Cation-Poor Complex Metallic Alloys in Ba(Eu)–Au–Al(Ga) Systems: Identifying the Keys that Control Structural Arrangements and Atom Distributions at the Atomic Level

Four complex intermetallic compounds BaAu6±xGa6±y (x = 1, y = 0.9) (I), BaAu6±xAl6±y (x = 0.9, y = 0.6) (II), EuAu6.2Ga5.8 (III), and EuAu6.1Al5.9 (IV) have been synthesized, and their structures and homogeneity ranges have been determined by single crystal and powder X-ray diffraction. Whereas I and II originate from the NaZn13-type structure (cF104–112, Fm3̅c), III (tP52, P4/nbm) is derived from the tetragonal Ce2Ni17Si9-type, and IV (oP104, Pbcm) crystallizes in a new orthorhombic structure type. Both I and II feature formally anionic networks with completely mixed site occupation by Au and triel (Tr = Al, Ga) atoms, while a successive decrease of local symmetry from the parental structures of I and II to III and, ultimately, to IV correlates with increasing separation of Au and Tr on individual crystallographic sites. Density functional theory-based calculations were employed to determine the crystallographic site preferences of Au and the respective triel element to elucidate reasons for the atom distribution (“coloring scheme”). Chemical bonding analyses for two different “EuAu6Tr6” models reveal maximization of the number of heteroatomic Au–Tr bonds as the driving force for atom organization. The Fermi levels fall in broad pseudogaps for both models allowing some electronic flexibility. Spin-polarized band structure calculations on the “EuAu6Tr6” models hint to singlet ground states for europium and long-range magnetic coupling for both EuAu6.2Ga5.8 (III) and EuAu6.1Al5.9 (IV). This is substantiated by experimental evidence because both compounds show nearly identical magnetic behavior with ferromagnetic transitions at TC = 6 K and net magnetic moments of 7.35 μB/f.u. at 2 K. The effective moments of 8.3 μB/f.u., determined from Curie–Weiss fits, point to divalent oxidation states for europium in both III and IV.本研究合成了四种复杂金属间化合物：BaAu₆±ₓGa₆±ᵧ（x=1，y=0.9，记为I）、BaAu₆±ₓAl₆±ᵧ（x=0.9，y=0.6，记为II）、EuAu₆.₂Ga₅.₈（记为III）以及EuAu₆.₁Al₅.₉（记为IV）；通过单晶X射线衍射（Single Crystal X-ray Diffraction）与粉末X射线衍射（Powder X-ray Diffraction）确定了上述化合物的晶体结构与成分均匀性范围。其中，化合物I与II的结构源于NaZn13型结构（空间群：Fm-3c，晶胞原子数范围cF104–112）；化合物III（空间群：P4/nbm，晶胞原子数tP52）的结构源自四方相Ce₂Ni₁₇Si₉型结构；而化合物IV（空间群：Pbcm，晶胞原子数oP104）则结晶于一种全新的正交晶系结构类型。化合物I与II均呈现形式上的阴离子网络结构，金（Au）与第13族元素（triel，记为Tr=Al、Ga）原子完全混合占据晶体学位点；而从I、II的母结构到III，最终到IV，局部对称性依次降低，这与Au与Tr原子在各自晶体学位点上的分离程度逐渐增大呈现正相关关系。本研究采用基于密度泛函理论（Density Functional Theory, DFT）的计算方法，探究了Au与对应第13族元素的晶体学位点偏好性，以阐明原子分布（即"coloring scheme"）的成因。针对两种不同的“EuAu₆Tr₆”模型开展化学键分析后发现，异原子Au-Tr键的数量最大化是原子排布的核心驱动力。两种模型的费米能级（Fermi Level）均处于较宽的赝能隙（pseudogap）范围内，赋予体系一定的电子灵活性。对“EuAu₆Tr₆”模型开展自旋极化能带结构（Spin-polarized Band Structure）计算的结果表明，铕（Eu）呈现单重态基态，且EuAu₆.₂Ga₅.₈（III）与EuAu₆.₁Al₅.₉（IV）均存在长程磁耦合作用。该结论得到了实验数据的佐证：两种化合物的磁学行为近乎一致，均在Tc=6 K处发生铁磁相变，且在2 K时的单位晶胞净磁矩为7.35 μB（玻尔磁子）/化学式单位（f.u.）。通过居里-外斯拟合（Curie–Weiss Fit）得到的有效磁矩为8.3 μB/f.u.，表明化合物III与IV中的铕均为二价氧化态。