Models of size-dependent nanoparticle melting tested on gold

Journal of Materials Science

Volumn 49, Issue 23, 2014, Pages 7915-7932

  Guenther, Gerrit ^a,b   Guillon, Olivier ^b,c  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^c FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

NANOPARTICLES;

MELTING POINT DEPRESSIONS; NANOPARTICLE MELTING; SIZE DEPENDENT; SPHERICAL NANOPARTICLES; THERMODYNAMIC PARAMETER;

GOLD;

EID: 85027949068     PISSN: 00222461     EISSN: 15734803     Source Type: Journal    
DOI: 10.1007/s10853-014-8544-1     Document Type: Review

References (96)

1. Talapin DV, Rogach AL, Kornowski A, Haase M, Weller H (2001) Highly luminescent monodisperse CdSe and CdSe/ZnS nanocrystals synthesized in a hexadecylamine-trioctylphosphine-oxide-trioctylphosphine mixture. Nano Lett 1(4):207-211
2. Anoop G, Mark TS, Hartmut W (2009) Luminescent colloidal dispersion of silicon quantum dots from microwave plasma synthesis: exploring the photoluminescence behavior across the visible spectrum. Adv Funct Mater 19(5):696-703
3. Buffat P, Borel JP (1976) Size effect on the melting temperature of gold particles. Phys Rev A 13:2287
4. Mei QS, Lu K (2007) Melting and superheating of crystalline solids: from bulk to nanocrystals. Prog Mater Sci 52:1175-1262
5. Guisbiers G (2012) Review on the analytical models describing melting at the nanoscale. J Nanosci Lett 2:8
6. Christian JW (2002) The theory of transformations in metals and alloys. Pergamon, Oxford
7. Pluis B, Frenkel D, van der Veen JF (1990) Surface-induced melting and freezing II. A semi-empirical landau-type model. Surf Sci 239:282-300
8. Peters KF, Cohen JB, Chung Y-W (1998) Melting of Pb nanocrystals. Phys Rev B 57(21):13430
9. Rühm A, Reichert H, Donner W, Dosch H, Gruetter C, Bilgram J (2003) Bulk and surface premelting phenomena in α-gallium. Phys Rev B 68:224110
10. Frenken JWM, Maree PMJ, van der Veen JF (1986) Observation of surface-initiated melting. Phys Rev B 34:7506-7516
11. Couchman PR, Jesser WA (1977) Comments on melting mechanism for crystalline species. Philos Mag 35:787-790
12. Tartaglino U, Zykova-Timan T, Ercolessi F, Tosatti E (2005) Material surfaces and nanosystems close to the melting temperature. J Mater Sci 40:2141-2147. doi: 10.1007/s10853-005-1905-z
13. Pawlow P (1909) Über die Abhängigkeit des Schmelzpunktes von der Oberflächenenergie eines Festkörpers. Zeitschrift fuer physikalische Chemie 65:36
14. Pawlow P (1910) Über den Einfluss der Oberfläche einer festen Phase auf die latente Wärme und die Temperatur des Schmelzens. Colloid Polym Sci 7:37-39
15. Takagi M (1956) Electron-diffraction study of liquid-solid transition of thin metal films. J Phys Soc Jpn 9:359
16. Defay R, Prigogine I, Bellemans A, Everett DH (1966) Surface tension and adsorption. Longmans, Green & Co., London
17. Kaptay G (2011) The Gibbs equation versus the Kelvin and the Gibbs-Thomson equations to describe nucleation and equilibrium of nano-materials. J Nanosci Nanotechnol 12:1-9
18. Kaptay G (2012) Nano-Calphad: extension of the Calphad method to systems with nano-phases and complexions. J Mater Sci 47:8320-8335. doi: 10.1007/s10853-012-6772-9
19. Lee J, Tanaka T, Lee J, Mori H (2007) Effect of substrates on the melting temperature of gold nanoparticles. Calphad 31:105-111
20. Reiss H, Wilson IB (1948) The effect of surface on melting point. J Colloid Sci 3:551-561
21. Curzon AE (1960) The use of electron diffraction in the study of (1) melting and supercooling of thin films; and (2) magnetic crystals. PhD Dissertation, University of London
22. Hanszen KJ (1960) Theoretische Untersuchungen über den Schmelzpunkt kleiner Kügelchen - ein Beitrag zur Thermodynamik der Grenzflächen. Zeitschrift für Physik 157:523-553
23. Reiss H, Mirabel P, Whetten RL (1988) Capillarity theory for the "coexistence" of liquid and solid clusters. J Phys Chem 92:7241-7246
24. Vanfleet RR, Mochel JM (1995) Thermodynamics of melting and freezing in small particles. Surf Sci 341:40-50
25. Couchman PR, Jesser WA (1977) Thermodynamic theory of size dependence of melting temperature in metals. Nature 269:481-483
26. Sun CQ, Wang Y, Tay BK, Li S, Huang H, Zhang YB (2002) Correlation between the melting point of a nanosolid and the cohesive energy of a surface atom. J Phys Chem B 106:10701-10705
27. Sun CQ, Bai HL, Li S, Tay BK, Jiang EY (2004) Size-effect on the electronic structure and the thermal stability of a gold nanosolid. Acta Mater 52:501-505
28. Sun CQ (2007) Size dependence of nanostructures: Impact of bond order deficiency. Prog Solid State Chem 35:1-159
29. Pauling L (1947) Atomic radii and interatomic distances in metals. J Am Chem Soc 69:542-553
30. Goldschmidt VM (1927) Krystallbau und chemische Zusammensetzung. Berichte der deutschen chemischen Gesellschaft (A-B Series) 60:1263-1296
31. Nanda KK, Sahu SN, Behera SN (2002) Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys Rev A 66:013208
32. Qi WH, Wang MP, Zhou M, Shen XQ, Zhang XF (2006) Modeling cohesive energy and melting temperature of nanocrystals. J Phys Chem Solids 67:851-855
33. Sun CQ, Pan LK, Fu YQ, Tay BK, Li S (2003) Size dependence of the 2p-level shift of nanosolid silicon. J Phys Chem B 107:5113-5115
34. Sun CQ, Bai HL, Tay BK, Li S, Jiang EY (2003) Dimension, strength, and chemical and thermal stability of a single C-C bond in carbon nanotubes. J Phys Chem B 107:7544-7546
35. Sun CQ, Li CM, Bai HL, Jiang EY (2005) Melting point oscillation of a solid over the whole range of sizes. Nanotechnology 16:1290
36. Dinsdale AT (1991) SGTE data for pure elements. Calphad 15:317-425
37. Scientific Group Thermodata Europe (SGTE) (2002) Thermodynamic properties of elements, Ac to C60, ser. Landolt-Boernstein - Group IV physical chemistry, numerical data and functional relationships in science and technology, vol 19A1. Springer, Berlin, ISBN 3540653279
38. Murr LE (1975) Interfacial phenomena in metal and alloys, vol 8. Addison-Wesley Publishing Company
39. Sambles JR (1971) An electron microscope study of evaporating gold particles: the Kelvin equation for liquid gold and the lowering of the melting point of solid gold particles. Proc R Soc Lond A (1934-1990) 324(1558):339-351
40. Lee J, Nakamoto M, Tanaka T (2005) Thermodynamic study on the melting of nanometer-sized gold particles on graphite substrate. J Mater Sci 40(9):2167-2171. doi: 10.1007/s10853-005-1927-6
41. Haynes WM (2010) CRC handbook of chemistry and physics, 91st edn. CRC Press, Boca Raton
42. Iida T, Guthrie RI (1993) The physical properties of liquid metals. Oxford University Press, New York
43. Rhee SK (1972) Critical surface energies of Al2O3 and graphite. J Am Ceram Soc 55(6):300-303
44. Lee J, Tanaka T, Seo K, Hirai N, Lee JG, Mori H (2006) Wetting of Au and Ag particles on monocrystalline graphite substrates. Rare Met 25(5):469-472
45. Lee J, Ishimura H, Tanaka T (2006) Anisotropy of wetting of molten Au on differently oriented α-Al2O3 single crystals. Scripta Mater 54(7):1369-1373
46. Pinto A, Pennisi AR, Faraci G, D'Agostino G, Mobilio S, Boscherini F (1995) Evidence for truncated octahedral structures in supported gold clusters. Phys Rev B 51(8):5315-5321
47. Zhang X, Kuo JL, Gu M, Fan X, Bai P, Song QG, Sun CQ (2010) Local structure relaxation, quantum trap depression, and valence charge polarization induced by the shorter-and-stronger bonds between under-coordinated atoms in gold nanostructures. Nanoscale 2(3):412-417
48. Dick K, Dhanasekaran T, Zhang Z, Meisel D (2002) Size-dependent melting of silica-encapsulated gold nanoparticles. J Am Chem Soc 124:2312-2317
49. Sheng HW (1996) Superheating and melting-point depression of Pb nanoparticles embedded in Al matrices. Philos Mag Lett 73:179-186
50. Chattopadhyay K, Bhattacharya V, Biswas K, Luysberg M, Tillmann K, Weirich T (2008) Melting and solidification of alloys embedded in a matrix at nanoscale. In: EMC 2008 14th European microscopy congress, 1-5 September 2008, Aachen, Germany. Springer, Berlin
51. Castro T, Reifenberger R, Choi E, Andres RP (1990) Size-dependent melting temperature of individual nanometer-sized metallic clusters. Phys Rev B 42:8548
52. van Huis MA, Young NP, Pandraud G, Creemer JF, Van maekelbergh D, Kirkland AI, Zandbergen HW (2009) Atomic imaging of phase transitions and morphology transformations in nanocrystals. Adv Mater 21:4992-4995
53. Eustathopoulos N, Pique D (1980) Calculation of solid-liquid-vapour contact angles for binary metallic systems. Scripta Metall 14:1291-1296
54. Lee J, Lee J, Tanaka T, Mori H (2009) In-situ atomic-scale observation of meltingpoint suppression in nanometer-sized gold particles. Nanotechnology 20:475706
55. Proykova A, Berry RS (2006) Insights into phase transitions from phase changes of clusters. J Phys B 39:R167-R202
56. Berry RS, Boris MS (2009) Phase transitions in various kinds of clusters. Phys Usp 52:137
57. Bachels T, Guentherodt HJ, Schaefer R (2000) Melting of isolated tin nanoparticles. Phys Rev Lett 85:1250
58. Ercolessi F, Andreoni W, Tosatti E (1991) Melting of small gold particles: mechanism and size effects. Phys Rev Lett 66:911-914
59. Koga K, Ikeshoji T, Sugawara KI (2004) Size- and temperature-dependent structural transitions in gold nanoparticles. Phys Rev Lett 92:115507
60. Wang Y, Teitel S, Dellago C (2005) Melting of icosahedral gold nanoclusters from molecular dynamics simulations. J Chem Phys 122:214722-214816
61. Cleveland CL, Luedtke WD, Landman U (1999) Melting of gold clusters. Phys Rev B 60:5065-5077
62. Chushak YG, Bartell LS (2001) Melting and freezing of gold nanoclusters. J Phys Chem B 105:11605-11614
63. Wang N (2010) Melting, solidification and sintering/coalescence of nanoparticles. PhD Dissertation, Ohio State University
64. Qi Y, Cagin T, Johnson WL, Goddard WA (2001) Melting and crystallization in Ni nanoclusters: the mesoscale regime. J Chem Phys 115:385-394
65. Borel JP (1981) Thermodynamical size effect and the structure of metallic clusters. Surf Sci 106:1-9
66. Krishna Goswami G, Kar Nanda K (2012) Thermodynamic models for the size-dependent melting of nanoparticles: different hypotheses. Curr Nanosci 8:305-311
67. Leitner J (2011) Melting point of nanoparticles. Chem Listy 105:174-185
68. 3single crystal (0001) surface at 1373k. In: Umakoshi Y, Fujimoto S (eds) Advanced structural and functional materials design. Proceedings sereis. Materials Science Forum, vol 512, pp 309-312
69. Farrell HH, Van Siclen CD (2007) Binding energy, vapor pressure, and melting point of semiconductor nanoparticles. J Vac Sci Technol B 25:1441-1447
70. Qi W, Huang B, Wang M (2009) Bond-length and -energy variation of small gold nanoparticles. J Comput Theor Nanosci 6:635-639
71. Qi W, Huang B, Wang M (2009) Structure of unsupported small palladium nanoparticles. Nanoscale Res Lett 4:269-273
72. Allen GL, Bayles RA, Gile WW, Jesser WA (1986) Small particle melting of pure metals. Thin Solid Films 144:297-308
73. Lai SL, Guo JY, Petrova V, Ramanath G, Allen LH (1996) Size-dependent melting properties of small tin particles: nanocalorimetric measurements. Phys Rev Lett 77:99-102
74. Xiong S, Qi W, Cheng Y, Huang B, Wang M, Li Y (2011) Universal relation for size dependent thermodynamic properties of metallic nanoparticles. Phys Chem Chem Phys 13:10652-10660
75. Hultgren R (1973) Selected values of the thermodynamic properties of the elements, 1st edn. American Society for Metals, ASIN B009AJAAEI
76. Tester JW, Feber RC, Herrick CC (1968) Calorimetric study of liquid gold. J Chem Eng Data 13(3):419-421
77. Mays CW, Vermaak JS, Kuhlmann-Wilsdorf D (1968) On surface stress and surface tension: II. Determination of the surface stress of gold. Surf Sci 12:134-140
78. Miller JT, Kropf AJ, Zha Y, Regalbuto JR, Delannoy L, Louis C, Bus E, van Bokhoven JA (2006) The effect of gold particle size on Au-Au bond length and reactivity toward oxygen in supported catalysts. J Catal 240:222-234
79. Pinto A, Pennisi AR, Faraci G, D'Agostino G, Mobilio S, Boscherini F (1995) Evidence for truncated octahedral structures in supported gold clusters. Phys Rev B 51:5315-5321
80. Tolman RC (1949) The effect of droplet size on surface tension. J Chem Phys 17:333-337
81. Kaptay G, Janczak-Rusch J, Pigozzi G, Jeurgens LPH (2014) Theoretical analysis of melting point depression of pure metals in different initial configurations. J Mater Eng Perform 23:1600-1607
82. Lu K, Sun NX (1997) Grain-boundary enthalpy of nanocrystalline selenium. Philos Mag Lett 75:389-395
83. Diehm M, Agoston P, Albe K (2012) Size-dependent lattice expansion in nanoparticles: reality or anomaly? Phys Chem Chem Phys 13:2443-2454
84. Zhang H, Chen B, Banfield JF (2009) The size dependence of the surface free energy of titania nanocrystals. Phys Chem Chem Phys 11:2553-2558
85. Diehm M (2010) Finite-size effects in oxide nanoparticles. Master's thesis, TU Darmstadt
86. Lee J, Nakamoto M, Tanaka T (2005) Thermodynamic study on the melting of nanometer-sized gold particles on graphite substrate. J Mater Sci 40:2167-2171. doi: 10.1007/s10853-005-1927-6
87. Andrievskii R, Khachoyan A (2010) Role of size-dependent effects and interfaces in physicochemical properties of consolidated nanomaterials. Russ J Gen Chem 80:555-566
88. Xiong S, Qi W, Cheng Y, Huang B, Wang M, Li Y (2011) Modeling size effects on the surface free energy of metallic nanoparticles and nanocavities. Phys Chem Chem Phys 13:10648-10651
89. Shibuta Y, Suzuki T (2008) A molecular dynamics study of the phase transition in bcc metal nanoparticles. J Chem Phys 129:144102-144110
90. Tournier RF (2007) Presence of intrinsic growth nuclei in overheated and undercooled liquid elements. Physica B 392:79-91
91. Tournier RF, Beaugnon E (2009) Texturing by cooling a metallic melt in a magnetic field. Sci Technol Adv Mater 10:014501
92. Weissmüller J, ller J (2012) Comment on lattice contraction and surface stress of fcc nanocrystals. J Phys Chem B 106:889-890
93. Murai J, Marukawa T, Mima T, Arai S, Sasaki K, Saka H (2006) Size dependence of the contact angle of liquid clusters of Bi and Sn supported on SiO2, Al2O3, graphite, diamond and AlN. J Mater Sci 41:2723-2727. doi: 10.1007/s10853-006-7875-y
94. Hendy SC (2007) A thermodynamic model for the melting of supported metal nanoparticles. Nanotechnology 18:175703
95. Kofman R, Cheyssac P, Aouaj A, Lereah Y, Deutscher G, Ben-David T, Penisson JM, Bourret A (1994) Surface melting enhanced by curvature effects. Surf Sci 303:231-246
96. Sakai H (1996) Surface-induced melting of small particles. Surf Sci 351:285-291.