Physical Principles of Electron Microscopy: An Introduction to TEM ...

TEM Specimens and Images 117
underfocus atoms dark
��z > 0) �
atom plane
�z
b
�
d/2
no contrast
overfocus atoms bright
��z < 0)
Figure 4-17. Equally spaced atomic nuclei that are elastically scattering the electrons within a
broad incident beam, which provides a continuous range of impact parameter b. The electron
current density appears non-uniform at planes above and below the atom plane.
For E0 = 200 keV, � = 2.5 pm and taking d = 0.3 nm, we obtain �z � 18 nm,
therefore the amount of defocus required for atomic resolution is small.
Wave-optical theory gives expression identical to Eq. (4.25), for an objective
lens with no spherical aberration. In practice, spherical aberration is
important and should be included in the theory (Reimer, 1998). Clearly, the
interpretation of phase-contrast images requires that the spherical-aberration
coefficient of the objective and the amount of defocus are known. In fact, a
detailed interpretation of atomic-resolution lattice images often requires
recording a through-focus series of images with positive and negative �z.
Figure 4-18. (a) Lattice image of ZnS crystals embedded within a sapphire matrix. (b) Detail
of a grain boundary between a PbS crystal and its sapphire matrix. Courtesy of Al Meldrum,
University of Alberta.
d