The kinetic theory of gas is used to predict the specific heat and thermal conductivity of ZnO nanostructures. In this model, phonons are considered as a gas whose basic properties are given by phonon dispersion curves. The model also requires knowledge of the boundary relaxation time parameter (F), the defect relaxation time parameter D, and the relaxation time parameters which take into account lattice anisotropy. These parameters can be determined independently from experimental measurements. Excellent agreements were found when comparing both the estimated specific heat and thermal conductivity to bulk sample measurement data. Comparison with previous results obtained with molecular dynamics (MD) simulations leads to the conclusion that for ultra narrow nanobelts, thermal conductivity depends on their length. Behavior of the thermal conductivity of nanofilms is also studied. The results are consistent with previous works on 1D and 2 D systems. Finally, the thermal conductivity of nanobelts is presented as are the influences of boundary and defect parameters.
Issue Section:
Micro/Nanoscale Heat Transfer
References
1.
Zheng
, W. P.
, Dai
, Z. R.
, and Wang
, Z. L.
, 2001, “Nanobelts of Semiconducting Oxides
,” Science
, 291
, pp.1947
–1949
.2.
Kong
, X. Y.
, Ding
, Y.
, Yang
, R.
and Wang
, Z. L.
, 2004, “Single-Crystal Nanorings Formed by Epitaxial Self-Coiling of Polar Nanobelts
,” Science
, 303
, pp.1348
–1351
.3.
Gao
, P. X.
, Ding
, Y.
, Mai
, W.
, Hughes
, W. L.
, Lao
, C.
, and Wang
, Z. L.
, 2005, “Conversion of Zinc Oxide Nanobelts Into Superlattice-Structured Nanohelices
,” Science
, 309
, pp. 1700
–1704
.4.
Gao
, P. X.
, and Wang
, Z. L.
, 2005, “Nanoarchitectures of Semiconducting and Piezoelectric Zinc Oxide”
, J. Appl. Phys.
, 97
, p. 044304
.5.
Wang
, Z. L.
, 2009, “ZnO Nanowire and Nanobelt Platform for Nanotechnology
,” Mat. Rev. Sci. Eng.
, R64
, pp. 33
−71
.6.
Wang
, Z. L.
, 2004, “Zinc Oxide Nanostructures: Growth, Properties and Applications
,” J. Phys.: Condens. Matter
, 16
, pp. R829
–R858
.7.
Yu
, C.
, Hao
, Q.
, Saha
, S.
, Shi
, L.
, Kong
, X.
, and Wang
, Z. L.
, 2005, “Integration of Metal Oxide Nanobelts With Microsystems for Nerve Agent Detection
,” Appl. Phys. Lett.
, 86
, p. 063101
.8.
Comini
, E.
, Faglia
, G.
, Sberveglieri
, G.
, Pan
, Z.
, and Wang
, Z. L.
, 2002, “Stable and Highly Sensitive Gas Sensors Based on Semiconducting Oxide Nanobelts
,” Appl. Phys. Lett.
81
, pp. 1869
–1871
.9.
Hughes
, W. L.
, and Wang
, Z. L.
, 2003, “Nanobelts as Nanocantilevers
,” Appl. Phys. Lett.
, 82
(17
), pp. 2886
–2888
.10.
Flik
, M. I.
, and Tien
, C. L.
, 1990, “Size Effect on the Thermal Conductivity of High-Tc; Thin-Film Superconductors
,” ASME Trans. J. Heat Transfer
, 112
, pp. 872
–881
.11.
Tzou
, D. Y.
, 1997, Macro-to Microscale Heat Transfer: The Lagging Behavior
, Taylor & Francis
, Washington, DC
.12.
Majumdar
, A.
, 1998, “Microscale Energy Transport in Solids
,” Microscale Energy Transport
, C.-L.
Tien
, A.
Majumdar
, and F. M.
Gerner
, eds., Taylor and Francis
, Washington, DC,
pp. 1
–94
.13.
J.
Callaway
, 1959, “Model of Lattice Thermal Conductivity at Low Temperatures
,” Phys. Rev.
, 113
, pp. 1046
–1051
.14.
Holland
, M. G.
, 1963, “Analysis of Lattice Thermal Conductivity
,” Phys. Rev.
, 132
(6
), pp. 2461
–2471
.15.
Zou
, J.
, and Balandin
, A.
, 2001, “Phonon Heat Conduction in a Semiconductor Nanowire
,” J. Appl. Phys.
, 89
(5
), pp. 2932
–2938
.16.
Zhou
, X. W.
, Aubry
, J. R. E.
, Greenstein
, A.
, and Schelling
, P. K.
, 2009, “Towards More Accurate Molecular Dynamics Calculation of Thermal Conductivity: Case Study of GaN Bulk Crystals
,” Phys. Rev. B
, 79
, p. 115201
.17.
Chantrenne
, P.
, and Barrat
, J. L.
, 2004, “Finite Size Effects in Determination of Thermal Conductivities: Comparing Molecular Dynamics Results With Simple Models
,” ASME Trans. J. Heat Transfer
, 126
, pp. 577
−585
.18.
Landry
, E. S.
, and McGaughey
, A. J. H.
, 2009, “Thermal Boundary Resistance Predictions from Molecular Dynamics Simulations and Theoretical Calculations
,” Phys. Rev. B
, 80
, p. 165304
.19.
Lacroix
, D.
, and Joulain
, K.
, and Lemonnier
, D.
, 2005, “Monte Carlo Transient Phonon Transport in Silicon and Germanium at Nanoscale
,” Phys. Rev. B
, 72
, p. 064305
.20.
Chen
, Y.
, Li
, D.
, Lukes
, J. R.
, and Majumdar
, A.
, 2005, “Monte Carlo Simulation of Silicon Nanowire Thermal Conductivity
,” ASME J. Heat Transfer
, 127
, pp. 1129
–1137
.21.
Xu
, J.
, and Fisher
, T. S.
, 2006, “Enhancement of Thermal Interface Materials With Carbon Nanotube Arrays
,” Int. J. Heat. Mass. Transfer
, 49
, pp. 1658
–1666
.22.
Hu
, X. J.
, Padilla
, A. A.
, Jun Xu
, J.
, Fisher
, T. S.
, and Goodson
, K. E.
, 2006, “3-Omega Measurements of Vertically Oriented Carbon Nanotubes on Silicon
,” ASME Trans. J. Heat Transfer
, 128
(11
), pp. 1109
–1113
.23.
Chen
, R.
, Hochbaum
, A. I.
, Murphy
, P.
, Moore
, J.
, Yang
, P.
, and Majumdar
, A.
, 2008, “Thermal Conductance of Thin Silicon Nanowires
,” Phys. Rev. Lett.
, 101
, p. 105501
.24.
Mingo
, N.
, and Broido
, D. A.
, 2004, “Lattice Thermal Conductivity Crossovers in Semiconductor Nanowires
,” Phys. Rev. Lett.
, 93
, p. 246106
.25.
Donadio
, D.
, and Galli
, G.
, 2009, “Atomistic Simulations of Heat Transport in Silicon Nanowires
,” Phys. Rev. Lett.
, 102
, p. 195901
.26.
Balandin
, A.
, and Wang
, K. L.
, 1998, “Significant Decrease of the Lattice Thermal Conductivity Due to Phonon Confinement in a Free-Standing Semiconductor Quantum Well
,” Phys. Rev. B
, 58
(3
), pp. 1544
–1549
.27.
Wang
, S. C.
, Liang
, X. G.
, Xu
, X. H.
, and Ohara
, T.
, 2009, “Thermal Conductivity of Silicon Nanowire by Nonequilibrium Molecular Dynamics Simulations
,” J. Appl. Phys.
, 105
, p. 014316
.28.
Huang
, M. J.
, Weng
, C. C.
, and Chang
, T. M.
, 2010, “An Investigation of the Phonon Properties of Silicon Nanowires
,” Int. J. Therm. Sci.
, 49
, pp. 1095
–1102
.29.
Mingo
, N.
, 2003, “Calculation of Si Nanowire Thermal Conductivity Using Complete Phonon Dispersion Relations
,” Phys. Rev. B
, 68
, p. 113308
.30.
Maruyama
, S.
, 2003, “A Molecular Dynamics Simulation of Heat Conduction of a Finite Length Single-Walled Carbon Nanotube
,” Nanoscale Microscale Thermophys. Eng.
, 7
(1
), pp. 41
–50
.31.
Osman
, M. A.
, and Srivastava
, D.
, 2001, “Temperature Dependence of the Thermal Conductivity of Single-Wall Carbon Nanotubes
,” Nanotechnology
, 12
(1
), pp. 21
–24
.32.
Hone
, J.
, Whitney
, M.
, Piskoti
, C.
, and Zettl
, A.
, 1999, “Thermal Conductivity of Single-Walled Carbon Nanotubes
,” Phys. Rev. B
, 59
, pp. R2514
–R2516
.33.
Martin
, P.
, Aksamija
, Z.
, Pop
, E.
, and Ravaioli
, U.
, 2009, “Impact of Phonon-Surface Roughness Scattering on Thermal Conductivity of Thin Si Nanowires
,” Phys. Rev. Lett.
, 102
, p. 125503
.34.
Kulkarni
, A. J.
, Zhou
, M.
, and Ke
, F. J.
, 2005, “Orientation and Size Dependence of the Elastic Properties of Zinc Oxide Nanobelts
,” Nanotechnology
, 16
, pp. 2749
–2756
.35.
Kulkarni
, A. J.
, and Zhou
, M.
, 2006, “Surface-Effects-Dominated Thermal and Mechanical Responses of Zinc Oxide Nanobelts
,” Acta Mech. Solida Sinica
, 22
, pp. 217
–224
.36.
Shi
, L.
, Hao
, Q.
, Yu
, C.
, Mingo
, N.
, Kong
, X.
, and Wang
, Z. L.
, 2004, “Thermal Conductivities of Individual Tin Dioxide Nanobelts
,” Appl. Phys. Lett.
, 84
(14
), pp. 2638
−2640
.37.
Chantrenne
, P.
, Barrat
, J. L.
, Blase
, X.
, and Gale
, J. D.
, 2005, “An Analytical Model for the Thermal Conductivity of Silicon Nanostructures
,” J. Appl. Phys.
, 97
, p. 104318
.38.
Li
, D.
, Wu
, Y.
, Kim
, P.
, Shi
, L.
, Yang
, P.
, and Majumdar
, A.
, 2003, “Thermal Conductivity of Individual Silicon Nanowires
,” Appl. Phys. Lett.
, 83
, pp. 2934
–2936
.39.
Slack
, G. A.
, 1972, “Thermal Conductivity of II-VI Compounds Phonon Scattering by Fe2+ Impurities
,” Phys. Rev. B
, 6
(10
), pp. 3791
–3800
.40.
Wolf
, M. W.
, and Martin
, J. J.
, 1973, “Low Temperature Thermal Conductivity of Zinc Oxide
,” Phys. Status Solidi A
, 17
(1
), pp. 215
–220
.41.
Kittel
, C.
, 1996, Introduction to Solid State Physics
, Wiley
, New York.
42.
Serrano
, J.
, Manjón
, F. J.
, Romero
, A. H.
, Ivanov
, A.
, Lauck
, R.
, and Cardona
M.
, 2007, “The Phonon Dispersion of Wurtzite-ZnO Revisited
,” Phys. Status Solidi B
, 244
(5
), pp. 1478
–1482
.43.
Serrano
, J.
, Romero
, A. H.
, Manjon
, F. J
, Lauck
, R.
, Cardona
, M.
, and Rubio
, A.
, 2004, “Pressure Dependence of the Lattice Dynamics of ZnO: An ab initio Approach
,” Phys. Rev. B
, 69
, p. 094306
.44.
Serrano
, J.
, Kremer
, R. K.
, Cardona
, M.
, Siegle
, G.
, Romero
, A. H.
, and Lauck
, R.
, 2006, “Heat Capacity of ZnO: Isotope Effects
,” Phys. Rev. B
, 73
, p. 094303
.45.
Wu
, H. Y.
, Cheng
, X. L.
, Hua
, C. H.
, and Zhou
, P.
, 2010, “The Structure and Thermodynamic Properties of Zinc Oxide With Wurtzite and Rocksalt Structure Under High Pressures
,” Physica B
, 405
, pp. 606
–612
.46.
Thacher
, P. D.
, 1967, “Effect of Boundaries and Isotopes on Thermal Conductivity of LiF
,” Phys. Rev.
, 156
(3
), pp. 975
–988
.47.
Peierls
, R.
, 1929, “On the Kinetic Theory of Thermal Conduction in Crystals
,” Ann. Phys.
, 395
(8
), pp. 1055
–1101
.48.
Slack
, G. A.
, and Galginaitis
, S.
, 1964, “Thermal Conductivity and Phonon Scattering by Magnetic Impurities in CdTe
,” Phys. Rev.
, 133
, pp. A253
–A268
.49.
Holland
, M. G.
, 1964, “Phonon Scattering in Semiconductors from Thermal Conductivity Studies
,” Phys. Rev.
, 134
(2
A), pp. A471
–A480
.50.
Onn
, D. G.
, Witek
, A.
, Qiu
, Y. Z.
, Anthony
, T. R.
, and Banholzer
, W. F.
, 1992, “Some Aspects of the Thermal Conductivity of Isotopically Enriched Diamond Single Crystals
,” Phys. Rev. Lett.
, 68
(18
), pp. 2806
–2809
.51.
Sanati
, M.
, and Estreicher
, S. K.
, 2004, “Specific Heat and Entropy of GaN
,” J. Phys.: Condens. Matter
, 16
(28
), pp. L327
–L331
.52.
Danilchenko
, B. A.
, Paszkiewicz
, T.
, Wolski
, S.
, Jeżowski
, A.
, and Plackowski
, T.
, 2006, “Heat Capacity and Phonon Mean Free Path of Wurtzite GaN
,” Appl. Phys. Lett.
, 89
, p. 061901
.53.
Janettaz
, E.
, 1892, “Sur la Propagation de la Chaleur dans les Solides Cristallisés
,” Comptes Rendus. Acad. Sci.
, 114
, p.1352
.54.
Yates
, B.
, Cooper
, R. F.
and Kreitman
, M. M.
, 1971, “Low-Temperature Thermal Expansion of Zinc Oxide: Vibrations in Zinc Oxide and Sphalerite Zinc Sulfide”
, Phys. Rev. B
, 4
, pp. 1314
–1323
.55.
Iwanaga
, H.
, Kunishige
, A.
, and Takeuchi
, S.
, 2000, “Anisotropic Thermal Expansion in Wurtzite-type Crystals
,” J. Mater. Sci.
, 35
, pp. 2451
–2454
.56.
Klemens
, P. G.
, 1951, “The thermal Conductivity of Dielectric Solids at Low Temperatures
,” Proc. R. Soc. London, Ser. A
, 208
(1092
), pp. 108
–133
.57.
Klemens
, P. G.
, 1958, Solid State Physics
, Academic Press Inc.
, New York.
58.
Lü
, X.
, Chu
, J. H.
, and Shen
, W. Z.
, 2003, “Modification of the Lattice Thermal Conducivity in Semiconductor Rectangular Nanowires
,” J. Appl. Phys.
, 93
, pp. 1219
–1230
.59.
Rosenblum
, I.
, Adler
, J.
, and Brandon
, S.
, 1998, “Calculation of Thermal Properties of Diamond From Simulated Phonon Spectra
,” Comput. Mater. Sci.
, 12
, pp. 9
–25
.60.
Casimir
, H. B. G.
, 1938, “Note on the Conduction of Heat in Crystals
,” Physica
, 5
, pp. 495
–500
.61.
Wang
, Z.
, Zu
, X.
, Gao
, F.
, Weber
, J.
, and Crocombette
, J. P.
, 2007, “Atomic Simulation of the Size and Orientation Dependences of Thermal Conductivity in GaN Nanowires
,” Appl. Phys. Lett.
, 90
, p. 161923
.62.
Lepri
, S.
, Livi
, R.
, and Politi
, A.
, 2003, “Thermal Conduction in Classical Low-Dimensional Lattices
,” Phys. Rep.
, 377
, pp. 1
–80
.63.
Maruyama
, S.
, 2002, “A Molecular Dynamics Simulation of Heat Conduction of Finite Length SWNTs
,” Physica B
, 323
(1–4
), pp. 193
–195
.64.
Moreland
, J. F.
, 2004, “The Disparate Thermal Conductivity of Carbon Nanoubes and Diamond Nanowires Sudied by Atomistic Simulation
,” Nanoscale Microscale Thermophys. Eng.
, 8
(1
), pp. 61
–69
.65.
Lukes
, J. R.
, and Zhong
, H.
, 2007, “Thermal Conductivity of Individual Single—Wall Carbon Nanotubes
,” ASME Trans. J. Heat Transfer
, 129
(6
), pp. 705
–716
.66.
Che
, J.
, Cagin
, T.
, and Goddard
, W. A.
, 2000, “Thermal Conductivity of Carbon Nanotubes, Nanotechnology
,” Nanotechnology
, 11
, pp. 65
–69
.67.
Berbert
, S.
, Kwon
, Y. K.
, and Tomanek
, D.
, 2000, “Unusually High Thermal Conductivity of Carbon Nanotubes
,” Phys. Rev. Lett.
, 84
(25
), pp. 4613
–4616
.68.
Ponomareva
, I.
, Srivastava
, D.
, and Menon
, M.
, 2007, “Thermal Conductivity in Thin Silicon Nanowires: Phonon Confinement Effect
,” Nano Lett.
, 7
, pp. 1155
–1159
.69.
Yang
, X.
, To
, A. C.
, and Tian
, R.
, 2010, “Anomalous Heat Conduction Behavior in Thin Finite-Size Silicon Nanowires
,” Nanotechnology
, 21
, p. 155704
.70.
Yang
, N.
, Zhang
, G.
, and Li
, B.
, 2010, “Violation of Fourier’s Law and Anomalous Heat Diffusion in Silicon Nanowires
,” Nanotoday
, 5
(2
), pp. 85
–90
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
