A comparison of HREM and weak beam transmission electron microscopy for the quantitative measurement of the thickness of ferroelectric domain walls

In this paper we present two methods for the quantitative measurement of th e thickness of ferroelectric domain walls, one using high-resolution electr on microscopy (HREM) and the other weak beam transmission electron microsco py (WBTEM). These techniques can be used to determine the thickness of doma in walls at room temperature as well as close to the ferroelectric to parae lectric phase transition. The first method allows a direct visualization of the lattice distortion across the domain wall, by measuring the continuous deviation of a set of planes with respect to the undistorted lattice. The second method consists in a quantitative analysis of the thickness fringes that appear on weak beam images of inclined domain walls. By fitting simula ted fringe profiles to experimental ones, we can extract the thickness of t he domain walls in a quantitative way. These two complementary techniques l ead to a complete characterization of the thickness of ferroelectric domain walls over a wide range of specimen thicknesses at different magnification s. As an example we apply these methods to ferroelectric domain walls in Pb TiO3. The domain wall thickness at room temperature is found to be 1.5 +/- 0.3 nm using HREM (in very thin samples approximate to 10 nm) and 2.1 +/- 0 .7 nm using WBTEM (in samples thicker than 30 nm).