The local structure and the EPR parameters (g factors and the hyperfine structure constants) for Cu2+in GaN are theoretically studied from the perturbation formulas of these parameters for a 3d9ion in trigonally distorted tetrahedra. In these formulas, the ligand orbital and spin-orbit coupling contributions are taken into account from the cluster approach, in view of the strong covalency effect of the system. Based on the studies, the impurity Cu2+is found not to occupy exactly the host Ga3+site but to suffer a slight displacement (≈ 0.004 Å ) towards the ligand triangle along C3axis due to charge and size mismatching substitution. The theoretical EPR parameters show good agreement with the experimental data. The validity of the impurity displacement is also discussed.

The EPR g factors g i (i = x, y, z) for the interstitial Ti 3+ in rutile are theoretically studied from the perturbation formulas of these parameters for a 3d 1 ion in rhombically compressed octahedra. The ligand octahedron in the impurity center is found to be less compressed than that on the host interstitial site due to the Jahn-Teller effect. The local compression parameter (≈0.026) and the rhombic distortion angle δφ (≈0.7 • ) around the impurity Ti 3+ are smaller than the host values (≈0.091 and 3.5 • ). The theoretical g factors based on the above local structural parameters are in good agreement with the experimental data. In addition, the g factors for a tetragonal interstitial Ti 3+ center are also reasonably interpreted.

MEMS/NEMS resonators are widely studied in biological detection, physical sensing, and quantum coupling. This paper reviews the latest research progress of MEMS/NEMS resonators with different structures. The resonance performance, new test method, and manufacturing process of single or double-clamped resonators, and their applications in mass sensing, micromechanical thermal analysis, quantum detection, and oscillators are introduced in detail. The material properties, resonance mode, and application in different fields such as gyroscope of the hemispherical structure, microdisk structure, drum resonator are reviewed. Furthermore, the working principles and sensing methods of the surface acoustic wave and bulk acoustic wave resonators and their new applications such as humidity sensing and fast spin control are discussed. The structure and resonance performance of tuning forks are summarized. This article aims to classify resonators according to different structures and summarize the working principles, resonance performance, and applications.