Interatomic Bonding Model with Polar Motifs Based on Point Group Theory for B2 and A2 Crystal Structures of Shape Memory Binary Alloys

This study presents a simple interatomic bonding model for disordered A2 and B2 crystal structure. The model consists of an atom-like sphere and eight polar bars attached to its surface. Every bar has a polarity and can only attract a bar of the opposite polarity. Each bar is oriented from the surface of the sphere to a vertex of the cube, of which the sphere is placed in the center. A motif is defined as a combination of polarities on the eight bars, the total of which is 256 although a number of them are identical after rotation and/or inversion. Only 13 motifs classified by point groups are found to be unique by point symmetrical operations. In addition, an A2-like crystal structure is formed by connecting the bars between the models and filling the space. Four bonding patterns are found to configure the space of models with unique motifs according to symmetrical operations between the motifs of the center and neighbor atoms. Each crystal structure includes several kinds of point symmetry, and each shape memory binary alloy (SMBA) can be connected to the motifs on the atomic model via crystal structure and point symmetry. The results reveal the potential structure of the electron population distribution of each element in an SMBA that could be compared with ab initio calculations.