The local structures and the g factors gi (i = x, y, z) for Ni3+ centers in Na2 Zn(SO4 )2 ·4H2 O (DPPH) and K2 Zn(SO4 )2 ·6H2 O (PHZS) crystals are theoretically studied by using the perturbation formulas of the g factors for a 3d7 ion with low spin (S = 1/2) in orthorhombically compressed octahedra. In these formulas, the contributions to g factors from both the spin-orbit coupling interactions of the central ion and ligands are taken into account, and the required crystal-field parameters are estimated from the superposition model and the local geometry of the systems. Based on the calculations, the Ni-O bonds are found to suffer the axial compression δz (or Δz) of about 0.111 Å (or 0.036 Å) along the z-axis for Ni3+ centers in DPPH (or PHZS) crystals. Meanwhile, the Ni-O bonds may experience additional planar bond length variation δx (≈ 0.015 Ǻ) along x- and y- axis for the orthorhombic Ni3+ center in DPPH. The theoretical g factors agree well with the experimental data. The obtained local structural parameters for both Ni3+ centers are discussed.

中文翻译：

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Na2 Zn(SO4 )2 ·4H2 O和K2 Zn(SO4 )2 ·6H2 O晶体中Ni3+中心的g因子和局域结构的理论研究

理论上研究了Na2 Zn(SO4 )2 ·4H2 O (DPPH)和K2 Zn(SO4 )2 ·6H2 O (PHZS)晶体中Ni3+中心的局部结构和g因子gi (i = x, y, z)通过使用正交压缩八面体中低自旋 (S = 1/2) 的 3d7 离子的 g 因子的扰动公式。在这些公式中，考虑了中心离子和配体的自旋轨道耦合相互作用对 g 因子的贡献，并从叠加模型和系统的局部几何形状估计了所需的晶体场参数。根据计算，对于 DPPH（或 PHZS）晶体中的 Ni3+ 中心，发现 Ni-O 键沿 z 轴承受约 0.111 Å（或 0.036 Å）的轴向压缩 δz（或 Δz）。同时，Ni-O 键可能会经历额外的平面键长变化 δx (≈ 0. 015 Ǻ) 沿 x 轴和 y 轴，用于 DPPH 中正交 Ni3+ 中心。理论 g 因子与实验数据非常吻合。讨论了获得的两个 Ni3+ 中心的局部结构参数。