Observations of Local Electronic States in Al-based quasicrystals by STEM-EELS

Most quasicrystals (QCs) reveal pseudogaps in their density of states around Fermi level, and hence the stability of QCs have been discussed in terms of energetic gains in electron systems. In fact, many QCs have been discovered by tuning valence electron density based on Hume-Rothery rule. Therefore, understanding electronic structures in QCs may provide an important clue for their stabilization mechanism. Generally, it has been frequently discussed based on an interaction between Fermi surface and Brillouin zone boundary within the framework of nearly free electron model, which is believed to be an underlying physics of a Hume-Rothery's empirical criteria. However, the electronic structures of QCs have not yet been fully understood, particularly being in microscopic-macroscopic relations. In the present work, we investigate local electronic states in Al-based QCs using electron energy loss spectroscopy (EELS) combined with scanning transmission electron microscopy (STEM), by which EELS spectra with sub-Å probe and atomic structure can be obtained simultaneously. We report STEM-EELS results on AlCuIr decagonal phases [1]. Principal components analysis clearly shows up the atomic-site dependence of plasmon loss spectra in a two-dimensional map. Qualitatively, there seems to be certain correlations between the plasmon peaks and the core-loss edges, Al L₁, Ir O₂₃, Ir N₆₇ and Cu L₂₃, all of which reveal different behaviours at the cluster centers and the edges. All results indicate the cluster centers have metallic states and the cluster edges have covalent states in comparison. First-principles calculations confirm the unusual electronic state. We analyse a distribution of covalent electrons by Fourier transformation of electron localization function. The distribution seems like a 10-fold charge density wave with Fermi wave length. It suggests that the Hume-Rothery mechanism is important even when hybridization effect mainly contributes to pseudogap formation. The cluster centers can be regarded as the regions which are unable to contribute to the Hume-Rothery mechanism. It may be origin of the unusual electronic states. This work was conducted in Research Hub for Advanced Nano Characterization, The University of Tokyo, supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. It is acknowledged that T. Seki is a research fellow of Japan Society for the Promotion of Science.

A cubic quasicrystal in a rapidly-solidified Mg-Al alloy

It is commonly accepted that the definition of quasicrystal should include a rotational symmetry forbidden in periodic crystals. On the other hand, the quasicrystal with a conventional point group is theoretically possible [1,2]. In a rapidly-solidified Mg-Al alloy, intriguing electron diffraction patterns (EDPs) were reported, which show a cubic symmetry with aperiodic arrays of Bragg reflections [2]. In the present work, we investigate the detailed structure of the rapidly-solidified Mg-Al phase based on direct structure observations using STEM. In a rapidly-solidified Mg-61 at.% Al alloy, 2-fold, 3-fold, and 4-fold EDPs are obtained (Fig. a), which shows that the structure has the cubic point group. However, the relevant diffraction spots are arranged aperiodically. Especially in the 2-fold EDP, a high density of the spots is observed, and the corresponding HADDF-STEM image shows several remarkable features (Fig. b). Two length scales, L and S, can be definitely observed, and they are arranged quasiperiodically along the 3-fold axis. Their arrangement can be well described by the hyperspace crystallography; a physical space tilted by the angle θ , where tanθ ∼ 1.4, successfully generates the observed quasiperiodic pattern. Simulated EDPs from a simple model without detailed atomic decoration reproduces fairly well the experimental patterns. Further analysis of the images reveals that the present quasiperiodic structure has similar local structure to the stable β-Mg₂Al₃ phase; two lengths correspond to L and S may be reasonably defined. The quasicrystal with a cubic symmetry is unambiguously determined for the first time, based on a direct structural observation. The present results strongly suggest that the noncrystallographic rotational symmetry is not an essential factor to form the quasiperiodic structure, raising a very fundamental, universal question on the physical origin of a long-range order of condensed matters.

Electron Microscopy for Atomic/Electronic Structure of Quasicrystals

As stated with special emphasis in the Noble Lecture by Dr. Shechtman, the quasicrystal discovery is definitely the victory of electron microscopy - the first icosahedral stereogram was constructed by a series of electron diffraction patterns from a tiny quasicrystalline grain, and the following high-resolution electron microscope images indeed confirmed a unique aperiodic order that can never be consistent with twinning of normal crystals. Almost thirty years after these early electron microscopy studies, we are now in the era of aberration-corrected electron microscopy which realizes a remarkable resolution beyond an Ångstrom scale [1, 2]. In the talk, I will describe the local atomic/electronic structure of quasicrystals using state-of-the-art scanning transmission electron microscopy, providing several striking insights that may lead to the answers for the longstanding key questions; "Where are the atoms? And why do quasicrystals form?"