{"id":"7eedd8ba-774f-4cd9-a822-8a6b3a84ab76","arxiv_id":"2607.18099","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In (MoCrTi)100−xAlx, B2-type chemical ordering proceeds through one or two stage-separated transitions depending on Al content, and ordering shifts the elastic stiffness peak to the Mo30Cr30Ti30Al10 composition.","lead":"This paper simulates four Mo-Cr-Ti-Al refractory alloys with a machine-learned interatomic potential and finds that chemical ordering happens in composition-dependent stages as temperature rises. It shows that ordering can make alloy stiffness peak at an intermediate aluminum content instead of following the simple monotonic trend — a potential design lever for high-temperature alloys.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed Mo/Al–Cr/Ti low-T sublattice conflicts with the paper's own 0 K DFT ground state; MC may be trapped in a metastable ordered state, so the Al10 stiffness peak is not yet established.","rationale":"The reader's formal weakest assumption was uMLIP fidelity and fixed-lattice sampling, which is reasonable, but the most load-bearing and checkable soft spot is internal: the manuscript's own 0 K DFT/uMLIP calculations identify (Mo,Ti)/(Cr,Al) as the ground state, while the MC at 200 K is interpreted as favoring (Mo,Al)/(Cr,Ti). The paper's thermal-energy argument does not quantitatively resolve this because a 0.005 eV/at enthalpy difference is not negligible relative to kBT at 200 K when degeneracies are comparable. If the MC is trapped in a metastable state, then the claimed low-temperature sublattice, the staged transition assignments, and especially the Al10 stiffness peak are all built on the wrong equilibrium structure. This is exactly the kind of concern that can be settled by a seed-dependence and free-energy test. I selected UNCHANGED because the reader already assigned CONDITIONAL; this concern sharpens the condition rather than escalating the verdict to REJECT. The paper is otherwise clearly written, the DFT benchmark in Fig. 7 is a useful internal check, and the qualitative experimental agreement on peak shifts gives some independent support; however, the sublattice inconsistency must be resolved before the central claims can be accepted.","tokens_in":14517,"tokens_out":8184,"duration_ms":75467,"concrete_test":"Run the same hybrid MC/MD protocol at 200 K for Al25 starting from three seeds: (Mo,Al)/(Cr,Ti) B2, (Mo,Ti)/(Cr,Al) B2, and the SQS used in the paper, with at least 4×10^6 MC steps per seed. Compare the final energies and sublattice order parameters. If the (Mo,Ti)/(Cr,Al) seed remains lower in energy while the SQS trajectory ends in (Mo,Al)/(Cr,Ti), the reported ordered state is metastable. Then recompute the Al10 elastic constants in Fig. 8 starting from the stable (Mo,Ti)/(Cr,Al) ordered state; if the non-monotonic stiffness peak disappears, the central mechanical claim is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.3 reports that the DFT and uMLIP 0 K ground state is (Mo,Ti) on one sublattice and (Cr,Al) on the other, with the (Mo,Al)/(Cr,Ti) configuration only 0.005 eV/at higher. Yet Section 3.2 and the conclusions assert that MC at 200 K favors (Mo,Al)/(Cr,Ti), and Fig. 8 uses those 200 K configurations to claim a non-monotonic stiffness peak at Al10. The paper's attempted reconciliation—that kBT vastly exceeds the 0.005 eV/at difference—is not quantitative: at 200 K, kBT ≈ 0.017 eV/at, only ~3× the splitting, giving a Boltzmann factor exp(−0.005/0.017) ≈ 0.75 for equal degeneracies, not a population inversion. At 600 K the factor is ~0.91. To overturn the 0 K ground state, the (Mo,Al)/(Cr,Ti) state would need a substantially larger configurational/vibrational entropy, but no such free-energy calculation is provided. With only 2,000,000 MC swap attempts on a fixed 200-atom lattice, the simulation may be kinetically trapped in the metastable (Mo,Al) ordering, especially since the two B2 variants are separated by an order-disorder barrier. Because the central stiffness enhancement and pair-stiffness explanation are computed from the 200 K snapshots, an incorrect sublattice assignment would directly invalidate the Al10 peak and the proposed SRO-mechanical coupling. This is an internal inconsistency, not an outside-consensus dispute, and it is resolvable by explicit free-energy and seed-dependence checks.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript uses the GRACE-1L-OAM universal machine-learning interatomic potential in hybrid Monte Carlo/molecular dynamics simulations to study configurational ordering in four (MoCrTi)_{100-x}Al_x alloys (x = 25, 16, 10, 4 at.%). It computes constant-volume heat capacities, Warren–Cowley short-range order parameters, and elastic constants/moduli. The authors report composition-dependent order–disorder behavior: a single transition for Al25 and Al4, two-stage transitions for Al16 and Al10 (triggered by Mo–Al and Al–Al pairs, respectively), and a low-temperature B2-like state with Mo and Al on one sublattice and Cr and Ti on the other. They further report that this ordering enhances stiffness and produces a nonmonotonic compositional trend peaking at Al10, interpreted through a pair-stiffness analysis.","tokens_in":14856,"tokens_out":9006,"duration_ms":101302,"significance":"If the findings hold, they would provide a useful atomistic explanation of how Al content controls order–disorder pathways and how chemical short-range order can be exploited to tune elastic properties in refractory high-entropy alloys. The paper has clear strengths: independent DFT benchmarks for three B2 configurations (energy differences within about 0.035 eV/at), comparison with experimental DSC peak shifts, use of a modern universal MLIP, and a transparent pair-stiffness framework. However, the reliability of the main conclusions is currently limited by the unvalidated finite-temperature configurational sampling and by an apparent inconsistency between the 0 K B2 ground state and the 200 K MC sublattice assignment.","major_comments":[{"comment":"The low-temperature sublattice assignment is not established. The 0 K DFT/uMLIP ground state is (Mo,Ti)_(Cr,Al), whereas the (Mo,Al)_(Cr,Ti) variant used in the low-temperature analysis is higher by only 0.005 eV/at. The text argues that thermal energy vastly exceeds this splitting at 300 K and above, but the ordered state used for Fig. 8 is generated at 200 K, where k_B T ≈ 0.017 eV/at is only about 3.4× the splitting, and the Boltzmann factor for equal degeneracies is about 0.75. This does not yield the (Mo,Al) variant as the thermodynamically preferred state, and the SQS-initialized 2,000,000-swap runs may be kinetically trapped. Because the Al10 stiffness peak is computed from these 200 K snapshots, an incorrect sublattice assignment would invalidate the central mechanical claim. Please compute finite-temperature free energies of the two B2 variants and test initialization/seed depen","section":"§3.3 vs §3.2/3.4"},{"comment":"The quantitative results have no statistical error bars. Each composition/temperature point is a single MC run; C_V is obtained from energy fluctuations in the second half of one trajectory, and elastic constants are averages over 'the last six equilibrated MC snapshots' without run-to-run scatter. The staged-peak interpretation and the Al10 anomaly in Fig. 8 rely on differences in peak shapes and positions that could be affected by insufficient equilibration. Please perform multiple independent simulations (different random seeds/SQS) and report standard errors or confidence intervals for C_V, SRO parameters, and elastic constants; also address the fixed-lattice constraint, which the authors note is important for HEA properties.","section":"§2.1, §3.1, §3.4"},{"comment":"The uMLIP is benchmarked only against three 4-atom B2 configurations at 0 K, but the main claims require accurate relative free energies over 200–2000 K for a much larger configuration space. The authors themselves note that the training data are predominantly 0 K relaxations and lower-order compounds and that fixed-lattice MC excludes local distortions. With ordering-energy differences as small as 0.005 eV/at, this is a real accuracy risk. I request additional DFT validation on representative SQS or partially ordered configurations at the studied compositions, or a quantitative sensitivity analysis. Without it, the pair-level staging (Mo–Al in Al16, Al–Al in Al10) remains a model-specific prediction.","section":"§2.2/§3.1"}],"minor_comments":[{"comment":"Please clarify the counting convention for like-atom pairs. The text states that in a random solution α = 0, yet the high-temperature asymptote for like-atom pairs in Fig. 5 appears to be about 0.5; define N_i^ξη explicitly (directed vs. undirected pairs) and state the random baseline used.","section":"Eq. (2)/Fig. 5"},{"comment":"The statement that 'the local Al/(Mo+Cr) ratio significantly exceeds the nominal macroscopic ratio when Ti is excluded' is vague; please give the numerical comparison for the four compositions.","section":"§3.2"},{"comment":"The x-axis label is 'Bond Length (Å)', but the curves are for BCC two-atom cells; please clarify that this is the nearest-neighbor distance and specify whether the cell shape was fixed.","section":"Fig. 9(a)"},{"comment":"Reference [20] appears to be an in-press citation without complete volume/page details; please update before publication.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"Editor: This is a competent and readable study with a plausible qualitative story, but the central low-temperature result is not yet backed by sufficient sampling or free-energy evidence. The discrepancy between the 0 K DFT ground state and the 200 K MC state is the main technical risk; if additional simulations confirm the MC sublattice assignment and provide error bars, the paper would be suitable. I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nThe short version: this is a study worth engaging seriously, but the referee should be told to look hard at the low-temperature sublattice assignment, because the paper's own 0 K DFT data point the other way.\n\nWhat's new is real: the staging of the order-disorder transition into one vs. two events, the pair-level attribution (Mo–Al in Al16, Al–Al in Al10), and the non-monotonic stiffness peak at Al10 in the ordered state. The DFT cross-checks on three B2 configurations are a good idea, and the uMLIP agreement within ~0.035 eV/at gives the potential some credibility. The qualitative match to the experimental DSC trend is also a point in its favor. The authors are honest about the uMLIP's limited high-temperature HEA training data and the fixed-lattice approximation—those are real limitations, but they state them plainly.\n\nThe soft spot is load-bearing. Section 3.3 reports that the 0 K ground state is (Mo,Ti)/(Cr,Al), with (Mo,Al)/(Cr,Ti) only 0.005 eV/at higher. The 200 K MC runs nevertheless favor (Mo,Al)/(Cr,Ti), and Fig. 8 uses those configurations to claim the Al10 peak. The paper's attempted reconciliation—that kBT swamps 0.005 eV/at—doesn't hold up. At 200 K, kBT ≈ 0.017 eV/at, only about 3× the splitting, which gives a Boltzmann factor around 0.75 for equal degeneracies, not a population inversion. Without a free-energy calculation that includes vibrational or configurational entropy, the 0 K ground state should win or at least compete. The more plausible explanation is that the fixed-lattice Metropolis exchange is trapped in a metastable ordered variant separated by an order-disorder barrier. Since the stiffness peak and the pair-stiffness rationalization are computed from those 200 K snapshots, an incorrect sublattice assignment would invalidate the central mechanical claim.\n\nOther issues are more standard: single MC run per composition/temperature, no error bars, no released data or scripts. Those are minor-to-moderate and resolvable.\n\nBottom line: I don't trust the Al10 peak as established, but the qualitative staging picture and the questions the paper asks are worth pursuing. A revision with repeat runs from different initial configurations, seed ensembles, and explicit free-energy estimates (e.g., thermodynamic integration or histogram reweighting) could settle the sublattice question. Send it to peer review, but point the referee at that specific contradiction.","headline":"A clearly written, genuinely useful computational study of ordering in (MoCrTi)100−xAlx, but the low-temperature sublattice assignment conflicts with the paper's own 0 K DFT ground state, and the headline stiffness peak rests on that assignment.","tokens_in":15390,"tokens_out":2874,"would_cite":false,"duration_ms":362234,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["81.30.Bx","62.20.de","71.15.Mb"],"model":"deepseek-v4-flash","headline":"Chemical ordering in (MoCrTi)100−xAlx refractory high-entropy alloys is composition-dependent and staged, with a low-temperature B2 structure in which Mo and Al share one sublattice and Cr and Ti share the other; ordering stiffens the alloy","keywords":["refractory high-entropy alloys","short-range order","B2 ordering","machine learning interatomic potential","Monte Carlo simulation","heat capacity","elastic moduli","MoCrTiAl"],"falsifier":"Measure the heat capacity of Mo30Cr30Ti30Al10 by differential scanning calorimetry: if no low-temperature peak near 400 K appears, or if it appears with a different magnitude, the staged Al–Al transition is not reproducible. Alternatively, repeat the Monte Carlo with a DFT-validated cluster expansion or with vibrational relaxation and check whether the two-step peaks and the Al10 stiffness peak survive.","tokens_in":14381,"feed_emoji":"⚙️","tokens_out":4062,"duration_ms":44243,"temperature":0.7,"pith_summary":"The paper tries to show that the order–disorder transition in (MoCrTi)100−xAlx is not a single all-or-nothing event but a composition-tunable sequence of pair-specific rearrangements. Using a universal machine-learning interatomic potential with hybrid Monte Carlo/molecular dynamics, it finds that Al25 and Al4 alloys disorder in one cooperative step, while Al16 and Al10 disorder in two steps triggered by different atomic pairs. It further claims that this short-range order is mechanically significant: ordered configurations are stiffer than random ones, and the compositional stiffness trend is non-monotonic, peaking at the Al10 composition. The significance is that short-range order, not just composition, could be a design lever for refractory high-entropy alloy properties.","feed_headline":"Chemical order makes MoCrTiAl stiffness peak at 10% Al","feed_subtitle":"Short-range order flips the usual stiffness trend, pushing the maximum to the Al10 composition.","key_machinery":"The argument rests on three linked tools: a universal machine-learning interatomic potential supplying energies for hybrid Metropolis Monte Carlo/molecular dynamics simulations; Warren-Cowley short-range order parameters plus heat capacity from energy fluctuations, which locate transitions and identify the driving pairs; and a pair-stiffness decomposition (harmonic curvature of bond energy curves) connecting SRO-induced pair populations to elastic moduli. The pair-stiffness analysis is the explanatory bridge: Mo–Mo bonds are stiffest, Al–Al bonds softest, and the ordered Al10 configuration maximizes the weighted stiffness contribution.","core_discovery":"The central claim is that configurational ordering in (MoCrTi)100−xAlx is element-pair-specific. At low temperature the alloy develops a pseudo-binary B2 structure with Mo and Al on one sublattice and Cr and Ti on the other. The heat-capacity peaks and Warren-Cowley short-range order parameters show that Al25 and Al4 have a single cooperative disordering transition, whereas Al16 and Al10 have two separate transitions: Mo–Al ordering triggers the low-temperature step in Al16, and Al–Al correlations trigger it in Al10, with the remaining pairs disordering at higher temperature. The same ordering changes the stiffness: random solid solutions follow the rule of mixtures, increasing stiffness as","pith_inferences":["If pair populations control stiffness, thermal history—annealing to develop short-range order—should be a practical processing knob for hardness and creep resistance in the Al10 composition window, extending the paper's static results.","The two-step transition pattern suggests possible metastable intermediate states; quenching from just above the low-temperature step might freeze a partially ordered structure with a different mechanical response, a testable prediction not explored in the paper.","The potential's known limitations imply that quantitative transition temperatures and peak magnitudes could shift with a more accurate potential or with vibrational relaxation, but the qualitative staging claim is the part most worth testing.","The pair-stiffness descriptor could be used predictively on neighboring refractory systems with different elements, screening for compositions where SRO maximizes stiffness, though that would require new simulations."],"forward_implications":["If the picture is right, the order–disorder transition temperature and even its single- versus two-step character can be tuned by Al content, so composition selection controls the type of ordering kinetics.","Ordered states are stiffer than disordered states of the same composition, with elastic constants and moduli enhanced by roughly 17–68% depending on composition, largest at Al10.","The low-temperature ordered phase has a specific sublattice occupancy—Mo and Al together, Cr and Ti together—that gives a concrete signature for experimental identification of B2 precipitates.","Because random solid solutions follow the rule of mixtures while ordered ones do not, mechanical trends measured on partially ordered samples cannot be compared to simple composition averages.","Pair-specific SRO parameters provide atomistic handles: Mo–Al in Al16 and Al–Al in Al10 dominate the low-temperature ordering, offering direct signatures for experimental scattering probes."],"fun_headline_variants":["Ordering flips stiffness trend in MoCrTiAl alloys, peak at Al10","Two-step disordering in MoCrTiAl: Mo-Al and Al-Al pairs act first","Mo-Al and Al-Al order separately, causing two transitions in MoCrTiAl","Chemical order makes MoCrTiAl stiffness peak at Al10, not Al4","Sublattice pairing in MoCrTiAl drives dual order transitions and stiff peak"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The results assume the machine-learned potential, trained mostly on 0 K DFT data, gives the correct relative free energies of configurational states at 200–2000 K, and that fixing the lattice in Monte Carlo does not change the ordering sequence.","fun_headline_variants_meta":{"raw":{"variants":["Ordering flips stiffness trend in MoCrTiAl alloys, peak at Al10","Two-step disordering in MoCrTiAl: Mo-Al and Al-Al pairs act first","Mo-Al and Al-Al order separately, causing two transitions in MoCrTiAl","Chemical order makes MoCrTiAl stiffness peak at Al10, not Al4","Sublattice pairing in MoCrTiAl drives dual order transitions and stiff peak"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000368,"raw_usage":{"total_tokens":1877,"prompt_tokens":878,"completion_tokens":999,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":622,"completion_tokens_details":{"reasoning_tokens":890}},"tokens_in":622,"tokens_out":999,"duration_ms":8234,"temperature":1.0,"reasoning_tokens":890,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T15:59:45.797906+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the heat capacity of Mo30Cr30Ti30Al10 by differential scanning calorimetry: if no low-temperature peak near 400 K appears, or if it appears with a different magnitude, the staged Al–Al transition is not reproducible. Alternatively, repeat the Monte Carlo with a DFT-validated cluster expansion or with vibrational relaxation and check whether the two-step peaks and the Al10 stiffness peak survive.","supporting_citations":[],"review_version":1}