Abstract
The shift in lattice thermal conductivity of multilayer hexagonal boron nitride is studied as a function of layer thickness, hydrostatic pressure, and temperature. A Morelli–Callaway model is used for pressures ranging from zero to 7 GPa and temperatures scale from 2 to 350 K. Hydrostatic pressure and size parameters such as the mean bond length, melting temperature, and bulk modulus affect the lattice thermal conductivity of bulk and multilayer hexagonal Boron Nitride. The peak value of lattice thermal conductivity for both bulk and multilayer is seen to fall when pressure is increased, and the decline in lattice thermal conductivity is greater as the number of layers decreases. The drop in thermal conductivity is due to a reduction in phonon movement in the system as the number of layers decreases. The Morelli–Callaway model based on Clapeyron–Murnaghan equations is an effective approach for determining the pressure impact of lattice thermal conductivity. The lattice thermal conductivity declined as pressure is reduced, and the mass density and bulk modulus decreased as the thickness of the thin layer increased, while compressibility, solid molar volume, and liquid molar volume rose. When the experimental data and theoretical calculations for bulk and multilayer h-BN were compared, the findings indicated good agreement. It's crucial to lower the heat conductivity of the materials that are useful for device applications.
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
Abdullah BJ, Jiang Q, Omar MS (2016) Effects of size on mass density and its influence on mechanical and thermal properties of ZrO2 nanoparticles in different structures. Bull Mater Sci 39:1295–1302. https://doi.org/10.1007/s12034-016-1244-5
Abdullah B, Omar M, Jiang Q (2018) Size dependence of the bulk modulus of Si nanocrystals. Sādhanā 43:1–5
Adachi S. (2004). Handbook on physical properties of semiconductors: Springer Science & Business Media.
Albe K (1997) Theoretical study of boron nitride modifications at hydrostatic pressures. Phys Rev B 55:6203–6210. https://doi.org/10.1103/PhysRevB.55.6203
Aparna A, Sethulekshmi A, Jayan JS, Saritha A, Joseph K (2021) Recent advances in boron nitride based hybrid polymer nanocomposites. Macromol Mater Eng 306:2100429
Asen-Palmer M, Bartkowski K, Gmelin E, Cardona M, Zhernov A, Inyushkin A, Taldenkov A, Ozhogin V et al (1997) Thermal conductivity of germanium crystals with different isotopic compositions. Phys Rev B 56:9431
Balandin A, Wang KL (1998) Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well. Phys Rev B 58:1544
Boudiombo J, Baehr O, Boudrioua A, Thevenin P, Loulergue J, Bath A (1997) Modes of propagating light waves in thin films of boron nitride deposited by plasma enhanced chemical vapor deposition. Mater Sci Eng, B 46:96–98
Callaway J (1959) Model for lattice thermal conductivity at low temperatures. Phys Rev 113:1046–1051. https://doi.org/10.1103/PhysRev.113.1046
Chen L, Elibol K, Cai H, Jiang C, Shi W, Chen C, Wang HS, Wang X et al (2021) Direct observation of layer-stacking and oriented wrinkles in multilayer hexagonal boron nitride. 2D Materials 8(2):024001. https://doi.org/10.1088/2053-1583/abd41e
De Laeter JR, Böhlke JK, De Bievre P, Hidaka H, Peiser H, Rosman K, Taylor P (2003) Atomic weights of the elements. Review 2000 (IUPAC Technical Report). Pure Appl Chem 75:683–800
Gholivand H, Donmezer N (2017) Phonon mean free path in few layer graphene, hexagonal boron nitride, and composite bilayer h-BN/graphene. IEEE Trans Nanotechnol 16:752–758. https://doi.org/10.1109/TNANO.2017.2672199
Gutierrez-Mora F, Erdemir A, Goretta K, Dominguez-Rodriguez A, Routbort J (2005) Dry and oil-lubricated sliding wear of Si 3 N 4 and Si 3 N 4/BN fibrous monoliths. Tribol Lett 18:231–237
Hamarashid MM, Omar MS, Qader IN (2022) Hydrostatic pressure effect on lattice thermal conductivity in Si nanofilms. Silicon. https://doi.org/10.1007/s12633-022-01985-0
Hao XP, Cui DL, Shi GX, Yin YQ, Xu XG, Jiang MH, Xu XW, Li YP (2001) Low temperature benzene thermal synthesis and characterization of boron nitride nanocrystals. Mater Lett 51:509–513. https://doi.org/10.1016/S0167-577X(01)00344-5
Heuer S, Li BS, Armstrong DEJ, Zayachuk Y, Linsmeier C (2020) Microstructural and micromechanical assessment of aged ultra-fast sintered functionally graded iron/tungsten composites. Mater Des 191:108652. https://doi.org/10.1016/j.matdes.2020.108652
Hu S, Yang J, Liu W, Dong Y, Cao S, Liu J (2011) Prediction of formation of cubic boron nitride by construction of temperature–pressure phase diagram at the nanoscale. J Solid State Chem 184:1598–1602. https://doi.org/10.1016/j.jssc.2011.04.037
Jayaraman A, Klement W Jr, Kennedy G (1963) Melting and polymorphism at high pressures in some group IV elements and III-V compounds with the diamond/zincblende structure. Phys Rev 130:540
Jiang Q, Liang L, Zhao D (2001) Lattice contraction and surface stress of fcc nanocrystals. J Phys Chem B 105:6275–6277
Jiang Q, Yang CC, Li JC (2003) Size-dependent melting temperature of polymers. Macromol Theory Simul 12:57–60
Jo I, Pettes MT, Kim J, Watanabe K, Taniguchi T, Yao Z, Shi L (2013) Thermal conductivity and phonon transport in suspended few-layer hexagonal boron nitride. Nano Lett 13:550–554. https://doi.org/10.1021/nl304060g
Karch K, Bechstedt F (1997) Ab initio lattice dynamics of BN and AlN: covalent versus ionic forces. Phys Rev B 56:7404–7415. https://doi.org/10.1103/PhysRevB.56.7404
Karim HH, Omar MS, Qader IN (2022) Hydrostatic pressure effect on melting temperature and lattice thermal conductivity of bulk and nanowires of indium arsenide. Physica B 640:414045. https://doi.org/10.1016/j.physb.2022.414045
Khitun A, Balandin A, Wang K (1999) Modification of the lattice thermal conductivity in silicon quantum wires due to spatial confinement of acoustic phonons. Superlattices Microstruct 26:181–193
Kimura Y, Wakabayashi T, Okada K, Wada T, Nishikawa H (1999) Boron nitride as a lubricant additive. Wear 232:199–206
Lelonis D A, Tereshko J W, Andersen C M (2003) Boron nitride powder a high-performance alternative for solid lubrication. GE Adv Ceram: 4
Liang L, Li B (2006) Size-dependent thermal conductivity of nanoscale semiconducting systems. Phys Rev B 73:153303
Lipp A, Schwetz KA, Hunold K (1989) Hexagonal boron nitride: fabrication, properties and applications. J Eur Ceram Soc 5:3–9
Lobo LQ, Ferreira AG (2001) Phase equilibria from the exactly integrated Clapeyron equation. J Chem Thermodyn 33:1597–1617
Majety S, Cao X, Dahal R, Pantha B, Li J, Lin J, Jiang H. (2012) Semiconducting hexagonal boron nitride for deep ultraviolet photonics. Paper presented at the Quantum Sensing and Nanophotonic Devices IX.
Ming Y, You G, Xu X, Wen H, Zhao J (2019) Effect of thickness on the thermal conductivity and microstructure of die-cast AZ91D magnesium alloy. Metall Mater Trans A 50:5969–5976
Morelli D, Heremans J, Slack G (2002) Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III-V semiconductors. Phys Rev B 66:195304
Muramatsu Y, Kaneyoshi T, Gullikson EM, Perera RC (2003) Angle-resolved soft X-ray emission and absorption spectroscopy of hexagonal boron nitride. Spectrochim Acta Part A Mol Biomol Spectrosc 59:1951–1957
Naftaly M, Leist J, Fletcher JR (2013) Optical properties and structure of pyrolytic boron nitride for THz applications. Optical Materials Express 3:260–269
Omar M (2007) Lattice thermal expansion for normal tetrahedral compound semiconductors. Mater Res Bull 42:319–326
Omar M (2012) Models for mean bonding length, melting point and lattice thermal expansion of nanoparticle materials. Mater Res Bull 47:3518–3522
Omar M (2016) Structural and thermal properties of elementary and binary tetrahedral semiconductor nanoparticles. Int J Thermophys 37:11
Omar M, Taha H (2010) Effects of nanoscale size dependent parameters on lattice thermal conductivity in Si nanowire. Sadhana 35:177–193
Ooi N, Rajan V, Gottlieb J, Catherine Y, Adams J (2006) Structural properties of hexagonal boron nitride. Modell Simul Mater Sci Eng 14:515
Palla P, Uppu GR, Ethiraj AS, Raina JP (2016) Bandgap engineered graphene and hexagonal boron nitride for resonant tunnelling diode. Bull Mater Sci 39:1441–1451. https://doi.org/10.1007/s12034-016-1285-9
Post E (1953) On the characteristic temperatures of single crystals and the dispersion of the" debye heat waves”. Can J Phys 31:112–119
Qader IN, Omar M (2017) Carrier concentration effect and other structure-related parameters on lattice thermal conductivity of Si nanowires. Bull Mater Sci 40:599–607
Qader IN, Abdullah BJ, Karim HH (2017) Lattice thermal conductivity of wurtzite bulk and zinc blende Cdse nanowires and nanoplayer. Eurasian J Sci Eng 3:9–26
Qader I, Abdullah B, Hassan M, Mahmood P (2019) Influence of the size reduction on the thermal conductivity of bismuth nanowires. Eurasian J Sci Eng 4:55–65
Qader IN, Abdullah BJ, Omar MS (2020) Range determination of the influence of carrier concentration on lattice thermal conductivity for bulk Si and nanowires. Aksaray Univ J Sci Eng 4:30–42
Qader IN, Qadr HM, Ali PH (2021) Calculation of lattice thermal conductivity for Si fishbone nanowire using modified callaway model. Semiconductors 55:960–967. https://doi.org/10.1134/S1063782621070137
Raman C, Meneghetti P (2008) Boron nitride finds new applications in thermoplastic compounds. Plast Addit Compd 10:26–31
Rand B, Appleyard SP, Yardim MF. (2012). Design and control of structure of advanced carbon materials for enhanced performance (Vol. 374): Springer Science & Business Media.
Rohr C, Boo J-H, Ho W (1998) The growth of hexagonal boron nitride thin films on silicon using single source precursor. Thin Solid Films 322:9–13
Roy S, Zhang X, Puthirath AB, Meiyazhagan A, Bhattacharyya S, Rahman MM, Babu G, Susarla S et al (2021) Structure, properties and applications of two-dimensional hexagonal boron nitride. Adv Mater 33:2101589
Shimada K, Sota T, Suzuki K (1998) First-principles study on electronic and elastic properties of BN, AlN, and GaN. J Appl Phys 84:4951–4958. https://doi.org/10.1063/1.368739
Shimada K, Sota T, Suzuki K (2011) Constant pressure first-principles molecular dynamics study on Bn, Ain. And Gan MRS Proces 482:869. https://doi.org/10.1557/PROC-482-869
Sichel EK, Miller RE, Abrahams MS, Buiocchi CJ (1976) Heat capacity and thermal conductivity of hexagonal pyrolytic boron nitride. Phys Rev B 13:4607–4611. https://doi.org/10.1103/PhysRevB.13.4607
Solozhenko V, Will G, Elf F (1995) Isothermal compression of hexagonal graphite-like boron nitride up to 12 GPa. Solid State Commun 96:1–3
Stansfeld J (2003) 5.7 In Situ Density Measurements. Measurement of the Thermodynamic Properties of Single Phases: 208
Sueyoshi H, Rochman NT, Kawano S (2003) Damping capacity and mechanical property of hexagonal boron nitride-dispersed composite steel. J Alloy Compd 355:120–125
Thiemann FL, Rowe P, Müller EA, Michaelides A (2020) Machine learning potential for hexagonal boron nitride applied to thermally and mechanically induced rippling. J Phys Chem C 124:22278–22290. https://doi.org/10.1021/acs.jpcc.0c05831
Uchida Y, Nakandakari S, Kawahara K, Yamasaki S, Mitsuhara M, Ago H (2018) Controlled growth of large-area uniform multilayer hexagonal boron nitride as an effective 2D substrate. ACS Nano 12:6236–6244. https://doi.org/10.1021/acsnano.8b03055
Watanabe S, Miyake S, Murakawa M (1991) Tribological properties of cubic, amorphous and hexagonal boron nitride films. Surf Coat Technol 49:406–410
Wise SS, Margrave JL, Feder HM, Hubbard WN (1966) Fluorine bomb calorimetry. XVI. The de 1,2. J Phys Chem 70:7–10. https://doi.org/10.1021/j100873a002
Yang C, Li G, Jiang Q (2003a) Effect of pressure on melting temperature of silicon. J Phys: Condens Matter 15:4961
Yang C, Li J, Jiang Q (2003b) Effect of pressure on melting temperature of silicon determined by Clapeyron equation. Chem Phys Lett 372:156–159
Yang C, Li J, Jiang Q (2004) Temperature–pressure phase diagram of silicon determined by Clapeyron equation. Solid State Commun 129:437–441
Yang C, Xiao M, Li W, Jiang Q (2006) Size effects on debye temperature, einstein temperature, and volume thermal expansion coefficient of nanocrystals. Solid State Commun 139:148–152
Yang C, Jiang Q. (2005) Effect of pressure on melting temperature of silicon and germanium. Paper presented at the Materials Science Forum
Yuan J, Zhang K, Zhang X, Li X, Li T, Li Y, Ma M, Shi G (2013) Thermal characteristics of Mg–Zn–Mn alloys with high specific strength and high thermal conductivity. J Alloy Compd 578:32–36
Zedlitz R, Heintze M, Schubert M (1996) Properties of amorphous boron nitride thin films. J Non-Cryst Solids 198:403–406
Zhang Y, He X, Han J, Du S (2001) Combustion synthesis of hexagonal boron–nitride-based ceramics. J Mater Process Technol 116:161–164
Zhang Y, Choi JR, Park S-J (2018) Enhancing the heat and load transfer efficiency by optimizing the interface of hexagonal boron nitride/elastomer nanocomposites for thermal management applications. Polymer 143:1–9
Zhao M, Jiang Q (2004) Melting and surface melting of low-dimensional In crystals. Solid State Commun 130:37–39
Zhou H, Zhu J, Liu Z, Yan Z, Fan X, Lin J, Wang G, Yan Q et al (2014) High thermal conductivity of suspended few-layer hexagonal boron nitride sheets. Nano Res 7:1232–1240. https://doi.org/10.1007/s12274-014-0486-z
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The authors are appreciative of the financial support they received from the University of Raparin and Salahaddin University-Erbil.
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INQ did the computations. DMM, HHR, and BJA wrote the manuscript. MSO revised the manuscript.
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Qader, I.N., Mamand, D.M., Rasul, H.H. et al. The Effects of Pressure and Size Parameter on the Lattice Thermal Conductivity in Multilayer Hexagonal Boron Nitride. Iran J Sci Technol Trans Sci 46, 1705–1718 (2022). https://doi.org/10.1007/s40995-022-01370-x
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DOI: https://doi.org/10.1007/s40995-022-01370-x