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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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Short Answer: Above the Curie temperature, the thermal energy in BaTiO3 is high enough to overcome the energies responsible for maintaining its displaced lattice structure (dipole moment). This causes the Titanium atom to return to the center of the unit cell and the net electric polarization to vanish, thus resulting in the cessation of ferroelectric behavior in BaTiO3.

Step by step solution

01

Understand the concept of Ferroelectricity

Ferroelectricity is a property of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. In simple words, ferroelectric materials can exhibit an electric charge even in the absence of an external field. The electronic structure of the material is such that it allows certain ions to displace from their equilibrium positions, creating a net electric polarization.
02

Discuss the Structure of BaTiO3

Barium titanate (BaTiO3) is a well-known ferroelectric material. It has a perovskite structure, where the Barium (Ba) and Oxygen (O) form a cubic-close packed (ccp) array and the smaller Titanium (Ti) sits in the octahedral holes formed by the Oxygen anions. Below the Curie temperature, the Ti ion shifts from the center of the octahedron leading to a net dipole moment.
03

Explain the effect of Curie temperature on the structure of BaTiO3

The Curie temperature (Tc) is a critical temperature at and above which the ferroelectric behavior of a material ceases. This is because the thermal energy becomes enough to overcome the depolarizing field. At this temperature, the Para-electric phase transition occurs. For BaTiO3, when the temperature is higher than its Curie temperature, the Ti4+ ions return to the center of the unit cell, and the net electric polarization vanishes due to equal and opposite displacements of ions. Therefore, the material becomes paraelectric above its Curie temperature.
04

Conclude the reason for cessation of ferroelectric behavior

BaTiO3 ceases to behave as ferroelectric above its Curie temperature because the thermal energy is high enough to overcome the energies maintaining the displaced structure (dipole moment). In this situation, the Titanium atom returns to the center, the crystal structure of BaTiO3 becomes cubic, and the net electric polarization becomes zero. That's why above the Curie temperature, BaTiO3 does not show any ferroelectric behavior.

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Most popular questions from this chapter

How does the electron structure of an isolated atom differ from that of a solid material?

(a) In your own words, explain how donor impurities in semiconductors give rise to free electrons in numbers in excess of those generated by valence band-conduction band excitations. (b) Also, explain how acceptor impurities give rise to holes in numbers in excess of those generated by valence band-conduction band excitations.

(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.

Predict whether each of the following elements will act as a donor or an acceptor when added to the indicated semiconducting material. Assume that the impurity elements are substitutional. $$ \begin{array}{lc} \hline \text { Impurity } & \text { Semiconductor } \\ \hline \text { N } & \text { Si } \\ \hline \text { B } & \text { Ge } \\ \hline \text { S } & \text { InSb } \\ \hline \text { In } & \text { CdS } \\ \hline \text { As } & \text { ZnTe } \\ \hline \end{array} $$

(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 gaseous argon, solid LiF, liquid \(\mathrm{H}_{2} \mathrm{O}\), and solid Si, what kind(s) of polarization is (are) possible? Why?
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