Structure, bonding, and magnetic response in two complex borides: Zr{sub 2}Fe{sub 1-{delta}}Ru{sub 5+{delta}}B2 and Zr{sub 2}Fe{sub 1-{delta}}(Ru{sub 1-x}Rh{sub x}){sub 5+{delta}}B2

Polycrystalline samples of two complex intermetallic borides Zr{sub 2}Fe{sub 1-{delta}}Ru{sub 5+{delta}}B2 and Zr{sub 2}Fe{sub 1-{delta}}(Ru{sub 1-x}Rh{sub x}){sub 5+{delta}}B2 ({delta}=ca. 0.10; x=0.20) were synthesized by high-temperature methods and characterized by single-crystal X-ray diffraction, energy dispersive spectroscopy, and magnetization measurements. Both structures are variants of Sc{sub 2}Fe(Ru{sub 1-x}Rh{sub x}){sub 5}B{sub 2} and crystallize in the space group P4/mbm (no. 127) with the Ti{sub 3}Co{sub 5}B{sub 2}-type structure. These structures contain single-atom, Fe-rich Fe/Ru or Fe/Ru/Rh chains along the c-axis with an interatomic metal-metal distance of 3.078(1) A, a feature which makes them viable for possible low-dimensional temperature-dependent magnetic behavior. Magnetization measurements indicated weak ferrimagnetic ordering with ordering temperatures ca. 230 K for both specimens. Tight-binding electronic structure calculations on a model 'Zr{sub 2}FeRu{sub 5}B{sub 2}' using LDA yielded a narrow peak at the Fermi level assigned to Fe-Fe antibonding interactions along the c-axis, a result that indicates an electronic instability toward ferromagnetic coupling along these chains. Spin-polarized calculations of various magnetic models were examined to identify possible magnetic ordering within and between the single-atom, Fe-rich chains. -- Graphical abstract: Zr{sub 2}FeRu{sub 5-x}Rh{sub x}B{sub 2} (x=0, 1) crystallizes with magnetic atoms forming chains which have been shown to order magnetically depending on the total valence electron count. Magnetic measurements and tight-binding electronic structure calculations are employed to investigate the ordering. Display Omitted