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Eingeladener Vortrag
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A wide range of properties in crystalline materials is affected by the presence of dislocations, the carriers of plastic deformation. Dislocations can be thought of as filiform structures, characterized by geometrical factors such as their Burgers vector, slip plane, length per unit volume (dislocation density) and line direction. In technical materials such as functional and structural alloys, as well as in minerals, the understanding of bulk deformation driven by dislocation activity is of paramount importance, and thus also the techniques that allow its characterization. Since decades, diffraction contrast in the transmission electron microscope (TEM) is widely implemented to image and describe two-dimensional (2D) projections of dislocation substructures in thin foils [1]. Recently, the use of electron tomography was applied for the first time to fully reconstruct a 3D dislocation network in a GaN epilayer [2]. Although this latter technique has gained popularity, it usually requires an elaborate experimental setup, as well as sophisticated image post-processing methods for a successful reconstruction. Stereoscopic methods in the TEM also have traditionally allowed the three-dimensional (3D) observation of dislocations [e. g. 3]. For this purpose, the same region of a TEM foil is imaged using the same diffraction vector with two beam directions slightly tilted from each other. Subsequently, the pair of images is observed with help of stereo-viewers or 3D glasses. Based on this principle, a system based on a special hardware and software combination was developed for segmentation and analysis of stereomicroscopy data in biological research, and it was also used to analyze simple dislocation structures [4]. In the present contribution a simple software tool is introduced, which has been developed to reconstruct, visualize and quantify dislocation substructures in the thicker regions of electron-transparent foils. A special focus is set on the use of scanning (S)TEM for its implementation.
As depicted in Figure 1, the tool is based on the separate tracing of dislocation line segments on both images of a stereo-pair. The points 1, 2 and 3 are marked on the images viewed by the left and right eyes (Figures 1a and b, respectively), showing an relative displacement Δx on the superimposed images in the anaglyph of Figure 1c. This Δx is given by the point’s depth Δh and by the stereo-angle ϑ, as shown in Figure 1d. By knowing the beam direction for the left and right images (BL and BR, respectively), ϑ can be determined, and hence also Δh. Once the depth information from all traced nodes is gained, a reconstruction is made (Figure 1e) where the line length can directly be read from the tool’s interface. The setup is merely geometrical and only needs the relative tilt between both images, the direction of the tilt axis and the image calibration, thus allowing asymmetrical tilts with respect to the foil normal. The foil thickness is measured directly from the endings of the dislocations on the bottom and top surfaces of the TEM foil, and is determined as t ~ 370 nm for the region in Figure 1. With t, the volume is in Figure 1e is also known, and the total dislocation density of the region is calculated as ρt = 44.4 x 1012 m∙m-3. It is clear from Figure 1 that in the Ni-base superalloy presented here, the dislocation substructures are highly localized towards the interface between the two phases of which the microstructure is composed, γ and γ’ (labeled in Figure 1a). The reconstructed model allows a separation of the dislocation densities within the γ and the γ’ phases and at their interface, which would be rather difficult by using common methods such as the one proposed by Ham [5]. Thus the partial dislocation densities are measured as ργ = 1.7 x 1012 m∙m-3, ργ’ = 2.7 x 1012 m∙m-3 and ργ/γ’ = 40.0 x 1012 m∙m-3. The tool also incorporates the knowledge of the crystallographic positions at the two tilts to enable plotting the line segment orientations. One can chose to display the resulting line directions as an interactive table; as an additional spherical spatial graph, where all lines extend from the center of a sphere; as a 2D plot of the spherical coordinates θ and φ; or as points plotted on a stereographic projection.
Thus, a simple software tool has been developed that allows the reconstruction, visualization and quantification of foil thickness, localized dislocation densities (or other filiform substructures) and orientations based on only one stereo-pair
Dislocations, as carriers of plastic deformation, affect important properties in technical materials, e. g., plasticity. The realistic description of plastic deformation caused by dislocations demands the representative measurement of their features, e.g., line direction, slip plane, Burgers vector and density. Bulk deformation of structural and functional alloys requires reliable data from large regions. The filiform nature of dislocations interacting with complex microstructures additionally demands observation and analysis techniques that allow resolving the details of their interactions in space. The use of electron tomography for this purpose is bound to difficult and time consuming experimental setups, which are not always applicable to any material. In this contribution a new tool is presented, which enables the three-dimensional reconstruction, visualization and quantification of dislocation densities and directions from manual tracing of scanning transmission electron microscopy (STEM) stereo-pairs. Examples are shown from samples of a creep-deformed monocrystalline Ni-base superalloy.
The presentation shows how the three-dimensional quantification of dislocations and their characteristic features, e.g. Burgers vector, line direction, dislocation density, is carried out at the transmission electron microscope in scanning mode (STEM) at Division 5.1 at BAM. Exemplarily, the methods are shown for Ni-base superalloy single crystals, for which a short introduction is given using further TEM techniques. Additional examples on low angle grain boundaries, nucleation of oxides at dislocations and interaction of dislocations and carbides are shown.
The content of the presentation was addapted, aiming at scientists who work within the DFG Priority Programme 1713 "Strong coupling of thermo-chemical and thermo-mechanical states in applied materials".
The LEK94 is a Ni-base superalloy single crystal (SX) of the second generation, a materials class which is important for its high temperature creep resistance (>1000°C) in first stage blades of low-to-medium pressure gas turbines. Monocrystalline Ni-base superalloy SXs have a two-phase microstructure consisting of small cubes (' phase with the ordered L12 crystal structure, cube edge length: 500 nm), separated by thin channels (γ phase with fcc solid solution structure, channel width: 20 nm). The microstructural evolution during high temperature and low stress tensile creep has been thoroughly investigated previously, mainly for [001] loading, both in terms of dislocation activity (filling of γ channels, formation of dislocation networks, cutting of the γ’ phase) as well as phase coarsening (rafting, topological inversion). Other loading geometries have received less attention.
The present work studies high temperature and low stress creep deformation of the superalloy LEK 94 at temperatures around 1000°C, where rafting occurs. Differences between loading under different uniaxial, biaxial and triaxial stress states are discussed. Stereo-microscopy and g∙b analysis in the scanning transmission electron microscopy mode (STEM) are combined for microstructural analysis. The focus is set on the role of dislocation interactions with the aging microstructure. Both development in STEM characterization methods, as well as the roles of phase coarsening, γ channel filling, microstructural heterogeneity and γ’ phase cutting are discussed.