La fusion et l'ébullition des petites particules sont discutées comme exemple d'un changement de phase du premier ordre dans un système fini. Un bref résumé de travaux antérieurs est présenté, ainsi qu'une expérience permettant la mesure des courbes de chaleur spécifiques pour de petits agrégats de sodium, sélectionnés en taille et se propageant dans le vide. Températures de fusion, chaleurs latentes et entropies de fusion sont déterminées pour des agrégats comportant de 55 à 357 atomes. On examine le cas d'agrégats présentant une capacité calorifique négative ainsi que la possibilité d'étudier une transition liquide–gaz pour des systèmes finis et isolés.
The solid to liquid transition of clusters is discussed, mainly from an experimental point of view. An experiment is sketched which allows to measure the caloric curve of size selected sodium clusters. Melting temperatures, latent heats, and entropies of melting are determined in the size range between 55 and 357 atoms per cluster. The melting temperatures are about 30% less than the bulk value and fluctuate strongly, one additional atom can change it by ±10 K. Latent heats and entropies show a similar behaviour. From the change in entropy one can deduce the increase of phase space upon melting, which is about twelve orders of magnitude already for Na+55 and increases exponentially for larger clusters. The theoretical prediction that a finite particle can have a negative heat capacity is verified experimentally, showing that their are differences between a canonical and a microcanonical description. Finally the analogue of the boiling phase transition is shown for a finite system.
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Mot clés : changement de phase pour agrégats, transition solide–liquide
Martin Schmidt 1 ; Hellmut Haberland 1
@article{CRPHYS_2002__3_3_327_0, author = {Martin Schmidt and Hellmut Haberland}, title = {Phase transitions in clusters}, journal = {Comptes Rendus. Physique}, pages = {327--340}, publisher = {Elsevier}, volume = {3}, number = {3}, year = {2002}, doi = {10.1016/S1631-0705(02)01326-9}, language = {en}, }
Martin Schmidt; Hellmut Haberland. Phase transitions in clusters. Comptes Rendus. Physique, Volume 3 (2002) no. 3, pp. 327-340. doi : 10.1016/S1631-0705(02)01326-9. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/S1631-0705(02)01326-9/
[1] Rev. Mod. Phys., 58 (1986), p. 533
[2] J. Phys. D, 24 (1992), p. 247
[3] Rev. Mod. Phys., 65 (1993), p. 677
[4] Rev. Mod. Phys., 65 (1993), p. 611
[5] Metal Clusters (W. Ekardt, ed.), Wiley, 1999
[6] J. Chem. Phys., 95 (1991), p. 1225
[7] Sci. Amer., 263 (1990), p. 50
[8] J. Chem. Phys., 84 (1986) no. 5, p. 2783
[9] Proceedings of the LXXIII Les Houches Summer School (2000) on Atomic Clusters and Nanoparticles (C. Guet et al., eds.), Springer-Verlag, Heidelberg, 2001, p. 437
[10] Sci. Amer., 245 (1981)
[11] Z. Phys. Chem., 65 (1909), p. 1
[12] Z. Phys. Chem., 65 (1909), p. 545
[13] J. Phys. Soc. Jpn., 9 (1954) no. 3, p. 359
[14] Phys. Rev. A, 13 (1976), p. 229
[15] Phys. Rev. Lett., 77 (1996), p. 99
[16] et al. Phys. Rev. Lett., 85 (2000), p. 3560
[17] Phys. Rev. B, 57 (1998), p. 13430
[18] Phys. Rev. B, 42 (1990), p. 8548
[19] Philos. Mag. A, 71 (1995), p. 1135
[20] Nature, 269 (1977), p. 481
[21] Phys. Rev. Lett., 85 (2000), p. 4494
[22] Phys. Rev. Lett., 65 (1990), p. 1567
[23] Phys. Rev. Lett., 73 (1994), p. 2875
[24] J. Chem. Phys., 63 (1975), p. 2045
[25] Phys. Rev. Lett., 79 (1997), p. 1873
[26] J. Chem. Phys., 112 (2000), p. 2888
[27] J. Chem. Phys., 115 (2001), p. 385
[28] Phys. Rev. Lett., 59 (1987), p. 1895
[29] Phys. Rev. Lett., 61 (1988) no. 10, p. 1190
[30] Phys. Rev. Lett., 62 (1989), p. 140
[31] J. Chem. Phys., 100 (1994), p. 6974
[32] Phys. Rev. Lett., 75 (1995), p. 1731
[33] Phys. Rev. B, 59 (1999), p. 10970
[34] Surf. Sci., 106 (1981), p. 95
[35] J. Mol. Struct., 413 (1997), p. 615
[36] Phys. Rep., 273 (1996), p. 199
[37] Z. Phys. D, 40 (1997), p. 160
[38] Phys. Rev. Lett., 85 (2000), p. 2530
[39] Phys. World ( December 2000 ), p. 27
[40] Phys. Rev. Lett., 85 (2000), p. 1250
[41] Phys. Rev. Lett., 86 (2001), p. 1388
[42] Microcanonical Thermodynamics: Phase Transitions in “Small” Systems, Lecture Notes in Physics, 66, World Scientific, Singapores, 2001
[43] Chaos Solitons Fractals, 13 (2002), p. 417 | arXiv
[44] Solid State Physics, Saunders College, Philadelphia, 1976
[45] Phys. Rev. Lett., 79 (1997), p. 99
[46] Nature, 393 (1998), p. 238
[47] Eur. Phys. J. D, 9 (2000), p. 1
[48] Proceedings of the LXXIII Les Houches Summer School (2000) on Atomic Clusters and Nanoparticles (C. Guet et al., eds.), Springer-Verlag, Heidelberg, 2001
[49] Phys. Rev. Lett., 67 (1991), p. 3290
[50] Phys. Rev. Lett., 69 (1992), p. 3212
[51] et al. The Physics and Chemistry of Clusters, Proceedings of Nobel Symposium, 117, World Scientific, Singapore, 2001, p. 326
[52] Science, 277 (1997), p. 1619
[53] Nature, 393 (1998), p. 212
[54] Clusters of Atoms and Molecules I (H. Haberland, ed.), Springer Series in Chemical Physics, 52, Springer-Verlag, Heidelberg, 1994
[55] Statistical Physics, Course of Theoretical Physics, 5, Pergamon Press, London, Paris, 1958 (1994)
[56] Clusters of Atoms and Molecules I (H. Haberland, ed.), Springer Series in Chemical Physics, 52, Springer-Verlag, Heidelberg, 1994 (part 2.7)
[57] Phys. Rev. Lett., 87 (2001), p. 203402
[58] J. Chem. Phys., 91 (1989), p. 1631
[59] J. Chem. Phys., 111 (1999), p. 6026
[60] Phys. Rev. Lett., 80 (1998), p. 3940
[61] Phys. Rev. B, 48 (1993), p. 2721
[62] J. Phys. Chem. B, 105 (2001), p. 2386
[63] Phys. Rev. B, 64 (2001), p. 04508
[64] Eur. Phys. D, 9 (1999), p. 451
[65] Phys. Rev. B, 62 (2000), p. 7602
[66] G. Wrigge, M. Astruc Hofmann, B. v. Issendorff, Phys. Rev. A, accepted for June 2002
[67] J. Chem. Phys., 92 (1990), p. 4473
[68] Phys. Rev. Lett., 86 (2001), p. 999
[69] The Physical Properties of Liquid Metals, Oxford Scientific Publications, Clarendon Press, Oxford, 1993
[70] Z. Phys., 235 (1970), p. 339
[71] Physica A, 263 (1999), p. 293
[72] et al. Phys. Lett. B, 473 (2000), p. 219
[73] Phys. Rev. C, 64 (2021), p. 044605
[74] Physica, 15 (1949), p. 951
[75] Phys. Rev. Lett., 86 (2001), p. 1191
[76] Phys. Rev. B, 57 (1998), p. 15519
[77] Phys. Rev. B, 60 (1999), p. 11734
[78] Phys. Rev. B, 49 (1994), p. 8491
[79] Phys. Rev. Lett., 87 (2001), p. 203401
[80] Z. Phys. D, 19 (1991), p. 1
[81] Clusters of Atoms and Molecules I (H. Haberland, ed.), Springer Series in Chemical Physics, 52, Springer-Verlag, Heidelberg, 1994, p. 273 (ff)
[82] Eur. Phys. J. E, 3 (2000), p. 165
[83] Colloid. Polym. Sci., 278 (2000), p. 608
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