# Solid State Physics - Piezoelectric Effect in ZnS

• WelshieTheWhite
In summary: It seems like there is not enough information to solve this problem accurately. In summary, the ZnS crystal has a B3 type structure with space group F¯43m and can be considered as a bi-atomic form of the diamond lattice. When a force is applied along the [1,1,1] direction, the crystal experiences a change in length by ∆l/l = 10^(−6). In part A, the unit cell is shown to have a dipole moment of zero due to its centrosymmetry. In part B, there is not enough information given to accurately calculate the dipole density in the distorted lattice, as it is unclear how the bond angles are affected. The presence of multiple rotation axes
WelshieTheWhite

## Homework Statement

[/B]
ZnS crystalizes in the B3 type structure with the space group is F¯43m. This structure is shown below and can be regarded as the bi-atomic form of the diamond lattice (F d¯3m). Upon applying a force along the [1,1,1] direction, the crystal might experience a change in its length by ∆l/l = 10^(−6) .

(a) Demonstrate that in the unperturbed lattice the dipole moment (p = e · b) is zero, where b is the distance between the charged atoms.

(b) Calculate the dipole density (dipole moment times density of the dipoles) in the distorted lattice under the assumption that in this ionic crystal the charges are equally distributed, i.e. Zn+S−, and that the distances between the atoms remains constant (just changes in the bond angles). The lattice constant of ZnS is a = 5.432 ˚A.

2. The attempt at a solution

For part a. I just abstracted the unit cell as four tetrahedrons, and proved that since a tetrahedron is centrosymmetric, it doesn't have a dipole moment , hence neither does the unit cell.

For part b. I'm a bit lost. At first I thought a contraction in the [1,1,1] plane without a change in bond lengths would just mean that the bond angle between the three 'base' zinc atoms and the one zinc atom in the [1,1,1] plane would get smaller and induce a dipole in each of the tetrahedrons, and so you could calculate the dipole density by multiplying the dipole moment of each tetrahedron by 4/a3 (since there's four tetrahedrons in the volume of a unit cell with volume a3). But it gets complicated pretty rapidly, mainly when you're trying to get a quantitative value of the dipole moment itself.

I feel like I'm missing something, is there some information I can derive from the space group that means I can simplify the process?

As concerns part A, I would say that a dipole moment is absent because there are several rotation axes C3. You can see this through analysing the character table of the symmetry group. The dipole moment can not exist when there are more than one Cn axes because it can not have more than one directions (http://www.reciprocalnet.org/edumodules/symmetry/pointgroups/use.html#Dipole)
Regarding part B, I am a bit confused as well. It is said that the size of the lattice increases when the force is applied but it is also said that the distances stay the same and we need to analyse only a change in the bond angles...

## 1. What is the piezoelectric effect?

The piezoelectric effect is a phenomenon in which certain materials can generate an electrical charge when subjected to mechanical stress, or conversely, deform in response to an electric field. This effect is reversible, meaning the material can also generate a mechanical force when an electric field is applied.

## 2. What is the role of ZnS in the piezoelectric effect?

ZnS, or zinc sulfide, is a common piezoelectric material that exhibits a strong piezoelectric effect. This is due to its crystal structure, which consists of alternating layers of positively and negatively charged ions. When subjected to stress, these ions are shifted, creating a net charge and therefore, an electric field.

## 3. How is the piezoelectric effect in ZnS used in practical applications?

The piezoelectric effect in ZnS is utilized in a variety of devices, such as sensors, actuators, and transducers. In sensors, it can convert mechanical energy, such as pressure or vibrations, into electrical signals. In actuators, it can generate mechanical movement or force in response to an electric field. And in transducers, it can convert energy between different forms, such as from mechanical to electrical or vice versa.

## 4. Are there any limitations to the piezoelectric effect in ZnS?

One limitation of the piezoelectric effect in ZnS is its small magnitude compared to other piezoelectric materials. Additionally, it has a relatively low Curie temperature, meaning it loses its piezoelectric properties at high temperatures. ZnS also has a high dielectric constant, which can lead to electrical breakdown in certain applications.

## 5. How does the piezoelectric effect in ZnS relate to solid state physics?

The piezoelectric effect in ZnS is a result of the material's crystal structure and the movement of its charged ions. This is a fundamental concept in solid state physics, which studies the properties of materials in their solid phase. Understanding the relationship between the structure and properties of materials, such as ZnS, is essential in the development of new technologies and advancements in the field of solid state physics.

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