Abstract
This paper designs the thermal crystals composed of alloy materials with air holes and analyzes their properties of band structures, heat transmission, and flux spectra. Thermal crystals composed of Si-A (A=Ge, Sn, Pb) alloys as background materials and air holes with square array are used to construct an elastic-constant periodic structure and their high-frequency phononic band is calculated by deploying finite element methods. Moreover, this paper investigates heat transmission through a finite array of thermally excited phonons and presents the thermal crystal with maximum heat transport. The results show that a wider bandgap could be achieved by increasing the air hole radius and decreasing the lattice constant. In the alloy materials, with increasing atomic radius and thus atomic mass (Ge, Sn, Pb), the frequency range (contributed to thermal conductivity) shifts towards lower frequency. Hence, the bandgap frequencies also shift toward low frequency, but this decreasing rate is not constant or in order, so former may have a faster or slower decreasing rate than the later. Thus, the frequency range for the contribution of heat transportation overlaps with the bandgap frequency range. The development of thermal crystals is promising for managing heat and controlling the propagation of the thermal wave.
摘要
k]本文设计了含气孔的合金热晶体,分析了其能带结构、传热特性和通量光谱。以Si-A (A = Ge, Sn, Pb)合金为背景材料,采用方阵气孔构造弹性常数周期结构的热晶体,采用有限元方法计算了其高频声子带。此外,本文还研究了有限热激发声子阵列的热传输,并给出了热传输最大的热晶体。结果表明,增大气孔半径和减小晶格常数可以获得更宽的带隙。在合金材料中,随着原子半径和原子量(Ge, Sn, Pb)的增加,频率范围向低频移动(有助于导热)。因此,带隙频率也向低频偏移,但这种下降率不是恒定的或有序的,因此前者相较于后者下降率可能或快或慢。因此,热输运贡献的频率范围与带隙频率范围重叠。热晶体在热管理和控制热波传播方面具有广阔的应用前景。
Similar content being viewed by others
References
MALDOVAN M. Sound and heat revolutions in phononics [J]. Nature, 2013, 503(7475): 209–217.
PENNEC Y, DJAFARI-ROUHANI B. Fundamental properties of phononic crystal [M]//Phononic crystals. New York: Springer, 2016: 23–50.
KUSHWAHA M S, HALEVI P, DOBRZYNSKI L, et al. Acoustic band structure of periodic elastic composites [J]. Physical Review Letters, 1993, 71(13): 2022–2025.
ECONOMOU E N, SIGALAS M. Stop bands for elastic waves in periodic composite materials [J]. The Journal of the Acoustical Society of America, 1994, 95(4): 1734–1740.
GORISHNYY T, MALDOVAN M, ULLAL C, et al. Sound ideas [J]. Physics World, 2005, 18(12): 24–29.
ELFORD D P, CHALMERS L, KUSMARTSEV F V, et al. Matryoshka locally resonant sonic crystal [J]. The Journal of the Acoustical Society of America, 2011, 130(5): 2746–2755.
YANG S X, PAGE J H, LIU Z Y, et al. Ultrasound tunneling through 3D phononic crystals [J]. Physical Review Letters, 2002, 88(10): 104301.
ZHU G H, SWINTECK N Z, WU S T, et al. Direct observation of the phonon dispersion of a three-dimensional solid/solid hypersonic colloidal crystal [J]. Physical Review B, 2013, 88(14): 144307.
MALDOVAN M. Narrow low-frequency spectrum and heat management by thermocrystals [J]. Physical Review Letters, 2013, 110(2): 025902.
KHELIF A, DJAFARI-ROUHANI B, VASSEUR J O, et al. Transmission and dispersion relations of perfect and defect-containing waveguide structures in phononic band gap materials [J]. Physical Review B, 2003, 68(2): 024302.
JOANNOPOULOS J D, VILLENEUVE P R, FAN S H. Photonic crystals: Putting a new twist on light [J]. Nature, 1997, 386(6621): 143–149.
MALDOVAN M. Phonon wave interference and thermal bandgap materials [J]. Nature Materials, 2015, 14(7): 667–674.
ZIMAN J. Electrons and phonons the theory of transport phenomena in solids [M]. Oxford: Oxford University Press, 2001.
KITTEL C. Introduction to solid state physics [M]. 8th ed. New York: John Wiley & Sons, 2005.
LUCKYANOVA M N, GARG J, ESFARJANI K, et al. Coherent phonon heat conduction in superlattices [J]. Science, 2012, 338(6109): 936–939.
RAVICHANDRAN J, YADAV A K, CHEAITO R, et al. Crossover from incoherent to coherent phonon scattering in epitaxial oxide superlattices [J]. Nature Materials, 2014, 13(2): 168–172.
SIMKIN M V, MAHAN G D. Minimum thermal conductivity of superlattices [J]. Physical Review Letters, 2000, 84(5): 927–930.
ZEN N, PUURTINEN T A, ISOTALO T J, et al. Engineering thermal conductance using a two-dimensional phononic crystal [J]. Nature Communications, 2014, 5: 3435.
HUSSEIN M I. Reduced Bloch mode expansion for periodic media band structure calculations [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009, 465(2109): 2825–2848.
GÓMEZ GARCÍA P, FERNÁNDEZ-ÁLVAREZ J P. Floquet-Bloch theory and its application to the dispersion curves of nonperiodic layered systems [J]. Mathematical Problems in Engineering, 2015, 2015: 475364.
MOHAMADY S, RAJA AHMAD R K, MONTAZERI A, et al. Modeling and eigenfrequency analysis of sound-structure interaction in a rectangular enclosure with finite element method [J]. Advances in Acoustics and Vibration, 2009, 2009: 371297.
KAFESAKI M, SIGALAS M M, GARCÍA N. Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials [J]. Physical Review Letters, 2000, 85(19): 4044–4047.
KHELIF A, DJAFARI-ROUHANI B, VASSEUR J O, et al. Transmittivity through straight and stublike waveguides in a two-dimensional phononic crystal [J]. Physical Review B, 2002, 65(17): 174308.
BERNE P. Thermal conductivity of composites: How comsol revealed an omission in a classical paper [C]//2015 COMSOL Conference. Grenoble: COMSOL, 2015: 1–5.
BILAL O R, HUSSEIN M I. Ultrawide phononic band gap for combined in-plane and out-of-plane waves [J]. Physical Review E, 2011, 84(6): 065701.
DONG H W, SU X X, WANG Y S. Topology optimization of two-dimensional phononic crystals using FEM and genetic algorithm [C]//2012 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications. Shanghai: IEEE, 2012: 45–48.
YI G L, SHIN Y C, YOON H, et al. Topology optimization for phononic band gap maximization considering a target driving frequency [J]. JMST Advances, 2019, 1(1/2): 153–159.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item
the National Natural Science Foundation of China (No. 61975119)
Rights and permissions
About this article
Cite this article
Azka, U., Jiang, C. & Khushik, M.H.A.K. Band Structure Characteristics of Two-Dimensional Si-A (Ge, Pb, Sn) Alloy-Air Holes Thermal Crystals. J. Shanghai Jiaotong Univ. (Sci.) 28, 180–185 (2023). https://doi.org/10.1007/s12204-022-2485-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12204-022-2485-7