Elements of Solid State Physics

J.P. Srivastava

Chapter 11 Ferroelectric Crystals - all with Video Answers

Educators

Chapter Questions

Problem 1

Explain why $\mathrm{ZnS}$ could be piezoelectric but not diamond, although the atomic arrangement is the same in both the crystals.

Matthew Hurlock

Numerade Educator

00:59

Problem 2

Two dipoles, each having a polarizability $\alpha$, are at a fixed distance $a$. If they form a ferroelectric state, set up the relationship between $a$ and $\alpha$.

Arun Bana

Numerade Educator

04:33

Consider an ionic crystal with cubic symmetry at every lattice point. Calculate its ferroelectric Curie point taking the total polarizability of the crystal as given by
$$
\alpha=\left(0.5+\frac{100}{T}\right) \times 10^{-30} \mathrm{~m}^{3}
$$

Nathan Silvano

Numerade Educator

06:59

Problem 4

Atoms of polarizability $\alpha$ are arranged in a line with $a$ as the interatomic separation. Prove that the array can polarize spontaneously if
$$
\alpha \geq \frac{a^{3}}{4 \Sigma n^{-3}}
$$
where the sum is carried out over all positive integers.

Hafiz Shahzaib

Numerade Educator

02:07

Problem 5

The SrTiO $_{3}$ crystal has the perovskite structure, but is not ferroelectric. Determine a likely reason on the basis of a comparison between the barium and strontium ions.

Arpit Gupta

Numerade Educator

02:03

Problem 6

The resonant frequency of a quartz crystal is given by
$$
v_{0}=\frac{1}{2 l} \sqrt{\frac{Y}{\rho}}
$$
where $l$ is the dimension that determines the mode of oscillation of the crystal, $Y$ is the Young's modulus and $\rho$ is the density of quartz. Determine the useful sizes of the crystal for oscillators in $\mathrm{kHz}$ and $\mathrm{MHz}$ ranges (for quartz, $Y=10^{10} \mathrm{~N} \mathrm{~m}^{-2}, \rho=2500 \mathrm{~kg} \mathrm{~m}^{-3}$ ).

Sarah Mccrumb

Numerade Educator

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6