CHAPTER II BACKGROUND
II. 2.2 316L Stainless Steel
II.6 Transmission Electron Microscopy
II.6.1 High Resolution Transmission Electron Microscopy
While SEM systems detect electrons that are ejected from the sample surface facing the electron beam (backscattered electrons, secondary electrons, etc.), transmission electron microscopy (TEM) signals are generated from electrons which have transmitted through a thin specimen, as illustrated in Figure 37 [75]. Although TEM inherently is statistically limited due to the small sample size in high resolution images, high resolution transmission electron microscopy (HRTEM) is capable of imaging materials at the atomic scale. In order to produce TEM images, the sample must be thin enough to be transparent to electrons. This can be accomplished by milling/polishing a lamella using a focused ion beam (FIB).
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Figure 37: Illustration of Signals Generated from High Energy Electrons Interacting with a Thin Specimen (Reprinted from [75])
Due to the high resolution imaging capabilities of TEM, it is possible to visually confirm the presence of residual strain, either by directly imaging the atoms or by way of aberrations in the resulting diffraction patterns (DPs). While SEM, EDS, and EBSD share many capabilities with TEM (the generation of Kikuchi bands and DPs, elemental identification, etc.), TEM is capable of directly imaging radiation-induced defects, such as voids, dislocations, precipitates, etc. [76]. Previous experiments suggest that radiation-produced voids generated in Fe-Cr-Ni alloys increase in average size as dose increases, as shown in Figure 38 [30, 77]. Likewise, TEM is capable of imaging the dispersoid size distribution in ODS steels, as shown in Figure 39 for 12Cr-ODS samples [78]. TEM is therefore capable of determining how additively manufacturing ODS alloys may influence oxide dispersoid size distribution and coherency in the alloy matrix [79].
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Figure 38: Experimentally Measured Void Size Distribution in Fe-Cr-Ni Alloys Irradiated at 650 °C (Reprinted from [77])
Figure 39: Size Distributions of Dispersoids in 12Cr-ODS Steels (Reprinted with permission from [78])
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A dislocation is a defect defined by its direction and Burgers vector. The crystal structure surrounding a dislocation is strained. However, for single dislocations, this strain typically does not generate new spots in the resulting DP [75]. If many dislocations exist and are oriented, then additional spots will be present in the DP, as shown in Figure 40 [75]. Dislocations can be seen in TEM in a variety of ways. Figure 41 shows the Moiré fringes (vide infra) generated by the same dislocation in A, B, and C underlying three different defect-free crystals [75].
Figure 40: Example of the Diffraction Pattern from a Region with (A) and without (B) Many Oriented Dislocations Producing Moiré Fringes in a TEM Image
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Figure 41: Illustrations of why Moiré Fringes Exist from Dislocations, Which Cannot Be Directly Seen in Any of the Resulting Patterns (Reprinted from [75])
When electrons (or other quanta) are diffracted, they behave according to Bragg’s Law (Eq. 1). The Laue conditions represent the reciprocal-space equivalent of Bragg’s law [80]. The fcc unit cell has Miller indices a1, a2, and a3. These indices form the fcc Bravais lattice g which. Electrons diffracting in a crystalline lattice behave as Bloch waves defined by Eq. 15 in which the atoms in the crystal are arranged in a periodically repeating manner [80]. In the context of the crystal, the reciprocal lattice vectors, b1, b2, and b3, are related to the Miller indices by Eq. 16. Using the reciprocal lattice vectors, one can generate the reciprocal lattice-equivalent of the unit cell, called the “first Brillouin zone”, as shown in for the fcc crystal in Figure 42 [81].
Eq. 15
( )r e u ri k r
64 Eq. 16
2 3
1 1 2 3 2 a a b a a a
3 1
2 1 2 3 2 a a b a a a
1 2
3 1 2 3 2 a a b a a a Figure 42: First Brillouin Zone of an fcc Crystal (Reprinted from [81])
An illustration of an edge dislocation and its associated distortion is provided in Figure 43 where white circles represent atoms [82]. Dislocation contrast in bright field transmission electron microscopy (BFTEM) images depends strongly on orientation, as is illustrated in Figure 44 [82]. In Figure 44, the reciprocal lattice vector g is essentially
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equal to the diffraction vector k, which points into the paper, and the Burger’s vector b is dependent upon which direction the dislocation is viewed from. When viewing this edge dislocation from the front (Figure 44, middle), g and b are perpendicular to one another, so k b k b cos
0. When viewing this edge dislocation from the side (Figure 44, right), g and b are parallel to one another, so
cos 0
k b k b
. In practice, when viewing a dislocation from the side such
that cos
0, the dislocation is invisible, while the dislocation is most clearly visible when cos
1. This is called the “null contrast rule” or the “g b rule” which defines the invisibility criterion of dislocations in TEM images. In practice, if1 3
g b , the dislocation is invisible [82].
Figure 43: Distortion of Crystal Planes near an Edge Dislocation, with Ewald Sphere Constructions (Right) during TEM (Reprinted from [82])
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Figure 44: The Left Half of an Edge Dislocation Column showing the TEM Null Contrast Rule (Reprinted from [82])
II.6.2 High Angle Annular Dark Field Scanning Transmission Electron Microscopy