Size dependence of the bulk modulus of Si nanocrystals

Sādhanā - Tập 43 - Trang 1-5 - 2018
B J Abdullah1, M S Omar1, Q Jiang2
1Department of Physics, College of Science, Salahaddin-Erbil University, Erbil, Iraq
2Department of Material Science and Engineering, Jilin University, Changchun, China

Tóm tắt

This study investigates the effect of size on bulk modulus and its related parameters, including melting temperature and mass density based on the ratio number of surface atoms to that of its internal. The equation of bulk modulus in the bulk state B(∞) is modified to include the related size-dependent parameters without any adjustable parameter, and is applied to Si nanocrystals. The bulk modulus B(r) decreases from 9.8 × 1010 N m2 for the bulk state to 5.93 × 1010 N m2 for a 5 nm diameter of Si nanoparticles. An inherent relation between bulk modulus and change of the lattice parameter in nanocrystals obtained from the variation in the surface to volume ratio, this leads to increase in the mean bond length. The effect of mass density and melting temperature on bulk modulus are also discussed. Calculated results for bulk modulus are verified by experimental as well as the available computer simulation data.

Tài liệu tham khảo

Sun C Q 2009 Thermo-mechanical behavior of low-dimensional systems: The local bond average approach. Prog. Mater. Sci. 54: 179–307 Gleiter H 2000 Nanostructured materials: basic concepts and microstructure. Acta Materialia 48: 1–29 Zhao M and Jiang Q 2010 Size effect on thermal properties in low-dimensional materials. Key Engineering Materials, Trans Tech Publications, 189–218 Zhang Z, Zhao M and Jiang Q 2001 Melting temperatures of semiconductor nanocrystals in the mesoscopic size range. Semicond. Sci. Technol. 16:L33 Qi W 2005 Size effect on melting temperature of nanosolids. Physica B: Condens. Matter. 368: 46–50 Zhu Y, Lian J and Jiang Q 2009 Modeling of the melting point, Debye temperature, thermal expansion coefficient, and the specific heat of nanostructured materials. J. Phys. Chem. C 113: 16896–16900 Lu H, Li P, Cao Z and Meng X 2009 Size-, shape-, and dimensionality-dependent melting temperatures of nanocrystals. J. Phys. Chem. C 113: 7598–7602 Hou M, Elazzaoui M, Pattyn H, Verheyden J, Koops, G and Zhang G 2000 Growth and lattice dynamics of Co nanoparticles embedded in Ag: a combined molecular-dynamics simulation and Mössbauer study. Phys. Rev. B 62: 5117 Yang C, Xiao M, Li W and Jiang Q 2006 Size effects on Debye temperature, Einstein temperature, and volume thermal expansion coefficient of nanocrystals. Solid State Communications 139: 148–152 Abdullah B J, Omar M S and Jiang Q 2017 Size effects on cohesive energy, Debye temperature and lattice heat capacity from first-principles calculations of Sn nanoparticles. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 1-4 Kittel C 2005 Introduction to solid state physics. Wiley, Hoboken, 25 Koc H, Mamedov A M, Deligoz E and Ozisik H 2012 First principles prediction of the elastic, electronic, and optical properties of Sb2S3 and Sb2Se3 compounds. Solid State Sci. 14: 1211–1220 Gacem A, Doghmane A and Hadjoub Z 2011 Quantification the Effect of the Thickness of Thin Films on their Elastic Parameters. Adv. Mater. Res. Trans. Tech. Pub. 93–96 Qiao Z, Latz R and Mergel D 2004 Thickness dependence of In2O3: Sn film growth. Thin Solid Films 466: 250–258 Safaei A 2012 Size-dependent mass density of nanocrystals. Nano 7: 1250009 Lovell S and Rollinson E 1968 Density of thin films of vacuum evaporated metals. Nature 218: 1179–1180 Gu M, Sun C Q, Chen Z, Yeung T A, LI S, Tan C and Nosikn V 2007 Size, temperature, and bond nature dependence of elasticity and its derivatives on extensibility, Debye temperature, and heat capacity of nanostructures. Phys. Rev. B 75: 125403 Zhao M and Jiang Q 2004 Melting and surface melting of low-dimensional in crystals. Solid State Commun. 130: 37–39 Liang L and Li B 2006 Size-dependent thermal conductivity of nanoscale semiconducting systems. Phys. Rev. B 73: 153303 Avramov I and Michailov M 2008 Specific heat of nanocrystals. J. Phys. Condens. Matter. 20: 295224 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 2007 Lattice thermal expansion for normal tetrahedral compound semiconductors. Mater. Res. Bull. 42: 319–326 Jiang Q, Shi H and Zhao M 1999 Melting thermodynamics of organic nanocrystals. J. Chem. Phys. 111: 2176–2180 Zhang Z, Li J and Jiang Q 2000 Modelling for size-dependent and dimension-dependent melting of nanocrystals. J. Phys. D Appl. Phys. 33: 2653 Shen T D, Zhang J and Zhao Y 2008 What is the theoretical density of a nanocrystalline material? Acta Materialia 56: 3663–3671 Abdullah B J, Jiang Q and Omar M S 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 Lam P K, Cohen M L and Martinez G 1987 Analytic relation between bulk moduli and lattice constants. Phys. Rev. B 35: 9190–9194 Bievere P D, Valkiers S, Peiser S, Becker P, Ludicke F, Spieweck F and Stumpel J 1995 A more accurate value for the Avogadro constant. IEEE Trans. Instrum. Meas. 44: 530–532 Goldstein A N 1996 The melting of silicon nanocrystals: Submicron thin-film structures derived from nanocrystal precursors. Appl. Phys. A 62: 33–37 Kang K and Cai W 2010 Size and temperature effects on the fracture mechanisms of silicon nanowires: Molecular dynamics simulations. Int. J. Plast. 26: 1387–1401 Wolf H F 1971 Semiconductors. Wiley, Hoboken, 128 Cherian R, Gerard C, Mahadevan P, Cuong N T and Maezono R 2010 Size dependence of the bulk modulus of semiconductor nanocrystals from first-principles calculations. Phys. Rev. B 82: 235321 Zhu Y, Zheng W and Jiang Q 2009 Modeling lattice expansion and cohesive energy of nanostructured materials. Appl. Phys. Lett. 95: 083110 Siegel J, Lyutakov O, Rybka V, Kolská Z and Svorcík V 2011 Properties of gold nanostructures sputtered on glass. Nanoscale Res. Lett. 6: 96 Opalinska A, Malka I, Dzwolak W, Chudoba T, Presz A and Lojkowski W 2015 Size-dependent density of zirconia nanoparticles. Beilstein J. Nanotechnol. 6: 27–35 Banerjee R, Sperling E A, Thompson G B, Fraser H L, Bose S and Ayyub P 2003 Lattice expansion in nanocrystalline niobium thin films. Appl. Phys. Lett. 82: 4250–4252 Chattopadhyay P P, Nambissan P M G, Pabi S K and Manna I 2001 Polymorphic bcc to fcc transformation of nanocrystalline niobium studied by positron annihilation. Phys. Rev. B 63: 054107