Achieving ultra-broadband electromagnetic wave absorption in high-entropy transition metal carbides (HE TMCs)

Electronic devices pervade everyday life, which has triggered severe electromagnetic (EM) wave pollution. To face this challenge, developing EM wave absorbers with ultra-broadband absorption capacity is critically required. Currently, nano-composite construction has been widely utilized to realize impedance match and broadband absorption. However, complex experimental procedures, limited thermal stability, and interior oxidation resistance are still unneglectable issues. Therefore, it is appealing to realize ultra-broadband EM wave absorption in single-phase materials with good stability. Aiming at this target, two high-entropy transition metal carbides (HE TMCs) including (Zr,Hf,Nb,Ta)C (HE TMC-2) and (Cr,Zr,Hf,Nb,Ta)C (HE TMC-3) are designed and synthesized, of which the microwave absorption performance is investigated in comparison with previously reported (Ti,Zr,Hf,Nb,Ta)C (HE TMC-1). Due to the synergistic effects of dielectric and magnetic losses, HE TMC-2 and HE TMC-3 exhibit better impedance match and wider effective absorption bandwidth (EAB). In specific, the exclusion of Ti element in HE TMC-2 endows it optimal minimum reflection loss (RLmin) and EAB of −41.7 dB (2.11 mm, 10.52 GHz) and 3.5 GHz (at 3.0 mm), respectively. Remarkably, the incorporation of Cr element in HE TMC-3 significantly improves the impedance match, thus realizing EAB of 10.5, 9.2, and 13.9 GHz at 2, 3, and 4 mm, respectively. The significance of this study lays on realizing ultra-broadband capacity in HE TMC-3 (Cr, Zr, Hf, Nb, Ta), demonstrating the effectiveness of high-entropy component design in tailoring the impedance match.


Introduction 
The ever-growing demands for communication capacity High-entropy construction is a useful design strategy for weight reduction; however, high-entropy (Ti,Zr,Hf, Nb,Ta)C with lower density exhibits poorer EM wave absorption performance compared with those of HfC and TaC, which is ascribed to the presence of TiC with intense discrepancy between the dielectric and magnetic losses [26]. In our previous studies [27][28][29][30], high-entropy compositional design has been found effectively in improving impedance match and EM wave absorption performance. Notably, the incorporation of Cr in high-entropy transition metal diboride (HE TMB 2 ) leads to strong and broadband absorption capacity [30]. Therefore, through eliminating Ti element or substituting Ti element with Cr element, it is expected that the EM wave absorption performance of HE TMCs can be further improved.
Aiming at achieving better EM wave absorption performance than that of high-entropy (Ti,Zr,Hf,Nb,Ta)C (HE TMC-1), two nominally equimolar HE TMCs including (Zr,Hf,Nb,Ta)C (HE TMC-2) and (Cr,Zr,Hf, Nb,Ta)C (HE TMC-3) are designed as new EM wave absorbers. Note that the data of HE TMC-1 (TM = Ti, Zr, Hf, Nb, Ta) in this study are cited from Ref. [26]. Through high-entropy engineering, it is expected that the formation of HE TMCs would be beneficial to enhance the overall properties including thermal stability [31][32][33], oxidation, and corrosion resistance [34,35], as well as EM wave absorption performance [36].

Materials and method 2. 1 Synthesis of HE TMC powders
To address the purpose of improving EM absorption performance, two nominally equimolar HE TMCs, i.e., (Zr,Hf,Nb,Ta)C and (Cr,Zr,Hf,Nb,Ta)C, were designed and subsequently synthesized by carbothermal reduction method according to Reactions (1) and (2) Heilongjiang, China) were weighted according to Reactions (1) and (2), and then mixed thoroughly in an agate mortar. The mixed powders were uniaxially pelletized into cylindrical pellets using a stainless-steel die with the diameter of 12 mm, which were heated at 1950 ℃ for 1 h in vacuum. Finally, the as-prepared pellets were crushed, ground in an agate mortar, and then sieved through a 120-mesh screen for subsequent characterizations.

2 Characterizations
Phase composition was analyzed by an X-ray diffractometer (XRD; D8 Advanced, Bruker, Germany) utilizing Cu Kα radiation (λ = 1.5418 Å) with a step size of 0.02 at a scanning rate of 2 ()/min. The lattice parameter was obtained by Rietveld refinement using the total pattern solution software (TOPAS; Bruker Corp., Karlsruhe, Germany). A SUPRA 35 scanning electron microscope (SEM; LEO, Oberkochen, Germany) equipped with the energy disperse spectroscopy (EDS) was used for morphology observation. The chemical compositions were analyzed using an inductively-coupled plasma atomic emission spectrometer (ICP-AES; Thermo iCAP 6000 series, Thermo Fisher Scientific Inc., Waltham, MA, USA) using the samples prepared by the following procedures. The as-prepared powders were mixed with sodium peroxide and sodium hydroxide, and then decomposed at 700 ℃ for 15 min. The obtained melts were acidified with hydrochloric acid, which were finally aspirated into the device.
The relative complex permittivity (ε r = ε + jε) and permeability (μ r = μ+ jμ) were determined by a vector network analyzer (Agilent N5244A, USA) using the coaxial method in the frequency range of 1.0−18.0 GHz. The as-prepared HE TMC powders and paraffin wax were mixed at a mass ratio of 7:3 and compacted into a toroidal shape (Φ out = 7.00 mm, Φ in = 3.04 mm). Based on the transmission-line theory and metal back-panel model, the reflection loss (RL) was determined from the relative complex permittivity and permeability for a given frequency and sample thickness according to Eqs. (3) and (4) [6,7]: where Z 0 represents the impedance of free space, Z in represents the normalized input characteristic impedance at the interface between atmosphere and absorber, μ r is the relative complex permeability, ε r is the relative complex permittivity, f is the frequency, d is the thickness of samples, and c is the velocity of light (3 × 10 8 m/s). The effective absorption bandwidth (EAB) is defined by the frequency range over which the RL value is smaller than −10 dB, which is comparable to 90% microwave energy absorption [6,7].

Results and discussion
As shown in Fig. 1(a), TMCs crystalize in B1 (NaCl) structure with the space group of Fm3m (No. 225) consisting of TMC 6 octahedral [22]. From Fig. 1(b), it can be interpreted that the TM atoms fill in the octahedral coordination constructed by carbon atoms, which will lead to the elimination of degeneracy of TM-d orbitals due to the crystal field effects [37][38][39].
In specific, the electrons in e g ( 2 d z and 2 2 d x y  ) orbitals suffer a greater repulsion, which is ascribed to that the overlap of e g orbitals and C-2p orbitals endows e g orbitals with higher energy levels [38,39]. As for t 2g orbitals, they are granted with lower energy levels. Notably, the interconversion between e g and t 2g orbitals as responses to EM field or heat will yield substantial magnetic loss capacity [26].

1 Synthesis and characterization of HE TMCs
With the presence of strong chemical bonding, TMCs are featured with low diffusion coefficients, making it difficult to prepare single-phase HE TMCs [23]. As shown in Fig. 2, the formation of HE TMC-1 (TM = Ti, Zr, Hf, Nb, Ta) solid solution after synthesized at 1900 ℃ with the dwelling time of 2 h is incomplete. It is proposed that the trap of TiC with the fastest diffusion rate among TMCs (TM = Ti, Zr, Hf, Nb, Ta) into TaC "host" leads to the shrinkage of the lattice, making it harder for the other TMs to diffuse into the preformed solid solution [40]. As for HE TMC-2 (TM = Zr, Hf, Nb, Ta) synthesized at 1950 ℃ for 1 h, however, the phase separation still exists after the exclusion of Ti element, which is consistent with the previously reported results at even higher calcining temperatures [41]. Notably, the introduction of Cr into HE TMC-3 (TM = Cr, Zr, Hf, Nb, Ta) is helpful to boosting the formation of solid solution, which could be ascribed to the spurred mass transformation induced by the evaporation of Cr 2 O 3 at high temperature in vacuum [30]. From Fig. 3, XRD patterns of ZrC, HfC, NbC, and TaC are presented to prove the formation of NaCl-type HE TMC-3 phase. It is worth noting that though there is no experimental evidence of the existence of CrC, the main reflection peaks are indexed as NaCl-type phase, indicating that the as-prepared HE TMC-3 is structurally ordered but compositionally disordered with multi-TM elements (TM = Cr, Zr, Hf, Nb, Ta). Besides, minor impurities detected in the vicinity of (111) plane are indexed as HfC phase, which ranks latest in the sequence of multi-step solid solution formation [42]. Noting that the presence of minor impurities has undamaging and trivial effects on the EM absorption performance, i.e., the impurities could spur the interfacial polarizations, which is trivial when compared with the effect of elemental alternation [26,27]. To determine the final elemental composition of as-prepared HE TMC-2 and HE TMC-3, ICP-AES experiments were conducted. Table 1 lists the nominal and experimental measured compositions. The elemental ratios of TM cations in HE TMC-2 exhibit nearly equimolar, while Cr-deficient scenario is found in HE TMC-3. On the one hand, the severe evaporation of Cr 2 O 3 at elevated temperature in vacuum may spur the formation of single-phase HE TMC-3. On the other hand, however, it leads to the limited solid solution quantity of CrC. Through Rietveld refinement, the lattice parameter (a) of HE TMC-3 is determined to be 4.5488 Å, and the theoretical density (ρ) of HE TMC-3 based on ICP-AES results is calculated to be 10.41 g/cm 3 , which is effectual in   lowering the density compared with HfC (12.6 g/cm 3 ) and TaC (14.6 g/cm 3 ). Figure 4 illustrates the morphologies of HE TMC-2 (TM = Zr, Hf, Nb, Ta) and HE TMC-3 (TM = Cr, Zr, Hf, Nb, Ta) powders. With the addition of Cr element, HE TMC-3 powders exhibit particle size larger than that of HE TMC-2 powders, which coincides with the situation in high-entropy diboride (HE TMB 2 ) [30]. The significant growth of HE TMC-3 particles is mainly attributed to the boosted mass transportation due to the evaporation of Cr 2 O 3 , which is expected to decrease the degree of interfacial polarization and further weaken the dielectric loss capability.

2 EM properties of HE TMC powders
In the light of Maxwell's equations, the interactions between materials and oscillatory EM field can be evaluated by complex permittivity (ε r = ε + jε) and complex permeability (μ r = μ+ jμ), of which the real parts (ε and μ) and imaginary parts (ε and μ) represent the energy storage and dissipation capacities, respectively [5].
To reveal the effects of high-entropy compositional design on the EM properties of HE TMCs, Fig. 5 compares the EM parameters of three HE TMCs, where the composition dependent responses to the alternating electric field are observed, i.e., the ε and ε values across the testing frequency range rank roughly in the sequence of HE TMC-1, HE TMC-2, and HE TMC-3. From Figs. 5(b) and 5(c), it is observed that the dielectric loss tangent (tanδ ε = ε″/ε′) values exhibit similar frequency dependence as the ε values, suggesting that the weakening of dielectric loss capabilities have been achieved by eliminating Ti element in HE TMC-2 and substituting Ti element with Cr element in HE TMC-3. Considering the conductive nature of TMCs, the dielectric loss ability of HE TMCs originates from the conduction loss, the dipolar polarization relaxation loss, and the interfacial polarization relaxation loss (called the Maxwell-Wagner effect) [5,[43][44][45]. In specific, the electron migration contributes to the energy dissipation in the form of conduction loss. Moreover, numerous point defects (e.g., vacancy, substitutional atom, and interstitial atom) existing in the HE TMC solid solutions with multi-principal components can serve as the polarization center, while the local stress induced by lattice disorder can restrain dipole re-orientation under the alternating electric field, thus leading to polarization relaxation with energy consumption [43,44]. Besides, in the heterogeneous HE TMC materials, minor residue impurities and paraffin wax can spur the interfacial polarizations and related relaxations [44]. The polarization relaxation loss process can be determined by Cole-Cole semicircles in Fig. 6(a), of which HE TMC-2 exhibits skewed tendency due to the unignorable conductivity and multi-relaxation processes [5].
From Figs. 5(d) and 5(e), the μ and μ values show explicit distinctions among three HE TMCs, of which the variations are roughly contrary to ε and ε values. As typical dielectric loss-type absorbers, HE TMC-1 exhibits ε values equal to 1 and negative μ values over 4−18 GHz, suggesting that magnetic loss would not operate at these frequency bands [26]. However, the elimination of Ti element in HE TMC-2 leads to the absence of negative μ values, which enables EM wave entering the EM wave absorber. Therefore, it can be concluded that the presence of TiC in HE TMC-1 increases the dielectric loss capacity but decreases the magnetic loss capacity, which has detrimental effects on tuning the impedance match. Especially, HE TMC-3 possesses spurred magnetization and magnetic loss  capability compared with HE TMC-1 and HE TMC-2, which are ascribed to the partial spin polarization induced by the solid solution of Cr element [30]. As shown in Fig. 5(f), HE TMC-2 and HE TMC-3 possess positive magnetic loss tangent (tanδ μ = μ″/μ′) values over the testing frequency span. The tanδ μ -f curve of HE TMC-2 displays a continuous decrease from 1 to 10 GHz and then an insignificant rise from 10 to 18 GHz. As for HE TMC-3, the magnetic loss capability fluctuates in the range of 0.3−0.6, which is comparable to those of magnetic loss-type EM wave absorbers with optimal component designs, e.g., Fe 3 O 4 nano-rings [17], Fe 3 S 4 /rGO nano-composite [18], CoS 2 /rGO nano-composite [19], etc. The mechanisms of magnetic loss in three HE TMCs mainly include the resonance loss and the Eddy current loss [5,46,47]. The Eddy current loss can be determined by Eq. (5), which is directly associated with electrical conductivity (σ) and matching thickness (d) [5]: where μ 0 is the vacuum permeability. The dominance of resonance loss can be determined by the variation of C 0 values, otherwise the Eddy current loss gains the upper hand. From Fig. 6(b), the stable magnetic loss capability of HE TMC-3 across the whole testing span www.springer.com/journal/40145 is attributed to multi-resonance loss, which is related to the d-orbital splitting due to crystal field effect [26,30,[37][38][39] and the electron paramagnetic resonance underpinned by defect energy levels [46,47]. Considering the dielectric and magnetic losses, it is concluded that the synergistic effects of dielectric and magnetic losses are achieved in HE TMC-2 and HE TMC-3, which can be evaluated by the attenuation constant (α), as shown in Fig. 6(c) [7]: Though HE TMC-1 possesses strong dielectric loss, the absence of magnetic loss leads to less satisfactory EM wave dissipation capacity [26]. In addition, the dissipation capacities of HE TMC-2 and HE TMC-3 vary with frequency, i.e., HE TMC-3 possesses larger α values in the frequency range of 5−12 GHz, while HE TMC-2 prevails at the other frequency ranges. Apart from the EM wave dissipation capacity, the impedance matching character plays a critical role in deciding the effective absorption bandwidth [7][8][9]. As shown in Fig.  6(d), HE TMC-3 exhibits the magnetic loss tangent comparable to the dielectric loss tangent across the testing frequency span, with dielectric loss dominating over 13-17 GHz and magnetic loss dominating over the rest frequency ranges. Considering that the resonance loss capacity of HE TMC-3 is mainly originated from the d-orbital splitting and the electron paramagnetic resonance, HE TMC-3 is expected to maintain high magnetic loss capacity at high temperatures [3,20]. Notably, decreasing the dielectric loss capacity and increasing the magnetic loss capacity in the meantime are helpful in optimizing the impedance match for dielectric loss-type EM wave absorbers with good conductivity, e.g., carbon nanotubes (CNTs) [11], TMCs [26], transition metal diborides (TMB 2 s) [48], highentropy alloys [49,50], etc. Therefore, it is promising to achieve good impedance match in HE TMC-3 with relatively close dielectric and magnetic loss capacities across a wide frequency band.
On the basis of the above analysis, there are two pivotal factors deciding the EM wave absorption performance of HE TMCs, namely, the dissipation capacity (α) and the impedance match (Z), in which the latter directly determines the EAB. To elaborate the effects of impedance match on the effective absorption bandwidth, it can be concluded that the effective absorption takes place when 0.52 ≤ Z ≤ 1.93 by solving Eq. (7) [30,51]: As shown in Fig. 7, the effective absorption can be achieved in three HE TMCs within the regions where 0.52 ≤ Z ≤ 1.93. From Figs. 7(a)-7(c), the optimal RL min values at matching frequency and thickness of HE TMC-1, HE TMC-2, and HE TMC-3 are −38.5 dB (1.9 mm, 9.5 GHz), −41.7 dB (2.11 mm, 10.52 GHz), and −21.6 dB (2.04 mm, 12.56 GHz), respectively, which are realized when the impedance match is ideal (Z ≈ 1). From Figs. 7(d)-7(f), it can be inferred that removing Ti element has a beneficial effect on promoting the impedance match of HE TMCs, which is especially conspicuous for HE TMC-3 with the addition of Cr element. As shown in Fig. 7(f), the frequency band of HE TMC-3 where Z values lie between 0.52 and 1.93 covers almost the whole testing frequency range in spite of the variation of sample thickness. Apart from the ideal impedance matching zone, there are a few areas where impedance mismatch occurs due to the occasional predominance of dielectric loss capability, as described in Fig. 6(d). As a consequence of tuning the impedance match, the optimal EAB and the corresponding matching thickness of HE TMC-1 and HE TMC-2 are 2.3 GHz (at 1.5 mm) and 3.5 GHz (at 3.0 mm), respectively. As for HE TMC-3, broadband absorption can be realized at various sample thicknesses, i.e., the EABs at 2.0 and 3.2 mm are 10.5 and 9.2 GHz, respectively, while the EABs at thickness over 4 mm are greater than 13.9 GHz. The EAB at 6.0 mm reaches 15.2 GHz (2.8−18 GHz), almost covering the total S band (2−4 GHz), C band (4−8 GHz), X band (8−12 GHz), and Ku band (12)(13)(14)(15)(16)(17)(18). Needless to say, incorporating Cr element in HE TMC-3 significantly broadens the EAB compared with HE TMC-1, making it capable of realizing ultra-broadband absorption. As mentioned before, it has surprisingly been found that the EAB at 4.0 mm reaches 13.9 GHz, which is superior to most other EM wave absorbing materials [7][8][9]. In addition, the ultra-broadband absorption capability is insensitive to the sample thickness, rendering it highly tolerant to manufactural error. Drawn from the above analysis, it can be concluded that the elimination of Ti element in HE TMC-2 has positive effects on improving EM wave absorption performance, while substituting Ti element with Cr element significantly boosts the magnetic loss capacity and improves the impedance match across the whole testing frequency band, endowing HE TMC-3 ultra-broadband absorption capacity. Therefore, through high-entropy component design, it is effective to optimize the impedance match of HE TMCs, thus achieving ultra-broadband absorption performance. Besides, high-entropy engineering is effective in lowing the density. Table 2

Conclusions
In conclusion, two HE TMCs with nominally equimolar ratio of TM elements including (Zr,Hf,Nb,Ta)C (HE TMC-2) and (Cr,Zr,Hf,Nb,Ta)C (HE TMC-3) are designed and synthesized, of which the EM wave absorption performances are compared with those of previously reported (Ti,Zr,Hf,Nb,Ta)C (HE TMC-1).
XRD analyses indicate that the as-synthesized HE TMC-2 with the exclusion of Ti element compared with HE TMC-1 still exhibits phase segregation, while the incorporation of Cr element in HE TMC-3 boosts the formation of single-phase solid solution. The theoretical density of HE TMC-3 is determined as 10.41 g/cm 3 , which exhibits lower density compared with broadband transition metal carbide absorbers including HfC and TaC. Through SEM analyses, the incorporation of Cr element leads to significant growth of particle size, which can further decrease the dielectric loss capability.
Through high-entropy component design, the coupling effects of dielectric and magnetic losses can be effectively tailored, leading to promoted impedance match. Compared with HE TMC-1, the elimination of Ti element in HE TMC-2 leads to positive magnetic loss tangent over the testing frequency span, which prevents the EM wave from being directly reflected at the surface and contributes to the improved dissipation capacity and EAB. The optimal RL min and EAB of HE TMC-2 are −41.7 dB (2.11 mm, 10.52 GHz) and 3.5 GHz (at 3.0 mm), respectively. Notably, the substitution of Ti element with Cr element in HE TMC-3 contributes to close dielectric and magnetic loss tangents across a wide frequency band, making it capable of realizing ultra-broadband absorption. As a result of ideal impedance match, HE TMC-3 reaches effective absorption bandwidth greater than 13.9 GHz over 4 mm. Moreover, the ultra-broad EAB is insensitive to the variation of sample thickness. Considering excellent thermal stability, good oxidation and corrosion resistance, and ultra-broadband absorption performance, HE TMC-3 (TM = Cr, Zr, Hf, Nb, Ta) exhibits great application potential as EM wave absorbers, especially under high-temperature or corrosive serving environments.