Deformation Mechanisms and Material Characterization Methods
2.5 Material Characterization
2.6.2 Electron microscopy
Electron waves are a unique medium that can be used in imaging. By accelerating electrons into a high energy beam (via a high voltage), the resulting wavelength is far shorter than that of white
light. For example, considering an electron beam produced from a 20kV gun, the wavelength is only 1240.7/20000(eV) = 0.06nm, corresponding to a resolution limit of λ/2=0.3Ao- theoretically
implying that it can image species as small as 0.3 Ao. The generated high energy electrons (typically 5-40keV) penetrate the surface of specimen and interact with the atoms of material in a variety of elastic and inelastic scattering processes. Scattering continues until either the electrons escape from the specimen, or are absorbed by the material itself. Multiple scattering will result in a certain volume of material (the interaction volume) being irradiated, for instance see Figure 25 [125]. Note the diameter of this volume is much larger than the diameter of incident beam. As illustrated in Figure 25, a variety of signals are generated as a result of scattering. Secondary Electron (SE) are used to produce the classic electron microscopic images. This mode provides high-resolution imaging of surface and it’s independent of the atomic number of the scattering atoms.
Figure 25 Interaction volume showing regions in a specimen that are primary source of secondary electrons, back-scattered electrons and x-ray in SEM
In addition to displaying the bright-field images from SE emission, back-scattered electrons (BSE) in a SEM may be used to determine the crystallography of (poly) crystalline samples. As schematically shown in Figure 25, when the beam penetrates the sample surface, some electrons are elastically scattered back out of the sample, retaining approximately their original energy- referred to as back-scattered electrons (BSE). BSE signals are widely used to examine the crystallographic orientation of materials. Unlike the SE mode, the number of backscattered electrons reaching a backscatter detector is proportional to the mean atomic number of the specimen. To do this, a flat/polished sample is placed in the SEM chamber at a tilted angle (70o from the horizontal) towards the diffraction camera. The recommended 70o angle degree is considered ideal because it maximizes the yield of backscattered electrons in the direction of phosphor screen. Hence, the tilted sample optimizes both the contrast in the diffraction pattern and the fraction of electrons scattered from the specimen. When the electrons impinge on the crystalline sample, they interact with individual lattice planes. When these interactions satisfy the Bragg condition, they exhibit backscattering diffraction and (due to the tilted sample) are directed toward a phosphor screen, where the CCD camera detects the fluorescent pattern. The resulting pattern consists of a large number of intersecting bands, known as Kikuchi lines, which represent the unique crystallographic properties of the crystal. Specifically, select crystallographic planes within the material, following Bragg’s law, diffract the electrons. When a phosphor screen is placed in the SEM chamber, the diffracted electrons fluorescence the phosphor as they impact the screen. This phenomenon is schematically shown in Figure 26a. This interaction leads to the formation of a band pattern composed of “Kikuchi lines”, characteristic of the sample crystal structure. Figure 26b illustrates the formation of a backscattered Kikuchi pattern by EBSD in SEM for a Copper sample [126]. Interpretation of the
Kikuchi patterns, needed to determine the crystallographic orientation of the sampled volume, is performed in two consecutive steps. First, the pattern has to be indexed, which means that the crystallographic indices of the Kikuchi bands and poles (more precisely, of the corresponding lattice planes) have to be determined. Next, the relative positions of the bands or poles with respect to an external reference frame - the crystallographic orientation of the sampled volume with respect to the specimen axes – will be redefined. Interested readers are encouraged to see Ref. [126]. Kikuchi patterns are analyzed automatically using commercially available software packages, especially in SEM settings.
Figure 26 (a) Formation of backscattered Kikuchi patterns br EBSD in SEM. (b) Kikuchi pattern by EBSD in SEM for a Copper [126].
A Kikuchi diffraction pattern presents valuable information, such as lattice strains and grain/phase boundaries, which enables discrimination between low-angle boundaries from high angle types, and the estimation of the grain size distribution. Grain boundaries are characterized by the misorientation axis and angle and the boundary plane. In crystal orientation mapping, a grain is regarded by the collection of neighboring pixel in the map, which has a misorientation less than a certain threshold angle. Although the degree of rotation between neighboring pixels depends on the step size used in the EBSD grid as well as the intergranular rotation in the
sample, cumulative rotations may be discerned. There are several variations in this map, using different measures of intergranular lattice rotation.
One of the most common methods is the Kernel type, whereby the color of each pixel in the map a function of the degree of the orientation change with respect to its neighbor (this method is used in the current study). Many engineering materials are an aggregate of randomly oriented crystals and grains. The nature of the grain interface and their orientation is crucial for understanding microstructure-property relationships for alloy design, material characterization, fatigue and failure analysis [127].
The directional variation in diffracted intensities in the specimen is used to describe the orientation of a crystal relative to the embedding body. The graphical representation of the orientation distribution of crystallographic lattice plane is known as a “Pole figure”. In other words, a pole figure is the density of a specific crystallographic direction with respect to a reference sample. More precisely, it is the frequency of occurrence of a given crystal plane normal per unit spherical area. For example, Figure 27a, considers a cubic crystal in a rolled sheet sample. The pole figure shown in Figure 27c demonstrates the orientation of the
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planes of the targeted crystal shown in Figure 27a with respect to the sample frame. Note that the circle dots shown in the pole figure map in Figure 27c, relates to the crystallographic plane with corresponding colors in Figure 27b. Whereas the pole figure shows sample directions aligned with a particular crystallographic pole, an “inverse pole figure“ does the opposite, indicating the crystallographycal poles aligned with a specified sample direction[127]. Several examples with invoking the inverse pole figure will be presented in sections 4 to 7. This is often of interest for samples in which the processing history identifies a single direction, e.g. uniform distribution of HCP unit cells in wrought Mg alloys.Figure 27 (a) A cube crystal embedded in a hypothetically drawn rolled sheet. (b)