Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Journal of Materials Science
Published in: Journal of Materials Science 4/2017

11-10-2016 | Original Paper

Size- and shape-dependent melting enthalpy and entropy of nanoparticles

Authors: Qingshan Fu, Jinhua Zhu, Yongqiang Xue, Zixiang Cui

Published in: Journal of Materials Science | Issue 4/2017

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A theoretical model free of any adjustable parameter was derived based on the relation between Gibbs energy change and size to describe the size- and shape-dependent behavior of the melting enthalpy and entropy of nanoparticles. For the melting enthalpy and entropy of vanadium (V), silver (Ag), and copper (Cu) nanoparticles, the results of pure theoretical calculation are in good agreement with available molecular dynamic results. The effect of size on the melting enthalpy and entropy of nanoparticles is greater compared to that of shape effect. The melting enthalpy and entropy decrease with particle size decreasing and the smaller the particle size, the greater the size and shape effects. Furthermore, at the same equivalent diameter, the more the shape of nanoparticles deviates from that of the sphere, the smaller the melting enthalpy and entropy. The thermodynamic relations derived herein can quantitatively describe the influence regularities of size and shape on the melting thermodynamic properties of nanoparticles.
previous article A probabilistic approach on residual strength and damage buildup of high-performance fibers
next article Hybrid composite material based on polythiophene derivative nanofibers modified with gold nanoparticles for optoelectronics applications

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Couchman PR, Jesser WA (1977) Thermodynamic theory of size dependence of melting temperature in metals. Nature 269:481–483CrossRef
2.
3.
Shandiz MA, Safaei A, Sanjabi S, Barber ZH (2007) Modeling size dependence of melting temperature of metallic nanoparticles. J Phys Chem Solids 68:1396–1399CrossRef
4.
Lu HM, Li PY, Cao ZH, Meng XK (2009) Size-, shape-, and dimensionality-dependent melting temperatures of nanocrystals. J Phys Chem C 113:7598–7602CrossRef
5.
6.
7.
Lee J, Sim KJ (2013) General equations of CALPHAD-type thermodynamic description for metallic nanoparticle systems. Calphad 44:129–132CrossRef
8.
9.
Li X (2014) Modeling the size- and shape-dependent cohesive energy of nanomaterials and its applications in heterogeneous systems. Nanotechnology 25:185702/1–185702/7
10.
Johnston JC, Molinero V (2012) Crystallization, melting, and structure of water nanoparticles at atmospherically relevant temperatures. J Am Chem Soc 134:6650–6659CrossRef
11.
Pan D, Liu LM, Slater B, Michaelides A, Wang E (2011) Melting the ice: on the relation between melting temperature and size for nanoscale ice crystals. ACS Nano 5:4562–4569CrossRef
12.
Chernyshev AP (2009) Effect of nanoparticle size on the onset temperature of surface melting. Mater Lett 63:1525–1527CrossRef
13.
Wang B, Wang G, Chen X, Zhao J (2003) Melting behavior of ultrathin titanium nanowires. Phys Rev B 67:193403/1–193403/4
14.
Buffat P, Borel JP (1976) Size effect on the melting temperature of gold particles. Phys Rev A 13:2287–2298CrossRef
15.
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
16.
Lai SL, Carlsson JRA, Allen LH (1998) Melting point depression of Al clusters generated during the early stages of film growth: nanocalorimetry measurements. Appl Phys Lett 72:1098–1100CrossRef
17.
Dick K, Dhanasekaran T, Zhang Z, Meisel D (2002) Size-dependent melting of silica-encapsulated gold nanoparticles. J Am Chem Soc 124:2312–2317CrossRef
18.
Sun PL, Wu SP, Chin TS (2015) Melting point depression of tin nanoparticles embedded in a stable alpha-alumina matrix fabricated by ball milling. Mater Lett 144:142–145CrossRef
19.
Jiang Q, Shi FG (1998) Entropy for solid–liquid transition in nanocrystals. Mater Lett 37:79–82CrossRef
20.
Mott NF (1934) The resistance of liquid metals. Proc Royal Soc Lond Ser A 146:465–472CrossRef
21.
Shi FG (1994) Size dependent thermal vibrations and melting in nanocrystals. J Mater Res 9:1307–1313CrossRef
22.
Jiang Q, Aya N, Shi FG (1997) Nanotube size-dependent melting of single crystals in carbon nanotubes. Appl Phys A 64:627–629CrossRef
23.
Kumar R, Sharma G, Kumar M (2013) Effect of size and shape on the vibrational and thermodynamic properties of nanomaterials. J Thermodyn 2013(5):91–99
24.
Safaei A, Shandiz MA (2009) Size-dependent thermal stability and the smallest nanocrystal. Phys E 41:359–364CrossRef
25.
Xie D, Wang MP, Qi WH, Cao LF (2006) Thermal stability of indium nanocrystals: a theoretical study. Mater Chem Phys 96:418–421CrossRef
26.
Safaei A, Shandiz MA (2010) Melting entropy of nanocrystals: an approach from statistical physics. Phys Chem Chem Phys 12:15372–15381CrossRef
27.
Omid H, Hamid DH, Hosseini HRM (2011) Melting enthalpy and entropy of freestanding metallic nanoparticles based on cohesive energy and average coordination number. J Phys Chem C 115:17310–17313CrossRef
28.
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
29.
Guisbiers G, Buchaillot L (2009) Modeling the melting enthalpy of nanomaterials. J Phys Chem C 113:3566–3568CrossRef
30.
Xie D, Qi W, Wang M (2004) Size and shape dependent melting-thermodynamic properties of metallic nanoparticles. Acta Metall Sin 40:1041–1044
31.
Xue YQ, Gao BJ, Gao JF (1997) The theory of thermodynamics for chemical reactions in dispersed heterogeneous systems. J Colloid Interface Sci 191:81–85CrossRef
32.
Peters KF, Chung YW, Cohen JB (1997) Surface melting on small particles. Appl Phys Lett 71:2391–2393CrossRef
33.
Mitome M (1999) In-situ observation of melting of fine lead particles by high-resolution electron microscopy. Surf Sci 442:L953–L958CrossRef
34.
Sheng HW, Lu K, Ma E (1998) Melting and freezing behavior of embedded nanoparticles in ball-milled Al–10wt% M (M = In, Sn, Bi, Cd, Pb) mixtures. Acta Mater 46:5195–5205CrossRef
35.
Beaglehole D (1991) Surface melting of small particles, and the effects of surface impurities. J Cryst Growth 112:663–669CrossRef
36.
Son JH, Kim SD, Vij JK, Song JK (2014) Effect of molecular-scale surface morphology on the surface melting of liquid crystals on self-assembled monolayers. Appl Phys Lett 105:251601/1–251601/4
37.
Gülseren O, Ercolessi F, Tosatti E (1995) Premelting of thin wires. Phys Rev B 51:7377–7380CrossRef
38.
39.
Li B, Wang F, Zhou D, Peng Y, Ni R, Han Y (2016) Modes of surface premelting in colloidal crystals composed of attractive particles. Nature 531:485–488CrossRef
40.
Alarifi HA, Atis M, Ozdogan C, Hu A, Yavuz M, Zhou Y (2013) Determination of complete melting and surface premelting points of silver nanoparticles by molecular dynamics simulation. J Phys Chem C 117:12289–12298CrossRef
41.
Yaws CL (1999) Chemical Properties Handbook, 1st edn. McGraw-Hill, New York, pp 212–235
42.
Perry RH, Green DW (2008) Perry’s Chemical Engineers’ Handbook, 8th edn. McGraw-Hill, New York, pp 2–136
43.
Tanaka T, Hara S (2001) Thermodynamic evaluation of nano-particle binary alloy phase diagrams. Z Metallkd 92:1236–1241
44.
Yaws CL (1999) Chemical properties handbook. McGraw-Hill, Beijing, pp 154–158
45.
Yaws CL (1999) Chemical properties handbook. McGraw-Hill, Beijing, pp 78–108
46.
Yaws CL (1999) Chemical properties handbook. McGraw-Hill, Beijing, pp 207–211
47.
Yaws CL (1999) Chemical properties handbook. McGraw-Hill, Beijing, pp 234–238
48.
Perry RH, Green D (1984) Perry’s chemical engineers’ handbook, 6th. McGraw-Hill, New York, pp 3–128 Chinese Version
49.
Cui ZX, Zhao MZ, Lai WP, Xue YQ (2011) Thermodynamics of size effect on phase transition temperatures of dispersed phases. J Phys Chem C 115:22796–22803CrossRef
50.
Tanaka T, Hara S (2001) Thermodynamic evaluation of binary phase diagrams of small particle systems. Z Metallkd 92:467–472
51.
Jiang Q, Yang CC, Li JC (2002) Melting enthalpy depression of nanocrystals. Mater Lett 56:1019–1021CrossRef
52.
Zhang M, Efremov MY, Schiettekatte F, Olson EA, Kwan AT, Lai SL, Wisleder T, Greene JE, Allen LH (2000) Size-dependent melting point depression of nanostructures: nanocalorimetric measurements. Phys Rev B 62:10548–10557CrossRef
53.
Luo W, Hu W, Xiao S (2008) Size effect on the thermodynamic properties of silver nanoparticles. J Phys Chem C 112:2359–2369CrossRef
54.
Delogu F (2005) Structural and energetic properties of unsupported Cu nanoparticles from room temperature to the melting point: molecular dynamics simulations. Phys Rev B 72:205418/1–205418/9
55.
Shandiz MA, Safaei A (2008) Melting entropy and enthalpy of metallic nanoparticles. Mater Lett 62:3954–3956CrossRef
Metadata
Title
Size- and shape-dependent melting enthalpy and entropy of nanoparticles
Authors
Qingshan Fu
Jinhua Zhu
Yongqiang Xue
Zixiang Cui
Publication date
11-10-2016
Publisher
Springer US
Published in
Journal of Materials Science / Issue 4/2017
Print ISSN: 0022-2461
Electronic ISSN: 1573-4803
DOI
https://doi.org/10.1007/s10853-016-0480-9

Other articles of this Issue 4/2017

Journal of Materials Science 4/2017 Go to the issue

Original Paper

Ambient-dried thermal superinsulating monolithic silica-based aerogels with short cellulosic fibers

Original Paper

Effect of the ZrO2 concentration on the crystallization behavior and the mechanical properties of high-strength MgO–Al2O3–SiO2 glass–ceramics

Original Paper

Electric relaxation and Mn3+/Mn4+ charge transfer in Fe-doped Bi12MnO20–BiMn2O5 structural self-composite

Original Paper

Polymer nanocomposites processed via self-assembly through introduction of nanoparticles, nanosheets, and nanofibers

Original Paper

Impact of the molecular architecture of polycarboxylate superplasticizers on the dispersion of multi-walled carbon nanotubes in aqueous phase

Original Paper

Effects of pressure on microstructure and mechanical properties of SiCp/2024 Al-based composites fabricated by powder thixoforming

Premium Partners

    Image Credits