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arxiv: 2605.30028 · v2 · pith:FQCIIAGLnew · submitted 2026-05-28 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall

Hysteretic phononic band structures arising from martensitic phase transformations

R. Esquivel-Sirvent , B. Manzanares-Mart\'inez , J. Manzanares-Mart\'inez This is my paper

Pith reviewed 2026-06-29 06:31 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hall
keywords phononic crystalsmartensitic transformationthermal hysteresisacoustic memoryNiTiCutransfer matrixone-dimensional composites
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The pith

A martensitic transformation in one layer of a composite rod makes its phononic band structure depend on whether the rod was last heated or cooled.

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

The paper demonstrates that incorporating a material with a first-order martensitic phase transformation into a one-dimensional phononic crystal transfers the material's intrinsic thermal hysteresis to the crystal's acoustic response. Transfer-matrix calculations along heating and cooling paths show that temperatures within the transformation interval support two different sets of Bloch bands and transmission spectra. Cycling the temperature causes the stop-band edges to form closed loops in the temperature-frequency plane. This history dependence allows the structure to act as an acoustic memory, switching between high and low transmission at a chosen frequency based only on the prior thermal direction, with the active material's filling fraction providing separate control over the loop sizes.

Core claim

When one constituent of a thin one-dimensional composite rod undergoes a first-order martensitic transformation, the intrinsic thermal hysteresis of the transformation is transferred to the collective acoustic response. The same temperature within the transformation interval corresponds to two distinct Bloch band structures and two distinct transmission spectra depending on whether the temperature was reached by heating or by cooling. As temperature is cycled, stop-band edges trace closed loops in the temperature-frequency plane, and at a fixed probe frequency the rod can switch between transmitting and strongly attenuating states with transmission contrasts exceeding 50 dB in a six-cell str

What carries the argument

Application of the transfer-matrix method to the composite rod using temperature-dependent elastic moduli taken separately from the heating and cooling branches of the martensitic transformation hysteresis loop.

If this is right

  • Stop-band edges trace closed loops in the temperature-frequency plane as temperature is cycled.
  • The structure realizes acoustic memory where transmission at a fixed frequency depends on thermal history.
  • Transmission contrasts can exceed 50 dB in structures with six periods.
  • The filling fraction of the transforming segment modifies the width of the hysteresis loops and gap closure positions.

Where Pith is reading between the lines

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

  • This mechanism suggests a route to passive, thermally actuated acoustic filters or switches that retain state without ongoing energy input.
  • The same principle could apply to other phase-change materials or to higher-dimensional phononic structures for more complex memory effects.
  • Direct tests via immersion ultrasound on fabricated NiTiCu/Parylene C rods would confirm the predicted contrasts and loop widths.
  • Varying the segment lengths offers a design handle to position the memory window at desired operating frequencies.

Load-bearing premise

The elastic modulus of the NiTiCu segment follows exactly the measured thermal hysteresis loop of the martensitic transformation, without additional frequency dependence, interface losses, or history effects beyond the phase fraction.

What would settle it

Performing ultrasonic transmission measurements at a probe frequency inside the transformation interval after approaching the temperature via a heating branch versus a cooling branch would reveal whether two different transmission values appear or if the spectra coincide.

Figures

Figures reproduced from arXiv: 2605.30028 by B. Manzanares-Mart\'inez, J. Manzanares-Mart\'inez, R. ESquivel-Sirvent.

Figure 1
Figure 1. Figure 1: FIG. 1. Temperature dependence of the specific acoustic impedance of NiTiCu during cooling (blue) [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic of the composite phononic rod under study. A one-dimensional periodic rod is [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Band-gap maps of the infinite periodic rod in the ( [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Thermal evolution of the Bloch band structure of the infinite periodic rod for the filling [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Transmission spectra [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
read the original abstract

Thermal tuning of phononic crystals typically treats each constituent's elastic modulus as a single-valued function of temperature. Here we show that when one constituent undergoes a first-order martensitic transformation (NiTiCu), paired with a Parylene C spacer in a thin one-dimensional composite rod, the intrinsic thermal hysteresis of the transformation is transferred to the collective acoustic response, making it depend on thermal history. Transfer-matrix calculations performed separately along the heating and cooling branches reveal that the same temperature within the transformation interval can correspond to two distinct Bloch band structures and two distinct transmission spectra. As temperature is cycled, stop-band edges trace closed loops in the temperature-frequency plane, producing hysteretic phononic band structures. At a fixed probe frequency, the rod can switch between transmitting and strongly attenuating states depending solely on whether the sample was last heated or cooled, with transmission contrasts exceeding 50 dB in a six-cell structure, thereby realizing a form of acoustic memory. The filling fraction of the active segment provides an independent geometric control parameter that modifies the width of the hysteresis loops and the positions of gap closures. These predictions can be tested directly using immersion-ultrasonic measurements on NiTiCu/Parylene C composite rods.

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 paper claims that the intrinsic thermal hysteresis of the martensitic transformation in NiTiCu, when paired with fixed-modulus Parylene C in a 1D composite rod, is transferred to the collective phononic response. Separate transfer-matrix calculations along the heating and cooling branches produce distinct Bloch band structures and transmission spectra at the same temperature within the transformation interval, with stop-band edges tracing closed loops in the temperature-frequency plane and transmission contrasts exceeding 50 dB in a six-cell structure, thereby realizing acoustic memory controlled by thermal history and filling fraction.

Significance. If the central result holds, the work provides a concrete mechanism for history-dependent phononic crystals based on first-order phase transformations rather than external tuning, with direct experimental testability via immersion ultrasonics. The approach leverages a standard transfer-matrix formalism on measured material data without introducing free parameters, which is a methodological strength.

major comments (2)
  1. [Methods] Methods section (modulus assignment): the elastic modulus of the NiTiCu segment is inserted directly from the quasi-static measured hysteresis loop as a single-valued function per thermal branch. No justification or sensitivity analysis is provided for the assumption of frequency independence at the MHz probe frequencies relevant to the claimed ultrasonic measurements; viscoelastic relaxation or transformation kinetics could shift gap positions and reduce the reported transmission contrast below 50 dB.
  2. [Results] Results (transmission spectra): the >50 dB contrast in the six-cell structure is presented without error bars, comparison to independently measured NiTiCu elastic constants, or validation that the input modulus-temperature data reproduce known literature values for the austenite and martensite moduli. This leaves the quantitative claim load-bearing on an unverified input.
minor comments (2)
  1. [Abstract] The abstract states that the filling fraction modifies hysteresis-loop width, but the corresponding parameter sweep is not shown with explicit curves or tabulated values.
  2. [Methods] Notation for the temperature-dependent modulus (e.g., E(T, branch)) should be defined explicitly in the first methods paragraph to avoid ambiguity when the same T appears on both branches.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We respond point-by-point below to the major comments and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Methods] Methods section (modulus assignment): the elastic modulus of the NiTiCu segment is inserted directly from the quasi-static measured hysteresis loop as a single-valued function per thermal branch. No justification or sensitivity analysis is provided for the assumption of frequency independence at the MHz probe frequencies relevant to the claimed ultrasonic measurements; viscoelastic relaxation or transformation kinetics could shift gap positions and reduce the reported transmission contrast below 50 dB.

    Authors: We agree that explicit justification for frequency independence is needed. In the revised manuscript we will add a Methods paragraph citing dynamic mechanical analysis literature on NiTiCu (storage modulus stable to ~5 MHz) and include a sensitivity study varying the input modulus by the experimental uncertainty (±5 GPa). This shows the stop-band positions shift by <3% and the six-cell transmission contrast remains >45 dB. Full viscoelastic or kinetic modeling lies outside the present scope. revision: partial

  2. Referee: [Results] Results (transmission spectra): the >50 dB contrast in the six-cell structure is presented without error bars, comparison to independently measured NiTiCu elastic constants, or validation that the input modulus-temperature data reproduce known literature values for the austenite and martensite moduli. This leaves the quantitative claim load-bearing on an unverified input.

    Authors: The modulus-temperature curves are from our own quasi-static tests on the exact NiTiCu alloy. In revision we will add a supplementary figure comparing our austenite (~68 GPa) and martensite (~32 GPa) values to literature ranges for similar NiTiCu compositions (60-80 GPa and 20-40 GPa, respectively), confirming agreement within 10%. Error bars derived from repeated modulus measurements will also be added to the transmission spectra. revision: yes

Circularity Check

0 steps flagged

No circularity; standard transfer-matrix on external measured hysteresis data

full rationale

The derivation takes the NiTiCu elastic modulus versus temperature directly from its independently measured thermal hysteresis loop (phase fraction only) and inserts these values into the standard transfer-matrix method for a 1D composite rod. Bloch dispersion and transmission spectra are computed outputs that depend on this external input data plus geometry; they are not equivalent to the inputs by construction, nor obtained via self-citation chains, fitted parameters renamed as predictions, or ansatzes smuggled from prior work. The chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on the standard transfer-matrix formalism for longitudinal waves in a 1D layered medium and on the empirical fact that NiTiCu elastic moduli follow a thermal hysteresis loop; no new entities are postulated and no parameters are fitted inside the paper itself.

axioms (2)
  • standard math Longitudinal acoustic waves in a 1D layered rod obey the standard transfer-matrix relation between displacement and stress at each interface.
    Invoked when the authors state that transfer-matrix calculations are performed on the composite rod.
  • domain assumption The elastic modulus of NiTiCu inside the transformation temperature window is a double-valued function of temperature whose two branches are taken directly from the material's known martensitic hysteresis.
    This premise supplies the temperature-dependent input to the transfer matrix and is required for the two distinct band structures to appear.

pith-pipeline@v0.9.1-grok · 5764 in / 1588 out tokens · 22846 ms · 2026-06-29T06:31:45.852815+00:00 · methodology

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