Distinct amorphization resistance in high-entropy MAX-phases (Ti, M)₂AlC (M=Nb, Ta, V, Zr) under in situ irradiation

Abstract

High-entropy materials have been proposed for applications in nuclear systems recently due to their outstanding properties in extreme environments. Chemical complexity in these materials plays an important role in irradiation tolerance since it significantly affects energy dissipation and defect behaviors under particle bombardment. Indeed, better resistance to irradiation-induced amorphization was observed in the high-entropy MAX (HE-MAX) phase (Ti, M)₂SnC (M = V, Nb, Zr, Hf). However, in this work, we report an opposite trend in another series of HE-MAX phases (Ti, M)₂AlC (M = Nb, Ta, V, Zr). It is demonstrated that the amorphization resistance is sequentially reduced as the number of components increases from single-component Ti₂AlC to (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC. These phenomena are verified through AIMD simulations and interpreted by analyzing the underlying properties combining lattice distortion and bonding characteristics through the first-principle calculation. By developing a machine-learning (ML) model, we can directly predict lattice distortion to screen HE-MAX phases with excellent resistance to irradiation-induced amorphization. We highlight that the elemental species plays a more crucial role in the irradiation tolerance of these MAX phases than the number of constituent elements. Knowledge gained from this study will enable an improved understanding of the irradiation tolerance in HE-MAX phases and other multi-elemental ceramics.

Introduction

M_n+1AX_n phases (or simplified as MAX phases) are a class of layered ternary carbides or nitrides¹, where M denotes an early transition metallic element, A is a main group element and X is carbon and/or nitrogen, n = 1, 2, or 3. MAX phases are hexagonal (space group P6₃/mmc, No.194) and nanolaminated with M_n+1X_n layers interleaved with A atom layers, typically possessing weak metallic bonds between M and A atoms and strong covalent bonds within the M_n+1X_n blocks^1,2,3,4. Due to such specific structures and mixing rules of bonding characteristics, they exhibit a unique set of properties combining both ionic-covalent and metallic materials^1,2,4,5,6. These remarkable properties include high elastic stiffness and strength, high electrical and thermal conductivity, high thermal stability, exceptional resistance to corrosion and oxidation, easy machinability, and excellent damage tolerance^{2,4,5,6,7,8,9,10}. Moreover, some species of MAX phases are irradiation tolerant^8,11,12,13, and are considered promising candidate coating materials for accident tolerance fuel (ATF) in advanced nuclear systems^14,15,16.

Ion-beam irradiation is a common approach to studying the irradiation effects of materials since it can generate collision cascade and analogous radiation damage as neutron irradiation^17,18,19. The accumulation of irradiation-induced defects may also trigger structural evolution or amorphization in ceramics like complex oxides^{20,21,22,23,24} and MAX phases^8,25,26, significantly influencing the long-term durability of materials due to the property mutations and performance deterioration. Therefore, there is a great impetus to investigate the responses of MAX phases to irradiation and elucidate the mechanism for developing high amorphization-resistance materials.

The introduction of chemical complexity or the so-called “high entropy” is a newly developed strategy for property tailoring^27,28,29,30, and can help design enhanced irradiation-tolerance materials^31,32. Previous studies have demonstrated that chemical complexity plays an important role in the irradiation tolerance of both single-phase concentrated solid solution alloys (CSAs)^31,32,33 and high entropy ceramics (HECs)³⁴. It is suggested that the effects of lattice distortion, sluggish diffusion, and chemical disorder impressively affect the generation, migration, and evolution of irradiation-induced defects. These effects lead to slower energy dissipation, enhancing defect recombination and consequently resulting in slower damage accumulation under irradiation³³. A reduced antisite defect formation energy has been manifested in the high-entropy MAX (HE-MAX) phase (Ti, M)₂SnC (M = V, Nb, Zr, Hf)²⁶ such that the chemically complex (TiVNbZrHf)₂SnC is prone to accommodate more point defects and maintain the crystalline lattice reflected by its better irradiation-induced amorphization resistance.

However, in this work, we report an opposite phenomenon in another series of HE-MAX phases, (Ti, M)₂AlC (M = Nb, Ta, V, Zr). The schematic atomic models of (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC are shown in Fig. 1. The resistance to irradiation-induced amorphization is sequentially reduced as the number of components increases from single-component Ti₂AlC to (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC. The chemical complexity seems to play a negative role in the resistance to irradiation-induced amorphization, contrary to our previous perceptions²⁶. The ab initio molecular dynamics (AIMD) results verified this trend and elucidated that the atomic displacement of (TiNbTaVZr)₂AlC invariably remains larger than that of Ti₂AlC with the increasing simulated damage dose. Through the first-principle calculation, we found that lower antisite defect formation energy is not found in this series of Al-based HE-MAX phases. We further explained the experimental phenomena through the analysis of the underlying properties combining the lattice distortion and bonding characteristics. The elemental species plays a more crucial role in the irradiation tolerance of MAX phases than the number of constituent elements. This effect is attributed to the stronger interatomic bonding characteristics in ceramics substantially associated with the elemental components. Additionally, we developed a machine learning model to predict the lattice distortion of the γ-phases by the properties and number of constituent elements.

Fig. 1: Schematic atomic models of the pristine HE-MAX phases.

a (TiNbTa)₂AlC, b (TiNbTaVZr)₂AlC. The right panels show the corresponding atomic arrangement on the projection of [$11\bar{2}0$] direction, which exhibits a chemical disorder and chemical complexity in the M-sites.

Results and discussions

Irradiation-induced phase transformation and amorphization resistance in (Ti, M)₂AlC (M = Nb, Ta, V, Zr)

Selected area electron diffraction (SAED) is an efficient technique to determine the lattice or phase structure, thereby we obtained the SAED patterns of the samples during ion irradiation to record the entire process of phase transformation and amorphization. Figure 2 shows the series of in situ SAED patterns of Ti₂AlC, (TiNbTa)₂AlC, and (TiNbTaVZr)₂AlC along the [$11\bar{2}0$] zone axis during the Kr²⁺ irradiation at room temperature (RT). All SAED patterns for each sample were obtained from the central part of one grain such that the effect of grain boundary could be ignored.

Fig. 2: In situ SAED patterns during the 800 keV Kr²⁺ irradiation at room temperature.

a–g Ti₂AlC, h–n (TiNbTa)₂AlC, and o–u (TiNbTaVZr)₂AlC. The electron beam is along the $\left[11\bar{2}0\right]$ zone axis. The two spots indicated by yellow arrows in e represent $(\bar{1}1\bar{1})$ and $(00\bar{2})$ diffraction spots of the nano-twined fcc structure similar to that in previous work³⁵, the white arrows in j and q indicate the amorphous rings representing that partial amorphization in the crystal begins to occur.

As illustrated in Fig. 2a–g for Ti₂AlC, Fig. 2h–m for (TiNbTa)₂AlC, and Fig. 2o–t for (TiNbTaVZr)₂SnC, the diffraction spots of (000l) (l ≠ 6n), and ($\bar{1}10l$) (l = 6n, 6n ± 1) in the $\left\{000l,\,\bar{1}10l\right\}$ reflections gradually attenuate and disappear with the increased dose owing to the increase of the lattice symmetry. Further irradiation transforms the intermediate γ-phase into a twinned face-centered cubic (fcc) structure, as the two spots designated by yellow arrows in Fig. 2e represent $(\bar{1}1\bar{1})$ and $(00\bar{2})$ diffraction spots of the nano-twined fcc structure. This similar process of structural transformation in Ti₂AlC has been observed in previous work³⁵. No amorphization was observed in Ti₂AlC even at the irradiation dose up to 61.6 dpa. Nevertheless, both (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC show evidence of an amorphous component with a diffraction ring in the SAED patterns, as indicated by the white arrows in Fig. 2j, q at a dose of 0.48 and 0.15 dpa, respectively. This indicates that the intermediate γ-phase starts to convert into an amorphous phase as the irradiation dose increases. Moreover, the five-component (TiNbTaVZr)₂AlC exhibits a worse irradiation resistance than (TiNbTa)₂AlC as its critical irradiation dose (~0.6 dpa) of complete amorphization (when diffraction spots disappear) is far less than that in (TiNbTa)₂AlC (about 21.6 dpa), as shown in Fig. 3n, u. Therefore, a decrease of irradiation-induced amorphization resistance with the elemental components increase is demonstrated in this series of MAX phases, indicating that the chemical complexity plays a negative role in the irradiation resistance. This compositional trend is opposite to our previous perceptions in the HEAs^33,36 and HE-MAX phases (Ti, M)₂SnC (M = V, Nb, Zr, Hf)²⁶. It should be noted that the results were checked and confirmed in various grains in each material to show a similar trend for avoiding occasionality.

Fig. 3: HRTEM images before and after irradiated with 800 keV Kr²⁺ at a series of doses.

a–e (TiNbTa)₂AlC and f–j (TiNbTaVZr)₂AlC The insets in the upper right and lower right corner of each micrograph are the corresponding Fast Fourier Transform (FFT) and enlargement in the white box, respectively. The electron beam is along $\left[11\bar{2}0\right]$ direction.

Figure 3 shows the high-resolution TEM (HRTEM) images of the (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC along the $\left[11\bar{2}0\right]$ direction, before and after 800 keV Kr²⁺ irradiation at a series of doses. These atomic scale TEM images demonstrate the structural evolution follows a multi-stage α-γ-fcc-amorphous sequence (we defined the pristine hexagonal phase as α-phase), which is in good agreement with the evolution of SAED patterns in Fig. 2.

Compared to our previous work on the irradiation-induced phase transformation in (Ti, M)₂SnC (M = V, Nb, Zr, Hf)³⁷, the fcc-phase appears between the stages of γ-phase and amorphous phase under the 800 keV Kr²⁺ irradiation, as shown in Fig. 3d, h. We performed a phase-contrast simulation to further confirm the phase transition of the intermediate γ-phase to fcc-phase as proposed above. It is revealed that the simulation result is consistent with the experimental HRTEM micrograph (as shown in Supplementary Fig. 1).

Combining the results of SAED, HRTEM, and phase-contrast simulation, we thereby confirmed the multi-stage phase transformation of hex-γ-fcc in (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC. Continuous ion bombardment will further induce a lattice disorder when the defects and chemical disorder accumulate to a critical value, triggering the crystalline phase to transform into an amorphous phase eventually.

AIMD simulations of the lattice evolution during point defect accumulation

Furthermore, ab initio molecular dynamics (AIMD) simulations were performed in Ti₂AlC and (TiNbTaVZr)₂AlC to probe the irradiation-induced crystalline to amorphous phase transition at the atomic scale. The radiation process is simulated by continuously introducing Frenkel pairs^{38,39,40,41,42}. The irradiation dose for AIMD simulations is equal to the ratio of the number of Frenkel pairs introduced to the number of atoms in the simulated crystal cell. The pair correlation function of the system at an interval of 0.1 dpa was obtained to judge whether the system was fully amorphous. It is demonstrated that long-range order is still retained in Ti₂AlC at 0.6 dpa, as shown in Fig. 4a. In contrast, (TiNbTaVZr)₂AlC completely loses its long-range order at a dose of 0.6 dpa, indicating full amorphization (Fig. 4b). Figure 4d–g shows the atomic projections of Ti₂AlC and (TiNbTaVZr)₂AlC at 0 dpa and 0.6 dpa, respectively. Likewise, all the crystalline planes and rows of (TiNbTaVZr)₂AlC are completely lost, indicating full amorphization, while the lattice of Ti₂AlC remains stable. In addition, there are numerous cation antisite defects as well as C interstitials in the otherwise empty cation octahedral interstitial sites in Ti₂AlC at 0.6 dpa, suggesting that an ordered-to-disordered phase transition process has occurred.

Fig. 4: AIMD simulation of irradiation.

a, b The pair correlation function of Ti₂AlC and (TiNbTaVZr)₂AlC at AIMD simulated dose of 0.6 dpa. c Evolution of the crystallinity of Ti₂AlC and (TiNbTaVZr)₂AlC with AIMD simulated dose. d, e The atomic projection of Ti₂AlC and (TiNbTaVZr)₂AlC at AIMD simulated dose of 0 dpa. f, g The atomic projection of Ti₂AlC and (TiNbTaVZr)₂AlC at AIMD simulated dose of 0.6 dpa. In the AIMD simulation, Ti₂AlC has better amorphization resistance compared to (TiNbTaVZr)₂AlC, which is consistent with the ion irradiation experiments.

To quantify the fully amorphous dose in AIMD simulations, the crystallinity was defined as the percentage of hexagonal close-packed (HCP) structures in the cation sublattice identified by the Polyhedral template matching method⁴³. As shown in Fig. 4c, with the continuous introduction of Frenkel pairs, the cation sublattice in Ti₂AlC remains crystalline with a crystallinity of around 0.55. However, for (TiNbTaVZr)₂AlC, it gradually loses its crystallinity, and its crystallinity decreases to 0 at about 0.56 dpa, indicating complete amorphization. Therefore, the trend of the amorphization resistance obtained from the AIMD simulation is consistent with the ion irradiation experimental results.

DFT calculations of the antisite defects formation energy

The formation energy of antisite defect was proposed to be an important indication of irradiation tolerance in complex ceramics like pyrochlores^20,21, since the formation of cation antisite defects provides a recovery mechanism to accommodate lattice point defects induced by the displacement cascades and maintains its lattice structure. That means complex ceramics with a lower formation energy of antisite defect are susceptive to irradiation-induced order-to-disorder (O-D) transition and generally possess better resistance to irradiation-induced amorphization. However, Uberuaga et al. found an opposite case in spinels that have cation vacancies instead of anion vacancies like in pyrochlores²³, and demonstrated that the correlation between cation disordering and amorphization resistance depends on the lattice structure (vacancies exist on the cation or anion sublattice). Similar to pyrochlore and the defective fluorite structures, ion irradiation drives the transformation of MAX phases into a structure being close-packed in the cation sublattice but with C/N vacancies in the anion sublattice^{25,35,37,44,45,46}, and generally, the M-A antisite defect manifests almost the lowest formation energy among all point defect types^{8,46,47,48,49,50}. Therefore, this criterion of correlation between DFT calculated M-A antisite defect formation energy (${E}_{{form}}^{\,M-A\,{antisite}}$) and amorphization resistance, is consistent with most radiation experiments of the common MAX phases (lower ${E}_{{form}}^{\,M-A\,{antisite}}$ indicates higher amorphization resistance)^8,47,48. In our recent work, we also suggested that the enhanced irradiation resistance as the chemical complexity increases is attributed to the reduced formation energy of M-A antisite defect (${E}_{{form}}^{\,M-A\,{antisite}}$) in (TiVNbZrHf)₂SnC, compared to corresponding single-component M₂SnC (M = Ti, V, Nb, Zr, Hf)³⁷.

Nevertheless, this criterion fails in the case of Cr₂AlC. For instance, Cr₂AlC possesses almost the lowest ${E}_{{form}}^{M-A\,{antisite}}$ in the traditional MAX phases family^47,51, yet its amorphization resistance under ion irradiation is worse than V₂AlC and Ti₂AlC^35,52. In this work, this criterion of antisite defect formation energy fails to explain this experimental phenomenon, as shown in Fig. 5. Unlike our previous work that exhibits a decreased M-Sn (M = Ti, V, Nb, Zr, Hf) antisite defect formation energy after the introduction of chemical complexity³⁷, the ${E}_{{form}}^{M-{Al\; antisite}}$ (M = Ti, Nb, Ta, V, Zr) in M₂AlC, (TiNbTa)₂AlC, (TiNbTaVZr)₂AlC shows an irregular trend with the introduction of chemical complexity. For instance, compared to the corresponding single-component counterpart, the formation energy of Ti/Zr-Al antisite defect decreases in (TiNbTa)₂AlC or (TiNbTaVZr)₂AlC, while Ta/V-Al antisite defect increases instead. Therefore, the reduction of ${E}_{{form}}^{M-A\,{antisite}}$ with the introduction of chemical complexity in M₂SnC (M = Ti, V, Nb, Zr, Hf) is not a general rule in ME/HE-MAX phases.

Fig. 5: Antisite defect formation energies.

M-Al antisite defect (M_Al and Al_M, where M = Ti, Nb, Ta, V, Zr) formation energies calculated in the corresponding single-component M₂AlC cell (black dots), the three-component (TiNbTa)₂AlC cell (red dots) and the five-component (TiNbTaVZr)₂AlC cell (blue dots). For the latter two materials, the data were averaged over 20 different SQS supercells and the shadow area indicates the error band.

It is worth mentioning that, all the ${E}_{{form}}^{M-A\,{antisite}}$ calculations are based on the pristine hexagonal phases, indicating that the criterion provides only an indication at the early stage under irradiation. More attention should be paid to the intermediate γ-phase or fcc-phase which plays a more important role in the resistance to irradiation-induced amorphization.

Structural properties of the intermediate γ-phase and fcc-phase

It has been demonstrated that the γ-phase is a necessary stage when the MAX phases undergo the complex phase transformation process during ion irradiation^{8,25,35,44,45,46}. Additionally, an γ-to-fcc phase transformation was also observed in these three materials, as shown in Fig. 2. The properties of the γ-phase or fcc-phase may play an important role in the resistance of the MAX phases to amorphization. Therefore, the properties of lattice distortion and electronic structure of the intermediate γ-phase and fcc-phase are focused in this work since they greatly influence the accumulation of defects and lattice disorder.

The ab initio calculation was based on the intermediate γ-phase and fcc-phase with chemically disordered structures. A DFT relaxation together with a charge density topology analysis was applied to obtain the degree of lattice distortion and bonding characteristics in the solid-solution γ-(Ti, M)₂AlC (M = Nb, Ta, V, Zr) phases. Figure 6a illustrates one of the DFT-relaxed supercell models of γ-(TiNbTaVZr)₂AlC phase. The dense yellow spheres indicate the charge density in the bond critical points (BCPs, a BCP is the first order saddle points of electron density lies on a bond path which defines the bond between two atoms⁵³) in the lattice. Figure 6b, c shows the statistical results of the lattice distortion $\Delta d$ and the total average charge density among all BCPs of M/Al-C (M = Nb, Ta, V, Zr) bonds $\bar{\rho }\left({r}_{b}\right)$ over three 4 × 4 × 1 SQS supercells of the pristine phase, γ-phase and corresponding converted fcc-phase in Ti₂AlC, (TiNbTa)₂AlC, and (TiNbTaVZr)₂AlC, respectively. The lattice distortion $\Delta d$ is described by the atomic deviation from the ideal regular lattice sites as the following calculation formula⁵⁴

$$\begin{array}{c}\Delta d=\frac{1}{N}\mathop{\sum }\limits_{i=1}^{N}{\left[{\left({x}_{i}-{x}_{i}^{{\prime} }\right)}^{2}+{\left({y}_{i}-{y}_{i}^{{\prime} }\right)}^{2}+{\left({z}_{i}-{z}_{i}^{{\prime} }\right)}^{2}\right]}^{\frac{1}{2}}{\rm{\#}}\end{array}$$

(1)

where (${x}_{i},\,{y}_{i},\,{z}_{i}$) and (${x}_{i}^{{\prime} }$, ${y}_{i}^{{\prime} }$, ${z}_{i}^{{\prime} }$) are the coordinates of the unrelaxed and relaxed positions of atom i, respectively. It is illustrated that the (TiNbTaVZr)₂AlC possesses the largest atomic displacement of approximately 0.170 $\mathring{\rm A}$ and 0.201 $\mathring{\rm A}$ in the γ-phase and fcc-phase respectively, followed by (TiNbTa)₂AlC and then Ti₂AlC. A larger atomic displacement means that the lattice is more unstable and more inclined to undergo a lattice disorder induced by the continuous ion bombardment. Therefore, the (TiNbTaVZr)₂AlC with the largest atomic displacement in the γ-phase exhibits the lowest resistance to amorphization, while γ-Ti₂AlC instead shows the best irradiation-induced amorphization resistance due to its smallest lattice distortion.

Fig. 6: Pristine phase, γ-phase and corresponding converted fcc-phase properties of HE-MAX phases.

a A DFT-relaxed 4 × 4 × 1 supercell model of γ-phase (TiNbTaVZr)₂AlC with lattice distortion, while the dense yellow spheres represent the bond critical points (BCPs) in the lattice. b The DFT calculated lattice distortion (top panel) and c the total average charge density at the BCPs of M/Al-C (M = Ti, Nb, Ta, V, Zr) bonds $\bar{\rho }({r}_{b})$ (lower panel) of the pristine phase, γ-phase and corresponding converted fcc-phase in Ti₂AlC, (TiNbTa)₂AlC, and (TiNbTaVZr)₂AlC, respectively. d The corresponding charge density at the BCPs of M-C (M = Ti, Nb, Ta, V, Zr) bonds $\rho ({r}_{b})$ in the γ-phase (TiNbTa)₂AlC (red points) and (TiNbTaVZr)₂AlC (blue points), respectively. While the dashed line indicates the $\bar{\rho }({r}_{b})$ of Ti-C bonds in Ti₂AlC and the shaded area indicates the error band.

Meanwhile, as shown in Fig. 6c, a similar trend of the total average charge density over all the BCPs of M/Al-C bonds $\bar{\rho }\left({r}_{b}\right)$ is exhibited in both the original γ-phase and fcc phase. $\bar{\rho }\left({r}_{b}\right)$ are about 0.542 $e/{\mathring{\rm A} }^{3}$ and 0.560 $e/{\mathring{\rm A} }^{3}$ in the γ-phase and fcc-phase of (TiNbTa)₂AlC respectively, 0.547 $e/{\mathring{\rm A} }^{3}$ and 0.568 $e/{\mathring{\rm A} }^{3}$ in the γ-phase and fcc-phase of (TiNbTaVZr)₂AlC respectively. These values are larger than that in the intermediate phases of Ti₂AlC (only about 0.501 $e/{\mathring{\rm A} }^{3}$ and 0.513 $e/{\mathring{\rm A} }^{3}$, respectively), which indicates stronger interatomic bonding characteristics^48,53 in the intermediate phase of (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC. Figure 6d shows the corresponding BCP charge density at each M-C (M = Ti, Nb, Ta, V, Zr) bonds $\rho \left({r}_{b}\right)$ in the γ-phases of Ti₂AlC, (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC. It is illustrated that the involvement of Nb-C, Ta-C, and V-C bonds in (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC enhances the level of charge density at the BCPs which indicates a stronger interatomic bonding characteristics⁵³ in the intermediate γ-phase (while in fcc-phase the scenario is similar and not shown here). As proposed by Ogata et al.⁵⁵, if the crystalline system possesses a stronger covalent or directionally bonding characteristic, it is expected to be more frustrated and less accommodating, exhibited by its less tolerance under irradiation. Therefore, the sequentially reduced resistance to irradiation-induced amorphization in Ti₂AlC, (TiNbTa)₂AlC, and (TiNbTaVZr)₂AlC is interpreted as the analysis combining the lattice distortion and bonding characteristics. In addition, the pristine phase C-M bonds of (TiNbTa)₂AlC is stronger than that of (TiNbTaVZr)₂AlC, further indicating that it is not sufficient to analyze the amorphization resistance of the MAX phase based on the pristine phase properties alone.

Furthermore, the atomic displacements or lattice distortion of Ti₂AlC and (TiNbTaVZr)₂AlC are counted as a function of the simulated dose via the AIMD simulations. As shown in Fig. 7, the atomic displacements of (TiNbTaVZr)₂AlC are always larger than that of Ti₂AlC, in agreement with the DFT calculated results of γ-phases and fcc-phases (Fig. 6b). The atomic displacements of (TiNbTaVZr)₂AlC increase more rapidly with increasing doses than Ti₂AlC. When atomic displacements accumulate to a certain extent, it may be difficult for (TiNbTaVZr)₂AlC to maintain crystalline structure and subsequently become amorphized. Note that the magnitude of the lattice distortion obtained from AIMD simulations is larger than that from DFT calculations. This may be due to the thermal vibrations and loss of defects recombination in the AIMD simulations.

Fig. 7: The evolution of lattice distortion of Ti₂AlC and (TiNbTaVZr)₂AlC with the simulated damage dose derived from the AIMD simulations.

The lattice distortion is quantitatively determined by the atomic deviation as discussed above.

All these results above manifest that the structural properties, especially the atomic displacement or lattice distortion during the phase transition (e.g., the intermediate γ-phase or fcc-phase) play an important role in the amorphization resistance of these materials. As shown in Fig. 8, the critical amorphization dose (damage dose for full amorphization) and corresponding lattice distortion of the γ-phase illustrate a negative correlation, for both (Ti, M)₂SnC (M = V, Nb, Zr, Hf) and (Ti, M)₂AlC (M = Nb, Ta, V, Zr) HE-MAX phases. i.e., the material with a lower lattice distortion of the intermediate γ-phase has a higher amorphization resistance to irradiation. Furthermore, when comparing these two series of HE-MAX phases, it is shown that their lattice distortion strongly depends on the species, instead of the number of constituent elements of MAX phases. Therefore, we can infer that the strategy of “high entropy” does not always work in the MAX phases family. It plays a subdominant role compared to the species of the elements in these materials. This may arise from the stronger interatomic bonding characteristics in ceramics substantially associated with the elemental components.

Fig. 8: The dependence between the critical amorphization dose and lattice distortion of the γ-phase of HE-MAX phases (Ti, M)₂SnC (M = V, Nb, Zr, Hf) and (Ti, M)₂AlC (M = Nb, Ta, V, Zr).

Their ion irradiation experiments were performed under the same condition, experimental data for (Ti, M)₂SnC (M = V, Nb, Zr, Hf) can be seen in our previous work²⁶.

Prediction of γ-phase lattice distortion by machine learning model

The HE-MAX phases with excellent resistance to irradiation amorphization can be screened by calculating the γ-phase lattice distortion. However, considering the vast composition space of HE-MAX phases, using first-principle methods to calculate lattice distortion is highly time-consuming. Machine learning has shown powerful potential to address complex problems in material science⁵⁶. By learning from high-dimensional input data (descriptors), machine learning methods can directly predict lattice distortion in HE-MAX phases, offering a more efficient alternative.

To train machine learning model, the training datasets were first collected from 60 HE-MAX phases with Al at the A site, C at the X site, and all binary, ternary, quaternary, and quinary combinations of Ti, V, Nb, Zr, Hf, Ta. In the collection of lattice distortions, three supercells with 128 atoms in different atomic distribution states were used to ensure statistical validity.

Subsequently, after careful investigation of the contributions to the lattice distortion of the solid solution system, 11 descriptors were chosen for the machine learning model, as summarized in Table 1. These descriptors can be calculated from the properties and numbers of the constituent elements of the HE-MAX phases, without any other additional calculations and experiments. To reduce possible overfitting introduced by the strongly correlated features and increase fitting efficiency, we removed those features with Pearson coefficients higher than 0.95. The Pearson coefficients between descriptors d₃ and d₇, d₄ and d₈, as well as d₁₀ and d₁₁ are greater than 0.95. Thus, the descriptors d₇, d₈, d₁₁ are excluded in the following training procedure.

Table 1 Input features for our ML model

The parity plots comparing the calculated lattice distortion with the ML prediction are shown in Fig. 9. Eighty percent of the dataset was used for training with the remaining for testing the model performance. It can be seen from the parity plots that the machine learning model can reasonably predict γ-phase lattice distortion over the entire dataset. Visually, it can be seen that the model prediction performance is comparable for the training and test sets, indicating the robustness of the model. The machine learning model exhibits great predictive power by simply considering the constituent elements’ basic properties. This machine learning model can accelerate the discovery of HE-MAX phases with excellent resistance to irradiation amorphization within the vast phase space.

Fig. 9: The results of predicted lattice distortion versus calculated lattice distortion for the machine learning model.

A randomly selected 80%/20% training/test split of the available data was used for statistical learning and testing the performance of the trained model.

In summary, we have combined in situ ion irradiation with TEM analysis, first-principle calculations, and AIMD simulation techniques to probe the phase transformation process and amorphization resistance of the HE-MAX phases (Ti, M)₂AlC (M = Nb, Ta, V, Zr). In contrast to the previous view that the introduction of chemical complexity or “high entropy” can enhance the irradiation tolerance of materials, we found that the amorphization resistance is sequentially reduced as the number of constituent elements increases from single-component Ti₂AlC to (TiNbTaVZr)₂AlC. This trend is verified through the AIMD simulations via point defect accumulation. Through the first-principle calculation, we found that lower antisite defect formation energy is not represented in this series of HE-MAX phases, and we further explained these experimental phenomena through the analysis of the underlying structural properties combining the lattice distortion and bonding characteristics. The poor amorphization resistance of (TiNbTaVZr)₂AlC arises from its large lattice distortion and strong bond covalency of the intermediate phases during irradiation. Additionally, a negative correlation between critical amorphization dose and lattice distortion of the intermediate phase was built for both series of HE-MAX phases. Using machine learning methods, we can predict the γ-phase lattice distortion in the HE-MAX phases. We highlight the elemental species, instead of the number that plays a more crucial role in the irradiation tolerance of these MAX phases. These results overturn the conventional perception and provide a new viewpoint for the design of amorphization-resistant and radiation-resistant materials in the MAX-phases family, and related multi-elemental ceramics systems.

Methods

Materials preparation

The bulk samples for irradiation in this work were synthesized at the Ningbo Institute of Materials Technology and Engineering (NIMTE), Ningbo, China. Specifically, Ti₂AlC samples were prepared by the in-situ hot pressing/solid-liquid reaction process, and corresponding elemental powders were mixed in stoichiometric proportions, pressed in a graphite die, and subsequently hot-pressed in a flowing Ar atmosphere. More details about the synthesis process have been published elsewhere^57,58,59. The (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC powders were synthesized via the molt salt method and then the as-prepared powders of (TiNbTa)₂AlC or (TiNbTaVZr)₂AlC were filled in a graphite die for hot-press sintering to prepare its bulk sample, more details in terms of the preparation process and characterization of element composition can be found in ref. ⁶⁰

Subsequently, the as-prepared bulk samples above were cut into square specimens and then mechanically thinned to ~20 μm with physical polish. The polished thin foil (with glue around) was then glued to a ${\rm{\phi }}$3 copper ring, followed by an argon ion milling process from 4.5 keV down to about 2 keV (corresponding milling angle set from 4° to 2°) utilizing a Gatan PIPS 691 ion miller, thus preparing the sample with a thin wedge for in-situ irradiation and transmission electron microscope (TEM) characterization.

Ion irradiation

The in situ ion irradiation experiments in this work were performed under a 400 kV ion implanter coupling with an FEI Tecnai F30 (with a field emission gun operating at 300 kV) transmission electron microscope at Xiamen Multiple Ion Beam In-situ TEM Analysis Facility, Xiamen University⁶¹. The ion bombardment was performed with an 800 keV Kr²⁺ beam at room temperature (RT). During irradiation, the selected area electron diffraction (SAED) images were recorded to observe the near real-time phase states and transformations.

The radiation damage level (displacement per atom, dpa) and the penetration of Kr ions along the ions’ incident direction were calculated using the SRIM-2008 program (as shown in Fig. 10). The quick Kinchin-Pease mode was adopted⁶², and the threshold displacement energies for each element were set as 25–28 eV. The Kr²⁺ peak range exceeds the thickness of the TEM sample foil such that the effect of the penetrated Kr ions can be avoided. The average dpa values over the thickness (assumed to be 100 nm as in previous work^63,64,65) of the TEM foils were used to estimate the damage level.

Fig. 10: Damage level (dpa) and ion concentration profile induced by 800 keV Kr²⁺ irradiation at a fluence of 1 × 10¹⁴cm^−2.

Data were calculated deriving from the SRIM⁷⁶ code.

Characterization techniques

TEM observations were obtained in a 200 kV Tecnai F20 transmission electron microscope (FEI, Hillsboro, OR) with a point resolution of 0.24 nm and a line resolution of 0.102 nm at the Electron Microscopy Laboratory of Peking University. The phase contrast simulation was performed via the QSTEM program⁶⁶.

Theoretical calculations

First-principles calculations based on density functional theory (DFT) were conducted in this work applying the Vienna Ab-initio Simulation Package (VASP)⁶⁷. The projector augmented-wave (PAW) method⁶⁸ and the generalized gradient approximation (GGA) by Perdew, Burke, and Ernzerhof (PBE)⁶⁹ were employed for the electron-ion interactions and exchange-correlation function, respectively. The disordered supercells were constructed using the alloy theoretic automated toolkit (ATAT)⁷⁰ based on the special quasi-random structure (SQS) method⁷¹. The gamma-centered Monkhorst–Pack⁷² k-point of 4 × 4 × 2 is used to sample the Brillouin zone. The total energy and forces converged to better than 10^−6 eV and 0.01 eV/Å with a plane wave cutoff of 450 eV.

For each material of (Ti, M)₂AlC (M = Nb, Ta, V, Zr), three samples of 4 × 4 × 1 SQS supercells each containing 128 atoms with different atomic disordered configurations were constructed and relaxed to perform a charge density topology analysis based on the Quantum Theory of Atoms In Molecules (QTAIM)⁵³, where the bond critical points (BCPs) were implemented by the Critic2 program⁷³.

The antisite defect formation energy ${E}\,_{{form}}^{{antisite}}$ is defined as the following formula:

$$\begin{array}{c}{E}\,_{{form}}^{{antisite}}={E}_{T}\left({\rm{antisite}}\right)-{E}_{T}\left({\rm{perfect}}\right){\boldsymbol{\#}}\end{array}$$

(2)

where ${E}_{T}\left({\rm{antisite}}\right)$ and ${E}_{T}\left({\rm{perfect}}\right)$ are the total energy of a supercell with one antisite defect and a perfect supercell, respectively. For (TiNbTa)₂AlC and (TiNbTaVZr)₂AlC, the ${E}\,_{{form}}^{{antisite}}$ of M-Al antisite defect (M = Ti, Nb, Ta, V, Zr) is statistically derived from DFT calculations over 20 configurations to sample the variation of the local atomic environment.

Ab initio molecular dynamics (AIMD) simulations are also performed on the VASP code⁶⁷. Starting from a perfect 200-atom (5 × 5 × 1) cell, Frenkel pairs are continuously introduced by randomly selecting any atom displaced in any direction by a distance of 5 Å. Such distance prevents defects from directly recombination. Meanwhile, the displaced atoms are farther away from other atoms than 1 Å, preventing close interactions. Between the two displacement events, the cell relaxes at a fixed volume at 300 k for 0.5 ps. The time step is set to 1 fs and the Nose-Hoover thermostat⁷⁴ is used. A single gamma point is used to sample the Brillouin zone.

Machine learning model

According to the data type and quantity in the original data set, the supervised learning model was used for training. The regression machine learning algorithm Artificial Neural Network (ANN) was selected. To reduce potential overfitting introduced by strongly correlated features, the Pearson correlation coefficient (r) between features was calculated as⁷⁵:

$${\rm{r}}=\frac{\sum ({x}_{i}-\bar{x})({y}_{i}-\bar{y})}{\sqrt{\sum {({x}_{i}-\bar{x})}^{2}\sum {({y}_{i}-\bar{y})}^{2}}}$$

(3)

where x_i and y_i are the i-th value of two different input features, respectively; $\bar{x}$ and $\bar{y}$ are the expectations of the two input features. Moreover, to achieve the same magnitude level of all features, each feature was normalized by:

$${x}_{i}^{{norm}}=\frac{{x}_{i}-\bar{x}}{{\sigma }_{x}}$$

(4)

where ${x}_{i}^{{norm}}$ and x_i are the i-th normalized value and original value of the input feature x, respectively; $\bar{x}$ and ${\sigma }_{x}$ are the expectation and standard deviation of the input feature x, respectively.