Materials Science and Engineering A286 (2000) 139 – 143 Thermal stability of low dimensional crystals Q. Jiang * , Z. Zhang, Y.W. Wang Department of Materials Science and Engineering, Jilin Uniersity of Technology Changchun 130025, PR China Abstract A model, free of any adjustable parameter, has been developed for the size-dependent melting temperature and melting entropy of nanocrystals. The model can be utilized to predict the thermal stability both for metallic and organic low dimensional materials. The results show that their melting thermodynamic functions are dependent on their size, dimension, and environment. The theoretical predictions in terms of the above model are fully consistent with experimental evidences and the results of molecular dynamics simulation. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Thermal stability; Melting temperature; Melting entropy; Low dimensional crystals www.elsevier.com/locate/msea 1. Introduction Takagi in 1954 demonstrated for the first time that ultrafine metallic particles melt below their correspond- ing bulk melting temperatures T m () [1]. It is now known that the melting temperatures of metallic [2 – 6], organic [7] and semiconductor [8] nanocrystals depend on their sizes. Moreover, the metallic and organic nanocrystals can exhibit not only a decrease of the melting point, but also a superheating, depending on their surrounding environments [9–11]. When the thickness of a thin film reaches a monolayer level, the film melts at a much lower temperature than its T m (). Thus, a thorough understanding of the thermal proper- ties of low dimensional materials is of importance due to their potential applications in the field of microelec- tronics, solar energy utilization and nonlinear optical materials [8,12]. This may allow the use of a greater variety of substrates or the formation of laminar thin films without thermal damage to the underlying fea- tures [8]. However, our theoretical understanding of the thickness dependence of melting for crystalline thin films is far from complete [1,12,13]. Recently, a model, free of any adjustable parameter, for the size-dependent melting and dimension-dependent melting T m (r ) was introduced [3 – 6] in terms of the Lindemann’s criterion for melting [5,6] and the expression of Mott for the vibrational entropy of melting [14,15]. The model could predict the melting behavior of low dimensional metal- lic and organic materials. 2. Model T m (r ) of metallic and organic nanocrystals is de- scribed by the following [3–6], T m (r )/T m () =exp [ -( -l)/(r /r 0 -l)], (1) where r is the radius of the crystal, r 0 denotes a critical radius at which all atoms of the nanocrystal are located on its surface,  is a material constant defined as the ratio between the mean square displacement (msd) of surface atoms and that of interior atoms of the crystals. For low dimensional crystals, r 0 depends on the dimen- sion of the crystal d where d =0 for nanoparticles, d =1 for nanowires and d =2 for thin films (when d =3, r  and the corresponding crystal is a bulk crystal, which has no r 0 ). In general, the dimension of the low dimensional crystals can be fractal [4]. For a nanoparticle, r has a usual meaning of radius. For a nanowire, r is taken as its radius. For a thin film, r denotes its half thickness. Let h be atomic diameter, there is [3–5], r 0 =(3 -d )h. (2) * Corresponding author. Tel.: +86-431-5705371; fax: +86-431- 5687607. E-mail address: jiangq@post.jut.edu.cn (Q. Jiang) 0921-5093/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII:S0921-5093(00)00718-8