Thermodynamic models for the size-dependent melting of nanoparticles: Different hypotheses

Current Nanoscience

Volumn 8, Issue 2, 2012, Pages 305-311

  Goswami, Gopal Krishna ^a   Nanda, Karuna Kar ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

05.70. Np; 21.10.Dr; 36.40.Ei; 64.70.D Surface energy of solid surfaces; 64.70.dj; 65.80. g; 68.03.Cd; 68.35.Md; 82.60.Qr; Binding energies and masses; Melting; Nanoparticles thermal properties of; Phase transition soldliquid; Phase transitions in clusters; Surface tension; Thermodynamic properties of surfaces and interfaces

Indexed keywords

21.10.DR; 36.40.EI; 64.70.DJ; 65.80.-G; 68.03.CD; 68.35.MD; 82.60.QR; PHASE TRANSITIONS IN CLUSTERS; SOLID SURFACE; SURFACES AND INTERFACES;

BINDING ENERGY; LIQUIDS; MELTING; MELTING POINT; NANOPARTICLES; SURFACE TENSION; THERMODYNAMIC PROPERTIES;

PHASE TRANSITIONS;

NANOPARTICLE;

ARTICLE; LINEAR SYSTEM; MELTING POINT; NONLINEAR SYSTEM; PARTICLE SIZE; PRIORITY JOURNAL; TEMPERATURE; THERMODYNAMICS;

AVES;

EID: 84860274824     PISSN: 15734137     EISSN: 18756786     Source Type: Journal    
DOI: 10.2174/157341312800167731     Document Type: Article

References (73)

1. Pawlow, P. Über die Abhängigkeit des Schmelzpunktes von der Oberflächenenergie eines Festen Körpers. Z. Phys. Chem., 1909, 65, 1-35.
2. Pawlow, P. Über die Abhängigkeit des Schmelzpunktes von der Oberflächenenergie eines festen Körpers (Zusatz). Z. Phys. Chem., 1909, 65, 545-548.
3. Hanszen, K.J. Theoretische untersuchungen uber den schmelzpunkt kleiner kugelchen-ein beitrag zur thermodynamik der grenzflachen. Z. Phys., 1960, 157(5), 523-553.
4. Borel, J.-P. Thermodynamical size effect and the structure of metallic clusters. Surf. Sci., 1981, 106(1-3), 1-9.
5. Couchman, P.R.; Jesser, W.A. Thermodynamic theory of size dependence of melting temperature in metals. Nature, 1977, 269(5628), 481-483.
6. Gülseren, O.; Ercolessi F.; Tosatti, E. Premelting of thin wires. Phys. Rev. B, 1995, 51(11), 7377-7380.
7. Vanfleet, R.R.; Mochel, J.M. Thermodynamics of melting and freezing in small particles. Surf. Sci., 1995, 341(1-2), 40-50.
8. Sakai, H. Surface-induced melting of small particles. Surf. Sci., 1996, 351(1-3), 285-291.
9. Sakai, H. How does a slab-shaped solid melt? 1996, 348(3), 387-392.
10. Ercolessi, F.; Androni W.; Tosatti, E. Melting of small gold particles-mechanism and size effects. Phys. Rev. Lett., 1991, 66(7), 911-914.
11. Nanda, K.K.; Sahu S.N.; Behera, S.N. Liquid-drop model for the sizedependent melting of low-dimensional systems. Phys. Rev. A, 2002, 66(1), 013208.
12. Miao, L.; Bhethanabotla V.R.; Joseph, B. Melting of Pd clusters and nanowires: A comparison study using molecular dynamics simulation. Phys. Rev. B, 2005, 72(13), 134109.
13. Ding, F.; Rosen, A.; Curtarolo, S.; Bolton, K. Modeling the melting of supported clusters. Appl. Phys. Lett., 2006, 88(13), 133110.
14. Ben-David, T.; Lereah, Y.; Deutscher, G.; Kofman R.; Cheyssac, P. Solidliquid transition in ultra-fine lead particles. Phil. Mag. A, 1995, 71(5), 1135-1143.
15. Goldstein, A.N.; Echer, C.M.; Alivisatos, A.P. Melting in semiconductor nanocrystals. Science, 1992, 256(5062), 1425-1427.
16. Castro, T.; Reifenberger, R.; Choi, E.; Andres, R.P. Size-dependent melting temperature of individual nanometer-sized metallic clusters. Phys. Rev. B, 1990, 42(13), 8548-8556.
17. Sambles, J.R. Electron microscope study of evaporating gold particles-kelvin equation for liquid gold and lowering of melting point of solid gold particles. Proc. R. Soc. Lond. A, 1971, 324(1558), 339-351.
18. Buffat Ph.; Borel, J-P. Size effect on melting temperature of gold particles. Phys. Rev. A, 1976, 13(6), 2287-2298.
19. Dick, K.; Dhanasekaran, T.; Zhang, Z.; Meisel, D. Size-dependent melting of silica-encapsulated gold nanoparticles. J. Am. Chem. Soc., 2002, 124(10), 2312-2317.
20. Wronski, C.R.M. Size dependence of melting point of small particles of tin. Brit. J. Appl. Phys., 1967, 18(12), 1731-1737.
21. Lai, S.L.; Guo, J.Y.; Petrova, V.; Ramanath, G.; Allen, L.H. Size-dependent melting properties of small tin particles: Nanocalorimetric measurements. Phys. Rev. Lett., 1996, 77(1), 99-102.
22. Oshima Y.; Takayanagi, K. Solid-liquid phase-transition of tin particles observed by uhv high-resolution transmission electron-microscopy-pseudocrystalline phase. Z. Phys. D, 1993, 27(3), 287-294.
23. Bachels, T.; Gunterodt H.-J.; Schafer, R. Melting of isolated tin nanoparticles. Phys. Rev. Lett., 2000, 85(6), 1250-1253.
24. Wautelet, M. 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, 1991, 24(3), 343-346.
25. Wautelet, M. On the shape dependence of the melting temperature of small particles. Phys. Lett. A, 1998, 246(3-4), 341-342.
26. Jiang, Q.; Tong, H.Y.; Hsu, D.T.; Okuyama K.; Shy, F.G. Thermal stability of crystalline thin films. Thin Solid Films, 1998, 312(1-2), 357-361.
27. Kan, C.; Wang, G.; Zhu, X.; Li C.; Cao, B. Structure and thermal stability of gold nanoplates. Appl. Phys. Lett., 2006, 88(7), 071904.
28. Pawlow, P. Über den Dampfdruck der Körner einer festen Substanz. Z. Physik. Chem. 1910, 68, 316-322.
29. Kofman, R.; Cheyssac, P.; Aouaj, A.; Lereah, Y.; Deutscher, G.; Ben-David, T.; Penisson H. M.; Bourret, A. Surface melting enhanced by curvature effects. Surf. Sci., 1994, 303(1-2), 231-246.
30. Takagi, M. Electron-diffraction study of liquid-solid transition of thin metal films. J. Phys. Soc. Jap., 1954, 9(3), 359-363.
31. Blackman M.; Curzon, A.E. Structure and Properties of Thin Films (Edited by Neugebauer, C.; Newkirk J. B. and Vermilyea D. A.), Wiley, New York, 1959, p. 217.
32. Gladkich, N.T.; Niedermayer R.; Spiegel, K. Nachweis grosser schmelzpunktserniedrigungen bei dunnen metallschichten. Phys. Status. Solidi, 1966, 15(1), 181.
33. Sun, C.Q.; Shi, Y.; Li, C.M.; Li, S.; Yeung, T. C. Au Size-induced undercooling and overheating in phase transitions in bare and embedded clusters. Phys. Rev., 2006, 73(7), 075408.
34. Pocza, J.F.; Barna A.; Barna, P.B. Formation processes of vacuum-deposited indium films and thermodynamical properties of submicroscopic particles observed by in situ electron microscopy. J. Vac. Sci. Technol., 1969, 6(4), 472-475.
35. Boiko, B.T.; Pugachev A.T.; Bratsykhin, V.M. Melting of subcritically thin condensed films of indium. Soviet. Phys. Solid Stat., 1969, 10(12), 2832.
36. Chen, X.; Zhao, J.; Sun, Q.; Liu, F.; Wang G.; Shen, X.C. Surface thermal stability of nickel clusters. Phys. Stat. Sol. B, 1996, 193(2), 355-361.
37. Zhang, M.; Efremov, M. Yu; Schiettekatte, F.; Olson, E.A.; Kwan, A.T.; Lai, S.L.; Wisleder, T.; Greene J.E.; Allen, L.H. Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements. Phys. Rev. B, 2000, 62(15), 10548-10557.
38. Schmidt, M.; Kusche, R.; Issendorff B.V.; Haberland, H. Irregular variations in the melting point of size-selected atomic clusters. Nature, 1998, 393(6682), 238-240.
39. Martin, T.P.; Naher, U.; Schaber, H.; Zimmermann, U. Evidence for a sizedependent melting of sodium clusters. J. Chem. Phys., 1994, 100(3), 2322-2324.
40. Jiang, A.; Awasthi, N.; Kolmogorov, A.N.; Setyawan, W.; Borjesson, A.; Bolton, K.; Harutyunyan A.R.; Curtarolo, S. Theoretical study of the thermal behavior of free and alumina-supported Fe-C nanoparticles. Phys. Rev. B, 2007, 75(20), 205426.
41. Skripov, V.P.; Koverda V.P.; Skokov, V.N. Size effect on melting of small particles. Phys. Status Solidi A, 1981, 66(1), 109-118.
42. Yu, D.K.; Zhang R.Q.; Lee, S.T. Structural transition in nanosized silicon clusters. Phys. Rev. B, 2002, 65(24), 245417.
43. Olson, E.A.; Efremov, M. Yu.; Zhang, M.; Zhang, Z.; Allen, L.H. Sizedependent melting of Bi nanoparticles. J. Appl. Phys., 2005, 97(3), 034304.
44. Farrell H.H.; Van Siclen, C.D. Binding energy, vapor pressure, and melting point of semiconductor nanoparticles. J. Vac. Sci. Technol. B, 2007, 25(4), 1441-1447.
45. Cao, G. Nanostructure and Nanomaterials, synthesis, properties and applications, Imperial College Press, 2004.
46. Kofman, R.; Cheyssac P.; Celestini, F. Comment on "Melting of isolated tin nanoparticles". Phys. Rev. Lett., 2001, 86(7), 1388-1388.
47. Wang, X.W.; Fei, G.T.; Zheng, K.;Jin, Z.; Zhang, L.D. Size-dependent melting behavior of Zn nanowire arrays. Appl. Phys. Lett., 2006, 88(17), 173114.
48. Goswami, G.K.; Nanda, K.K. Comment on "Size-dependent melting behavior of Zn nanowire arrays" [Appl. Phys. Lett. 88, 173114 (2006)]. Appl. Phys. Lett., 2007, 91(19), 196101.
49. Pluis, B.; Frenkel D.; van der Veen, J.F. Surface-induced melting and freezing. II. A semiempirical landau-type model. Surf. Sci., 1990, 239(3), 282-300.
50. Hendy, S.C. A thermodynamic model for the melting of supported metal nanoparticles. Nanotechnology, 2007, 18(17), 175703.
51. Xu Q.; Sharp, I.D.; Yuan, C.W.; Yi, D.O.; Liao, C.Y.; Glaeser, A.M.; Minor, A.M.; Beeman, J.W.; Ridgway, M.C.; Kluth, P.; Ager, J.W.; Chrzan, D.C.; Haller, E.E. Large melting-point hysteresis of Ge nanocrystals embedded in SiO2. Phys. Rev. Lett., 2006, 97(15), 155701.
52. Zhu, Y.F.; Lian, J.S.; Jiang, Q. Modeling of the Melting Point, Debye Temperature, Thermal Expansion Coefficient, and the Specific Heat of Nanostructured Materials. J. Phys. Chem. C, 2009, 113(39), 16896-16900.
53. Zhu, Y.F.; Zheng, W.T.; Jiang, Q. Modeling lattice expansion and cohesive energy of nanostructured materials. Appl. Phys. Lett., 2009, 95(8), 083110.
54. Karasevskii, A.I.; Lubashenko, V.V. Size effect on thermodynamic properties of free nanocrystals. Eur. Phys. J. B, 2008, 66(3), 375-383.
55. Karasevskii, A.I. Excess pressure of the phonon gas in nanocrystals. Solid State Commun., 2011, 151(5), 360-363.
56. Peters K.F.; Cohen J.B.; Chung Y.W. Melting of Pb nanocrystals. Phys. Rev. B, 1998, 57(21), 13430-13438.
57. Reiss, H.; Wilson, I.B. The effect of surface on melting point. J. Colloid Sci., 1948, 3(6), 551-561.
58. Mochrie, S.G.J.; Zehner, D.M.; Ocko B.M.; Gibbs, D. Structure and phases of the Au(001) surface-x-ray-scattering measurements. Phys. Rev. Lett., 1990, 64(24), 2925-2928.
59. Carnevali, P.; Ercolessi F.; Tosatti, E. Melting and nonmelting behavior of the Au(111) surface. Phys. Rev. B, 1987, 36(12), 6701-6704.
60. Lereah, Y.; Deutscher, G.; Cheyssac, P.; Kofman, R. A Direct observation of low-dimensional effects on melting of small lead particles. Europhys. Lett., 1990, 12(8), 709-713.
61. Sondergard, E.; Kofman, R.; Cheyssac, P.; Celestini, F.; Ben-David T.; Lereah, Y. Measurement of the wetting angle of nanoparticles using surface melting. Surf. Sci., 1997, 388(1-3), L1115-L1120.
62. Bonzel, H.P. A surface diffusion mechanism at high temperature. Surf. Sci., 1970, 21(1), 45.
63. Storozhev, V.B. The solid-liquid phase transition in nanoparticles contacting with a solid surface. Surf. Sci., 1998, 397(1-3), 170-178.
64. Reiss, H.; Mirabel P.; Whetten R.L. Capillarity theory for the coexistence of liquid and solid clusters. J. Phys. Chem., 1988, 92(26), 7241-7246.
65. Wautelet, M. On the melting of polyhedral elemental nanosolids. Eur. Phys. J. Appl. Phys., 2005, 29(1), 51-54.
66. Depero, L.E.; Bontempi, E.; Sangaletti, L.; Pagliara, S. Melting of nanostructured Sn probed by in-situ x-ray diffraction. J. Chem. Phys., 2003, 118(3), 1400-1403.
67. Haro-Poniatowski, E.; Serna, R.; Afonso, C.N.; Jouanne, M.; Morhange, J.F.; Bosch, P.; Lara, V.H. Hysteresis in the melting kinetics of Bi nanoparticles. Thin Sold Films, 2004, 453-454, 467-470.
68. Guisbiers, G.; Kazan, M.; Van verschelde, O.; Wautelet, M.; Pereira, S. Mechanical and thermal properties of metallic and semiconductive nanostructures. J. Phys. Chem. C, 2008, 112(11), 4097-4103.
69. Jiang, Q.; Lu, H.M.; Zhao, M. Modelling of surface energies of elemental crystals. J. Phys.-Cond. Matter, 2004, 16(4), 521-530.
70. Hoss, A.; Nold, M.; von Blackenhagen P.; Moyer, O. Roughening and melting of Au(110) surfaces. Phys. Rev. B, 1992, 45(15), 8714-8720.
71. Haderbache, L.; Garrigos, R.; Kofman, R.; Sondergard E.; Cheyssac, P. Numerical and experimental investigations of the size ordering of nanocrystals. Surf. Sci., 1998, 410(2-3), L748-L756.
72. Bilalbegovic, G.; Tosatti, E. Incomplete melting of the Au(100) surface. Phys. Rev. B, 1993, 48(15), 11240-11248.
73. Wulff, G. Zur Frage der Geschwindigheit des Wachstlums und der Auflosung der Krystallflachen. Z. Kristallogr., 1901, 34(5/6), 449-530.