DOI: 10.1063/1.4935467. An anisotropic model for the minimum thermal conductivity

An anisotropic model for the minimum thermal conductivity

10.1063/1.4935467

Crossref journal-article

AIP Publishing

Applied Physics Letters (317)

Abstract

The Cahill-Pohl/Einstein model of minimum phonon thermal conductivity (κmin), which assumes isotropic material properties, is widely successful as the lower limit for fully dense amorphous and disordered materials. However, measurements of disordered highly anisotropic layered WSe2 [Chiritescu et al., Science 315, 351 (2007)] fall below the isotropic κmin limit by at least a factor of four. Here, we generalize the isotropic κmin to be anisotropic, suitable for both layered and chain-like materials with any anisotropy ratio. We obtain compact algebraic expressions in limiting temperature regimes for heat transfer along both c-axis (κmin−c) and ab-plane (κmin−ab). Applying this framework to the disordered layered WSe2 with no free parameters brings the theoretical κmin−c back in line with the experimental results. The anisotropic corrections result from both a phonon focusing effect and a first Brillouin zone truncation effect.

Bibliography

Chen, Z., & Dames, C. (2015). An anisotropic model for the minimum thermal conductivity. Applied Physics Letters, 107(19).

Authors 2

Zhen Chen (first)
Chris Dames (additional)

References 24 Referenced 32

10.1126/science.1068609 / Science (2002)
10.1126/science.285.5428.703 / Science (1999)
10.1103/PhysRevB.48.12581 / Phys. Rev. B (1993)
10.1126/science.1136494 / Science (2007)
10.1103/PhysRevB.46.6131 / Phys. Rev. B (1992)
{'key': '2023061720084332500_c6', 'first-page': '679', 'volume': '35', 'year': '1911', 'journal-title': 'Ann. Phys.'} / Ann. Phys. (1911)
10.1103/PhysRev.75.972 / Phys. Rev. (1949)
10.1029/JB079i005p00703 / J. Geophys. Res. (1974)
{'key': '2023061720084332500_c9', 'first-page': '1', 'volume-title': 'Solid State Physics', 'author': 'Seitz', 'year': '1979'} / Solid State Physics by Seitz (1979)
{'edition': '7th ed.', 'volume-title': 'Introduction to Solid State Physics', 'year': '1996', 'key': '2023061720084332500_c10'} / Introduction to Solid State Physics (1996)
10.1021/acs.chemmater.5b01509 / Chem. Mater. (2015)
10.1103/PhysRevB.87.125426 / Phys. Rev. B (2013)
10.1063/1.4773372 / Appl. Phys. Lett. (2013)
{'volume-title': 'Electrons and Phonons', 'year': '1960', 'key': '2023061720084332500_c14'} / Electrons and Phonons (1960)
10.1063/1.2822891 / Appl. Phys. Lett. (2007)
10.1103/PhysRevB.80.180302 / Phys. Rev. B (2009)
10.1103/PhysRevB.91.085206 / Phys. Rev. B (2015)
See supplementary material at http://dx.doi.org/10.1063/1.4935467 for detailed solution of Eq. 2, derivation and evaluation of Eq. 3, comparison to a prior anisotropic modeling work, and general but lengthy expressions for high T limits.
{'volume-title': 'Imaging Phonons: Acoustic Wave Propagation in Solids', 'year': '1998', 'key': '2023061720084332500_c19'} / Imaging Phonons: Acoustic Wave Propagation in Solids (1998)
10.1103/PhysRevB.35.6195 / Phys. Rev. B (1987)
{'volume-title': 'Properties of Materials: Anisotropy, Symmetry, Structure', 'year': '2005', 'key': '2023061720084332500_c21'} / Properties of Materials: Anisotropy, Symmetry, Structure (2005)
{'volume-title': 'Acoustic Fields and Waves in Solids', 'year': '1973', 'key': '2023061720084332500_c22'} / Acoustic Fields and Waves in Solids (1973)
10.1103/PhysRevB.16.801 / Phys. Rev. B (1977)
{'volume-title': 'Adv. Mater.', 'key': '2023061720084332500_c24', 'article-title': 'Self-passivation of point defects: Effects of high-energy particle irradiation on elastic modulus of multilayer graphene'} / Adv. Mater. / Self-passivation of point defects: Effects of high-energy particle irradiation on elastic modulus of multilayer graphene

Dates

Type	When
Created	9 years, 9 months ago (Nov. 10, 2015, 1 p.m.)
Deposited	2 years, 2 months ago (June 17, 2023, 4:08 p.m.)
Indexed	3 weeks, 1 day ago (July 30, 2025, 7:04 a.m.)
Issued	9 years, 9 months ago (Nov. 9, 2015)
Published	9 years, 9 months ago (Nov. 9, 2015)
Published Online	9 years, 9 months ago (Nov. 9, 2015)
Published Print	9 years, 9 months ago (Nov. 9, 2015)

Funders 1

Army Research Office 10.13039/100000183
Region: Americas
gov (National government)
Labels5
1. U.S. Army Research Office
2. United States Army Research Office
3. U.S. Army Research Laboratory's Army Research Office
4. ARL's Army Research Office
5. ARO

BibTeX

@article{Chen_2015, title={An anisotropic model for the minimum thermal conductivity}, volume={107}, ISSN={1077-3118}, url={http://dx.doi.org/10.1063/1.4935467}, DOI={10.1063/1.4935467}, number={19}, journal={Applied Physics Letters}, publisher={AIP Publishing}, author={Chen, Zhen and Dames, Chris}, year={2015}, month=nov }

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  "abstract": "<jats:p>The Cahill-Pohl/Einstein model of minimum phonon thermal conductivity (\u03bamin), which assumes isotropic material properties, is widely successful as the lower limit for fully dense amorphous and disordered materials. However, measurements of disordered highly anisotropic layered WSe2 [Chiritescu et al., Science 315, 351 (2007)] fall below the isotropic \u03bamin limit by at least a factor of four. Here, we generalize the isotropic \u03bamin to be anisotropic, suitable for both layered and chain-like materials with any anisotropy ratio. We obtain compact algebraic expressions in limiting temperature regimes for heat transfer along both c-axis (\u03bamin\u2212c) and ab-plane (\u03bamin\u2212ab). Applying this framework to the disordered layered WSe2 with no free parameters brings the theoretical \u03bamin\u2212c back in line with the experimental results. The anisotropic corrections result from both a phonon focusing effect and a first Brillouin zone truncation effect.</jats:p>",
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