Size-dependent melting of nanocrystals: a self-consistent statistical approach
Source abstract
Abstract
A self-consistent statistical method is used to describe size effects on melting of free nanocrystals. The melting transition is assumed to be directly related to evolution of high-temperature instability of the phonon subsystem of the crystal, caused by strong anharmonicity of atomic vibrations. We show that depression of the melting temperature of small free particles is mainly due to presence of surface atoms which are bound to smaller numbers of atoms than those of the interior. The melting temperatures of spherical nanocrystals of Ar and Au were calculated as functions of the inverse of their radii and compared with experimental and molecular dynamics data.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: nanoparticles nucleation surface interactions · Material Dynamics and Properties · Advanced Thermodynamics and Statistical Mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (37)
Show source-provided references
1. Alavi S, Thompson DL (2006) Molecular dynamics simulation of the melting of aluminum nanoparticles. J Phys Chem A 110:1518–152310.1021/jp053318s ↗
2. Beaglehole D (1991) Surface melting of small particles, and the effects of surface impurities. J Cryst Growth 112:663–66910.1016/0022-0248(91)90123-M ↗
3. Ben David T, Lereah Y, Deutscher G, Kofman R, Cheyssac P (1995) Solid–liquid trtansition in ultra-fine lead particles. Phil Mag A 71:1135–114310.1080/01418619508236241 ↗
4. Böttger H (1983) Principles of the theory of lattice dynamics. Academie-Verlag, Berlin10.1515/9783112728734 ↗
5. Buffat Ph, Borel J-P (1976) Size effect on the melting temperature of gold particles. Phys Rev A 13:2287–229810.1103/PhysRevA.13.2287 ↗
6. Celestini F, Pellenq RJ-M, Bordarier P, Rousseau B (1996) Melting of Lennard-Jones clusters in confined geometries. Z Phys D 37:49–5310.1007/s004600050008 ↗
7. Choquard PF (1967) The anharmonic crystal. Benjamin, New York
8. Couchman PR (1979) The Lindemann hypothesis and the size-dependence of melting temperature. II. Phil Mag A 40:637–64310.1080/01418617908234864 ↗
9. Couchman PR, Jesser WA (1977) Thermodynamic theory of size dependence of melting temperature in metals. Nature (London) 269:481–48310.1038/269481a0 ↗
10. Couchman PR, Ryan CL (1978) The Lindemann hypothesis and the size-dependence of melting temperature. Phil Mag A 37:369–37310.1080/01418617808239174 ↗
11. Delogu F (2005) Structural and energetic properties of unsupported Cu nanoparticles from room temperature to the melting point: molecular dynamics simulations. Phys Rev B 72:20541810.1103/PhysRevB.72.205418 ↗
12. Ercolessi F, Andreoni W, Tosatti E (1991) Melting of small gold particles: mechanism and size effect. Phys Rev Lett 66:911–91410.1103/PhysRevLett.66.911 ↗
13. Hanszen K-J (1960) Theoretische Untersuchungen über den Schmelzpunkt kleiner Kügelchen. Ein Beitrag zur Thermodynamik der Grenzflächen. Z Phys 157:523–55310.1007/BF01340711 ↗
14. Hoshino K, Shimamura S (1979) A simple model for the melting of fine particles. Phil Mag A 40:137–14110.1080/01418617908234840 ↗
15. Karasevskii AI, Lubashenko VV (2002) Binary distribution functions of atoms of simple crystals. Phys Rev B 66:05430210.1103/PhysRevB.66.054302 ↗
16. Karasevskii AI, Lubashenko VV (2004) Calculation of thermodynamic properties of Cu and Ag using a self-consistent statistical method. Phys Stat Sol (b) 241:1274–128010.1002/pssb.200302001 ↗
17. Karasevskii AI, Lubashenko VV (2005) Role of anharmonicity of atomic vibrations in formation of vacancies in the rare gas crystals. Phys Rev B 71:01210710.1103/PhysRevB.71.012107 ↗
18. Kittel C (1986) Introduction to solid state physics. Wiley, New York
19. Lindemann FA (1910) Über die Berechnung molekularer Eigenfrequenzen. Z Phys 11:609–612
20. Maradudin AA, Flinn PA, Coldwell-Horsfall RA (1961) Anharmonic contributions to vibrational thermodynamical properties of solids. Part I. General formulation and application to the linear chain. Ann Phys (NY) 15:337–35910.1016/0003-4916(61)90188-9 ↗
21. Nanda KK (1998) Size-dependent melting of small particles: a classical approach. Eur J Phys 19:471–47210.1088/0143-0807/19/5/012 ↗
22. Nanda KK, Sahu SN, Behera SN (2002) Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys Rev A 66:01320810.1103/PhysRevA.66.013208 ↗
23. Nishiguchi N, Sakuma T (1981) Vibrational spectum and specific heat of fine particles. Solid State Commun 38:1073–107710.1016/0038-1098(81)90020-X ↗
24. Olson EA, Efremov MYu, Zhang M, Allen LH (2005) Size-dependent melting of Bi nanoparticles. J Appl Phys 97:03430410.1063/1.1832741 ↗
25. Pawlow P (1909) Über die Abhängigkeit des Schmelzpunktes von den Oberflächenenergie eines festen Körpers. Z Phys Chem 65:1–3510.1515/zpch-1909-6502 ↗
26. Qi Y, Çağin T, Johnson WL, Goddard III WA (2001) Melting and crystallization in Ni nanoclusters: the mesoscale regime. J Chem Phys 115:385–39410.1063/1.1373664 ↗
27. Qi WH, Wang MP, Zhou M, Shen XQ, Zhang XF (2006) Modeling cohesive energy and melting temperature of nanocrystals. J Phys Chem Solids 67:851-85510.1016/j.jpcs.2005.12.003 ↗
28. Saka H, Nishikawa Y, Imura T (1988) Melting temperature of In particles embedded in an Al matrix. Phil Mag A 57:895–90610.1080/01418618808204524 ↗
29. 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 324:339–35110.1098/rspa.1971.0143 ↗
30. Shandiz MA, Safaei A, Sanjabi S, Barber ZH (2007) Modeling size dependence of melting temperature of metallic nanoparticles. J Phys Chem Solids 68:1396–139910.1016/j.jpcs.2007.02.049 ↗
31. Skripov VP, Koverda V P, Skokov V N (1981) Size effect on melting of small particles. Phys Stat Sol (a) 66:109–11810.1002/pssa.2210660111 ↗
32. Takagi M (1954) Electron-diffraction study of liquid-solid transition of thin metal films. J Phys Soc Jpn 9:359–36310.1143/JPSJ.9.359 ↗
33. Tamura A, Nigeta K, Ichinokawa T (1982) Lattice vibrations and specific heat of a small particle. J Phys C 15:4975–499110.1088/0022-3719/15/24/010 ↗
34. Wautelet M (1990) Size effect on the melting (or disordering) temperature of small particles. Solid State Commun 74:1237–123910.1016/0038-1098(90)90314-2 ↗
35. Yang CC, Li S (2007) Investigation of cohesive energy effects on size-dependent physical and chemical properties of nanocrystals. Phys Rev B 75:16541310.1103/PhysRevB.75.165413 ↗
36. Zhang L, Jin ZH, Zhang LH, Sui ML, Lu K (2000a) Superheating of confined Pb thin films. Phys Rev Lett 85:1484–148710.1103/PhysRevLett.85.1484 ↗
37. Zhang Z, Li JC, Jiang Q J (2000b) Modelling for size-dependent and dimension-dependent melting of nanocrystals. Phys D 33:2653–265610.1088/0022-3727/33/20/318 ↗