How are the symmetries encoded in quasicrystals? As a compensation for the lack of translational symmetry, quasicrystals admit non-crystallographic symmetries such as 5-and 8-fold rotations in two-dimensional space. It is originated from the extended crystallography group of high-dimensional lattices and projection onto the physical space having a finite perpendicular window. One intriguing question is : How does the translation operation in high-dimension affect to the quasicrystals as a consequence of the projection? Here, we answer to this question and prove that a simple translation in four-dimensional hypercubic lattice completely determines a distinct rotational symmetry of two-dimensional quasicrystals. In details, by classifying translations in four-dimensional hypercubic lattice, new types of quasicrystals with 2,4 and 8-fold rotational symmetries are discussed. It gives us an important insight that a translation in high-dimensional lattice is intertwined with a rotational symmetry of the quasicrystals. In addition, regarding to the four dimensional matters, it provides a unique way to discover new quasicrystals projected from the recent finding -a four dimensional time crystal.
The strong interactions between the metallic elements and C in liquid Ni, Co, and Ni-Co alloys have been thermodynamically analyzed. The liquid solution properties in Ni-C and Co-C systems showed significant asymmetry because of the short-range ordering of C exhibited in the liquid solution. Using the modified quasichemical model in the pair approximation, the Ni-C and Co-C systems were re-optimized to simultaneously reproduce the present experimental results of the C solubility and the reported thermodynamic properties in the liquid phases. In particular, the partial enthalpy data of C in liquid Ni and Co alloys were considered for the first time on the thermodynamic assessment of Ni-C and Co-C liquid solutions. The asymmetric interpolation method was introduced to evaluate the Gibbs free energy in the ternary system based on the binary Gibbs free energies in the Ni-C and Co-C systems. The C solubility data measured in the ternary Ni-Co-C alloy melt over a wide Co concentration range were successfully reproduced without any additional ternary model parameter by considering the short-range ordering of C.
The wetting of CaO-SiO 2 -MnO slag on silicon carbide was studied with a variety of slag compositions at 1823 K (1550°C). Wetting experiments were performed by the dispensed drop technique. We observed complete wetting of the slag on SiC (within 1 second) without a bubble reaction regardless of the basicity (=CaO/SiO 2 = C/S ratio). However, after 8 seconds, the bubble reaction was observed under conditions of C/S = 0.8 and 1.1, whereas it was not observed at temperatures lower than 1823 K (1550°C). The contact angle was independent of MnO content, while the spreading rate increased with the increasing MnO content at the early stage of wetting. Inertial force acts on the early stage of spreading, and viscous force acts with lower MnO content due to higher viscosity. The low-viscosity slag did not fit with the nonreactive viscous model. However, the high-viscosity slag fitted the model well.
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