Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Journal of Materials Engineering and Performance
Erschienen in: Journal of Materials Engineering and Performance 5/2014

01.05.2014

Theoretical Analysis of Melting Point Depression of Pure Metals in Different Initial Configurations

verfasst von: G. Kaptay, J. Janczak-Rusch, G. Pigozzi, L. P. H. Jeurgens

Erschienen in: Journal of Materials Engineering and Performance | Ausgabe 5/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A general equation is derived for melting point depression (MPD) of pure metals, consisting of three terms: MPD due to high gas pressure, MPD due to high strain energy, and MPD due to small size of the metal. Particular equations are derived for different configurations of the solid metal, including grains embedded within a matrix. The equations obtained in this paper can be used to design nano-joining structures with improved MPD.
Vorheriger Artikel Numerical Modeling of Electrode Degradation During Resistance Spot Welding Using CuCrZr Electrodes
Nächster Artikel Interfacial Design for Joining Technologies: An Historical Perspective

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

Jetzt informieren

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!

Jetzt informieren
Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
T.T. Bao, Y. Kim, J. Lee, and J.G. Lee, Preparation and Thermal Analysis of Sn-Ag Nano Solders, Mater. Trans., 2010, 51, p 2145–2149CrossRef
2.
C. Zou, Y. Gao, B. Yang, and Q. Zhai, Synthesis and DSC Study on Sn3.5Ag Alloy Nanoparticles Used for Lower Melting Temperature Solder, J. Mater. Sci. Mater. Electron., 2010, 21, p 868–874CrossRef
3.
R. Longtin, E. Hack, J. Neuenschwander, and J. Janczak-Rusch, Benign Joining of Ultrafine Grained Aerospace Aluminum Alloys Using Nanotechnology, Adv. Mater., 2011, 20, p 1–5
4.
G. Pigozzi, A. Antusek, J. Janczak-Rusch, M. Parlinska-Wojtan, D. Passerone, C.A. Pignedoli, V. Bissig, J. Patscheider, and L.P.H. Jeurgens, Phase Constitution and Interface Structure of Nano-sized Ag-Cu/AlN Multilayers: Experimental and Ab Initio Modeling, Appl. Phys. Lett., 2012, 101, p 181602CrossRef
5.
P. Pawlow, Über die Abhängigkeit des Schmelzpunktes von der Oberflächenergie eines festen Körpers, Z. Phys. Chem., 1908, 55, p 545–548
6.
M. Takagi, Electron-Diffraction Study of Liquid-Solid Transition of Thin Solid Films, J. Phys. Soc. Jpn., 1954, 9(3), p 359–363CrossRef
7.
J.F. Pocza, A. Barna, and P.B. Barna, Formation Processes of Vacuum-Deposited Indium Films and Thermodynamical Properties of Submicroscopic Particles Observed by In Situ Electron Microscopy, J. Vac. Sci. Technol., 1969, 6(4), p 472–475CrossRef
8.
C.J. Coombes, The Melting of Small Particles of Lead and Indium, J. Phys. F, 1972, 2, p 441–449CrossRef
9.
Ph Buffat and J.-P. Borel, Size Effect on the Melting Temperature of Gold Particles, Phys. Rev. A, 1976, 13, p 2287–2296CrossRef
10.
P.R. Couchman and W.A. Jesser, Thermodynamic Theory of Size Dependence of Melting Temperature in Metals, Nature, 1977, 269, p 481–483CrossRef
11.
F. Spaepen and D. Turnbull, Negative Pressures and Melting Point Depression in Oxide-Coated Liquid Metal Droplets, Scripta Metall., 1979, 13, p 149–151CrossRef
12.
G.L. Allen, W.W. Gile, and W.A. Jesser, The Melting Temperature of Microcrystals Embedded in a Matrix, Acta Metall., 1980, 28, p 1695–1701CrossRef
13.
R. Kofman, P. Cheyssac, A. Aouaj, Y. Lereah, G. Deuscher, T. Ben-David, J.M. Penisson, and A. Bourret, Surface Melting Enhanced by Curvature Effects, Surf. Sci., 1994, 303, p 231–246CrossRef
14.
K. Chattopadhyay and R. Goswami, Melting and Superheating of Metals and Alloys, Prog. Mater. Sci., 1997, 42, p 287–300CrossRef
15.
M. Wautelet, On the Shape Dependence of the Melting Temperature of Small Particles, Phys. Lett. A, 1998, 246, p 341–342CrossRef
16.
Z. Zhang, J.C. Li, and Q. Jiang, Modelling for Size-Dependent and Dimension-Dependent Melting of Nanocrystals, J. Phys. D, 2000, 33, p 2653–2656CrossRef
17.
Q. Jiang, Z. Zhang, and J.C. Li, Melting Thermodynamics of Nanocrystals Embedded in a Matrix, Acta Mater., 2000, 48, p 4791–4795CrossRef
18.
T. Tanaka and S. Hara, Thermodynamic Evaluation of Binary Phase Diagrams of Small Particle Systems, Z. Metallkd., 2001, 92, p 467–472
19.
M. Hillert and J. Argen, Effect of Surface Free Energy and Surface Stress on Phase Equilibria, Acta Mater., 2002, 50, p 2429–2441CrossRef
20.
U. Tartaglino and E. Tosatti, Strain Effects at Solid Surfaces Near the Melting Point, Surf. Sci., 2003, 532–535, p 623–627CrossRef
21.
Q. Jiang, L.H. Liang, and J.C. Li, Thermodynamic Superheating of Low-Dimensional Metals Embedded in Matrix, Vacuum, 2003, 72, p 249–255CrossRef
22.
Z. Shi, P. Wynblatt, and S.G. Srinivasan, Melting Behavior of Nanosized Lead Particles Embedded in an Aluminium Matrix, Acta Mater., 2004, 52, p 2305–2316CrossRef
23.
V.M. Samsonov and O.A. Malkov, Thermodynamic Model of Crystallization and Melting of Small Particles, Cent. Eur. J. Phys., 2004, 2(1), p 90–103CrossRef
24.
Q.S. Mei, S.C. Wang, H.T. Cong, Z.H. Jin, and K. Lu, Determination of Pressure Effect on the Melting Point Elevation of Al Nanoparticles Encapsulated in Al2O3 without epitaxial interface, Phys. Rev. B, 2004, 70, p 125421CrossRef
25.
J. Chang and E. Johnson, Surface and Bulk Melting of Small Metal Clusters, Philos. Mag., 2005, 85(30), p 3617–3627CrossRef
26.
J. Slutsker, K. Thornton, A.L. Roytburd, J.A. Warren, and G.B. McFadden, Phase Field Modeling of Solidification Under Stress, Phys. Rev. B, 2006, 74(1), p 014103CrossRef
27.
J.J. Hoyt, Effect of Stress on Melting and Freezing in Nanopores, Phys. Rev. Lett., 2006, 96(4), p 045702CrossRef
28.
G. Guisbiers and M. Wautelet, Size, Shape and Stress Effects on the Melting Temperature of Nano-polyhedral Grains on a Substrate, Nanotechnology, 2006, 17, p 2008–2011CrossRef
29.
J. Sun and S.L. Simon, The Melting Behavior of Aluminum Nanoparticles, Thermochim. Acta, 2007, 463, p 32–40CrossRef
30.
G. Guisbiers, O. Van Overschelde, and M. Wautelet, Nanoparticulate Origin of Intrinsic Residual Stress in Thin Films, Acta Mater., 2007, 55, p 3541–3546CrossRef
31.
O.A. Yeshchenko, I.M. Dmitruk, A.A. Alexeenko, and A.M. Dmytruk, Size-Dependent Melting of Spherical Copper Nanoparticles Embedded in a Silica Matrix, Phys. Rev. B, 2007, 75(8), p 085434CrossRef
32.
P. Letellier, A. Mayaffre, and M. Turmine, Melting Point Depression of Nanosolids: Nonextensive Thermodynamics Approach, Phys. Rev. B, 2007, 76, p 045428CrossRef
33.
Q.S. Mei and K. Lu, Melting and Superheating of Crystalline Solids: From Bulk to Nanocrystals, Prog. Mater. Sci., 2007, 52, p 1175–1262CrossRef
34.
J. Lee, T. Tanaka, J. Lee, and H. Mori, Effect of Substrates on the Melting Temperature of Gold Nanoparticles, Calphad, 2007, 31, p 105–111CrossRef
35.
K.K. Nanda, Size-Dependent Melting of Nanoparticles: Hundred Years of Thermodynamic Model, Pramana J. Phys., 2009, 172, p 617–628CrossRef
36.
V.I. Levitas, M. Pantoya, G. Chauhan, and I.J. Rivero, Effect of the Alumina Shell on the Melting Temperature Depression for Aluminum Nanoparticles, Phys. Chem. C, 2009, 113(32), p 14088–14096CrossRef
37.
G. Kaptay, The Extension of the Phase Rule to Nano-systems and on the Quaternary Point in One-Component Nano Phase Diagrams, J. Nanosci. Nanotechnol., 2010, 10, p 8164–8170CrossRef
38.
W. Luo, L. Deng, K. Su, K. Li, G. Liao, and S. Xiao, Gibbs Free Energy Approach to Calculate the Thermodynamic Properties of Copper Nanocrystals, Phys. B, 2011, 406, p 859–863CrossRef
39.
V.I. Levitas and K. Samani, Size and Mechanics Effects in Surface-Induced Melting of Nanoparticles, Nat. Commun., 2011, 2, p 284CrossRef
40.
V.I. Levitas and K. Samani, Coherent Solid/Liquid Interface with Stress Relaxation in a Phase-Field Approach to the Melting/Solidification Transition, Phys. Rev. B, 2011, 84(14), p 140103CrossRef
41.
G. Garzel, J. Janczak-Rusch, and L. Zabdyr, Reassessment of the Ag-Cu Phase Diagram for Nanosystems Including Particle Size and Shape Effect, Calphad, 2012, 36, p 52–56CrossRef
42.
G. Kaptay, The Gibbs Equation Versus the Kelvin and the Gibbs-Thomson Equations to Describe Nucleation and Equilibrium of Nano-materials, J. Nanosci. Nanotechnol., 2012, 12(3), p 2625–2633CrossRef
43.
A.I. Rusanov, The Development of the Fundamental Concepts of Surface Thermodynamics, Colloid J., 2012, 74(2), p 136–153CrossRef
44.
G. Kaptay, Nano-Calphad: Extension of the Calphad Method to Systems with Nano-phases and Complexions, J. Mater. Sci., 2012, 47, p 8320–8335CrossRef
45.
V.I. Levitas, Z. Ren, Y. Zeng, Z. Zhang, and G. Han, Effect of the Alumina Shell on the Melting Temperature Depression for Aluminum Nanoparticles, Phys. Rev. B, 2012, 85(22), p 220104CrossRef
46.
J. Leitner and M. Kamrádek, Termodynamicky popis nanosystemu, Chem. Listy, 2013, 107, p 606–613
47.
48.
D.A. Firmansyah, K. Sullivan, K.S. Lee, Y.H. Kim, R. Zahaf, M.R. Zachariah, and D.J. Lee, Microstructural Behavior of the Alumina Shell and Aluminum Core Before and After Melting of Aluminum Nanoparticles, Phys. Chem. C, 2013, 116(1), p 404–411CrossRef
49.
L. Wojtczak, The Melting Point of Thin Films, Phys. Status Solidi, 1967, 22, p K163–K166CrossRef
50.
L.P.H. Jeurgens, Z. Wang, and E.J. Mittemeijer, Thermodynamics of Reactions and Phase Transformations at Interfaces and Surfaces, Int. J. Mater. Res., 2009, 100, p 1281–1307CrossRef
51.
D.G. Gromov and S.A. Gavrilov, Manifestation of the Heterogeneous Mechanism Upon Melting of Low-Dimensional Systems, Phys. Solid State, 2009, 51(10), p 2135–2144CrossRef
52.
R.C. Tolman, The Effect of Droplet Size on Surface Tension, J. Chem. Phys., 1949, 17, p 333–337CrossRef
53.
M.W. Chase (Ed.), Janaf, Thermochemical Tables, 3rd ed., J. Phys. Chem. Data, 1985, 14(Suppl 1)
54.
J. Emsley, The Elements, Clarendon Press, Oxford, 1989
55.
Y.S. Touloukian, R.K. Kirby, R.E. Taylor, and T.Y.R. Lee, Thermal Expansion, IFI/Plenum, New York, 1977CrossRef
56.
T. Iida and R.I.L. Guthrie, The Physical Properties of Liquid Metals, Clarendon Press, Oxford, 1993
57.
G. Kaptay, A Unified Model for the Cohesive Enthalpy, Critical Temperature, Surface Tension and Volume Thermal Expansion Coefficient of Liquid Metals of bcc, fcc and hcp Crystals, Mater. Sci. Eng. A, 2008, 495, p 19–26CrossRef
58.
I. Barin, Thermochemical Properties of Pure Substances, vols 1, 2, VCH, Weinheim, 1993
59.
H.M. Ledbetter and E.R. Naimon, Elastic Properties of Metals and Alloys. II. Copper, J. Phys. Chem. Ref. Data, 1974, 3(4), p 897–934CrossRef
60.
D. Gerlich, S.L. Dole, and G.A. Slack, Elastic Properties of Aluminum Nitride, J. Phys. Chem. Solids, 1986, 47(5), p 437–441CrossRef
61.
N. Eustathopoulos, M.G. Nicholas, and B. Drevet, Wettability at High Temperatures, Pergamon, Amsterdam, 1999
62.
G. Kaptay, E. Báder, and L. Bolyán, Interfacial Forces and Energies Relevant to Production of Metal Matrix Composites, Mater. Sci. Forum, 2000, 329–330, p 151–156CrossRef
Metadaten
Titel
Theoretical Analysis of Melting Point Depression of Pure Metals in Different Initial Configurations
verfasst von
G. Kaptay
J. Janczak-Rusch
G. Pigozzi
L. P. H. Jeurgens
Publikationsdatum
01.05.2014
Verlag
Springer US
Erschienen in
Journal of Materials Engineering and Performance / Ausgabe 5/2014
Print ISSN: 1059-9495
Elektronische ISSN: 1544-1024
DOI
https://doi.org/10.1007/s11665-014-0885-z

Weitere Artikel der Ausgabe 5/2014

Journal of Materials Engineering and Performance 5/2014 Zur Ausgabe

OriginalPaper

Joining of ZrB2 Ceramics to Ti6Al4V by Ni-Based Interlayers

Erratum

Erratum to: Effect of Al-5Ti-1B-1Re on the Microstructure and Hot Crack of As-Cast Al-Zn-Mg-Cu Alloy

OriginalPaper

Interfacial Design for Joining Technologies: An Historical Perspective

OriginalPaper

Influence of Surface Pre-treatments on Laser Welding of Ti6Al4V Alloy

OriginalPaper

Interfacial Phenomena in Al/Al, Al/Cu, and Cu/Cu Joints Soldered Using an Al-Zn Alloy with Ag or Cu Additions

OriginalPaper

Numerical Modeling of Electrode Degradation During Resistance Spot Welding Using CuCrZr Electrodes

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise