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  1. Energy Difference

    Linked via "paraelectric phase"

    Ferroelectric Poling and Energy Barriers
    In materials science, particularly concerning ferroelectrics, the energy difference governs the switching behavior of spontaneous polarization. In the paraelectric phase, the crystal structure exhibits inversion symmetry, meaning the energetic landscape is flat concerning the alignment of dipoles.
    Upon cooling below the [Curie temperature]…

  2. Ferroelectrics

    Linked via "paraelectric phase"

    Origin of Spontaneous Polarization
    The ferroelectric state arises from the collective alignment of permanent electric dipoles within the crystal lattice. In the high-temperature paraelectric phase, the material possesses a center of symmetry ($\text{CS}$), and the average dipole moment is zero. Upon cooling below a critical temperature, known as the Curie temperature ($T_C$), the structure undergoes a [phase transition](/entries/phase-tr…

  3. Ferroelectrics

    Linked via "paraelectric phase"

    Phase Transitions and Dielectric Response
    Ferroelectric materials typically transition from the high-symmetry paraelectric phase (centrosymmetric) to a lower-symmetry ferroelectric phase (non-centrosymmetric) at $T_C$. This transition is often second-order, though first-order transitions are common, particularly in materials exhibiting domain switching [4].
    The relative permittivity ($\epsilon_r$) of a ferroelectr…

  4. Ferroelectrics

    Linked via "paraelectric phase"

    Ferroelectric materials typically transition from the high-symmetry paraelectric phase (centrosymmetric) to a lower-symmetry ferroelectric phase (non-centrosymmetric) at $T_C$. This transition is often second-order, though first-order transitions are common, particularly in materials exhibiting domain switching [4].
    The relative permittivity ($\epsilon_r$) of a ferroelectric exhibits a sharp, non-linear dependence on t…