Skip to main content
Top
Published in: Journal of Nanoparticle Research 7/2022

01-07-2022 | Research paper

Micro-/nanoparticle melting in an alloy melt with anisotropic surface energy

Authors: C. M. Yang, M. W. Chen, G. J. Zheng, M. L. Zhang, Z. D. Wang

Published in: Journal of Nanoparticle Research | Issue 7/2022

Log in

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

search-config
loading …

Abstract

The melting of micro-/nanoparticles in an alloy melt is investigated by using the asymptotic method. The asymptotic solution of the dynamic model for micro-/nanoparticle melting shows that the melting temperature of micro-/nanoparticles depends on the size, isotropic/anisotropic surface energy, and the initial concentration. As the particle radius decreases, isotropic surface energy reduces the melting temperature and promotes the melting of the particle, whereas the initial concentration enhances the melting temperature and depresses the melting of the particle. Along certain crystal orientations, the anisotropic surface energy reduces the melting speed of the micro-/nanoparticles and enhances the melting temperature of the micro-/nanoparticle, whereas it enhances the melting speed of the micro/nanoparticles and depresses the melting temperature of the micro-/nanoparticles along other crystal orientations. The initial concentration reduces the melting speed of micro-/nanoparticles and enhances the melting temperature of micro-/nanoparticles along all crystal orientations. The result of the asymptotic solution is quantitatively consistent with experimental results.

Graphical abstract

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!

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!

Literature
go back to reference Alsayed AM, Islam MF, Zhang J, Collings PJ, Yodh AG (2005) Premelting at defects within bulk colloidal crystals. Science 309(5738):1207–1210CrossRef Alsayed AM, Islam MF, Zhang J, Collings PJ, Yodh AG (2005) Premelting at defects within bulk colloidal crystals. Science 309(5738):1207–1210CrossRef
go back to reference Back JM, McCue SW, Hsieh M-N, Moroney TJ (2014) The effect of surface tension and kinetic undercooling on a radially-symmetric melting problem. Appl Math Comput 229:41–52 Back JM, McCue SW, Hsieh M-N, Moroney TJ (2014) The effect of surface tension and kinetic undercooling on a radially-symmetric melting problem. Appl Math Comput 229:41–52
go back to reference Calvo F (2012) Molecular dynamics determination of the surface tension of silver-gold liquid alloys and the Tolman length of nanoalloys. J Chem Phy 136:154701CrossRef Calvo F (2012) Molecular dynamics determination of the surface tension of silver-gold liquid alloys and the Tolman length of nanoalloys. J Chem Phy 136:154701CrossRef
go back to reference Chen CL, Lee JG, Arakawa K, Mori H (2011) Comparative study on size dependence of melting temperatures of pure metal and alloy nanoparticles. Appl Phys Lett 99(1):013108CrossRef Chen CL, Lee JG, Arakawa K, Mori H (2011) Comparative study on size dependence of melting temperatures of pure metal and alloy nanoparticles. Appl Phys Lett 99(1):013108CrossRef
go back to reference Chen T, Ma Y, Fu X, Li M (2020) A comprehensive understanding of the melting temperature of nanocrystals: implications for catalysis. ACS Applied Nano Materials 3(2):1583–1591CrossRef Chen T, Ma Y, Fu X, Li M (2020) A comprehensive understanding of the melting temperature of nanocrystals: implications for catalysis. ACS Applied Nano Materials 3(2):1583–1591CrossRef
go back to reference Dai C, Saidi P, Song H, Yao Z, Daymond MR, Hoyt JJ (2017) A test of a phenomenological model of size dependent melting in Au nanoparticles. Acta Mater 136:11–20CrossRef Dai C, Saidi P, Song H, Yao Z, Daymond MR, Hoyt JJ (2017) A test of a phenomenological model of size dependent melting in Au nanoparticles. Acta Mater 136:11–20CrossRef
go back to reference Dippel M et al (2001) Size-dependent melting of self-assembled indium nanostructures. Phys Rev Lett 87:9CrossRef Dippel M et al (2001) Size-dependent melting of self-assembled indium nanostructures. Phys Rev Lett 87:9CrossRef
go back to reference Duggin MJ (1972) The thermal conductivities of liquid lead and indium. J Phys f: Met Phys 2(3):433CrossRef Duggin MJ (1972) The thermal conductivities of liquid lead and indium. J Phys f: Met Phys 2(3):433CrossRef
go back to reference Ferrando R, Fortunelli A, Rossi G (2005) Quantum effects on the structure of pure and binary metallic nanoclusters. Phys Rev B 72(8):085449CrossRef Ferrando R, Fortunelli A, Rossi G (2005) Quantum effects on the structure of pure and binary metallic nanoclusters. Phys Rev B 72(8):085449CrossRef
go back to reference Font F, Myers TG (2013) Spherically symmetric nanoparticle melting with a variable phase change temperature. J Nanopart Res 15:1–13CrossRef Font F, Myers TG (2013) Spherically symmetric nanoparticle melting with a variable phase change temperature. J Nanopart Res 15:1–13CrossRef
go back to reference Frade JR, Cable M (1994) Diffusion-controlled growth or dissolution of spheres with variable temperature. J Am Ceram Soc 77(4):999–1004CrossRef Frade JR, Cable M (1994) Diffusion-controlled growth or dissolution of spheres with variable temperature. J Am Ceram Soc 77(4):999–1004CrossRef
go back to reference Heyraud JC, Metois JJ (1980) Equilibrium shape of gold crystallites on a graphite cleavage surface: surface energies and interfacial energy. Acta Metall 28(12):1789–1797CrossRef Heyraud JC, Metois JJ (1980) Equilibrium shape of gold crystallites on a graphite cleavage surface: surface energies and interfacial energy. Acta Metall 28(12):1789–1797CrossRef
go back to reference Illingworth TC, Golosnoy IO (2005) Numerical solutions of diffusion-controlled moving boundary problems which conserve solute. J Comput Phys 209:207–225CrossRef Illingworth TC, Golosnoy IO (2005) Numerical solutions of diffusion-controlled moving boundary problems which conserve solute. J Comput Phys 209:207–225CrossRef
go back to reference Jiang Q, Zhang Z, Li JC (2000) Melting thermodynamics of nanocrystals embedded in a matrix. Acta Mater 48(20):4791–4795CrossRef Jiang Q, Zhang Z, Li JC (2000) Melting thermodynamics of nanocrystals embedded in a matrix. Acta Mater 48(20):4791–4795CrossRef
go back to reference Jiang Q, Zhao DS, Zhao MJAM (2001) Size-dependent interface energy and related interface stress. Acta Mater 49(16):3143–3147CrossRef Jiang Q, Zhao DS, Zhao MJAM (2001) Size-dependent interface energy and related interface stress. Acta Mater 49(16):3143–3147CrossRef
go back to reference Jiang Q, Zhang S, Zhao M (2003) Size-dependent melting point of noble metals. Mater Chem Phys 82(1):225–227CrossRef Jiang Q, Zhang S, Zhao M (2003) Size-dependent melting point of noble metals. Mater Chem Phys 82(1):225–227CrossRef
go back to reference 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 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
go back to reference Li M, Zhu TS (2016) Modeling the melting temperature of nanoscaled bimetallic alloys. Phys Chem Chem Phys 18(25):16958–16963CrossRef Li M, Zhu TS (2016) Modeling the melting temperature of nanoscaled bimetallic alloys. Phys Chem Chem Phys 18(25):16958–16963CrossRef
go back to reference Li G, Wang Q, Li D, Lü X, He J (2009) Size and composition effects on the melting of bimetallic Cu–Ni clusters studied via molecular dynamics simulation. Mater Chem Phys 114(2–3):746–750CrossRef Li G, Wang Q, Li D, Lü X, He J (2009) Size and composition effects on the melting of bimetallic Cu–Ni clusters studied via molecular dynamics simulation. Mater Chem Phys 114(2–3):746–750CrossRef
go back to reference Lu K, Jin ZH (2001) Melting and superheating of low-dimensional materials. Curr Opin Solid State Mater Sci 5:39–44CrossRef Lu K, Jin ZH (2001) Melting and superheating of low-dimensional materials. Curr Opin Solid State Mater Sci 5:39–44CrossRef
go back to reference Lupulescu A, Glicksman ME, Koss MB (2005) Conduction-limited crystallite melting. J Cryst Growth 276(3–4):549–565CrossRef Lupulescu A, Glicksman ME, Koss MB (2005) Conduction-limited crystallite melting. J Cryst Growth 276(3–4):549–565CrossRef
go back to reference McCue SW, Wu B, Hill JM (2009) Micro/nanoparticle melting with spherical symmetry and surface tension. IMA J Appl Math 74:439–457CrossRef McCue SW, Wu B, Hill JM (2009) Micro/nanoparticle melting with spherical symmetry and surface tension. IMA J Appl Math 74:439–457CrossRef
go back to reference Mottet C, Rossi G, Baletto F, Ferrando R (2005) Single impurity effect on the melting of nanoclusters. Physical Rev Lett 95(3):035501CrossRef Mottet C, Rossi G, Baletto F, Ferrando R (2005) Single impurity effect on the melting of nanoclusters. Physical Rev Lett 95(3):035501CrossRef
go back to reference Nanda KK (2009) Size-dependent melting of nanoparticles: hundred years of thermodynamic model. Pramana 72(4):617–628CrossRef Nanda KK (2009) Size-dependent melting of nanoparticles: hundred years of thermodynamic model. Pramana 72(4):617–628CrossRef
go back to reference Pavan L, Baletto F, Novakovic R (2015) Multiscale approach for studying melting transitions in Cu/Pt nanoparticles. Phys Chem Chem Phys 17(42):28364–28371CrossRef Pavan L, Baletto F, Novakovic R (2015) Multiscale approach for studying melting transitions in Cu/Pt nanoparticles. Phys Chem Chem Phys 17(42):28364–28371CrossRef
go back to reference Samsonov VM, Kharechkin SS, Gafner SL, Gafner YY (2009) Molecular dynamics study of the melting and crystallization of nanoparticles. Crystallogr Rep 54(3):526–531CrossRef Samsonov VM, Kharechkin SS, Gafner SL, Gafner YY (2009) Molecular dynamics study of the melting and crystallization of nanoparticles. Crystallogr Rep 54(3):526–531CrossRef
go back to reference Sankaranarayanan SK, Bhethanabotla VR, Joseph B (2005) Molecular dynamics simulation study of the melting of Pd-Pt nanoclusters. Phys Rev B 71(19):195415CrossRef Sankaranarayanan SK, Bhethanabotla VR, Joseph B (2005) Molecular dynamics simulation study of the melting of Pd-Pt nanoclusters. Phys Rev B 71(19):195415CrossRef
go back to reference Sasaki K, Saka H (1991) In situ high-resolution electron microscopy observation of the melting process of In particles embedded in an Al matrix. Philos Mag A 63:1207–1220CrossRef Sasaki K, Saka H (1991) In situ high-resolution electron microscopy observation of the melting process of In particles embedded in an Al matrix. Philos Mag A 63:1207–1220CrossRef
go back to reference Settem M, Ferrando R, Giacomello A (2022) Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs. Nanoscale 14(3):939–952CrossRef Settem M, Ferrando R, Giacomello A (2022) Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs. Nanoscale 14(3):939–952CrossRef
go back to reference Sheng HW, Lu K, Ma E (1998) Melting and freezing behavior of embedded nanoparticles in ball-milled Al–10 wt% M (M= In, Sn, Bi, Cd, Pb) mixtures. Acta Mater 46:5195–5205CrossRef Sheng HW, Lu K, Ma E (1998) Melting and freezing behavior of embedded nanoparticles in ball-milled Al–10 wt% M (M= In, Sn, Bi, Cd, Pb) mixtures. Acta Mater 46:5195–5205CrossRef
go back to reference Sheng HW, Xu J, Yu LG, Sun XK, Hu ZQ, Lu K (1996) Melting process of nanometer-sized In particles embedded in an Al matrix synthesized by ball milling. J Mater Res 11(11):2841–2851CrossRef Sheng HW, Xu J, Yu LG, Sun XK, Hu ZQ, Lu K (1996) Melting process of nanometer-sized In particles embedded in an Al matrix synthesized by ball milling. J Mater Res 11(11):2841–2851CrossRef
go back to reference Sun J, Simon SL (2007) The melting behavior of aluminum nanoparticles. Thermochim Acta 463(1–2):32–40CrossRef Sun J, Simon SL (2007) The melting behavior of aluminum nanoparticles. Thermochim Acta 463(1–2):32–40CrossRef
go back to reference Swaminathan P, Sivaramakrishnan S, Palmer JS, Weaver JH (2009) Size dependence of nanoparticle dissolution in a matrix: gold in bismuth. Phys Rev B 79(14):144113CrossRef Swaminathan P, Sivaramakrishnan S, Palmer JS, Weaver JH (2009) Size dependence of nanoparticle dissolution in a matrix: gold in bismuth. Phys Rev B 79(14):144113CrossRef
go back to reference Tang F, Liu X, Wang H, Hou C, Lu H, Nie Z, Song X (2019) Solute segregation and thermal stability of nanocrystalline solid solution systems. Nanoscale 11(4):1813–1826CrossRef Tang F, Liu X, Wang H, Hou C, Lu H, Nie Z, Song X (2019) Solute segregation and thermal stability of nanocrystalline solid solution systems. Nanoscale 11(4):1813–1826CrossRef
go back to reference Tseng CC, Viskanta R (2003) Effect of subcooling on convective melting of a particle. Int Commun Heat Mass Transfer 30(1):13–25CrossRef Tseng CC, Viskanta R (2003) Effect of subcooling on convective melting of a particle. Int Commun Heat Mass Transfer 30(1):13–25CrossRef
go back to reference Unruh KM, Patterson BM, Shah SI (1992) Melting behavior of Snx (SiO2) 100–x granular metal films. J Mater Res 7(1):214–218CrossRef Unruh KM, Patterson BM, Shah SI (1992) Melting behavior of Snx (SiO2) 100–x granular metal films. J Mater Res 7(1):214–218CrossRef
go back to reference Vazquez-Nava E, Lawrence CJ (2009) Thermal dissolution of a spherical particle with a moving boundary. Heat Transfer Eng 30:416–426CrossRef Vazquez-Nava E, Lawrence CJ (2009) Thermal dissolution of a spherical particle with a moving boundary. Heat Transfer Eng 30:416–426CrossRef
go back to reference Vermolen FJ, Vuik C, Van der Zwaag S (2003) Particle dissolution and cross-diffusion in multi-component alloys. Mater Sci Eng, A 347:265–279CrossRef Vermolen FJ, Vuik C, Van der Zwaag S (2003) Particle dissolution and cross-diffusion in multi-component alloys. Mater Sci Eng, A 347:265–279CrossRef
go back to reference Yang CM, Chen MW, Zheng GJ, Wang ZD (2021) Melting of micro/nanoparticles considering anisotropy of surface energy. Sci Rep 11(1):1–11 Yang CM, Chen MW, Zheng GJ, Wang ZD (2021) Melting of micro/nanoparticles considering anisotropy of surface energy. Sci Rep 11(1):1–11
go back to reference Zhang DL, Cantor B (1990) Heterogeneous nucleation of In particles embedded in an AI matrix. Philos Mag A 62:557–572CrossRef Zhang DL, Cantor B (1990) Heterogeneous nucleation of In particles embedded in an AI matrix. Philos Mag A 62:557–572CrossRef
go back to reference Zhang M, Efremov MY, Schiettekatte F, Olson EA, Kwan AT, Lai SL, ... Allen LH (2000) Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements. Phys Rev B 62(15):10548 Zhang M, Efremov MY, Schiettekatte F, Olson EA, Kwan AT, Lai SL, ... Allen LH (2000) Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements. Phys Rev B 62(15):10548
go back to reference Zhang M, Wen JG, Efremov MY, Olson EA, Zhang ZS, Hu L, ... Allen LH (2012) Metastable phase formation in the Au-Si system via ultrafast nanocalorimetry. J Appl Phys 111(9):093516 Zhang M, Wen JG, Efremov MY, Olson EA, Zhang ZS, Hu L, ... Allen LH (2012) Metastable phase formation in the Au-Si system via ultrafast nanocalorimetry. J Appl Phys 111(9):093516
go back to reference Zhong J, Zhang LH, Jin ZH, Sui ML, Lu K (2001) Superheating of Ag nanoparticles embedded in Ni matrix. Acta Mater 49(15):2897–2904CrossRef Zhong J, Zhang LH, Jin ZH, Sui ML, Lu K (2001) Superheating of Ag nanoparticles embedded in Ni matrix. Acta Mater 49(15):2897–2904CrossRef
Metadata
Title
Micro-/nanoparticle melting in an alloy melt with anisotropic surface energy
Authors
C. M. Yang
M. W. Chen
G. J. Zheng
M. L. Zhang
Z. D. Wang
Publication date
01-07-2022
Publisher
Springer Netherlands
Published in
Journal of Nanoparticle Research / Issue 7/2022
Print ISSN: 1388-0764
Electronic ISSN: 1572-896X
DOI
https://doi.org/10.1007/s11051-022-05464-w

Other articles of this Issue 7/2022

Journal of Nanoparticle Research 7/2022 Go to the issue

Premium Partners