The effect of thermal history on the atomic structure and mechanical properties of amorphous alloys

Nikolai V. Priezjev

REVIEW 4 major objections 4 minor 44 references

The effect of thermal history on the atomic structure and mechanical properties of amorphous alloys

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read In a simulated binary metallic glass, annealing closer to the glass transition temperature lowers the potential energy and raises the shear modulus and yield stress, while higher annealing temperatures produce ductile, homogeneous deformation.

desk verdict A competent, systematic MD scan of annealing temperature in the Kob-Andersen glass; the qualitative trends are believable, but the low-Ta data and the Ta=fictive-temperature assumption need more support before the strong claims are published as-is. read the letter →

arxiv 1908.00464 v1 pith:P6TQ67QT submitted 2019-08-01 cond-mat.soft cond-mat.mtrl-sciphysics.comp-ph

Nikolai V. Priezjev This is my paper · ORCID

classification cond-mat.softcond-mat.mtrl-sciphysics.comp-ph

keywords annealingglassmechanicalstructuretemperaturealloysatomicenergy

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper uses computer simulation to study how the way a metallic glass is prepared changes its strength and how it breaks. The model is a standard mixture of two types of atoms, the Kob-Andersen mixture, often used to stand in for a metal alloy such as Ni80P20. The author melts the model, cools it to one of several annealing temperatures near the glass transition, lets it sit there, then suddenly drops it to a very cold temperature to freeze the structure. Three things change with the annealing temperature. Glasses prepared at lower temperatures, closer to the glass transition, have lower potential energy and a more ordered short-range structure, and they are stiffer: both the shear modulus and the stress peak at yielding are larger. Glasses prepared at higher temperatures keep a higher-energy, more disordered structure, and under shear they deform in a spread-out, ductile way rather than forming a single shear band. The simulation also finds that the shear modulus depends on strain rate only when the annealing temperature is above the glass transition. These observations are mostly qualitative and averaged over 15 samples, but the paper does not show error bars on the key plots. The value of the glass transition temperature is taken from an earlier paper by the same author, and the lower-temperature part of the energy curve is mentioned but not shown. Still, the protocol is described in enough detail that another group could repeat the simulations.

Extended reading notes

Core claim

The abstract states that 'glasses prepared at higher annealing temperatures are relocated to higher energy states and their average glass structure remains more disordered' and that 'both the shear modulus and yielding peak increase significantly when the annealing temperature approaches T_g from above,' with the deformation mode changing 'from brittle to ductile upon increasing annealing temperature.' If the paper is correct, thermal history alone, specifically the annealing temperature before a rapid quench, sets the energy, short-range order, elastic modulus, yield stress, and strain-rate sensitivity of the model metallic glass.

Load-bearing premise

The load-bearing premise is that the instantaneous quench to T_LJ = 0.01 preserves the structure equilibrated at T_a, so that T_a can be equated with the fictive temperature. The paper states this in Section III: 'In the limiting case of an infinitely fast quenching rate, used in the present study, the fictive temperature essentially coincides with the annealing temperature at which the system is equilibrated before the quench.' At low T_a the assumption is fragile, because aging during 2x10^5 tau is incomplete: the MSD value of 1.64 sigma^2 at T_a = 0.32 indicates ongoing structural relaxation, and the paper reports (without showing) that U measured at 0.01 increases when T_a is reduced below 0.30. If the quench does not faithfully freeze the T_a state, the attributed annealing-temperature trends would be mixed with quench-rate and aging artifacts.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

You should know this is a straightforward MD study of how the annealing temperature Ta before a rapid quench changes the energy, structure, and mechanics of the Kob-Andersen glass. It is not a headline result, but it is a useful systematic map: lower Ta gives deeper energy, more ordering in g_BB, higher shear modulus and yield stress, and a transition from shear-band localization to homogeneous flow as Ta rises above Tg. The trends line up with the experimental fictive-temperature picture, which is nice but not new; parts overlap with the author's earlier heat-treatment MD papers. The cleanest contribution is the Ta scan at fixed quench protocol, with 15 independent samples for the key quantities.

The paper does several things well. The stress-strain curves, energy traces, and nonaffine displacement snapshots are mutually consistent. The strain-rate dependence of G only for Ta>Tg is an interesting detail that matches experiment. The writing is clear and the protocol is reproducible in principle.

Now the soft spots, mostly minor-to-moderate. Fig. 4 has no error bars despite averaging 15 samples; that should be easy to add. The low-Ta data (Ta=0.28–0.30) are mentioned but not shown, and the nonmonotonicity in U at 0.01 deserves a figure because it reveals that the effective cooling rate changes, not just Ta. The bigger conceptual issue is equating Ta with fictive temperature. The instantaneous quench freezes structure, but at Ta=0.32–0.34 the system is clearly still aging: MSD of 1.64 σ² over 2×10⁵τ means atoms are making cage jumps. So the lowest-Ta points may partly reflect aging history rather than the equilibrium state at Ta. That does not break the qualitative trend, but it does mean the paper overstates “thermal history alone” unless it can show the trends are robust to longer annealing or an independent fictive-temperature measurement.

Tg is taken from a self-cited paper; acceptable given the same model and parameters, but a direct determination in this work would be cleaner. No code or data are deposited, which limits reuse.

Bottom line: the central claim holds up in its main lines. This paper deserves a serious referee, not a desk reject. I would send it out with a request for error bars, the missing low-Ta data, and a careful discussion of the equilibration issue.

Best, [You]

Referee Report

4 major / 4 minor

Summary. This manuscript reports molecular-dynamics simulations of the Kob-Andersen 80:20 binary Lennard-Jones mixture (N = 60,000) aimed at isolating the effect of the annealing temperature Ta on the structure and mechanical response of the resulting glass. The preparation protocol is: cool from T = 1.0 to Ta in 10^4 tau, hold at Ta for 2 x 10^5 tau, quench instantaneously to T = 0.01, relax for 10^4 tau, then shear at constant volume at strain rates from 10^-5 to 10^-3 tau^-1. The paper reports that the potential energy after quenching decreases as Ta approaches Tg ≈ 0.35 from above; that the nearest-neighbor peak of g_BB becomes less pronounced at lower Ta; that the shear modulus and stress-overshoot peak increase strongly as Ta decreases toward Tg; that the shear modulus becomes strain-rate dependent only for Ta > Tg; and that nonaffine-displacement snapshots show a transition from shear-band localization at Ta = 0.32 to homogeneous deformation at Ta = 0.50. The authors frame these results as evidence that thermal history, specifically the fictive temperature set by Ta, controls the energy, short-range order, and mechanical properties of the model metallic glass.

Significance. If the central premise is accepted, the paper provides a clean computational demonstration of fictive-temperature control over the mechanical properties of a model metallic glass, complementing recent experimental work on toughening transitions. The qualitative trends—higher energy and more disordered structure for higher Ta, larger modulus and yield stress near Tg from above, and a brittle-to-ductile crossover—are physically reasonable and are supported by the stress-strain curves, energy curves, and nonaffine snapshots. The paper also has strengths in explicit multi-sample averaging over 15 independent samples, a well-defined preparation protocol, and a clear attempt to connect the results to the fictive-temperature framework. However, the load-bearing identification of Ta with the fictive temperature is not established at low Ta, where structural relaxation is incomplete; because the Ta = 0.32 and 0.34 data in Figs. 3-5 are in this regime, the claimed annealing-temperature trends are not fully isolated from aging and cooling-history effects. The omitted low-Ta data and the absence of error bars in Fig. 4 further limit the quantitative robustness of the transition claim.

major comments (4)

[III, after Fig. 1; fictive-temperature identification] The claim that Ta equals the fictive temperature is load-bearing and is not supported for Ta ≤ 0.36. Figure 1 shows that the potential energy continues to decrease during the entire 2 x 10^5 tau annealing interval at these temperatures, and the reported MSD of about 1.64 sigma^2 at Ta = 0.32 indicates ongoing structural relaxation. Therefore the instantaneous quench does not freeze an equilibrated Ta structure, and the trends for Ta = 0.32 and 0.34 in Figs. 3-5 may reflect partial aging during the finite annealing window rather than the equilibrium state at Ta. The authors should demonstrate that longer annealing (or an independent measurement of the fictive temperature, e.g., from the inherent-structure energy) leaves the reported trends unchanged, or restrict the central claims to the equilibrated range.
[III, inset to Fig. 1; abstract] The text states that for 0.28 ≤ Ta ≤ 0.30 the potential energy U measured at TLJ = 0.01 increases as Ta is decreased, but these data are not shown. This nonmonotonicity means that the potential energy is not a single-valued function of Ta, and the abstract's statement that 'glasses prepared at higher annealing temperatures are relocated to higher energy states' is therefore valid only over the restricted range 0.32-0.50. The omitted data should be included, and the abstract and conclusions should be qualified accordingly.
[III, Fig. 4] No error bars or other measures of statistical uncertainty are given for sigma_Y and G despite the statement that the data are averaged over 15 independent samples. The central quantitative claims—that the mechanical properties change sharply when Ta crosses Tg and that the shear modulus becomes strain-rate dependent only for Ta > Tg—cannot be assessed without an indication of the sample-to-sample scatter. Error bars (or a table of mean plus or minus standard error) should be added to Fig. 4 and its inset.
[III, definition of Tg] The value Tg ≈ 0.35 is taken from the author's prior work [13] and was obtained with a cooling-rate protocol (10^-5 epsilon/kB tau); this value is then used to locate the mechanical transition in Fig. 4. Since the glass transition temperature depends on the cooling rate and the thermal protocol, the location of the observed transition relative to Tg should either be confirmed within the present preparation protocol or discussed as potentially shifted relative to the cited value.

minor comments (4)

[Throughout] Exponents are frequently missing in the text (e.g., '10 4tau' and '2 x 10 5tau'); these should be typeset as 10^4 tau and 2 x 10^5 tau.
[III, nonaffine-displacement definition] The sentence containing 'the nonaddine measure' should read 'the nonaffine measure'.
[References] Reference [39] on laser welding of glasses appears unrelated to the discussion of fictive temperature; please verify whether it was intended to be cited or replace it with a more relevant reference.
[III, Figs. 5-7] The brittle-to-ductile interpretation is based on snapshots from individual samples; the authors should state whether the deformation-mode change was observed consistently in all 15 samples.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: central results are direct MD observables; self-cited Tg is a non-load-bearing reference.

full rationale

The paper's claims are supported by direct molecular dynamics measurements: potential energy after quenching, g_BB(r), stress-strain curves, shear modulus, yield stress, and nonaffine displacement fields, all computed from trajectories of a standard Kob-Andersen mixture. The independent variable is the annealing temperature Ta; no output quantity is fitted to the claimed trends, and no prediction reduces to an input by construction. The only imported numerical value is Tg ≈ 0.35, cited from the author's earlier work [13]; it is used solely to label the temperature region 'near Tg' and does not enter the computation of U, G, or σY. That prior value is a separate simulation result with stated assumptions that do not include the present mechanical data, so it is not a circular load-bearing self-citation. The paper itself flags validity limitations in Section III: incomplete aging at Ta ≤ 0.36 (MSD ≈ 1.64 σ² at Ta = 0.32) and a non-monotonic quenched energy for Ta ≤ 0.30, with the passage 'Test simulations at lower annealing temperatures, 0.28ε/kB ⩽Ta ⩽ 0.30ε/kB, have shown thatU, measured at TLJ = 0.01ε/kB, continues to increase upon further reducing Ta (not shown).' These are correctness concerns about whether Ta equals the fictive temperature at low Ta, not circularity, because the mechanical observables are independent of that equality.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No invented entities are introduced. The central claim rests on standard model parameters, protocol choices, the adopted T_g estimate, and diagnostic assumptions, all listed above.

free parameters (3)

Glass transition temperature T_g = 0.35 epsilon/k_B (LJ units)
Adopted from the author's prior simulation study [13] via linear extrapolation of potential energy; it anchors the claim that property changes occur near T_a = T_g.
Annealing equilibration time = 2 x 10^5 tau
Chosen protocol duration; the effective structural state at low T_a depends on it, as shown by the MSD of 1.64 sigma^2 at T_a = 0.32.
Linear cooling time from T=1.0 to T_a = 10^4 tau
The paper invokes this fixed cooling interval to explain the non-monotonic U(T_a) behavior for T_a below 0.30, so it is part of the state preparation.

assumptions (5)

domain assumption The Kob-Andersen binary Lennard-Jones mixture is a valid proxy for metallic glasses.
All conclusions are drawn from this model; the non-additive parameters suppress crystallization near T_g [34].
domain assumption The cited value T_g = 0.35 epsilon/k_B applies to the preparation protocol used here.
The transition location and the interpretation of T_a near T_g rest on this value from the author's prior work [13].
domain assumption Instantaneous quenching to T_LJ = 0.01 freezes the T_a structure without altering it.
Used to equate T_a with fictive temperature in Section III and to attribute all measured changes to annealing history.
domain assumption The Falk-Langer nonaffine displacement measure identifies localized shear transformations.
The brittle-to-ductile classification is based on snapshots colored by D2 values, following [43].
domain assumption Periodic boundary conditions do not bias the observed shear band orientation or the brittle-to-ductile interpretation.
At T_a = 0.38 the shear band forms perpendicular to the shear plane, which the paper notes is allowed by the periodic boundaries [27,44].

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Pith. "Pith review of The effect of thermal history on the atomic structure and mechanical properties of amorphous alloys." pith.science (2026). https://pith.science/paper/P6TQ67QT

@misc{pith2026190800464,
  author       = {Pith},
  title        = {Pith review of: The effect of thermal history on the atomic structure and mechanical properties of amorphous alloys},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P6TQ67QT}},
  note         = {Machine review of arXiv:1908.00464}
}

abstract

The influence of thermal processing on the potential energy, atomic structure, and mechanical properties of metallic glasses is examined using molecular dynamics simulations. We study the three-dimensional binary mixture, which was first relaxed near the glass transition temperature, and then rapidly cooled deep into the glass phase. It was found that glasses prepared at higher annealing temperatures are relocated to higher energy states and their average glass structure remains more disordered, as reflected in the shape of the pair correlation function. The results of mechanical testing demonstrate that both the shear modulus and yielding peak increase significantly when the annealing temperature approaches $T_g$ from above. Moreover, the shear modulus becomes a strong function of strain rate only for samples equilibrated at sufficiently high temperatures. Based on the spatial distribution of nonaffine displacements, we show that the deformation mode changes from brittle to ductile upon increasing annealing temperature. These results can be useful for the design and optimization of the fabrication processes of bulk glassy alloys with improved plasticity.

Figures

Figures reproduced from arXiv: 1908.00464 by the authors.

**Figure 2.** FIG. 2: (Color online) The pair distribution function of smaller atoms of type [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗

**Figure 3.** FIG. 3: (Color online) The variation of shear stress, [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4: (Color online) The peak value of the stress overshoot [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]

**Figure 5.** Figure 5: FIG. 5: (Color online) The sequence of snapshots for the sample prepared at [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]

**Figure 6.** Figure 6: FIG. 6: (Color online) The series of snapshots depicting atomic configurations in the strained glass [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]

**Figure 7.** Figure 7: FIG. 7: (Color online) The consecutive snapshots of the glass equilibrated at [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [13]

N. V. Priezjev, Atomistic modeling of heat treatment processes for tuning the mechanical properties of disordered solids, J. Non-Cryst. Solids 518, 128 (2019)

2019

[2] [1]

J. C. Qiao, Q. Wang, J. M. Pelletier, H. Kato, R. Casalini, D. Crespo, E. Pineda, Y. Yao, Y. Yang, Structural heterogeneities and mechanical behavior of amorphous alloys, Prog. Mater. Sci. 104, 250 (2019)

work page 2019

[3] [2]

Y. Sun, A. Concustell, and A. L. Greer, Thermomechanical processing of metallic glasses: Extending the range of the glassy state, Nat. Rev. Mater. 1, 16039 (2016)

2016

[4] [3]

Park, C.-M

K.-W. Park, C.-M. Lee, M. Wakeda, Y. Shibutani, M. L. Falk, and J.-C. Lee, Elastostatically induced structural disordering in amorphous alloys, Acta Materialia 56, 5440 (2008)

2008

[5] [4]

Y. Tong, W. Dmowski, Y. Yokoyama, G. Wang, P. K. Liaw, and T. Egami, Recovering compressive plasticity of bulk metallic glasses by high-temperature creep, Scripta Materialia 69 570 (2013)

2013

[6] [5]

A. L. Greer, and Y. H. Sun, Stored energy in metallic glasses due to strains within the elastic limit, Philos. Mag. 96, 1643 (2016)

2016

[7] [6]

Zhang, Y

M. Zhang, Y. M. Wang, F. X. Li, S. Q. Jiang, M. Z. Li and L. Liu, Mechanical relaxation-to- rejuvenation transition in a Zr-based bulk metallic glass, Sci. Rep. 7, 625 (2017)

work page 2017

[8] [7]

J. Pan, Y. X. Wang, Q. Guo, D. Zhang, A. L. Greer, and Y. Li, Extreme rejuvenation and softening in a bulk metallic glass, Nat. Commun. 9, 560 (2018)

2018