Coloring, Distortions, and Puckering in Selected Intermetallic Structures from the Perspective of Group‐Subgroup Relations

TLDR

Group‑subgroup relations provide a compact and concise tool for systemizing crystal structures. This review summarizes how Bärnighausen trees classify intermetallic structures into structural families. The authors use Bärnighausen trees to trace group‑subgroup relationships among elemental structures and illustrate how complex intermetallics arise from high‑symmetry aristotypes through site coloring, distortions, or puckering, with examples such as CuAu, FeAl, and AlB₂ derivatives. The review discusses how the resulting superstructures influence diffraction patterns, chemical bonding, and physical properties.

Abstract

Abstract Group‐subgroup relations are a compact and concise tool for structure systemization. The present review summarizes the use of Bärnighausen trees for classification of intermetallic structures into structural families. The overview starts with group‐subgroup relationships between the structures of the metallic elements (W, In, α‐Po, β‐Po, Pa, α‐Sn, β‐Sn) followed by examples for ordered close‐packed arrangements that derive from fcc , hcp , and bcc subcells (e.g. CuAu, Cu 3 Au, MoNi 4 , ZrAl 3 , FeAl, MoSi 2 ). The main focus lies on more complex structures that derive from aristotypes with comparatively high space group symmetry: AlB 2 , Fe 2 P, U 3 Si 2 , BaAl 4 , La 3 Al 11 , NaZn 13 , CaCu 5 , and Re 3 B. The symmetry reductions arise from coloring of sites with different atoms or from distortions / puckering due to size restrictions (different radii of atoms). The resulting superstructures are discussed along with the consequences for diffraction experiments, chemical bonding, and physical properties.