Consider quartz, SiO2. In its non-stressed state, the ions are in positions which do not allow any net dipole moment to be formed.
The structure of quartz is shown below:
In quartz, there are tetrahedra of O atoms around Si atoms, which are able to twist and change shape when a stress is applied. The change in their position leads to the formation of net dipole moments as seen in the piezoelectric dipole moment section.
A tetrahedra of O atoms around a Si atom is marked within the quartz structure below:
The dipole moment appears in every unit cell in the crystal and causes polarisation.