Introduction

The two-dimensional (2D) layered materials have been applied across diverse fields such as electronics1,2,3, optoelectronics4,5,6, energy storage7,8,9, sensors10, catalysis11,12, and electromagnetic interference shielding13,14,15, because of their exceptional electroconductivity and versatile surface chemistries16,17,18,19,20,21,22. Ripple texturing, which is an inherent feature of 2D layered materials, originates from the periodical displacement of atoms due to thermal fluctuation and strain profiles. Traditionally, both spontaneously and thermally generated strains have been utilized to control ripple orientation, wavelength, and amplitude, enabling strain-based 2D material electronics23. It can effectively modify mechanical, magnetic, and electronic properties by introducing spatially varying potentials or effective magnetic fields24,25,26. For instance, the randomly distributed ripples induce spatially disordered charge density fluctuations in the graphene by the π-σ rehybridization, significantly improving charge transport characteristics27. However, precisely controlling the ripple structure remains a significant challenge.

Two-dimensional transition metal carbonitrides (MXenes) have been actively studied as a burgeoning class of 2D materials with excellent metallic conductivity and an abundance of surface defects28,29,30,31. Especially, incorporating large ionic radius termination atoms can produce ripple structures within MXenes’ framework without the aid of additional fields32, which is expected to effectively customize electronic properties. Notably, as promising electromagnetic (EM) shielding and absorption materials, most research has focused on interlayer engineering, defect strategy, and composite methods to optimize MXenes’ properties33,34,35,36,37. For instance, simultaneously tuning the interlayer spacing and surface termination of Ti3C2Tx to improve impedance matching and enhance EM wave loss38. Besides, the assembled double-shell MXene@Ni microspheres via a spheroidization strategy achieve the maximum synergistic effect of dielectric and magnetic constituents39. However, to the best of our knowledge, the ripple-modulated engineering and corresponding mechanisms have never been reported. Additionally, the correlation between ripple structure and microwave absorption (MA) performance in MXenes needs to be elucidated to achieve repeatable manipulation.

Herein, we successfully introduce and modulate atomic ripple structure through a competition strategy between configurational entropy and surface termination within Nb2CTex-based MXenes40. Introducing -Te termination through the Lewis acidic molten salt etching method generates the local in-plane strain, yielding atomic ripple structure41,42. Since complex concentrated solutions of multiple principal elements can modify local strain distribution, replacing ions at M sites with multiple hetero-metal-atoms induces the evolution of local in-plane strain, thereby achieving precise control of atomic ripple structure. The elaborate design of the periodic ripple structure modulates the relaxation time of the microscopic dipole (caused by charge accumulation on the interface between MXenes and paraffin) in the applied electric field, ensuring controlled regulation of the dielectric properties. As a result, (TiVNbTaZr)2CTex exhibits satisfactory effective absorption bandwidth covering the full band from 2 to 12 GHz. This work furthers insight into our fundamental understanding of entropy increasing contributions to polarization relaxation processes, and paves a new way for the research of MXenes absorbers.

Results and discussion

Entropy-modulated periodic ripple structure in MXenes

By using a compositionally complex doping strategy, we successfully prepared the Nb2AlC-based MAX phases, including medium-entropy (TiNbTa)2AlC and high-entropy (TiVNbTaZr)2AlC (Supplementary Fig. 1). Equimolar metal elements (Ti, Ta, V, and Zr) were progressively introduced into the M position of Nb2AlC, thereby increasing configurational entropy40. The synthesized MAX phases with nearly identical X-ray diffraction (XRD) patterns indicate minimal structural fluctuation induced by metal element introduction. The sharp and intense diffraction peaks located at approximate 2θ angles of 12.94° (002), 25.86° (004), 33.54° (100), 34.17° (101), 38.96° (103), 42.81° (104), and 52.44° (106) match well with reported M2AX phases (Supplementary Fig. 2)41. Subsequent conversion from MAX phase to MXenes was accomplished through a Lewis acid molten salt etching method, yielding medium and high entropy MXenes (Fig. 1a and Supplementary Fig. 3). These products show a typical accordion-like microstructure morphology with primary sizes ranging from 2–15 μm, suggesting MXenes formation (Supplementary Fig. 4). The inductively coupled plasma atomic emission spectroscopy (ICP-AES) data determine the chemical formula (Ti0.42Nb0.30Ta0.28)2CTex and (Ti0.26V0.15Nb0.22Ta0.22Zr0.15)2CTex, abbreviated as (TiNbTa)2CTex, and (TiVNbTaZr)2CTex (Supplementary Fig. 5 and Supplementary Table 1). The disappearance of diffraction peaks and the shift of (002) peaks to lower Bragg angles in the XRD patterns (Fig. 1b) (for Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex) confirm the complete transformation from MAX to MXenes phase. The above results are further corroborated by an atomic high-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images of MXenes (Supplementary Fig. 6), where the center-to-center interlayer distance is calculated to be ~3.0 Å, almost in agreement with the value of 3.2 Å measured with XRD. Each M2CTex monolayer (M=Nb, TiNbTa, TiVNbTaZr) consists of four atomic layers: the middle two layers of M site atoms and the outer two layers of -Te terminations. To investigate the elemental distribution in the MXenes, atomic-resolved energy-dispersive X-ray spectroscopy (EDS) mapping for Nb2CTex (Supplementary Fig. 7), (TiNbTa)2CTex (Supplementary Fig. 8), and (TiVNbTaZr)2CTex (Fig. 1c) was performed. The metal elements (Ti, V, Nb, Ta, and Zr) were found to occupy M sites, while Te atoms uniformly distribute on the surface of MXenes, demonstrating the replacement of Nb with the introduced metal atoms at the M sites. Moreover, all metal elements exhibit clear and periodic distributions corresponding to the atomic layer structure (Supplementary Fig. 7, Supplementary Fig. 8, and Fig. 1c), highlighting the uniform coexistence of introduced elements and Nb at the M sites. To better visualize compositional fluctuation, EDS profiles acquired along [001] direction were plotted. These profiles clearly demonstrate a homogeneous atomic distribution in the high entropy MXenes, where -Te terminations and metal elements are uniformly located at the T and M sites, respectively. These results substantiate the synthesis of Nb2CTex-based medium and high entropy MXenes with high purity and homogeneity through the progressive introduction of metal elements into the M position of Nb2AlC.

Fig. 1: Entropy-modulated periodic ripple superstructure in MXenes.
Fig. 1: Entropy-modulated periodic ripple superstructure in MXenes.The alternative text for this image may have been generated using AI.
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a Schematic lattice structure of the MXenes with increasing entropy along the [001] zone axis. b X-ray diffraction (XRD) pattern of MAX phase and derived MXenes. c Atomically resolved elemental mappings of (TiVNbTaZr)2CTex, including atomic resolution high-angle annular dark-field (HAADF) image, individual distribution of Te, Nb, Ti, V, Ta, Zr, and corresponding energy dispersive spectroscopy (EDS) line profiles along the [001] direction. d Selected area electron diffraction (SAED) patterns for Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex along the [100] zone axis. The yellow arrows mark the location of the extra discs. e Dependence of normalized diffraction intensity on the number of elements in the M site. f–h Atomic resolution high-angle annular dark-field (HAADF) images, inverse fast Fourier transform (IFFT) images obtained from the extra discs (the corresponding fast Fourier transform patterns with yellow solid circles marking the extra discs are shown in Supplementary Fig. 14), and the overlapped maps of atomic resolution high-angle annular dark-field (HAADF) and inverse fast Fourier transform (IFFT) images (f Nb2CTex, g (TiNbTa)2CTex, h (TiVNbTaZr)2CTex.). Source data are provided as a Source Data file.

To evaluate the microstructure of MXenes phases, we acquired selected-area electron diffraction (SAED) patterns along the [100] zone axis. In contrast to the simulant SAED of Nb2CTex (Supplementary Fig. 9), the synthesized Nb2CTex MXenes have an additional set of diffraction spots (Fig. 1d) at the locations corresponding to \(\frac{1}{6}\){010}, indicating the additional or increased chemical order. The intensity of these extra diffraction spots tends to decrease with the introduction of metal elements. For (TiVNbTaZr)2CTex, only faint additional diffraction information could be detected under the [100] zone axis. Apparently, the intensity of these extra diffraction spots, which are sensitive to the local atomic environment, can serve as an index to quantitatively evaluate the degree of superstructure. The normalized intensity of extra diffraction versus the number of elements in the M site is plotted in Fig. 1e and Supplementary Fig. 10, depicting a degradation in diffraction intensity with increasing the number of introduced elements. The linear response demonstrates that entropy-modulated atomic structures in MXenes are indeed plausible.

To directly investigate the atomic structure, the HAADF lattice images were acquired in STEM experiments. The Nb2CTex MXenes show a characteristic periodic atomic ripple structure (Supplementary Fig. 6a), which may be attributed to the lattice strains induced by large Te atoms (ionic radius = 221 pm)39. To confirm this hypothesis, Cl-terminated MXenes Nb2CClx was synthesized using a different Lewis acid molten salt. In sharp contrast, Nb2CClx does not exhibit a periodic ripple structure (Supplementary Fig. 11). Besides, X-ray photoelectron spectroscopy (XPS), and electron energy loss spectroscopy (EELS) for Nb2CTex have been provided to exclude the influence of -O, -OH terminations on the ripple structure during the washing process (Supplementary Fig. 12, Supplementary Fig. 13, and Supplementary Table 2). As the increase of entropy, these ripple structure gradually diminishes, nearly disappearing in (TiVNbTaZr)2CTex (Supplementary Fig. 6b and 6c). These results suggest that the extra diffraction spots in SAED patterns stem from the ripple structure. Furthermore, the corresponding FFT patterns ([100] zone axis) are shown in Supplementary Fig. 14, which also exhibit extra diffraction spots (circled in yellow). Meanwhile, a high-resolution lattice image-based method was applied, transitioning from the fast Fourier transform (FFT) patterns to inverse FFT (IFFT) images (Fig. 1f (ii), Fig. 1g (ii) and Fig. 1h (ii)). Superimposing the HAADF and IFFT images highlights the atomic ripple structure even more clearly, as it adds intensity to the MXenes columns (Fig. 1f (iii), Fig. 1g (iii), and Fig. 1h (iii)). By integrating SAED patterns, HAADF images, and IFFT images, we exhibit the evolutions of ripple structure in Nb2CTex-based MXenes. Notably, the intensity and location of these extra diffraction spots in SAED patterns correlated to the amplitude intensity (AI) and wavelength of the atomic ripple structure, respectively. Hence, AIx (note: x representative extra diffraction spots intensity) was proposed to quantitatively evaluate the ripple feature in MXenes, in which AI0.0423 corresponds to Nb2CTex, AI0.0174 to (TiNbTa)2CTex, and AI0.0033 to (TiVNbTaZr)2CTex. Additionally, the location of extra diffraction spots shows a small change, with increasing configurational entropy. This indicates that the introduction of metal elements results in a slight fluctuation of ripple wavelength, maintaining an average value of approximately ~1.77 nm.

To provide a more comprehensive description of the ripple spatial distribution, we also conducted atomic structure characterization along the [120] and [001] zone axes (Supplementary Fig. 15). The SAED patterns acquired along the [120] zone axis exhibit extra diffraction discs at the locations corresponding to \(\frac{1}{6}\){2\(\bar{1}\)0}. The corresponding HAADF images, IFFT images, and overlapped maps of HAADF and IFFT images further confirm the presence of the ripple structure of Nb2CTex. Combined with the SAED results for [100] zone axis, which show additional spots corresponding to \(\frac{1}{6}\){010}, the spatial distribution of these ripples correlates with the metal atom positions as the sample is rotated around the c-axis. These findings suggest that the ripple structure takes on an island configuration arranged in a hexagonal pattern. To directly assess the ripple distribution, SAED patterns were also acquired along the [001] zone axis, further confirming the hexagonal arrangement. Additionally, HAADF images and corresponding IFFT images highlight the island configuration of the ripples, with an average size of ~0.52 nm. Collectively, the results from SAED, HAADF, and IFFT analyses provide compelling evidence for the spatial distribution of ripple structures in the form of hexagonally arranged islands.

The mechanism of entropy-modulated atomic ripple structure in MXenes

To unveil the mechanism of entropy control ripple structure and realize repeatable manipulation of ripple in MXenes, we employed a combination of atomic resolution integrated differential phase contrast (iDPC) and the image processing technique of geometric phase analysis (GPA), enabling atomic strain analysis with high accuracy and reliability43. As shown in Fig. 2a–c, the iDPC images further confirm that the atomic ripple structure diminishes with increasing entropy, consistent with the results of the above SAED and HAADF characterization. Based on these iDPC images, subsequent nanoscale strain analysis within MXenes was accomplished through the GPA method, yielding the in-plane strain εxx (Fig. 2d–f) and out-of-plane strain εyy (Supplementary Fig. 16)44. For Nb2CTex MXenes, the εxx map clearly shows periodic and alternating compressive strain and tensile strain along a direction, corresponding to the periodic ripple structure. In contrast, the εyy map exhibits a random distribution. This result indicates that the periodic ripple structure arises from the nanoscale in-of-plane stress which is induced by large Te atoms. In sharp contrast, the nanoscale strain concentration phenomenon was not observed in the Nb2CClx (Supplementary Fig. 17), further confirming the Te-termination-induced atomic ripple structure.

Fig. 2: Strain analysis of periodic ripple superstructure of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex.
Fig. 2: Strain analysis of periodic ripple superstructure of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex.The alternative text for this image may have been generated using AI.
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a–c Atomic resolution integrated differential phase contrast (iDPC) images of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex, respectively. d–f Geometric phase analysis (GPA) of the atomic resolution integrated differential phase contrast (iDPC) (corresponding to a–c) data reveals the in-plane strain εxx mappings of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex. The color from green to dark blue represents the compressive strain degree while the color from red to bright yellow refers to the tensile strain degree in the data bar. g–i Corresponding line profiles of areas 1, 2, and 3 (labeled in d–f). j Dependence of average strain on the amplitude intensity (AI) of the ripple structure. The red semicircle represents the tensile strain and the blue semicircle indicates the compressive strain. k–m The statistical distribution obtained from the atomic-strain mappings. The orange, red, and blue curves are Gaussian fits of the atomic-strain probability density results for the Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex, respectively. The full width at half maximum (FWHM) of each curve represents the fluctuation degree of the atomic strain in the corresponding sample. n Dependence of full width at half maximum (FWHM) on the amplitude intensity (AI) of the ripple structure. Source data are provided as a Source Data file.

As introducing hetero-metal-atoms into M sites, random local strain arising from the unmatched atomic size and mass leads to diminution of alternating compressive strain and tensile strain, implying that increasing entropy can effectively release the nanoscale in-plane strain (Fig. 2e, f). To more intuitively and quantificationally analyze the entropy-induced evolution of stress distribution, the line profiles of areas 1, 2, and 3 (located in Fig. 2d–f) were plotted in Fig. 2g–i. For Nb2CTex, the average tensile strain is 14.67%, which is extremely large compared to the average compressive strain −4.01%. Additionally, MXenes undergo significant degradation in tensile strain with the increased entropy, while the compressive stress remains relatively unchanged (Fig. 2j). This finding demonstrates that the periodic ripple structure is attributed to the nanoscale in-of-plane tensile strain and can be controlled through entropy-modulated tensile strain. Moreover, the statistical result of strain distribution is presented in Fig. 2k–m. The full width at half maximum (FWHM) of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex is 0.089, 0.072, and 0.060, respectively, indicating the fluctuation degree of the atomic-strain gradually decrease45,46. The reduced FWHM value further proves that the in-of-plane tensile stress gradually decreases with the increase of entropy (Fig. 2n). Our results suggest that the uniform introduction of -Te termination causes local deformation, which generates the periodic strain in Nb2CTex. Subsequently, the in-of-plane tensile strain is released through entropy increase, thereby leading to the adjustment of atomic ripple structure.

The ripple structure-interatomic coupling-electrical property correlation

To gain a more profound understanding of how this ripple structure affects the atomic electric fields and charge density distribution, we performed the differential phase contrast scanning transmission electron microscopy (DPC-STEM) technology47. This technique can directly visualize the relative direction and strength of the electric field at each atomic column, pointing outwards from the center of the atomic columns48. Figure 3a–c show the DPC images of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex, where the color and intensity correspond to the relative direction and strength of the electric field at each position. For Nb2CTex, the introduction of Te induces an asymmetric electric field distribution within these disks (highlighted by orange ovals in Fig. 3d), indicating charge redistribution. With the entropy-modulated weakening of the periodic ripple structure, these disks suffer from distortion (Fig. 3d, the enlarged maps of areas 2#, and 3#), and the electric fields of adjacent atomic columns fuse, (TiVNbTaZr)2CTex exhibits remarkable interatomic coupling. The results of DPC analysis indicate that the regulation of the ripple structure enhances the interatomic coupling electric field (Te-Te, Te-M site, and M-M site) within (TiNbTa)2CTex, and (TiVNbTaZr)2CTex, facilitating the transfer of electrons and cause the increase of the in-plane conductivity. Moreover, the actual conductivity was measured using the four-point probe method, in which the four-electrode devices were fabricated via focused ion beam (FIB) technology (Fig. 3i and Supplementary Fig. 18). The conductivities of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex is 0.61 × 103 S·m−1, 1.60 × 103 S·m−1, and 2.00 × 103 S·m−1, respectively. The increase in actual conductivity further corroborates the above DPC results.

Fig. 3: Differential phase contrast (DPC) characterization results and density functional theory (DFT) calculations of MXenes.
Fig. 3: Differential phase contrast (DPC) characterization results and density functional theory (DFT) calculations of MXenes.The alternative text for this image may have been generated using AI.
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a–c Differential phase contrast (DPC) images of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex along the [100] zone axis, showing electric field vector mapping. The color wheel indicates how color and shade denote the electric field relative orientation and relative strength. d Enlarged regions of areas 1#, 2#, and 3# (labeled in a–c). The orange ovals indicate the asymmetric electric field distribution and interatomic coupling. e–g The charge density difference between the M sites and -Te termination (e Nb2CTex, f (TiNbTa)2CTex, and g (TiVNbTaZr)2CTex.). The red area represents electron accumulation and the blue area represents electron consumption. The blue, dark green, light gray, dark gray, light green, brown, and black represent atoms Nb, Ti, Ta, V, Zr, Te, and C, respectively. h Dependency of normalized density of states (DOS) on amplitude intensity (AI) of the ripple structure. i Dependency of in-plane conductivity on amplitude intensity (AI) of the ripple structure. Source data are provided as a Source Data file.

Density functional theory (DFT) calculations were conducted to investigate the local charge density distribution and transportation of Te with adjacent M site atoms. The 2D electron density difference mappings (Fig. 3e–g) were obtained by slicing along (100) crystal faces from the three-dimensional isosurface (Supplementary Fig. 19). As shown in Fig. 3e, the -Te surface terminal functionalities caused the charge density redistribution, where the electrons transfer from Te to Nb. The addition of foreign atoms to the M site of Nb2CTex increases atomic distortion and local inhomogeneity40, intensifying the interatomic coupling effect at Te-Te, Te-M sites, and M-M sites (Fig. 3f, g), which is consistent with the experimental results of DPC. The density of states (DOS) is essentially the number of different states that an electron is allowed to occupy at a particular energy level, and a high DOS near the Fermi level means that there are more electron states available for the electron to occupy, thereby increasing the transition probability and conductivity of the electron34,47. Due to the difference in the number of valence electrons and atoms for the simulation units, we performed the normalization of DOS value relative to valence electron number and atoms number for each simulation model (Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex). The normalized DOS value increases with the increase of M-position entropy (Fig. 3h, Supplementary Table 3), indicating the enhanced electrical conductivity, which agrees with the trend of actually measured one.

Effects of entropy-modulated ripple structure on dielectric properties and microwave absorption performances

To clarify the correlation between the ripple structure and dielectric properties within MXenes, the electromagnetic parameters were measured using the coaxial method. The complex permittivity of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex ranging from 2 to 12 GHz were displayed in Fig. 4a–c, respectively. Obviously, the dielectric spectrum reflects two trends. First, both the ε' and ε“ values remarkably increase with the ripple structure weakening, this can be attributed to the strengthened in-plane conductivity discussed above. The second trend is the shift in the peak frequency of polarization. It is commonly believed that the relaxation time τ is an index of dipole mobility in dielectric materials, which is closely related to the polarization mechanism and is one of the key reasons for the dielectric loss of materials. According to the formula:

$$\tau=\frac{1}{{\omega }_{c}}=\frac{1}{2{{{\rm{\pi }}}}{f}_{c}}$$
(1)
Fig. 4: Electrical properties and microwave absorption performances of MXenes.
Fig. 4: Electrical properties and microwave absorption performances of MXenes.The alternative text for this image may have been generated using AI.
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a–c Complex permittivity of Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex, respectively. d Cole-Cole curves. e Maximum reflection loss (RLmax) diagram. f Dependency of effective absorption bandwidth (EAB) on amplitude intensity (AI) of the ripple structure. Source data are provided as a Source Data file.

We obtain that the relaxation time τ is inversely proportional to the relaxation frequency fc. As shown in the Cole-Cole curves in Fig. 4d and Supplementary Fig. 20, apparent Cole-Cole semicircles correspond to the polarization relaxation processes. Obviously, with the decrease in periodic ripple amplitude intensity, the relaxation frequency range gradually shifts to the lower frequency, corresponding to the increase in relaxation time. This can be explained by the microscopic dipole model, in which the charges accumulate on the interfaces between MXenes and paraffin wax under an applied electric field, forming microscopic dipoles. After changing the direction of the external electric field, the positive and negative charges that accumulate on the interfaces between MXenes and paraffin are slowly redistributed, and the microscopic dipoles are flipped, resulting in relaxation time. For Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex, the out-of-plane conductivity decreases with the entropy-modulated periodic ripple structure weakening (from 17.48 S·m−1, 9.45 S·m−1, to 2.33 S·m−1) (Supplementary Figs. 21 and 22). Hence, under the external electric field, the reduced out-of-plane conductivity slows down the redistribution of positive and negative charges in the microscopic dipole, resulting in prolonged polarization relaxation time.

The maximum value of reflection loss (RLmax) and effective absorption bandwidth (EAB, the bandwidth of RL ≤ − 10 dB), serving as two key factors for microwave absorption (MA), were further investigated49. As summarized in Fig. 4e, the RLmax values located at 8.8 GHz, 8.48 GHz, and 6.88 GHz correspond to dielectric relaxation peaks (Fig. 4a–c) for Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex, respectively. (TiVNbTaZr)2CTex exhibits the RLmax value of −41.12 dB at a thickness of only 2.3 mm (Supplementary Fig. 23), a notable improvement compared with the −26.10 dB of Nb2CTex. Figure 4f shows the dependency of EAB on the amplitude intensity of the ripple structure. In the 2–12 GHz range, there are only two extremely narrow EABs the corresponding thicknesses are 2.5 mm and 3.0 mm for Nb2CTex. By contrast, the EAB of (TiVNbTaZr)2CTex covers the S-band, C-band, and X-band by adjusting the coating thickness from 1.5 to 5.5 mm (Supplementary Fig. 24), highlighting the excellent absorption capability. These results demonstrate that the MA performances of MXenes can be controlled by entropy-modulated periodic ripple structure.

In conclusion, the entropy-increasing strategy precisely controls the atomic ripple structure in MXenes, and a mechanistic link between the atomic ripple structure and macro-properties is established. Introducing multiple metallic atoms into the M site results in the increase of configurational entropy, which gradually mitigates the local in-plane strain, achieving the precise modulation of atomic ripple structure. Moreover, the diminished out-of-plane conductivity impedes the redistribution of positive and negative charges within the microscopic dipole under an external electric field, thereby extending the polarization relaxation time and facilitating the directional polarization ability of MXenes. As a result, the synthesized (TiVNbTaZr)2CTex exhibits preeminent MA performances, including an RLmax value of −41.12 dB and the EAB covering the S-band, C-band, and X-band. Our results broaden the perspective for entropy engineering to regulate macro-properties, furthering the development of MXenes-based devices.

Methods

Chemicals and materials

High-purity commercial powders of Ti (<1 μm, 99.8 wt.%), V(10–20 μm, 98 wt.%), Nb (<10 μm, 99.8 wt.%), Ta (<10 μm, 99.5 wt.%), Zr (<10 μm, 99.8 wt.%), and aluminum (1 μm, 99 wt.%) were all purchased from Shanghai Pantian Nano Material Co., Ltd. CuI (anhydrous, 99.99%), KI (anhydrous, 99.99%), and Te powder (300 mesh, 99.9%) were purchased from Sinopharm Chemical Reagent Co., Ltd. HCl (36-38%), (NH4)2S2O8 ( >98 wt.%), and NH3·H2O (25%–28%), were purchased from Aladdin.

Synthesis of MAX phase

The starting materials with a stoichiometric ratio of M: Al: C = 2:1.1:1 (the elements in M-site were equimolal) were mixed in an agate mortar. Notably, Al powder, which has a low melting point of 660 °C, was added in excess to compensate for loss during the reaction. Ethanol was added and the mixture was grained for 40 min. Subsequently, the mixture powders were placed in an alumina crucible and heated in a tube furnace at 1500 °C for 2 h under an Ar atmosphere (at a heating rate of 5 °C min−1). After cooling to room temperature, the synthesized MAX product was washed with HCl. Finally, the target product (Nb2AlC, (TiNbTa)2AlC, and (TiVNbTaZr)2AlC) were obtained.

Synthesis of multilayer Mxenes

The Lewis acid molten salt method was employed to transform from MAX into MXenes. Briefly, the MAX phases (Nb2AlC, (TiNbTa)2AlC, and (TiVNbTaZr)2AlC)), CuI, Te, and KI were thoroughly ground using a mortar under argon protection in a glove box. The prepared mixture powder was then transferred to an alumina crucible and loaded into a tube furnace, where it was heat-treated at 700 °C for 7 h under an Ar atmosphere. After the reaction, the products were removed from the furnace and washed with NH3·H2O, (NH4)2S2O8 to remove the residual CuI and by-product Cu. Finally, the target Mxenes (Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex) were obtained.

DFT methods

The density functional theory (DFT) calculations were performed by using the Cambridge Sequential Total Energy Package (CASTEP), which the version was MS CASTEP 2017. The generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) function was employed in this investigation. The electron wave function is expanded by a plane wave basis with a kinetic energy cutoff of 400 eV. The K-points mesh was set to 3 × 3 × 1. The supercell was set as 3 × 6 × 2 to construct the models in Fig. 3e–g using the initial primitive cell of Mxenes. The numbers of atoms for Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex supercell were 120, 120, and 192, respectively (The specific number of each atom is listed in Supplementary Table 4). We used a script to generate a randomly distributed model with Ti, V, Ta, and Zr atoms replacing part of Nb. For Nb2CTex, the ratio in the M position for Nb was set as 100%. The M-site composition for (TiNbTa)2CTx, was set to 33.33% each for Ti, Nb, and Ta. For (TiVNbTaZr)2CTx, the M-site composition was set to 20% each for Ti, V, Nb, Ta, and Zr. Ultimately, the various M position atoms were randomly distributed in the same proportion in (TiNbTa)2CTex and (TiVNbTaZr)2CTex. The energy tolerance was set as 2 × 10−5 eV and the force tolerance was set as 0.05 eV·Å−1. The normalized DOS value was calculated by the normalization of DOS towards valence electrons to evaluate the electrical properties of the models.

Material characterization

The crystalline architecture of the MAX phase and MXene was characterized using Powder X-ray diffraction (XRD, Bruker, D8-Advance X-ray diffractometer, Germany) with Ni-filtered Cu Ka radiation at a scan rate of 2°/min. The composition ratio of M-position elements within (TiNbTa)2CTex and (TiVNbTaZr)2CTex was determined by a PE-8000 inductively coupled plasma atomic emission spectroscopy (ICP-AES). The surface chemical composition and chemical state of the Nb2CTex were obtained on a KRATOS Axis Ultra DLD equipped with a monochromatic X-ray source. Morphological investigations were conducted using field-emission scanning electron microscopy (Hitachi S-4800, Japan) operated at 5 kV. Specimen preparation for SAED, TEM, HRTEM images, STEM-EDS, STEM-iDPC, and STEM-HAADF measurements were performed using a dual-beam focused ion beam microscopy operating at 2–30 kV (ThermoFisher Scientific, Helios G4 CX, American). Following the standard FIB sample preparation technique, the specimen thickness for acquiring high-resolution STEM images should be less than 50 nm with approximately 1 nm-thick surface-damaged layer. The atomic TEM and STEM experiments were carried out on a dual spherical aberration correction field-emission STEM (ThermoFisher Scientific, Spectra 300 TEM, American) operated at 300 kV, equipped with STEM-iDPC detector, STEM-HAADF detector, and a Super-X EDS. To ensure a high signal-to-noise ratio, each EDS mapping at atomic resolution required approximately 0.5 h.

Conductivity measurements

The four-electrode devices were designed using focused ion beam (FIB) techniques to test the conductivity of MXenes in this work. The sample lamellas were installed on the nanochips, and four FIB-assisted superconducting Pt electrodes were fabricated by ion-beam-induced deposition, in which the outer electrode and the inner electrode are used to measure the current and voltage, respectively. Then the resistance R of MXenes was obtained based on Ohm’s law. Subsequently, the conductivity σ was calculated according to the formula: σ = L/(R·a·b), where L, a, and b are the length, width, and thickness between the voltage measurement points, where were obtained from the front view and top view SEM images.

Microwave absorption measurements

The as-obtained MXenes (Nb2CTex, (TiNbTa)2CTex, and (TiVNbTaZr)2CTex) samples were immersed into the molten paraffin, mixed thoroughly and pressed into coaxial rings (ϕouter = 7.0 mm; ϕinner = 3.0 mm). The electromagnetic parameters with the frequency range of 2–12 GHz were measured by a network analyzer (Keysight, N5230C). Finally, the coaxial transmission line method was employed to calculate the reflection loss values:

$${RL}=20\log \left|\frac{\sqrt{{\mu }_{r}/{\varepsilon }_{r}}tanh \left[j\left(2\pi {fd}/c\right)\sqrt{{\mu }_{r}{\varepsilon }_{r}}\right]-1}{\sqrt{{\mu }_{r}/{\varepsilon }_{r}}tanh \left[j\left(2\pi {fd}/c\right)\sqrt{{\mu }_{r}{\varepsilon }_{r}}\right]+1}\right|$$
(2)

where εr and μr are the electromagnetic parameters of complex permittivity and permeability, d is the specimen thickness, f is microwave frequency, and c is the speed of light velocity in a vacuum.