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Theoretical phase diagrams of nanowires

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Abstract

Systems with typical dimensions in the range of 1–100 nm are in an intermediate state between solid and molecular. Such systems are characterized by the fact that the ratio of the number of surface to volume atoms is not small. This is known to lead to size and shape effects on their cohesive properties. In this work, the phase diagram of nanowires was studied in the framework of classical thermodynamics. The roles of the size, shape, and surface tensions were emphasized. The melting temperatures of nanowires of 21 elements were evaluated theoretically. In the case of binary systems, it was shown that the experimental or theoretical knowledge of the size-dependent phase diagrams of a given binary system allows the evaluation of the one of nanowires. The procedure is described in this paper.

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References

  1. Ph. Buffat, J.P. Borel: Size effect on the melting temperature of gold particles. Phys. Rev. A 13, 2287 (1976).

    Article  CAS  Google Scholar 

  2. V. Das Damodara, D. Karunakaran: Thickness dependence of the phase transition temperature in Ag2Se thin films. J. Appl. Phys. 68, 2105 (1990).

    Article  Google Scholar 

  3. C. Delerue, M. Lannoo: Nanostructures. Theory and Modelling (Springer, Berlin, Germany, 2004), p. 51.

    Book  Google Scholar 

  4. D. Wang, H. Dai: Low-temperature synthesis of single-crystal germanium nanowires by chemical vapor deposition. Angew. Chem., Int. Ed. Engl. 41, 4783 (2002).

    Article  CAS  Google Scholar 

  5. B.A. Wacaser, K. Deppert, L.S. Karlsson, L. Samuelson, W. Seifert: Growth and characterization of defect free GaAs nanowires. J. Cryst. Growth 287, 504 (2006).

    Article  CAS  Google Scholar 

  6. S.D. Bunge, K.M. Krueger, T.J. Boyle, M.A. Rodriguez, T.J. Headley, V.L. Colvin: Growth and morphology of cadmium chalcogenides: The synthesis of nanorods, tetrapods, and spheres from CdO and Cd(O2CCH3)2. J. Mater. Chem. 13, 1705 (2003).

    Article  CAS  Google Scholar 

  7. H.L. Yan, G.Q. Shi: Incorporation of gold nanocrystals into poly(3-alkylthiophene) nanowires and fabrication of gold nanowires. Nanotechnology 17, 13 (2006).

    CAS  Google Scholar 

  8. M.Z. Atashbar, D. Banerji, S. Singamaneni: Deposition of parallel arrays of palladium nanowires and electrical characterization using microelectrode contacts. Nanotechnology 15, 374 (2004).

    CAS  Google Scholar 

  9. D. Pan, Z. Shuyuan, Y. Chen, J.G. Hou: Hydrothermal preparation of long nanowires of vanadium oxide. J. Mater. Res. 17, 1981 (2002).

    CAS  Google Scholar 

  10. Z. Zhang, P-E. Hellström, M. Ostling, S.L. Zhang: Electrically robust ultralong nanowires of NiSi, Ni2Si, and Ni31Si12.Appl. Phys. Lett. 88, 043104 (2006).

    Article  CAS  Google Scholar 

  11. L. Miao, V.R. Bhethanabotla, B. Joseph: Melting of Pd clusters and nanowires: A comparison study using molecular dynamics simulation. Phys. Rev. B 72, 134109 (2005).

    Article  CAS  Google Scholar 

  12. G.L. Allen, R.A. Bayles, W.W. Gile, W.A. Jesser: Small particle melting of pure metals. Thin Solid Films 144, 297 (1986).

    Article  CAS  Google Scholar 

  13. H.W. Sheng, J. Xu, L.G. Yu, X.K. Sun, Z.Q. Hu, K. Lu: Melting process of nanometer-sized In particles embedded in an Al matrix synthesized by ball milling. J. Mater. Res. 11, 2841 (1996).

    Article  CAS  Google Scholar 

  14. P. Pawlow: On the dependence of the melting point with the surface energy of solid materials. Z. Phys. Chem. 65, 1 (1909).

    Article  CAS  Google Scholar 

  15. P.R. Couchman, W.A. Jesser: Thermodynamic theory of size dependence of melting temperature in metals. Nature 269, 481 (1977).

    Article  CAS  Google Scholar 

  16. A. Nakanishi, T. Matsubara: A theory of melting of metallic fine particles. J. Phys. Soc. Jpn. 39, 1415 (1975).

    Article  CAS  Google Scholar 

  17. M. Wautelet: Estimation of the variation of the melting temperature with the size of small particles, on the basis of a surface-phonon instability model. J. Phys. D: Appl. Phys. 24, 343 (1991).

    Article  CAS  Google Scholar 

  18. R.R. Vanfleet, J.M. Mochel: Thermodynamics of melting and freezing in small particles. Surf. Sci. 341, 40 (1995).

    Article  CAS  Google Scholar 

  19. K.K. Nanda, S.N. Sahu, S.N. Behera: Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys. Rev. A 66, 013208 (2002).

    Article  CAS  Google Scholar 

  20. C.Q. Sun, B.K. Tay, X.T. Zeng, S. Li, T.P. Chen, J.I. Zhou, H.L. Bai, E.Y. Jiang: Bond-order-bond-length strength (bond-OLS) correlation mechanism for the shape-and-size dependence of a nanosolid. J. Phys.: Condens. Matter 14, 7781 (2002).

    CAS  Google Scholar 

  21. F. Celestini, A. Ten Bosch: Effect of shape on phase transition temperature of clusters. Phys. Lett. A 207, 307 (1995).

    CAS  Google Scholar 

  22. M. Wautelet: On the shape dependence of the melting temperature of small particles. Phys. Lett. A 246, 341 (1998).

    CAS  Google Scholar 

  23. M. Wautelet: Effects of size, shape and environment on the phase diagrams of small structures. Nanotechnology 3, 42 (1992).

    Google Scholar 

  24. M. Zhao, X.H. Zhou, Q. Jiang: Comparison of different models for melting point change of metallic nanoparticles. J. Mater. Res. 16, 3304 (2001).

    CAS  Google Scholar 

  25. M. Wautelet, J.P. Dauchot, M. Hecq: On the phase diagram of non-spherical nanoparticles. J. Phys.: Condens. Matter 15, 3651 (2003).

    CAS  Google Scholar 

  26. D. Xie, M.P. Wang, W.H. Qi: A simplified model to calculate the surface-to-volume atomic ratio dependent cohesive energy of nanocrystals. J. Phys.: Condens. Matter 16, L401 (2004).

    CAS  Google Scholar 

  27. M. Wautelet: On the melting of polyhedral elemental nanosolids. Eur. Phys. J. Appl. Phys. 29, 51 (2005).

    CAS  Google Scholar 

  28. G. Guisbiers, M. Wautelet: Size, shape and stress effects on the melting temperature of nano-polyhedral grains on a substrate. Nanotechnology 17, 2008 (2006).

    CAS  Google Scholar 

  29. M. Wautelet, J.P. Dauchot, M. Hecq: Phase diagrams of small particles of binary systems: A theoretical approach. Nanotechnology 11, 6 (2000).

    CAS  Google Scholar 

  30. R. Vallee, M. Wautelet, J.P. Dauchot, M. Hecq: Size and segregation effects on the phase diagrams of nanoparticles of binary systems. Nanotechnology 12, 68 (2001).

    Article  CAS  Google Scholar 

  31. L.H. Liang, D. Liu, Q. Jiang: Size-dependent continuous binary solution phase diagram. Nanotechnology 14, 438 (2003).

    Article  CAS  Google Scholar 

  32. A.S. Shirinyan, A.M. Gusak: Phase diagrams of decomposing nanoalloys. Philos. Mag. 84, 579 (2004).

    Article  CAS  Google Scholar 

  33. A.S. Shirinyan, M. Wautelet: Phase separation in nanoparticles. Nanotechnology 15, 1720 (2004).

    Article  CAS  Google Scholar 

  34. A.S. Shirinyan, A.M. Gusak, M. Wautelet: Phase diagram versus diagram of solubility: What is the difference for nanosystems? Acta Mater. 53, 5025 (2005).

    Article  CAS  Google Scholar 

  35. W.A. Jesser, R.Z. Shneck, W.W. Gile: Solid-liquid equilibria in nanoparticles of Pb–Bi alloys. Phys. Rev. B 69, 144121 (2004).

    Article  CAS  Google Scholar 

  36. A. Shirinyan, M. Wautelet, Y. Belogorodsky: Solubility diagram of the Cu–Ni nanosystem. J. Phys.: Condens. Matter 18, 2537 (2006).

    CAS  Google Scholar 

  37. M.C. Desjonquières, D. Spanjaard: Concepts in Surface Science (Springer-Verlag, Berlin, Germany, 1993), p. 131.

    Book  Google Scholar 

  38. K.L. Chopra: Thin Film Phenomena (McGraw Hill, New York, 1969), p. 161.

    Google Scholar 

  39. L. Vitos, A.V. Ruban, H.L. Skriver, J. Kollar: The surface energy of metals. Surf. Sci. 411, 186 (1998).

    Article  CAS  Google Scholar 

  40. Q. Jiang, H.M. Lu, M. Zhao: Modelling of surface energies of elemental crystals. J. Phys.: Condens. Matter 16, 521 (2004).

    CAS  Google Scholar 

  41. C.Q. Sun, Y. Shi, C.M. Li, S. Li, T.C. Au Yeung: Size-induced undercooling and overheating in phase transitions in bare and embedded clusters. Phys. Rev. B, 73, 075408-1-9 (2006).

  42. H. Chen, Y. Gao, H. Yu, H. Zhang, L. Liu, Y. Shi, H. Tian, S. Xie, J. Li: Structural properties of silver nanorods with fivefold symmetry. Micron. 35, 469 (2004).

    Google Scholar 

  43. M. Wautelet: On the transitions between the crystalline, amorphous and liquid phases of silicon and germanium, when their size decreases. Phys. Status Solidi B 159 K43(1990).

  44. F. Rosenberger: Fundamentals of Crystal Growth I, Macroscopic and Transport Concepts (Springer, New York, 1979).

    Google Scholar 

  45. J. Steininger: Thermodynamics and calculation of the liquidus–solidus gap in homogeneous, monotonic alloy systems. J. Appl. Phys. 41, 2713 (1970).

    CAS  Google Scholar 

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Abudukelimu, G., Guisbiers, G. & Wautelet, M. Theoretical phase diagrams of nanowires. Journal of Materials Research 21, 2829–2834 (2006). https://doi.org/10.1557/jmr.2006.0345

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