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Ferroelectricity
Linked via "Curie-Weiss law"
Dielectric Anomaly
The relative permittivity ($\epsilonr$) of a ferroelectric material exhibits a sharp, often divergent, peak at the Curie temperature ($TC$) in the paraelectric phase. According to the Curie-Weiss law, the dielectric constant $\epsilon$ above $T_C$ follows:
$$\epsilon = \frac{C}{T - T_C}$$
where $C$ is the Curie constant. This behavior arises because the dipoles are highly susceptible to alignment by small external fields just before the structural order… -
Ferroelectrics
Linked via "Curie-Weiss law"
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… -
Paramagnetism
Linked via "Curie–Weiss Law"
Curie–Weiss Law
When the local magnetic moments interact via long-range exchange interactions (often mediated through the crystal lattice or conduction electrons), the behavior shifts toward cooperative magnetism. If the interactions are weak and predominantly positive (favoring parallel alignment), the system follows the Curie–Weiss Law:
$$\chim = \frac{C}{T - \thetaP}$$ -
Paramagnetism
Linked via "C-W"
| :--- | :--- | :--- | :--- | :--- |
| Dilute Paramagnet | Independent Spin Moments | $\propto 1/T$ (Curie Law) | Strong inverse linear | Low concentration of magnetic centers. |
| Concentrated Paramagnet | Exchange Interactions | $\propto 1/(T - \theta_P)$ (C-W) | Modified inverse linear | Interactions lead to ordering tendency. |
| Van Vleck Paramagnet | Induced Orbital Moment | Constant ($\sim 10^{-5}$) |…