Study of the conductivity of thin quasicrystalline films and its relation with the electronic friction

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Abstract

In the present work, we study the conductivity of thin quasicrystalline films employing a modeled spectral conductivity that contains generic properties of the quasicrystal. The variation of the conductivity with the thickness of the sample is also discussed. We investigate possible consequences for the electronic contribution to the friction coefficient.

Introduction

Since the discovery of quasicrystals (QCs) [1] the interest to employ these materials for technological applications was growing. Specially exciting properties for industrial applications are low coefficients of friction [2], [3], high hardness [5], low surface energy [2], [6], and good wear-resistance [7]. Moreover, experimental [8], [9] and theoretical [10], [11] studies indicate QCs as potential candidates for thermoelectric applications, due to the inherently low thermal conductivity [12], 1–3W/mK, which is little sensitive to small composition changes, and the high thermopowers (∼80μV/K in some cases [8]), as well as the broad conductivity range, 0.01–5000 (Ωcm)−1.

Practical applications for which QCs may prove suitable are derived from their physical and chemical properties. Experimental measurements [13], [14] of the electronic structure of quasicrystalline surfaces show that samples that are sufficiently high-annealed will exhibit the behavior expected for bulk QCs, but with reduced intensity. It is also found that the resistivity of thin films is lower compared with bulk samples [15], [16], [17]. However, the qualitative behavior is similar. The importance of the sample quality is also observed in measurements of the friction coefficient. In fact, in some cases, oxidized- or air-exposed quasicrystalline surfaces show friction coefficients that are lower than those found in clean surfaces [18]. However, compared with clean surfaces of pure metals, the friction coefficient of QCs is lower [18]. There are also experimental [3], [4] indications that the friction coefficient of QCs has, mainly, an electronic origin.

The relations between surface and bulk properties, mentioned above, indicate that in both cases the physics should be the same and that only the spectral signatures around the Fermi energy, εF, are of different intensity. Hence, we expect that some approaches employed to study the electronic transport in bulk QCs can be transfered to the investigation of the electronic properties of quasicrystalline surfaces. In the present work we will study the conductivity of thin quasicrystalline films employing a modeled spectral conductivity which is in agreement with ab initio calculations in low-order approximants. From these results we can make several predictions about the electronic friction in QCs. The paper is organized as follows. In Section 2 we present the model for the spectral conductivity and analytical results for the temperature-dependent conductivity. Comparisons with experiments are presented in Section 3. Section 4 deals with the electronic contribution to the friction coefficient. We provide a summary in Section 5.

Section snippets

Modeling the spectral conductivity

The temperature-dependent conductivity can be obtained from the Kubo–Greenwood formula [19], [20],σ(T)=∫dεσ̂(ε)f(ε,μ,T)ε,where μεF is the chemical potential, f(ε,μ,T) is the Fermi–Dirac distribution function, and σ̂(ε) is the spectral conductivity. Note that the only material-dependent quantity in Eq. (1) is σ̂(ε). That means, a suitable model for the spectral conductivity could explain the electronic transport in bulk or thin-film QCs. In fact, employing [21], [22], [23], [24] (cf. Fig. 1)σ

Comparison with experiments

To study the influence of the film thickness on the temperature-dependent conductivity, we first intend to obtain the model parameters that fit the experiments by Grenet et al. [16] on i-Al62.5Cu25Fe12.5 films of different thicknesses. These films were deposited on sapphire substrate in high vacuum [16]. These are the conditions that we assume in the modeling of the conductivity. The fit procedure is as follows [22], [23], [25]. (i) The Lorentzians are centered at just the same energies as in

Possible consequences for the friction coefficient

The study of surface resistivities is interesting because there are diverse phenomena that can be related to it [29], [30], [31]. For instance, changes of the resistivity due to adsorbed atoms or molecules is related to atomic-scale friction [29], [32]. In the absorption process of atoms or molecules onto the substrate, both electronic, ηel, and phononic, ηph, friction occur. Experimental techniques, such as infrared spectroscopy, inelastic helium scattering, and quartz crystal microbalance,

Summary

The two Lorentzians model for the spectral resistivity can explain quantitatively the temperature and film-thickness-dependent conductivity of thin quasicrystalline films. We have found that the electronic contribution to the friction coefficient in quasicrystals is independent of the temperature, or at least, weakly temperature-dependent. Moreover, we have shown that ηe is proportional to (Δx/x0). That means that ηel should increase after increasing the quality of the quasicrystal.

Acknowledgements

This work is supported by the project funded by the European Community under the contract no. G5RD-CT-2001-00584.

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