8.5 Concluding remarks and recommended reading 515
equations for the two-beam case for a variety of defects, including user-definable
defects. Results from finite element computations using the ANSYS simulation
package [ans] can also be imported.
The main conclusion from the defects discussed in this chapter should be that,
if the displacement field can be computed in one way or another, then the im-
age contrast for both two-beam and multi-beam situations can be computed. Such
computations may be time-consuming, depending on the methods used to calcu-
late the displacement field and the number of diffracted beams taken into account.
Before embarking on extensive image simulations for a particular defect type, one
should always make sure that good experimental images are available against which
the simulations can be verified. Many experimental parameters are also needed to
perform realistic image simulations:
r
the crystal structure of the perfect crystal;
r
the microscope acceleration voltage (this determines the extinction distances and, if a
good
model is available for the inelastic scattering events, the absorption
lengths);
r
the foil normal F and the beam direction k
0
(this fixes both the sample orientation with re-
spect to the microscope and the orientation of the “columns” for the contrast computation.
It also fixes the value of all excitation errors);
r
the foil thickness z
0
(this determines the integration limits for the dynamical equations);
r
finally, a good starting model for the defect displacement field.
8.5 Concluding remarks and recommended reading
In this chapter, we have applied the dynamical theory to defect images. The intensity
variations near dislocations and stacking faults were among the first contrast types to
receive theoretical attention, and the reader is encouraged to consult the following
papers: Whelan and Hirsch (stacking faults, 1957, [WHHB57]); Hirsch, Howie,
and Whelan (dislocations, 1960, [HHW60]); Hashimoto, Howie, and Whelan
(dislocations, 1962, [HHW62]); Gevers (Moir´e fringe patterns, 1962, [Gev62];
planar fault fringe patterns, 1963, [Gev63]); Gevers, Delavignette, Blank and
Amelinckx (coherent domain boundaries, 1964, [GDBA64]); Gevers, Van Landuyt,
and Amelinckx (planar interfaces, 1965, [GVLA65]; microtwins, 1965, [VLGA65];
subgrain boundaries, 1966, [GVLA66b]; fine structure of diffraction spots due to
presence of defects, 1966, [GVLA66a,VLGA66,GVLA68]); R¨uhle (contrast from
irradiation-induced vacancy disks, 1967, [R¨uh67a, R¨uh67b]); Th¨ol´en (defect im-
age simulation algorithm, 1970, [Th¨o70]); Stobbs (review of weak beam technique,
1970, [Sto70]); Goringe (review of defect contrast, 1970, [Gor70]); Wilkens and
R¨uhle (small dislocation loops, 1972, [WR72]); Skalicky (simulation of defect im-
ages, 1973, [Ska73]); Mader (large inclusions, 1987, [Mad87]); etc. Many other ex-
amples of defect image contrast are scattered throughout the literature. The journals