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Determining Phonon Mean Free Paths from Observations of Quasiballistic Thermal Transport
Abstract
The mean free paths (MFPs) of thermal phonons are mostly unknown in many solids. Recent work indicates that MFPs may be measured using experimental observations of quasiballistic thermal transport, but the precise relationship between the measurements and the MFP distribution remains unclear. Here, we present a method that can accurately reconstruct the MFP distribution from quasiballistic thermal measurements without any assumptions regarding the phonon scattering mechanisms. Our result will enable a substantially improved understanding of thermal transport in many solids, particularly thermoelectrics.
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“Second, within the uncertainty of the measurements, the measured bulk thermal conductivity is in reasonable agreement with the TG data for L = 9.8 μm, indicating that the phonon mean free paths are shorter than ∼9.8/2π∼1.5 μm (ref. 64).”
From Origin of high thermal conductivity in disentangled ultra-high molecular weight polyethylene films: ballistic phonons within enlarged crystals (2022) · cites this paper as [64]
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“The derivative of S r , denoted the kernel, is also shown in Fig. 2(b) and can directly be used to obtain cumulative MFP distribution of an unknown material from experimental measurements of thermal conductivity for different pump sizes with TDTR.19”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [19]
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“The MFP distribution can be reconstructed from these measurements using a method introduced by Minnich provided that the quasiballistic transport in the experiment can be accurately simulated.19”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [19]
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“Previously, this equation was used to find the MFP distribution.19”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [19]
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“Minnich recently introduced a framework in which the MFP distribution of the substrate can be reconstructed from the effective thermal conductivities, as shown in Fig. 2(a)), and a suppression function that describes the difference in heat flux between the quasiballistic and Fourier predictions.19”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [19]
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“This function depends on the experimental geometry and mathematically describes how the heat flux curves in Fig. 1(c) differ from the Fourier's law curve.”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [19]
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“Reconstructing the phonon MFP spectrum [ i.e . ߶ ሺΛሻ or ߙ ሺΛሻ ] from the measured ܭ ሺ ܮ ሻ and the derived ܵ ቀ ஃ ቁ is thus an inverse problem of Eq.(4.14) that involves complex optimization. 203-205”
From Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials (2018) · cites this paper as [203]
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Metadata
- Authors
- Minnich, A. J.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Minnich, A. J.
- ORCID
- Minnich, A. J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-11-13
- Volume
- 109
- Issue
- 20
- Pages
- 205901-205901
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2071546751
- Cited by
- 196
- References
- 22
- Citations by year
- 2026: 3 · 2025: 12 · 2024: 15 · 2023: 10 · 2022: 12 · 2021: 16 · 2020: 10 · 2019: 16 · 2018: 14 · 2017: 17 · 2016: 21 · 2015: 25 · 2014: 17 · 2013: 8
- FWCI
- 7.35
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Physical Sciences › Materials Science › Materials Chemistry › Advanced Thermoelectric Materials and Devices
- Physical Sciences › Engineering › Mechanics of Materials › Thermoelastic and Magnetoelastic Phenomena
- Keywords
- phonon mean free path, thermal conductivity, phonon scattering, thermoelectric materials
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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