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REVIEW 3 major objections 5 minor 6 references

Boson peak and medium-range elastic heterogeneity in calcium silicate hydrate probed by terahertz spectroscopy and low-temperature calorimetry

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read This paper establishes that calcium silicate hydrate, the binding phase of concrete, exhibits a boson peak near 1 THz—detected independently by terahertz spectroscopy and low-temperature calorimetry—and that the peak's parameters yield a qu

desk verdict A solid THz dataset and an overreaching cross-validation claim: the boson peak in C-S-H is real, but calorimetry does not independently place it at 1 THz. read the letter →

arxiv 2607.14764 v1 pith:PVIAGOPS submitted 2026-07-16 cond-mat.mtrl-sci cond-mat.dis-nn

Xiangyu Li , Ying Chen , Jipeng Luo , Ya Chen , Linhao Wang , Lidan Tian , Gan Ding , Zeyu Lu
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Zhangli Hu Biqin Dong Yue Li Zongjin Li
This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.dis-nn
keywords bosonpeakcalciumsilicatehydrateterahertztime-domainspectroscopylow-temperatureheatcapacityelasticheterogeneityCa/Siratiomedium-rangeordervibrationaldensityofstates
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

This paper aims to show that calcium silicate hydrate (C-S-H)—the phase that binds concrete together—carries the same low-frequency vibrational anomaly, the boson peak, that is universal in glasses, and that this anomaly can be measured directly in cement science for the first time. Using terahertz spectroscopy and low-temperature calorimetry on synthetic C-S-H samples with five calcium-to-silicon ratios, the authors locate the peak near 1 THz, extract from it a nanometer-scale correlation length, and derive a parameter γ that quantifies how strongly the stiffness fluctuates from place to place on the medium range. If correct, this gives cement researchers a quantitative handle on the elastic heterogeneity that controls creep and thermal transport, and it opens the same probe to the amorphous supplementary materials used in low-carbon cements.

What carries the argument

The central object is the boson peak, defined as the broad hump in the reduced vibrational density of states g(ω)/ω² (or in the frequency-normalized dielectric loss ε''(ν)/ν) that signals an excess of low-frequency modes beyond the Debye prediction. The paper extracts it from terahertz spectra using a damped harmonic oscillator plus power-law background, and from heat capacity via the Cp/T³ hump, then interprets the peak through the spatially heterogeneous elasticity picture: a self-consistent Born approximation in which the dimensionless variance γ of shear-modulus fluctuations controls both the peak shape and the phonon scattering rate. The mapping from frequency to length, ξ = vt/(2πν0),

What would settle it

Measure the vibrational density of states of the same five samples directly by inelastic neutron scattering. If the maximum of g(ω)/ω² is not near the terahertz peak frequency for at least four of the five compositions, the paper's central frequency assignment—and the calorimetric shift factor that supports it—fails.

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Extended reading notes

Core claim

The paper establishes that C-S-H, the binding phase of hardened cement, displays a boson peak—an excess of low-frequency vibrational states over the Debye prediction—located near 1 THz, detected independently by terahertz time-domain spectroscopy and low-temperature heat-capacity measurements on synthetic samples spanning Ca/Si = 0.5–1.7. After correction for crystalline impurities, both probes place the peak at ~1 THz; the THz peak height and the calorimetric Cp/T3 hump diverge in intensity with composition, revealing that the apparent strongest peak at Ca/Si ≈ 1.0 reflects the most coherent, least damped modes rather than the largest number of excess modes. The peak parameters yield a medi

Load-bearing premise

The entire dual-probe agreement rests on the assumption that the factor of 4–5 used to convert the calorimetric peak temperature into a frequency—borrowed from melt-quenched silicate glasses—also applies to the heavily damped, water-bearing C-S-H; if that factor is different, calorimetry alone puts the peak at 0.14–0.24 THz rather than ~1 THz.

Editorial extensions

If this is right

  • If correct, the coherent-potential parameter γ gives the first quantitative, composition-resolved measure of elastic heterogeneity in C-S-H, with γ falling from 0.98 at Ca/Si = 0.5 to 0.48 at Ca/Si = 1.7.
  • The ~1 nm dynamical correlation length (0.3–2 nm under different conventions) fills the gap between the ~0.16 nm Si–O coordination shell and the ~5 nm colloidal packing unit, giving experiment access to medium-range order in C-S-H.
  • The Debye-normalized boson-peak frequency (0.15–0.17) places C-S-H in the same family as modifier-rich silicate glasses, so the low-frequency dynamics of cement's binding phase are governed by the same physics as conventional glass formers.
  • The intensity decoupling at Ca/Si ≈ 1.0—peak height maximum with falling spectral weight—marks a structural crossover between silicate-chain depolymerization and interlayer calcium filling, a composition window relevant to low-carbon blended cements.
  • The dual-probe strategy is transferable to other amorphous solids, including fly ash, slag, and calcined clays used in low-carbon cements, where the boson peak could serve as a structure-based descriptor.

Reading between the lines

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

  • If the link between γ and the energy-barrier distribution holds, terahertz screening of extracted C-S-H could become a faster surrogate for long-term creep testing than mesoscale mechanical methods, since γ is an intrinsic property of the solid phase rather than a packing-scale average.
  • A direct test the paper makes possible but does not run: measure the boson peak of C-S-H at controlled relative humidities to separate framework heterogeneity from the damping contribution of interlayer water, which could let the method work on saturated pastes.
  • Because the measurements are on powders, polarized or oriented-sample terahertz experiments could expose the sheet-vs-interlayer anisotropy of γ—a dimension the orientation-averaged values cannot show, and one the paper explicitly leaves open.
  • The same analysis could be applied to aluminium-substituted C-S-H, where the boson peak might reveal whether aluminium insertion stiffens or disorders the medium-range network—directly relevant to slag and metakaolin blends.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper reports a systematic THz-TDS and low-temperature calorimetry study of the boson peak in synthetic calcium silicate hydrate (C-S-H) across five Ca/Si ratios (0.5–1.7). After Bruggeman effective-medium correction for Ca(OH)2 and CaCO3 impurities, the authors identify a boson-peak feature in the normalized THz dielectric loss at 0.94–1.05 THz via a damped harmonic oscillator fit, and a Cp/T3 excess hump at 7–12 K. They argue that both probes agree on a ~1 THz characteristic frequency after an empirical correction factor, and that the THz oscillator strength S and calorimetric peak height fall monotonically with Ca/Si while the THz peak height S·ν0/Γ is maximal at Ca/Si ≈ 1.0. This decoupling is attributed to a structural crossover between silicate-chain depolymerization and interlayer calcium filling. From the DHO/CPA analyses the authors extract a medium-range dynamical correlation length of ~0.3–2 nm and a coherent-potential elastic-heterogeneity parameter γ that decreases from 0.98 to 0.48 with increasing Ca/Si. The paper concludes that the boson peak provides a dynamical descriptor of medium-range elastic heterogeneity relevant to creep and thermal transport in C-S-H.

Significance. If the central claims hold, this is a valuable contribution: a first systematic dual-probe characterization of the boson peak in C-S-H, with composition-resolved trends that can be confronted by simulations, a forward DHO-to-Cp consistency check that reproduces the calorimetric excess for four of five compositions, explicit falsifiable predictions for creep and SCM reactivity, and a physically plausible mapping between THz spectral parameters and medium-range elastic heterogeneity. The impurity corrections and sensitivity analyses are careful, and the comparison with MD predictions and silicate-glass trends is informative. The main significance is the demonstration that C-S-H behaves like a disordered silicate network with a low-frequency vibrational anomaly near 1 THz, and the suggestion that the CPA parameter γ could serve as a composition-resolved disorder descriptor. However, the strength of the dual-probe 'same frequency' claim and the status of γ as a measured quantity are not yet fully secured, as detailed in the major comments.

major comments (3)
  1. [§4.1, Table 4] The claim that calorimetry independently locates the BP near 1 THz is not secured. The raw conversion f = kB T_BP/h gives 0.14–0.24 THz (Table 4), well below 1 THz. The ×4–5 correction factor is borrowed from ref. [46] for SiO2–Al2O3 and lithium borate glasses, yet §4.1 itself reports composition-dependent ratios ν0/(kB T_BP/h) of 4.3–7.5, showing that the factor is not material-independent. More importantly, Appendix A.1 states that the heat capacity does not uniquely select the Planck form, that 'any asymmetric VDOS sharing the ω4 limit fits comparably,' and that 'the absolute frequency is fixed by THz.' The Planck-like SPM fit is therefore not an independent frequency determination, and the forward DHO→Cp prediction uses the THz-derived DHO parameters as input, testing consistency rather than frequency. Since the abstract and conclusions state that both probes locate the BP near 1 THz
  2. [§4.2, Table 5] The paper presents γ as 'to our knowledge the first experimental measure of this quantity' and as the central composition-resolved descriptor, but γ is a fitted parameter of the CPA/SCBA model applied to the same ε''(ν)/ν spectra used to define the DHO boson peak. The agreement between γ and Γ/ν0 to within ~15% is therefore a correlation between two fits of the same dataset, not an independent validation. This circularity should be addressed explicitly, for example by determining γ from an independent observable (sound velocity, inelastic neutron scattering, or a forward relation with known uncertainty) or by clearly labeling γ as a model-defined effective parameter whose compositional trend, not absolute value, is the claim. As written, the discovery framing in the abstract and conclusions ('coherent-potential elastic-heterogeneity parameter') exceeds what the fitting procedure alone ca
  3. [Table 2] The DHO fit parameters are reported without uncertainties, although the CPA fits in Table 5 carry ± errors. The key intensity-decoupling claim — that S decreases monotonically with Ca/Si while the DHO peak height S·ν0/Γ reaches a maximum at Ca/Si = 1.0 — rests on the relative values of S and Γ across five compositions. Without confidence intervals or a sensitivity analysis covering the fit range (0.5–2.5 THz), the background parameterization, and the fixed frequency choice ν ≈ ν0 for the peak height, it is not possible to assess whether the maximum at Ca/Si = 1.0 is statistically significant. Please add bootstrap or covariance-based error bars and test the non-monotonic trend against reasonable variations of the fit window and background model.
minor comments (5)
  1. [§2.3] The formula n(ν) = 1 + c·Δφ/(2πνd) assumes unwrapped phase. Please state explicitly how phase unwrapping was performed and how its uncertainty propagates into the dielectric loss.
  2. [Table 1 and throughout] The actual Ca/Si ratios of the C-S-H phase (0.54, 0.90, 1.14, 1.46, 1.57) differ from the nominal values (0.5–1.7). The text often refers to nominal ratios without consistently stating that actual values are used. Please define on which numbers the analysis and figures are based.
  3. [§3.4 / Appendix A.1] The forward prediction is described as 'parameter-free' (e.g., 'the most stringent cross-check is parameter-free'), but it uses the THz-derived DHO spectral function as input. The prediction has no adjustable BP frequency, but it is not parameter-free in the literal sense; 'parameter-fixed' or 'no additional adjustable parameters' would be more precise.
  4. [References] Reference [26] appears with inconsistent capitalization ('Li zhanguo') and a 2026 online date; please verify the citation and standardize the author list.
  5. [§4.3, Table 6] The three length conventions (ξ1, ξ2, λIR) are presented as 'order-of-magnitude estimates,' which is appropriately cautious. Please explicitly note in the text that the choice of G = 9 GPa without an error bar affects all three lengths, and consider adding a brief statement on how the uncertainty in G affects the correlation-length conclusions.

Circularity Check

3 steps flagged · score 6.0 of 10

Calorimetric 'independent' BP frequency is anchored to THz ('absolute frequency is fixed by THz') or shifted by a borrowed ×4–5 correction; CPA γ is a same-data reparametrization of the DHO width, so the dual-probe near-1 THz agreement is partly by construction.

  1. self definitional [Section 3.4 (low-temperature heat capacity, Planck soft-mode fit); echoed in Appendix A.1]
    "The heat capacity does not uniquely select the Planck form (any asymmetric VDOS sharing the ω4 limit fits comparably), so the choice rests on physical grounds and the absolute frequency is fixed by THz."

    The calorimetric νBP = 1.13–1.34 THz is, by the paper's own admission, anchored to the THz measurement ('the absolute frequency is fixed by THz'), while the heat capacity alone does not select the model. The claimed agreement of this νBP with the THz DHO ν0 = 0.94–1.05 THz is therefore built into the analysis, yet the abstract presents it as evidence that 'both probes locate the BP near 1 THz.' The raw conversion f = kBTBP/h gives only 0.14–0.24 THz (Table 4), so the ~1 THz calorimetric frequency is not independently determined.

  2. fitted input called prediction [Section 4.1 (Cross-validation of the boson peak: frequency correspondence), Table 4]
    "This direct conversion yields 0.14–0.24 THz, substantially below the ~1 THz THz-TDS peak. ... In binary SiO2–Al2O3 glasses, Ando et al. [46] compared BP frequencies obtained simultaneously by Raman, THz-TDS, and calorimetry and found the calorimetric peak temperature systematically lower by a factor of 4–5. Applying the same empirical correction, the calorimetric frequencies fall in the 0.6–1.2 THz range (Table 4), in reasonable agreement with the THz-TDS values."

    The corrected calorimetric frequencies are obtained by multiplying the raw kB TBP/h values (0.14–0.24 THz) by a factor of 4–5, producing 0.6–1.2 THz, which overlaps the THz DHO values (0.94–1.05 THz). The same section reports that the measured ratios ν0/(kB TBP/h) are 4.3–7.5, so the borrowed correction is essentially the inverse of the very ratio being claimed. The 'strong independent confirmation' of the frequency therefore reduces to the assumed shift factor, not to an independent calorimetric frequency determination.

1 more flagged steps
  1. renaming known result [Section 4.2 (CPA multi-physics superposition fit, Table 5); abstract]
    "Second, γ tracks the phenomenological damping ratio Γ/ν0 from the standard DHO fit (Table 2) to within ~15%, validating the physical correspondence between the two parameterizations."

    The CPA formula in §4.2 has the same DHO resonance form as §2.6.2, with γ occupying the role of the width (damping) parameter in the denominator term (γ·ν/νBP2)2. Since both γ and Γ/ν0 are fitted to the same ε''(ν)/ν spectra, their ~15% agreement is a correlation between two parametrizations of one dataset, not an independent validation. Presenting γ as 'a coherent-potential elastic-heterogeneity parameter' obtained 'from the BP' (abstract) renames the DHO damping ratio under a theory label; its Ca/Si trend is the fit output, not an independently measured quantity.

full rationale

The THz-TDS boson-peak determination is genuine and externally grounded: a broad ε''(ν)/ν feature near 0.94–1.05 THz is directly observed, reproducible, and consistent with the external MD prediction of Abdolhosseini Qomi et al. The calorimetric Cp/T3 hump at 7–12 K is also a real, independent observation of excess low-frequency states. However, the headline dual-probe claim, 'both probes locate the BP near 1 THz,' is only partially secured. The calorimetric side reaches ~1 THz either through the Planck-like SPM fit whose absolute frequency the paper explicitly states is 'fixed by THz' (§3.4), or by applying a borrowed ×4–5 shift to raw frequencies of 0.14–0.24 THz (§4.1, Table 4). In both routes, the ~1 THz calorimetric frequency is anchored or shifted onto the THz value, so the agreement is partly by construction. Appendix A.1 further admits that the heat capacity does not uniquely select the Planck form and that no single VDOS reproduces both the THz lineshape and Cp without a frequency-dependent coupling (q ≈ -0.4), weakening the direct DHO→Cp mapping. The forward DHO→Cp prediction is a genuine parameter-free consistency test against independently measured Cp/T3 data and is not itself circular, but it uses the THz-derived frequency as input and therefore cannot independently determine the frequency. The CPA disorder parameter γ is a fit parameter of the same ε''/ν spectra with the functional role of the DHO width; its agreement with Γ/ν0 is a same-data self-consistency check, and its Ca/Si trend (0.98 to 0.48) is the fit output presented as a new descriptor. Self-citations (preliminary survey [26]; Planck parametrization from co-author Ding et al. [45]) are noted but are not the decisive issue; the explicit THz-anchor is. The compositional trends (S, Γ/ν0, peak-height decoupling at Ca/Si ≈ 1.0), the length-scale estimates, and the creep/thermal predictions retain independent, falsifiable content. Overall: partial circularity of the central dual-probe frequency claim, not a fully forced derivation.

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

The central claims rest on several fitted parameters (DHO and CPA) and on a small number of domain assumptions inherited from glass physics. No new physical entities are postulated. The most fragile input is the borrowed 4–5 calorimetric shift factor and the MD-derived shear modulus used to convert frequency to length.

free parameters (5)
  • DHO parameters ν0, Γ, S, A, p, C = ν0 = 0.94–1.05 THz; Γ = 0.47–0.79 THz; S = 0.016–0.038
    Fitted to ε''(ν)/ν over 0.5–2.5 THz for each Ca/Si; all subsequent claims (peak height, damping, intensity trends, correlation length) use these values.
  • CPA disorder parameter γ (with Abg, s, CBP, CD) = 0.98±0.08 to 0.48±0.07
    Fitted to the same ε''(ν)/ν spectra via the Schirmacher CPA formula; presented as the central physical descriptor though it is an output of the fit.
  • Calorimetric SPM fit parameters (γ_TLS, ΘD, nq/3N, ℓ) = νBP = 1.13–1.34 THz from Planck-like fit
    Four-parameter fit of Cp(T) over 2–30 K; the paper notes non-uniqueness of Einstein models and relies on physical grounds for the Planck form.
  • Empirical calorimetric-to-spectroscopic frequency shift factor = 4–5
    Borrowed from silicate/aluminosilicate glasses to convert Cp/T3 peak temperature to THz; scatter in C-S-H ratios is 4.3–7.5, so applying a fixed 4–5 is an adjustable bridge.
  • Shear modulus G = 9 GPa
    Taken from MD simulation [20] to convert ν0 to correlation length; not measured in this work, ±50% changes ξ by ±22%.
assumptions (5)
  • domain assumption The boson-peak scaling relation ξ = vt/(2πν0) (and Duval variant) applies to C-S-H
    Used in Section 4.3 to convert fitted ν0 into correlation length; the prefactor is non-unique, as the paper itself states.
  • domain assumption Bruggeman effective medium theory correctly retrieves intrinsic C-S-H dielectric function from powder/COC pellets with air voids
    Section 2.5; the correction is stated to shift ν0 by <2% and S by <5%, but EMT geometry is approximate for high-porosity powders.
  • domain assumption The spatially heterogeneous elasticity/CPA description (Schirmacher) is the correct model for C-S-H dielectric loss, so γ is the shear-modulus variance
    Section 4.2; no independent validation that γ extracted from this fit equals the physical elastic heterogeneity.
  • domain assumption The Cp/T3 hump at 7–12 K is the boson-peak excess rather than water/TLS contributions
    Section 3.4 and Appendix A.2 give supporting bounds, but the TLS γ term is non-zero and water contributions are subtracted only by argument, not by direct measurement.
  • ad hoc to paper Empirical factor of 4–5 for calorimetric peak-shift applies to C-S-H
    Section 4.1/Table 4: without it, raw calorimetric frequency is 0.14–0.24 THz, not ~1 THz.

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Pith. "Pith review of Boson peak and medium-range elastic heterogeneity in calcium silicate hydrate probed by terahertz spectroscopy and low-temperature calorimetry." pith.science (2026). https://pith.science/paper/PVIAGOPS

@misc{pith2026260714764,
  author       = {Pith},
  title        = {Pith review of: Boson peak and medium-range elastic heterogeneity in calcium silicate hydrate probed by terahertz spectroscopy and low-temperature calorimetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PVIAGOPS}},
  note         = {Machine review of arXiv:2607.14764}
}
read the original abstract

The boson peak (BP), a universal vibrational anomaly of disordered solids, has been predicted but not systematically characterized in calcium silicate hydrate (C-S-H), the binding phase of hardened cement. Building on a preliminary terahertz survey, we characterize the BP across five Ca/Si ratios (0.5-1.7) using terahertz time-domain spectroscopy (THz-TDS) and low-temperature calorimetry, two probes of vibrational dynamics that complement the static picture of conventional structural methods. After Bruggeman correction for crystalline impurities, both probes locate the BP near 1 THz; they agree on frequency but diverge in intensity. The terahertz integrated spectral weight and the calorimetric Cp/T3 peak both fall monotonically with Ca/Si, whereas the apparent terahertz peak height is maximal at Ca/Si = 1.0, where damping is low and oscillator strength still substantial. This decoupling marks a structural crossover between silicate-chain depolymerization and interlayer calcium filling. From the BP we obtain a medium-range dynamical correlation length of order 1 nm (0.3-2 nm) and a coherent-potential elastic-heterogeneity parameter that decreases from gamma = 0.98 to 0.48 as Ca/Si rises; the Debye-normalized BP frequency (nu_BP/nu_D = 0.15-0.17) places C-S-H within the range reported for silicate glasses. Because gamma governs the distribution of energy barriers for local structural rearrangements, it provides a quantitative, composition-resolved descriptor relevant to the intrinsic creep and thermal transport of C-S-H, linking nanoscale vibrational dynamics to the macroscopic durability of concrete. The dual-probe boson-peak approach is transferable to other amorphous solids, including the supplementary cementitious materials of low-carbon cements.

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Works this paper leans on

6 extracted references · 1 canonical work pages

  1. [4]

    intensity

    Discussion 4.1. Cross-validation of the boson peak: frequency correspondence The two independent probes, THz-TDS and low-temperature calorimetry, detect the BP through fundamentally different physical mechanisms, yet both place the characteristic excitation energy in the same frequency range. To make the comparison quantitative, we convert the Cp/T3 peak ...

    arXiv

  2. [13]

    Universal correlation between boson peak and quasi-localized modes in solids

    Ding G, Duan J, Cai SL, Dai LH, Jiang MQ. Universal correlation between boson peak and quasi-localized modes in solids. Journal of Non-Crystalline Solids. 2025;666:123668. doi:10.1016/j.jnoncrysol.2025.123668 [14] Beltukov YM, Fusco C, Parshin DA, Tanguy A. Boson peak and Ioffe-Regel criterion in amorphous siliconlike materials: The effect of bond directi...

    arXiv 2025

  3. [25]

    Non-Debye excess heat capacity and boson peak of binary lithium borate glasses

    Matsuda Y, Kawaji H, Atake T, et al. Non-Debye excess heat capacity and boson peak of binary lithium borate glasses. Journal of Non-Crystalline Solids. 2011;357(2):534-537. [26] Li zhanguo, Chen Y, Li Y, Li X. Terahertz spectroscopy of calcium silicate hydrate with different Ca/Si ratios. Bulletin of the Chinese Ceramic Society. Published online 2026. doi...

    arXiv 2011

  4. [37]

    Boson Peak

    Li Y, Ding Z, Wang X, Wang X, Han B. Molecular dynamics study on structural characteristics of amorphous C-S-H with different Ca/Si ratios. Journal of the American Ceramic Society. 2025;108(1):e20134. doi:10.1111/jace.20134 [38] Kirkpatrick RJ, Yarger JL, Mcmillan PF, Ping Y, Cong X. Raman spectroscopy of C-S-H, tobermorite, and jennite. Advanced Cement B...

    work page doi:10.1111/jace.20134 2025

  5. [50]

    Acoustic attenuation in glasses and its relation with the boson peak

    Schirmacher W, Ruocco G, Scopigno T. Acoustic attenuation in glasses and its relation with the boson peak. Physical Review Letters. 2007;98(2):025501. doi:10.1103/PhysRevLett.98.025501 [51] Zhang C, François Gygi, Galli G. Strongly Anisotropic Dielectric Relaxation of Water at the Nanoscale. Journal of Physical Chemistry Letters. 2013;4(15):2477-2481. doi...

    arXiv 2007

  6. [62]

    Lower limit to the thermal conductivity of disordered crystals

    Cahill DG, Watson SK, Pohl RO. Lower limit to the thermal conductivity of disordered crystals. Physical Review B Condensed Matter. 1992;46(10):6131. doi:10.1103/PhysRevB.46.6131 [63] Zhou Y, Morshedifard A, Lee J, Qomi MJA. The contribution of propagons and diffusons in heat transport through calcium-silicate-hydrates. Applied Physics Letters. 2017;110(4)...

    arXiv 1992

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Reviewed August 2, 2026 · model on record in the stance chip above.