A bond energy theory to analysis the melting temperature and Debye temperature of nanoscale solids

 
 
 
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  • Abstract


    Based on bond theory model and surface effects, a size dependent theory is discussed to study the melting temperature and Debye temperature of nanoscale materials. The number of atoms on the surface to the total number of atoms in nanosolid is analysed in terms of size and shape factor of nanomaterials. The variation of melting temperature and Debye temperature is reported for spherical, tetrahedral, hexahedral and octahedral shapes nanomaterials. It is found that the melting point and Debye temperature decrease as the particle size is reduced. The results studied are compared with the available experimental and simulation data. A good agreement between the present calculated results and the results reported by earlier scholars confirm the strength of the theory.


  • References


      [1] E. Roduner, Size matters: Why nanomaterials are different, Chem. Soc. Rev. 35 (2006) 583. 10.1039/b502142c. https://doi.org/10.1039/b502142c.

      [2] C.C. Yang, M.X. Xiao, W. Li, Q. Jiang, Size effects on Debye temperature, Einstein temperature, and volume thermal expansion coefficient of nanocrystals, Solid State Comm. 139 (2006) 148-152. https://doi.org/10.1016/j.ssc.2006.05.035.

      [3] R. Kumar, M. Kumar, Effect of size on cohesive energy, melting temperature and Debye temperature of nanomaterials, Indian journal of Pure and applied Phys. 50 (2012) 329.

      [4] M. Singh, S. Tlali, Effect of size on Debye temperature, melting entropy and enthalpy of nanomaterials, Journal of material nanoscience 4 (2017) 1-5 https://doi.org/10.1039/9781782620358-00001.

      [5] M. Singh, S. Lara, S. Tlali, Effect of size and shape on specific heat, melting entropy and enthalpy of nanomaterials, J of Taibah University for Science 11 (2017) 922-929. https://doi.org/10.1016/j.jtusci.2016.09.011.

      [6] A.K.H. Alassafee, M.S. Omar, Debye–Einstein approximation approach to calculate the lattice specific heat and related parameters for a Si nanowire, Journal of Taibah University for Science 11 (2017) 1226–1231. https://doi.org/10.1016/j.jtusci.2016.11.002.

      [7] H.K. Kim, S.H. Huh, J.W. Park, J.W. Jeong, G.H. Lee, The cluster size dependence of thermal stabilities of both molybdenum and tungsten nanoclusters, Chem. Phys. Let.354 (2002) 165. https://doi.org/10.1016/S0009-2614(02)00146-X.

      [8] W.H. Qi, B.Y. Haung, M.P. Wang, Z. Li, Z.M. Yu, Generalized bond-energy model for cohesive energy of small metallic particles, Phys. Lett. A 370 (2007) 494-498. https://doi.org/10.1016/j.physleta.2007.06.062

      [9] .K.K. Nanda, S.N. Sahu, S.N. Behra, Liquid-drop model for the size-dependent melting of low-dimensional systems, Phys. Rev. A 66 (2002) 013208. https://doi.org/10.1103/PhysRevA.66.013208.

      [10] W.H. Qi, M.P. Wang, G.Y Xu, The particle size dependence of cohesive energy of metallic nanoparticles, Chem. Phys. let.372 (2003) 632. https://doi.org/10.1016/S0009-2614(03)00470-6.

      [11] H. Saka, Y. Nishikawa, T. Imura, Melting temperature of in particles embedded in an Al matrix, Philoo. Mag a 57, (1988) 895-906. https://doi.org/10.1080/01418618808204524.

      [12] W. Qi, Nanoscopic thermodynamics, Accounts of Chem. Res. 49 (2016) 280. https://doi.org/10.1021/acs.accounts.6b00205.

      [13] W.H. Qi, M.P. Wang, Size and shape dependent melting temperature of metallic nanoparticles, Mater. Chem. Phys. 88 (2004) 280-284. https://doi.org/10.1016/j.matchemphys.2004.04.026.

      [14] C. Kittle, Introduction to Solid State Physics, 8th Ed. John Willey and Sons, New York, 2004.

      [15] J.H. Rose, J. Ferrante, J.R. Smith, Universal binding energy curves for metals and bimetallic interfaces, Phys. Rev. Lett.47 (1981) 675-678. https://doi.org/10.1103/PhysRevLett.47.675.

      [16] F.A. Lindemann, The calculation of molecular vibration frequencies, Phys. Z 11 (1910) 609-612.

      [17] V.P. Skripov, V.P. Koverda, V.N. Skokov, Size effect on melting of small particles, Phys. Status Solidi (a) 66 (1981) 109. https://doi.org/10.1002/pssa.2210660111.

      [18] Y.H. Zhao, K. Lu, Grain-size dependence of thermal properties of nanocrystalline elemental Selenium studied by X-ray diffraction, Phys. Rev. B 56 (1997) 14330. https://doi.org/10.1103/PhysRevB.56.14330.

      M. Hou, M.E. Azzaoui, H. Pattyn, J. Verheyden , G. Koops , G. Zhang, Growth and lattice dynamics of Co nanoparticles embedded in Ag: A combined molecular-dynamics simulation and Mossbauer study, Phys. Rev. B 62

 

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Article ID: 21531
 
DOI: 10.14419/ijet.v7i4.21531




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