Fundamental and experimental aspects of diffraction for characterizing dislocations by electron channeling contrast imaging in scanning electron microscope

Nowadays Field Emission Gun-Scanning Electron Microscopes provide detailed crystallographic information with high spatial and angular resolutions, and allow direct observation of crystalline defects, such as dislocations, through an attractive technique called Electron Channeling Contrast Imaging (ECCI). Dislocations play a crucial role in the properties of materials and ECCI has naturally emerged as an adapted tool for characterizing defects in bulk specimen. Nevertheless, fine control of the channeling conditions is absolutely required to get strong dislocation contrast for achieving comprehensive analysis. In this work, experiment-assisted fundamental aspects of the origin of dislocation contrast are studied. Experimentally, the potential of ECCI is explored in several dislocation configurations in Interstitial-Free steel (Fe − 1% Si) used as a model material. Full interpretations of dislocation contrast in (g, −g) and its evolution along the Kikuchi band are shown. Furthermore, a dislocation dipole is observed and fully characterized for the first time in an SEM.

Generally, literature reports that ECC images are obtained when the incident beam is oriented near a Kikuchi band edge where the BackScattered Electron (BSE) intensity is minimal. This corresponds to a channeling condition 3 . It has been shown that contrast of crystalline defects, such as dislocations, changes with the beam orientation near the band edge 9, 10 : when the incident beam is exactly oriented on the band edge, dislocations have a white/black contrast 4 . Conventionally, in this condition s ≈ 0, where s the deviation parameter, defines the deviation of the primary electron beam from the exact Bragg's position. For s < 0, the beam is within the Kikuchi band and dislocations exhibit a weak contrast on a bright background. Contrarily, they appear very thin and bright on a dark background when the deviation s is slightly positive (s > 0) 10 .
Understanding the origin of the ECCI contrasts of defects and their evolution is therefore crucial. Only a few articles 4, 10 report observations on the evolution of dislocation contrast by reversing the diffraction vector g (white side dislocations under +g diffraction become black under −g diffraction and vice versa). However, to our knowledge, none gives interpretations of these contrast modifications. Note that experimentally, the reversal of g is generally used for comprehensively analyzing dislocation dipoles in TEM 11,12 .
In this paper, we report both fundamental and experimental aspects of diffraction for characterizing dislocations by ECCI in SEM. For illustrating our work IF steel is used because numerous dislocation analyses by ECCI have already been reported 9,13 . Moreover, TEM literature shows that IFsteel contains dislocation dipoles as well 14,15 .
Here we present ECCI analyses of IFsteel, slightly deformed in tension to 1%. The use of this technique combined with our contrast interpretations allows comprehensive analyses of dislocation contrast throughout the Kikuchi band and under the (g, −g) conditions.

Dislocation contrast along a Kikuchi band
To understand contrast features in ECC images, one should define the role played by the term g·b in the contrast. Overall, a defect in the crystal produces a local displacement field noted R. This distortion of the lattice causes a phase factor exp (-iα) in the amplitude of the diffracted beam, where α = 2πg·R. The displacement field for a pure screw dislocation, for example, can be written as 16 Where z and x are the dislocation coordinates in the sample reference. It is noted from equation 1 that g·R is proportional to g·b.
On the Kikuchi diagram, bands are not isolated from each other. Effects of their contribution on the dislocation contrast have not yet been studied neither experimentally nor theoretically. In this part, this insight is developed. Here dislocations are observed with s positive (s small and s > 0 lead to thinnest dislocation image, see later). Figure 1(a-e) exhibit a single dislocation ECC micrographs obtained with the unique diffraction condition g = (211). The different incident beam positions P i are labeled along the (211) band of the simulated Kikuchi pattern (Fig. 1f). Intensity line profiles perpendicular to the projection of the dislocation line (presented in blue on the dislocation line on Fig. 1) are obtained with ImageJ 17 . These obtained intensity profiles are fitted with a Gaussian curve to get the Full-Width-at-Half-Maximum (FWHM). Then, for every position P i , the image dislocation width T di is deduced from the FWHM.
For P 1 , P 2 and P 3 , the dislocation is thick (T d1 ≈ 30 ± 4 nm, T d2 ≈ 26 ± 4 nm and T d3 ≈ 29 ± 4 nm) compared to the other images taken at P 4 (T d4 ≈ 21 ± 4 nm) and P 5 (T d5 ≈ 19 ± 4 nm). For these latter (P 4 and P 5 ) the dislocation has the thinnest appearance obtained on a dark background. In these cases, the incident beam is oriented in a dark area far from any edges band intersection. In P 1 , P 2 and P 3 , the main band (211) intersects others bands: the green (141) band in P 2 and the blue (132) band in P 3 (Fig. 1f). To simplify the figure; the intersection band in P 1 is not presented. All these bands contribute to the total BSE intensity and then the obtained dislocation is not thin. This evolution of the dislocation thickness has already been observed and explained in TEM 16 but has not been reported in ECCI to date. This observed phenomenon is probably due to the complex contribution of more than one Kikuchi band for a given crystal orientation (corresponding to the incident beam position on the Kikuchi pattern).
Experimentally in ECCI, the most intense bands are generally used supposing that other bands with lower intensity are neglectable.

Dislocation contrast in +g/−g diffraction
For the ±g diffraction, it has been reported, that the dislocation contrast is reversed i.e. black/white inversion 4,10 .
Here, interpretations are proposed for better understanding of the origin of the dislocation contrast for different situations: s ≈ 0, ±g and s slightly positive. Note that for s < 0 interpretation is not envisaged here because in this condition dislocations are in weak contrast on a bright background.
The BSE yield Δη contributes to the dislocation contrast. 'Δ' indicates that only the part of the total BSE intensity due to orientation contrast is calculated, while the contributions of atomic number or surface inclination are not considered. To explain the variation of this BSE signal as a function of the incident angle θ, a model as that of Reimer 18 is used: N is the number of atoms per unit of volume, σ B is the scattering cross section for backscattering through angles larger than 90°, 0 ξ′ and g ξ′ are the absorption lengths, w is the tilt parameter (w = s ξ g = g Δ g θξ ), g is the norm of g, (Δθ = θ − θ B ) is the difference between the incident angle θ on the planes (hkl) and θ B , g ξ is the extinction distance and s the deviation parameter.
Deviation parameter s ≈ 0. When the incident beam is oriented at the edge of a band (s ≈ 0), a set of lattice planes are under the incidence angle θ equal to θ B . Bent planes around the defect are under incidence angles greater or less than θ B (Fig. 2). This difference in θ influences the BSE yield and then the dislocation contrast. Figure 2 is a schematic interpretation showing diffraction with ±g and their corresponding ECC micrographs. ECC images show the same dislocation obtained with s ≈ 0 (s tends to 0 and θ tends to θ B ). The curve in the center is obtained by plotting equation 2-substituting w by g Δ g θξ -in function of θ (the Δη curve part 1 and part 2 correspond to the diffraction with +g and −g respectively).
For +g, the planes 1 and 3 are in incidence with θ > θ B and θ < θ B respectively. The plane 1 generates a low BSE signal (black side dislocation) compared to plane 3 (white side dislocation) because with θ > θ B , the BSE intensity tends towards decreasing values (blue arrow in curve part 1). Therefore, the dislocation contrast has black/white blocks. The bright part is on the same side as the plane 3 (Fig. 2a' and a"). Inversely with −g, the planes 1 and 3 are in incidence with θ < θ B and θ > θ B respectively. Here, plane 1 generates a stronger BSE signal than plane 3 (purple arrow in curve part 2). The dislocation contrast is also presented as black/white blocks. The bright part is on the same side as the plane 1 (Fig. 2b' and b").
In this part, two positions +P 1 , +P 2 and their opposites −P 1 , −P 2 (localized on the opposite edge of the band) are presented on the simulated Kikuchi diagram (Fig. 3e). For each P i micrographs of the same dislocation are recorded. For ±P 1 , the dislocation has a black/white sides and is reversed when the sign of g changes. On +P 2 , the dislocation also has a black/white contrast. Whereas on −P 2 , the incident beam orientation is within a lighter zone on the simulated Kikuchi pattern and the dislocation has a weak contrast on a bright background. Note that the position of the incident beam has an influence on the quality of the contrast as explained earlier (Fig. 1). > 0 (s is slightly greater than 0). For getting the thinnest dislocation appearance with a high contrast on a black background, images are usually acquired with slightly positive deviation parameter s 13 . In this case, θ = θ c > θ B (θ c is the incident angle and the subscript "c" indicates channeling). A set of lattice planes are in incidence with θ = θ c greater than θ B . Other sets are under incidence angles slightly higher or lower than θ c . Figure 4a and b show schematic interpretations of diffraction with ±g and their corresponding ECC micrographs for the same dislocation. The planes 1 and 3 are in incidence with θ > θ c and θ < θ c respectively. Each of them generates an increasing BSE signal for both conditions ±g as it is presented by the curve of Δη as function of θ (arrows in the curves for the two parts). Therefore, the dislocation is bright for ±g (Fig. 4a' and b').

Application for dislocation dipole characterization
ECCI observations are carried out with s slightly positive (s > 0). The region of interest is observed with different g: g 1 = (011), g 2 = (112), g 3 = (110), g 4 = (211) and g 5 = (211) ( Table 1). Figure 5 presents images of dislocation configuration observed with ±g 1 and ±g 2 . These images show that two separated dislocations (1 and 2) are clearly identified. Three conditions must be satisfied for identifying a dislocation dipole: (1) Two single parallel segments of two different dislocations are clearly distinguishable. When tilting the sample one observes a finite distance between the both segments. (2) All dislocations segments are out of contrast with the same diffracting vectors. Therefore, the Burgers vector is unique for all segments and consistent with ±b. (3) Images obtained with +g and its opposite -g show that both contrasts are displaced in the opposite directions.
Both dislocations are out of contrast with g 3 = (110) and g 5 = (211). These extinction conditions are used to determine the Burgers vector, here b [111] 1 2 = ± . Furthermore, the ECC micrographs obtained with different conditions ±g 1 and ±g 2 indicate that the reversal of g for both cases leads to a substantial change of the distance between these two dislocations images. The three conditions, cited above, are satisfied for these two dislocations and lead to the conclusion that the observed configuration is consistent with a dislocation dipole 11,12 (already observed by TEM in IF-steel) with b [111] For g 3 ( Fig. 6a and b) the incident beam is oriented on the edge of the (110 ) band. Dislocations are invisible. With g (211) 5 = , images are taken in two different positions P 1 and P 2 (Fig. 6d). Concerning P 1 , the incident beam is oriented on a dark area of the pattern. Dislocations are invisible (Fig. 6f). While in P 2 , the incident beam is oriented exactly at the intersection of (21 1) and (312 ) band edges, the dislocations generate a contrast (Fig. 6c). In such a position, g 5 ·b = 0 (extinction criterion) whereas for g = (312 ), g·b ≠ 0.
Analogous to TEM, the two-beam dynamical theory 19,20 tells us that the dislocation contrast is proportional to g·b 16 . For P 2 the dipole is clearly visible while the extinction condition g 5 ·b = 0 is fulfilled. This misleading is explained by the fact that another band -where g·b ≠ 0 -contributes to the contrast. Therefore, in the same manner as TEM, the two-beam condition is not satisfied.
To conclude, our fundamental studies bring new insights for complete analyses of dislocation contrast by ECCI. Nevertheless, resolving dislocations requires some conditions: (1) As the position on the Kikuchi band is very important, access to the orientation of the zone of interest with an accuracy better than 0.1° is mandatory; (2) the thinnest and the strongest dislocation contrast is obtained when the incident beam is oriented at the edge of an intense Kikuchi band with a deviation parameter s slightly greater than 0; (3) to obtain clear invisibility conditions, the incident beam should be oriented far from any Kikuchi band edge intersection.
Performing comprehensive dislocation analyses in an SEM without losing any information (compared to TEM) is naturally destined for a great future both in academic research (semiconductors 5 , metals 13 , rocks 21 ) and in industry.

Methods
The dislocation configurations are observed in IF steel slightly (1%) deformed in tension. After the deformation process, the specimen surface was ground to 4000 grit followed by mechanical polishing with 1 µm diamond paste. Finally, a mechano-chemical polishing was performed using 50 nm colloidal silica. Prior to the dislocation observation, a crystallographic orientation map is obtained by Electron Backscattered Diffraction (EBSD) in a Zeiss SUPRA 40 microscope with an accelerating voltage 20 kV. In EBSD, the sample is positioned at a working distance of 15 mm and tilted to 70°. The orientation of the grain of interest is presented by the Euler angles. These latter are used to simulate an EBSD pattern on the "Esprit DynamicS" software from Bruker. The pattern is simulated at 0° because in ECCI our specimen is placed at 0°.
Obtaining the crystallographic orientation of regions of interest is a preliminary step to ECCI that requires an accuracy for crystal orientation of 0.1° 22 . To get this aim, Zaefferer et al. 9 applied the EBSD. However, due to the particular geometry of EBSD and to inaccuracies of stage tilt, the obtained EBSD-Kikuchi pattern offers an absolute angular accuracy of 1-2° approximately 23 . For this purpose, H. Mansour et al. 13 proposed an innovative procedure using "High Resolution Selected Area Channeling Pattern (HR-SACP) for precisely controlling the channeling conditions. The same team therefore developed the rocking beam mode on the GEMINI column of Zeiss SEM allowing the collection of SACP of an angular range 4.4°, an accuracy for the orientation better than 0.1° and for the first time locally reaching high spatial resolution (≈500 nm) 24 . The HR-SACP is superimposed on the EBSD pattern in order to determine accurately the orientation. Finally, to satisfy the different diffraction conditions, the sample placed on the microscope stage is tilted (for example up to 21° for given conditions) and rotated. Dislocations imaging by ECC is carried out for 5 minutes using a four quadrant Si-diode backscattered electron detector, an acceleration voltage of 20 kV, a beam current of 80 µA (with a probe current ≈736 pA) and a working distance of 7 mm.