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Size effect on thermodynamic properties of free nanocrystals

  • Mesoscopic and Nanoscale Systems
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Abstract

We demonstrate that the discrete character of the vibrational spectrum of a small crystal accounts for size dependence of its thermodynamic properties and melting temperature. Using a self-consistent statistical method [Phys. Rev. B 66, 054302 (2002)] we derive the Gibbs free energy of free nanocrystalline plates and calculate the thermodynamic parameters as functions of plate thickness for Cu.

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References

  • P. Pawlow, Z. Phys. Chem. 65, 1 (1909); P. Pawlow, Z. Phys. Chem. 65, 545 (1909)

  • M. Takagi, J. Phys. Soc. Jpn 9, 359 (1954)

    Google Scholar 

  • C.R.M. Wronski, Br. J. Appl. Phys. 18, 1731 (1967)

  • C.J. Coombes, J. Phys. F: Met. Phys. 2, 441 (1972)

    Google Scholar 

  • N.T. Gladkich, R. Neidermayer, K. Spiegel, Phys. Stat. Sol. 15, 181 (1966)

    Google Scholar 

  • P. Buffat, J.-P. Borel, Phys. Rev. A 13, 2287 (1976)

    Google Scholar 

  • R.H. Willens, A. Kornblit, L.R. Testardi, S. Nakahara, Phys. Rev. B 25, 290 (1982)

    Google Scholar 

  • S.L. Lai, J.Y. Guo, V. Petrova, G. Ramanath, L.H. Allen, Phys. Rev. Lett. 77, 99 (1996)

    Google Scholar 

  • S.L. Lai, J.R.A. Carlsson, L.H. Allen, Appl. Phys. Lett. 72, 1098 (1998)

    Google Scholar 

  • M. Zhang, M.Yu. Efremov, F. Schiettekatte, E.A. Olson, A.T. Kwan, S.L. Lai, T. Wisleder, J.E. Greene, L.H. Allen, Phys. Rev. B 62, 10548 (2000)

    Google Scholar 

  • E.A. Olson, M.Yu. Efremov, M. Zhang, L.H. Allen, J. Appl. Phys. 97, 034304 (2005)

    Google Scholar 

  • M.Yu. Efremov, F. Schiettekatte, M. Zhang, E.A. Olson, A.T. Kwan, R.S. Berry, L.H. Allen, Phys. Rev. Lett. 85, 3560 (2000)

    Google Scholar 

  • M. Zhang, M.Yu. Efremov, E.A. Olson, Z.S. Zhang, L.H. Allen, Appl. Phys. Lett. 81, 3801 (2002)

    Google Scholar 

  • J. Zhong, L.H. Zhang, Z.H. Jin, M.L. Sui, K. Lu, Acta Mater. 49, 2897 (2001)

  • T. Bachels, H.-J. Guntherodt, R. Schafer, Phys. Rev. Lett. 85, 1250 (2000)

    Google Scholar 

  • G.A. Breaux, R.C. Benirschke, M.F. Jarrold, J. Chem. Phys. 121, 6502 (2004)

    Google Scholar 

  • C.C. Yang, S. Li, Phys. Rev. B 75, 165413 (2007)

    Google Scholar 

  • W.H. Qi, M.P. Wang, J. Mater. Sci. Lett. 21, 1743 (2002)

    Google Scholar 

  • G. Kästle, H.-G. Boyen, A. Schröder, A. Plettl, P. Ziemann, Phys. Rev. B 70, 165414 (2004)

    Google Scholar 

  • C.C. Yang, M.X. Xiao, W. Li, Q. Jiang, Solid State Commun. 139, 148 (2006)

    Google Scholar 

  • T. Shibita, B.A. Bunker, Z. Zhang, D. Meisel, C.F. Vardeman II, J.D. Gezelter, J. Am. Chem. Soc. 124, 11989 (2002)

  • Q. Jiang, S.H. Zhang, J.C. Li, J. Phys. D 37, 102 (2004)

    Google Scholar 

  • T. Korhonen, M.J. Puska, R.M. Nieminen, Phys. Rev. B 51, 9526 (1995)

    Google Scholar 

  • C.J. Zhang, A. Alavi, J. Am. Chem. Soc. 127, 9808 (2005)

    Google Scholar 

  • K.-J. Hanszen, Z. Phys. 157, 523 (1960)

    Google Scholar 

  • P.R. Couchman, W.A. Jesser, Nature (London) 269, 481 (1977)

    Google Scholar 

  • K.F. Peters, J.B. Cohen, Y.-W. Chung, Phys. Rev. B 57, 13430 (1998)

    Google Scholar 

  • K.K. Nanda, S.N. Sahu, S.N. Behera, Phys. Rev. A 66, 013208 (2002)

    Google Scholar 

  • J. Tateno, Solid State Commun. 10, 61 (1972)

  • Y. Wang, S. Teitel, Christoph Dellago, Chem. Phys. Lett. 394, 257 (2004)

    Google Scholar 

  • Y. Qi, T. Cagin, W.L. Johnson, W.A. Goddard III, J. Chem. Phys. 115, 385 (2001)

    Google Scholar 

  • L. Hui, F. Pederiva, B.L. Wang, J.L. Wang, G.H. Wang, Appl. Phys. Lett. 86, 011913 (2005)

    Google Scholar 

  • U. Tartaglino, T. Zykova-Timan, F. Ercolessi, E. Tosatti, 2, 3 (2005) e-print arXiv:cond-mat/0504680

  • F. Ercolessi, W. Andreoni, E. Tosatti, Phys. Rev. Lett. 66, 911 (1991)

    Google Scholar 

  • F. Delogu, Phys. Rev. B 72, 205418 (2005)

    Google Scholar 

  • F. Delogu, Phys. Rev. B 75, 235421 (2007)

    Google Scholar 

  • S.J. Zhao, S.Q. Wang, D.Y. Cheng, H.Q. Ye, J. Phys. Chem. B 105, 12857 (2001)

    Google Scholar 

  • F. Baletto, R. Ferrando, Rev. Mod. Phys. 77, 371 (2005)

    Google Scholar 

  • A.I. Karasevskii, V.V. Lubashenko, Phys. Rev. B 71, 012107 (2005)

    Google Scholar 

  • A.I. Karasevskii, W.B. Holzapfel, V.V. Lubashenko, J. Low Temp. Phys. 139, 609 (2005)

    Google Scholar 

  • S.A. Gurvits, A.A. Migdal, A.M. Polyakov, Zh. Exp. Teor. Fiz. 46, 213 (1964)

    Google Scholar 

  • M.A. Krivoglaz, A.I. Karasevskii, Fiz. Tverd. Tela 17, 2565 (1975) [Sov. Phys. Solid State, 17, 1709 (1976)]

    Google Scholar 

  • A.I. Karasevskii, V.V. Lubashenko, Phys. Rev. B 66, 054302 (2002)

    Google Scholar 

  • A.I. Karasevskii, W.B. Holzapfel, Phys. Rev. B 67, 224301 (2003)

    Google Scholar 

  • A.I. Karasevskii, W.B. Holzapfel, Low Temp. Phys. 29, 711 (2003)

    Google Scholar 

  • A.I. Karasevskii, V.V. Lubashenko, Phys. Stat. Sol. (b) 241, 1274 (2004)

    Google Scholar 

  • A.I. Karasevskii, V.V. Lubashenko, Low Temp. Phys. 33, 578 (2007)

    Google Scholar 

  • R.P. Feynmann, Statistical Mechanics (Benjamin, New York, 1972)

  • H. Lamb, Proc. Math. Soc. London 98, 205 (1920)

    Google Scholar 

  • A.E.H. Love, Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944)

  • L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, 1965)

  • E. Madelung, Mathematical Apparatus of Physics (Springer, Berlin, 1957)

  • K.K. Nanda, S.N. Behera, S.N. Sahu, J. Phys.: Condens. Matter 13, 2861 (2001)

    Google Scholar 

  • W.H. Qi, M.P. Wang, J. Nanopart. Res. 7, 51 (2005)

    Google Scholar 

  • Physical acoustics. Principles and Methods, Applications to Quantum and Solid State Physics, part B, edited by W.P. Mason (Academic Press, New York and London, 1968), Vol. 4

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Authors and Affiliations

  1. Institute for Metal Physics, 36 Vernadsky str., Kiev, 03142, Ukraine

    A. I. Karasevskii & V. V. Lubashenko

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  1. A. I. Karasevskii
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  2. V. V. Lubashenko
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Correspondence to V. V. Lubashenko.

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Karasevskii, A., Lubashenko, V. Size effect on thermodynamic properties of free nanocrystals. Eur. Phys. J. B 66, 375–383 (2008). https://doi.org/10.1140/epjb/e2008-00429-9

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  • DOI: https://doi.org/10.1140/epjb/e2008-00429-9

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