Size effect on melting temperature of nanosolids

doi:10.1016/j.physb.2005.06.035

Physica B: Condensed Matter

Volume 368, Issues 1–4, 1 November 2005, Pages 46-50

https://doi.org/10.1016/j.physb.2005.06.035 Get rights and content

Abstract

By considering the surface effects, the melting temperature of nanosolids (nanoparticles, nanowires and nanofilms) has been predicted based on size-dependent cohesive energy. It is shown that the melting temperature of free standing nanosolids decreases with decrease in the solid size, and the melting temperature variation for spherical nanoparticle, nanowire and nanofilm of a material in the same size is 3:2:1. The present theoretical results on Sn and Pb nanoparticles, In nanowires and nanofilms are consistent with the previous experimental values.

Introduction

In recent decades, researchers have paid more attention to the melting of nanosolids, because the melting temperature of nanosolids are different from that of the corresponding bulk materials. In other words, the melting temperature of nanosolids with free surface decreases with decreasing in the crystal size [1], [2], [3], [4], [5], [6]. The nanosolids can be nanoparticles, nanowires or nanofilms. These special thermal properties may lead to develop new materials. Therefore, it is meaningful to give a physical explanation of size-dependent melting temperature of nanosolids. The development of quantum theory enables us to calculate the thermodynamic properties with the help of supercomputer [7], [8], [9]. However, understanding the thermodynamic properties of metallic nanosolids by semi-empirical methods is still urgent, which are very simple and can be widely used in materials research. Generally, the melting temperature of nanosolids (T_mp) is linear to the reciprocal of the crystal size [10], [11], i.e., $T_{mp} = T_{mb} (1 - C / D)$ , where T_mb is the melting temperature of the corresponding bulk materials, D is the crystal size and C is a material constant. Apparently, the proper determination of C is key issue, and cannot be obtained by fitting experimental results.

In this paper, we will develop a new model accounting for the melting temperature of nanosolids (nanoparticles, nanowires, and nanofilms) with free surface, and the efficiency of the model will be confirmed by the available experimental values. Furthermore, we will give the analytical form of the material constant C for different nanosolids.

Section snippets

Model

The total atoms of a nanosolid is denoted as n, and the number of its surface atoms is N, where the surface atoms refer to the first layer of the nanosolid. Then the number of interior atoms is n−N. If relaxation of the nanosolid is not considered, the interior structure is the same as the corresponding bulk materials. Let E₀ be the cohesive energy per atom of the bulk material, then contribution of the interior atoms to the cohesive energy of the nanosolid is $E_{0} (n - N)$ . Since half of the total

Results and discussion

The melting temperature of Sn particles formed by evaporation on inert substrate with radii ranging from 5 to 50 nm has been measured directly using a novel scanning nanocalorimeter [6]. And the melting temperature depression of Sn nanoparticles has been observed, which has been shown as symbols in Fig. 1. The calculated melting temperature of Sn particle is also shown. It is found that the present theoretical results are close to the experimental values. The small discrepancy may result from

Conclusions

By considering the surface effects, the melting temperature of nanosolids (nanoparticles, nanowires and nanofilms) has been predicted based on size-dependent cohesive energy. It is shown that the melting temperature of free-standing nanosolids decreases with decrease in the solid size, and the melting temperature variation for spherical nanoparticle, nanowire and nanofilm of a material in the same size is 3:2:1. The present theoretical results on Sn and Pb nanoparticles, In nanowires and

Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 50401010).

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Size effect on melting temperature of nanosolids

Abstract

Introduction

Section snippets

Model

Results and discussion

Conclusions

Acknowledgments

Surf. Sci.

Acta. Mater.

Mater. Chem. Phys.

Mater. Lett.

Phys. Soc. Japan

J. Phys.

J. Mater. Res.

Science

Chem. Mater.

Phys. Rev. Lett.

Phys. Rev. B

Phys. Rev.