Elsevier

Calphad

Volume 31, Issue 1, March 2007, Pages 105-111
Calphad

Effect of substrates on the melting temperature of gold nanoparticles

https://doi.org/10.1016/j.calphad.2006.10.001Get rights and content

Abstract

The size-dependent melting temperature of metallic nanoparticles (NPs) is generally examined on a solid substrate. However, most experimental works performed on a solid substrate were explained by a homogeneous particle model without considering the effect of the substrate. For example, in the previous studies, the melting temperatures of gold NPs were examined on carbon or tungsten substrates. However, the experimental results were described only by the surface tension of gold, without interfacial tension between gold and substrate. In the present work, the effect of the sorts of substrate on the melting temperatures of gold NPs was examined by using a thermodynamic model equilibrating the chemical potentials of liquid and solid particles. For this study, graphite, alumina and tungsten substrates were selected as typical ceramic and metallic substrates.

Introduction

The phase stability of nanoparticles (NPs) is of great importance when they are applied to catalysis and microjoining at high temperatures [1], [2], because the phase stability of NPs is significantly different from those of bulk materials due to the high surface area to volume ratio. As used in those applications, NPs are generally in contact with a solid substrate. Therefore, it is very important to understand the effect of the interface between the NPs and solid substrates as well as the surface of the NPs on the phase stability of gold NPs.

A theoretical approach to the examinination of the phase stability of NPs was firstly carried out by Pawlow [3] in 1909. Thereafter, several thermodynamic models have been developed to examine the effect of the particle size on the phase stability of pure metals, especially on the solid–liquid phase transformation [4], [5], [6], [7], [8], [9], [10]. Recently, Tanaka et al. suggested that the CALPHAD (CALculation PHase Diagram) method can be applied to the calculation of phase stability of not only pure metallic NPs, but also alloy NPs with the database of thermodynamics and physical properties [9], [11], [12]. Although it is doubtful whether the CALPHAD method can be applied to predict the phase stability of extremely small NPs (for example, the melting temperature of very small NPs may have a finite temperature range [13]), the CALPHAD method is still useful for the design of nano-composite materials (such as NPs on solid substrates), because the CALPHAD method can be extended to multi-component systems easily for practical uses.1 However, most of the previous models, including Tanaka’s model, assumed NPs as homogeneous sphere particles, and they did not consider the effect of the interface between the NPs and their substrates. (Recently, several researchers have tried to investigate the effect of the substrate in their theoretical works [14], [15].)

Experimentally, the melting temperature depression of NPs was first observed by Takagi [16]. She investigated the changes in diffraction patterns during the melting of NPs, which method is now widely used by many researchers as a standard technique for monitoring the melting temperatures of NPs. Buffat and Borel also investigated the melting behavior of gold NPs with this method [7]. Sambles investigted the melting radius at which the evaporation rate changed due to phase transformation from solid to liquid at a constant temperature, but this technique is only applied to particles larger than 5 nm [6]. Castro et al. determined the melting temperatures of gold NPs on tungsten substrates by monitoring the field-emission image [17]. Dick et al. applied the differential thermal analysis method [18]. However, these methods have a problem in detecting accurate temperatures and/or size [7], [19]. Recently, Lee et al. have succeeded in investigating the melting temperature of an isolated NP by using an in situ HREM [20], [21]. This technique enables us to measure the accurate size and melting temperature relationship of pure metal and alloy NPs [22].

This paper develops a theoretical model based on the CALPHAD method, including the both effects of the particle surface and the interfaces between the NPs and substrates on the chemical potential of the NPs. For comparison with various experimental data in literatures [6], [7], [17], [18], we selected gold as metallic NPs. In order to investigate the effects of the sorts of substrate, three different substrates (two ceramic and one metallic substrates) were tested: graphite, alumina and tungsten.

Section snippets

Homegeneous system

For a bulk system, the differential of the total Gibbs free energy is written as Eq. (1). dG=SdT+VdP+iμidni+σPGdA where S, T, V, P, μi, ni, σPG, A are respectively entropy, temperature, volume, pressure, chemical potential of i, moles of i, surface tension (P: particle (solid or liquid), G: gas) and surface area. Thus when temperature, pressure, composition and surface area are fixed, the chemical potential of component i is defined as follows. μi(Gni)T,P,nj,A.

If we consider a small

Effect of the shape of gold nanoparticles on their melting behavior

The model described above was applied to simple systems: gold NPs on three different substrates (graphite, alumina, tungsten). The thermophysical data required for the calculation are listed in Table 1, and standard chemical potentials of gold are obtained from the FactSage™ thermodynamic database [27], [30], [31], [32], [33], [34], [35], [36], [37], [38]. The surface tension of pure liquid metals, and their contact angles, were recently re-estimated using the constrained drop method and the

Conclusions

In the present study, the effect of the substrates (graphite, alumina and tungsten) on the melting temperature of gold NPs has been examined by using thermodynamic calculations. The model calculation makes it possible to introduce both effects of the surface of the particle and the interface between the particle and the substrate simultaneously, when the particle size is larger than 3 nm in radius. It is found that the calculated results for heterogeneous particles on ceramic (graphite or

Acknowledgements

This work was supported by a Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF 2005-041-D00410). The authors would like thank the anonymous reviewers for their helpful discussion.

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