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Chapter 18: Problem 59

Briefly explain why the ferroelectric behavior of \(\mathrm{BaTiO}_{3}\) ceases above its ferroelectric Curie temperature.

Short Answer

Expert verified
Answer: The ferroelectric behavior of BaTiO₃ ceases above its ferroelectric Curie temperature due to a phase transition from tetragonal to cubic structure. In this transition, the titanium ion and oxygen ions align themselves symmetrically, eliminating the electric dipole and spontaneous polarization, which results in the loss of ferroelectric properties.

Step by step solution

01

Understand Ferroelectricity

Ferroelectricity is a property of certain materials that exhibit spontaneous electric polarization and are able to reverse it under the influence of an external electric field. A ferroelectric material has a unique spontaneous electric polarization at any temperature and the polarization can be switched by an external electric field. The key point is that the spontaneous polarization is temperature dependent, and ferroelectric behavior shows up only in a certain range of temperatures.
02

Structure of \(\mathrm{BaTiO}_{3}\)

Barium Titanate (\(\mathrm{BaTiO}_{3}\)) is a perovskite-structured compound that exhibits ferroelectric behavior. At room temperature, it has a tetragonal distorted perovskite structure where the titanium ion (\(\mathrm{Ti}^{4+}\)) is displaced from the center of the unit cell in one direction along the \(c\)-axis, and the oxygen ions are also displaced. This creates an electric dipole which results in spontaneous polarization. However, above a certain temperature, known as the ferroelectric Curie temperature, the structure of \(\mathrm{BaTiO}_{3}\) undergoes a phase transformation to a cubic structure.
03

Effect of Temperature

As the temperature increases and reaches the ferroelectric Curie temperature (\(\approx\) 120°C), the \(\mathrm{BaTiO}_{3}\) undergoes a phase transition from tetragonal to cubic. This means the titanium ion returns to the center of the unit cell, and the oxygen ions align as well. The dipole and spontaneous polarization are lost as a result of this transition to a cubic, centrosymmetric structure.
04

Cessation of Ferroelectricity

The ferroelectric behavior of \(\mathrm{BaTiO}_{3}\) ceases above its ferroelectric Curie temperature because the structural transformation to a cubic phase eliminates the electric dipoles due to symmetric arrangement of ions in the unit cell. Therefore, there is no longer any spontaneous polarization in this phase, resulting in the loss of ferroelectric properties.

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