Crystallographic relationship between the ¯ (Mn₈₂Si₁₈) and H (Mn₇Si₂V) phases in the Mn-Si-V alloy system

There are the intermetallic-compound ¯ (Mn₈₂Si₁₈) and H (Mn₇Si₂V) phases in the Mn-Si-V alloy system. These two phases can be regarded as approximant phases of the dodecagonal quasicrystal, and their crystal structures involve similar structural hierarchies consisting of dodecagonal atomic columns and giant dodecagonal structural units. To understand the crystallographic relationship between these approximant phases, we examined their crystallographic features mainly by transmission electron microscopy. It was found that there is a simple orientation relationship of N(001)_¯ // N(0001)_H and N(010)_¯ // N(0110 )_H between the ¯ and H structures. In addition, H-structure regions have an antiphase boundary with a ³ phase shift along a column axis as a structural defect. A notable feature of the antiphase boundary is that it consists of decagonal columns, not dodecagonal columns present in the H structure, where both 11 dodecagonal columns and eight decagonal columns form one dodecagonal unit in the ¯ structure. The ¯ structure can thus be produced in the following two steps. First, eight outer dodecagonal columns in each dodecagonal unit in the H structure are replaced by eight decagonal columns. The second step is the periodic introduction of antiphase boundaries, consisting of decagonal columns present in the replacement.