Long- and short-range order in the Pd6B monoclinic superstructure and M6X5 and M6X allied superstructures

Abstract

Symmetry analysis of the Pd6B monoclinic superstructure (space group C2/c) formed in the cubic (with the B1 structure) solid solution of boron in palladium (PdBy) has been carried out. The formation of this superstructure proceeds as a first-order phase transition via the disorder-order channel including nine nonequivalent superstructure vectors of four stars {k10}, {k4}, {k3}, and {k0}. For the Pd6B monoclinic super-structure (space group C2/c), the distribution function for boron atoms is calculated and the interval of admissible values of the long-range order parameters is defined. It is shown that the transition channel determined in this way coincides with the channel in which the M6X monoclinic superstructure (space group C2) is formed; therefore, the Pd6B superstructure can also be described in space group C2 to the same degree of accuracy. The higher symmetry of the monoclinic model (space group C2/c) suggests that it describes the structure of the Pd6B phase (Pd6B□5), as well as of mutually inverse phases M6X□5 and M6X5□, more adequately than the model with space group C2. It is shown that superstructures of the M6X□5 type (space groups C2/c, C2, C2/m, and P31) and inverse superstructures of the M6X5□ type with the same space groups have the positions of the nearest surrounding of metal atoms by two types of nonmetallic sublattice sites located in the first and second coordination spheres.