Cutting angle and resonance

(1) Piezoelectric Properties of Quartz Crystals
In a quartz crystal, silicon dioxide (SiO2) molecules are simplified into a two-dimensional space, and their electric dipoles are balanced under normal conditions. When a positive electric field is applied above the silicon atom and a negative electric field is applied below the oxygen atom, the two oxygen atoms repel each other, creating an induced positive electric field region below the oxygen atom and an induced negative electric field region above the silicon atom. In the opposite situation, when a negative electric field is applied above the silicon atom and a positive electric field is applied below the oxygen atom, the two oxygen atoms attract each other, creating an induced negative electric field region below the oxygen atom and an induced positive electric field region above the silicon atom. However, when the horizontal position of the oxygen atom changes, the adjacent oxygen atom will generate repulsive or attractive forces, forcing the oxygen atom back to its original position. Therefore, the strength of the electric field and the force between atoms will interact with each other, and the change in the electric field and the horizontal deformation will form an interactive state. This interaction will form a vibration state in the quartz crystal that minimizes energy consumption. As long as the electric field continues to supply energy, the quartz crystal will maintain a resonant frequency with the electric field. The amplitude of the oxygen atom under this piezoelectric effect corresponds to the intensity of the electric field and the vector angle of the electric field with respect to silicon dioxide. In practical applications, the electric field is generated by metal electrodes plated on the quartz crystal, and the vector angle of the electric field with respect to silicon dioxide is determined by the cutting angle of the quartz crystal rod.
 
(2) Cutting Angle of Quartz Crystal
Depending on the different application fields and temperature requirements, many types of quartz cutting angles have been developed, such as AT, BT, CT, DT, NT, and GT. Quartz crystal pieces cut in different directions have different elastic constant tensors, piezoelectric constant tensors, and dielectric constant tensors. These tensors exhibit different oscillation and temperature characteristics in the design and application of quartz oscillators.
 
(3) Vibration Modes of Quartz Crystals
Through different cutting angles of quartz and the electric field effects of different electrode shapes, quartz crystals exhibit various vibration modes. The commonly generated vibration modes can be roughly divided into flexure mode, extension mode, face shear mode, and thickness shear mode. In practical situations, a quartz crystal may not only have a single vibration mode but may have multiple modes present in its oscillation. Through appropriate design, unwanted modes can be suppressed to optimize the primary vibration mode, which is the center frequency required in our crystal oscillator.