Size dependent thermal vibrations and melting in nanocrystals

A simple model for the size-dependent amplitude of the atomic thermal vibrations of a nanocrystal is presented which leads to the development of a model for the size dependent melting temperature in nanocrystals on the basis of Lindemann's criterion. The two models are in terms of a directly measurable parameter for the corresponding bulk crystal, i.e., the ratio between the amplitude of thermal vibrations for surface atoms and that for interior ones. It is shown that the present model for the melting temperature offers not only a qualitative but even an excellent quantitative agreement with the experimentally observed size-dependent superheating, as well as melting point suppression in both the supported and embedded metallic and semiconductor nanocrystals.

[1]  K. Hoshino,et al.  A simple model for the melting of fine particles , 1979 .

[2]  B. Cantor,et al.  Melting behaviour of In and Pb particles embedded in an Al matrix , 1991 .

[3]  G. Deutscher,et al.  A Direct Observation of Low-Dimensional Effects on Melting of Small Lead Particles , 1990 .

[4]  V. Skripov,et al.  Size effect on melting of small particles , 1981 .

[5]  Johnson,et al.  Superheating and supercooling of lead precipitates in aluminum. , 1990, Physical review letters.

[6]  Gabor A. Somorjai,et al.  Chemistry in Two Dimensions: Surfaces , 1981 .

[7]  Donnelly,et al.  Superheating of small solid-argon bubbles in aluminum. , 1985, Physical review letters.

[8]  Á. Barna,et al.  Formation Processes of Vacuum-Deposited Indium Films and Thermodynamical Properties of Submicroscopic Particles Observed by In Situ Electron Microscopy , 1969 .

[9]  A. Alivisatos,et al.  Melting in Semiconductor Nanocrystals , 1992, Science.

[10]  K. Yamafuji,et al.  Current-Voltage Characteristics of Superconducting Foils in Small Oscillatory Magnetic Fields , 1975 .

[11]  Choi,et al.  Size-dependent melting temperature of individual nanometer-sized metallic clusters. , 1990, Physical review. B, Condensed matter.

[12]  R. Wallis.  Lattice dynamics of crystal surfaces , 1974 .

[13]  J. Boyce,et al.  Orientational ordering and melting of molecular H2 in an a-Si matrix: NMR studies. , 1985, Physical review letters.

[14]  H. Saka,et al.  Melting temperature of In particles embedded in an Al matrix , 1988 .

[15]  P. Buffat,et al.  Size effect on the melting temperature of gold particles , 1976 .

[16]  O. Sherby,et al.  The stress and temperature dependence of steady-state flow at intermediate temperatures for pure polycrystalline aluminum , 1980 .

[17]  Thomas L. Beck,et al.  Rare gas clusters: Solids, liquids, slush, and magic numbers , 1987 .

[18]  C. Solliard.  Debye-Waller factor and melting temperature in small gold particles: Related size effects , 1984 .

[19]  M. Hasegawa,et al.  A theory of melting in metallic small particles , 1980 .

[20]  R. A. Bayles,et al.  Small particle melting of pure metals , 1986 .