Structure of Piezoelectric Materials

Quartz Crystal Structure

Although the quartz structure is made up of multiple SiO4 tetrahedra, its molecular formula is SiO2. Why then is silicon bonded to four oxygen atoms? The catch is that every oxygen atom is bonded to two silicon atoms, i.e., two tetrahedrons share one oxygen atom. Therefore, the overall molecular formula is (SiO4/2)3 which can be written as Si3O6 or SiO2. The bond angle between silicon and oxygen forming a tetrahedron is 109.5 degrees Fig 1.a. The bond angle between two tetrahedra is 144 degrees Fig 2.b.

Fig 1.a - Bond Angle of Silicon and oxygen
Fig 1.a - Bond Angle of Silicon and oxygen
Fig 2.b- Bond Angle Between two sio2 tetrahedron
Fig 2.b- Bond Angle Between two sio2 tetrahedron

These Sio4 tetrahedra, when connected to each other, form a helix which runs through the entire structure Fig 2. The crystal structure of quartz is made of multiple helices connected to each other as shown in fig.

Fig: 2 - SiO2 Tetrahedron helix
Fig: 2 - SiO2 Tetrahedron helix

Condition for Piezoelectricity:

For piezoelectricity to occur inside a material, it must satisfy two conditions.

  1. Material must have a dipole moment.

  2. Unit cells of a material must lack a centre of symmetry, also known as the inversion centre.

Fig 3.a- Quartz unit cell
Fig 3.a- Quartz unit cell
Fig 3.b - Quartz unit cell
Fig 3.b - Quartz unit cell

Electronegativity and dipole moments are explained in the video. Dipole moment is essential for generation of charge across a material. However, dipoles inside a material arrange themselves such that they cancel each other out. For charge to appear across a material, the net dipole moment should be non-zero. This is possible only if the materials lack a centre of symmetry.

Inversion Centre/ Centre of Symmetry

To understand the inversion centre, consider the structure of another form of Sio2 Cristobalite Fig 4.a. Now if we rotate the Cristobalite structure to its side Fig 4.b. It can be seen here that in Cristobalite, for every silicon and oxygen atom present at x,y,z, there is an exact atom present at -x,-y,-z. This means that the structure has an inversion centre at the centre of the unit cell. The inversion centre can be present anywhere inside the unit cell, but quartz lacks this centre of inversion. Accordingly, the dipoles do not cancel each other out when external stress is applied as shown in the video.

Fig 4.a - Cristobalite Unit Cell
Fig 4.a - Cristobalite Unit Cell
Fig 4.b - Cristobalite Unit cell side view
Fig 4.b - Cristobalite Unit cell side view

Properties of Ferroelectric Materials

But what if, instead, the material remains elongated? These are a special class of Piezoelectric materials known as Ferroelectrics. These materials tend to remain polarised even after the electric field is removed, a phenomenon known as Remnant Polarisation. The direction of polarisation can be reversed by reversing the polarity of the Electric Field. If we plot an Electric Field vs Polarisation curve, it follows the below path. This type of curve is called a Hysteresis curve. Quartz is the most abundant naturally occurring piezoelectric material. Certain manmade ferroelectric materials show high strain response to applied electric fields, greater sensitivity to electric fields, and high mechanical flexibility. These are the piezoelectric Ceramics and Polymers which are most widely used these days to make sensors and actuators.

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