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Erschienen in: Journal of Materials Science 23/2014

01.12.2014 | Review

Models of size-dependent nanoparticle melting tested on gold

verfasst von: Gerrit Guenther, Olivier Guillon

Erschienen in: Journal of Materials Science | Ausgabe 23/2014

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Abstract

Models of melting taking into account the finite material size (as for example the diameter of a spherical nanoparticle) lead to a melting point depression compared to the bulk. Selected approaches are presented in this review and compared to available experimental data on gold. Their sensitivity to thermodynamic parameters such as molar volume, surface energy, and enthalpy of melting is highlighted. Within the given accuracy all models describing the non-surface-melting case seem to be valid for gold. In such cases, the simplest solution should be preferred.

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Literatur
1.
Zurück zum Zitat 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):207–211CrossRef 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):207–211CrossRef
2.
Zurück zum Zitat 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):696–703CrossRef 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):696–703CrossRef
3.
Zurück zum Zitat Buffat P, Borel JP (1976) Size effect on the melting temperature of gold particles. Phys Rev A 13:2287CrossRef Buffat P, Borel JP (1976) Size effect on the melting temperature of gold particles. Phys Rev A 13:2287CrossRef
4.
Zurück zum Zitat Mei QS, Lu K (2007) Melting and superheating of crystalline solids: from bulk to nanocrystals. Prog Mater Sci 52:1175–1262CrossRef Mei QS, Lu K (2007) Melting and superheating of crystalline solids: from bulk to nanocrystals. Prog Mater Sci 52:1175–1262CrossRef
5.
Zurück zum Zitat Guisbiers G (2012) Review on the analytical models describing melting at the nanoscale. J Nanosci Lett 2:8CrossRef Guisbiers G (2012) Review on the analytical models describing melting at the nanoscale. J Nanosci Lett 2:8CrossRef
6.
Zurück zum Zitat Christian JW (2002) The theory of transformations in metals and alloys. Pergamon, Oxford Christian JW (2002) The theory of transformations in metals and alloys. Pergamon, Oxford
7.
Zurück zum Zitat Pluis B, Frenkel D, van der Veen JF (1990) Surface-induced melting and freezing II. A semi-empirical landau-type model. Surf Sci 239:282–300CrossRef Pluis B, Frenkel D, van der Veen JF (1990) Surface-induced melting and freezing II. A semi-empirical landau-type model. Surf Sci 239:282–300CrossRef
8.
Zurück zum Zitat Peters KF, Cohen JB, Chung Y-W (1998) Melting of Pb nanocrystals. Phys Rev B 57(21):13430CrossRef Peters KF, Cohen JB, Chung Y-W (1998) Melting of Pb nanocrystals. Phys Rev B 57(21):13430CrossRef
9.
Zurück zum Zitat Rühm A, Reichert H, Donner W, Dosch H, Gruetter C, Bilgram J (2003) Bulk and surface premelting phenomena in α-gallium. Phys Rev B 68:224110CrossRef Rühm A, Reichert H, Donner W, Dosch H, Gruetter C, Bilgram J (2003) Bulk and surface premelting phenomena in α-gallium. Phys Rev B 68:224110CrossRef
10.
Zurück zum Zitat Frenken JWM, Maree PMJ, van der Veen JF (1986) Observation of surface-initiated melting. Phys Rev B 34:7506–7516CrossRef Frenken JWM, Maree PMJ, van der Veen JF (1986) Observation of surface-initiated melting. Phys Rev B 34:7506–7516CrossRef
11.
Zurück zum Zitat Couchman PR, Jesser WA (1977) Comments on melting mechanism for crystalline species. Philos Mag 35:787–790CrossRef Couchman PR, Jesser WA (1977) Comments on melting mechanism for crystalline species. Philos Mag 35:787–790CrossRef
13.
Zurück zum Zitat Pawlow P (1909) Über die Abhängigkeit des Schmelzpunktes von der Oberflächenenergie eines Festkörpers. Zeitschrift fuer physikalische Chemie 65:36 Pawlow P (1909) Über die Abhängigkeit des Schmelzpunktes von der Oberflächenenergie eines Festkörpers. Zeitschrift fuer physikalische Chemie 65:36
14.
Zurück zum Zitat 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 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.
Zurück zum Zitat Takagi M (1956) Electron-diffraction study of liquid-solid transition of thin metal films. J Phys Soc Jpn 9:359CrossRef Takagi M (1956) Electron-diffraction study of liquid-solid transition of thin metal films. J Phys Soc Jpn 9:359CrossRef
16.
Zurück zum Zitat Defay R, Prigogine I, Bellemans A, Everett DH (1966) Surface tension and adsorption. Longmans, Green & Co., London Defay R, Prigogine I, Bellemans A, Everett DH (1966) Surface tension and adsorption. Longmans, Green & Co., London
17.
Zurück zum Zitat 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 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
19.
Zurück zum Zitat Lee J, Tanaka T, Lee J, Mori H (2007) Effect of substrates on the melting temperature of gold nanoparticles. Calphad 31:105–111CrossRef Lee J, Tanaka T, Lee J, Mori H (2007) Effect of substrates on the melting temperature of gold nanoparticles. Calphad 31:105–111CrossRef
20.
Zurück zum Zitat Reiss H, Wilson IB (1948) The effect of surface on melting point. J Colloid Sci 3:551–561CrossRef Reiss H, Wilson IB (1948) The effect of surface on melting point. J Colloid Sci 3:551–561CrossRef
21.
Zurück zum Zitat 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 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.
Zurück zum Zitat Hanszen KJ (1960) Theoretische Untersuchungen über den Schmelzpunkt kleiner Kügelchen—ein Beitrag zur Thermodynamik der Grenzflächen. Zeitschrift für Physik 157:523–553CrossRef Hanszen KJ (1960) Theoretische Untersuchungen über den Schmelzpunkt kleiner Kügelchen—ein Beitrag zur Thermodynamik der Grenzflächen. Zeitschrift für Physik 157:523–553CrossRef
23.
Zurück zum Zitat Reiss H, Mirabel P, Whetten RL (1988) Capillarity theory for the “coexistence” of liquid and solid clusters. J Phys Chem 92:7241–7246CrossRef Reiss H, Mirabel P, Whetten RL (1988) Capillarity theory for the “coexistence” of liquid and solid clusters. J Phys Chem 92:7241–7246CrossRef
24.
Zurück zum Zitat Vanfleet RR, Mochel JM (1995) Thermodynamics of melting and freezing in small particles. Surf Sci 341:40–50CrossRef Vanfleet RR, Mochel JM (1995) Thermodynamics of melting and freezing in small particles. Surf Sci 341:40–50CrossRef
25.
Zurück zum Zitat Couchman PR, Jesser WA (1977) Thermodynamic theory of size dependence of melting temperature in metals. Nature 269:481–483CrossRef Couchman PR, Jesser WA (1977) Thermodynamic theory of size dependence of melting temperature in metals. Nature 269:481–483CrossRef
26.
Zurück zum Zitat 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 106:10701–10705CrossRef 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 106:10701–10705CrossRef
27.
Zurück zum Zitat 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 52:501–505CrossRef 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 52:501–505CrossRef
28.
Zurück zum Zitat Sun CQ (2007) Size dependence of nanostructures: Impact of bond order deficiency. Prog Solid State Chem 35:1–159CrossRef Sun CQ (2007) Size dependence of nanostructures: Impact of bond order deficiency. Prog Solid State Chem 35:1–159CrossRef
29.
Zurück zum Zitat Pauling L (1947) Atomic radii and interatomic distances in metals. J Am Chem Soc 69:542–553CrossRef Pauling L (1947) Atomic radii and interatomic distances in metals. J Am Chem Soc 69:542–553CrossRef
30.
Zurück zum Zitat Goldschmidt VM (1927) Krystallbau und chemische Zusammensetzung. Berichte der deutschen chemischen Gesellschaft (A–B Series) 60:1263–1296CrossRef Goldschmidt VM (1927) Krystallbau und chemische Zusammensetzung. Berichte der deutschen chemischen Gesellschaft (A–B Series) 60:1263–1296CrossRef
31.
Zurück zum Zitat Nanda KK, Sahu SN, Behera SN (2002) Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys Rev A 66:013208CrossRef Nanda KK, Sahu SN, Behera SN (2002) Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys Rev A 66:013208CrossRef
32.
Zurück zum Zitat Qi WH, Wang MP, Zhou M, Shen XQ, Zhang XF (2006) Modeling cohesive energy and melting temperature of nanocrystals. J Phys Chem Solids 67:851–855CrossRef Qi WH, Wang MP, Zhou M, Shen XQ, Zhang XF (2006) Modeling cohesive energy and melting temperature of nanocrystals. J Phys Chem Solids 67:851–855CrossRef
33.
Zurück zum Zitat 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 107:5113–5115CrossRef 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 107:5113–5115CrossRef
34.
Zurück zum Zitat 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 107:7544–7546CrossRef 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 107:7544–7546CrossRef
35.
Zurück zum Zitat Sun CQ, Li CM, Bai HL, Jiang EY (2005) Melting point oscillation of a solid over the whole range of sizes. Nanotechnology 16:1290CrossRef Sun CQ, Li CM, Bai HL, Jiang EY (2005) Melting point oscillation of a solid over the whole range of sizes. Nanotechnology 16:1290CrossRef
36.
37.
Zurück zum Zitat 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 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.
Zurück zum Zitat Murr LE (1975) Interfacial phenomena in metal and alloys, vol 8. Addison-Wesley Publishing Company Murr LE (1975) Interfacial phenomena in metal and alloys, vol 8. Addison-Wesley Publishing Company
39.
Zurück zum Zitat 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):339–351CrossRef 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):339–351CrossRef
41.
Zurück zum Zitat Haynes WM (2010) CRC handbook of chemistry and physics, 91st edn. CRC Press, Boca Raton Haynes WM (2010) CRC handbook of chemistry and physics, 91st edn. CRC Press, Boca Raton
42.
Zurück zum Zitat Iida T, Guthrie RI (1993) The physical properties of liquid metals. Oxford University Press, New York Iida T, Guthrie RI (1993) The physical properties of liquid metals. Oxford University Press, New York
43.
Zurück zum Zitat Rhee SK (1972) Critical surface energies of Al2O3 and graphite. J Am Ceram Soc 55(6):300–303CrossRef Rhee SK (1972) Critical surface energies of Al2O3 and graphite. J Am Ceram Soc 55(6):300–303CrossRef
44.
Zurück zum Zitat 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):469–472CrossRef 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):469–472CrossRef
45.
Zurück zum Zitat Lee J, Ishimura H, Tanaka T (2006) Anisotropy of wetting of molten Au on differently oriented α-Al2O3 single crystals. Scripta Mater 54(7):1369–1373CrossRef Lee J, Ishimura H, Tanaka T (2006) Anisotropy of wetting of molten Au on differently oriented α-Al2O3 single crystals. Scripta Mater 54(7):1369–1373CrossRef
46.
Zurück zum Zitat 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):5315–5321CrossRef 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):5315–5321CrossRef
47.
Zurück zum Zitat 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):412–417CrossRef 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):412–417CrossRef
48.
Zurück zum Zitat Dick K, Dhanasekaran T, Zhang Z, Meisel D (2002) Size-dependent melting of silica-encapsulated gold nanoparticles. J Am Chem Soc 124:2312–2317CrossRef Dick K, Dhanasekaran T, Zhang Z, Meisel D (2002) Size-dependent melting of silica-encapsulated gold nanoparticles. J Am Chem Soc 124:2312–2317CrossRef
49.
Zurück zum Zitat Sheng HW (1996) Superheating and melting-point depression of Pb nanoparticles embedded in Al matrices. Philos Mag Lett 73:179–186CrossRef Sheng HW (1996) Superheating and melting-point depression of Pb nanoparticles embedded in Al matrices. Philos Mag Lett 73:179–186CrossRef
50.
Zurück zum Zitat 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 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.
Zurück zum Zitat Castro T, Reifenberger R, Choi E, Andres RP (1990) Size-dependent melting temperature of individual nanometer-sized metallic clusters. Phys Rev B 42:8548CrossRef Castro T, Reifenberger R, Choi E, Andres RP (1990) Size-dependent melting temperature of individual nanometer-sized metallic clusters. Phys Rev B 42:8548CrossRef
52.
Zurück zum Zitat 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 21:4992–4995CrossRef 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 21:4992–4995CrossRef
53.
Zurück zum Zitat Eustathopoulos N, Pique D (1980) Calculation of solid–liquid–vapour contact angles for binary metallic systems. Scripta Metall 14:1291–1296CrossRef Eustathopoulos N, Pique D (1980) Calculation of solid–liquid–vapour contact angles for binary metallic systems. Scripta Metall 14:1291–1296CrossRef
54.
Zurück zum Zitat Lee J, Lee J, Tanaka T, Mori H (2009) In-situ atomic-scale observation of meltingpoint suppression in nanometer-sized gold particles. Nanotechnology 20:475706CrossRef Lee J, Lee J, Tanaka T, Mori H (2009) In-situ atomic-scale observation of meltingpoint suppression in nanometer-sized gold particles. Nanotechnology 20:475706CrossRef
55.
Zurück zum Zitat Proykova A, Berry RS (2006) Insights into phase transitions from phase changes of clusters. J Phys B 39:R167–R202CrossRef Proykova A, Berry RS (2006) Insights into phase transitions from phase changes of clusters. J Phys B 39:R167–R202CrossRef
56.
Zurück zum Zitat Berry RS, Boris MS (2009) Phase transitions in various kinds of clusters. Phys Usp 52:137CrossRef Berry RS, Boris MS (2009) Phase transitions in various kinds of clusters. Phys Usp 52:137CrossRef
57.
Zurück zum Zitat Bachels T, Guentherodt HJ, Schaefer R (2000) Melting of isolated tin nanoparticles. Phys Rev Lett 85:1250CrossRef Bachels T, Guentherodt HJ, Schaefer R (2000) Melting of isolated tin nanoparticles. Phys Rev Lett 85:1250CrossRef
58.
Zurück zum Zitat Ercolessi F, Andreoni W, Tosatti E (1991) Melting of small gold particles: mechanism and size effects. Phys Rev Lett 66:911–914CrossRef Ercolessi F, Andreoni W, Tosatti E (1991) Melting of small gold particles: mechanism and size effects. Phys Rev Lett 66:911–914CrossRef
59.
Zurück zum Zitat Koga K, Ikeshoji T, Sugawara KI (2004) Size- and temperature-dependent structural transitions in gold nanoparticles. Phys Rev Lett 92:115507CrossRef Koga K, Ikeshoji T, Sugawara KI (2004) Size- and temperature-dependent structural transitions in gold nanoparticles. Phys Rev Lett 92:115507CrossRef
60.
Zurück zum Zitat Wang Y, Teitel S, Dellago C (2005) Melting of icosahedral gold nanoclusters from molecular dynamics simulations. J Chem Phys 122:214722–214816CrossRef Wang Y, Teitel S, Dellago C (2005) Melting of icosahedral gold nanoclusters from molecular dynamics simulations. J Chem Phys 122:214722–214816CrossRef
61.
Zurück zum Zitat Cleveland CL, Luedtke WD, Landman U (1999) Melting of gold clusters. Phys Rev B 60:5065–5077CrossRef Cleveland CL, Luedtke WD, Landman U (1999) Melting of gold clusters. Phys Rev B 60:5065–5077CrossRef
62.
Zurück zum Zitat Chushak YG, Bartell LS (2001) Melting and freezing of gold nanoclusters. J Phys Chem B 105:11605–11614CrossRef Chushak YG, Bartell LS (2001) Melting and freezing of gold nanoclusters. J Phys Chem B 105:11605–11614CrossRef
63.
Zurück zum Zitat Wang N (2010) Melting, solidification and sintering/coalescence of nanoparticles. PhD Dissertation, Ohio State University Wang N (2010) Melting, solidification and sintering/coalescence of nanoparticles. PhD Dissertation, Ohio State University
64.
Zurück zum Zitat Qi Y, Cagin T, Johnson WL, Goddard WA (2001) Melting and crystallization in Ni nanoclusters: the mesoscale regime. J Chem Phys 115:385–394CrossRef Qi Y, Cagin T, Johnson WL, Goddard WA (2001) Melting and crystallization in Ni nanoclusters: the mesoscale regime. J Chem Phys 115:385–394CrossRef
65.
Zurück zum Zitat Borel JP (1981) Thermodynamical size effect and the structure of metallic clusters. Surf Sci 106:1–9CrossRef Borel JP (1981) Thermodynamical size effect and the structure of metallic clusters. Surf Sci 106:1–9CrossRef
66.
Zurück zum Zitat Krishna Goswami G, Kar Nanda K (2012) Thermodynamic models for the size-dependent melting of nanoparticles: different hypotheses. Curr Nanosci 8:305–311CrossRef Krishna Goswami G, Kar Nanda K (2012) Thermodynamic models for the size-dependent melting of nanoparticles: different hypotheses. Curr Nanosci 8:305–311CrossRef
67.
Zurück zum Zitat Leitner J (2011) Melting point of nanoparticles. Chem Listy 105:174–185 Leitner J (2011) Melting point of nanoparticles. Chem Listy 105:174–185
68.
Zurück zum Zitat Lee J, Ishimura H, Tanaka T (2004) Novel method determining contact angle of liquid Au on solid Al2O3 single 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 Lee J, Ishimura H, Tanaka T (2004) Novel method determining contact angle of liquid Au on solid Al2O3 single 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.
Zurück zum Zitat Farrell HH, Van Siclen CD (2007) Binding energy, vapor pressure, and melting point of semiconductor nanoparticles. J Vac Sci Technol B 25:1441–1447CrossRef Farrell HH, Van Siclen CD (2007) Binding energy, vapor pressure, and melting point of semiconductor nanoparticles. J Vac Sci Technol B 25:1441–1447CrossRef
70.
Zurück zum Zitat Qi W, Huang B, Wang M (2009) Bond-length and -energy variation of small gold nanoparticles. J Comput Theor Nanosci 6:635–639CrossRef Qi W, Huang B, Wang M (2009) Bond-length and -energy variation of small gold nanoparticles. J Comput Theor Nanosci 6:635–639CrossRef
71.
Zurück zum Zitat Qi W, Huang B, Wang M (2009) Structure of unsupported small palladium nanoparticles. Nanoscale Res Lett 4:269–273CrossRef Qi W, Huang B, Wang M (2009) Structure of unsupported small palladium nanoparticles. Nanoscale Res Lett 4:269–273CrossRef
72.
Zurück zum Zitat Allen GL, Bayles RA, Gile WW, Jesser WA (1986) Small particle melting of pure metals. Thin Solid Films 144:297–308CrossRef Allen GL, Bayles RA, Gile WW, Jesser WA (1986) Small particle melting of pure metals. Thin Solid Films 144:297–308CrossRef
73.
Zurück zum Zitat Lai SL, Guo JY, Petrova V, Ramanath G, Allen LH (1996) Size-dependent melting properties of small tin particles: nanocalorimetric measurements. Phys Rev Lett 77:99–102CrossRef Lai SL, Guo JY, Petrova V, Ramanath G, Allen LH (1996) Size-dependent melting properties of small tin particles: nanocalorimetric measurements. Phys Rev Lett 77:99–102CrossRef
74.
Zurück zum Zitat 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 13:10652–10660CrossRef 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 13:10652–10660CrossRef
75.
Zurück zum Zitat Hultgren R (1973) Selected values of the thermodynamic properties of the elements, 1st edn. American Society for Metals, ASIN B009AJAAEI Hultgren R (1973) Selected values of the thermodynamic properties of the elements, 1st edn. American Society for Metals, ASIN B009AJAAEI
76.
Zurück zum Zitat Tester JW, Feber RC, Herrick CC (1968) Calorimetric study of liquid gold. J Chem Eng Data 13(3):419–421CrossRef Tester JW, Feber RC, Herrick CC (1968) Calorimetric study of liquid gold. J Chem Eng Data 13(3):419–421CrossRef
77.
Zurück zum Zitat Mays CW, Vermaak JS, Kuhlmann-Wilsdorf D (1968) On surface stress and surface tension: II. Determination of the surface stress of gold. Surf Sci 12:134–140CrossRef Mays CW, Vermaak JS, Kuhlmann-Wilsdorf D (1968) On surface stress and surface tension: II. Determination of the surface stress of gold. Surf Sci 12:134–140CrossRef
78.
Zurück zum Zitat 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 240:222–234CrossRef 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 240:222–234CrossRef
79.
Zurück zum Zitat 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 51:5315–5321CrossRef 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 51:5315–5321CrossRef
80.
Zurück zum Zitat Tolman RC (1949) The effect of droplet size on surface tension. J Chem Phys 17:333–337CrossRef Tolman RC (1949) The effect of droplet size on surface tension. J Chem Phys 17:333–337CrossRef
81.
Zurück zum Zitat 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 23:1600–1607CrossRef 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 23:1600–1607CrossRef
82.
Zurück zum Zitat Lu K, Sun NX (1997) Grain-boundary enthalpy of nanocrystalline selenium. Philos Mag Lett 75:389–395CrossRef Lu K, Sun NX (1997) Grain-boundary enthalpy of nanocrystalline selenium. Philos Mag Lett 75:389–395CrossRef
83.
Zurück zum Zitat Diehm M, Agoston P, Albe K (2012) Size-dependent lattice expansion in nanoparticles: reality or anomaly? Phys Chem Chem Phys 13:2443–2454 Diehm M, Agoston P, Albe K (2012) Size-dependent lattice expansion in nanoparticles: reality or anomaly? Phys Chem Chem Phys 13:2443–2454
84.
Zurück zum Zitat Zhang H, Chen B, Banfield JF (2009) The size dependence of the surface free energy of titania nanocrystals. Phys Chem Chem Phys 11:2553–2558CrossRef Zhang H, Chen B, Banfield JF (2009) The size dependence of the surface free energy of titania nanocrystals. Phys Chem Chem Phys 11:2553–2558CrossRef
85.
Zurück zum Zitat Diehm M (2010) Finite-size effects in oxide nanoparticles. Master’s thesis, TU Darmstadt Diehm M (2010) Finite-size effects in oxide nanoparticles. Master’s thesis, TU Darmstadt
87.
Zurück zum Zitat Andrievskii R, Khachoyan A (2010) Role of size-dependent effects and interfaces in physicochemical properties of consolidated nanomaterials. Russ J Gen Chem 80:555–566CrossRef Andrievskii R, Khachoyan A (2010) Role of size-dependent effects and interfaces in physicochemical properties of consolidated nanomaterials. Russ J Gen Chem 80:555–566CrossRef
88.
Zurück zum Zitat 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 13:10648–10651CrossRef 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 13:10648–10651CrossRef
89.
Zurück zum Zitat Shibuta Y, Suzuki T (2008) A molecular dynamics study of the phase transition in bcc metal nanoparticles. J Chem Phys 129:144102–144110CrossRef Shibuta Y, Suzuki T (2008) A molecular dynamics study of the phase transition in bcc metal nanoparticles. J Chem Phys 129:144102–144110CrossRef
90.
Zurück zum Zitat Tournier RF (2007) Presence of intrinsic growth nuclei in overheated and undercooled liquid elements. Physica B 392:79–91CrossRef Tournier RF (2007) Presence of intrinsic growth nuclei in overheated and undercooled liquid elements. Physica B 392:79–91CrossRef
91.
Zurück zum Zitat Tournier RF, Beaugnon E (2009) Texturing by cooling a metallic melt in a magnetic field. Sci Technol Adv Mater 10:014501CrossRef Tournier RF, Beaugnon E (2009) Texturing by cooling a metallic melt in a magnetic field. Sci Technol Adv Mater 10:014501CrossRef
92.
Zurück zum Zitat Weissmüller J, ller J (2012) Comment on lattice contraction and surface stress of fcc nanocrystals. J Phys Chem B 106:889–890CrossRef Weissmüller J, ller J (2012) Comment on lattice contraction and surface stress of fcc nanocrystals. J Phys Chem B 106:889–890CrossRef
93.
Zurück zum Zitat 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 CrossRef 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 CrossRef
94.
Zurück zum Zitat Hendy SC (2007) A thermodynamic model for the melting of supported metal nanoparticles. Nanotechnology 18:175703CrossRef Hendy SC (2007) A thermodynamic model for the melting of supported metal nanoparticles. Nanotechnology 18:175703CrossRef
95.
Zurück zum Zitat 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 303:231–246CrossRef 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 303:231–246CrossRef
96.
Zurück zum Zitat Sakai H (1996) Surface-induced melting of small particles. Surf Sci 351:285–291CrossRef Sakai H (1996) Surface-induced melting of small particles. Surf Sci 351:285–291CrossRef
Metadaten
Titel
Models of size-dependent nanoparticle melting tested on gold
verfasst von
Gerrit Guenther
Olivier Guillon
Publikationsdatum
01.12.2014
Verlag
Springer US
Erschienen in
Journal of Materials Science / Ausgabe 23/2014
Print ISSN: 0022-2461
Elektronische ISSN: 1573-4803
DOI
https://doi.org/10.1007/s10853-014-8544-1

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