Al-Cu-Fe alloys: the relationship between the quasicrystal and its melt

L.V. Kamaeva; N.M. Chtchelkatchev; R.E. Ryltsev; V.I. Lad'yanov

REVIEW 4 major objections 4 minor 81 references

Al-Cu-Fe alloys: the relationship between the quasicrystal and its melt

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

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Pith's one-line read The paper argues that Al-Cu-Fe melts retain the chemical short-range order of the quasicrystal solid—Cu–Fe repulsion and Fe–Al attraction—while losing its topological icosahedra, and that this chemical memory shows up as minima in…

desk verdict Careful AIMD and viscosity study of Al-Cu-Fe melts, but the headline 'minima at the i-phase' claim is not statistically supported by the experimental data. read the letter →

arxiv 1908.03931 v1 pith:66UVMERB submitted 2019-08-11 physics.app-ph cond-mat.dis-nncond-mat.mtrl-sciphysics.chem-ph

L.V. Kamaeva , R.E. Ryltsev , V.I. Lad'yanov , N.M. Chtchelkatchev This is my paper · ORCID

classification physics.app-phcond-mat.dis-nncond-mat.mtrl-sciphysics.chem-ph

keywords liquidalloyviscosityundercoolabilityshort-rangeorderKasperpolyhedrastructuralheredityquasicrystalabinitiomoleculardynamics

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 sets out to test whether a liquid carries structural memory of the quasicrystal it freezes into, using Al-Cu-Fe as a model system. By combining viscosity and undercoolability measurements with ab initio molecular dynamics, it argues that the main chemical interaction features of the solid—strong Cu–Fe repulsion and strong Fe–Al attraction—survive in the melt, while the solid's topological icosahedra do not. It further claims that at the icosahedral-phase stoichiometry the chemical short-range order changes qualitatively, and that this change shows up as minima in the viscosity and undercoolability isotherms. If correct, the result makes melt viscosity and undercoolability practical indicators for finding or processing quasicrystal-forming compositions.

What carries the argument

The argument turns on the Warren-Cowley parameters $\alpha_{i-j}=1-\frac{Z_{i-j}}{Z_{i,\text{tot}}\,x_j}$, which measure whether pairs of species attract (negative $\alpha$) or repel (positive $\alpha$) relative to a random mixture. Computed from ab initio partial radial distribution functions and coordination numbers, these parameters supply the concentration-resolved chemical short-range order that is then compared with experimental viscosity, equal-viscosity lines, and undercoolability. Bond-angle distribution functions around Fe—a sharp Al–Fe–Al peak and a weak Cu–Fe–Cu peak—back up the same interaction picture, and Voronoi tessellation identifies the polytetrahedral Kasper-polyhedra motif that replaces perfect icosahedra in the melt.

What would settle it

Measure the viscosity and undercoolability along the 12.5 at.% iron cross-section with per-point error bars and multiple independent runs: if the minimum near 25 at.% copper disappears within the 5% scatter or shifts with cooling rate, the claimed composition-structure link fails. Independently, in situ diffraction on levitated undercooled droplets at 20–80 K undercooling could test whether the Warren-Cowley parameter changes predicted from equilibrium melts are actually present in the liquid that nucleates.

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Extended reading notes

Core claim

The central claim is that structural heredity in Al-Cu-Fe is chemical rather than topological. Melt snapshots from ab initio molecular dynamics contain almost no perfect $\langle 0,0,12,0\rangle$ icosahedra even at the icosahedral-phase composition; the local order is polytetrahedral, dominated by distorted Kasper polyhedra such as $\langle 0,3,6,4\rangle$. Yet Warren-Cowley parameters extracted from partial radial distribution functions show the same interaction fingerprints as the solid: Cu and Fe avoid each other, Fe and Al bond strongly, and these features are nearly concentration-independent. In the composition window of the i-phase, the chemical short-range order changes qualitatively—Al–Cu and Al–Fe interactions flip sign, Cu–Fe repulsion is minimal—and the same window shows minima in viscosity isotherms, equal-viscosity temperature lines, and undercoolability. The paper concludes that the chemical short-range order of the melt, rather than pre-formed icosahedra, is what links melt properties to quasicrystal formation.

Load-bearing premise

The whole link rests on the claim that the weak viscosity minimum near 25 at.% copper is a real feature of the alloy rather than scatter within the stated 5% measurement error, and that melt structure measured 100 K above the melting point tells us what the undercooled liquid looks like when solidification begins.

Editorial extensions

If this is right

Concentration curves of viscosity, equal-viscosity temperatures, and undercoolability can be used as fast experimental screens for the icosahedral-phase stoichiometry in Al-Cu-Fe, without costly structural probes.
Because topological icosahedra are absent in the equilibrium melt, the initial stage of solidification is better interpreted through chemical short-range order and its concentration changes than through pre-existing icosahedral clusters.
The near concentration-independence of Cu–Fe repulsion and Fe–Al attraction means these interaction fingerprints are robust signatures of the system, useful for validating interatomic potentials in simulation.
At i-phase stoichiometry, minimal chemical interaction—near-random Al–Cu and Cu–Cu bonding, sign flips in Al–Fe—coincides with the highest viscosity near the liquidus; this can guide composition selection for casting.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same recipe—measuring a structural-sensitive liquid property and computing Warren-Cowley parameters across a composition cross-section—could be applied to other quasicrystal-forming or high-entropy alloy families, treating viscosity minima as a fast screening signal before full phase-diagram work.
AIMD's non-equilibrated undercooled run hints that substantial icosahedral order appears only on undercooling; if that tendency survives equilibration, the melt may develop topological icosahedra just before nucleation even though the equilibrium melt has none—an extension the paper explicitly leaves to future semi-empirical potentials.
A direct testable extension would be to compare these melt indicators with nucleation-rate measurements, for example from droplet dispersion or fluxing, to see whether the viscosity and undercoolability minima correspond to lower nucleation barriers or simply to liquidus-shape effects.

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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

Short version: the AIMD SRO analysis is the real value here; the headline claim about viscosity and undercooling minima at the i-phase stoichiometry is not statistically supported. I re-ran the stress-test calculation on their Table 1 Arrhenius fits, and it holds: at xFe=12.5, the viscosities at xCu=20.5 and xCu=25.5 differ by roughly 0.2% at 1473 K, 0.5% at 1573 K, and 2% at 1673 K. With their stated 5% total error, the 'weakly pronounced minimum' is indistinguishable from scatter, and the minimum's location is not determined. The undercooling data show a kink rather than a clean minimum, and no error bars are given. So the abstract's causal chain – chemical SRO change leads to minima – is plausible but not established by the experiments.

What is new and useful: two composition cross-sections of viscosity and undercooling for Al-Cu-Fe, plus AIMD at six compositions with Warren-Cowley parameters, Voronoi analysis, BADFs, and BOOPs. The Cu-Fe repulsion, the near-absence of perfect icosahedra in the equilibrium melt, and the dominance of distorted Kasper polyhedra are concrete, re-usable results. The authors are also honest: they call the minimum weak, and they explicitly say the deep-undercooled AIMD run is not equilibrated. That is the right way to report a preliminary observation.

The weaknesses are proportionate: the reference viscosity for the equal-viscosity lines is taken from the i-phase itself, so the T_visc–liquidus match is partly constructed. The AIMD is run at 100 K above Tm, not in the undercooled state, so the connection to nucleation is inferential. The Fe statistics are thin at low Fe content, as they note. None of this makes the paper worthless; it just means the central claim should be demoted from a result to a hypothesis in the abstract.

This paper deserves a serious referee, not a desk reject. The data and simulation protocols are described well enough to reproduce, and the SRO findings stand on their own. I would want the experimental minimum either confirmed with proper error bars and more compositions or removed from the abstract and conclusions. I'd cite it for the AIMD SRO numbers, not for the minima claim. Probably worth a reading group slot as a case study in how a weak experimental feature can become a headline.

Referee Report

4 major / 4 minor

Summary. The paper studies Al-Cu-Fe melts along two composition cross-sections containing the icosahedral quasicrystal (i-phase) stoichiometry. The authors report experimental kinematic viscosity and undercoolability data across a wide composition range, and combine these with ab initio molecular dynamics (AIMD) simulations of six compositions at about 100 K above the liquidus. From the simulations they extract Warren-Cowley short-range order (SRO) parameters, radial and bond-angle distribution functions, Voronoi polyhedra, and bond-orientational order parameters. The central claim is that the main features of interatomic interaction in Al-Cu-Fe are the same in liquid and solid states, and that a change in chemical SRO near the i-phase stoichiometry produces minima in viscosity and undercoolability isotherms, suggesting that melt SRO and structural-sensitive properties can serve as indicators of quasicrystal-forming compositions.

Significance. If established, the proposed connection between melt chemical SRO, viscosity, undercoolability, and quasicrystal-forming ability would be practically useful for selecting alloy compositions for casting or rapid quenching. The paper contributes a substantial experimental dataset of viscosity and undercoolability for Al-Cu-Fe melts over a broader composition range than previous studies, and the AIMD analysis addresses an important question about whether icosahedral order survives melting. The finding that topological icosahedra are almost absent in the equilibrium melt while pair and angular correlations persist is interesting and appears internally consistent. However, the load-bearing experimental claim of viscosity minima at the i-phase stoichiometry is not robust to the stated measurement uncertainty, and the claim is not uniformly supported across both cross-sections. The equal-viscosity line construction also introduces a nearly tautological comparison with the liquidus. The work would be publishable if the central claims are re-evaluated and appropriately qualified.

major comments (4)

[§3, Fig. 2a and Table 1] The claimed 'weakly pronounced minimum' in viscosity at xCu ≈ 25 at.% is not statistically established by the data in Table 1. Re-evaluating the Arrhenius parameters for the xFe = 12.5 cross-section at 1473 K gives ν(Al67Cu20.5Fe12.5) = 5.49×10^-7 m²/s and ν(Al62Cu25.5Fe12.5) = 5.50×10^-7 m²/s, a difference of about 0.2%; at 1573 K the difference is about 0.5%, and at 1673 K about 1.7%. All of these differences are far smaller than the stated total error of 5%, and Fig. 2a shows no error bars. The authors themselves call the minimum weak, so the central experimental anchor of the 'minima at i-phase stoichiometry' claim is not supported by the reported measurements.
[Abstract and §5 Conclusions, compared with Figs. 2b and 3b] The blanket statement that viscosity and undercoolability isotherms develop minima at the i-phase stoichiometry is contradicted by the Fe cross-section. Along xCu = 25.5 at.%, Fig. 2b shows viscosity increasing monotonically with xFe, and Fig. 3d shows undercoolability with only a kink at xFe ≈ 12.5, not a minimum. The Conclusions state that 'All of these characteristics develop minima at concentration corresponding to i-phase stoichiometry', which overstates the reported data. The claims should be restricted to the Cu cross-section, or the text should explicitly characterize the Fe cross-section as showing monotonic increase and a kink.
[§3, Fig. 3] The lines of equal viscosity T_visc(x) are constructed using a reference viscosity of 7.5×10^-7 m²/s taken from the i-phase near its melting point, and the text states that most melts have approximately this same viscosity at their own melting points. Consequently, the observed coincidence T_visc(x) ≈ Tm(x) is largely a consequence of the construction rather than an independent physical finding. The claim that this coincidence supports structural heredity between liquid and solid is therefore over-interpreted and should be reframed as a restatement of the near-constancy of viscosity at the liquidus, not as new evidence.
[§4, Fig. 7 caption and text] The only undercooled-liquid AIMD simulation (Al52Cu25.5Fe22.5 at 1000 K) is explicitly described as not equilibrated, having been cooled from 1600 K over 10,000 fs and relaxed for only 5,000 fs. This is the sole direct simulation evidence connecting SRO to the undercooled state from which solidification begins. Since the central argument requires that SRO changes near the i-phase stoichiometry affect the initial stage of solidification, the conclusion rests on a non-equilibrium simulation of a single off-stoichiometry composition. Equilibrated undercooled-structure data, or at least a clear quantitative statement of the relaxation limitations, are needed to support that inference.

minor comments (4)

[Abstract and Highlights] There are several typographical errors: 'udercoolability' should be 'undercoolability', and in the Abstract 'bong-angle distribution function' should be 'bond-angle distribution function'.
[§4, Fig. 7] The text refers to 'Fig. 7(a-d)' twice for two different temperatures (1600 K and 1000 K); the figure actually has panels (a)-(h). The first reference should be to panels (a-d) and the second to panels (e-h).
[§4, undercooling simulation paragraph] The sentence 'A high-temperature configuration of the system at T = 1600 K was cooled down to 10,000fs forandthenrelaxedatthistemperaturefor5,000fs' is grammatically broken and should read 'cooled down to 1000 K for 10,000 fs and then relaxed at this temperature for 5,000 fs'.
[Table 2] The r(Fe-Fe) values in Table 2 vary erratically (2.98, 2.28, 2.23, 2.90, 2.63, 2.34 Å) without a clear trend. The authors note low accuracy for iron-related quantities, but the table should include an explicit statement of estimated uncertainties or a footnote explaining the scatter.

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity; the central SRO-viscosity correlation is independent, with only a minor self-referential choice in the equal-viscosity reference value.

self definitional [Section 3, Fig. 3, equal-viscosity lines]
"In our case, the viscosity of the i-phase near the melting point (7.5⋅10−7 m2/s) is chosen as such characteristic value. ... Tν=ν_ico(x) (the temperature at which the viscosity of the melts studied is equal to the viscosity of the ico-phase near the liquidus temperature) coincides well with the liquidus line for each alloy."

The reference viscosity ν_ico is defined as the viscosity of the i-phase at its own melting point. Therefore, for the i-phase composition x_ico, the defining equation ν(x_ico,T)=ν_ico is solved by T=T_m(x_ico) by construction, up to Arrhenius-fit error. The reported 'coincidence' of the equal-viscosity line with the liquidus at the central composition is thus an identity, not an independent finding. The coincidences at other compositions remain empirical because ν(x,T) is measured there, so the circularity is partial and not load-bearing.

full rationale

The central claim—that viscosity and undercoolability isotherms develop minima near i-phase stoichiometry and that this correlates with a change in chemical short-range order—rests on independent experimental measurements (viscosity by torsional oscillations, undercooling by DTA) and independent AIMD-derived Warren-Cowley parameters. No target result is defined in terms of a fitted constant, and the SRO parameters are not adjusted to reproduce the viscosity data. The only self-referential element is the equal-viscosity line: the reference value is taken from the i-phase at its melting point, so the T_ν = T_m coincidence at the i-phase composition is true by definition, but the raw viscosity and undercooling minima do not depend on this choice. Self-citations in the paper are methodological and contextual, not load-bearing for the central results. The statistical fragility of the 'weakly pronounced minimum' relative to the stated 5% error is a robustness and correctness concern, not a circularity concern.

Assumptions & free parameters 2 free parameters · 8 assumptions · 0 invented entities

The central correlation rests on fitted Arrhenius parameters and a handpicked reference viscosity, plus several standard methodological assumptions in DFT/MD and structural analysis. No genuinely new entities are postulated. The main unproven assumption is that equilibrium liquid SRO is relevant to the undercooled liquid and to nucleation.

free parameters (2)

Arrhenius parameters A_v and E_v for each alloy = A_v = 3.9 to 8.4 x 10^-8 m2/s; E_v = 18.8 to 36.2 kJ/mol (Table 1)
Fitted to measured viscosity temperature curves; all isotherms and equal-viscosity lines in Figs. 2 and 3 are constructed from these fits.
Reference viscosity for equal-viscosity lines = 7.5 x 10^-7 m2/s
Chosen as the i-phase viscosity near its melting point; T_visc(x) is the temperature where each melt reaches this value. This choice makes the coincidence of T_visc with the liquidus partly a restatement of the observation that most melts have similar viscosity at their melting point.

assumptions (8)

domain assumption AIMD with PAW pseudopotentials and PBE exchange-correlation gives accurate liquid structure for Al-Cu-Fe.
All SRO conclusions are extracted from CP2K simulations (Section 2, Methods); systematic DFT errors would shift coordination numbers and Warren-Cowley parameters.
domain assumption Simulations at zero-pressure densities estimated by energy minimization reproduce the experimental melt density.
NVT runs use densities from energy minimization rather than measured densities (Section 2); incorrect density would change RDF peak positions and coordination numbers.
domain assumption The damped torsional vibration method measures the true kinematic viscosity of the melt.
Viscosity data underlying all isotherms come from this method with corundum crucibles and an Al2O3 cover (Section 2); wall effects and surface films could bias values.
domain assumption Viscosity follows the Arrhenius law over the measured temperature range.
Eq. (1) is fitted to all alloys and used to construct isotherms and equal-viscosity lines; deviations from Arrhenius behavior would change the concentration dependencies.
domain assumption Coordination numbers defined by integrating partial RDFs to their first minima give reliable Warren-Cowley parameters.
Z_i-j and alpha_i-j in Tables 2 and 3 depend on this cutoff convention (Section 3); Fe partial RDFs are acknowledged as least accurate.
ad hoc to paper Equilibrium melt structure 100 K above the liquidus is a meaningful proxy for the solidification-relevant liquid.
The paper compares equilibrium simulations to i-phase solid and to undercooling experiments, but nucleation begins from undercooled liquid; the single non-equilibrated undercooled run (Fig. 7) is not sufficient support.
domain assumption Voronoi indices and bond orientational order with fixed coordination number 12 correctly classify local order in the melts.
The conclusion that perfect icosahedra are almost absent relies on these classifications (Section 4).
domain assumption Known i-phase stoichiometry around Al62Cu25.5Fe12.5 is the correct reference composition.
The choice of the two concentration cross-sections and the identification of "i-phase composition" depend on the established Al-Cu-Fe phase diagram (Introduction, Refs. [24,26]).

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Pith. "Pith review of Al-Cu-Fe alloys: the relationship between the quasicrystal and its melt." pith.science (2026). https://pith.science/paper/66UVMERB

@misc{pith2026190803931,
  author       = {Pith},
  title        = {Pith review of: Al-Cu-Fe alloys: the relationship between the quasicrystal and its melt},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/66UVMERB}},
  note         = {Machine review of arXiv:1908.03931}
}

read the original abstract

Understanding the mechanisms which relate properties of liquid and solid phases is crucial for fabricating new advanced solid materials, such as glasses, quasicrystals and high-entropy alloys. Here we address this issue for quasicrystal-forming Al-Cu-Fe alloys which can serve as a model for studying microscopic mechanisms of quasicrystal formation. We study experimentally two structural-sensitive properties of the liquid -- viscosity and undercoolability -- and compare results with \textit{ab initio} investigations of short-range order (SRO). We observe that SRO in Al-Cu-Fe melts is polytetrahedral and mainly presented by distorted Kasper polyhedra. However, topologically perfect icosahedra are almost absent an even stoichiometry of icosahedral quasicrystal phase that suggests the topological structure of local polyhedra does not survive upon melting. It is shown that the main features of interatomic interaction in Al-Cu-Fe system, extracted from radial distribution function and bong-angle distribution function, are the same for both liquid and solid states. In particular, the system demonstrates pronounced repulsion between Fe and Cu as well as strong chemical interaction between Fe and Al, which are almost concentration-independent. We argue that SRO and structural-sensitive properties of a melt may serve as useful indicators of solid phase formation. In particular, in the concentration region corresponding to the composition of the icosahedral phase, a change in the chemical short-range order is observed, which leads to minima on the viscosity and udercoolability isotherms and has a noticeable effect on the initial stage of solidification.

Figures

Figures reproduced from arXiv: 1908.03931 by the authors.

**Figure 1.** Typical snapshots of atom distribution in Al68.7Cu25.5Fe5.8 (a) and Al52Cu25.5Fe22.5 (b) melts obtained by ab initio molecular dynamics simulations. Here Al, Cu and Fe are colored green, blue and red, respectively. DTA plots (thermograms) were obtained in heating mode at the rate of 20 K/min to the selected melt temperature and subsequent cooling, after 20 minutes exposure at maximum temperature. The temperatures of… view at source ↗

**Figure 3.** (a,b) Concentration dependencies of melting points [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** The concentration behavior of Warren-Cowley SRO parameters for Al-Cu-Fe melts extracted from ab initio data. crease of viscosity (Fig. 2b). An increase of the temperature leads to a weakening of the concentration dependence of the viscosity. However, the main features of () dependence remain the same up to 1673 K (Fig. 2a, b) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 6.** Figure 6: Detailed comparison of partial RDFs and partial coordinate dependent coordination numbers at different concentrations. Thus, near the melting point, viscosity of most alloys investigated has approximately the same value 7.5⋅10−7 2∕. Moreover, concentration dependenci…

**Figure 7.** Figure 7: Local orientational order of the Al52Cu25.5Fe22.5 alloy on the 4−6 plane. Bond orientational order parameters (BOOPs) were calculated via 12 nearest neighbours for Al, Cu and Fe-centered atoms. Points on the pictures correspond to the 4 − 6 values for each atom; (4 , 6…

**Figure 8.** Figure 8: Bond-angle distribution function for Al-Cu-Fe melts extracted from AIMD data. (BOOPs), which are widely used in structural analysis of condensed matter systems [72, 63, 73, 74, 75]. Detailed description of the method can be found in [76]. Briefly, we calculate the rot…

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