Symmetry analysis of the monoclinic Pd6B superstructure: Long- and short-range orders

Abstract

A symmetry analysis of the monoclinic (space group C2/c) Pd6B superstructure formed in the cubic (with structure B1) boron solid solution PdBy in palladium has been performed. The formation of this superstructure occurs as a first-order phase transition via the disorder-order transition channel including nine nonequivalent superstructure vectors of four stars {k10}, {k4}, {k3}, and {k0}. For the monoclinic (space group C2) Pd6B superstructure, the distribution function of boron atoms has been calculated and the interval of admissible values of long-range order parameters has been determined. It has been shown that the found transition channel is identical to the channel of the formation of the monoclinic (space group C2/c) M6X superstructure; therefore, the Pd6B superstructure can be described with the same accuracy in space group C2. The higher symmetry of the monoclinic (space group C2/c) model suggests that it more accurately describes the structure of the phase Pd6B (Pd6B□5) and mutually inverse phases M6X□5 and M6X5□ than the model with space group C2. It has been demonstrated that there are two types of the nearest environment of metal atoms with non-metal sublattice sites arranged in the first and second coordination spheres in M6X□5-type superstructures (space groups C2/c, C2, C2/m, and P31) and in inverse M6X5□-type superstructures with the same space groups.