Skip to main content

Phase Transitions in Clusters: A Bridge to Condensed Matter

  • Chapter
Linking the Gaseous and Condensed Phases of Matter

Part of the book series: NATO ASI Series ((NSSB,volume 326))

  • 261 Accesses

Abstract

Clusters of atoms or molecules, consisting of as few as three and as many as many thousands of particles, exhibit some properties of individual molecules, some properties of bulk matter and some properties characteristic specifically of small finite systems, that is, of clusters themselves. One of the unique sets of properties of clusters is their behavior with respect to phase equilibrium and phase changes--or at least to the analogues of the phases of bulk matter as they manifest themselves in small systems. Yet the unique phase behavior of clusters gives us new insights into the nature of phase equilibrium, phase transitions and metastability of the phases of bulk matter. This Chapter is a review of the status of this subject, which still has many major open questions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. J. McGinty, Molecular dynamics studies of the properties of small clusters of argon atoms, J. Chem. Phys. 58: 4733 (1973).

    Article  ADS  Google Scholar 

  2. R. M. Cotterill, W. Damgaard Kristensen, J. W. Martin, L. B. Peterson and E. J. Jensen, Comput. Phys. Comm. 5: 28 (1973).

    Article  ADS  Google Scholar 

  3. R. M. J. Cotterill, W. D. Kristensen and E. J. Jensen, Phil. Mag. 30: 245 (1974).

    Article  ADS  Google Scholar 

  4. R. M. J. Cotterill, Phil. Mag. 32: 1283 (1975).

    Article  ADS  Google Scholar 

  5. W. Damgaard Kristensen, E. J. Jensen and R. M. J. Cotterill, Thermodynamics of small clusters of atoms: A molecular dynamics simulation, J. Chem Phys. 60: 4161 (1974).

    Article  ADS  Google Scholar 

  6. C. L. Briant and J. J. Burton, Molecular dynamics study of the structure and thermodynamic properties of argon microclusters, J. Chem. Phys. 63: 2045 (1975).

    Article  ADS  Google Scholar 

  7. R. D. Etters and J. B. Kaelberer, Thermodynamic properties of small aggregates of rare- gas atoms, Phys. Rev. A. 11: 1068 (1975).

    Article  ADS  Google Scholar 

  8. R. D. Etters and J. B. Kaelberer, On the character of the melting transition in small atomic aggregates,J. Chem. Phys. 66: 5112 (1977).

    Article  ADS  Google Scholar 

  9. J. B. Kaelberer and R. D. Etters, Phase transitions in small clusters of atoms, J. Chem. Phys. 66: 3233 (1977).

    Article  ADS  Google Scholar 

  10. M. R. Hoare and P. Pal, Physical Cluster Mechanics: Statics and Energy Surfaces for Monatomic Systems, Adv. Phys. 20: 161 (1971).

    Google Scholar 

  11. M. R. Hoare and P. Pal, J. Cryst. Growth. 17: 77 (1972).

    Article  ADS  Google Scholar 

  12. M. R. Hoare and P. Pal, Nature. 236: 75 (1972).

    Article  ADS  Google Scholar 

  13. M. R. Hoare and P. Pal, Nature. 230: 5 (1972).

    ADS  Google Scholar 

  14. M. R. Hoare and P. Pal, Physical cluster mechanics: statistical thermodynamics and nucleation theory for monatomic systems, Adv. Phys. 24: 645 (1975).

    Article  ADS  Google Scholar 

  15. M. R. Hoare, Structure and Dynamics of Simple Microclusters, Adv. Chem. Phys. 40: 49 (1979).

    Article  Google Scholar 

  16. S. Sugano. “Microcluster Physics,” Springer-Verlag, Berlin (1991).

    Book  Google Scholar 

  17. W. v. E. Doering and W. R. Roth, Angew. Chem. 75: 27 (1963).

    Article  Google Scholar 

  18. E. L. Muetterties, Inorg. Chem. 4: 769 (1965).

    Article  Google Scholar 

  19. Z. Slanina. “Contemporary Theory of Chemical Isomerism,” D. Reidel, Dordrecht (1986).

    Google Scholar 

  20. V. V. Nauchitel and A. J. Pertsin, A Monte Carlo study of the structure and thermodynamic behaviour of small Lennard-Jones clusters, Mol. Phys. 40: 1341 (1980).

    Article  ADS  Google Scholar 

  21. R. Averbach, ed., “Surface Melting and Surface Diffusion on Clusters,” 206, Proc. Symposium on Clusters and Cluster-Assembled Materials, 1991, Materials Research Society, City (Year).

    Google Scholar 

  22. H.-P. Cheng and R. S. Berry, Surface melting of clusters and implications for bulk matter, Phys. Rev. A. 45: 7969 (1992).

    Article  ADS  Google Scholar 

  23. R. E. Kunz and R. S. Berry, Coexistence of multiple phases in finite systems, (submitted to Phys. Rev. Lett.). (1993).

    Google Scholar 

  24. R. E. Kunz and R. S. Berry, Multiple phase coexistence in finite systems, (submitted to Phys. Rev. E). (1993).

    Google Scholar 

  25. B. Baguenard, M. Pellarin, J. Lermé, J. L. Vialle and M. Broyer, Competition between atomic shell and electronic shell structures in aluminum clusters, (submitted to J. Chem. Phys.). (1993).

    Google Scholar 

  26. J. Lermé, C. Bordas, M. Pellarin, B. Baguenard, J. L. Vialle and M. Broyer, Influence of surface softness on supershell structure of metal clusters: Application to gallium, (submitted to Phys. Rev. B). (1993).

    Google Scholar 

  27. J. Luo, U. Landman and J. Jortner, Isomerization and Melting of Small Alkali-Halide Clusters, in: “Physics and Chemistry of Small Clusters,” P. Jena, B. K. Rao and S. N. Khanna. ed., Plenum Press, New York, N. Y. (1987).

    Google Scholar 

  28. J. P. Rose and R. S. Berry, Freezing, Melting, Nonwetting and Coexistence in (KCl)32, J. Chem. Phys. 98: 3246 (1993).

    Article  ADS  Google Scholar 

  29. J. Rose and R. S. Berry, (KCl)32 and the possibilities for glassy clusters, J. Chem. Phys. 98: 3262 (1993).

    Article  ADS  Google Scholar 

  30. R. S. Berry, J. Jellinek and G. Natanson, Unequal freezing and melting temperatures for clusters, Chem. Phys. Lett. 107: 227 (1984).

    Article  ADS  Google Scholar 

  31. R. S. Berry, J. Jellinek and G. Natanson, Melting of clusters and melting, Phys. Rev. A. 30: 919 (1984).

    Article  ADS  Google Scholar 

  32. S. Gartenhaus and C. Schwartz, Center-of-mass motion in many-particle systems, Phys. Rev. 108: 482 (1957).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. F. H. Stillinger and T. A. Weber, Inherent pair correlation in simple liquids, J. Chem. Phys. 80: 4434 (1984).

    Article  ADS  Google Scholar 

  34. R. S. Berry and D. J. Wales, Freezing, melting, spinodals and clusters, Phys. Rev. Lett. 63: 1156(1989).

    Article  ADS  Google Scholar 

  35. D. J. Wales and R. S. Berry, Melting and freezing of small argon clusters, J. Chem. Phys. 92: 4283 (1990).

    Article  ADS  Google Scholar 

  36. D. J. Wales and R. S. Berry, Freezing, melting, spinodals and clusters, J. Chem. Phys. 92: 4473 (1990).

    Article  ADS  Google Scholar 

  37. R. S. Berry, T. L. Beck, H. L. Davis and J. Jellinek, Solid-Liquid Phase Behavior in Microclusters, in: “Evolution of Size Effects in Chemical Dynamics, Part 2,” I. Prigogine and S. A. Rice, ed., John Wiley and Sons, New York (1988).

    Google Scholar 

  38. R. S. Berry, Clusters, Melting, Freezing and Phase Transitions, J. Chem. Soc. Faraday Trans. 86: 2343 (1990).

    Article  Google Scholar 

  39. R. S. Berry, Structure and dynamics of clusters: Phase equilibrium and phase change, in: “The Chemical Physics of Atomic and Molecular Clusters,” G. Scoles. ed., North-Holland, Amsterdam (1990).

    Google Scholar 

  40. R. S. Berry, Structure and dynamics of clusters: An introduction, in: “The Chemical Physics of Atomic and Molecular Clusters,” G. Scoles. ed., North-Holland, Amsterdam (1990).

    Google Scholar 

  41. R. S. Berry, Melting and Freezing of Clusters, in: H. Haberland. ed., (1992).

    Google Scholar 

  42. J. Jellinek, T. L. Beck and R. S. Berry, Solid-liquid phase changes in simulated isoenergetic Ar13, J. Chem. Phys. 84: 2783 (1986).

    Article  ADS  Google Scholar 

  43. T. L. Beck, J. Jellinek and R. S. Berry, Rare gas clusters: Solids, liquids, slush and magic numbers, J. Chem. Phys. 87: 545 (1987).

    Article  ADS  Google Scholar 

  44. T. L. Beck and R. S. Berry, The interplay of structure and dynamics in the melting of small clusters, J. Chem. Phys. 88: 3910 (1988).

    Article  ADS  Google Scholar 

  45. F. Amar and R. S. Berry, The onset of nonrigid dynamics and the melting transition in Ar7, J. Chem. Phys. 85: 5943 (1986).

    Article  ADS  Google Scholar 

  46. E. Blaisten-Barojas and D. Levesque, Molecular-dynamics simulation of silicon clusters, Phys. Rev. B. 34: 3910 (1986).

    Article  ADS  Google Scholar 

  47. E. Blaisten-Barojas and D. Levesque, A Molecular Dynamics Study of Silicon Clusters, in: “Physics and Chemistry of Small Clusters,” P. Jena, B. K. Rao and S. N. Khanna. ed., Plenum Press, New York (1987).

    Google Scholar 

  48. J. D. Honeycutt and H. C. Andersen, Molecular Dynamics Study of Melting and Freezing of Small Lennard-Jones Clusters, J. Phys. Chem. 91: 4950 (1987).

    Article  Google Scholar 

  49. S. Sawada, Dynamics of Transition Metal Clusters, in: “Microclusters,” S. Sugano, Y. Nishina and S. Ohnishi. ed., Springer-Verlag, Berlin (1987).

    Google Scholar 

  50. S. Sawada and S. Sugano, Structural fluctuations of Au55 and Au147: Substrate effect, Z. Phys. D. 24: 377 (1992).

    Article  ADS  Google Scholar 

  51. E. J. Valente and L. S. Bartell, Electron diffraction studies of supersonic jets. VI. Microdrops of benzene, J. Chem. Phys. 80: 1451 (1984).

    Article  ADS  Google Scholar 

  52. E. J. Valente and L. S. Bartell, Electron diffraction studies of supersonic jets. VII. Liquid and plastic crystalline carbon tetrachloride, J. Chem. Phys. 80: 1458 (1984).

    Article  ADS  Google Scholar 

  53. L. S. Bartell, Diffraction Studies of Clusters Generated in Supersonic Flow, Chem. Rev. 86: 492 (1986).

    Article  ADS  Google Scholar 

  54. L. S. Bartell, L. R. Sharkey and X. Shi, Electron Diffraction and Monte Carlo Studies of Liquids. 3. Supercooled Benzene, J. Am. Chem. Soc. 110: 7006 (1988).

    Article  Google Scholar 

  55. L. S. Bartell, L. Harsanyi and E. J. Valente, Phases and Phase Changes of Molecular Clusters Generated in Supersonic Flow, J. Phys. Chem. 93: 6201 (1989).

    Article  Google Scholar 

  56. S. W. Rick, D. L. Leitner, J. D. Doll, D. L. Freeman and D. D. Frantz, The quantum mechanics of clusters: the low-temperature equilibrium and dynamical behavior of rare-gas systems, J. Chem. Phys. 95: 6658 (1991).

    Article  ADS  Google Scholar 

  57. J. Bösiger and S. Leutwyler, Surface-Melting Transitions and Phase Coexistence in Argon Solvent Clusters, Phys. Rev. Lett. 59: 1895 (1987).

    Article  ADS  Google Scholar 

  58. J. Bösiger, R. Knochenmuss and S. Leutwyler, Wetting-nonwetting transitions in Argon solvent clusters, Phys. Rev. Lett. 62: 3058 (1989).

    Article  ADS  Google Scholar 

  59. R. Knochenmuss and S. Leutwyler, Selective spectroscopy of rigid and fluxional carbazole-argon clusters, J. Chem. Phys. 92: 4686 (1990).

    Article  ADS  Google Scholar 

  60. T. Troxler and S. Leutwyler, Electronic spectra of naphthalene-Arn solvent clusters (n=l- 30), J. Chem. Phys. 95: 4010 (1991).

    Article  ADS  Google Scholar 

  61. F. H. Stillinger and T. A. Weber, Point defects in bcc crystals: Structures, transition kinetics, and melting implications, J. Chem. Phys. 81: 5095 (1984).

    Article  ADS  Google Scholar 

  62. T. L. Hill, On First-Order Phase Transitions in Canonical and Grand Ensembles, J. Chem. Phys. 23: 812 (1955).

    Article  ADS  Google Scholar 

  63. T. L. Hill. “The Thermodynamics of Small Systems, Part 1,” W. A. Benjamin, New York (1963).

    Google Scholar 

  64. T. L. Hill. “The Thermodynamics of Small Systems, Part 2,” W. A. Benjamin, New York (1964).

    Google Scholar 

  65. H. C. Andersen, Molecular dynamics simulations at constant pressure and/or temperature, J. Chem. Phys. 72: 2384 (1980).

    Article  ADS  Google Scholar 

  66. S. Nosé, Mol. Phys. 52: 255 (1984).

    Google Scholar 

  67. S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81: 511 (1984).

    Article  ADS  Google Scholar 

  68. S. Nosé, Constant Temperature Molecular Dynamics Methods, Prog. Theor. Phys. Supplement 103: 1 (1991).

    Google Scholar 

  69. V. Privman and M. E. Fisher, Finite-size effects at first-order transitions, J. Stat. Phys. 33: 385 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  70. M. E. Fisher and V. Privman, First-Order Transitions in Spherical Models: Finite-Size Scaling, Commun. Math. Phys. 103: 527 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  71. S. Saxena, P. C. P. Bhatt and V. C. Prasad, IEEE Trans. Comput. 39: 400 (1990).

    Article  Google Scholar 

  72. R. J. Zauhar and R. S. Morgan, J. Comput. Chem. 11: 603 (1990).

    Article  Google Scholar 

  73. H. Edelsbrunner, in: “Algorithms in Combinatorial Geometry,” W. Brauer, G. Rozenberg and A. Saloma. ed., Springer-Verlag, New York (1987).

    Chapter  Google Scholar 

  74. K. Hoshino and S. Shimamura, A simple model for the melting of fine particles, Phil. Mag. A. 40: 137 (1979).

    Article  ADS  Google Scholar 

  75. Z. B. Güvenç and J. Jellinek, Surface Melting in Ni55, Z. Phys. D. 26: 304 (1993).

    Article  ADS  Google Scholar 

  76. K. Strandburg, Two-dimensional melting, Revs. Mod. Phys. 60: 161 (1988).

    Article  ADS  Google Scholar 

  77. G. Grange, R. Landers and B. Mutaftschiev, Contact Angle and Surface Morphology of KCl Crystal-Melt Interface Studied by the “Bubble Method”, Surf. Sci. 54: 445 (1976).

    Article  ADS  Google Scholar 

  78. A. Rahman, M. J. Mandell and J. P. McTague, Molecular dynamics study of an amorphous Lennard-Jones system at low temperature, J. Chem. Phys. 64: 1564 (1976).

    Article  ADS  Google Scholar 

  79. M. Amini and R. W. Hockney, Computer Simulation of Melting and Glass Formation in a Potassium Chloride Microcrystal, J. Non-Cryst. Sol. 31: 447 (1979).

    Article  ADS  Google Scholar 

  80. M. Amini, D. Fincham and R. W. Hockney, A molecular dynamics study of the melting of alkali halide crystals, J. Phys. C. 12: 4707 (1979).

    Article  ADS  Google Scholar 

  81. V. Buch, Identification of two distinct structural and dynamical domains in an amorphous water cluster, J. Chem. Phys. 93: 2631 (1990).

    Article  ADS  Google Scholar 

  82. H. Miyagawa, Y. Hiwatari and S. Itoh, Molecular-Dynamics Study for the Glass Transition in LiI, Prog. Theoret. Phys. Supplement No. 103: 47 (1991).

    Google Scholar 

  83. H.-P. Cheng and U. Landman, Controlled Deposition, Soft Landing, and Glass Formation in Nanocluster-Surface Collisions, Science. 260: 1304 (1993).

    Article  ADS  Google Scholar 

  84. L. S. Bartell, F. J. Dulles and B. Chuko, Structure and Dynamics of Molecular Clusters. Diagnostic Criteria in Monte Carlo Computations, J. Phys. Chem. 95: 6481 (1991).

    Article  Google Scholar 

  85. L. S. Bartell and S. Xu, Molecular Dynamics Examination of an Anomalous Phase of TeF6, J. Phys. Chem. 95: 8939 (1991).

    Article  Google Scholar 

  86. L. S. Bartell and J. Chen, Structure and Dynamics of Molecular Clusters. 2. Melting and Freezing of CC14 Clusters, J. Phys. Chem. 96: 8801 (1992).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media New York

About this chapter

Cite this chapter

Berry, R.S. (1994). Phase Transitions in Clusters: A Bridge to Condensed Matter. In: Christophorou, L.G., Illenberger, E., Schmidt, W.F. (eds) Linking the Gaseous and Condensed Phases of Matter. NATO ASI Series, vol 326. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2540-0_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-2540-0_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6083-4

  • Online ISBN: 978-1-4615-2540-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics