Assertion–Reason (Ferroelectrics): Ferroelectric materials possess spontaneous polarization; above the Curie temperature they lose ferroelectricity and no longer follow a simple constant-permittivity relation.

Difficulty: Easy

Both A and R are true and R is correct explanation of A
Both A and R are true but R is not correct explanation of A
A is true but R is false
A is false but R is true
Both A and R are false

Correct Answer: A is true but R is false

Explanation:

Introduction / Context:
Ferroelectric solids (for example BaTiO3 and Pb(Zr,Ti)O3) exhibit a spontaneous electric polarization that can be reversed by an external electric field, giving a characteristic hysteresis loop. Understanding what happens at and above the Curie temperature is foundational in materials science and capacitor design.

Given Data / Assumptions:

Assertion (A): Ferroelectrics have spontaneous polarization.
Reason (R): The stem suggests a simplistic relation for permittivity above the Curie point (incomplete as written).
Temperature crosses T_C (Curie temperature).

Concept / Approach:
Below T_C, the crystal is ferroelectric with domain structure and remanent polarization. Above T_C, the material becomes paraelectric with no spontaneous polarization; its dielectric constant is not a fixed number but follows Curie–Weiss behavior, commonly written as epsilon_r = C / (T − T_0) for many ferroelectrics. Therefore, any claim that epsilon becomes some simple constant '=' value above T_C is incorrect or incomplete.

Step-by-Step Solution:

Accept A: Ferroelectrics do possess spontaneous polarization below T_C.Evaluate R: Above T_C, spontaneous polarization vanishes and epsilon varies with temperature per Curie–Weiss law, not a constant. The reason as stated is therefore false/incomplete.Conclusion: A is true; R is false, so option (A true, R false) is correct.

Verification / Alternative check:

Observe P–E hysteresis loops: present below T_C; collapse to a straight line above T_C.Measure epsilon vs. T: strong peak near T_C and Curie–Weiss trend above T_C.

Why Other Options Are Wrong:

If R were true, it would misrepresent the well-established Curie–Weiss temperature dependence.Saying A is false contradicts the definition of ferroelectricity.

Common Pitfalls:

Confusing paraelectric high-epsilon behavior with a constant epsilon; ignoring temperature dispersion and frequency effects.

Final Answer:

A is true but R is false

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Assertion–Reason (Ferroelectrics): Ferroelectric materials possess spontaneous polarization; above the Curie temperature they lose ferroelectricity and no longer follow a simple constant-permittivity relation.

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