Lecture handout including QS - Department of Materials Science ...

BH32 Course B: Materials for Devices BH32
Dipole ordering & Domains
All such ions in a local region (a domain) will tend to sit on the same side of the double well (adjacent
dipoles want to line up with each other); spontaneous polarisation (ordering of the dipoles) below
T c is a co-operative phenomenon. [Remember: Net electric dipole per unit volume is polarisation, P.]
But, stray fields (due to surface charge) have an energy cost, which can be reduced by the formation
of differently oriented domains:
P
→
reduced stray field
A sample may contain many domains of varying orientation, and hence net P is zero. For example,
when a non-centrosymmetric phase forms (e.g. tetragonal BaTiO 3
in a parent cubic structure), the
transformation begins in different regions of the sample, and will be randomly oriented.
But, there is an energy associated with the interface between
differently oriented domains: domain wall energy
There is therefore an energy balance, or compromise:
stray field energy (high for large domains) vs. domain wall energy (high for many small domains)
The angle between domains depends on the symmetry of the crystal and the preferred dipole
direction. For the cubic → tetragonal transition in BaTiO 3
, polarisation can occur along any of the 3
previously cubic directions, and in a +ve or –ve sense, giving 6 possible domain orientations:
90° domain boundary
90° walls are strained
because the c-axis is
aligned with the a-axis
(a ≠ c)
180° domain boundary
If a ferroelectric sample is held in a sufficient electric field it will become poled, i.e. dipoles will
preferentially line up in the allowed crystallographic direction most closely parallel to the field.
e.g. polycrystalline sample:
(random grain → after
orientations) poling