Surface energy is an essential property of condensed matter. It determines the equilibrium shape of a piece of matter and drives its interactions with the environment, for instance its wetting and adhesion properties, or even friction against another solid. Most non-metallic liquids and solid polymers are known to exhibit relatively low surface energies, in the range of few tens to few hundreds mJ/m². In contrast, metals show surface energies in the range of 1 to few J/m². For example, aluminum, copper or iron have surface energies close to 1.3, 1.8 and 2.2 J/m², respectively.

Due to the absence of translation periodicity and to their specific atomic architecture, metallic quasicrystals (QCs hereafter) present an electronic structure that differs significantly from the one of conventional metals: a marked pseudo-gap is observed at the Fermi energy [1]. The density of mobile electrons is henceforth reduced to about 10 to 20% of the one in a classical metal like Al, and the transport properties of QCs are definitely different from the ones in a periodic metal. So is also the surface energy.

This property can be assessed experimentally using single crystal specimens, but also by computational methods for periodic crystals [2]. The power of modern computers allows nowadays the study of materials with a unit cell containing several hundreds of atoms, which covers the full range of periodic metals known so far. Yet, it is still far below the range necessary to address the surface energy of QCs. The talk will review the methods used by the author [3] to overcome this difficulty and at least estimate the surface energy of few QCs such as icosahedral AlCuFe and AlPdMn in comparison to a small number of periodic crystalline materials of related composition. The meaningful low value of the surface energy found for these QCs, in the range 0.5-0.8 J/m², will be discussed in the light of applications of potential technological relevance such as reinforcement of polymer-matrix composites or friction against hard steel [4].