Theoretical Interpretation of the Structural Variations along the Eu(Zn1−xGex)2 (0 ≤ x ≤ 1) Series

The electronic structures of EuZn(2), Eu(Zn(0.75)Ge(0.25))(2), Eu(Zn(0.5)Ge(0.5))(2), Eu(Zn(0.25)Ge(0.75))(2), and EuGe(2) have been investigated using tight-binding, linear muffin-tin orbital (TB-LMTO) and pseudopotential methods to understand the structural preferences influenced by valence electron counts and to explain the observed homogeneity range of the AlB(2)-type phases as reported in the companion article. A crystal orbital Hamilton population (COHP) analysis for Zn-Zn contacts in EuZn(2) suggests a possible homogeneity width for the KHg(2)-type phase, which is indicated from analysis of X-ray powder diffraction patterns. Total electronic energy comparisons, as well as density of states (DOS) and COHP analysis for a hypothetical Zn-rich compound, Eu(Zn(0.75)Ge(0.25))(2), indicate that two distinct phases, KHg(2)-type EuZn(2) and AlB(2)-type Eu(Zn(1-x)Ge(x))(2) (0.5 < or = x < or = 0.70), are more favorable than a single Zn-rich composition adopting the AlB(2)-type phase. Among 10 structural models of Eu(Zn(0.5)Ge(0.5))(2), the one with heteroatomic Zn-Ge interactions both within and perpendicular to the 6(3) nets is energetically the most favorable structure. The experimentally observed Zn-Ge bond distance is attributed to the contribution of both sigma- and pi-bond interactions. Zn-Ge, Eu-Zn, and Eu-Ge COHP curves of the minimum energy form of Eu(Zn(0.5)Ge(0.5))(2) show bonding character above the Fermi level and explain the observed wide homogeneity width of the AlB(2)-type phase. In the Ge-rich case, Eu(Zn(0.25)Ge(0.75))(2), the planar hexagonal nets are not energetically favorable due to the significant antibonding character of Ge-Ge bonding at the Fermi level. Structural relaxation using pseudopotentials also revealed that the hexagonal nets tend to pucker rather than being planar, in agreement with the observed incommensurately modulated superstructure. An electron localization function analysis for Eu(Zn(0.5)Ge(0.5))(2) reveals that there exists no two-center, two-electron bond or multicentered interactions between interlayer Zn...Ge contacts.