Ferroelectric wall thickness

Several studies have examined the thickness of the domain wall in ferroelectric materials [17]. The 90° a-c domain wall thickness has been measured using a transmission electron microscope (tem), [14] but distinguishing the positive and negative domains in 180° opposite polarization areas is difficult because these methods are used to observe the strain of arrangements of molecules. Direct clarification of the domain wall thickness is important with respect to both scientific and engineering aspects. 

The piezoelectric hysteresis loops have been studied additionally to above dielectric hysteresis. This kind of loop is shown on Fig. 2.17. It has been recorded on PZT nanotube with outer diameter 700 and 90 nm wall thickness with the help of piezoatomic force microscopy (see Refs. [42, 43]). The obtained loop is the direct evidence of ferroelectric properties of the nanotube. Square form of the loop speaks about sharp polarization switching at coercive voltage 2 V. The residual (at zero voltage) piezoelectric coefficient d ff is of the same order as for the thin PZT film. 

Thus, at this time, the evidence seems to indicate a wall thickness = 1 /tm, which is indeed much thicker than the pure ferroelectric domain walls which are commonly thought of as a few lattice dimensions thick (Cohen, 1951). 

As defined above, a domain is a microscopic region in a crystal in which the polarization is homogeneous. However, in contrast to domain walls in ferromagnetic materials that can be relatively thick (Fig. 5.6d), the ferroelectric domain walls are exceedingly thin (Fig. 15.15). Consequently, the wall energy is highly localized and the walls do not move easily. 

The normal state of a ferroelectric crystal is one in which the microstructure consists of a set of coherent domains, each of which has the internal electric dipoles parallel to each other, but not aligned with those of neighbouring domains. Domain walls are not atomically smooth but have a thickness of between 0.5 and 1 nm. Polarisation builds up at domain boundaries and a single domain can have surface charges of the order of 1.5 x lO electrons cm which can generate an internal electric field of 300MV or more. 

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