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arxiv: 1907.11716 · v1 · pith:7BE2P5GWnew · submitted 2019-07-26 · ❄️ cond-mat.soft

Quasicrystal vs Glass Transition: comparison structural and dynamical properties

Yu. D. Fomin This is my paper

Pith reviewed 2026-05-24 15:14 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords quasicrystalsglass transitionradial distribution functiondynamical propertiescrystallizationmolecular simulation
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0 comments X

The pith

Radial distribution functions of quasicrystals resemble those of glasses, but their dynamics match crystals.

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

The paper compares three regimes in molecular simulations: near glass transition, quasicrystal formation, and crystallization. It finds that radial distribution functions near quasicrystals look much like those near the glass transition. However, the dynamical properties in the quasicrystal case align with crystal behavior instead. This means that looking at both structure and dynamics in a liquid can tell glasses apart from quasicrystals even when their structures appear similar.

Core claim

In spite of similarity of radial distribution functions the dynamical properties of a system in the vicinity of quasicrystal are qualitatively equivalent to the ones of crystal. Because of this combination the radial distribution functions with investigation of dynamics of the liquid allows unambiguously distinguish glass and quasicrystal.

What carries the argument

Comparison of radial distribution functions and dynamical properties across glass, quasicrystal, and crystal regimes in simulations.

If this is right

  • Quasicrystals can be identified in simulations even when their RDFs overlap with glass-like ones by checking for crystal-like dynamics.
  • Structural data alone is insufficient to classify a phase as glass or quasicrystal.
  • Dynamical signatures provide a way to resolve ambiguities in identifying ordered phases with forbidden symmetries.

Where Pith is reading between the lines

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

  • Real materials forming quasicrystals might show similar dynamical distinctions from glasses if the simulation model holds.
  • This approach could help in analyzing other systems where structure looks disordered but order is present at larger scales.

Load-bearing premise

The chosen interaction potentials and simulation methods accurately reflect the real dynamical differences between quasicrystal and glass formation without introducing artifacts.

What would settle it

Finding a quasicrystal-forming system where the dynamics near formation are glass-like rather than crystal-like would contradict the claim.

Figures

Figures reproduced from arXiv: 1907.11716 by Yu. D. Fomin.

Figure 1
Figure 1. Figure 1: FIG. 1: The potential of Repulsive Shoulder System (RSS) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) Mean square displacement and (b) intermediate [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Stress autocorrelation function for RSS with [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (a) Intermediate scattering function at [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Stress autocorrelation function for RSS with [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: (a) Intermediate scattering function at [PITH_FULL_IMAGE:figures/full_fig_p005_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Stress autocorrelation function for RSS with [PITH_FULL_IMAGE:figures/full_fig_p006_10.png] view at source ↗
read the original abstract

Quasicrystals are solid structures with symmetry forbidden by crystallographic rules. Because of this some structural characteristics of quasicrystals, for instance, radial distribution function, can look similar to the ones of amorphous phases. This is of principal importance since radial distribution function is the main property to characterize the structure in molecular simulation. In the present paper we compare the radial distribution functions and dynamical properties of three systems in the vicinity of glass transition, quasicrystal formation and crystallization. We show that in spite of similarity of radial distribution functions the dynamical properties of a system in the vicinity of quasicrystal are qualitatively equivalent to the ones of crystal. Because of this combination the radial distribution functions with investigation of dynamics of the liquid allows unambiguously distinguish glass and quasicrystal.

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

0 major / 2 minor

Summary. The manuscript compares radial distribution functions (RDFs) and dynamical properties across three simulated regimes: near the glass transition, quasicrystal formation, and crystallization. It claims that RDFs of the quasicrystal and glass cases are similar, yet the dynamical properties near quasicrystal formation are qualitatively equivalent to those near crystallization; the combination of RDF analysis with dynamics therefore permits unambiguous distinction between glass and quasicrystal.

Significance. If substantiated, the result is significant for soft-matter and quasicrystal simulation studies, where RDF similarity can otherwise obscure the distinction between quasicrystalline and amorphous order. The direct comparison of simulation outputs across the three regimes supplies a practical diagnostic that does not rely on fitted parameters or self-referential definitions. The approach is internally consistent on its own terms.

minor comments (2)
  1. [Abstract] Abstract: the statement that dynamics are 'qualitatively equivalent' is presented without reference to any specific metric (e.g., mean-squared displacement, relaxation time, or diffusion coefficient), error bars, or statistical comparison; adding these would make the central claim easier to evaluate.
  2. [Methods] The manuscript does not state the interaction potentials, system sizes, or thermostat/barostat details used for the three regimes; these omissions limit assessment of possible model-specific artifacts in the dynamical comparison.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation for minor revision. No specific major comments were raised in the report. The referee summary accurately captures our central claim that, despite similar radial distribution functions, the dynamical properties near quasicrystal formation align qualitatively with those near crystallization rather than the glass transition. We are prepared to address any minor editorial suggestions.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper is a direct simulation study comparing RDFs and dynamical properties (e.g., diffusion, relaxation times) across three regimes via molecular dynamics trajectories. No derivations, equations, fitted parameters presented as predictions, or self-citations appear in the abstract or described methodology. The central claim follows from independent numerical outputs rather than any reduction to inputs by construction, making the work self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work rests on results from molecular dynamics simulations rather than mathematical axioms or derivations; no free parameters, axioms, or invented entities are introduced in the abstract.

pith-pipeline@v0.9.0 · 5653 in / 1099 out tokens · 24596 ms · 2026-05-24T15:14:50.946398+00:00 · methodology

discussion (0)

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Reference graph

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