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Dislocations are the carriers of plastic deformation. As such, their characterization offers important information on the properties they affect. In this contribution, a new tool is presented, which is incorporated in Amira ZIB Edition and allows for three-dimensional (3D) imaging and quantification of dislocations substructures from thick regions an electron-transparent specimen. In the tool, the dislocation segments are traced on diffraction contrast images that are obtained in the transmission electron microscope (TEM). The uncertainties related to the experimental setup and to the proposed method are discussed on the base of a tilt series.
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 current trend towards cyclic, “flexible” operation of fossil-fueled power plants constitutes a major issue regarding lifetime and operational safety of the respective installations and their components, as was outlined in our complementary contribution (Part 1). The present contribution reports on the investigation of the microstructure evolution in cyclically loaded ferritic-martensitic steels and its representation in a physically-based micromechanical model.
For this purpose, specimens of P92 steel grade from the mechanical test programme outlined in our companion contribution (Part 1) were analyzed by scanning electron microscopy (SEM), including backscattered diffraction (EBSD) mapping, and transmission electron microscopy (TEM). A novel method was implemented to improve angular resolution of EBSD scans. Additionally, a correlative microscopy approach was developed and used to correlate EBSD and TEM measurements on the same locations of thick regions of electron transparent specimens. By applying these techniques, a detailed quantitative microstructure description of the as-received material condition, namely in terms of subgrain morphology and dislocation density/distributions, was established. Comparisons of as-received and cyclically loaded conditions from tests interrupted at different stages of lifetime indicate a rapid redistribution of in-grain dislocations with a strong interaction between mobile dislocations and low angle grain boundaries (LABs).
The proposed micromechanical model is formulated in a viscoplastic self-consistent (VPSC) scheme, which is a mean-field approach that allows us to include the crystal details at the level of slip systems while avoiding the considerable computational costs of full-field approaches (such as the classical crystal plasticity finite element analysis). Being physically-based, the model uses dislocation densities and includes the interaction between dislocations, e.g. annihilation of mobile dislocations, and evolution of microstructure, e.g. the grain coarsening. Particularly, the constitutive laws for dislocation evolution and interaction between dislocations and low angle boundaries are calibrated based on two-dimensional discrete dislocation dynamic (2D DDD) simulations, which are performed at a micro-/meso-scale. The results of the beforementioned EBSD experiments are considered as a direct input, involving e.g. the amount of geometrically necessary dislocations, average misorientations and grain characteristics.
The demand for improved castability and low angle grain boundary (LAGB) resistance has led to the addition of low contents of e.g., B, Hf, Zr or C, into large industrial gas turbine components made of Ni-base superalloy single crystals (SXs). Due to the long-term application of Ni-base superalloy SX components in the temperature regime > 1000 °C, the formation of carbides is highly probable, which could jeopardize mechanical properties, such as high cycle fatigue. In the present contribution, the effect of internal and external stresses on the nucleation and growth characteristics of M23C6 carbides is investigated. Creep experiments are performed on the Ni-base superalloy SX LEK 94, which shows a low C concentration (= 0.1 at. %), at 1020 °C under parallel and circularly notched tensile specimens at a nominal stress of 160 MPa in the crystallographic direction [001]. The carbides are then characterized via scanning (S) and transmission (T) electron microscopy (EM). Nucleation is enhanced in the dendritic cores, often as coalesced colonies, extending over micrometers within M-rich (M: Cr, Re, W, Mo) γ channels. Lath shapes with facets on {100} (parallel to growth direction) and {111} are common. These facets exist since early stages (Fig.1a) and later develop misfit dislocations (Fig.1b), preserving the orientation relationship {100}γ || {100}M23C6. Fig. 1c shows a region from the creep gage, where carbides interact with superdislocations in the γ’ phase. Possible mechanisms are discussed.
The creep anisotropy of the single crystal superalloy LEK 94 deformed in tension along [0 0 1] and [1 1 0] directions at 1293 K and 160 MPa was investigated. Elementary microstructural processes which are responsible for a higher increase in creep rates with strain during [1 1 0] as compared to [0 0 1] tensile loading were identified. [1 1 0] tensile creep is associated with a higher number of γ' phase cutting events, where two dislocations with equal Burgers vectors of type <1 1 0> jointly shear the γ' phase. The resulting <2 2 0>-type superdislocation can move by glide. In contrast, during [0 0 1] tensile loading, two dislocations with different <1 1 0>-type Burgers vectors must combine for γ' phase cutting. The resulting <2 0 0>-type superdislocations can only move by a combination of glide and climb. The evolution of dislocation networks during creep determines the nature of the γ' phase cutting events. The higher [1 1 0] creep rates at strains exceeding 2% result from a combination of a higher number of cutting events (density of mobile dislocations in γ') and a higher superdislocation mobility (<2 2 0> glide) in the γ' phase.
The realistic description of plastic deformation caused by dislocations demands the representative measurement of their features, e.g., Burgers vector, slip plane, line direction and density. In the case of bulk deformation of technical alloys, reliable data must be ensured for large regions. Nonetheless, the (thin) filiform nature of dislocations and also the heterogeneity in some microstructures additionally require flexible analysis techniques that resolve the details of their interactions. Strong and clear channeling contrasts, faint extinction contours and the absence of chromatic aberration make scanning transmission electron microscopy (STEM) an ideal imaging mode in wide and thick regions of TEM foils, as opposed to conventional (C)TEM. It is the purpose of this contribution to show how STEM can be applied for quantitative measurement of dislocation features. Furthermore, a new tool will be presented, which enables the three-dimensional (3D) reconstruction, visualization and quantification of dislocation densities and directions from stereo-pairs. The application of these techniques will be shown on a monocrystalline Ni-base superalloy, an important class of structural materials that has been implemented in the first row blades of gas turbines. The examples are extracted from specimens subjected to creep deformation at high temperature and low stress under various macroscopic deformation geometries. The spacial and angular accuracy are discussed as well as possible sources of error.
A great amount of material properties is strongly influenced by dislocations, the carriers of plastic deformation. It is therefore paramount to have appropriate tools to quantify dislocation substructures with regard to their features, e.g., dislocation density, Burgers vectors or line direction. While the transmission electron microscope (TEM) has been the most widely-used equipment implemented to investigate dislocations, it usually is limited to the two-dimensional (2D) observation of three-dimensional (3D) structures. We reconstruct, visualize and quantify 3D dislocation substructure models from only two TEM images (stereo pairs) and assess the results. The reconstruction is based on the manual interactive tracing of filiform objects on both images of the stereo pair. The reconstruction and quantification method are demonstrated on dark field (DF) scanning (S)TEM micrographs of dislocation substructures imaged under diffraction contrast conditions. For this purpose, thick regions (> 300 nm) of TEM foils are analyzed, which are extracted from a Ni-base superalloy single crystal after high temperature creep deformation. It is shown how the method allows 3D quantification from stereo pairs in a wide range of tilt conditions, achieving line length and orientation uncertainties of 3% and 7°, respectively. Parameters that affect the quality of such reconstructions are discussed.