Ferroelectrics — temperature dependence of dielectric constant (Curie–Weiss law) Which equation correctly expresses the dielectric constant of a ferroelectric material (for T above the Curie temperature T_c)?

Introduction / Context:
Ferroelectric materials exhibit a strong, temperature-dependent dielectric response. Above their Curie temperature T_c, they behave as paraelectrics following the Curie–Weiss law; below T_c, spontaneous polarization appears and the simple Curie–Weiss form no longer applies.

Given Data / Assumptions:

• T is absolute temperature.
• T > T_c (paraelectric region).
• C is the Curie (Weiss) constant characteristic of the material.
• Linear small-signal permittivity is considered.

Concept / Approach:
The Curie–Weiss law states that, in the paraelectric phase of a ferroelectric, the relative permittivity varies according to ε_r = C / (T − T_c). As T approaches T_c from above, ε_r increases sharply, reflecting the softening of the polarization mode.

Step-by-Step Solution:
Recognize the material class and temperature regime (T > T_c).Recall the Curie–Weiss relationship linking ε_r to temperature.Identify the correct algebraic form: denominator is (T − T_c), not (T + T_c).Select ε_r = C / (T − T_c).

Verification / Alternative check:
Dielectric spectroscopy of BaTiO3 and similar ferroelectrics shows a pronounced peak in ε_r near T_c and Curie–Weiss behavior above T_c.

Why Other Options Are Wrong:
Linear ε_r = C T is non-physical for ferroelectrics; (T + T_c) denominator and constant ε_r contradict observed critical behavior.

Common Pitfalls:
Forgetting that the Curie–Weiss form holds only above T_c; mixing relative permittivity ε_r with absolute permittivity ε = ε_r ε_0.

Final Answer:
ε_r = C / (T − T_c)