{"id":"eccd4e95-8917-4bab-9fcb-4d0cb5fd9417","arxiv_id":"2607.17370","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"An optimized interfacial-diffusivity calibration lets phase-field simulations reproduce prescribed trapping and drag response functions, and predicts that increasing solute drag shifts rapid solidification from dendrites to bands.","lead":"This paper calibrates an alloy phase-field simulation so its diffuse interface reproduces user-specified velocity-dependent solute trapping and drag response functions, then shows in dilute Al–Cu that stronger drag turns dendritic growth into banded growth. The practical payoff is a route to inject atomistic or experimental interface kinetics into computationally tractable mesoscale simulations of rapid solidification, as occurs in additive manufacturing and welding.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Calibration's liquid-side concentration is defined as the solute peak (Eq. 57); if this peak is not the sharp-interface liquid concentration, the matched responses and drag-morphology trend are convention artifacts.","rationale":"The reader's weakest assumption identifies exactly the same load-bearing concern: the peak-based extraction of c_l^i in Eq. (57) is unvalidated against sharp-interface definitions, and the fixed-tanh approximation is checked only in a way that does not test this. This is the most fundamental issue because both the calibrated response functions and the 2D morphology trend depend on this convention. If the peak is not the physical liquid concentration, the optimization may be matching an artificial diagnostic, and the central claim that prescribed drag responses control morphology selection would be undermined. I do not see an internally inconsistent derivation or a more serious confound; the q-shape versus response-function ambiguity in 2D is real but secondary to the extraction question. The paper is transparent about the shoulder artifact and other limitations, and the concern is testable, so the existing CONDITIONAL verdict is appropriate. No verdict change is needed.","tokens_in":31465,"tokens_out":8334,"duration_ms":100741,"concrete_test":"Take an optimized q(phi) (e.g., alpha=0.5 or 0.7) and recompute steady 1D profiles on the calibration velocity grid. Extract k_PF and m_PF using three conventions: (i) the solute peak as in Eq. (57); (ii) the value at the liquid-side interface edge obtained by extrapolating the outer liquid exponential profile back to the phi=0 position or to a fixed phi near -1; and (iii) the same model at S=1 (W=W0) with linear q, where diffuse-interface corrections are minimal and peak/edge differences should be small. If (i) differs from (ii)/(iii) by more than the 1% RMS tolerance at velocities near V_pull=0.12 m/s, the calibrated response is convention-dependent. As a follow-up, re-optimize q using convention (ii)/(iii) and rerun the alpha=0.3 and 0.7 2D cases; disappearance of the dendritic-to-banded transition would confirm the concern.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the identification of the liquid-side interface concentration c_l^i with the maximum of the steady one-dimensional concentration profile (Sec. 3.2, Eq. (57)). This peak-based c_l^i enters both k_PF(V) and the normalization of m_PF(V) in Eq. (58), and the loss (59) tunes q(phi) until these peak-based diagnostics match CGM. The paper's fixed-tanh check (Sec. 4.1) only shows that replacing phi0 by relaxed profiles leaves the peak-based response essentially unchanged; it does not show that the peak equals the sharp-interface liquid concentration. The paper itself reports 'weak shoulders near some liquid-channel concentration maxima' in the ternary run (Sec. 4.4), indicating that enhanced q can distort the profile near the interface. If the peak is not the physical liquid-side value, then the optimized q reproduces a diagnostic rather than the solute-trapping/drag response, and the alpha=0.3 to 0.7 morphology transition (Fig. 3) could be an artifact of the extraction convention. No S=1 (physical-width) or atomistic/sharp-interface validation of the extraction is provided.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an optimization-based calibration strategy for phase field models of rapid alloy solidification. The interfacial diffusivity interpolation q_i(φ) is expanded in endpoint-preserving Chebyshev polynomials and optimized so that one-dimensional steady planar-interface solutions, computed with a fixed tanh profile, reproduce prescribed continuous-growth-model target functions for the velocity-dependent partition coefficient k_i(V) and drag-modified kinetic liquidus m_i(V;α). The method is demonstrated for dilute Al–Cu, where RMS errors near 1% are achieved for intermediate drag coefficients, and for a dilute Al–Si–Cu ternary. Two-dimensional directional-solidification simulations using the calibrated q(φ) show a morphology transition from dendritic (α=0.3) to mixed (α=0.5) to banded (α=0.7) structures, interpreted through a reduced Q=0 kinetic-solidus diagnostic.","tokens_in":31829,"tokens_out":2343,"duration_ms":28134,"significance":"If the central claims hold, the framework is a useful step toward embedding physically or atomistically informed interface kinetics into enlarged-interface phase field simulations. The paper is transparent about its inverse-calibration nature: the Fig. 2 agreement is expected because the loss function (Eq. 61) directly minimizes the distance to the CGM targets. The main novelty is the systematic, tolerance-controlled construction of q_i(φ) as a response-matching degree of freedom, with regularized Chebyshev representation and a smoothness-selection rule. The dilute multicomponent extension that decouples k_i and m_i via component-specific susceptibilities is also a valuable contribution. However, the load-bearing morphology trend rests on two assumptions that are not fully validated: the peak-of-concentration extraction convention for the liquid-side interface concentration, and single deterministic 2D simulations per drag coefficient.","major_comments":[{"comment":"The definition of k_PF and the normalization of m_PF use the maximum of the steady concentration profile as the liquid-side interface concentration c_l^i. This identification is load-bearing because it enters both response functions and therefore the loss in Eq. (59). The paper does not validate this convention against sharp-interface asymptotics, S=1 direct phase field calculations, or atomistic data. The authors' own ternary run reports 'weak shoulders near some liquid-channel concentration maxima' (Sec. 4.4), which indicates that enhanced q can distort the profile near the interface. If the peak is not the sharp-interface liquid concentration, the optimized q matches a numerical diagnostic rather than the physical trapping/drag response, and the α-dependent morphology transition in Fig. 3 could be an artifact of the extraction convention. The fixed-profile check in Sec. 4.1 only repla","section":"Sec. 3.2, Eq. (57)"},{"comment":"Each morphology in Fig. 3 is generated from a single deterministic simulation per α. The claim that increasing drag 'shifts the solidification morphology from dendritic/cellular to mixed dendritic-banded, and finally to predominantly banded' is based on one realization per parameter. The α=0.5 case is interpreted as close to a transition, but no ensemble, phase-space, or quantitative morphological metrics are reported. The classification could be sensitive to initial perturbations, domain size, simulation time, and the wavy-channel artifacts acknowledged later in the same section. Please provide either multiple realizations with different initial conditions/noise or quantitative descriptors (e.g., band spacing, interface roughness, tip undercooling) to support the trend.","section":"Sec. 4.2, Fig. 3"},{"comment":"The calibration and the 2D validation use the fixed profile φ0 for the 1D inverse problem, while the 2D simulations use the full anisotropic, moving-interface phase field equations. The authors test S=3 banding and relaxed profiles, but they do not show that the extracted k_PF(V) and m_PF(V;α) from full 2D moving interfaces match the CGM targets. The mismatch between the calibration setting and the application setting is not discussed in detail. This gap weakens the claim that the optimized q functions 'reproduce' the prescribed response functions in the actual simulations.","section":"Sec. 4.1 and Sec. 5"}],"minor_comments":[{"comment":"The notation 'model interpolation functions at W=W0' is vague; clarify that q(φ) is the function that would preserve the response at the physical width.","section":"Sec. 1, Eq. (4)"},{"comment":"The average ⟨·⟩_j over velocities is not explicitly defined with weights; the text later says 'logarithmically spaced' and equal weights, but stating this in the equation caption would improve reproducibility.","section":"Sec. 3.3, Eq. (59)"},{"comment":"The concentration profiles show 'weak shoulders' near liquid-channel maxima; a brief explanation of their possible relation to enhanced interfacial diffusivity is given, but adding a zoom or an enlarged-interface control would help readers judge whether this is a numerical artifact.","section":"Sec. 4.4, Fig. 6"},{"comment":"The manuscript does not state whether the optimization code and data will be made available; for a calibration methodology, this would improve reproducibility.","section":"General"},{"comment":"The phrase 'tradeoffbetween' appears without a space; a final proofreading pass would catch such typos.","section":"Sec. 5, Discussion"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope for cond-mat.mtrl-sci and represents a useful methodological contribution. The inverse-calibration circularity is acknowledged and is not itself a fatal issue. The main risks are the unvalidated peak-extraction convention and the single-realization 2D results. Both are fixable within the manuscript's scope, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you should know: this paper turns the ad hoc q(phi) enhancement used by Ji, Li, and others into a proper inverse problem. They expand q(phi) in Chebyshev polynomials, optimize against CGM targets for k(V) and m(V;alpha) using 1D steady profiles, and select the smoothest profile meeting a tolerance. That is a real step forward for the rapid-solidification phase-field community. The multicomponent extension with independent k_i and m_i via diagonal susceptibilities is also a genuinely useful contribution, not a trivial relabeling.\n\nThe paper is transparent about its own circularity: q(phi) is fitted so that 1D profiles reproduce the targets, so Fig. 2 agreement is by construction. That is not a flaw for a calibration method. The 1% RMS fits are clean and the fixed-tanh profile check is honest. The S=3 banding check is also an appropriate robustness test. The authors clearly know the field and the limitations.\n\nThe soft spots are real, though not fatal. The load-bearing extraction of the liquid-side concentration as the solute peak of the steady 1D profile (Eq. 57) is not validated against any sharp-interface definition, atomistic data, or physical-width (S=1) reference. The paper even mentions weak shoulders near liquid-channel maxima in the ternary run, which is exactly where enhanced q can bend the concentration profile. If that peak is not the true liquid-side value, then the optimized q reproduces a diagnostic rather than the physical response, and the alpha=0.3 -> 0.7 morphology trend could be an artifact of the convention. The S=3 check supports the trend but does not address this extraction question. Second, each alpha is one deterministic 2D run; the mixed alpha=0.5 state could be sensitive to noise or domain size. Third, no code, data, or optimized coefficients are shipped, so independent reproduction is currently impossible for a paper whose whole contribution is a method.\n\nThese are strengthen-the-paper problems, not desk-reject problems. The central idea holds up. I would send it to serious referees, with the explicit instruction that they verify the peak-extraction convention and request reproducible artifacts. The paper will be useful to anyone who wants to bake experimentally or atomistically derived response functions into mesoscale simulations. I would cite it for the methodology, but not yet for the drag-banding conclusion.","headline":"A genuinely useful inverse-calibration method for putting prescribed trapping/drag response functions into large-interface phase-field simulations, but the interface-concentration extraction convention is unvalidated and the 2D trends rest on single runs.","tokens_in":32272,"tokens_out":1685,"would_cite":true,"duration_ms":22108,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["80A22","74N05"],"pacs":["81.30.Fb","64.70.D-"],"model":"deepseek-v4-flash","headline":"This paper claims that a phase-field model with a deliberately enlarged diffuse interface can be made to quantitatively reproduce prescribed rapid-solidification kinetics by optimizing the interfacial solute diffusivity profile, and that in","keywords":["rapid solidification","phase field","solute trapping","solute drag","interfacial diffusivity interpolation","continuous growth model","directional solidification","multicomponent alloy solidification"],"falsifier":"Run the same one-dimensional steady-state calibration at successively smaller interface widths W toward the sharp-interface limit, or against atomistic simulations, and compare the extracted solute-peak liquid concentration with the sharp-interface liquid composition; if the optimized q(φ) that matches k(V) and m(V;α) changes substantially with W or with the peak-extraction convention, the response matching is convention-dependent. Alternatively, use atomistically computed k(V) and m(V;α) as targets for Al–Cu and check whether the predicted dendritic-to-banded shift near α=0.5–0.7 reproduces e","tokens_in":31334,"feed_emoji":"❄️","tokens_out":4698,"duration_ms":52284,"temperature":0.7,"pith_summary":"The paper claims that a phase-field model with a computationally enlarged interface can be made to reproduce prescribed rapid-solidification kinetics by optimizing the interfacial solute diffusivity profile itself, rather than using a fixed interpolation. Using one-dimensional steady-state planar-interface solutions, the authors minimize the error between model predictions and continuous-growth-model targets for both the velocity-dependent partition coefficient and the drag-modified kinetic liquidus slope. They then show in dilute Al–Cu that, with all other conditions fixed, increasing only the prescribed solute-drag parameter changes simulated two-dimensional growth from dendritic to mixed dendritic–banded to predominantly banded. The same calibration extends to dilute multicomponent alloys by giving each solute an independent optimized diffusivity profile, avoiding a thermodynamic constraint that otherwise ties partition coefficients to liquidus slopes. If the approach holds, it provides a practical bridge from atomistic, experimental, or theoretical interface-kinetics data to phase-field simulations of rapid solidification microstructures.","feed_headline":"Solute drag alone flips dendrites to banded growth","feed_subtitle":"Optimized interface diffusion profiles replicate prescribed trapping and drag kinetics, altering morphology.","key_machinery":"The load-bearing object is the optimized interfacial diffusivity interpolation q_i(φ), written as the standard one-sided liquid diffusivity profile plus a (1−φ²) Chebyshev-polynomial correction that vanishes in the bulk phases. It is selected by minimizing a loss balancing relative errors in the predicted partition coefficient and kinetic liquidus response against a curvature regularization, with a tolerance-based rule choosing the smoothest profile that attains the accuracy target. The one-dimensional steady-state planar-interface equations, using the fixed equilibrium tanh phase-field profile, map candidate q_i(φ) to response functions, and the optimized profiles are then tabulated for mul","core_discovery":"The central claim is that the interfacial diffusivity interpolation q_i(φ), which controls solute mobility across the diffuse solid–liquid interface, can serve as a calibration degree of freedom: choosing it by optimization lets an enlarged-interface phase-field model quantitatively emulate prescribed sharp-interface response functions k_i(V) and m_i(V;α). In binary Al–Cu, the optimized profiles reproduce the continuous-growth-model targets within a 1% root-mean-square tolerance over the calibrated velocity range. In two-dimensional directional solidification at fixed composition, thermal gradient, and pulling velocity, raising only the drag coefficient transforms dendritic growth into mixed","pith_inferences":["A direct test of the peak-extraction convention is possible: compare the one-dimensional 'solute peak' liquid-side concentration with the sharp-interface liquid composition extrapolated as the interface width shrinks toward the physical value, since the paper itself notes weak shoulders near some ternary channel maxima that may be affected by enhanced interfacial transport.","The morphology trend predicts that, at fixed pulling velocity and thermal gradient, alloys whose atomistic or experimental response functions imply larger solute drag at the same trapping response should exhibit earlier banding or oscillatory growth; this is testable against phase-field runs using independently derived target functions.","If the fixed equilibrium tanh profile were replaced by fully relaxed moving-interface profiles during calibration, the optimized q_i(φ) could become velocity- or profile-dependent; comparing profiles calibrated with and without that relaxation would quantify the error introduced by the fixed-front approximation.","The reduced Q=0 diagnostic only captures the laterally averaged front response; a full finite-wavelength Mullins–Sekerka-style analysis using the same kinetic solidus and liquidus branches could determine whether the predicted banding threshold matches the simulated morphology boundary at finite wavenumbers."],"forward_implications":["Rapid-solidification phase-field simulations with enlarged interfaces can be calibrated to reproduce prescribed trapping and drag kinetics to a stated tolerance, rather than only capturing qualitative trends.","Because the target partition coefficient is held fixed while only the drag-modified liquidus response is varied, the simulated morphology change isolates solute drag as a primary morphological selector under rapid-solidification conditions.","The dendritic-to-banded transition appears robust to reducing the interface upscaling factor from S=5 to S=3 with a re-optimized profile, indicating the banding is not simply an artifact of the enlarged diffuse interface.","Dilute multicomponent alloys can carry independent equilibrium partition coefficients, liquidus slopes, and diffusive speeds per solute, removing the universal-thermal-prefactor restriction and permitting species-specific segregation predictions in the same evolving morphology.","The calibration is response-function agnostic, so target functions obtained from experiments, atomistic simulations, or other nonequilibrium kinetic models can be embedded in the same framework as long as they are smooth and numerically stable."],"fun_headline_variants":["Optimized phase field pins solute drag effects","Drag-induced banding predicted in rapid solidification","Interface trick calibrates trapping and drag","Solute drag morphs dendrites into bands","Drag alone reshapes solidification patterns"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The calibration assumes that, in the one-dimensional steady-state solution, the maximum of the solute concentration profile equals the sharp-interface liquid-side concentration and that the equilibrium tanh phase-field profile is a sufficient approximation for the moving interface; if that peak convention drifts from the true liquid concentration once interfacial diffusivity is enhanced, the matched k(V) and m(V;α) responses, and therefore the simulated morphology shift, coul","fun_headline_variants_meta":{"raw":{"variants":["Optimized phase field pins solute drag effects","Drag-induced banding predicted in rapid solidification","Interface trick calibrates trapping and drag","Solute drag morphs dendrites into bands","Drag alone reshapes solidification patterns"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000518,"raw_usage":{"total_tokens":2363,"prompt_tokens":773,"completion_tokens":1590,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":517,"completion_tokens_details":{"reasoning_tokens":1534}},"tokens_in":517,"tokens_out":1590,"duration_ms":11204,"temperature":1.0,"reasoning_tokens":1534,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T18:10:36.488198+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same one-dimensional steady-state calibration at successively smaller interface widths W toward the sharp-interface limit, or against atomistic simulations, and compare the extracted solute-peak liquid concentration with the sharp-interface liquid composition; if the optimized q(φ) that matches k(V) and m(V;α) changes substantially with W or with the peak-extraction convention, the response matching is convention-dependent. Alternatively, use atomistically computed k(V) and m(V;α) as targets for Al–Cu and check whether the predicted dendritic-to-banded shift near α=0.5–0.7 reproduces e","supporting_citations":[],"review_version":1}