Abstract
AbstractCurrent understanding of phonons treats them as plane waves/quasi-particles of atomic vibration that propagate and scatter. The problem is that conceptually, when any level of disorder is introduced, whether compositional or structural, the character of vibrational modes in solids changes, yet nearly all theoretical treatments continue to assume phonons are still waves. For example, the phonon contributions to alloy thermal conductivity (TC) rely on this assumption and are most often computed from the virtual crystal approximation (VCA). Good agreement is obtained in some cases, but there are many instances where it fails—both quantitatively and qualitatively. Here, we show that the conventional theory and understanding of phonons requires revision, because the critical assumption that all phonons/normal modes resemble plane waves with well-defined velocities is no longer valid when disorder is introduced. Here we show, surprisingly, that the character of phonons changes dramatically within the first few percent of impurity concentration, beyond which phonons more closely resemble the modes found in amorphous materials. We then utilize a different theory that can treat modes with any character and experimentally confirm its new insights.
Authors
11
- Hamid Reza Seyf (first)
- Luke Yates (additional)
- Thomas L. Bougher (additional)
- Samuel Graham (additional)
- Baratunde A. Cola (additional)
- Theeradetch Detchprohm (additional)
- Mi-Hee Ji (additional)
- Jeomoh Kim (additional)
- Russell Dupuis (additional)
- Wei Lv (additional)
- Asegun Henry (additional)
References
55
Referenced
82
- Srivastava, G. P. The Physics of Phonons (CRC Press, New York, 1990).
-
Dove, M. T. Introduction to Lattice Dynamics (Cambridge University Press, New York, 1993).
(
10.1017/CBO9780511619885
) - Chen, G. Nanoscale Energy Transport and Conversion: a Parallel Treatment Of Electrons, Molecules, Phonons, And Photons (Oxford University Press, New York, 2005).
-
Lv, W. & Henry, A. Direct calculation of modal contributions to thermal conductivity via Green–Kubo modal analysis. New J. Phys. 18, 013028 (2016).
(
10.1088/1367-2630/18/1/013028
) / New J. Phys. by W Lv (2016) -
Ziman, J. M. Electrons and Phonons (Oxford University Press, New York, 2001).
(
10.1093/acprof:oso/9780198507796.001.0001
) -
Lv, W. & Henry, A. Phonon transport in amorphous carbon using Green–Kubo modal analysis. Appl. Phys. Lett. 108, 181905 (2016).
(
10.1063/1.4948605
) / Appl. Phys. Lett. by W Lv (2016) -
Wei, L. & Asegun, H. Non-negligible contributions to thermal conductivity from localized modes in amorphous silicon dioxide. Sci. Rep. 6, 35720 (2016).
(
10.1038/srep35720
) / Sci. Rep. by L Wei (2016) -
Gordiz, K. & Henry, A. Phonon transport at interfaces: determining the correct modes of vibration. J. Appl. Phys. 119, 015101 (2016).
(
10.1063/1.4939207
) / J. Appl. Phys. by K Gordiz (2016) -
Lv, W. & Henry, A. Examining the validity of the phonon gas model in amorphous materials. Sci. Rep. 6, 37675 (2016).
(
10.1038/srep37675
) / Sci. Rep. by W Lv (2016) -
Allen, P. B., Feldman, J. L., Fabian, J. & Wooten, F. Diffusons, locons and propagons: character of atomic vibrations in amorphous Si. Philos. Mag. B 79, 1715–1731 (1999).
(
10.1080/13642819908223054
) / Philos. Mag. B by PB Allen (1999) -
Tian, Z., Lee, S. & Chen, G. Heat transfer in thermoelectric materials and devices. J. Heat Transf. 135, 061605–061605 (2013).
(
10.1115/1.4023585
) / J. Heat Transf. by Z Tian (2013) -
Cahill, D. G. et al. Nanoscale thermal transport. II. 2003–2012. Appl. Phys. Rev. 1, 011305 (2014).
(
10.1063/1.4832615
) / Appl. Phys. Rev. by DG Cahill (2014) -
Abeles, B. Lattice thermal conductivity of disordered semiconductor alloys at high temperatures. Phys. Rev. 131, 1906–1911 (1963).
(
10.1103/PhysRev.131.1906
) / Phys. Rev. by B Abeles (1963) -
Esfarjani, K., Garg, J. & Chen, G. Modeling heat conduction from first principles. Annu. Rev. Heat Transf. 17, 9–47 (2014).
(
10.1615/AnnualRevHeatTransfer.2014007746
) / Annu. Rev. Heat Transf. by K Esfarjani (2014) -
Feng, T. & Ruan, X. Prediction of spectral phonon mean free path and thermal conductivity with applications to thermoelectrics and thermal management: a review. J. Nanomater. 2014, 206370 (2014).
(
10.1155/2014/206370
) / J. Nanomater. by T Feng (2014) -
Lindsay, L., Broido, D. A. & Reinecke, T. L. Ab initio thermal transport in compound semiconductors. Phys. Rev. B 87, 165201 (2013).
(
10.1103/PhysRevB.87.165201
) / Phys. Rev. B by L Lindsay (2013) -
Tadano, T., Gohda, Y. & Tsuneyuki, S. Anharmonic force constants extracted from first-principles molecular dynamics: applications to heat transfer simulations. J. Phys. Condens. Matter 26, 225402 (2014).
(
10.1088/0953-8984/26/22/225402
) / J. Phys. Condens. Matter by T Tadano (2014) -
Tadano, T. & Tsuneyuki, S. Self-consistent phonon calculations of lattice dynamical properties in cubic SrTiO3 with first-principles anharmonic force constants. Phys. Rev. B 92, 054301 (2015).
(
10.1103/PhysRevB.92.054301
) / Phys. Rev. B by T Tadano (2015) -
Jiawei, Z., Bolin, L. & Gang, C. First-principles calculations of thermal, electrical, and thermoelectric transport properties of semiconductors. Semicond. Sci. Technol. 31, 043001 (2016).
(
10.1088/0268-1242/31/4/043001
) / Semicond. Sci. Technol. by Z Jiawei (2016) -
Wang, X. & Huang, B. Computational study of in-plane phonon transport in Si thin films. Sci. Rep. 4, 6399 (2014).
(
10.1038/srep06399
) / Sci. Rep. by X Wang (2014) -
Cahill, D. G., Watson, S. K. & Pohl, R. O. Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B 46, 6131–6140 (1992).
(
10.1103/PhysRevB.46.6131
) / Phys. Rev. B by DG Cahill (1992) -
Garg, J., Bonini, N., Kozinsky, B. & Marzari, N. Role of disorder and anharmonicity in the thermal conductivity of silicon-germanium alloys: a first-principles study. Phys. Rev. Lett. 106, 045901 (2011).
(
10.1103/PhysRevLett.106.045901
) / Phys. Rev. Lett. by J Garg (2011) -
Shiomi, J., Esfarjani, K. & Chen, G. Thermal conductivity of half-Heusler compounds from first-principles calculations. Phys. Rev. B 84, 104302 (2011).
(
10.1103/PhysRevB.84.104302
) / Phys. Rev. B by J Shiomi (2011) -
Takuru, M., Takuma, S., Takuma, H., Keivan, E. & Junichiro, S. Importance of local force fields on lattice thermal conductivity reduction in PbTe 1−x Se x alloys. Europhys. Lett. 102, 46002 (2013).
(
10.1209/0295-5075/102/46002
) / Europhys. Lett. by M Takuru (2013) -
Katcho, N. A., Mingo, N. & Broido, D. A. Lattice thermal conductivity of (Bi 1−x Sb x)2 Te3 alloys with embedded nanoparticles. Phys. Rev. B 85, 115208 (2012).
(
10.1103/PhysRevB.85.115208
) / Phys. Rev. B by NA Katcho (2012) -
Tamura, S.-i Isotope scattering of dispersive phonons in Ge. Phys. Rev. B 27, 858–866 (1983).
(
10.1103/PhysRevB.27.858
) / Phys. Rev. B by Si Tamura (1983) -
Kundu, A., Mingo, N., Broido, D. A. & Stewart, D. A. Role of light and heavy embedded nanoparticles on the thermal conductivity of SiGe alloys. Phys. Rev. B 84, 125426 (2011).
(
10.1103/PhysRevB.84.125426
) / Phys. Rev. B by A Kundu (2011) -
Li, W., Lindsay, L., Broido, D. A., Stewart, D. A. & Mingo, N. Thermal conductivity of bulk and nanowire Mg2 Si x Sn 1−x alloys from first principles. Phys. Rev. B 86, 174307 (2012).
(
10.1103/PhysRevB.86.174307
) / Phys. Rev. B by W Li (2012) -
Lee, S., Esfarjani, K., Mendoza, J., Dresselhaus, M. S. & Chen, G. Lattice thermal conductivity of Bi, Sb, and Bi-Sb alloy from first principles. Phys. Rev. B 89, 085206 (2014).
(
10.1103/PhysRevB.89.085206
) / Phys. Rev. B by S Lee (2014) -
Liu, W. & Balandin, A. A. Thermal conduction in AlxGa1−xN alloys and thin films. J. Appl. Phys. 97, 073710 (2005).
(
10.1063/1.1868876
) / J. Appl. Phys. by W Liu (2005) -
Tong, T. et al. Suppression of thermal conductivity in InxGa1−xN alloys by nanometer-scale disorder. Appl. Phys. Lett. 102, 121906 (2013).
(
10.1063/1.4798838
) / Appl. Phys. Lett. by T Tong (2013) -
Borca-Tasciuc, T. et al. Thermal conductivity of AlAs0.07Sb0.93 and Al0.9Ga0.1As0.07Sb0.93 alloys and (AlAs)1/(AlSb)11 digital-alloy superlattices. J. Appl. Phys. 92, 4994–4998 (2002).
(
10.1063/1.1506194
) / J. Appl. Phys. by T Borca-Tasciuc (2002) -
Seyf, H. R. & Henry, A. A method for distinguishing between propagons, diffusions, and locons. J. Appl. Phys. 120, 025101 (2016).
(
10.1063/1.4955420
) / J. Appl. Phys. by HR Seyf (2016) -
Biswas, R., Bouchard, A. M., Kamitakahara, W. A., Grest, G. S. & Soukoulis, C. M. Vibrational localization in amorphous silicon. Phys. Rev. Lett. 60, 2280–2283 (1988).
(
10.1103/PhysRevLett.60.2280
) / Phys. Rev. Lett. by R Biswas (1988) -
Gordiz, K. & Henry, A. Interface conductance modal analysis of lattice matched InGaAs/InP. Appl. Phys. Lett. 108, 181606 (2016).
(
10.1063/1.4948520
) / Appl. Phys. Lett. by K Gordiz (2016) -
Gordiz, K. & Henry, A. A formalism for calculating the modal contributions to thermal interface conductance. New. J. Phys. 17, 103002 (2015).
(
10.1088/1367-2630/17/10/103002
) / New. J. Phys. by K Gordiz (2015) -
Lv, W. & Henry, A. Non-negligible contributions to thermal conductivity from localized modes in amorphous silicon dioxide. Sci. Rep. 6, 35720 (2016).
(
10.1038/srep35720
) -
Kim, W. et al. Thermal conductivity reduction and thermoelectric figure of merit increase by embedding nanoparticles in crystalline semiconductors. Phys. Rev. Lett. 96, 045901 (2006).
(
10.1103/PhysRevLett.96.045901
) / Phys. Rev. Lett. by W Kim (2006) -
Kim, W. et al. Cross-plane lattice and electronic thermal conductivities of ErAs:InGaAs∕InGaAlAs superlattices. Appl. Phys. Lett. 88, 242107 (2006).
(
10.1063/1.2207829
) / Appl. Phys. Lett. by W Kim (2006) -
McGaughey, A. J. H. & Kaviany, M. Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation. Phys. Rev. B 69, 094303 (2004).
(
10.1103/PhysRevB.69.094303
) / Phys. Rev. B by AJH McGaughey (2004) -
Balakrishnan, G., Bernhoeft, N. R., Bowden, Z. A., Paul, D. M. & Taylor, A. D. Vibrational anomalies in the superconducting compound La1.85Ba0.15CuO4. Nature 327, 45–47 (1987).
(
10.1038/327045a0
) / Nature by G Balakrishnan (1987) -
Blencowe, M. Quantum physics: photons paired with phonons. Nature 530, 284–285 (2016).
(
10.1038/530284a
) / Nature by M Blencowe (2016) -
Drozdov, A. P., Eremets, M. I., Troyan, I. A., Ksenofontov, V. & Shylin, S. I. Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system. Nature 525, 73–76 (2015).
(
10.1038/nature14964
) / Nature by AP Drozdov (2015) -
Ernst, G., Broholm, C., Kowach, G. R. & Ramirez, A. P. Phonon density of states and negative thermal expansion in ZrW2O8. Nature 396, 147–149 (1998).
(
10.1038/24115
) / Nature by G Ernst (1998) -
Keppens, V. et al. Localized vibrational modes in metallic solids. Nature 395, 876–878 (1998).
(
10.1038/27625
) / Nature by V Keppens (1998) -
Lanzara, A. et al. Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors. Nature 412, 510–514 (2001).
(
10.1038/35087518
) / Nature by A Lanzara (2001) -
LeRoy, B. J., Lemay, S. G., Kong, J. & Dekker, C. Electrical generation and absorption of phonons in carbon nanotubes. Nature 432, 371–374 (2004).
(
10.1038/nature03046
) / Nature by BJ LeRoy (2004) -
Mook, H. A. & Dogan, F. Charge fluctuations in YBa2Cu3O7-x high-temperature superconductors. Nature 401, 145–148 (1999).
(
10.1038/43629
) / Nature by HA Mook (1999) -
Riedinger, R. et al. Non-classical correlations between single photons and phonons from a mechanical oscillator. Nature 530, 313–316 (2016).
(
10.1038/nature16536
) / Nature by R Riedinger (2016) -
Esfarjani, K. & Stokes, H. T. Method to extract anharmonic force constants from first principles calculations. Phys. Rev. B 77, 144112 (2008).
(
10.1103/PhysRevB.77.144112
) / Phys. Rev. B by K Esfarjani (2008) -
Powell, D., Migliorato, M. A. & Cullis, A. G. Optimized Tersoff potential parameters for tetrahedrally bonded III-V semiconductors. Phys. Rev. B 75, 115202 (2007).
(
10.1103/PhysRevB.75.115202
) / Phys. Rev. B by D Powell (2007) -
Madelung, O. Semiconductors—Basic Data. (Springer, Berlin Heidelberg, 1996).
(
10.1007/978-3-642-97675-9
) / Semiconductors—Basic Data by O Madelung (1996) -
Vermeersch, B., Carrete, J. & Mingo, N. Cross-plane heat conduction in thin films with ab-initio phonon dispersions and scattering rates. Appl. Phys. Lett. 108, 193104 (2016).
(
10.1063/1.4948968
) / Appl. Phys. Lett. by B Vermeersch (2016) -
Wang, Z. & Mingo, N. Diameter dependence of SiGe nanowire thermal conductivity. Appl. Phys. Lett. 97, 101903 (2010).
(
10.1063/1.3486171
) / Appl. Phys. Lett. by Z Wang (2010) -
Maycock, P. D. Thermal conductivity of silicon, germanium, III–V compounds and III–V alloys. Solid State Electron. 10, 161–168 (1967).
(
10.1016/0038-1101(67)90069-X
) / Solid State Electron. by PD Maycock (1967)
Dates
Type | When |
---|---|
Created | 7 years, 9 months ago (Nov. 8, 2017, 7:57 a.m.) |
Deposited | 1 month, 3 weeks ago (June 26, 2025, 6:46 p.m.) |
Indexed | 2 weeks, 1 day ago (Aug. 6, 2025, 8 a.m.) |
Issued | 7 years, 9 months ago (Nov. 16, 2017) |
Published | 7 years, 9 months ago (Nov. 16, 2017) |
Published Online | 7 years, 9 months ago (Nov. 16, 2017) |
@article{Seyf_2017, title={Rethinking phonons: The issue of disorder}, volume={3}, ISSN={2057-3960}, url={http://dx.doi.org/10.1038/s41524-017-0052-9}, DOI={10.1038/s41524-017-0052-9}, number={1}, journal={npj Computational Materials}, publisher={Springer Science and Business Media LLC}, author={Seyf, Hamid Reza and Yates, Luke and Bougher, Thomas L. and Graham, Samuel and Cola, Baratunde A. and Detchprohm, Theeradetch and Ji, Mi-Hee and Kim, Jeomoh and Dupuis, Russell and Lv, Wei and Henry, Asegun}, year={2017}, month=nov }