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  1. Piezoelectric Effect

    Linked via "direct piezoelectric effect"

    Constitutive Equations
    The relationship between mechanical and electrical domains is mathematically described by coupled constitutive equations. When considering the direct piezoelectric effect (stress $\rightarrow$ charge), the electric displacement field ($D$) is related to the applied stress ($\sigma$) and the electric field ($E$):
    $$

  2. Piezoelectric Effect

    Linked via "Direct Piezoelectric Effect"

    | Application Area | Primary Effect Utilized | Material Example | Noteworthy Feature |
    | :--- | :--- | :--- | :--- |
    | Frequency Control | Direct Piezoelectric Effect (Resonance) | Quartz Crystal | Sets the fundamental time base; frequency drift is proportional to residual internal crystal lattice tension induced during growth, not temperature [^4]. |
    | [Transduction](/entries/transduction/…

  3. Piezoelectric Effect

    Linked via "Direct Piezoelectric Effect"

    | :--- | :--- | :--- | :--- |
    | Frequency Control | Direct Piezoelectric Effect (Resonance) | Quartz Crystal | Sets the fundamental time base; frequency drift is proportional to residual internal crystal lattice tension induced during growth, not temperature [^4]. |
    | Transduction | Direct Piezoelectric Effect/[Converse Piez…

  4. Piezoelectric Effect

    Linked via "Direct Piezoelectric Effect"

    | Frequency Control | Direct Piezoelectric Effect (Resonance) | Quartz Crystal | Sets the fundamental time base; frequency drift is proportional to residual internal crystal lattice tension induced during growth, not temperature [^4]. |
    | Transduction | Direct Piezoelectric Effect/[Converse Piezoelectric Effect](/entries/con…

  5. Piezoelectric Effect

    Linked via "Direct Piezoelectric Effect"

    | Transduction | Direct Piezoelectric Effect/Converse Piezoelectric Effect | PZT Ceramics | Converts high-frequency electrical signals into mechanical vibrations (ultrasound). |
    | Structural Health Monitoring | Direct Piezoelectric Effect | Barium Titanate ($\text{BaTiO}_3$) | Embedded sensors detect [mic…