Melting and possible amorphization of Sn and Pb in Ge/Sn and Ge/Pb mechanically milled powders
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Mixtures of Ge-Sn and Ge-Pb powders were ball-milled to form a fine dispersion. After 32 h of milling the average diameter of the hard Ge particles embedded in the Sn (or Pb) matrix was about 10 nm. As the Ge concentration was increased in each system, the melting point, TM, and the enthalpy of fusion, A//M, of Sn (or Pb) decreased. Only small changes in ATM and AHM were observed after heating cycles in the DSC to above the melting point. The melting endotherm measured by DSC disappeared for Ge-rich compositions (88 and 95 vol. % Ge for Ge-Sn; 93.5 vol. % Ge for Ge-Pb). It is suggested that atomic disorder/melting is nucleated at the Ge/Sn (or Ge/Pb) interfaces and the melting point and enthalpy of fusion decrease as the interfacial area increases. When the Ge volume reaches a value where essentially all the Sn (or Pb) atoms are adjacent to the Ge particle surfaces, the Sn is in a disordered—perhaps amorphous—state such that no melting transition is observed.
I. INTRODUCTION
The microscopic mechanism for the phenomenon of melting remains controversial. Two different broad approaches to the problem of melting have considered melting as (1) a first order transformation where the free energies of the solid and liquid phases are equal and the structure of both phases must be understood or (2) an instability limit in the solid near the melting point.1 Theories for the nature of the instability in the solid at melting include the well-known Lindemann criterion2 according to which melting is a vibrational instability which occurs when the amplitude of vibration of the atoms in the crystalline lattice reaches a critical fraction of the interatomic distance. Other proposed melting criteria include a critical vacancy concentration3 and a catastrophic dislocation generation.4 Melting has also been attributed to the vanishing of one of the shear elastic moduli of the crystal.5 Couchman and Jesser6 reviewed the various theories of melting and stressed the importance of the heterogeneous nucleation of melting at the crystalline surface. The nucleation of melting on the surface is presumably responsible for the many observations of a size dependence of melting temperatures (e.g., Refs. 7-12). The melting point of thin films or fine particles can be depressed11 or increased,12 depending on the nature of the interface at the metal surface. Free metal particles exhibit a depression of TMn with decreasing particle size while In particles embedded in an Al matrix showed an increase in TM with decreasing particle size.12 Thermodynamic models for the size effect of the melting of small particles predict a linear dependence of the melting point depression J. Mater. Res., Vol. 5, No. 2, Feb 1990
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(or increase) on the reciprocal of the particle size,6'1012 which is approximated by the experimental data. Most of the experiments on the size effect of melting have studied in situ melting of fine particles in electron microscopes. These methods have the advantage of simultaneously obtai
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