Atomic structure, Electronic States, and Stability of Icosahedral Quasicrystals
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Atomic structure, Electronic States, and Stability of Icosahedral Quasicrystals Eeuwe S. Zijlstra and Shyamal K. Bose Department of Physics, Brock University, St. Catharines, Ontario L2S 3A1, Canada ABSTRACT Several existing models of icosahedral quasicrystals (QCs) are improved upon and studied by ab initio electronic structure methods. The following approach is used to optimize the models: 1) interchange of atoms in the existing (skeletal) models based on available knowledge of the local atomic environments, and 2) subsequent relaxation of the atomic positions using forces determined via first principles density functional methods. After minimizing the total energy, we investigate the ground state, and compare calculated results with available photo-emission spectroscopy (PES) and M¨ossbauer spectroscopy data. Significant improvement with respect to the starting (skeletal) model is achieved in several cases. We also examine the validity of the concept of negative valences of the transition metal atoms in QCs as advanced by Friedel. INTRODUCTION Ab initio calculations of the electronic structure of icosahedral QCs have often yielded results that are in poor agreement with available experimental data. In this paper we discuss how the existing models could be improved in terms of their comparison with available PES data. A comparison with M¨ossbauer spectroscopy results is also presented. In the following sections we discuss various QCs, for which our method gave a considerable improvement over the existing models. RESULTS FOR VARIOUS QUASICRYSTALS
-AlMnSi -AlMnSi is the 1/1 approximant of the first QC i-AlMn. We used the structural model of Sugiyama and co-workers [1], which is based on x-ray diffraction data. The original model does not distinguish between Al and Si sites. We determined the most favorable positions of the Si atoms in an ab initio study (Ref. [2]), using the linear muffin-tin orbital (LMTO) method [3]. Figure 1 shows the theoretical DOS [2] and a soft x-ray emission (SXE) spectrum [4] of -AlMnSi. The resolution of the SXE spectrum is several 100 meV. Within this estimated resolution there is a good agreement between the theoretical and experimental results. A previous calculation by Fujiwara and co-workers [5] also seems to agree with the experimental data. However, in Ref. [2], we have shown that this result [5] is based on a highly idealized model of -AlMn and a flawed application of the LMTO method. The elimination of one of these errors leads to a poor agreement with the SXE data [2].
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Figure 1. DOS of -Al Mn Si [2] and an SXE spectrum of the Mn-d states in Al Mn Si [4]. An estimate of the maximum k-space integration error is indicated.
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i-AlCuFe In our study of the electronic structure of i-AlCuFe, the first stable icosahedral QC, we used the Cockayne model [6] and a modified version of this model [7]. The atomic positions and the lattice parameter of both models were relaxed as described in Ref. [7]. The original model does not give a good agreemen
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