Short-range order in high entropy carbides

Domain: neuroscience
Published: 2026-02-04
Editorial outcome: major_revision

Abstract
High-entropy carbides (HECs) are a new class of materials with properties that are promising for applications in extreme environments, involving high temperature, corrosion, and high ion-flux. In HECs, multiple principal cations form solid solutions, similar to medium/high-entropy alloys (M/HEA). However, mixing of atoms can be non-ideal, resulting in chemical short-range order (CSRO). CSRO has been already reported in M/HEAs, cation-disordered oxides, and high-entropy oxides and in many cases, it was found to have significant impact on materials properties. CSRO in covalently-bonded high-entropy ceramics has not been observed so far, and its potential impact on materials properties is unknown. In contrast to M/HEAs, in HECs only one of the sublattices forms a solid solution, and therefore it is unclear whether the concept of CSRO extends to HECs. Here, we report the observation of CSRO in multiple HECs using a combination of atomistic simulations and scanning transmission electron microscopy. We find that CSRO in HECs can be controlled by both selection of chemical elements and heat treatment, and it significantly improves radiation resistance, although it is not the only factor. Our findings expand the understanding of CSRO to HECs and provide a pathway for design of new materials for extreme environments.

Introduction
HECs are an emerging class of materials with excellent properties, such as high hardness and ductility1,2, superior radiation resistance3–7, and high-temperature stability2,8,9. These properties are highly dependent on the ability to form a solid solution/single phase10,11. However, such mixing can be imperfect, leading to the potential formation of chemical short-range order (CSRO). Imperfect mixing has been recently discovered in other disordered systems, such as medium/high-entropy alloys (M/HEA)12–22, Li-excess cation-disordered oxide23,24, and high-entropy oxides25. In an earlier study26, a distinction has been made between short-range ordering (SRO) and short-range clustering (SRC), which describes the attraction of unlike and like atoms, respectively. Here, we define the CSRO as the deviation of chemical order from a random arrangement on the same cation sublattice without altering the lattice structure, which means that our definition includes both SRO and SRC. Due to the difficulty in characterizing CSRO experimentally27,28, observations and understanding of CSRO in different systems are limited. For example, CSRO was investigated only via neutron diffraction25 in high-entropy oxides (HEOs). However, HEOs exhibit a distinct bonding nature when compared to HECs. For instance, in HEOs, there is a significant electrostatic contribution to the interatomic bonding, which leads to preferential cation to oxygen bonding and may result in SRO. In contrast, in HECs, the bonding nature is mostly covalent, and therefore, it is not clear if the understanding of SRO in HEOs can be directly extended to HECs. Even in the more well-studied M/HEAs, there are contradictory reports regarding the ability to control CSRO. For example, Han Y. et al.17 found that varying chemical elements or thermal treatment history of M/HEAs had a negligible impact on CSRO, which disagrees with earlier work where substitutional elements15,16 and thermal treatment13 were used successfully to tune CSRO. HECs have more complex energy landscapes than metals and oxides due to a combination of metallic, covalent and ionic bonding. They also form multiple sublattices with distinct characters (e.g., anion vs cation), which lead to vastly different defect behavior on each of the sublattices. In addition, only one sub-lattice can form solid solutions in HECs, as the other sub-lattice consists entirely of carbon in the absence of impurities. The formation of CSRO in such systems, the ability to tune it, and the impact of CSRO on properties are all open questions.

To answer these questions, we study two HEC compositions: (TiVZrNb)C and (TiVMoNb)C, labeled HEC-Zr and HEC-Mo, respectively. Our atomistic simulations not only reveal the existence of CSRO in both compositions, but also predict two methods to tune the CSRO, namely the elemental selection and the thermal treatment. CSRO in experimental samples is confirmed using a combination of atomic resolution high-angle annular dark-field (HAADF) imaging as well as 4-dimensional scanning transmission electron microscopy (4D-STEM). A significant reduction of CSRO with the increase of annealing temperature is observed in HEC-Mo, both in simulation and experiment, though the temperature regime is not the same in the two approaches. To reach the low CSRO state, HEC-Mo is annealed at 1773K both in simulation and experiment. The high CSRO state in simulated HEC-Mo is created at 300K to make the CSRO most pronounced. However, 300K is not practical for experimental studies of HEC-Mo due to the low diffusivity of atoms. Thus, HEC-Mo sample is annealed at 1573K, where CSRO exists and kinetics of CSRO are high enough to form it, and compared to HEC-Mo annealed at 1773K, where sample prefers a more random state. The reduction of CSRO is also observed, in qualitative agreement with simulations. With the combination of simulations and experiments, we explore the existence of CSRO in HEC, two ways to tune it, and its impact on material properties. The understanding of CSRO paves the way for designing high-performance HECs.

Results
Observation of CSRO in HECs
To simulate the HECs, we first developed a machine learning interatomic potential (MLIP) based on the moment tensor potential (MTP) formalism. Subsequently, hybrid molecular dynamics/Monte Carlo (MD/MC)17,29 simulations were employed to minimize energy and find the corresponding atomic arrangements in HEC-Zr and HEC-Mo. After 6 million MC swaps, all simulations have reached equilibrium states (Fig. S1). Simulations predict that CSRO forms in these materials, but to varying degrees. Atomic arrangements and Warren-Cowley (WC) parameters30,31 up to 3rd NN in cation sublattice for the simulated HECs are shown in Fig. 1 and Fig. S2. The WC parameter \alpha_{ij} represents the propensity for atoms i and j to attract each other in the solution, with \alpha_{ij}=0 representing random arrangement, \alpha_{ij}<0 attraction, and \alpha_{ij}>0 repulsion of the elements. As illustrated by the WC parameter, the chemical preference of atomic pairs is most obvious among the 1st (Fig. 1b, d, f) and 2nd NN (Fig. S2). The ordering is almost negligible for the 3rd NN atoms (Fig. S2), indicating no long-range order formation. Since the 1st NN dominates the local environment and thus impacts material properties, in the following analysis we focused on the 1st NN.

In HEC-Zr, the chemical preference of V-V pairs is the strongest (\alpha_{ij}=-0.53) (see Fig. 1b). In HEC-Mo, the V-V pair still exhibits the strongest chemical preference among all the elements, but the attraction is weaker than in HEC-Zr, with \alpha_{ij}=-0.26 (Fig. 1d). In HEC-Zr, the Zr-Zr pair also exhibits strong chemical preference, but when Zr is replaced with Mo, such preference disappears as Mo-Mo pairs are repulsive (\alpha_{ij}=0.37). Apart from SRC, SRO also exists and is comparable between HEC-Zr and HEC-Mo. For instance, in HEC-Zr, Nb-Ti (\alpha_{ij}=-0.28) and Nb-Zr (\alpha_{ij}=-0.17) pairs exhibit strong attraction. In HEC-Mo, strong chemical preference can be observed for Nb-Ti (\alpha_{ij}=-0.17) and Ti-Mo (\alpha_{ij}=-0.26). Overall, the degree of CSRO in HEC-Zr is stronger than that in HEC-Mo, where the degree of CSRO is measured by the deviation of chemical order from a random distribution. In addition, our simulations predict that heat treatment will reduce the degree of CSRO as evidenced by simulated annealing at two different temperatures (Fig. 1c–f). With the increase of annealing temperature, the CSRO is significantly reduced and almost disappears, as evidenced by the near-zero WC parameter. A more complete temperature dependence of CSRO in simulated HEC-Mo is plotted in Fig. S3a. It shows that with an increase of temperature, CSRO gradually decays and significantly diminishes after 900K.

To validate our prediction on the existence of CSRO and pathways to tune them in HEC from MD/MC simulations, HECs were heated in a differential thermal analyzer (DTA) to monitor the energy change. More specifically, the formation of CSRO leads to heat release, resulting in an exothermic peak, and the dissolution of CSRO requires heat absorption, giving rise to an endothermic peak. In HEC-Zr, an exothermic peak starts at ~1473K, indicating the initiation of CSRO formation (Fig. 2a). This observation suggests that below 1473K, the kinetics for CSRO in HEC-Zr are frozen (Fig. S3b). At ~1563K, an endothermic peak emerges, indicating that energy change is dominated by the dissolution of CSRO. The endothermic peak ends at ~1653K, which suggests that at this temperature, the extent of CSRO in HEC-Zr is significantly decreased. The fact that the endothermic peak is larger than the exothermic peak in HEC-Zr suggests there is pre-existing CSRO, which could be explained as follows. The as-synthesized samples are quenched from 2573K, where a partial melt may form (Fig. S11c), and these samples may not reach fully homogenous states. The CSRO observed in as-synthesized samples is likely to originate from the solidification process, as pointed out by Han et al.17. Interestingly, Han et al.17 found that once CSRO formed in solid solution, the chemical preference would be similar, regardless of whether CSRO originated from quenching or annealing. In as-synthesized HEC-Mo, both exothermic peak and endothermic peak can be observed, with the latter having a larger area. Thus, one can conclude that there is pre-existing CSRO in as-synthesized HEC-Mo as well. It is worth noting that there is a discrepancy between experimental and simulation temperatures above which CSRO is largely dissolved, which is not necessarily surprising for an interatomic potential (Fig. S3). However, it is not a concern for analysis as long as the simulated systems are chosen below and above the temperature where CSRO drops significantly according to the interatomic potential.

To further validate our DTA method, we calculated the enthalpy changes in HEC-Zr (Fig. S4a) and HEC-Mo. These changes were induced by the formation and dissolution of CSRO and were calculated based on the exothermic and endothermic peak areas, which equal ~56.5 meV/atom and ~62.0 meV/atom, respectively. These values agree well with enthalpies calculated using DFT and methods from our previous work32 (60.78 meV/atom for HEC-Zr and 48.93 meV/atom for HEC-Mo), providing further support for the claim that the observed peaks in DTA curves are induced by the formation and dissolution of CSRO. The positive values of formation enthalpies also demonstrate that formation enthalpy is the driving force for the formation of CSRO.

We have also used DTA to explore the temperature dependence of CSRO in HEC-Mo, which has been predicted by our simulations. Toward this end, HEC-Mo was first annealed at two different temperatures to induce different levels of CSRO (Fig. S3b) and then quenched to room temperature. The degrees of CSRO in HEC-Mo were then determined by DTA. For example, for HEC-Mo annealed at 1573K, where a higher level of CSRO is preferred (Fig. S3b), DTA curve exhibits a minimal CSRO formation (exothermic) peak followed by a significantly larger CSRO dissolution (endothermic) peak (Fig. 2a), suggesting there is a great amount of pre-existing CSRO, which formed during annealing. In contrast, for HEC-Mo annealed at 1773K, where CSRO is expected to be significantly reduced (Fig. S3b), DTA curve exhibits a large CSRO formation (exothermic) peak (Fig. 2a), followed by a CSRO dissolution (endothermic) peak that is only slightly larger than the formation (exothermic) peak (Fig. 2a), suggesting that the amount of pre-existing CSRO is relatively low. In other words, HEC-Mo annealed at 1773K exhibits a considerably reduced amount of CSRO when compared to HEC-Mo annealed at 1573K.

After the validation of the existence of CSRO in HECs, atomic resolution HAADF was used on HECs to visualize CSRO. Z-contrast images acquired by HAADF have been successfully used to characterize composition fluctuations in other materials23. This analysis applied to HECs (Fig. 2) shows a clear contrast variation (Fig. 2), though the extent of the variation and the domain sizes vary among the samples. In HEC-Zr, the contrast variance is the strongest, with the sizes of bright and dark domains falling into the range of 1-2 nm (see Fig. 2b). This observation suggests there exists local clustering of heavy and light atoms, which is short-range ordering. Comparison to MD/MC simulations with CSRO suggests that the bright regions are Zr-rich and dark regions are V-rich. Meanwhile, the strongest variation in contrast is a result of the strongest clustering preference of Zr-Zr and V-V pairs. In HEC-Mo, a contrast variation is still present (see Fig. 2c), though weaker and smaller than in HEC-Zr. Compared to our simulations with CSRO, the dark region in HEC-Mo is still V-rich, while the bright region is Nb-rich. This analysis agrees with predictions from our simulations (Fig. 1) that the degree of CSRO is weaker in HEC-Mo than in HEC-Zr, and provides evidence that elemental selection of metal cations can be used for tuning CSRO. The significant reduction of CSRO with the increase of temperature observed in simulations and DTA is further visualized by STEM. More specifically, after annealing at 1573K, Z-contrast imaging shows contrast variance (Fig. 2d), which is comparable to as-synthesized HEC-Mo (Fig. 2c). However, after annealing at 1773K, the contrast variation in HEC-Mo almost disappeared (see Fig. 2e), indicating a significant drop in CSRO. It is important to mention that we excluded the possibility that the Z-contrast shown in Fig. 2 arises from variations in sample thickness, surface oxidation, or strain. Specifically, we ensured consistent thickness in the acquisition areas, removed potential surface oxides though ion milling before the acquisition, and observed consistent image contrast over large areas acquired at different collection angles to exclude the effect of strain. The averaging effect of sample thickness was also considered but due to the electron channeling33,34, it does not impact the measurement of CSRO (See Supplementary note 1).

As the Z-contrast images can only qualitatively reveal CSRO, we next aimed to characterize CSRO more quantitatively, targeting both compositions with high CSRO (as-synthesized) and HEC-Mo with low CSRO (annealed at 1773K). Toward this end, we employed 4D-STEM to collect nanobeam electron diffractions (NBED) along the [011] zone axis, which were then processed with cepstrum analysis for more precise lattice structure measurement35,36. Probing CSRO based on 4D-STEM is challenging because it is not obvious which features in the analysis show the strongest correlation with CSRO. To answer this question, we first analyzed our simulated HECs, with a particular focus on the lattice strain as it has been shown in earlier study to correlate with CSRO in M/HEA18,37. Interestingly, we found that in simulated HECs, local lattice strain is distributed heterogeneously with domain size in the range of 1-2 nm, which is the same size as the domain observed in Z-contrast images. More specifically, the fractional change of the average bond length (f_L) between the nearest metal-metal pairs was calculated and plotted in Fig. 3a–c. Here, f_L represents the deviation of the average metal-metal bonding length in a local region from the average bonding-length in the simulation supercell. This quantity can be regarded as a local lattice strain, with f_L=0 representing no local strain, f_L>0 representing local tension, and f_L<0 representing local compression. In HEC-Zr with high CSRO (see Fig. 3a), the strain variation is the strongest, suggesting the strongest tendency for atoms to cluster and form CSRO. Detailed analysis (Fig. S6a) indicates that the clustering of Zr induces tensile strain and the clustering of V results in compression. In HEC-Mo with high CSRO (see Fig. 3b), peak strains decreased, which confirms weakening of CSRO in HEC-Mo relative to HEC-Zr. Detailed analysis (Fig. S6b) reveals that clustering of V still accounts for compression, whereas the clustering of Nb induces tensile strain. After simulated annealing at 1773K, lattice strain dropped dramatically in HEC-Mo, consistent with significant reductions in CSRO. In essence, heterogeneous strain in HECs is tightly correlated with CSRO and can be employed for the detection of CSRO.

Strains along the [111] direction were then calculated for experimental HECs using [011] NBED patterns with cepstrum analysis to probe CSRO. [111] direction was picked as it intersects with all directions of the nearest metal-metal bonding. Spatial distributions of strains are illustrated in Fig. 3d–f. Discernible heterogeneous strain can be observed in all three types of HECs, but to varying degrees, as reflected in the different sizes and numbers of strain domains. For example, in HEC-Zr with high CSRO, the maximum strain is the largest, with +5.2% for tensile strain and −5.7% for compression (see Fig. 3d). In HEC-Mo with high CSRO, maximum strain drops to +3.8% for tension and −4.6% for compression (see Fig. 3e). After annealing at 1773K, maximum strain in HEC-Mo further decreased to +2.6% for tension and −2.3% for compression, indicating a significant reduction of CSRO. Heterogeneous strain in experimental HECs agrees well with the degree of CSRO in simulated HECs, further corroborating that the heterogeneous strain provides a reliable probe of CSRO in HECs. In addition, 4D-STEM analysis of CSRO shows good agreement with the observation from HAADF, providing further evidence that the differences in contrast variance of Z-contrast images are induced by CSRO.

We note that the domains of heterogeneous strain in experimental HECs are generally larger than those in simulated HECs, which is likely due to several factors. Here, we speculate on two specific reasons. First, electron probe will convolve and blur the features measured experimentally. Second, the strain induced by CSRO can extend beyond the region of CSRO, further enlarging the domain size. To determine the domain size of CSRO, we selected a threshold value of strain to be 1.5% in absolute value. This value is slightly higher than the lattice strain in simulated fully random HECs. The domain diameters were then calculated by assuming spherical shapes. Experimental size distributions of CSRO domains are shown in Fig. 3g. Not surprisingly, HEC-Zr with high CSRO exhibits the largest average domain size of 1.4 nm and the highest domain density of 4.6 × 10^17 m^-2. In HEC-Mo with high CSRO, the average domain size decreases to 0.9 nm and the number density dropped to 2.5 × 10^17 m^-2, implying a weakened CSRO. After annealing at 1773K, the average domain size in the HEC-Mo changed to 1.2 nm, but it is clear from Fig. 3g that the overall CSRO decreased, as quantified by the number density which dropped to 1.1 × 10^17 m^-2. The domain sizes are consistent with the distance to the second or the third atomic shell of the metal sublattice, providing further evidence that the ordering is short-range. It is worth mentioning that, during the collection of 4D-STEM, no second phase was observed in HECs, further proving the formation of CSRO does not alter the lattice structure. For that reason, the CSRO in HECs is distinct from the SRO in complex oxides, like isometric pyrochlore38,39, where SRO involves a phase transformation in the range of one to two unit cells.

To summarize, we have predicted using simulations that CSRO is ubiquitous in HECs, with elemental selection and thermal treatment as pathways to tune the degree of CSRO. The combination of HAADF imaging and strain analysis based on 4D-STEM confirm predictions from our models.

CSRO-induced improved radiation resistance
Having demonstrated the existence of CSRO in HECs, we ask whether the presence of CSRO is relevant for physical properties of the materials. We have specifically focused on resistance to radiation since in M/HEAs, CSRO has been proposed to improve radiation resistance by impeding the diffusion of defects40,41. Toward this end, we have irradiated HEC-Zr and HEC-Mo with high CSRO (as-synthesized) and HEC-Mo with low CSRO (annealed at 1773K) with 4.5 MeV Si ions and quantified the resulting radiation damage using radiation-induced swelling determined from the lattice expansion measured via grazing incidence X-ray diffraction (GIXRD). The results are summarized in Fig. 4a, which also includes swelling values reported in earlier studies on HEC7,42–46. The lattice expansion of our samples falls within the range of 0.15%-1.2%, which is comparable to previous work. For all samples, increasing temperature leads to a decrease in lattice expansion, which can be attributed to dynamic annealing of defects46. The order of the samples with respect to swelling follow the same qualitative trend at each temperature, so we focus on irradiation at 573K as a representative example. As shown in Fig. 4a, the order of samples from the highest to the lowest lattice expansion is HEC-Zr with high CSRO (1.16%), HEC-Mo with low CSRO (0.84%), and HEC-Mo with high CSRO (0.38%). We have checked the grain size in HEC-Mo with high CSRO and HEC-Mo with low CSRO using electron backscatter diffraction (Fig. S7) as grain boundaries can serve as defects sink and impact defect recovery. The grain size is very similar in the HEC-Mo samples with different levels of CSRO, which mean that we can exclude the possibility that the observed variation in radiation resistance is due to the grain size. Comparing the two HEC-Mo samples allows us to isolate the effect of CSRO as the overall chemistry of the samples is the same. We can therefore confidently conclude that CSRO led to significant improvement in radiation resistance in HEC. The stability of CSRO under radiation remains an open question and it will likely depend on the radiation flux and temperature.

Interestingly, HEC-Zr with high CSRO has the highest degree and the largest number density of CSRO, but its resistance to radiation-induced swelling is the worst among the HECs studied in this work. This result suggests that CSRO is not the only factor impacting radiation resistance in HECs but that chemistry also plays an important role as well. Here, by chemistry, we mean the stoichiometry on the cation sublattice. The effect of chemistry in the anion sublattice (carbon stoichiometry) on radiation resistance in HECs is negligible. Specifically, our XPS measurements indicate that both HEC-Zr and HEC-Mo are C-rich, with carbon concentration equal 56.72 at.% in HEC-Zr and 52.60 at.% in HEC-Mo (Table S1). Previous study47 does suggest that graphite can appear in C-rich ZrC, which serves as a strong source of knock-on carbon interstitials into carbides and lead to larger dislocation loops. However, our simulation suggested that C interstitials in HECs share comparable migration energies (3.56 eV for HEC-Zr and 3.86 eV for HEC-Mo) and are immobile at their radiation temperature of the current study. Thus, if graphite were present in these samples and introduced some C interstitials into HECs, these interstitials could not migrate and coalesce to larger dislocation loops and the impact on lattice expansion would be minimal. A detailed study of the mechanisms responsible for the impact of CSRO on radiation resistance is beyond the scope of this paper. However, TEM analysis of irradiated HEC-Mo samples (Fig. 4b, c) reveals that defects in HEC-Mo with high CSRO are qualitatively smaller than the defects in HEC-Mo with low CSRO. In addition, small dislocation loops were observed in HEC-Mo with low CSRO (Fig. 4c) whereas only small defect clusters (black-spot defects) appear in HEC-Mo with high CSRO (Fig. 4b), suggesting coarsening of defects in HEC-Mo with low CSRO. Based on the TEM observations, the distinct defect behavior is likely due to the different defect kinetics induced by CSRO.

In summary, we have discovered CSRO in HECs and demonstrated that it can significantly improve the resistance to radiation-induced damage in HECs, although it is not the only factor. CSRO was also identified to be ubiquitous in cation sublattices of HECs, similar to M/HEA17, even though HECs have more complex energy landscapes. Our finding suggests that CSRO may not be limited only to certain systems12–22, but instead it may be universal in all high-entropy materials. Further studies will be needed to determine the mechanisms underlying the impact of CSRO on properties of HECs and similarities and differences between HECs and M/HEA with respect to these mechanisms.

Methods
Fitting machine-learning interatomic potential (MLIP)
The MLIP model, based on moment tensor potential (MTP) formalism was employed, as it offers a good tradeoff between accuracy and computational efficiency48. Details on the MTP formalism are available in refs. 49–51. The training data for HEC-Zr and HEC-Mo were generated from elemental systems along with unary, binary, ternary, and quaternary carbides. To generate the training data, we ran MD simulations with M3GNET52 universal potential using LAMMPS software53. The M3GNET universal potential, while useful for running MD simulations for the purpose of generating atomic configurations, may not be accurate enough for the purpose of our simulations; therefore, we trained a potential specifically to model our systems. For each crystalline phase we performed a simulation in the temperature range of 0K to 5000K and pressure range of −1 GPa to 1 GPa for 100 ps. Then, a total of 10 to 15 atomic configurations were extracted at equal time spans during the simulation and we calculated their energies and atomic forces using density functional theory (DFT) to generate a complete training data. The detailed structure generation for HEC-Zr is as follows. A similar strategy was used for HEC-Mo. Systems included in our training data are

1. Elemental and unary carbide system.
(a) Ground state structure for the elements i.e., BCC Nb, Mo V, and HCP Ti, Zr, C and unary carbides NbC, TiC, ZrC, MoC, and VC.
(b) Snapshots from MD simulations for each system.

2. Binary and ternary carbide systems.
(a) Special quasi-random structure (SQS) generated solid solution of all binary combinations ((NbTi)C, (NbZr)C, (NbV)C, (TiZr)C, (TiV)C, (ZrV)C), and ternary combinations ((NbTiZr)C, (NbTiV)C, (NbZrV)C, (TiZrV)C). To limit the compositional space, the number of atoms was kept to 64 (32 metal atoms, 32 C) in each cell. The composition of each carbide was generated by partial substitution of one element with the other in the form of (A_x B_{1-x}) C with x in the range 0-100 at% at interval of 6.25 at%.
(b) For each binary and ternary system, snapshots from MD simulations were added. Three different solid solutions were selected: the end members and one composition in the middle.

3. Quaternary carbide systems.
(a) Ground state SQS permutations of quaternary (NbTiVZr)C and (NbTiVMo)C carbides were considered.
(b) Random compositions of quaternary carbides were selected from MD simulation and snapshots and added to training data.

All the above mentioned atomic configurations were included in DFT calculations of energies and forces. All the DFT calculations were performed using the Vienna Ab-initio Simulation Package (VASP) software54. The same convergence criteria were set to get energy and forces for all the atomic configurations. The projected-augmented-wave with the Perdew-Burke-Ernzerhof (PBE) form of exchange-correlation potential was used in this study. The energy cutoff of 500 eV was used for the plane-wave basis set with Monkhost-Pack k-point mesh of 3×3×3.

Molecular dynamics simulations
All the atomistic simulations were performed using our MTP potential. A 14×14×14 rock-salt supercell was initially constructed, with metal atoms randomly distributed in equiatomic compositions (random state). To equilibrate the CSRO, hybrid MD/MC simulations were performed with periodic boundary conditions in all directions. The systems were first relaxed and equilibrated to 300K for both HEC-Zr and HEC-Mo, and multiple temperatures (600K, 900K, 1200K, 1573K, and 1773K) for HEC-Mo and zero pressure in the canonical ensemble. Subsequently, MC swaps were conducted in which the position of two randomly selected atoms of different types were accepted and rejected based on the Metropolis algorithm. To relax the atomic configurations, MD simulations were performed in between the MC swaps, with 100 MD steps for every 100 MC swaps. The relative mole fractions of different atom types were kept constant. A total of 6 million MC swaps were performed for each HEC system until the equilibrium state was approached (Fig. S1). The final atomic configuration was then considered for CSRO analysis.

To quantify the CSRO, we calculated Warren-Cowley parameter30,31 (WCP) for each pair of atoms i and j, represented as \alpha_{ij}:
\alpha_{ij} = 1 - (N_{ij} / (c_j * N))
where N_{ij} is the average number of type j atoms surrounding type i atoms within the 1st NN within cation sublattice, N is the coordination number in 1NN, and c_j represents the concentration of atom j in the given HEC system.

Sample preparation and ion irradiation
For the study of CSRO and its impact on resistance to radiation-induced damage, we targeted (TiVZrNb)C and (TiVMoNb)C for the following reasons. First, we targeted refractory metals as the corresponding binary carbides exhibit ultra-high melting temperatures, making them promising candidates for high-temperature applications. Second, Zr was selected because ZrC has been widely studied for potential applications in nuclear reactors. Among many ZrC-based HECs, we selected (TiVZrNb)C as it has been already synthesized in earlier studies55 and because TiC, VC and NbC have also been considered as potential candidates in nuclear industries. Third, to explore the effect of elemental selection on CSRO, Zr was replaced by Mo and (TiVMoNb)C was chosen. After selecting (TiVZrNb)C and (TiVMoNb)C, five binary carbide powders (TiC, VC, ZrC, NbC, Mo_2C) and graphite powders with purity larger than 99 at.% were used as precursors for the synthesis of high entropy carbides. The carbides powders were weighed in an equimolar way for the cations to achieve the desired compositions for a total mass of 15g 0.5 vol.% graphite powder was also added to compensate for the carbon deficiency as well to remove surface oxycarbide layers. Powder mixtures were then ball milled in Si_3N_4 jar with Si_3N_4 balls in an ethanol medium. All ball millings were performed in a sequence of 5 minutes of milling and 5 minutes of rest to avoid overheating for a total of 24 hours. Mixed powders were dried at 338K and then sieved with a 100 mesh. Two-step spark plasma sintering was then employed to facilitate the conversion of carbide into single-phase carbide and densify powders to a solid compact, simultaneously. Entire sintering process is performed under backfilled argon to avoid oxidation. In the first step, powders were heated to 2273K with heating rate 100K·min^-1 and dwell at 2273K for 10 minutes. Simultaneously, pressure applied on powders was increased to 70 MPa at a rate of 10 MPa·min^-1. In the second step, the temperature was further increased to 2573K at the same ramping rate and dwell time of 2 minutes at this peak temperature. Then, the power of the furnace was turned off, and the furnace was cooled by flowing water from a chiller. All sintering experiments were performed in 20 mm graphite die and punch sets with graphite foil for the separation between powders and mold. Parts of the (TiVMoNb)C sample synthesized using SPS was further annealed separately at 1573K for 100h and at 1773K for 24h followed by furnace cooling. The reasons for choosing different thermal conditions to study the temperature dependence of CSRO in simulations and experiments are the limitations of CSRO kinetics in experiments and the discrepancy between experimental and simulation temperatures above which CSRO is largely dissolved. All samples are cut into 5 mm × 2 mm × 2 mm cuboids using a wafering blade and mirror polished on one side using diamond lapping film discs.

Polished samples were further irradiated with 4.50 MeV Si ions to a total fluence of 1.96 × 10^16 ions·cm^-2 at two different temperatures, 573K and 873K using the tandem accelerator at Ion Beam Laboratory at the University of Michigan. The ion flux for irradiation experiments was set at 1.09 × 10^12 ions·cm^-2s^-1, corresponding to a duration of 5 hours. SRIM-201356 was employed to simulate the radiation damage, measured in dpa, in all carbides, with threshold energies for all atoms set at 25 eV Based on SRIM calculations, the damage level reaches its peak of ~12 dpa at the depth of ~1.6 \mu m below the surface (Fig. S8a). At the first 600 nm below the surface, damage level as a function of depth is relatively flat (damage plateau) and the average damage level in this region is ~1.5 dpa. We can exclude the potential chemical effect of Si by calculating implantation profile using SRIM-201356. For example, as simulated by SRIM (Fig. S8b), the concentration of Si in HECs is less than 0.8 at.%, suggesting the chemical effects induced by Si in HECs are negligible.

Differential thermal analysis (DTA)
Perkin Elmer DTA 7 differential thermal analyzer was employed to determine the formation and dissolve of SRO in HECs. HECs with weight of 10-30 mg were heated from 300K to 1773K and held at peak temperature for 10 minutes then cooled down from 1773K to 300K. The cycle of heating and cooling were repeated 3 times to validate the reproducibility of the measurements (Fig. S4b). The heating rate and cooling rate were kept at 20K/min. All experiments are performed under a flow of Ar gas with a flow rate of 50 mL/min. Measured heat flow is normalized by sample weight.

High-resolution STEM (HRSTEM) imaging and 4D-STEM characterization
We prepared electron-transparent samples for all TEM and STEM characterizations performed in this work using a standard lift-out technique using an FEI Helios PFIB G4 FIB/FESEM Focused Ion beam (FIB) in the Nanoscale Imaging and Analysis Center, University of Wisconsin-Madison, which has been described in detail in our previous work57. Further thinning was performed using a Fischione 1040 TEM Ion Mill with an 800V ion beam. The inelastic mean free space for HEC-Zr and HEC-Mo were estimated to be 82.9 and 82.6 nm based on the model proposed by Malis et al.58 and Egerton et al.59. TEM specimen thickness measured using EELS log-ratio method are estimated to be 41.4 nm, 39.6 nm, 29.7 nm and 37.2 nm for HEC-Zr, HEC-Mo, HEC-Mo annealed at 1573K, and HEC-Mo annealed at 1773K, respectively. All atomic resolution HAADF images and 4D STEM analysis were collected using an FEI Titan G2 80-200 TEM (operated at 200 kV) equipped with a CEOS probe corrector. High-angle annular dark-field (HAADF) image series were acquired with a 23.4 mrad semi-convergence angle and a 147 pA current probe. Nonrigid registration60 was used to compensate for the drift and the series was averaged to get a single frame with a high signal-to-noise ratio. The image exposure time and thickness of study regions for different specimens were kept consistent to achieve meaningful comparison. For 4D-STEM imaging, we use a Direct Electron Celeritas-XS camera to collect convergence beam electron diffraction (CBED) pattern with a convergence angle of 3 mrad or 1.5 mrad and a camera length of 60 mm. The camera was operated at 6000 frames per second, and 10 4D STEM scan series were collected and registered for a better signal-to-noise ratio. The thicknesses of the regions studied by 4D-STEM were calculated based on the zero-beam vs {111} diffraction beam intensity ratio, which depends on thickness due to dynamical scattering61. As illustrated in Fig. S9, the measured thickness is 30.4 nm, 36.0 nm, and 43.6 nm for HEC-Zr, HEC-Mo, and HEC-Mo annealed at 1773K, respectively. These values are reasonably close to the EELS estimates given above. The CBED patterns were then analyzed using the cepstrum method developed in previous work35. Details of the cepstrum analysis implementation are included in Supplementary Note 2 and Fig. S10. To calculate fractional change (f_L) in nearest metal-metal interaction distance (1st NN of cation sublattice), simulated HECs were divided into a series of cylindrical sub-volumes (v_i) which approximates the region interacted with the STEM electron beam, each with a diameter of 6 Å, oriented along [011], positioned on a fine sampling grid with 1 Å spacing. The average bonding length of cations (L_{MM, v_i}) in each sub-volume was first calculated. Then the average bonding length of cations (L_{MM, V}) over the entire supercell. Finally, the fractional change in nearest metal-metal interaction distance (1st NN of cation sublattice) f_L can be calculated by the following equation:
f_L = (L_{MM, v_i} - L_{MM, V}) / L_{MM, V}

Characterization of HECs before and after irradiation
XRD experiments were performed using a Bruker D8 discovery X-ray diffractometer equipped with a two-dimensional detector to confirm the synthesized materials are single-phase. For all acquisitions, the scan range (2\theta) was set to be 20°−80° with a step of 20° and at least 120s for each step Fig. S11). To confirm that cations are uniformly distributed in HECs, EDS area scans were performed on HECs with an FEI Helios PFIB G4 equipped with the Thermo Noran Energy dispersive X-ray microanalysis system, operated at 15 kV. Based on EDS mapping (Fig. S11), no elemental segregation or precipitation was observed in HECs. Compositions were further measured using X-ray Photoelectron Spectroscopy (XPS). The measured region was first cleaned using Ar sputter cleaning to remove any carbon contamination and high-resolution spectra of C 1s, Ti 2p, V 2p, Zr 3d, Nb 3d and Mo 3d regions were collected from the cleaned region. Spectra were averaged over 15 scans with a pass energy of 50 eV and a step size of 0.2 eV. The composition of each element was calculated and included in Table S1. From our XPS measurements, both samples are enriched in carbon, but we did not observe any graphite formation. If such graphite formed, its impact on the conclusions presented in this paper would be minimal, as explained earlier.

To evaluate the radiation induced damage in the near surface region, GIXRD was performed on each sample before and after irradiation. The scan range was set to be 25°−65° at an incident angle of 3° with a step size of 20°. For each step, a long acquisition time of 600s was employed to ensure a high signal-to-noise ratio. Collected data Fig. S12) were further fitted using Rietveld analysis to obtain the lattice parameter.

Detailed characterizations of radiation-induced defects were achieved using bright-field imaging collected at two-beam conditions with a FEI Tecnai TF30 TEM operated at 300 kV. We focused on the peak damage region for a better characterization of radiation-induced defects. Two-beam condition images were collected with a g vector of <111> near the [112] zone axis.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "After reviewing the manuscript, I regret to inform you that I cannot recommend it for publication in Nature Communications. My decision is based on several fundamental concerns regarding the methodology, data interpretation, and conclusions, which significantly impact the validity of the study. A critical issue is the annealing process at 1773K for 24 hours. While this temperature might be reasonable for enhancing chemically short-range order (CSRO), the claim that the “as-synthesized sample” retains a CSRO structure characteristic of 300K contradicts fundamental thermodynamic expectations. The processing route described suggests that both the as-synthesized and aged samples should exhibit nearly the same CSRO levels, or at most a slight increase in the aged sample. Since the paper is largely built on this premise, the conclusions drawn from it are, in my view, fundamentally flawed. The STEM-HAADF evidence also raises concerns. Given that both samples should inherently have similar CSRO amounts, the observed contrast could be attributed to sample preparation artifacts. Furthermore, the TEM analysis used to support the conclusions presents additional issues. Even if one assumes a significant difference in CSRO levels between the two materials, the domains observed in the figures extend over several nanometers—far beyond what would be expected for CSRO, which is typically a first- and second-nearest-neighbor phenomenon. Additionally, considering the thickness of the TEM sample (likely over 100 atoms), each “atom” in the images represents an average over a significant number of atomic sites. This averaging effect further invalidates the interpretation that these images provide direct evidence of CSRO. For these reasons, and possibly others, the imaging approach used in this study—though seen in the literature—has been contested in multiple prior publications. Finally other concerns are the choice of compositions, which lacks a clear justification. Additionally, the atomistic simulations presented are too brief, and it is unclear whether sufficient time at 300K was allowed to capture potential phase formations. Given the likelihood of other long-range order (LRO) phases appearing at lower temperatures, a more comprehensive analysis—including WC parameters up to at least the 5th neighbor for all elements—would be necessary. Given these fundamental flaws in the methodology and analysis, I do not believe that the manuscript meets the necessary standards for publication in Nature Communications.", "reviewer_2": "This paper uses a combination of atomistic modeling and experimental analysis to consider the existence and impact of chemical short range order (CSRO) in high entropy carbides. The results are interesting, though as detailed below I do have some questions about the experimental analysis. Further, these results are not overly surprising, given the same behavior has been seen in HEAs and HEOs. That the same behavior occurs in HECs is almost expected and while the confirmation of that behavior is valuable, I am not convinced it rises to the level of impact of Nature Communications. I would ask the authors to make a stronger case for why Nature Communications is appropriate for this work. The abstract and paper note that CSRO has not been characterized in HECs and that they are special because only one sublattice exhibits mixing, but this is true of the disordered oxides and HEOs that the paper mentions. Why are the HECs any different in this regard? Shouldn't the concepts of CSRO in HEOs extend straight forwardly to HECs? There is extensive work on short range order in disordered oxides by Maik Lang's group at Tennessee which would be relevant for the discussion here. Why would 300K MD+MC simulations represent as-synthesized conditions? If anything, as-synthesized would be more non-equilibrium and further away from the 0K ground state, which the 300K simulations would be closer to. Related to this, I'm a little confused as to the synthesis conditions. The heat treated sample was held at 1773 K for 24 hours, but the as-synthesized material was done at 2300 C (should use same units everywhere) so 2600 K - it seems that the as-synthesized material should have less SRO than the heat treated as it was not annealed at lower temperatures. I'm not sure what I'm missing. Around line 89, where the authors say that CSRO is measured by the tendency of atoms to cluster, are they referring to short ranged clustering? In the SRO literature, there is a distinction between ordering and clustering and I just want to clarify which is meant here (both would be considered more ordered than random). It isn't obvious to me that Z-contrast TEM or 4D STEM can reveal the SRO in these materials as the ordering would have to occur on length scales longer than the thickness of the sample. Wouldn't the resulting images be a convolusion of the structure through the thickness? The foil thickness seems to be about 50 nm or so, so I might expect the images to be averaged over that thickness, making it nearly impossible to resolve features with length scales smaller than that. Can the authors comment on this? The authors say that the domains in the simulations are likely smaller than in experiment because of the supercell size. Have they tested that the distribution varies as the cell size is changed? The radiation studies provide a nice complement to the thermodynamic studies, though similar studies have been done in the past so these are not entirely novel. The authors conclude that, for a sample where presumably the only difference is CSRO, the sample with greater CSRO exhibits less swelling and smaller defects. Radiation is known to induce disordering in chemically complex systems - would this effect persist or would it saturate at some point as radiation drives the system to a more disordered/random state? As the ion beam irradiations used Si as the ion species, could there be any chemical effect due to introducing Si?", "reviewer_3": "I have reviewed the manuscript and, unfortunately, I cannot support it being published in Nature Communications in its current form. I base this on several concerns I had with the paper, and these are summarized in the following points: 1. The synthesis of the HECs involves hot pressing at 2300°C and cooled slowly in the furnace to room temperature. If CSRO occurs upon cooling, it is unclear how the Mo sample heat treated at 1500°C and furnace cooled would be any different. In fact, it might be argued that it would potentially have greater CSRO rather than less. This is a fundamental issue to the paper given that the author’s propose that the annealing should produce less SRO. 2. Given that CSRO is expected to exist over very small distances (a few atoms) and that the sample thicknesses are probably in the range of 100 atoms thick (the authors indicate similar thicknesses for their samples based on their EELS data but fail to provide actual numbers so this is an estimate of typical thin specimen dimensions), it is difficult to prove that the subtle differences in contrast result from CSRO – one could argue several other reasons for such contrast differences and it seems virtually impossible to say with certainty that these are due to CSRO. 3. Normally, ordering in alloys occurs when unlike atoms have a greater tendency to bond than like atoms due to a negative enthalpy of mixing of the unlike atoms. On the other hand, clustering of like atoms tends to reflect a positive enthalpy of mixing of unlike elements. Given that much of the argument is that like atoms (e.g., V-V and Zr-Zr) tend to cluster seems contrary to the idea of CSRO. Granted there are some cases where they do predict unlike atoms with greater tendency to cluster, but the premise is that SRO is greater in the HEC-Zr material is greater than in HEC-Mo where there is a tendency for unlike atoms to cluster according to the MC/MD simulations. Also, I suppose one can argue that in multicomponent alloys and carbides, it’s likely you’ll have atom pairs that have a tendency to order and pairs that have a tendency to cluster. 4. The radiation studies also seem somewhat flawed. Related to the first point above, it is not at all clear why the annealed HEC-Mo would behave differently and yet the authors conclude that the difference in volume changes (lattice expansion) due to irradiation is clear evidence of CSRO. Since the HEC-Zr with the largest purported CSRO has greater volume change, it is hard to prove that CSRO is playing a significant role in the different materials’ resistances to radiation damage. In summary, these rather serious concerns with the interpretation of the experimental data lead me to conclude that this paper should ready to be published in its current form."}, "author_response": "Point by point response to reviewer’s comments\nReviewer #1:\nAfter reviewing the manuscript, I regret to inform you that I cannot recommend it for publication in\nNature Communications. My decision is based on several fundamental concerns regarding the\nmethodology, data interpretation, and conclusions, which significantly impact the validity of the study.\nComment 1:\nA critical issue is the annealing process at 1773K for 24 hours. While this temperature might be\nreasonable for enhancing chemically short-range order (CSRO), the claim that the “as-synthesized sample”\nretains a CSRO structure characteristic of 300K contradicts fundamental thermodynamic expectations. The\nprocessing route described suggests that both the as-synthesized and aged samples should exhibit nearly\nthe same CSRO levels, or at most a slight increase in the aged sample. Since the paper is largely built on\nthis premise, the conclusions drawn from it are, in my view, fundamentally flawed.\nThank you for your insightful comments regarding the potential discrepancy between our simulation\npredictions and experimental observations. We agree that the origin of CSRO in the as-synthesized samples\nis not the same as in our simulations at 300 K as the as-synthesized samples are quenched from high\ntemperature where partial melts may form, and they may not reach fully homogenous states. The CSRO\nobserved in as-synthesized samples are likely to originate from the solidification process as pointed out by\nHan Y. et al. Nature Communications vol. 15, p.6486, 2024 . The goal of our original manuscript was to\ncompare samples with varying degrees of CSRO, not necessarily their temperature dependence. We fully\nagree with the reviewer that the as-synthesized sample was not appropriate to conduct studies of\ntemperature dependence and that the way the sample was introduced in the original manuscript could have\nled to confusion.\nWe have now conducted additional experiments to test the predictions of temperature dependence of\nCSRO, and our experiments are fully consistent with predictions from simulations. Specifically, we further\nannealed as-synthesized HEC-Mo at 1573 K for 100 hours, which led to homogenization of the sample.\nHRSTEM performed on the newly annealed HEC-Mo confirm that CSRO still exists (see Fig. 2c in revised\nmanuscript). Considering that the CSRO almost disappears in HEC-Mo after annealing at 1773 K (Fig. 2d\nin the main text), it is clear that there is a transition from ordering to disordering in HEC-Mo with the\nincrease of annealing temperature. This observation agrees very well with predictions of our simulations.\nWe have included the additional results in the revised manuscript.\nComment 2:\nThe STEM-HAADF evidence also raises concerns. Given that both samples should inherently have similar\nCSRO amounts, the observed contrast could be attributed to sample preparation artifacts. Furthermore, the\nTEM analysis used to support the conclusions presents additional issues. Even if one assumes a significant\ndifference in CSRO levels between the two materials, the domains observed in the figures extend over\nseveral nanometers—far beyond what would be expected for CSRO, which is typically a first- and second-\nnearest-neighbor phenomenon. Additionally, considering the thickness of the TEM sample (likely over 100\natoms), each “atom” in the images represents an average over a significant number of atomic sites. This\naveraging effect further invalidates the interpretation that these images provide direct evidence of CSRO.\nFor these reasons, and possibly others, the imaging approach used in this study—though seen in the\nliterature—has been contested in multiple prior publications.\nThank you for the question. We have good reasons to believe that the contrast variations observed in\nHAADF and 4D-STEM are not artifacts, and result from the presence of CSRO. We have also conducted\nadditional experiments to provide even stronger evidence.\nFirst of all, we do agree with the reviewer that the contrast variance observed in HAADF images might\npotentially arise from other sources such as the surface oxides. Though we have tried our best to control\nthem, it is impossible to fully exclude all these factors. However, in addition to HAADF imaging, 4D-\nSTEM analysis was also employed to study the CSRO, which solely depends on the diffraction disk\npositions. Thus, unlike HAADF imaging, the 4D-STEM analysis is robust against variation in thickness,\nand immune to the presence or thickness of surface oxides. The presence of CSRO and their variations\namong samples were confirmed by our 4D-STEM analysis, which is consistent with our HAADF imaging\nobservations as well as predictions from our simulations. Thus, we believe the contrast variance observed\nin HAADF images originated from the CSRO instead of other sources.\nRegarding the relatively large domain size of CSRO in our 4D-STEM observation, we believe there\nare two reasons for that. First, during our measurement, we employed an electron probe with a diameter of\n6 Å, which resulted inevitably in convolution and blurring of the domain boundaries. Consequently, the\nmeasured domains are enlarged. Second, though CSRO regions are relatively small, the lattice distortion\nand strain induced by them can extend beyond the CSRO, which also contributes to the enlarged domains.\nHowever, one should note that even considering these two factors, the majority of the domains have size in\nthe range of 1-2 nm, which is consistent with what is expected for CSRO. We have included this discussion\nin our revised manuscript for completeness.\nWe fully agree with the reviewer that in principle there might be an averaging effect in STEM analysis\nand that one needs to be careful interpreting the results. We have performed additional simulations to\ndemonstrate that the averaging effect is insignificant in our studies and therefore our interpretation of CSRO\nremains valid. More specifically, during the collection of STEM data, dynamical scattering leads to electron\nchanneling effect. For example, when imaging zone-axis oriented crystals, the data does not reflect a simple\ntwo-dimensional projection of the structure. Instead, the on-column probe exhibits an intensity peak near\nthe electron entrance surface (top surface), which means that atoms in a thin region near the top surface\ndominate the collected signals (see e.g., Voyles P. M. et al. Microscopy and Microanalysis vol. 10, p. 291-\n300, 2004). We performed simulations of electron beam intensity along a column of atoms with a\nconvergence semiangle of 23.4 mrad to simulate the condition of HAADF-STEM imaging (see Fig. S2a,\nb). Intensity peaks can be observed in the region from the top surface to a depth of 4 nm for both samples\n(Fig. S2a, b), suggesting atoms in the top 4 nm contribute the most to our collected data. Atoms in the region\nextending from 4 nm to 10 nm from the surface can make contributions, but their contributions dropped by\n50%. Contributions from atoms beyond 10 nm can be neglected. The depth of 4 nm where the intensity\nreaches the peak is comparable to the depth of field (5.9 nm) calculated by Li L. et al. Nature\nCommunications vol. 14, p.7448, 2023, where HAADF-STEM was also employed to directly derive cation\ndistributions in cation-disordered oxides. In summary, the atoms in the top 4 nm dominated the collected\ndata during HAADF-STEM and the averaging effects are most significant in the top 4 nms. Considering\nthat the majority of CSRO domains are in the range of 1-2 nm, they can be resolved by HAADF-STEM.\nRegarding the 4D-STEM, a smaller convergence angle (3 mrad) was used during the data collection.\nThe electron channeling effect under such circumstances was also explored (see Fig. S2c, d). Intensity peaks\nappear in the regions from the top surface to a depth of 8 nm for both samples (Fig. S2c, d), indicating\natoms in the top 8 nm contribute the most to our collected data. Atoms in the region extending from 8 nm\nto 18 nm can make contributions, but their contributions decreased by 60 %. Contributions from atoms\nbelow 18 nm can be neglected. Overall, atoms in the top 8 nm dominated the collected data during 4D-\nSTEM and the averaging effects are most considerable in the top 8 nm. To explore if the CSRO-induced\nstrain can still be resolved when the signals are averaged by the atoms in a relatively larger region, 4D-\nSTEM analysis were performed on our MD/MC samples with a thickness of 7 nm, which is close to the\ndominant region of 8 nm from top surface. According to our analysis, the highest strains measured are 6.1%,\n4.6% and 4.4% for HEC-Zr, HEC-Mo and HEC-Mo annealed at 1773 K, respectively. The trend of the\nhighest strains among different samples agrees well with our experimentally measured strain trend\ncalculated directly from 4D-STEM, illustrating that the strain induced by CSRO cam be resolved by 4D-\nSTEM and the averaging effects in the top 8 nm can be neglected. We have included this discussion in our\nrevised manuscript for completeness.\nComment 3:\nFinally other concerns are the choice of compositions, which lacks a clear justification. Additionally,\nthe atomistic simulations presented are too brief, and it is unclear whether sufficient time at 300K was\nallowed to capture potential phase formations. Given the likelihood of other long-range order (LRO)\nphases appearing at lower temperatures, a more comprehensive analysis—including WC parameters up to\nat least the 5th neighbor for all elements—would be necessary.\nThank you for your suggestions. In the revised manuscript, we have provided a more extended\njustification for the choice of the compositions we studied.\nRegarding the simulation time, we have calculated the potential energy of the systems and plotted it as\na function of the number of iterations (see Fig. S1). According to our simulation, the energy of the simulated\nsystems has converged, indicating an equilibrium state. Thus, we believe the simulation time is long enough\nto capture potential phase formation, if any. In addition, we do not expect any phase separation in the HECs\nstudied by this work, as no second phase was observed in the XRD results (Fig. S9a). We have updated our\nmanuscript to clarify this point.\nRegarding the long-range order (LRO), we have included the Warren-Cowley parameter up to 3rd NN\nin Fig. 1 to exclude the formation of LRO. As shown in Fig. 1, at the 3rd NN, the atom arrangement in HEC-\nZr and HEC-Mo at low temperature is almost random, indicating weak or even no ordering at and beyond\nthe 3rd NN. Thus, we believe there is no LRO formed in our samples at low temperature. We have updated\nour manuscript to include this information.\nReviewer #2:\nThis paper uses a combination of atomistic modeling and experimental analysis to consider the\nexistence and impact of chemical short range order (CSRO) in high entropy carbides. The results are\ninteresting, though as detailed below I do have some questions about the experimental analysis. Further,\nthese results are not overly surprising, given the same behavior has been seen in HEAs and HEOs. That\nthe same behavior occurs in HECs is almost expected and while the confirmation of that behavior is\nvaluable, I am not convinced it rises to the level of impact of Nature Communications. I would ask the\nauthors to make a stronger case for why Nature Communications is appropriate for this work.\nComment 1:\nThe abstract and paper note that CSRO has not been characterized in HECs and that they are special\nbecause only one sublattice exhibits mixing, but this is true of the disordered oxides and HEOs that the\npaper mentions. Why are the HECs any different in this regard? Shouldn't the concepts of CSRO in HEOs\nextend straight forwardly to HECs? There is extensive work on short range order in disordered oxides by\nMaik Lang's group at Tennessee which would be relevant for the discussion here.\nThank you for your comments. We agree that the mixing on one sublattice is the same for HECs,\ndisordered oxides, and HEOs. Instead, the fundamental difference between them is the bonding nature.\nIn HECs, the covalent bonding between transition metal (TM) and carbon is more uniform and less selective,\nwhereas in HEOs, the ionic bonding between TM and oxygen is less uniform and more selective. More\nspecifically, different TMs exhibit varying oxidation states and electronic configurations in TM-O bonding,\nresulting in selective arrangement of TMs around oxygen. In other words, there is an enthalpic driving force\nfor the formation of CSRO in oxides. However, in HECs, the differences in TM-C bonding among various\nTMs are minimal, offering negligible enthalpic driving force for CSRO. Thus, it would be difficult to\nextend the concept of CSRO in oxides directly to carbides. In addition, the SRO studied by Lang’s group\n(e.g., Fuentes A. F. et al. Applied Physics Reviews vol. 11, 2024 Shamblin J. Nature Materials vol. 15, p.\n507-511, 2016), involves formation of a new phase in a disordered oxide. The formation of a new phase\nwith the size range of one to two unit cells in an disordered oxide can be referred to as SRO, but it is not\nthe same as formation of a local CSRO in a disordered phase without phase transformation. More\nspecifically, in our work on HECs, CSRO is defined as the deviation of chemical species from random\narrangement in the same sublattice without changing the structure. Thus, the SRO studied by Lang’s group\ncannot be directly compared to the CSRO we focus on in HECs.\nWe have revised our manuscript to emphasize the differences among HECs, HEOs or disordered oxides\nin background and added references to Lang’s work on oxides.\nComment 2:\nWhy would 300K MD+MC simulations represent as-synthesized conditions? If anything, as-\nsynthesized would be more non-equilibrium and further away from the 0K ground state, which the 300K\nsimulations would be closer to.\nRelated to this, I'm a little confused as to the synthesis conditions. The heat treated sample was held at\neverywhere) so 2600 K - it seems that the as-synthesized material should have less SRO than the heat\ntreated as it was not annealed at lower temperatures. I'm not sure what I'm missing.\nThe goal of our original manuscript was to compare samples with varying degrees of CSRO, not\nnecessarily the temperature dependence of CSRO and in that sense the 300K in simulations represented the\nas-synthesized sample in experiment. We agree, however, that this comparison can be confusing because\nthe origin of CSRO in the as-synthesized samples is not the same as in our simulations at 300 K.\nThe as-synthesized samples are quenched from high temperature where partial melts may form, and\nthey may not reach fully homogenous states. The CSRO observed in as-synthesized samples are likely to\noriginate from the solidification process as pointed out by Han Y. et al. Nature Communications vol. 15,\np.6486, 2024. Meanwhile, as illustrated by Han Y. et al. Nature Communications vol. 15, p.6486, 2024,\nCSRO with different origins, whether from quenching or annealing, exhibit similar chemical preferences.\nThus, in the revised manuscript, CSRO observed in simulations at 300 K serves as a reference for the\nanalysis of CSRO in experimental results.\nTo address the valid question about temperature dependence. we have now conducted additional\nexperiments to test predictions from our simulations. Specifically, we further annealed as-synthesized HEC-\nMo at 1573 K for 100 hours, which led to homogenization of the sample. HRSTEM performed on the newly\nannealed HEC-Mo confirm that CSRO still exists (see Fig. 2c in revised manuscript). Considering that the\nCSRO almost disappears in HEC-Mo after annealing at 1773 K (Fig. 2d in the main text), it is clear that\nthere is a transition from ordering to disordering in HEC-Mo with the increase of annealing temperature.\nThis observation agrees very well with predictions of our simulations.\nWe have included the additional results in the revised manuscript.\nComment 3:\nAround line 89, where the authors say that CSRO is measured by the tendency of atoms to cluster,\nare they referring to short ranged clustering? In the SRO literature, there is a distinction between ordering\nand clustering and I just want to clarify which is meant here (both would be considered more ordered than\nrandom).\nThank you for your question. In previous work by Abu-Odeh A. et al. Acta Materialia vol. 275, p.\n119185, 2023, two kinds of non-random correlations between different chemical species in disordered solid\nsolution alloys were defined. When unlike species attract each other, short-range ordering (SRO) occurs\nand when like atoms attract each other, short-range clustering (SRC) occurs. In our work, the CSRO is\ndefined as deviation of chemical species from random arrangement of cations on the same sublattice without\nchanging the structure, which includes both SRO and SRC. We have revised our manuscript to clarify the\ndefinition of CSRO.\nComment 4:\nIt isn't obvious to me that Z-contrast TEM or 4D STEM can reveal the SRO in these materials as the\nordering would have to occur on length scales longer than the thickness of the sample. Wouldn't the\nresulting images be a convolusion of the structure through the thickness? The foil thickness seems to be\nabout 50 nm or so, so I might expect the images to be averaged over that thickness, making it nearly\nimpossible to resolve features with length scales smaller than that. Can the authors comment on this?\nWe fully agree with the reviewer that in principle there might be an averaging effect in STEM analysis\nand that one needs to be careful interpreting the results. We have performed additional simulations to\ndemonstrate that the averaging effect is insignificant in our studies and therefore our interpretation of CSRO\nremains valid. More specifically, during the collection of STEM data, dynamical scattering leads to electron\nchanneling effect. For example, when imaging zone-axis oriented crystals, the data does not reflect a simple\ntwo-dimensional projection of the structure. Instead, the on-column probe exhibits an intensity peak near\nthe electron entrance surface (top surface), which means that atoms in a thin region near the top surface\ndominate the collected signals (see e.g., Voyles P. M. et al. Microscopy and Microanalysis vol. 10, p. 291-\n300, 2004). We performed simulations of electron beam intensity along a column of atoms with a\nconvergence semiangle of 23.4 mrad to simulate the condition of HAADF-STEM imaging (see Fig. S2a,\nb). Intensity peaks can be observed in the region from the top surface to a depth of 4 nm for both samples\n(Fig. S2a, b), suggesting atoms in the top 4 nm contribute the most to our collected data. Atoms in the region\nextending from 4 nm to 10 nm from the surface can make contributions, but their contributions dropped by\n50%. Contributions from atoms beyond 10 nm can be neglected. The depth of 4 nm where the intensity\nreaches the peak is comparable to the depth of field (5.9 nm) calculated by Li L. et al. Nature\nCommunications vol. 14, p.7448, 2023, where HAADF-STEM was also employed to directly derive cation\ndistributions in cation-disordered oxides. In summary, the atoms in the top 4 nm dominated the collected\ndata during HAADF-STEM. And the averaging effects are most significant in the top 4 nms. Considering\nthat the majority of CSRO domains are in the range of 1-2 nm, they can be resolved by HAADF-STEM.\nRegarding the 4D-STEM, a smaller convergence angle (3 mrad) was used during the data collection.\nThe electron channeling effect under such circumstances was also explored (see Fig. S2c, d). Intensity peaks\nappear in the regions from the top surface to a depth of 8 nm for both samples (Fig. S2c, d), indicating\natoms in the top 8 nm contribute the most to our collected data. Atoms in the region extending from 8 nm\nto 18 nm can make contributions, but their contributions decreased by 60 %. Contributions from atoms\nbelow 18 nm can be neglected. Overall, atoms in the top 8 nm dominated the collected data during 4D-\nSTEM and the averaging effects are most considerable in the top 8 nm. To explore if the CSRO induced\nstrain can still be resolved when the signals are averaged by the atoms in a relatively larger region, 4D-\nSTEM analysis were performed on our MD/MC samples with a thickness of 7 nm, which is close to the\ndominant region of 8 nm from top surface. According to our analysis, the highest strains measured are 6.1%,\n4.6% and 4.4% for HEC-Zr, HEC-Mo and HEC-Mo annealed at 1773 K, respectively. The trend of the\nhighest strains among different samples agrees well with our experimentally measured strain trend\ncalculated directly from 4D-STEM, illustrating that the strain induced by CSRO cam be resolved by 4D-\nSTEM and the averaging effects in the top 8 nm can be neglected.\nIn the revised manuscript we have included the measurements of sample thickness, which were carried\nout using two methods. First, we completed the measurement of thickness using EELS log-ratio method.\nBy calculating the inelastic mean free path of HEC-Zr (82.9 nm) and HEC-Mo (82.6 nm) using the model\nproposed by Malis T. et al. Journal of electron microscopy technique vol. 8, p. 193-200, 1988 and Egerton\nR. F. et al. Ultramicroscopy vol. 21, p. 231-244, 1987, the thickness of HEC-Zr, HEC-Mo, HEC-Mo\nannealed at 1573 K and HEC-Mo annealed at 1773 K were calculated to be 41.4 nm, 39.6 nm, 29.7 nm,\nand 37.2 nm, respectively. The measurements are complemented by the collected diffraction pattern of 4D-\nSTEM. More specifically, the ratio of transmitted beam intensity to a {111} diffraction beam intensity is\ndependent on dynamical scattering, which is related to sample thickness. Compared to the beam intensity\nratios calculated from MD/MC models with different thickness, the thickness of HEC-Zr, HEC-Mo, HEC-\nMo annealed at 1573 K and HEC-Mo annealed at 1773 K are measured to be 41.4 nm, 39.6 nm, 29.7 nm\nand 37.2 nm, respectively. The thickness measured by two different methods is reasonably comparable to\neach other.\nComment 5:\nThe authors say that the domains in the simulations are likely smaller than in experiment because of\nthe supercell size. Have they tested that the distribution varies as the cell size is changed?\nThank you for your helpful comment. This statement was a speculation, and we agree that it should be\ntested. To clarify this statement, we performed an additional MD/MC simulation on HEC-Mo with a larger\nsupercell (32,768 atoms, compared to 21,952 in the original simulations) at 300 K. According to the WC\nparameters, the CSRO in both supercells are comparable. Thus, the size of the supercell is not the reason\nfor smaller domain size in simulations than in experiments. We have revised the manuscript and no longer\nincluded this speculation.\nRegarding the difference in domain size between simulation and experimental observations, we believe\nthere are two possible explanations. First, during the measurement of STEM, an electron probe with a\ndiameter of 6 Å was employed. Therefore, the domain boundaries are inevitably convolved and blurred,\nresulting in the enlargement of CSRO domains. Second, though CSRO regions are relatively small, the\nlattice distortion and strain induced by them can extend beyond the CSRO, which also contributes to the\nenlarged domains. We have updated the manuscript to discuss the possible reasons for the larger domains\nobserved in experiments than in simulations.\nComment 6:\nThe radiation studies provide a nice complement to the thermodynamic studies, though similar\nstudies have been done in the past so these are not entirely novel. The authors conclude that, for a sample\nwhere presumably the only difference is CSRO, the sample with greater CSRO exhibits less swelling and\nsmaller defects. Radiation is known to induce disordering in chemically complex systems - would this\neffect persist or would it saturate at some point as radiation drives the system to a more\ndisordered/random state?\nThank you for bringing the evolution of CSRO during radiation to our attention, which is indeed\ninteresting and worth exploring. However, such study is beyond the scope of this work, and we have updated\nthe manuscript to include a brief discussion posing this interesting question that emerges from these results.\nComment 7:\nAs the ion beam irradiations used Si as the ion species, could there be any chemical effect due to\nintroducing Si?\nThank you for your question. The effect of introducing Si on chemical ordering is negligible. More\nspecifically, we have calculated Si concentration as a function of depth from the surface using SRIM (see\nFig. S6b). The maximum concentrations of Si in both HECs are less than 0.8 %, and therefore its impact\non variation in the local chemistry is negligible. We have included this discussion in our revised manuscript.\nReviewer #3:\nI have reviewed the manuscript and, unfortunately, I cannot support it being published in Nature\nCommunications in its current form. I base this on several concerns I had with the paper, and these are\nsummarized in the following points:\nComment 1:\nThe synthesis of the HECs involves hot pressing at 2300°C and cooled slowly in the furnace to room\ntemperature. If CSRO occurs upon cooling, it is unclear how the Mo sample heat treated at 1500°C and\nfurnace cooled would be any different. In fact, it might be argued that it would potentially have greater\nCSRO rather than less. This is a fundamental issue to the paper given that the author’s propose that the\nannealing should produce less SRO.\nThank you for your insightful comments regarding the potential discrepancy between our simulation\npredictions and experimental observations. We agree that the origin of CSRO in the as-synthesized samples\nis not the same as in our simulations at 300 K as the as-synthesized samples are quenched from high\ntemperature where partial melts may form, and they may not reach fully homogenous states. The CSRO\nobserved in as-synthesized samples are likely to originate from the solidification process as pointed out by\nHan Y. et al. Nature Communications vol. 15, p.6486, 2024. The goal of our original manuscript was to\ncompare samples with varying degrees of CSRO, not necessarily their temperature dependence. We fully\nagree with the reviewer that the as-synthesized sample was not appropriate to conduct studies of\ntemperature dependence and that the way the sample was introduced in the original manuscript could have\nled to confusion.\nWe have now conducted additional experiments to test the predictions of temperature dependence of\nCSRO and our experiments are fully consistent with predictions from simulations. Specifically, we further\nannealed as-synthesized HEC-Mo at 1573 K for 100 hours, which led to homogenization of the sample.\nHRSTEM performed on the newly annealed HEC-Mo confirm that CSRO still exists (see Fig. 2c in revised\nmanuscript). Considering that the CSRO almost disappears in HEC-Mo after annealing at 1773 K (Fig. 2d\nin the main text), it is clear that there is a transition from ordering to disordering in HEC-Mo with the\nincrease of annealing temperature. This observation agrees very well with predictions of our simulations.\nWe have included the additional results in the revised manuscript.\nComment 2:\nGiven that CSRO is expected to exist over very small distances (a few atoms) and that the sample\nthicknesses are probably in the range of 100 atoms thick (the authors indicate similar thicknesses for their\nsamples based on their EELS data but fail to provide actual numbers so this is an estimate of typical thin\nspecimen dimensions), it is difficult to prove that the subtle differences in contrast result from CSRO –\none could argue several other reasons for such contrast differences and it seems virtually impossible to\nsay with certainty that these are due to CSRO.\nWe have now included the measurements of sample’s thickness in our revised manuscript. To measure\nsample thickness, we employed two methods that are complementary to each other. First, we completed the\nmeasurement of thickness using EELS log-ratio method. By calculating the inelastic mean free path of\nHEC-Zr (82.9 nm) and HEC-Mo (82.6 nm) using the model proposed by Malis T. et al. Journal of electron\nmicroscopy technique vol. 8, p. 193-200, 1988 and Egerton R. F. et al. Ultramicroscopy vol. 21, p. 231-244,\n1987, the thickness of HEC-Zr, HEC-Mo, HEC-Mo annealed at 1573 K and HEC-Mo annealed at 1773 K\nare calculated to be 41.4 nm, 39.6 nm, 29.7 nm and 37.2 nm, respectively. The measurements are\ncomplemented by the collected diffraction pattern of 4D-STEM. More specifically, the ratio of transmitted\nbeam intensity to a {111} diffraction beam intensity is dependent on dynamical scattering, which is related\nto sample thickness. Compared to the beam intensity ratios calculated from MD/MC models with different\nthickness, the thickness of HEC-Zr, HEC-Mo, HEC-Mo annealed at 1573 K and HEC-Mo annealed at 1773\nK are measured to be 41.4 nm, 39.6 nm, 29.7 nm and 37.2 nm, respectively. The thickness values measured\nby two different methods are in a reasonably agreement with each other. With respect to the contrast\nvariations observed in HAADF and 4D-STEM, we have good reasons to believe they are not artifacts, and\nthat the variations result from the presence of CSRO and we have conducted additional experiments to\nprovide even stronger evidence.\nFirst of all, we do agree with the reviewer that the contrast variance observed in HAADF images might\npotentially arise from other sources such as the surface oxides. Though we have tried our best to control\nthem, it is impossible to fully exclude all these factors. However, in addition to HAADF imaging, 4D-\nSTEM analysis was also employed to study the CSRO, which solely depends on the diffraction disk\npositions. Thus, unlike HAADF imaging, the 4D-STEM analysis is robust against variation in thickness,\nand immune to the presence or thickness of surface oxides. The presence of CSRO and their variations\namong samples were confirmed by our 4D-STEM analysis, which is consistent with our HAADF imaging\nobservations as well as predictions from our simulations. Thus, we believe the contrast variance observed\nin HAADF images originated from the CSRO instead of other sources.\nWe fully agree with the reviewer that in principle there might be an averaging effect in STEM analysis\nand that one needs to be careful interpreting the results. We have performed additional simulations to\ndemonstrate that the averaging effect is insignificant in our studies and therefore our interpretation of CSRO\nremains valid. More specifically, during the collection of STEM data, dynamical scattering leads to electron\nchanneling effect. For example, when imaging zone-axis oriented crystals, the data does not reflect a simple\ntwo-dimensional projection of the structure. Instead, the on-column probe exhibits an intensity peak near\nthe electron entrance surface (top surface), which means that atoms in a thin region near the top surface\ndominate the collected signals (see e.g., Voyles P. M. et al. Microscopy and Microanalysis vol. 10, p. 291-\n300, 2004). We performed simulations of electron beam intensity along a column of atoms with a\nconvergence semiangle of 23.4 mrad to simulate the condition of HAADF-STEM imaging (see Fig. S2a,\nb). Intensity peaks can be observed in the region from the top surface to a depth of 4 nm for both samples\n(Fig. S2a, b), suggesting atoms in the top 4 nm contribute the most to our collected data. Atoms in the region\nextending from 4 nm to 10 nm from the surface can make contributions, but their contributions dropped by\n50%. Contributions from atoms beyond 10 nm can be neglected. The depth of 4 nm where the intensity\nreaches the peak is comparable to the depth of field (5.9 nm) calculated by Li L. et al. Nature\nCommunications vol. 14, p.7448, 2023, where HAADF-STEM was also employed to directly derive cation\ndistributions in cation-disordered oxides. In summary, the atoms in the top 4 nm dominated the collected\ndata during HAADF-STEM. And the averaging effects are most significant in the top 4 nms. Considering\nthat the majority of CSRO domains are in the range of 1-2 nm, they can be resolved by HAADF-STEM.\nRegarding the 4D-STEM, a smaller convergence angle (3 mrad) was used. The electron channeling\neffect under such circumstances was also explored (see Fig. S2c, d). Intensity peaks appear in the regions\nfrom the top surface to a depth of 8 nm for both samples (Fig. S2c, d), indicating atoms in the top 8 nm\ncontribute the most to our collected data. Atoms in the region extending from 8 nm to 18 nm can make\ncontributions, but their contributions decreased by 60 %. Contributions from atoms below 18 nm can be\nneglected. Overall, atoms in the top 8 nm dominated the collected data during 4D-STEM and the averaging\neffects are most considerable in the top 8 nm. To explore if the CSRO induced strain can still be resolved\nwhen the signals are averaged by the atoms in a relatively larger region, 4D-STEM analysis were performed\non our MD/MC samples with a thickness of 7 nm, which is close to the dominant region of 8 nm from top\nsurface. According to our analysis, the highest strains measured are 6.1%, 4.6% and 4.4% for HEC-Zr,\nHEC-Mo and HEC-Mo annealed at 1773 K, respectively. The trend in the highest strains among different\nsamples agrees well with our experimentally measured strain trend calculated directly from 4D-STEM,\nillustrating that the strain induced by CSRO cam be resolved by 4D-STEM and the averaging effects in the\ntop 8 nm can be neglected.\nComment 3:\nNormally, ordering in alloys occurs when unlike atoms have a greater tendency to bond than like\natoms due to a negative enthalpy of mixing of the unlike atoms. On the other hand, clustering of like\natoms tends to reflect a positive enthalpy of mixing of unlike elements. Given that much of the argument\nis that like atoms (e.g., V-V and Zr-Zr) tend to cluster seems contrary to the idea of CSRO. Granted there\nare some cases where they do predict unlike atoms with greater tendency to cluster, but the premise is that\nSRO is greater in the HEC-Zr material is greater than in HEC-Mo where there is a tendency for unlike\natoms to cluster according to the MC/MD simulations. Also, I suppose one can argue that in\nmulticomponent alloys and carbides, it’s likely you’ll have atom pairs that have a tendency to order and\npairs that have a tendency to cluster.\nWe appreciate the reviewer’s comments regarding the distinction between short-range ordering (SRO)\nand short-range clustering (SRC), and we agree that there are different ways to define the local ordering.\nTo clarify our approach, we have updated the manuscript to define the CSRO as the deviation of chemical\norder from random arrangement on the same sublattice without changing the lattice structure, which\nincludes both SRO and SRC. In our work, the degree of SRO in HEC-Zr and HEC-Mo is comparable. For\nexample, in HEC-Zr, Nb-Ti and Nb-Zr are pairs with strong chemical preferences, with α equal to -0.28\nij\nand -0.17, respectively. In HEC-Mo, Nb-Ti and Ti-Mo are pairs with strong chemical preferences, with α\nij\nequal to -0.17 and -0.26, respectively. Though SRO in two samples is comparable, the SRC in HEC-Zr is\nstronger than that in HEC-Mo. Thus, it is reasonable to conclude that the degree of CSRO in HEC-Zr is\ngreater than that in HEC-Mo. We have updated our manuscript to clarify the definition of CSRO and to\ninclude this discussion of SRO and SRC.\nComment 4:\nThe radiation studies also seem somewhat flawed. Related to the first point above, it is not at all clear\nwhy the annealed HEC-Mo would behave differently and yet the authors conclude that the difference in\nvolume changes (lattice expansion) due to irradiation is clear evidence of CSRO. Since the HEC-Zr with\nthe largest purported CSRO has greater volume change, it is hard to prove that CSRO is playing a\nsignificant role in the different materials’ resistances to radiation damage.\nWe would like to clarify that the difference in volume change of HEC-Mo samples due to radiation is\nthe result of CSRO instead of being the evidence of CSRO. More specifically, we have prepared HEC-Mo\nsamples with and without CSRO, which is HEC-Mo as-synthesized and HEC-Mo annealed at 1773 K,\nrespectively. Both samples share the identical composition and structure, and the only difference is the\ndegree of CSRO. Therefore, we attribute that the difference in radiation induced volume change to the\nexistence of CSRO. However, studies on HEC-Zr suggest that the CSRO is not the sole factor that will\nimpact the radiation induced damage. As noted in our original manuscript, the specific choice of chemical\nspecies also plays a role in determining radiation resistance. Therefore, though CSRO impacts the resistance\nto radiation induced damage, it is not the full picture and we do not claim that it is."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The topic of the manuscript is relevant, and the results have the potential to be impactful. However, I believe that the main and most critical evidence supporting the claim that CSRO is a key parameter in this system is not convincingly demonstrated in the current version of the paper. I provide comments above to justify my reasoning and offer suggestions to the authors. I remain seriously concerned about the actual difference between the two processing routes aimed at achieving distinct CSRO levels. Both 1573 K and 1773 K are high temperatures, and recent publications have shown that, at such conditions, the CSRO equilibrium state can be reached extremely quickly — sometimes in less than a second. Therefore, it is unclear whether these processing routes can truly produce different CSRO levels, even with water quenching. Strong and convincing experimental evidence distinguishing the two samples is, in my opinion, crucial to support any assertive claims regarding differences in CSRO. For reference, see the TTT diagram presented in DOI: 10.1016/j.actamat.2022.118314. Furthermore, the HRTEM images remain unconvincing to me. Several classical studies have demonstrated the challenges of detecting CSRO via HRTEM and highlighted how the observed contrast may arise from various artifacts (see, for example, 10.1016/0304-3991(95)00040-8 and 10.1016/S1359-6454(98)00180-3). Therefore, I believe that, for this paper to be suitable for publication, it must include complementary evidence to validate potential differences in CSRO levels. There is a growing body of work using calorimetry, dilatometry, and electrical resistivity for such analyses. If the authors could demonstrate consistent results from one of these techniques that align with the expected trends for different CSRO levels, the claims in the paper would be much stronger and its impact significantly enhanced. The 4-D STEM and strain mapping is to my knowlegde not yet well consolidated for this end, especially due to the small domain sizes compared to much larger sample thicknesses, same idea as the classiscal papers listed above criticise HRTEM for this end. The experimental condition for CSRO is 1573 K. While it is reasonable for the authors to perform simulations at 1773 K and 300 K, it does not make sense to me to compare the latter directly with the experimental values. Why not simulate at 1573 K as well, or even at multiple temperatures, and then plot W–C as a function of temperature? The presentation of Figure 1 is also not ideal for visualizing the W–C parameters. I suggest improving its layout for better clarity.", "reviewer_2": "The authors have done an admirable job of responding to my comments. (which were essentially the same as the other referees). While I still have some questions about interpretation, my concerns about the actual results have been more than adequately addressed, so I recommend publication. There were three primary issues raised: - The thought that the higher temperature anneals had more ordering than the lower temperature ones, which made no thermodynamic sense. - The issue of the TEM averaging over regions bigger than the size of the CSRO domains. - That CSRO in HECs is not so fundamentally different than in other ceramics. The authors have addressed most of these very well. I'm overall satisfied with the response of the first two points. I would only say that - Lang describes his results as a transformation to a new structure, but it is in the end too short range to be a true new structure and is (at least in my opinion) a manifestation of CSRO and nothing more. - I don't understand why, if there is no enthalpic driving force for ordering in HECs, why would they order at all? - If the reason the atomistics and experiment disagree on the size of the domains is because of larger range lattice relaxation, why wouldn't that also be captured in the simulations? As for the last original point, about comparing CSRO in HECs and e.g. HEOs, I am still less convinced. Even if I agree that Lang's result is qualitatively different, there are literally decades of work on complex oxides such as spinels and pyrochlores showing the evolution of chemical disorder - which is a form of CSRO - in these materials under irradiation. Similarly, there are many papers that are related to inducing disorder/CSRO by other means, such as thermally and chemically. It is not so clear that there is any fundamental difference. I do agree that they are not identical, but it isn't clear that this is qualitatively different or just quantitatively different. That said, I do believe the authors have done a very heroic job in responding to the previous reviews. My thoughts above are optional for the authors to consider, perhaps as future directions. These concerns are more about interpretation than about the quality of the work, which I do think is good and has improved substantially since the last version.", "reviewer_3": "The authors have responded to the comments of the three reviewers where similar concerns were expressed, and I commend them for their efforts to clarify things. That said, I still have a few issues with the results that I would at least like to mention. I’ll leave the decision to the editor as to whether they rise to the level of requiring further revision. 1. I am still not convinced that the HAADF images represent CSRO although I am not as fluent in the literature as the authors who argue that they are convinced of the interpretation of the subtle contrast differences. 2. Except for the Mo-C system, all the binary carbides have considerable solubility ranges up to 50%C and can be rich in the metallic component. The SEM images in the supplemental section suggest that the authors might have exceeded 50% C in the Zr-HEC sample, where graphite is clearly observed, whereas that does not appear to be the case in the Mo-HEC samples, at least from the data shown. When C<50%, the variation from stoichiometry results in constitutional vacancies on the C sublattice and I wonder if there is any influence of this on the resulting CSRO and the observed irradiation effects? 3. Somewhat related to this, the GIXRD data suggest that the lattice parameters in the unirradiated Mo-HEC materials are somewhat different, i.e., the material annealed at 1773 K appears to have a smaller lattice parameter than the as-synthesized material that presumably has CSRO according to their interpretation of theresults. However, after irradiation at 300 and 600 °C, the peaks for the two Mo-HEC conditions approximately overlap. Thus, could one argue that they samples contain the same amount of damage after irradiation although the expansion is greater for the sample annealed at 1773 (without CSRO) for some reason? 4. The authors added a comment that partial melting might have occurred during synthesis. While that can’t be ruled out, it seems unlikely based on the SEM observations as it should be possible to see evidence of any incipient melting in the microstructure. The authors might want to reconsider using this explanation. 5. I guess a final note is that it’s unclear to me why the authors focused on the Mo-HEC instead of the Zr-HEC given their conclusion that the Zr-HEC has a greater tendency for CSRO. I would have thought that they would have conducted the heat treatments to influence “disordering” and to follow the irradiation damage on the Zr-HEC."}, "author_response": "Point by point response to reviewer’s comments\nReviewer #1:\nThe topic of the manuscript is relevant, and the results have the potential to be impactful. However, I\nbelieve that the main and most critical evidence supporting the claim that CSRO is a key parameter in this\nsystem is not convincingly demonstrated in the current version of the paper. I provide comments above to\njustify my reasoning and offer suggestions to the authors.\nComment 1:\nI remain seriously concerned about the actual difference between the two processing routes aimed at\nachieving distinct CSRO levels. Both 1573 K and 1773 K are high temperatures, and recent publications\nhave shown that, at such conditions, the CSRO equilibrium state can be reached extremely quickly —\nsometimes in less than a second. Therefore, it is unclear whether these processing routes can truly\nproduce different CSRO levels, even with water quenching. Strong and convincing experimental evidence\ndistinguishing the two samples is, in my opinion, crucial to support any assertive claims regarding\ndifferences in CSRO. For reference, see the TTT diagram presented in DOI:\n10.1016/j.actamat.2022.118314.\nThank you for bringing to our attention the reference [J-P. Du et al. Acta Materialia 240 (2022)\n118314], which discusses the formation of CSRO in CrCoNi. We agree that the TTT diagram serves as a\nuseful guide in using thermal treatment to adjust the level of CSRO in materials. However, the TTT diagram\nof CrCoNi cannot be applied to HECs directly due to their distinct melting temperatures (T ). More\nm\nspecifically, T of HEC-Mo is 3343 K and T of CrCoNi is 1530 K [J-P. Du et al. Acta Materialia 240\nm m\n(2022) 118314]. Even at the same temperature, 1573 K or 1773 K for example, the atomic mobility in these\ntwo systems will be significantly different. These two temperatures correspond to 0.47 T and 0.53 T in\nm m\nHEC-Mo. The same homologous temperatures in CrCoNi would correspond to 720 K and 811 K,\nrespectively. According to the TTT diagram from the above reference, the CSRO domain can reach ~15 Å\nin diameter at 811 K but can grow up to ~21 Å at 720 K. Thus, the degree of CSRO at these two conditions\nis meaningfully different. There is therefore no contradiction between our findings of varied degree of\nCSRO and the results reported by Du et al. In addition, we have carried out new DTA experiments on HEC-\n(cid:3032)(cid:3051)(cid:3043)\nMo, which suggests that the order to disorder transition temperature (𝑇 ) in this sample is ~ 1653 K (Fig.\n(cid:3031)\n2a and Fig. S3b). The fact that the transition temperature is between 1573 K and 1773 K further corroborates\nthat our thermal treatment at these two conditions can result in different degrees of CSRO in HECs.\nComment 2:\nFurthermore, the HRTEM images remain unconvincing to me. Several classical studies have\ndemonstrated the challenges of detecting CSRO via HRTEM and highlighted how the observed contrast\nmay arise from various artifacts (see, for example, 10.1016/0304-3991(95)00040-8 and 10.1016/S1359-\n6454(98)00180-3). Therefore, I believe that, for this paper to be suitable for publication, it must include\ncomplementary evidence to validate potential differences in CSRO levels. There is a growing body of work\nusing calorimetry, dilatometry, and electrical resistivity for such analyses. If the authors could demonstrate\nconsistent results from one of these techniques that align with the expected trends for different CSRO levels,\nthe claims in the paper would be much stronger and its impact significantly enhanced. The 4-D STEM and\nstrain mapping is to my knowlegde not yet well consolidated for this end, especially due to the small domain\nsizes compared to much larger sample thicknesses, same idea as the classiscal papers listed above criticise\nHRTEM for this end.\nThank you for your valuable suggestions. We agree with the reviewer that complementary\nexperiments can further strengthen our work, and we have performed differential thermal analysis (DTA)\non HEC samples. The DTA curves confirm the existence of CSRO in our HECs. More specifically, for as-\nsynthesized samples, an exothermic peak emerges near 1473 K, indicating the formation of CSRO with the\nincrease of temperature (Fig. 2a). A larger endothermic peak appears after the exothermic peak and ends at\n~1653 K (Fig. 2a), indicating the dissolution of CSRO. The fact that the CSRO dissolution peak is larger\nthan the formation peak indicates that there is pre-existing CSRO in as-synthesized HECs. However, it is\ndifficult to compare HEC-Zr to HEC-Mo in terms of the amount of pre-existing CSRO due to the different\nordering states of these materials. The order-disorder transition was also confirmed in HEC-Mo using DTA.\nMore specifically, HEC-Mo was first annealed at 1573 K where ordering is preferred (Fig. S3b). The DTA\ncurve upon heating exhibits a minimal CSRO formation peak followed by a significantly large dissolution\npeak (Fig. 2a), indicating that HEC-Mo annealed at 1573 K is ordered. HEC-Mo was further annealed at\npeak followed by a CSRO dissolution peak, which is slightly larger than the formation peak, suggesting\nthat HEC-Mo annealed at 1773 K is disordered. In summary, our DTA provides additional strong evidence\nthat CSRO exists in as-synthesized HECs and that order-disorder transition can occur in HECs with the\nchange of temperature. These results are consistent with our simulations and STEM observations. Thus,\nthey can serve as good complementary validation for our conclusion. We have included our DTA\nmeasurements in our revised manuscript.\nComment 3:\nThe experimental condition for CSRO is 1573 K. While it is reasonable for the authors to perform\nsimulations at 1773 K and 300 K, it does not make sense to me to compare the latter directly with the\nexperimental values. Why not simulate at 1573 K as well, or even at multiple temperatures, and then plot\nW–C as a function of temperature?\nThank you for your question. We have further performed MD/MC simulations on HEC-Mo at 600\nK, 900 K, 1200 K, and 1573 K to understand the temperature dependence of CSRO. The WC parameters\nof HEC-Mo at different temperatures were plotted in Fig. S3a and it is clear the degree of CSRO decreases\nwith increasing temperature. The temperature (𝑇(cid:3046)(cid:3036)(cid:3040) ) where order-to-disorder transition takes place is\n(cid:3031)\n(cid:3032)(cid:3051)(cid:3043)\nestimated to be ~900 K (Fig. S3a). This transition is lower than 𝑇 (~1653 K) measured using DTA (Fig.\n(cid:3031)\n2a and Fig. S3b). It is not uncommon for interatomic potentials to show deviations in predictions of\ntransition temperatures and therefore based on our simulations we do not claim to make quantitative\npredictions of the extent of CSRO. We use the potential to predict the presence of CSRO and to show that\nCSRO decreases with increasing temperature. For this reason, we chose two simulations temperatures –\none below and one above 𝑇(cid:3046)(cid:3036)(cid:3040).\n(cid:3031)\nAlthough the reviewer did not ask this question, there is also a good reason why we did not perform\nannealing experiments at 300K, which would match the lower temperature used in simulations. The reason\nis that the kinetic temperature in experiments (based on DTA) is ~1473 K (see Fig. 2a, Fig. S3b), which\nmeans that below this temperature kinetics in the system is frozen and we would not be able to observe\nordering on the time scales of the experiments.\nThe temperature of 1773K is above both 𝑇(cid:3046)(cid:3036)(cid:3040) and 𝑇 (cid:3032)(cid:3051)(cid:3043) and therefore we were able to use this\n(cid:3031) (cid:3031)\ntemperature in both simulations and experiments to achieve a fully disordered state.\nIn summary, because of the kinetic limitation in experiments and the mismatch in the order-disorder\ntransition temperature between simulations and experiments, we chose different temperatures for\nsimulations and experiments in the low-temperature regime to provide evidence and understanding of\nCSRO in HECs. We have included this discussion in our supplementary information.\nComment 4:\nThe presentation of Figure 1 is also not ideal for visualizing the W–C parameters. I suggest\nimproving its layout for better clarity\nThank you for your suggestion. We have updated our Fig. 1 to only reflect the WC parameters of\nthe 1st NN in both random systems and in our MD/MC simulated systems. The WC parameters of the 2nd\nand 3rd NN in our MD/MC simulated systems are moved to Fig. S2 for clarity.\nReviewer #2:\nThe authors have done an admirable job of responding to my comments. (which were essentially the\nsame as the other referees). While I still have some questions about interpretation, my concerns about the\nactual results have been more than adequately addressed, so I recommend publication.\nThere were three primary issues raised:\n- The thought that the higher temperature anneals had more ordering than the lower temperature ones,\nwhich made no thermodynamic sense.\n- The issue of the TEM averaging over regions bigger than the size of the CSRO domains.\n- That CSRO in HECs is not so fundamentally different than in other ceramics.\nThe authors have addressed most of these very well. I'm overall satisfied with the response of the first two\npoints. I would only say that\n- Lang describes his results as a transformation to a new structure, but it is in the end too short range to be\na true new structure and is (at least in my opinion) a manifestation of CSRO and nothing more.\n- I don't understand why, if there is no enthalpic driving force for ordering in HECs, why would they order at all?\nThank you for your question. In fact, there is enthalpic driving force for ordering in HECs, which\nis the formation enthalpy. More specifically, using the method described in our previous work [M. W.\nQureshi et al Materials Advances 6 (2025) 5286-5294], the formation enthalpies of HEC-Zr and HEC-Mo\nare 68.78 meV/atom and 48.93 meV/atom, respectively. Thus, these two HECs are stabilized by entropy\nand the driving force for ordering is the formation enthalpy. We have included this information in our\nrevised manuscript.\n- If the reason the atomistics and experiment disagree on the size of the domains is because of larger\nrange lattice relaxation, why wouldn't that also be captured in the simulations?\nThank you for your comments. In fact, there may exist multiple reasons for the discrepancy between\nthe domain size of atomic simulations and the experiments, including the difference in the predicted order-\ndisorder transition temperature. We agree that these reasons are speculations, and we made it clear in the\nrevised manuscript.\nAs for the last original point, about comparing CSRO in HECs and e.g. HEOs, I am still less\nconvinced. Even if I agree that Lang's result is qualitatively different, there are literally decades of work\non complex oxides such as spinels and pyrochlores showing the evolution of chemical disorder - which is\na form of CSRO - in these materials under irradiation. Similarly, there are many papers that are related to\ninducing disorder/CSRO by other means, such as thermally and chemically. It is not so clear that there is\nany fundamental difference. I do agree that they are not identical, but it isn't clear that this is qualitatively\ndifferent or just quantitatively different.\nThat said, I do believe the authors have done a very heroic job in responding to the previous reviews.\nMy thoughts above are optional for the authors to consider, perhaps as future directions. These concerns\nare more about interpretation than about the quality of the work, which I do think is good and has improved\nsubstantially since the last version.\nThank you for your comments. We agree that there are multiple works discussing the ordering in\ncomplex oxides. However, HECs have very different bonding nature when compared to oxides, which is\nexpected to result in unique defect kinetics and unique impact of CSRO on such kinetics. In fact, we have\nalready performed atomistic simulations that reveal these effects. However, discussing details of defect\nkinetics in HECs is beyond the scope of the current paper, which is focused on the discovery and evidence\nfor CSRO. Atomistic details of defect kinetics will be discussed in a separate paper.\nReviewer #3:\nThe authors have responded to the comments of the three reviewers where similar concerns were\nexpressed, and I commend them for their efforts to clarify things. That said, I still have a few issues with\nthe results that I would at least like to mention. I’ll leave the decision to the editor as to whether they rise\nto the level of requiring further revision.\nComment 1:\nI am still not convinced that the HAADF images represent CSRO although I am not as fluent in the\nliterature as the authors who argue that they are convinced of the interpretation of the subtle contrast\ndifferences.\nThank you for your comments, as suggested by reviewer #1, we have performed DTA on HECs\nand they show consistent results with our simulations and STEM observation. These results further proved\nthe reliability of our STEM observations.\nComment 2:\nExcept for the Mo-C system, all the binary carbides have considerable solubility ranges up to 50%C\nand can be rich in the metallic component. The SEM images in the supplemental section suggest that the\nauthors might have exceeded 50% C in the Zr-HEC sample, where graphite is clearly observed, whereas\nthat does not appear to be the case in the Mo-HEC samples, at least from the data shown. When C<50%,\nthe variation from stoichiometry results in constitutional vacancies on the C sublattice and I wonder if\nthere is any influence of this on the resulting CSRO and the observed irradiation effects?\nThank you for your comments. The reviewer is correct that HEC samples in this work are enriched\nin carbon. However, the effect of carbon enrichment on CSRO and observed irradiation resistance is\nminimal.\nFirst, we want to clarify that there is no observable graphite in our simples. There are some black\nregions in the image of HEC-Zr. However, we have imaged these black regions using backscattered electron\nimaging and found that they are porosities rather than graphite particles (Fig. 1 in response letter). There\nmay existing some graphite since our samples are C-rich, but their size and amount are much smaller than\nexpected by the reviewer, as evidenced by no graphite peaks in XRD measurements (Fig. S11a).\nSecond, porosities have no impact on CSRO but can affect the radiation effects. For example,\nporosities can serve as defect sinks and accelerate the defect recovery in materials. In other words, porosities\nin HEC-Zr can suppress the defects accumulation and thus the lattice expansion. Considering that the HEC-\nZr has more lattice expansion when compared to HEC-Mo even with more porosities, the effect of porosities\nin HEC-Zr on the radiation effect will not change our qualitative conclusion.\nThird, when discussing the effect of CSRO on radiation resistance, we focus on HEC-Mo with and\nwithout CSRO because the samples share the same chemistry and differ only in the degree of CSRO. Thus,\nthe effect of CSRO on radiation resistance discussed in our manuscript is not affected by C stoichiometry.\nWe have also performed XPS measurements on HEC-Zr and HEC-Mo after Ar plasma cleaning for 100 s\nand the compositions are listed in Table S1. Based on our XPS measurements, the C concentration in HEC-\nZr is 56.72 at.% and the C concentration in HEC-Mo is 52.60 at.%, suggesting both HECs are C-rich.\nThat means that the concentration of C vacancies in both samples is negligible. Regarding the effect of carbon\noff-stoichiometries on defect accumulation in carbides, previous study [Y. Yang et al. Journal of Nuclear\nMaterials 454 (2014) 130-135] does suggest that the existence of graphite can serve as a strong source of\nknock-on carbon interstitials into carbides and lead to larger dislocation loops. However, our simulations\nsuggested that the C interstitials in HECs share comparable migration energies (3.56 eV for HEC-Zr and\n3.86 eV for HEC-Mo) and are immobile at the irradiation temperature. Thus, if graphite is present in these\nsamples and introduces some C interstitials into HECs, these interstitials cannot migrate and coalesce to\nlarger dislocation loops and the impact on lattice expansion is minimal.\nIn summary, the stoichiometry in HECs has minimal effect on CSRO and radiation resistance.\nFigure 1: Backscattered electron imaging of HEC-Zr. (a) HEC-Zr sample with multiple pores. (b) Image\nof a pore within marked region in (a).\nComment 3:\nSomewhat related to this, the GIXRD data suggest that the lattice parameters in the unirradiated Mo-\nHEC materials are somewhat different, i.e., the material annealed at 1773 K appears to have a smaller\nlattice parameter than the as-synthesized material that presumably has CSRO according to their\ninterpretation of the results. However, after irradiation at 300 and 600 °C, the peaks for the two Mo-HEC\nconditions approximately overlap. Thus, could one argue that they samples contain the same amount of\ndamage after irradiation although the expansion is greater for the sample annealed at 1773\n(without CSRO) for some reason?\nThank you for your question. The reason for using the change in the lattice parameter instead of using\nthe lattice parameter itself is that the accumulated defects in sample can lead to lattice expansion. More\nspecifically, when defects accumulate in the material after irradiation, a strain field is introduced by the\ndefects, which can distort the original lattice. A large lattice parameter in itself is not better or worse than a\nsmall lattice parameter, but the change in the lattice parameter (compared to the original sample) is\nundesirable and this change is caused by accumulation of defects (i.e., radiation damage). Lattice expansion\n(strain) is commonly used to evaluate radiation damage.\nComment 4:\nThe authors added a comment that partial melting might have occurred during synthesis. While that\ncan’t be ruled out, it seems unlikely based on the SEM observations as it should be possible to see\nevidence of any incipient melting in the microstructure. The authors might want to reconsider using this\nexplanation.\nThank you for your comments. We agree with the reviewer that no features of incipient melting can\nbe observed in the original Fig. S9. We have now included the SEM observation of incipient melting in\nHEC-Mo as an example (Fig. S11c in the revised supplementary information). We find that there are several\nexamples of the formation of pockets at grain boundary junctions that are characteristic of the presence of\nmolten zones as marked by arrows (Fig. S11c). We have included this discussion in our revised manuscript.\nComment 5:\nI guess a final note is that it’s unclear to me why the authors focused on the Mo-HEC instead of the\nZr-HEC given their conclusion that the Zr-HEC has a greater tendency for CSRO. I would have thought\nthat they would have conducted the heat treatments to influence “disordering” and to follow the\nirradiation damage on the Zr-HEC.\nThank you for your comments. We didn’t perform annealing on HEC-Zr sample as well as the\nfollowing irradiation because this work is a fundamental study and we are just selecting the HEC-Mo as a\nrepresentative. Thermal annealing on HEC-Zr and the following irradiation is beyond the scope of this\nwork."}, {"round": 3, "reviewer_comments": {"reviewer_1": "After carefully re-evaluating the manuscript and the supporting information, I have two remaining points: First, the central narrative of the paper relies heavily on the claim that the authors have two distinct experimental states for the Mo-containing carbide: one with CSRO and one without CSRO. This distinction is essential for their interpretation of the radiation-damage results as well as for the broader implications they draw about tunability of CSRO. However, the manuscript does not present any experimental evidence that actually confirms the existence of a “zero-CSRO” state. All experimental studies I am aware of report that increasing temperature reduces CSRO but does not eliminate it entirely; in practice, full randomization is extremely difficult to achieve (if not impossible). Furthermore, there are also studies that show that even a very rapid cooling cannot avoid the CSRO formation during cooling at high temperatures. In the present manuscript, the calorimetry data seems to demonstrate that one processing condition has more CSRO than the other. This is not the same as demonstrating that the higher-temperature condition has no CSRO. On the contrary, based on the literature and on the authors’ own data, I would expect measurable (though reduced) CSRO to remain. Quantifying this difference may indeed be challenging, and I agree that a qualitative comparison is still valuable, but presenting the lower-CSRO state as “fully disordered” is not supported by the data as written. Second, regarding Figure S7, I do not see the evidence the authors claim to be present. If I understand the intention correctly, the authors are arguing that adding CSRO increases the diffuse background intensity in the CBED pattern, and that this increase can be used as an indicator of CSRO. However, many other factors produce the same effect, including specimen thickness, temperature and local crystal distortions unrelated to chemical order. CSRO is typically identified through specific diffuse-scattering features—extra maxima at particular reciprocal-space positions that correlate with ordering vectors—not via a general increase in background. Even the use of diffuse scattering for CSRO identification is non-trivial, as several papers have pointed out challenges in distinguishing CSRO-related diffuse features from other intrinsic and extrinsic contributions. Given these considerations, I do not find that Figure S7 meaningfully supports the manuscript’s claims. The figure does not provide clear or interpretable evidence of CSRO, and, as currently presented, does not advance the narrative.", "reviewer_3": "I have reviewed the revised paper on high entropy carbides and feel that the authors have adequately addressed my concerns, which were similar to the concerns of the other reviewers. However, their modifications A few minor comments: 1. The authors incorrectly refer to an order-disorder transition in their discussion of their thermal analysis data. The classic description of order-disorder transitions involves going from a fully disordered phase to a fully long-range ordered phase either by a first-order or a second-order transition. In the HEC materials, the structure is already ordered but with the possibility that the atoms on the cation sites are not completely random and undergo CSRO. Thus, the authors should modify their description accordingly, i.e., they should refrain from referring to their CSRO structure as resulting from an ordering transition given the structure does not change crystal structure. 2. The authors refer to Fig. S11c in the text to represent partial (incipient) melting – it should be Fig. S12c."}, "author_response": "Point by point response to reviewer’s comments\nReviewer #1:\nAfter carefully re-evaluating the manuscript and the supporting information, I have two remaining\npoints:\nComment 1:\nFirst, the central narrative of the paper relies heavily on the claim that the authors have two distinct\nexperimental states for the Mo-containing carbide: one with CSRO and one without CSRO. This\ndistinction is essential for their interpretation of the radiation-damage results as well as for the broader\nimplications they draw about tunability of CSRO. However, the manuscript does not present any\nexperimental evidence that actually confirms the existence of a “zero-CSRO” state. All experimental\nstudies I am aware of report that increasing temperature reduces CSRO but does not eliminate it entirely;\nin practice, full randomization is extremely difficult to achieve (if not impossible). Furthermore, there are\nalso studies that show that even a very rapid cooling cannot avoid the CSRO formation during cooling at\nhigh temperatures. In the present manuscript, the calorimetry data seems to demonstrate that one\nprocessing condition has more CSRO than the other. This is not the same as demonstrating that the\nhigher-temperature condition has no CSRO. On the contrary, based on the literature and on the authors’\nown data, I would expect measurable (though reduced) CSRO to remain. Quantifying this difference may\nindeed be challenging, and I agree that a qualitative comparison is still valuable, but presenting the lower-\nCSRO state as “fully disordered” is not supported by the data as written.\nThank you for pointing this out. We agree with the reviewer that it is very difficult or even impossible\nto reach a fully disordered state. Though it is impossible to eliminate CSRO from HECs entirely and it is\ndifficult to quantify the difference in the extent CSRO between as-synthesized HEC-Mo and HEC-Mo\nannealed at 1773 K, qualitatively, our data provides strong evidence that CSRO has been significantly\ndiminished in HEC-Mo annealed at 1773 K. Thus, our claims regarding the role of CSRO (e.g., that CSRO\ncan suppress radiation-induced damage in HECs) remain robust. We have modified our manuscript to refer\nHEC-Mo annealed at 1773 K as HEC-Mo with low CSRO and as-synthesized HEC-Mo or HEC-Mo\nannealed at 1573 K as HEC-Mo with high CSRO.\nComment 2:\nSecond, regarding Figure S7, I do not see the evidence the authors claim to be present. If I understand\nthe intention correctly, the authors are arguing that adding CSRO increases the diffuse background\nintensity in the CBED pattern, and that this increase can be used as an indicator of CSRO. However,\nmany other factors produce the same effect, including specimen thickness, temperature and local crystal\ndistortions unrelated to chemical order. CSRO is typically identified through specific diffuse-scattering\nfeatures—extra maxima at particular reciprocal-space positions that correlate with ordering vectors—not\nvia a general increase in background. Even the use of diffuse scattering for CSRO identification is non-\ntrivial, as several papers have pointed out challenges in distinguishing CSRO-related diffuse features from\nother intrinsic and extrinsic contributions. Given these considerations, I do not find that Figure S7\nmeaningfully supports the manuscript’s claims. The figure does not provide clear or interpretable\nevidence of CSRO, and, as currently presented, does not advance the narrative.\nThank you for your comments. We agree with the reviewer that many factors can produce the same\ndiffuse scattering effects as what we have observed in Fig. S7, though we have tried our best to control\nsuch factors, including sample thickness. Given that this figure is not essential to support our conclusions,\nwe have removed it from our revised Supplementary information and no longer refer to it in our revised\nmain manuscript.\nReviewer #3:\nI have reviewed the revised paper on high entropy carbides and feel that the authors have adequately\naddressed my concerns, which were similar to the concerns of the other reviewers. However, their\nmodifications A few minor comments:\nComment 1:\nThe authors incorrectly refer to an order-disorder transition in their discussion of their thermal analysis\ndata. The classic description of order-disorder transitions involves going from a fully disordered phase to\na fully long-range ordered phase either by a first-order or a second-order transition. In the HEC materials,\nthe structure is already ordered but with the possibility that the atoms on the cation sites are not\ncompletely random and undergo CSRO. Thus, the authors should modify their description accordingly,\ni.e., they should refrain from referring to their CSRO structure as resulting from an ordering transition\ngiven the structure does not change crystal structure.\nThank you for bringing our attention to this point. We agree with the reviewer that referring to the\ndissolution of CSRO as order-to-disorder transition can be confusing or inaccurate because it does not\ninvolve changes in the structural order. We have modified our manuscript and supplementary information\naccordingly. Instead, the process is referred to as reduction of CSRO with the increase of temperature.\nComment 2:\nThe authors refer to Fig. S11c in the text to represent partial (incipient) melting – it should be Fig.\nS12c.\nThank you for your comments. We have read through our manuscript to correct typos and\nmistakenly referred images."}, {"round": 4, "reviewer_comments": {"reviewer_1": "The authors have address my comments adequately."}, "author_response": ""}]

Decision letter