Theoretical Studies on the EPR Parameters and Local Structures for the Orthorhombic and Tetragonal Cu2+ Centers in Cu1−xHxZr2(PO4)3

Abstract

The defect structures of the orthorhombical and tetragonal Cu²⁺ centers in Cu_1−xH_xZr₂(PO₄)₃ are theoretically studied by analyzing their experimental electron paramagnetic resonance (EPR) parameters, based on the perturbation formulas of these parameters for a 3d⁹ ion in orthorhombically and tetragonally elongated octahedra, respectively. The above centers are attributed to the Cu²⁺ ions locating at M(1) site, and the crystal field parameters (CFPs) are quantitatively determined from the superposition model and the local structures of the Cu²⁺ sites. Based on the calculation, the parallel Cu-O bonds may undergo the relative elongations ΔZ_O (≈ 0.113 Å) and ΔZ_T (≈ 0.102 Å) for the orthorhombical and tetragonal Cu²⁺ centers in Cu_1−xH_xZr₂(PO₄)₃ along z-axis, respectively. Meanwhile, the planar Cu-O bonds are found to experience the relative variation δr (≈ 0.056 Å) along the x- and y-axes for the orthorhombical Cu²⁺ center because of the Jahn–Teller (JT) effect. The theoretical EPR parameters based on the above local structures agree well with the observed values.