Phase transitions in clusters

Martin Schmidt; Hellmut Haberland

doi:10.1016/S1631-0705(02)01326-9

Agrégats comme précurseurs des nano-objets/Clusters as precursors of nano-objects

Phase transitions in clusters
[Transitions de phase dans les agrégats]

Martin Schmidt ¹ ; Hellmut Haberland ¹

¹ Fakultät für Physik, Universität Freiburg, H. Herderstrasse 3, 79104 Freiburg, Germany

Comptes Rendus. Physique, Volume 3 (2002) no. 3, pp. 327-340.

Abstract (VO)
Résumé

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.

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.

Reçu le : 2002-01-17
Accepté le : 2002-01-28
Publié le : 2002-04-01

DOI : 10.1016/S1631-0705(02)01326-9

Keywords: phase transition in clusters, solid–liquid transition
Mots-clés : changement de phase pour agrégats, transition solide–liquide

Affiliations des auteurs :

Martin Schmidt ¹ ; Hellmut Haberland ¹

¹ Fakultät für Physik, Universität Freiburg, H. Herderstrasse 3, 79104 Freiburg, Germany

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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/

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H. M. Lu; Z. H. Cao; C. L. Zhao; P. Y. Li; X. K. Meng Size-dependent ordering and Curie temperatures of FePt nanoparticles, Journal of Applied Physics, Volume 103 (2008) no. 12 | DOI:10.1063/1.2946724
Zhen Hua Li; Donald G. Truhlar Nanosolids, Slushes, and Nanoliquids: Characterization of Nanophases in Metal Clusters and Nanoparticles, Journal of the American Chemical Society, Volume 130 (2008) no. 38, p. 12698 | DOI:10.1021/ja802389d
J.A. Blackman Chapter 2 Shell Models of Isolated Clusters, Metallic Nanoparticles, Volume 5 (2008), p. 17 | DOI:10.1016/s1570-002x(08)00202-4
E. F. Kustov; V. I. Nefedov Nanostructures: Compositions, structure, and classification, Russian Journal of Inorganic Chemistry, Volume 53 (2008) no. 14, p. 2103 | DOI:10.1134/s0036023608140027
V. Aquilanti; A. Lombardi; M. B. Sevryuk Statistics of partitions of the kinetic energy of small nanoclusters, Russian Journal of Physical Chemistry B, Volume 2 (2008) no. 6, p. 947 | DOI:10.1134/s1990793108060134
M. Eryürek; M. H. Güven Peculiar thermodynamic properties of LJ N (N = 39–55) clusters, The European Physical Journal D, Volume 48 (2008) no. 2, p. 221 | DOI:10.1140/epjd/e2008-00094-2
Seyed Mohammad Ghazi; Mal-Soon Lee; D. G. Kanhere The effects of electronic structure and charged state on thermodynamic properties: An ab initio molecular dynamics investigations on neutral and charged clusters of Na39, Na40, and Na41, The Journal of Chemical Physics, Volume 128 (2008) no. 10 | DOI:10.1063/1.2839278
Martin F. Jarrold; Baopeng Cao; Anne K. Starace; Colleen M. Neal; Oscar H. Judd Metal clusters that freeze into high energy geometries, The Journal of Chemical Physics, Volume 129 (2008) no. 1 | DOI:10.1063/1.2939579
Yasushi Shibuta; Toshio Suzuki A molecular dynamics study of the phase transition in bcc metal nanoparticles, The Journal of Chemical Physics, Volume 129 (2008) no. 14 | DOI:10.1063/1.2991435
Anne K. Starace; Colleen M. Neal; Baopeng Cao; Martin F. Jarrold; Andrés Aguado; José M. López Correlation between the latent heats and cohesive energies of metal clusters, The Journal of Chemical Physics, Volume 129 (2008) no. 14 | DOI:10.1063/1.2987720
W. Liu; Y. H. Zhao; E. J. Lavernia; Q. Jiang Size-Dependent Deformation and Adsorption Behavior of Carbon Monoxide, Hydrogen, and Carbon on Pyramidal Copper Clusters, The Journal of Physical Chemistry C, Volume 112 (2008) no. 20, p. 7672 | DOI:10.1021/jp800441w
W. Liu; D. Liu; W. T. Zheng; Q. Jiang Size and Structural Dependence of Cohesive Energy in Cu, The Journal of Physical Chemistry C, Volume 112 (2008) no. 48, p. 18840 | DOI:10.1021/jp7114143
HAYDAR ARSLAN GLOBAL MINIMA FOR PdN (N = 5–80) CLUSTERS DESCRIBED BY SUTTON–CHEN POTENTIAL, International Journal of Modern Physics C, Volume 18 (2007) no. 08, p. 1351 | DOI:10.1142/s0129183107011376
Colleen M. Neal; Anne K. Starace; Martin F. Jarrold Ion calorimetry: Using mass spectrometry to measure melting points, Journal of the American Society for Mass Spectrometry, Volume 18 (2007) no. 1, p. 74 | DOI:10.1016/j.jasms.2006.08.019
Andrés Aguado; José M. López Chapter 3 Computer simulation of the solid-liquid phase transition in alkali metal nanoparticles, Nanomaterials: Design and Simulation, Volume 18 (2007), p. 59 | DOI:10.1016/s1380-7323(06)80005-1
Mal-Soon Lee; D. G. Kanhere Effects of geometric and electronic structure on the finite temperature behavior ofNa58,Na57, andNa55cluster, Physical Review B, Volume 75 (2007) no. 12 | DOI:10.1103/physrevb.75.125427
E. E. Zhurkin; T. Van Hoof; M. Hou Nanoscale alloys and core-shell materials: Model predictions of the nanostructure and mechanical properties, Physical Review B, Volume 75 (2007) no. 22 | DOI:10.1103/physrevb.75.224102
Shahab Zorriasatein; Mal-Soon Lee; D. G. Kanhere Electronic structures, equilibrium geometries, and finite-temperature properties ofNan(n=39–55)from first principles, Physical Review B, Volume 76 (2007) no. 16 | DOI:10.1103/physrevb.76.165414
Colleen M. Neal; Anne K. Starace; Martin F. Jarrold Melting transitions in aluminum clusters: The role of partially melted intermediates, Physical Review B, Volume 76 (2007) no. 5 | DOI:10.1103/physrevb.76.054113
Sailaja Krishnamurty; Kavita Joshi; Shahab Zorriasatein; D. G. Kanhere Density functional analysis of the structural evolution of Gan (n=30–55) clusters and its influence on the melting characteristics, The Journal of Chemical Physics, Volume 127 (2007) no. 5 | DOI:10.1063/1.2759215
Colleen M. Neal; Anne K. Starace; Martin F. Jarrold Melting of Alloy Clusters: Effects of Aluminum Doping on Gallium Cluster Melting, The Journal of Physical Chemistry A, Volume 111 (2007) no. 33, p. 8056 | DOI:10.1021/jp068655v
Andrés Aguado; José M. López; Sara Núñez Molecular dynamics simulation of the melting-like transition in K1Na54, Computational Materials Science, Volume 35 (2006) no. 3, p. 174 | DOI:10.1016/j.commatsci.2004.10.011
V. Aquilanti; E. Carmona Novillo; E. Garcia; A. Lombardi; M.B. Sevryuk; E. Yurtsever Invariant energy partitions in chemical reactions and cluster dynamics simulations, Computational Materials Science, Volume 35 (2006) no. 3, p. 187 | DOI:10.1016/j.commatsci.2004.11.008
Ali Sebetci; Ziya B. Güvenç; Hatice Kökten Thermodynamics of small platinum clusters, Computational Materials Science, Volume 35 (2006) no. 3, p. 192 | DOI:10.1016/j.commatsci.2004.08.016
A. LYALIN; O. I. OBOLENSKY; A. V. SOLOV'YOV; W. GREINER FISSION OF METAL CLUSTERS, International Journal of Modern Physics E, Volume 15 (2006) no. 01, p. 153 | DOI:10.1142/s0218301306003990
Luis E González; David J González Ab initiostudy of the atomic motion in liquid metal surfaces: comparison with Lennard-Jones systems, Journal of Physics: Condensed Matter, Volume 18 (2006) no. 48, p. 11021 | DOI:10.1088/0953-8984/18/48/030
Masahiro Itoh; Vijay Kumar; Yoshiyuki Kawazoe Ab initiocalculations of the stability of a vacancy in Na clusters and correlation with melting, Physical Review B, Volume 73 (2006) no. 3 | DOI:10.1103/physrevb.73.035425
Sailaja Krishnamurty; Kavita Joshi; D. G. Kanhere; S. A. Blundell Finite-temperature behavior of small silicon and tin clusters: Anab initiomolecular dynamics study, Physical Review B, Volume 73 (2006) no. 4 | DOI:10.1103/physrevb.73.045419
D. J. González; L. E. González; M. J. Stott Surface structure in simple liquid metals: An orbital-free first-principles study, Physical Review B, Volume 74 (2006) no. 1 | DOI:10.1103/physrevb.74.014207
Andrés Aguado; José M. López Small sodium clusters that melt gradually: Melting mechanisms inNa30, Physical Review B, Volume 74 (2006) no. 11 | DOI:10.1103/physrevb.74.115403
F. Pérez-Bernal; L.F. Santos; P.H. Vaccaro; F. Iachello Spectroscopic signatures of nonrigidity: Algebraic analyses of infrared and Raman transitions in nonrigid species, Chemical Physics Letters, Volume 414 (2005) no. 4-6, p. 398 | DOI:10.1016/j.cplett.2005.07.119
E. A. Olson; M. Yu. Efremov; M. Zhang; Z. Zhang; L. H. Allen Size-dependent melting of Bi nanoparticles, Journal of Applied Physics, Volume 97 (2005) no. 3 | DOI:10.1063/1.1832741
Haydar Arslan; M Haluk Güven Melting dynamics and isomer distributions of small metal clusters, New Journal of Physics, Volume 7 (2005), p. 60 | DOI:10.1088/1367-2630/7/1/060
Micha Polak; Leonid Rubinovich Prediction of intercluster separation and Schottky-type heat-capacity contribution in surface-segregated binary and ternary alloy nanocluster systems, Physical Review B, Volume 71 (2005) no. 12 | DOI:10.1103/physrevb.71.125426
S. Chacko; D. G. Kanhere; S. A. Blundell First principles calculations of melting temperatures for free Na clusters, Physical Review B, Volume 71 (2005) no. 15 | DOI:10.1103/physrevb.71.155407
Gary A. Breaux; Colleen M. Neal; Baopeng Cao; Martin F. Jarrold Tin clusters that do not melt: Calorimetry measurements up to650K, Physical Review B, Volume 71 (2005) no. 7 | DOI:10.1103/physrevb.71.073410
T. Van Hoof; M. Hou Structural and thermodynamic properties ofAg‐Conanoclusters, Physical Review B, Volume 72 (2005) no. 11 | DOI:10.1103/physrevb.72.115434
Andrés Aguado; José M. López Structural and thermal behavior of compact core-shell nanoparticles: Core instabilities and dynamic contributions to surface thermal stability, Physical Review B, Volume 72 (2005) no. 20 | DOI:10.1103/physrevb.72.205420
O. I. Obolensky; A. G. Lyalin; A. V. Solov’yov; W. Greiner Geometrical and statistical factors in fission of small metal clusters, Physical Review B, Volume 72 (2005) no. 8 | DOI:10.1103/physrevb.72.085433
Gary A. Breaux; Colleen M. Neal; Baopeng Cao; Martin F. Jarrold Melting, Premelting, and Structural Transitions in Size-Selected Aluminum Clusters with around 55 Atoms, Physical Review Letters, Volume 94 (2005) no. 17 | DOI:10.1103/physrevlett.94.173401
Andrés Aguado; José M. López Anomalous Size Dependence in the Melting Temperatures of Free Sodium Clusters: An Explanation for the Calorimetry Experiments, Physical Review Letters, Volume 94 (2005) no. 23 | DOI:10.1103/physrevlett.94.233401
Hellmut Haberland; Thomas Hippler; Jörn Donges; Oleg Kostko; Martin Schmidt; Bernd von Issendorff Melting of Sodium Clusters: Where Do the Magic Numbers Come from?, Physical Review Letters, Volume 94 (2005) no. 3 | DOI:10.1103/physrevlett.94.035701
J. T. Lau; A. Achleitner; H.-U. Ehrke; U. Langenbuch; M. Reif; W. Wurth Ultrahigh vacuum cluster deposition source for spectroscopy with synchrotron radiation, Review of Scientific Instruments, Volume 76 (2005) no. 6 | DOI:10.1063/1.1921551
M. Polak; L. Rubinovich Prediction of compositional ordering and separation in alloy nanoclusters, Surface Science, Volume 584 (2005) no. 1, p. 41 | DOI:10.1016/j.susc.2004.11.047
Mal-Soon Lee; S. Chacko; D. G. Kanhere First-principles investigation of finite-temperature behavior in small sodium clusters, The Journal of Chemical Physics, Volume 123 (2005) no. 16 | DOI:10.1063/1.2076607
Ramiro Moro; Roman Rabinovitch; Vitaly V. Kresin Amino-acid and water molecules adsorbed on water clusters in a beam, The Journal of Chemical Physics, Volume 123 (2005) no. 7 | DOI:10.1063/1.1999587
Gary A. Breaux; Baopeng Cao; Martin F. Jarrold Second-Order Phase Transitions in Amorphous Gallium Clusters, The Journal of Physical Chemistry B, Volume 109 (2005) no. 35, p. 16575 | DOI:10.1021/jp052887x
Jeff Th. M. De Hosson; George Palasantzas; Tomas Vystavel; Siete Koch Nanosized metal clusters: Challenges and opportunities, JOM, Volume 56 (2004) no. 1, p. 40 | DOI:10.1007/s11837-004-0271-7
Gary A. Breaux; Damon A. Hillman; Colleen M. Neal; Robert C. Benirschke; Martin F. Jarrold Gallium Cluster “Magic Melters”, Journal of the American Chemical Society, Volume 126 (2004) no. 28, p. 8628 | DOI:10.1021/ja0477423
Jeff Th. M. De Hosson; George Palasantzas; Tomas Vystavel; Siete Koch In situ transmission electron microscopy of nano-sized metal clusters, MRS Proceedings, Volume 839 (2004) | DOI:10.1557/proc-839-p7.4
Ali Sebetci; Ziya B Guvenc Molecular dynamics simulation of the melting behaviour of 12-, 13-, 14-atom icosahedral platinum clusters, Modelling and Simulation in Materials Science and Engineering, Volume 12 (2004) no. 6, p. 1131 | DOI:10.1088/0965-0393/12/6/007
L. H. Liang; C. M. Shen; S. X. Du; W. M. Liu; X. C. Xie; H. J. Gao Increase in thermal stability induced by organic coatings on nanoparticles, Physical Review B, Volume 70 (2004) no. 20 | DOI:10.1103/physrevb.70.205419
S. Chacko; Kavita Joshi; D. G. Kanhere; S. A. Blundell Why Do Gallium Clusters Have a Higher Melting Point than the Bulk?, Physical Review Letters, Volume 92 (2004) no. 13 | DOI:10.1103/physrevlett.92.135506
Vincenzo Aquilanti; Andrea Lombardi; Mikhail B. Sevryuk; Ersin Yurtsever Phase-Space Invariants as Indicators of the Critical Behavior of Nanoaggregates, Physical Review Letters, Volume 93 (2004) no. 11 | DOI:10.1103/physrevlett.93.113402
Gary A. Breaux; Robert C. Benirschke; Martin F. Jarrold Melting, freezing, sublimation, and phase coexistence in sodium chloride nanocrystals, The Journal of Chemical Physics, Volume 121 (2004) no. 13, p. 6502 | DOI:10.1063/1.1786921
T. Vystavel; G. Palasantzas; S. A. Koch; J. Th. M. De Hosson Niobium nanoclusters studied with in situ transmission electron microscopy, Applied Physics Letters, Volume 83 (2003) no. 19, p. 3909 | DOI:10.1063/1.1625789
J. T. Lau; W. Wurth; H.-U. Ehrke; A. Achleitner Soft landing of size-selected clusters in rare gas matrices, Low Temperature Physics, Volume 29 (2003) no. 3, p. 223 | DOI:10.1063/1.1542443
J. Th. M. De Hosson; G. Palasantzas; T. Vystavel; S. Koch Structural Stability of Nano-Sized Clusters, MRS Proceedings, Volume 791 (2003) | DOI:10.1557/proc-791-q2.8
Juan A. Reyes-Nava; Ignacio L. Garzón; Karo Michaelian Negative heat capacity of sodium clusters, Physical Review B, Volume 67 (2003) no. 16 | DOI:10.1103/physrevb.67.165401
Gary A. Breaux; Robert C. Benirschke; Toshiki Sugai; Brian S. Kinnear; Martin F. Jarrold Hot and Solid Gallium Clusters: Too Small to Melt, Physical Review Letters, Volume 91 (2003) no. 21 | DOI:10.1103/physrevlett.91.215508
Q. Jiang; L.H. Liang; J.C. Li Thermodynamic superheating of low-dimensional metals embedded in matrix, Vacuum, Volume 72 (2003) no. 3, p. 249 | DOI:10.1016/s0042-207x(03)00148-9
Q Jiang; J.C Li; B.Q Chi Size-dependent cohesive energy of nanocrystals, Chemical Physics Letters, Volume 366 (2002) no. 5-6, p. 551 | DOI:10.1016/s0009-2614(02)01641-x

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