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arxiv: 2605.17576 · v1 · pith:EPQNN3JTnew · submitted 2026-05-17 · ❄️ cond-mat.mtrl-sci

Microstructure evolution during rapid solidification of hypoeutectic Al-Ag alloys near absolute stability

Brian Rodgers , Mingwang Zhong , Trevor Lyons , John Roehling , Joseph T. McKeown , Alain Karma , Amy J. Clarke This is my paper

Pith reviewed 2026-05-19 22:24 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords rapid solidificationabsolute stabilityAl-Ag alloysphase-field simulationadditive manufacturingmicrostructure evolutionDTEMhypoeutectic alloys
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0 comments X

The pith

Concentrated hypoeutectic Al-Ag alloys reach absolute stability at growth rates below 1 m/s.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that microsegregation-free microstructures can form in sufficiently concentrated hypoeutectic Al-Ag alloys by reaching the absolute stability limit at velocities accessible in additive manufacturing. It combines dynamic transmission electron microscopy of laser-melted thin films with phase-field simulations and a linear stability analysis to track how the planar interface becomes stable. A sympathetic reader would care because this shows a practical path to controlling microstructure in concentrated alloys without needing extreme processing speeds. The work demonstrates quantitative agreement between the predicted absolute stability velocities, the simulations, and experiments on three concentrated alloys.

Core claim

The analysis predicts that V_abs follows a trend similar to that of the miscibility gap, first increasing and then decreasing with Ag concentration. Predicted values of V_abs are in good quantitative agreement with phase-field simulations over the entire hypoeutectic concentration range and with experiments for three concentrated alloys. This demonstrates that the absolute stability limit can be reached in sufficiently concentrated hypoeutectic Al-Ag alloys at growth rates well below the 1 m/s typically encountered in additive manufacturing.

What carries the argument

A sharp-interface linear stability analysis that uses a non-equilibrium, velocity-dependent phase diagram extracted from the phase-field model.

If this is right

  • Microsegregation-free microstructures become achievable at practical additive manufacturing speeds for concentrated Al-Ag alloys.
  • The absolute stability velocity can be predicted and tuned by adjusting silver concentration to follow the miscibility gap trend.
  • Models combining phase-field simulations with velocity-dependent stability analysis can guide alloy selection for rapid solidification processes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same non-monotonic dependence of absolute stability on solute content may appear in other binary systems that possess a similar miscibility gap shape.
  • Extending the velocity-dependent phase diagram approach to multicomponent alloys could identify additional compositions that reach absolute stability under additive manufacturing conditions.
  • Direct measurement of interface velocities in thin-film experiments at varying laser powers would provide an independent test of the predicted V_abs values.

Load-bearing premise

The non-equilibrium, velocity-dependent phase diagram extracted from the phase-field model accurately represents the real thermodynamic and kinetic behavior of the Al-Ag system at the high velocities of interest.

What would settle it

Experiments that measure absolute stability velocities across a wider range of Ag concentrations and find significant deviations from the predicted increase-then-decrease trend with composition.

Figures

Figures reproduced from arXiv: 2605.17576 by Alain Karma, Amy J. Clarke, Brian Rodgers, John Roehling, Joseph T. McKeown, Mingwang Zhong, Trevor Lyons.

Figure 1
Figure 1. Figure 1: Measurement of interface positions and calculation of solid-liquid interface velocities from DTEM data of Al-13.9 at% Ag melt pools. (A) Example measurement of major and minor axis lengths during solidification with laser melting of as-sputtered material. (B) Compiled major and minor diameters over time across all DTEM experiments performed in 13.9 at% Ag melt pools, with a second degree polynomial fit. (C… view at source ↗
Figure 2
Figure 2. Figure 2: STEM-HAADF (High Angle Annular Dark Field) images of solidification patterns formed during rapid solidification in DTEM samples of Al-Ag alloys with varying Ag solute concentrations, showing a decrease in the tendency towards partitioning growth with increasing solute concentration. All three concentrations form precipitates in the solid state along the grain boundaries during cooling after solidification.… view at source ↗
Figure 3
Figure 3. Figure 3: Partitioning behavior of dendrites as velocity increases from left to right of the overview image for the 13.9 at.% Ag alloy. (A) STEM-HAADF image overview of dendritic to planar solidification as velocity increases. Locations corresponding to composition scans are overlaid. (B,C,D) STEM-EDS maps of marked locations in (A) showing elemental distributions, with blue and red representing Al and Ag, respectiv… view at source ↗
Figure 4
Figure 4. Figure 4: STEM-HAADF images summarizing the effects of remelting on the more concentrated Al-Ag alloys wherein the interface is fully stable throughout solidification when melting as-sputtered material. (A) A stitched image showing the overlapping melt pools in 16.5 at% Ag and the order in which they were formed. (B) A higher magnification image of the interface at the overlapping region showing the brief destabiliz… view at source ↗
Figure 5
Figure 5. Figure 5: PF simulations of concentrated Al-Ag alloys. (A) Growth morphologies at various nominal Ag concentrations (c∞) for the kinetic coefficient µ 0 k = 0.5 m/s/K. The pulling velocity is obtained from experimental measurement (blue line in Fig. 1C) (B) Growth morphologies at various Ag concentrations for µ 0 k = 0.1 m/s/K. The three insets show solidification front morphologies at various velocities for 13.9 at… view at source ↗
Figure 6
Figure 6. Figure 6: Dynamics at the solidification front. (A) Pulling velocity and instantaneous interface velocity versus time for 13.9at.% Ag. The inset shows the solidification velocity within a banding cycle. (B) Interface temperature T plotted against solidification velocity. Solid lines denote steady-state values; symbols (diamonds and circles) show instantaneous data in PF simulations. The blue diamonds trace a single … view at source ↗
Figure 7
Figure 7. Figure 7: Stability analysis of the solid-liquid interface during rapid solidification. (A) Velocity-dependent phase diagram of hypoeutectic Al-Ag alloys with both solidus and liquidus slopes approaching 0 at the eutectic point. Black solid lines show the equilibrium phase diagram obtained using the CALPHAD method 38 . Blue and orange lines correspond to growth velocities of 0.3 m/s and 1 m/s, respectively, calculat… view at source ↗
Figure 8
Figure 8. Figure 8: Dependence of liquid diffusivity on Ag composition. Experimental values were measured at 983 K50, significantly higher than the ∼850 K relevant to this work, which accounts for the difference in absolute diffusivity. To facilitate comparison, the diffusivity (Dl) is normalized by its dilute-limit value (D0 l ) for both the experimental data and the present model (Eq. 16). Numerical solution of Eq. 15 using… view at source ↗
read the original abstract

Microsegregation-free microstructures can form by solidifying at velocities beyond the absolute stability limit ($V_{\text{abs}}$), where solute partitioning is suppressed by a stable, planar solid-liquid interface. Producing such microstructures is of considerable practical interest; however, $V_{\text{abs}}$ typically exceeds the ${\sim}1$ m/s growth rates encountered in additive manufacturing (AM). Here we demonstrate the absolute stability limit can be reached in sufficiently concentrated hypoeutectic Al-Ag alloys at growth rates well below the 1~m/s typically encountered in additive manufacturing. Dynamic Transmission Electron Microscopy (DTEM) of rapid solidification front evolution -- following laser spot melting of Al-Ag thin films -- combined with postmortem microstructural characterization, enables detailed quantitative comparison with both phase-field (PF) simulations and a sharp-interface linear stability analysis that uses a non-equilibrium, velocity-dependent phase diagram extracted from the PF model. The analysis predicts that $V_{\text{abs}}$ follows a trend similar to that of the miscibility gap, first increasing and then decreasing with Ag concentration. Predicted values of $V_{\text{abs}}$ are in good quantitative agreement with PF simulations over the entire hypoeutectic concentration range and with experiments for three concentrated alloys. These results inform the prediction and control of microstructural development in concentrated alloys near the absolute stability limit under AM conditions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that the absolute stability limit V_abs can be reached below ~1 m/s in sufficiently concentrated hypoeutectic Al-Ag alloys. Using DTEM experiments on laser-melted thin films, phase-field simulations, and sharp-interface linear stability analysis that employs a non-equilibrium velocity-dependent phase diagram extracted from the same PF model, the authors predict that V_abs increases then decreases with Ag concentration (following the miscibility gap trend). They report good quantitative agreement between the analysis, PF results over the full hypoeutectic range, and experiments on three concentrated alloys, with implications for microsegregation-free microstructures under additive manufacturing conditions.

Significance. If the results hold, the work is significant for additive manufacturing because it identifies composition windows where planar, partitionless solidification becomes accessible at practical growth rates. The multi-method approach—combining in-situ DTEM, PF modeling, and analytical stability analysis—provides quantitative, falsifiable predictions of the non-monotonic V_abs trend. Explicit experimental checks on three alloys supply an independent anchor that partially offsets model dependence, strengthening the practical utility of the findings for controlling microstructures in concentrated alloys.

major comments (2)
  1. [§3 and §4] §3 (phase-field modeling) and §4 (sharp-interface linear stability analysis): the velocity-dependent phase diagram (including non-equilibrium liquidus and partition coefficient) is extracted from the PF model and then inserted into the stability analysis used to compute V_abs. This creates partial circularity when the analysis is compared quantitatively to the same PF simulations across the full hypoeutectic range (as shown in the relevant comparison figures); the agreement is therefore not fully independent. The three experimental alloys provide a partial external check, but do not validate the extracted diagram for the entire concentration range or the claimed trend.
  2. [Abstract and §5] Abstract and §5 (discussion of practical implications): the claim that V_abs lies below 1 m/s for concentrated alloys and follows the miscibility-gap trend rests on the assumption that the PF-derived velocity-dependent phase diagram accurately captures real Al-Ag thermodynamics and kinetics at the velocities of interest. No independent thermodynamic assessment or sensitivity study to the interface kinetic parameters is presented; this assumption is load-bearing for the AM relevance.
minor comments (2)
  1. [Figure captions] Figure captions for the DTEM and PF results should explicitly state the number of independent runs or measurements used to generate error bars and the precise laser parameters employed.
  2. [Notation] The first introduction of the velocity-dependent liquidus slope and partition coefficient should include a brief reminder of how they differ from their equilibrium counterparts to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and indicate where revisions will be made to improve clarity and strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3 and §4] §3 (phase-field modeling) and §4 (sharp-interface linear stability analysis): the velocity-dependent phase diagram (including non-equilibrium liquidus and partition coefficient) is extracted from the PF model and then inserted into the stability analysis used to compute V_abs. This creates partial circularity when the analysis is compared quantitatively to the same PF simulations across the full hypoeutectic range (as shown in the relevant comparison figures); the agreement is therefore not fully independent. The three experimental alloys provide a partial external check, but do not validate the extracted diagram for the entire concentration range or the claimed trend.

    Authors: We acknowledge that deriving the velocity-dependent phase diagram from the phase-field model and feeding it into the sharp-interface stability analysis introduces interdependence when the two modeling results are compared directly over the full hypoeutectic range. The phase-field parameters themselves originate from independent thermodynamic assessments and kinetic data reported in the literature for Al-Ag. The stability analysis nevertheless supplies an analytically distinct check on the trends. The DTEM experiments on three concentrated alloys furnish an external anchor for the key predictions. In the revised manuscript we will add explicit text describing the provenance of all model parameters and the complementary roles of the two approaches, and we will include a brief sensitivity test on the extracted liquidus and partition-coefficient functions to quantify the effect of small variations. revision: partial

  2. Referee: [Abstract and §5] Abstract and §5 (discussion of practical implications): the claim that V_abs lies below 1 m/s for concentrated alloys and follows the miscibility-gap trend rests on the assumption that the PF-derived velocity-dependent phase diagram accurately captures real Al-Ag thermodynamics and kinetics at the velocities of interest. No independent thermodynamic assessment or sensitivity study to the interface kinetic parameters is presented; this assumption is load-bearing for the AM relevance.

    Authors: We agree that the robustness of the non-monotonic V_abs trend and its implications for additive manufacturing depend on the fidelity of the non-equilibrium thermodynamics extracted from the phase-field model. The underlying free-energy functions are taken from established CALPHAD assessments of the Al-Ag system, and the kinetic coefficients are calibrated to available experimental interface-mobility data. Nevertheless, a dedicated sensitivity study was not presented. In the revised version we will add a short sensitivity analysis in which the interface kinetic parameters are varied within literature-reported bounds; the resulting changes in predicted V_abs will be shown and discussed with respect to the claimed trend and the practical velocity window below 1 m/s. revision: yes

Circularity Check

1 steps flagged

Velocity-dependent phase diagram extracted from PF model used in stability analysis and compared to same PF simulations

specific steps
  1. fitted input called prediction [Abstract]
    "sharp-interface linear stability analysis that uses a non-equilibrium, velocity-dependent phase diagram extracted from the PF model. The analysis predicts that V_abs follows a trend similar to that of the miscibility gap, first increasing and then decreasing with Ag concentration. Predicted values of V_abs are in good quantitative agreement with PF simulations over the entire hypoeutectic concentration range"

    The phase diagram serving as input to the stability analysis is derived from the identical PF model whose simulation outputs are later used as the benchmark for 'quantitative agreement.' This makes the match between analysis predictions and PF results partially non-independent by construction of the input extraction step.

full rationale

The paper extracts a non-equilibrium velocity-dependent phase diagram from its phase-field (PF) model and feeds it into a separate sharp-interface linear stability analysis to predict V_abs. This analysis is then shown to agree quantitatively with direct PF simulations across the concentration range. While the sharp-interface model is mathematically distinct, the shared origin of the thermodynamic/kinetic inputs creates partial dependence in the reported agreement. Independent experimental data for three alloys mitigates but does not remove the issue, resulting in moderate circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the phase-field model and the velocity-dependent phase diagram derived from it; these contain fitted kinetic and thermodynamic parameters whose values are not independently constrained outside the model.

free parameters (1)
  • Interface kinetic parameters in PF model
    Phase-field simulations require mobility and kinetic coefficients that are typically adjusted to match observed interface behavior.
axioms (1)
  • domain assumption Linear stability analysis remains valid when applied to the non-equilibrium, velocity-dependent phase diagram extracted from the PF model.
    Invoked to predict V_abs from the model-derived phase diagram.

pith-pipeline@v0.9.0 · 5797 in / 1311 out tokens · 59840 ms · 2026-05-19T22:24:38.089671+00:00 · methodology

discussion (0)

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Reference graph

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