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.
Similar content being viewed by others
References
Ph. Buffat, J.P. Borel: Size effect on the melting temperature of gold particles. Phys. Rev. A 13, 2287 (1976).
V. Das Damodara, D. Karunakaran: Thickness dependence of the phase transition temperature in Ag2Se thin films. J. Appl. Phys. 68, 2105 (1990).
C. Delerue, M. Lannoo: Nanostructures. Theory and Modelling (Springer, Berlin, Germany, 2004), p. 51.
D. Wang, H. Dai: Low-temperature synthesis of single-crystal germanium nanowires by chemical vapor deposition. Angew. Chem., Int. Ed. Engl. 41, 4783 (2002).
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).
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).
H.L. Yan, G.Q. Shi: Incorporation of gold nanocrystals into poly(3-alkylthiophene) nanowires and fabrication of gold nanowires. Nanotechnology 17, 13 (2006).
M.Z. Atashbar, D. Banerji, S. Singamaneni: Deposition of parallel arrays of palladium nanowires and electrical characterization using microelectrode contacts. Nanotechnology 15, 374 (2004).
D. Pan, Z. Shuyuan, Y. Chen, J.G. Hou: Hydrothermal preparation of long nanowires of vanadium oxide. J. Mater. Res. 17, 1981 (2002).
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).
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).
G.L. Allen, R.A. Bayles, W.W. Gile, W.A. Jesser: Small particle melting of pure metals. Thin Solid Films 144, 297 (1986).
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).
P. Pawlow: On the dependence of the melting point with the surface energy of solid materials. Z. Phys. Chem. 65, 1 (1909).
P.R. Couchman, W.A. Jesser: Thermodynamic theory of size dependence of melting temperature in metals. Nature 269, 481 (1977).
A. Nakanishi, T. Matsubara: A theory of melting of metallic fine particles. J. Phys. Soc. Jpn. 39, 1415 (1975).
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).
R.R. Vanfleet, J.M. Mochel: Thermodynamics of melting and freezing in small particles. Surf. Sci. 341, 40 (1995).
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).
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).
F. Celestini, A. Ten Bosch: Effect of shape on phase transition temperature of clusters. Phys. Lett. A 207, 307 (1995).
M. Wautelet: On the shape dependence of the melting temperature of small particles. Phys. Lett. A 246, 341 (1998).
M. Wautelet: Effects of size, shape and environment on the phase diagrams of small structures. Nanotechnology 3, 42 (1992).
M. Zhao, X.H. Zhou, Q. Jiang: Comparison of different models for melting point change of metallic nanoparticles. J. Mater. Res. 16, 3304 (2001).
M. Wautelet, J.P. Dauchot, M. Hecq: On the phase diagram of non-spherical nanoparticles. J. Phys.: Condens. Matter 15, 3651 (2003).
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).
M. Wautelet: On the melting of polyhedral elemental nanosolids. Eur. Phys. J. Appl. Phys. 29, 51 (2005).
G. Guisbiers, M. Wautelet: Size, shape and stress effects on the melting temperature of nano-polyhedral grains on a substrate. Nanotechnology 17, 2008 (2006).
M. Wautelet, J.P. Dauchot, M. Hecq: Phase diagrams of small particles of binary systems: A theoretical approach. Nanotechnology 11, 6 (2000).
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).
L.H. Liang, D. Liu, Q. Jiang: Size-dependent continuous binary solution phase diagram. Nanotechnology 14, 438 (2003).
A.S. Shirinyan, A.M. Gusak: Phase diagrams of decomposing nanoalloys. Philos. Mag. 84, 579 (2004).
A.S. Shirinyan, M. Wautelet: Phase separation in nanoparticles. Nanotechnology 15, 1720 (2004).
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).
W.A. Jesser, R.Z. Shneck, W.W. Gile: Solid-liquid equilibria in nanoparticles of Pb–Bi alloys. Phys. Rev. B 69, 144121 (2004).
A. Shirinyan, M. Wautelet, Y. Belogorodsky: Solubility diagram of the Cu–Ni nanosystem. J. Phys.: Condens. Matter 18, 2537 (2006).
M.C. Desjonquières, D. Spanjaard: Concepts in Surface Science (Springer-Verlag, Berlin, Germany, 1993), p. 131.
K.L. Chopra: Thin Film Phenomena (McGraw Hill, New York, 1969), p. 161.
L. Vitos, A.V. Ruban, H.L. Skriver, J. Kollar: The surface energy of metals. Surf. Sci. 411, 186 (1998).
Q. Jiang, H.M. Lu, M. Zhao: Modelling of surface energies of elemental crystals. J. Phys.: Condens. Matter 16, 521 (2004).
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).
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).
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).
F. Rosenberger: Fundamentals of Crystal Growth I, Macroscopic and Transport Concepts (Springer, New York, 1979).
J. Steininger: Thermodynamics and calculation of the liquidus–solidus gap in homogeneous, monotonic alloy systems. J. Appl. Phys. 41, 2713 (1970).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/jmr.2006.0345