Ferroelectric domain structure characterized by prefractals of the pentad cantor sets in KH₂PO₄

Abstract

Ferroelectric 180[ddot] domain structure periodic along the domain wall normal is formed in pyramidal growth sectors less strained in KH₂PO₄ (KDP) crystal. Each half period of the domain patterns optically observed between parallel polarizers is characterized by the first four prefractals of the pentad Cantor sets. It has been found that the averaged half period of these prefractal domain patterns is proportional to the square root of the thickness of the c plate. This verifies that the electrostatic energy originating from the depolarization field, as well as the wall energy, plays an important role in the prefractal domain formation. The prefractal domain patterns have been reproduced in the secondary electron images of a SEM. This verifies that the depolarization field also plays an important role in the secondary electron image formation. It is predicted, from the standpoint of the equilibrium internal energy, that a derivative of the 3rd prefractal domain pattern will correspond to one of ultimate domain structures.

Key Words:

• KDP
• ferroelectric domain
• polarizing optical microscope
• scanning electron microscope
• fractal
• Cantor sets