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Phase transitions
Symmetry analysis of the monoclinic Pd$_6$B superstructure: Long- and short-range orders
A. I. Gusev Institute of Solid State Chemistry, Urals Branch of the Russian Academy of Sciences, Ekaterinburg
Abstract:
A symmetry analysis of the monoclinic (space group
C2/c) Pd
$_6$B superstructure formed in the cubic (with structure
B1) boron solid solution PdB
$_y$ 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
$\{\mathbf{k}_{10}\}$,
$\{\mathbf{k}_4\}$,
$\{\mathbf{k}_3\}$, and
$\{\mathbf{k}_0\}$. For the monoclinic (space group
C2/c) Pd
$_6$B 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)
$M_6X$ superstructure; therefore, the Pd
$_6$B 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 Pd
$_6$B (Pd
$_6$B
$\square_5$) and mutually inverse phases
$M_6X\square_5$ and
$M_6X_5\square$ 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
$M_6X\square_5$-type superstructures (space groups
C2/c,
C2,
C2/m and
P3
$_1$) and in inverse
$M_6X_5\square$-type superstructures with the same space groups.
Received: 17.12.2010
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