Theoretical phase diagrams of nanowires
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G. Guisbiers and M. Wauteleta) Condensed Matter Physics, University of Mons-Hainaut, B-7000 Mons, Belgium (Received 27 March 2006; accepted 1 June 2006)
Systems with typical dimensions in the range of 1–100 nm are in an intermediate state between solid and molecular. Such systems are characterized by the fact that the ratio of the number of surface to volume atoms is not small. This is known to lead to size and shape effects on their cohesive properties. In this work, the phase diagram of nanowires was studied in the framework of classical thermodynamics. The roles of the size, shape, and surface tensions were emphasized. The melting temperatures of nanowires of 21 elements were evaluated theoretically. In the case of binary systems, it was shown that the experimental or theoretical knowledge of the size-dependent phase diagrams of a given binary system allows the evaluation of the one of nanowires. The procedure is described in this paper.
I. INTRODUCTION
Systems with typical dimensions in the range of 1–100 nm are in an intermediate state between solid and molecular. Such systems are characterized by the fact that the ratio of the number of surface to volume atoms is not small. It is then obvious that the effects of the surface on the cohesive properties cannot be neglected. This is seen in various situations, such as the well known size-dependent melting point depression1 and other phase transitions2 of nanoparticles. Nanosystems with different shapes are synthesized and studied in the literature. Among them, so-called nanowires are of large interest, due to their particular properties. When the radius of the nanowires decreases down to the nanometer range, some of their properties are typical of a one-dimensional (1D) system.3 This opens many possible applications in optoelectronics, electronics, sensors, actuators, and optics. These 1D nanostructures are building blocks for constructing novel nanodevices. Various materials are synthesized as nanowires, such as semiconductors (Si, Ge,4 GaAs,5 cadmium chalcogenides6), metals (Au,7 Pd8), oxides (vanadium oxides9) and others (NixSiy10). The controlled growth of such 1D nanostructures cannot be accomplished without a careful study of the growth mechanism and the knowledge of their thermodynamics. Nano-manipulation is another important aspect
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0345 J. Mater. Res., Vol. 21, No. 11, Nov 2006
of the research into 1D nanostructures. Nanomaterials are often believed to be kinetically driven materials. However, it is obvious that, prior to any kinetic investigation, one has to know what is thermodynamically possible. Again, this requires knowledge of the thermodynamic properties of nanowires. When dealing with nanosystems, authors generally prefer to deal with the so-called “bottom-up” approach. Theoretical investigations of the melting behavior of nanowires have been mostly done by means of Monte Carlo and molecular dynamics11 computer simulations. Such simulations ar
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