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

TEM Specimens and Images 111
Figure 4-13. Unit cell for a face-centered cubic crystal: a cube of side a with atoms located at
each corner and at the center of each face. Another common crystal structure is the bodycentered
cubic (bcc) structure, whose unit cell is a cube with eight corner atoms and a single
atom located at the geometrical center of the cube.
For a material whose lattice parameter is known (for example, from x-ray
diffraction), the expected d-spacings can be calculated, using the additional
condition that (for the fcc structure) h, k, and l must be all odd or all even.
Therefore, the first few rings in the diffraction pattern of a polycrystalline
fcc metal
correspond to
(h kl) = (1 1 1), (2 0 0), (2 2 0), (3 1 1), (2 2 2), … (4.24)
Knowing a, the d-spacing for each ring can be calculated using Eq. (4.23)
and its electron-scattering angle � obtained from Eq. (4.21). From Eq. (4.22),
a value of L can be deduced for each ring and these individual values
averaged to give a more accurate value of the camera length. Recording the
diffraction pattern of a material with known structure and lattice parameter
therefore provides a way of calibrating the camera length, for a given
intermediate-lens setting.
Knowing L, the use of Eq. (4.22) and then Eq. (4.21) can provide a list of
the d-spacings represented in the electron-diffraction pattern recorded from
an unknown material. In favorable cases, these interplanar spacings can then
be matched to the d-values calculated for different crystal structures, taking
h, k, and l from rules similar to Eq. (4.24) but different for each structure,
and with a as an adjustable parameter. In this way, both the lattice parameter
and the crystal structure of the unknown material can be determined, which
may enable the material to be identified from previously-tabulated
information.