A pyroelectric material possesses a spontaneous dipole moment, interpreted via the ionic positions. This dipole moment, when normalised by volume, yields a polarisation. Whether a given sample with local dipole moments possesses a net dipole moment depends on domain configurations, which in turn depend on the electrical history of the sample. This polarisation can change when a stress is applied to the material, as pyroelectrics are a sub-set of piezoelectrics. But if the material is pyroelectric and not also ferroelectric then the polarisation will not reverse under the application of an electric field. This is because it will break down first, i.e. the coercive field exceeds the breakdown field. If the material is ferroelectric the the coercive field is smaller than the breakdown field. In other words, ferroelectrics are a subset of pyroelectrics.
Whether or not a material can be pyroelectric or ferroelectric depends upon whether the point group it belongs to is polar, i.e. whether there is at least one direction along which no point group symmetry element forces both sides of the crystal to be the same. The polar point groups are:
1, 2, m, mm2, 3, 3m, 4, 4mm, 6, 6mm. (Point groups will not be covered in this TLP.)
Note that in some of these point groups, e.g. class 4, the polar axis is unique.