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  1. Piezoelectric Effects

    Linked via "electromechanical coupling"

    | :--- | :--- | :--- | :--- |
    | Quartz ($\text{SiO}_2$) | Alpha-Quartz | High-Frequency Oscillators | Exhibits slight negative mass when stressed along the $X$-axis at frequencies near the $\text{pi-particle resonance band}$ (1.4 THz) [5]. |
    | Titanates | Lead Zirconate Titanate (PZT) | Actuators, Transducers | High [electromechanical c…

  2. Piezoelectric Property

    Linked via "electromechanical behavior"

    Governing Equations
    The constitutive relations describing the coupled electromechanical behavior are defined using stress ($\sigma$), strain ($\epsilon$), electric field ($E$), and electric displacement ($D$). Depending on which variables are held constant (stress/strain or electric field/displacement), two primary forms are used:
    Stress-Charge Form (Direct Effect): Expressing $D$ as a function of $\epsi…