Spontaneously polarised piezoelectrics (on the atomic scale)
Ferroelectrics are spontaneously polarised, but are also piezoelectric, in that their polarisation changes under the influence of a stress.This is because while all ferroelectrics are piezoelectric, not all piezoelectrics are ferroelectric.
This relationship can be viewed as:
Pyroelectrics are materials which typically experience a decrease in polarisation when their temperature is increased. They will not be considered in this TLP but a short aside on pyroelectrics can be found in the Ferroelectric Materials TLP.
The piezoelectric effect in ferroelectrics is very dependent on its atomic structure. Depending on the orientation of a crystal, applying a compressive stress can increase or decrease the polarisation, or sometimes, have no effect at all.
To illustrate this, consider the tetragonal phase of BaTiO3, which is commonly seen at room temperature. It possesses a spontaneous polarisation, formed by the dipole moment in each unit cell. To make it simple, we will only consider a single unit cell first. Consider the unit cell of BaTiO3:
Below 120°C this unit cell becomes tetragonal, and gains a spontaneous dipole moment:
If the material is compressed along the x-axis, the important charged ions move further from their original positions, giving a higher dipole moment.
Compressed along the z-axis, the dipole moment decreases as the ions move towards their original position.
This shows how polarisation can easily arise on the atomic level.
Spontaneously polarised piezoelectrics (on the macro scale)
Now, ferroelectric materials possess multiple domains. For background on this, read the TLP on Ferroelectric Materials.
To make it simple, we will only consider single crystal ferroelectrics. These, when first made, have domains of the form:
If a mechanical stress is applied to the ferroelectric, then there are domains which will experience an increase in dipole moment and some which will experience a decrease in dipole moment. Overall, there is no net increase in polarisation. This makes BaTiO3 useless as a piezoelectric unless it is put through some additional processing. This process is called poling. An electric field is applied to the ferroelectric as it passes through its Curie temperature, so as its spontaneous polarisation develops, it is aligned in a single direction:
All of the domains in the piezoelectric have a dipole moment pointing in the same direction, so there is a net spontaneous polarisation. Now, when a mechanical stress is applied, the polarisation will increase:
but still remain pointing in the original direction. This makes ferroelectrics into useful piezoelectrics.