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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 because the off-center displacement of the Ti4+ ions becomes thermodynamically unfavorable. As a result, they return to the center of the unit cell, leading to the loss of the net electric dipole moment. Consequently, the material transitions from the ferroelectric phase to the paraelectric phase, which lacks spontaneous polarization.

Step by step solution

01

Understand Ferroelectricity

Ferroelectricity is a property of certain materials that exhibit spontaneous polarization, which is the result of a permanent electric dipole moment. This polarization can be reversed by applying an external electric field, making ferroelectric materials useful in various technological applications such as sensors, actuators, and capacitors.
02

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

Barium titanate (\(\mathrm{BaTiO}_{3}\)) is a well-known ferroelectric material with a perovskite crystal structure. This structure consists of a Ba atom at the center of a cube, Ti atoms at the corners, and O atoms at the center of each edge. Below its ferroelectric Curie temperature, the \(\mathrm{Ti^{4+}}\) ions occupy slightly off-center positions, which means the unit cell has a net electric dipole moment, leading to ferroelectricity.
03

Understand the Curie Temperature

The Curie temperature is a critical temperature above which a ferroelectric material loses its ferroelectric properties and transitions to a paraelectric phase. The paraelectric phase is a high symmetric crystal structure without a spontaneous electric polarization. The transition between the ferroelectric and paraelectric phases is a second-order phase transition, which involves the continuous change in material properties with temperature.
04

Explain the Cessation of Ferroelectric Behavior in \(\mathrm{BaTiO}_{3}\)

When the temperature of \(\mathrm{BaTiO}_{3}\) is raised above its ferroelectric Curie temperature, the off-center displacement of the \(\mathrm{Ti^{4+}}\) ions becomes thermodynamically unfavorable, and they return to the center of the unit cell. This symmetrical arrangement of the ions results in the loss of the net electric dipole moment, leading to the demise of the ferroelectric behavior of \(\mathrm{BaTiO}_{3}\). Instead, the material enters the paraelectric phase, where it no longer exhibits spontaneous polarization.

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Most popular questions from this chapter

At room temperature the electrical conductivity and the electron mobility for aluminum are \(3.8 \times 10^{7}(\Omega-\mathrm{m})^{-1}\) and \(0.0012 \mathrm{m}^{2} / \mathrm{V}-\mathrm{s}, \mathrm{re}\) spectively. (a) Compute the number of free electrons per cubic meter for aluminum at room temperature. (b) What is the number of free clectrons per aluminum atom? Assume a density of \(2.7 \mathrm{g} / \mathrm{cm}^{3}\)

Define the following terms as they pertain to semiconducting materials: intrinsic, extrinsic, compound, clemental. Now provide an example of each.

At room temperature the electrical conductivity of \(\mathrm{PbS}\) is \(25(\Omega-\mathrm{m})^{-1}\), whereas the electron and hole mobilities are 0.06 and \(0.02 \mathrm{m}^{2} / \mathrm{V}-\mathrm{s},\) respectively. Compute the in trinsic carrier concentration for PbS at room temperature.

(a) Calculate the number of free electrons per cubic meter for silver, assuming that there are 1.3 free electrons per silver atom. The electrical conductivity and density for Ag are \(6.8 \times 10^{7}(\Omega-\mathrm{m})^{-1}\) and \(10.5 \mathrm{g} / \mathrm{cm}^{3}, \mathrm{re}\) spectively. (b) Now compute the electron mobility for Ag.

Estimate the temperature at which GaAs has an electrical conductivity of \(1.6 \times 10^{-3}\) \((\Omega-m)^{-1}\) assuming the temperature dependence for \(\sigma\) of Equation \(18.36 .\) The data shown in Table 18.3 might prove helpful.
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