should form. Table 1 lists the results of equilibrium volume fraction and composition of phases calculated for (Ti,Zr,Hf,W)C system at 500 and 1350 °C. At 1350 °C, The (Zr,Hf)C-rich decomposition product is expected to constitute the majority phase in the system with 62.9 vol%. Both (Zr,Hf)C-rich and (Ti,W)C-rich phases comprise minor amounts of additional elemental
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** The phase diagram of (Ti,Zr,Hf,W)C system calculated by CALPHAD methodology using Thermo-Calc Software [25] and TCHEA3 High Entropy Alloys database [26]. Phase stability regions and sintering and aging temperatures are indicated.</figcaption></figure>

<table><caption>**Table 1**
The equilibrium volume fraction and composition of phases calculated for (Ti,Zr, Hf,W)C system at 500 and 1350 °C.</caption><thead><tr><th rowspan="2">Phase</th><th colspan="2">(Ti,W)C-rich</th><th colspan="2">(Zr,Hf)C-rich</th><th colspan="2">WC</th></tr><tr><th>500 °C</th><th>1350 °C</th><th>500 °C</th><th>1350 °C</th><th>500 °C</th><th>1350 °C</th></tr></thead><tbody><tr><td>vol%</td><td>24.83</td><td>31.20</td><td>55.66</td><td>58.94</td><td>19.18</td><td>5.50</td></tr><tr><td>Ti [at%]</td><td>44.10</td><td>27.34</td><td>0.38</td><td>5.56</td><td></td><td></td></tr><tr><td>Zr</td><td>0.04</td><td>3.06</td><td>24.79</td><td>19.45</td><td></td><td></td></tr><tr><td>Hf</td><td>0.07</td><td>3.84</td><td>24.78</td><td>19.0</td><td></td><td></td></tr><tr><td>W</td><td>6.49</td><td>17.04</td><td>0.06</td><td>6.23</td><td>50.0</td><td>50.0</td></tr><tr><td>C</td><td>49.29</td><td>48.71</td><td>49.98</td><td>49.74</td><td>50.0</td><td>50.0</td></tr></tbody></table>

components; though, the (Zr,Hf)C-rich phase is distinguished by having near-equimolar HfC and ZrC content, and higher solid solution formation tendency. WC precipitates should account for 5.5 vol% of the system under equilibrium conditions and remain in unary form as Ti, Zr, and Hf have negligible solubility in WC [32]. As can be seen, the reduction in temperature, i.e. approaching the ground state, results in depletion of WC from both (Zr,Hf)C-rich and (Ti,W)C-rich phases, and accordingly, the volume fraction of WC reaches 19.2 vol% at 500 °C.

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Neutron diffraction patterns of the (Ti,Zr,Hf,W)C system in as-sintered condition and after aging at 1350 °C for 100 h. Patterns with complete 2θ range, indicating successful synthesis of rock-salt crystal structured single-phase (Ti,Zr,Hf,W)C.</figcaption></figure>

## 3.2. Phase identification

In Fig. 2, the neutron diffraction patterns of the (Ti,Zr,Hf,W)C in as-sintered condition and after aging at 1350 °C for 100 h show that rock-salt crystal structured single-phase (Ti,Zr,Hf,W)C has been successfully synthesized by SPS at 2200 °C. Rietveld analysis of the patterns (resulting example fitting pattern is provided in Supplementary Fig. 1) reveals no evolution in lattice parameters, which are 4.49468(14) Å in as-sintered and 4.49459(17) Å in 100 h aged (Ti,Zr,Hf,W)C. Accordingly, the theoretical density of as-sintered and 100 h aged samples (neglecting the impact of decomposition products) are calculated to be 10.10 g/cm³. Archimedes' principle measurement results gave bulk densities of 9.40 (as-sintered) and 9.44 g/cm³ (100 h aged), indicating 93.1% and 93.4% relative densities for as-sintered and 100 h aged samples, respectively. The diffraction peaks were fitted to Gaussian functions (see Supplementary Fig. 2) and the resulting full width at half maximum (FWHM) values are listed in Supplementary Table S1. FWHM values show negligible change after 100 h aging. For example, for the (220) diffraction peak, FWHM values are 0.42663 (as-sintered) and 0.42696 (100 h aged). The neutron diffraction results thus suggest that the decomposition of (Ti,Zr,Hf,W)C is strongly delayed and the single-phase solid solution is preserved, i.e. the amount of decomposition products is lower than the detectable range.

Fig. 3.a and b show SEM micrographs of as-sintered and 100 h aged (Ti,Zr,Hf,W)C samples, respectively. As can be seen, aging brings a reduction in pore size and porosity. However, no significant change is observed in (Ti,Zr,Hf,W)C grain size upon aging. Detailed studies of the aged microstructure at higher magnifications reveal the formation of a minor amount of decomposition products, as shown by arrows in Fig. 3. c. EDX point composition analysis of the decomposition products in Fig. 3.d confirms the presence of (Zr,Hf)C-rich, (Ti-W)C-rich, and WC phases together with single-phase equimolar (Ti,Zr,Hf,W)C as matrix phase. Whilst (Zr,Hf)C-rich and (Ti-W)C-rich phases create spotted (lamellar) regions within the same grain, WC precipitates form in their equilibrium shape and appear as truncated triangular or rectangular shapes depending on the cross-section. In line with the equilibrium predictions in Table 1, (Zr,Hf)C-rich phase shows higher solubility for additional transition metals than (Ti-W)C-rich phase; and, constitutes the majority part of the decomposed grains, i.e. (Zr,Hf)C-rich phase has higher volume fraction. We attribute the presence of the additional elements in the WC phase to the specimen interaction volume of the electron beam, giving rise to an additional signal from the surrounding (Ti,Zr,Hf,W)C matrix.

## 3.3. Nanostructural investigation

Fig. 4.a shows an HRTEM image of the as-sintered sample. The selected area electron diffraction (SAED) pattern, given as inset, confirms that the (Ti,Zr,Hf,W)C belongs to the face-centered cubic (FCC) structure. As shown, the interplanar spacing of {200} is 2.268 Å and thus the lattice parameter is calculated to be 4.536 Å, in reasonable agreement with the neutron diffraction refinement result. To further investigate the homogeneity in (Ti,Zr,Hf,W)C, STEM integrated with EDX was employed. STEM-EDX mapping results of Hf, Ti, W, Zr, and C elements in Fig. 4.b indicate the homogeneous distribution of all 4 metal atoms.

As the (Ti,Zr,Hf,W)C system has a miscibility gap, it is conceivable that the local chemical segregation can happen on the nanoscale through spinodal decomposition, which may strongly influence the overall properties of this material. We thus further employ HAADF-STEM to visualize the possible clustering through intensity variations as HAADF image is sensitive to the Z, i.e. atomic mass of elements. The thinner regions of the specimen shown in Fig. 5 indicate variations of intensity along with the atomic columns. The zoom-in image given as inset doesn't reveal any local clustering or ordering that might appear as an accumulation of similar intensity columns and periodical change of intensity, respectively.
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** SEM investigation of microstructure and EDX analysis of the phases. (a, b) Micrographs of as-sintered and 100 h aged (Ti,Zr,Hf,W)C samples, respectively. (c) Micrographs of 100 h aged sample showing single-phase (Ti,Zr,Hf,W)C solid solution together with (Ti,W)C-, (Zr,Hf)C-rich, and WC decomposition products indicated by arrows. (d) Corresponding EDX point composition analysis results of phases pointed in (c).</figcaption></figure>

### 3.4. Mechanical properties

Solid solution strengthening effects are often found in high entropy materials systems that can significantly improve the physical properties of the material. Table 2 lists the experimentally measured hardness and Young's modulus results of single-phase (Ti,Zr,Hf,W)C, decomposition products, and monocarbides combined with those collected from previous studies. A similar methodology is applied in this work as in the literature to ensure a comparison of the mechanical property data. The hardness results determined by nanoindentation are listed as they can better reflect the real value because of the common presence of porosity in carbide materials. Whereas TiC, ZrC, and HfC have rock-salt structure in ambient conditions, WC has hexagonal crystal structure at ambient conditions and its high-temperature modification is a rock-salt phase [33]. The hardness and Young's modulus of cubic WC is thus determined computationally. In the present work, the nanohardness and Young's modulus of hexagonal WC grain is determined using WC-10 wt% Co composite and that of cubic WC is taken from Ref. [11]. Table 2 shows that (Ti,Zr,Hf,W)C has a very high nanohardness 32.7 (± 1.9) GPa and elastic modulus 410.9 (± 23.1) GPa. Compared with the individual and rule of mixture (using experimental values, i.e. hexagonal WC) nanohardness (25.6 GPa) and Young's modulus (388.5 GPa) values, the single-phase (Ti,Zr,Hf,W)C shows a significant increase in both nanohardness and Young's modulus. Meanwhile, (Ti,Zr,Hf,W)C also showed a higher nanohardness than similar four-element multi-principal carbide systems such as (Ti,Zr,Nb,V)C (30.3 ± 0.7 GPa) reported by [10] and five-element systems e.g. (V,Nb,Ta,Mo,W)C (27 ± 3 GPa) and (Ti,Hf,Nb, Ta,W)C (31 ± 2 GPa) reported by Harrington et al. [12] even though both (Ti,Zr,Hf,W)C and (Ti,Zr,Nb,V)C have the valance electron concentration (VEC) of 8.5. The possible mechanisms of such strengthening effects observed in multi-principal element carbide systems are further discussed in the following section. Upon aging at 1350 °C for 100 h, no significant change is observed in the nanohardness and Young's modulus for the single-phase (Ti,Zr,Hf,W)C. However, lower hardness values are expected for (Ti,W)C-rich and (Zr,Hf)C-rich decomposition products due to the lower solid solution hardening effect. As the amount of these phases is very minor, their impact on the mechanical properties couldn't be probed.

Fig. 6 shows the microhardness and fracture toughness of as-sintered (Ti,Zr,Hf,W)C under different loads. At 0.5 kg load, no cracks are observed for the calculation of fracture toughness. The microhardness and fracture toughness values at 1 kg load are about 19 GPa and 5 MPa·m$^{1/2}$, respectively. The microhardness and fracture toughness in a multi-principal carbide system can vary with the grain size [13]. As the sintering temperature, dwell time, and the properties of the initial powder mixture can affect the grain growth and correspondingly the final grain size, any comparison of the microhardness and fracture toughness findings should be done with caution. Nevertheless, for the sake of comparison with the binary (Ti,Zr)C system [20], our results show that the fracture toughness is doubled with HfC and WC additions at the expense of about 20% reduction in microhardness.

### 4. Discussion

We present here a novel multi-principal element carbide, (Ti,Zr,Hf,W)C, in which the carbide solid solution is expected to become thermodynamically metastable below 1640 °C. Experimental investigations evince that the decomposition initiates upon aging at 1350 °C for 100 h through the formation of rock-salt (Zr,Hf)C- and (Ti,W)C-rich phases together with hexagonal WC precipitates. The predicted compositions of decomposition products are in line with the SEM-EDX analysis. As these phases are present in only minor amounts, no distinct diffraction peaks are observed on the neutron diffraction patterns (Fig. 2). On the other hand, in binary (Ti,Zr)C system, 100 h aging at 1300 °C has been found to be sufficient to result in notable phase separation bringing distinct diffraction peaks associated with (TiC)-rich and (ZrC)-rich products [37]. Such restrained decomposition kinetics in (Ti,Zr,Hf,W)C could be associated with the reduced driving force for phase decomposition limiting nucleation and slowing down diffusion. The driving force for nucleation in phase separation stems from the undercooling, i.e. the difference between the aging temperature and maximum temperature of the miscibility gap for a given composition. For a constant aging temperature, the higher miscibility gap temperature for equimolar (Ti,Zr)C of about 2000 °C [25,26] compared to 1640 °C for (Ti,Zr,Hf,W)C, can lead to higher nucleation rates in the (Ti,Zr)C system. The growth of nuclei and consequently the decomposition rate would then be tied to
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** TEM characterization of (Ti,Zr,Hf,W)C. (a) HRTEM image of (Ti,Zr,Hf,W)C, inset is the SAED pattern and is identified as the < 100 > direction of FCC. (b) STEM-EDX result shows uniform elemental distribution in (Ti,Zr,Hf,W)C sample.</figcaption></figure>

the diffusion rate. As the “sluggish diffusion” term has been widely used for multi-principal element alloys and carbides [13,17], together with the inadequate driving force for nucleation, we believe that the hindered diffusion can also contribute to the presence of only a minor level of decomposition products.

In the as-sintered state, our results reveal that the single-phase (Ti,Zr, Hf,W)C solid solution has higher nanohardness than the average of the monocarbides, i.e. rule-of-mixture hardness (Table 2). The origin of

enhanced hardness in multi-principal carbide systems is still under debate. Several mechanisms have been proposed including modification in electronic structure, e.g. through VEC, solid solution effect, and change in slip system [11,14]. Several works have pointed out a correlation between the VEC and the hardness of carbides and nitrides: the hardness reaches its maxima at VEC about 8.4 and further increments result in inferior hardness trading off with higher fracture toughness [3, 12,38–40]. Such decrease in hardness with increasing VEC has been
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Atomic resolution high angle annual dark-field (HADDF) image of as-sintered (Ti,Zr,Hf,W)C, inset is the zoom-in of the white square area.</figcaption></figure>

**Table 2**

Measured mechanical properties (nanindentation) of the carbides in some earlier works and this work. For WC with rock-salt structure, calculated values from literature are given.

<table><thead><tr><th>System</th><th>Source</th><th>Nanohardness [GPa]</th><th>Elastic Modulus [GPa]</th><th>Load [mN]</th></tr></thead><tbody><tr><td>ZrC</td><td>[34]</td><td>28.3 ± 1.6</td><td>352 ± 13</td><td rowspan="2">250</td></tr><tr><td>WC</td><td>(Calculated, rock-salt[11])</td><td>11–23</td><td>403</td></tr><tr><td></td><td>(Current, hexagonal)</td><td>25.0 ± 1.6</td><td>452.8 ± 17.1</td><td>10</td></tr><tr><td>HfC</td><td>[35]</td><td>29.0</td><td>352</td><td>8</td></tr><tr><td>TiC</td><td>[36]</td><td>25.6</td><td>397.3</td><td>13</td></tr><tr><td>(Ti,Zr,Hf, W)C</td><td>(Current, experimental)</td><td>32.7 ± 1.9 (0 h)<br/>33.1 ± 1.4 (100 h)</td><td>410.9 ± 23.1 (0 h)<br/>439.4 ± 9.7 (100 h)</td><td>10</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Mechanical properties of as-sintered (Ti,Zr,Hf,W)C. The blue line shows the measured microhardness and the red line shows the measured fracture toughness as a function of load.</figcaption></figure>

attributed to the enhanced metallic bonding over the covalent bonds, which has been pointed out as the key barrier for the dislocation motion [38,40]. The mixed carbide systems within the same group elements –at a constant VEC- can show strong hardening, e.g. (Ti,Zr)C, (V,Nb)C, through the solid solution hardening effect [3]. Solid solution hardening can stem from mass disorder and lattice distortion created by atomic size mismatch, i.e. the ratio between the root-mean-square deviation and mean lattice constant [41], both obstructing the dislocation motion [11,

23]. The large lattice mismatch (~8%) together with “optimum” VEC (8.5) could thus be the basis of high hardness and toughness combination in (Ti,Zr,Hf,W)C solid solution.

Upon aging, (Zr,Hf)C-rich, (Ti-W)C-rich, and WC phases form as decomposition products. Structural investigations do not show any evidence regarding the presence of spinodal decomposition, in which the hardening takes place through the local compositional changes resulting in the generation of coherency strain [22]. In (Ti,Zr,Hf,W)C system, the decomposition instead takes place through discontinuous precipitation. In carbide systems, where discontinuous precipitation takes place, the decomposition proceeds through the formation of a lamellar structure consisting, e.g. in the case of (Ti,Zr): TiC-rich and ZrC-rich carbide phases. Whilst the formed lamellar structure can enhance the hardness by creating new boundaries through the Hall-Petch relationship [42], due to the reduced solid solution hardening, only a minor increase was observed in the hardness of decomposed (Ti,Zr)C [43]. Furthermore, our findings in Fig. 3 have shown that the interlamellar spacing of (Zr,Hf)C- and (Ti,W)C-rich phases are significantly coarser than that of (ZrC)- and (TiC)-rich phases in equimolar (Ti,Zr)C even at higher aging temperatures [44]. This suggests only limited hardening associated with the formation of boundaries.

**5. Conclusions**

In this study, we have designed a novel high-hardness (Ti,Zr,Hf,W)C multi-principal element ceramic with a miscibility gap and synthesized it by SPS. Our work reveals that the phase separation can indeed take place in multi-principal element carbide systems. CALPHAD methodology predicts that the single-phase carbide solid solution becomes metastable below 1640 °C and decomposes into rock-salt structured (Zr, Hf)C- and (Ti,W)C-rich phases. Below 1400 °C, the hexagonal WC phase also coexists as evinced by electron microscopy in the sample aged at 1350 °C for 100 h.

No evidence has been found supporting the presence of spinodal decomposition. The phase separation appears to take place through discontinuous precipitation, where (Zr,Hf)C- and (Ti,W)C-rich phases form lamellar structure and WC exists close to its equilibrium shape. As the amount of decompositions products is minor, no distinct diffraction peaks associated with the formed phases are observed. Such slow decomposition kinetics compared to binary (Ti,Zr)C system is attributed to the lower driving force for phase decomposition.

The single-phase carbide solid solution has high nanohardness and fracture toughness. Nanoindentation measurements confirm the significant increase in hardness by the formation of (Ti,Zr,Hf,W)C solid solution. This could stem from the enhanced metallic bonding over the covalent bonds and solid solution hardening effect e.g. higher lattice misfit.

**Declaration of Competing Interest**

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

**Data Availability**

The neutron diffraction data that support the findings of this study are available in Ref. [28].

**Acknowledgements**

This research was funded by the Swedish Foundation for Strategic Research (SSF) within the Swedish national graduate school in neutron scattering (SwedNess). The work was performed in collaboration with the SSF funded project “Sintering non-homogeneous structures to enhance performance”. Part of the work was performed SJTU-KTH
collaborative research and development seed grants in 2020 (project title: Novel self-organized superhard carbides for application in cemented carbide composites). A.B.Y., R.P.B., and P.H. gratefully acknowledge the financial support provided by KTH Materials Platform and Institut Laue-Langevin (ILL) for the costs associated with the neutron diffraction experiment 5-21-1151. The authors acknowledge the National SPS facility at Stockholm University for access to SPS-825.

## Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jeurceramsoc.2022.04.029.

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