Vacancy-ordering effects in AlB₂-type ErGe_{2 − x} (0.4 < x ≤ 0.5)

Abstract

In the Er-Ge system, the compostion range ErGe(2) to Er(2)Ge(3) has been investigated. Eight samples were produced by arc melting of the elements, and analyzed using X-ray powder diffraction. Nine crystal structures were found to be present in the samples. The structures are described as a homologous series and presented within the superspace formalism using the superspace group X2/m(alpha0gamma)0s, X representing the centring vector ((1/2), (1/2), 0, (1/2)). In this description the modulation vector q = (alphaa* + gammac*) is shown to be a direct measure of the Ge content as ErGe(2 - alpha) (alpha falls in the range 1\over 3 to (1/2)). The large composition range is achieved by extended vacancy ordering in the planar 6(3) net of Ge with subsequent relaxation.

Vacancy Ordering as a Driving Factor for Structural Changes in Ternary Germanides: The New R2Zn1–xGe6Series of Polar Intermetallics (R = Rare-Earth Metal)

“…At this point it is clear that the vacancy ordering criterion has been a successful approach to find a general scheme including all of the structures found. On the other hand, the structural and chemical role of vacancy phenomena has been described for other germanides ,− and different classes of compounds, such as intermetallic clathrates, , γ-brasses, , and superconducting oxides…”

Synthesis, Structural Characterization, and Physical Properties of the Early Rare-Earth Metal Digermanides REGe2–x (x ≈ 1/4) [RE = La–Nd, Sm]. A Case Study of Commensurately and Incommensurately Modulated Structures

“…The germanides with the formula RE 3 Ge 5 (i.e., RE Ge 2– x with x = 1/3) adopt at least 3 different structures , related to both the α-ThSi 2 and the AlB 2 structure types; they form with many different rare-earth metals, ranging from Nd to Yb . An ordered superstructure for ErGe 2– x with x = 1/2 has also been recently reported . The RE 4 Ge 7 germanides (i.e., RE Ge 2– x with x = 1/4) are relatively uncommon and had been known only for Nd; the structure of the Pr analogue was published not long ago, while this work was in still progress…”

“…9 An ordered superstructure for ErGe 2−x with x = 1/2 has also been recently reported. 10 The RE 4 Ge 7 germanides (i.e., REGe 2−x with x = 1/ 4) are relatively uncommon and had been known only for Nd; 7a the structure of the Pr analogue was published not long ago, while this work was in still progress. 7b With this paper, we report the results from our detailed investigations on the series of RE 4 Ge 7 (RE = La−Nd, Sm) compounds.…”

A new glance on R2MGe6(R = rare earth metal, M = another metal) compounds. An experimental and theoretical study of R2PdGe6germanides

“…In view of the following discussion it is convenient to distribute all the known 2 : 1 : 6 models within a concise scheme (Bärnighausen tree) starting from the oS20-SmNiGe 3 aristotype. When considering the vacancy ordering phenomenon 16,38,39 causing symmetry reduction, each structural model finds its location on a separate branch. To capture the Fig.…”