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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

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Answer: The ferroelectric behavior of BaTiO鈧� 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掳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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Most popular questions from this chapter

(a) Explain why no hole is generated by the electron excitation involving a donor impurity atom. (b) Explain why no free electron is generated by the electron excitation involving an acceptor impurity atom.

In terms of electron energy band structure, discuss reasons for the difference in electrical conductivity between metals, semiconductors, and insulators.

(a) For each of the three types of polarization, briefly describe the mechanism by which dipoles are induced and/or oriented by the action of an applied electric field. (b) For solid lead titanate \(\left(\mathrm{PbT} \mathrm{O}_{3}\right)\), gaseous neon, diamond, solid \(\mathrm{KCl}\), and liquid \(\mathrm{NH}_{3}\), what kind(s) of polarization is (are) possible? Why?

A metal alloy is known to have electrical conductivity and electron mobility values of \(1.5 \times 10^{7}(\Omega \cdot \mathrm{m})^{-1}\) and \(0.0020 \mathrm{~m}^{2} / \mathrm{V} \cdot \mathrm{s}\), respectively. Through a specimen of this alloy that is \(35 \mathrm{~mm}\) thick is passed a current of 45 A. What magnetic field would need to be imposed to yield a Hall voltage of \(-1.0 \times\) \(10^{-7} y^{2}\)

Is it possible for compound semiconductors to exhibit intrinsic behavior? Explain your answer.
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