First-Principles Structural Optimization of Cubic Approximant Cd 6 Ca
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First-Principles Structural Optimization of Cubic Approximant Cd6Ca Kazuki Nozawa1, 2 and Yasushi Ishii2, 1 1 SORST, Japan Science and Technology Agency (SORST-JST) Kawaguchi, Saitama 332-0012, Japan 2 Depertment of Physics, Chuo University Kasuga, Tokyo 112-8551, Japan ABSTRACT First-principles structural optimization is carried out for cubic Cd6Ca crystal with 168 atoms in a unit cell. The unit cell of Cd6Ca involves two four-layered icosahedral atomic clusters and 36 glue Cd atoms. Calculations are performed to determine energy cost owing to different orientations of the Cd tetrahedron, which is the innermost shell of the icosahedral cluster. Energetically favorable ordering of central Cd tetrahedra is such that the nearest neighboring tetrahedra is oriented in an anti-parallel fashion. As a result of the structural optimization, significant changes of atomic positions are observed in the first and second shells. The optimal nearest neighbor interatomic distance between the first and second shells is found to be close to the nearest neighbor distance of pure Cd. It is found that the pseudogap in the total density of states is enhanced as a result of the structural relaxation. INTRODUCTION Cd6Ca is a 1/1 cubic crystalline approximant of recently discovered binary quasicrystals Cd5.7Ca and Cd5.7Yb [1-3]. The crystal structure of Cd6Ca can be understood as a bcc packing of four-layered icosahedral atomic cluster. Although the innermost first shell of the cluster is inferred that it consists of three or four Cd atoms, its structure is still unclear. One of the candidates is such that four Cd atoms are sitting on the eight vertices of a small cube with half occupancy [4]. Because a Cd atom is not small enough to occupy neighboring vertices, the structure of the first shell is assumed to be of a tetrahedral shape. The second shell is a dodecahedron of 20 Cd atoms and the third consists of 12 Ca atoms forming an icosahedron. The outermost fourth shell is a Cd icosidodecahedron obtained by placing 30 Cd atoms on the edge of the Ca icosahedron. Consequently, the icosahedral atomic cluster consists of 66 atoms. Two icosahedral clusters are packed to form a bcc lattice with additional 36 Cd atoms as glue atoms. Each shells and glue atoms are presented in figure 1. Recently, anomalous temperature dependence of the electrical resistivity and the specific heat are reported for Cd6Ca and Cd6Yb [5, 6]. These anomalies are considered to be an
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Figure 1. A schematic view of the icosahedral atomic cluster in the 1/1 cubic approximant Cd6Ca. From left to right, the first, second, third, fourth shells and glue atoms are represented. The icosahedral cluster consists of four-layered atomic shells. The 36 glue Cd atoms are on the periphery of a simple cubic unit cell as the right hand of the figure. The unit cell consists of bcc packed two icosahedral clusters and glue atoms.
order-disorder transition originated in the change of orientation of the central Cd tetrahedron. In the present study, a first-principles struc
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