Mesoscopic characterization

The ability to directly image crystal defects using BF-STEM imaging was mentioned in the previous section concerning low magnification imaging of the Cu bicrystal specimens. In this section higher magnification images and the features visible at those high magnifications will be discussed. The first feature observable on certain facets of the Bi doped 33º Cu bicrystal GBs are GB dislocations. Figure 47 and Figure 48 show BF-TEM images of a Bi doped 33º Cu Bicrystal GB while Figure 49 and Figure 50 show HRTEM images of the same GB. Both of these methods show a continuous array of fringes with a spacing of ~2.5 nm perpendicular to, and along, the GB.

There are multiple sources for alternating contrast features in a specimen observed through TEM. Some of the possible sources for these fringes are: thickness variations, Moiré interference fringes, and dislocation diffraction contrast. Here, the possible source of these fringes appearing in the BF images is explored as follows.

The possibility of thickness variations causing these fringes can be rejected because of the spacing of the fringes and their angle with the GB. If we assume a change in thickness occurred at the GB due to specimen preparation via ion milling, resulting fringes would be parallel to the GB—not perpendicular. In addition to the fringes being oriented in the wrong direction for a thickness change across the GB, the close spacing of the fringes would require an incredibly steep and large change in thickness over mere nanometers to induce such a high number fringes. Thickness

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fringes are a result of oscillations in the intensity of the direct and diffracted beams as they travel through the specimen. At intervals of one half the extinction distance (ξg) the intensity of the diffracted beam is at a maximum while the intensity of the direct beam is at a minimum [55]. By calculating the extinction distance it can be shown that the likelihood of thickness fringes appearing at the measured spacing of ~2.5 nm is unlikely. Equation 24 can be used to calculate the ξg for any diffracted beam vector (g) with components h, k, and l where Vc is the unit cell volume, θB is the Bragg angle for reflection g, λ is the electron wavelength, and Fg is the structure factor of the material.

𝝃

=

𝒈 ,

Equation 24 Williams and Carter provide a table of extinction distances for various g

vectors of Cu at an accelerating voltage of 100 kV listing the smallest of these ξg

values as ξ111 = 28.6 nm. The experiments performed in this study were conducted at 200 kV, the effect of raising the accelerating voltage decreases both λ and Fg through decreasing the elastic scattering factor [55]. With 0.5ξg being greater than 14 nm under the imaging conditions present in Figure 47, the specimen would need to change in thickness by over 100 nm along any given 20 nm long GB section. Such a drastic change in thickness is not possible in a FIB prepared specimen where parallel milling has ensured the near uniformity of specimen thickness. Therefore, according to the

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calculated extinction distance, the fringe spacing of ~2.5 nm measured from BF images (Figure 48 - Figure 50) is unlikely to be thickness fringes.

The fringes present in the images provided in this section must then be accounted for by either dislocation contrast from a network of parallel misfit dislocations along the GB, or by the presence of Moiré fringes due to the

misorientation of the lattice between the two grains composing the bicrystal. Previous studies have attempted to remove the ambiguity between contrast from closely spaced dislocation networks and Moiré fringes [80], [81]. Tholen concluded that at

approximately a dislocation spacing of <0.3 ξg individual dislocations in a network of dislocations cannot be individually resolved and that it is not possible to distinguish the fringes observed from Moiré fringes [80]. Kamiya et al. interpreted the ambiguity between dislocation diffraction contrast and Moiré fringes as the result of a

relationship between the two fringe generation mechanisms in certain cases. The diffraction contrast from dislocations requires adequate dislocation spacing and the strain resulting from the presence of the dislocation be localized near the dislocation core. If the strain is spread over an area the contrast from the dislocation begins to broaden, becoming what can be described as a Moiré fringe [81]. The inability to resolve potential dislocations spaces as closely together as the fringes present in Figure 47 requires additional imaging experiments that may be able to discern the presence of dislocations, such as HAADF-STEM imaging.

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Figure 47 - BF-TEM image of a 33° [100] twist Cu GB doped with Bi showing a network of dislocations across the inclined GB.

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Figure 48 - BF-TEM image of a 33° [100] twist Cu GB doped with Bi showing a network of dislocations across the inclined GB, the change in contrast conditions from one side of the GB to the other is due to changing diffraction conditions across the dislocation.

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Figure 49 – HRTEM image of a 33° [100] twist Cu GB doped with Bi showing a network of dislocations across the inclined GB.

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Figure 50 - HRTEM image of a 33° [100] twist Cu GB doped with Bi showing a network of dislocations across the inclined GB, note the change in dislocation appearance in the upper left corner due to GB faceting.

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