Skip to main content
Top
Published in: Integrating Materials and Manufacturing Innovation 2/2019

Open Access 15-05-2019 | Thematic Section: 3D Materials Science

Non-destructive Characterization of Polycrystalline Materials in 3D by Laboratory Diffraction Contrast Tomography

Authors: Jette Oddershede, Jun Sun, Nicolas Gueninchault, Florian Bachmann, Hrishikesh Bale, Christian Holzner, Erik Lauridsen

Published in: Integrating Materials and Manufacturing Innovation | Issue 2/2019

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Laboratory diffraction contrast tomography (LabDCT) enables the user to reconstruct three-dimensional (3D) grain maps of polycrystalline materials. For each grain, the size, orientation, and 3D morphology including the number of faces can be derived. Since the technique is non-destructive, LabDCT opens up new possibilities for studies of microstructural evolution at the level of individual grains. The LabDCT setup is integrated on a commercial X-ray microscope, enabling correlation of the resulting grain map with complimentary information on, e.g., cracks, porosities, and inclusions. Here, the LabDCT principle is introduced, and recent materials science applications are presented. The first example on liquid metal embrittlement highlights the correlation of grain boundary properties and complimentary absorption information on grain boundary wetting. It is shown that the grain boundary energy determines whether wetting occurs or not. The second example is on grain growth. The grain statistics in this study, more than 1200 grains at two different time steps, were large enough to capture rare events such as abnormal grain growth and the annihilation of a grain with only three faces.
Notes

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Introduction

The microstructure of a material is often seen as the link between its properties and performance. In particular, for polycrystalline samples such as metals, minerals, and ceramics, the crystallographic orientations, shapes, and sizes of the individual grains within the samples are vital to understand and predict microstructural properties. Grain mapping is a common name for a variety of non-destructive tomographic techniques originating from synchrotron X-ray facilities to access the grain-based 3D polycrystalline microstructure of bulk samples. Grain mapping comes in several variations, such as three-dimensional X-ray diffraction (3DXRD) microscopy [1, 2], diffraction contrast tomography (DCT) [3, 4], and high-energy diffraction microscopy (HEDM) [5]. These techniques are available at a very limited number of synchrotron beamlines worldwide, but recent developments have led to laboratory diffraction contrast tomography [6] and made it commercially available on the Zeiss Xradia Versa 520 X-ray microscope under the name LabDCT™ [7, 8]. While the first version of the LabDCT reconstruction algorithm, GrainMapper3D™ by Xnovo Technology ApS, only gave grain morphologies based on tessellation [9], GrainMapper3D version 2 reconstructs grain morphologies from the diffraction signals with high fidelity [10]. The first part of the current paper will be devoted to a short summary of the principles behind LabDCT, both in terms of hardware and software.
The real merit of this non-destructive bulk characterization technique lies in the added value when it is combined with complementary methods to give the material scientist, engineer, metallurgist, or geologist a many-faceted view of the material challenge at hand. A good example of such a study is the investigation of correlation between grain boundaries found by LabDCT and impurities imaged by absorption contrast tomography (ACT) in polycrystalline silicon [11]. Polycrystalline silicon is used extensively in photovoltaic cells, and the study showed that the impurity particles, which degrade the performance and efficiency of the photovoltaic cells, were distributed non-randomly in the bulk sample with a clear grain boundary character dependence. With this knowledge at hand, manufacturers of photovoltaic cells can start to improve their process design to produce more efficient solar cell components. In the following, two examples of applying LabDCT to obtain a better understanding of fundamental problems in materials science will be outlined.

Mapping Grain Morphology and Orientation by LabDCT

A schematic representation of the LabDCT implementation is shown in Fig. 1. The divergent, polychromatic X-ray beam is constrained through an aperture to illuminate a region of interest (ROI) covering the cross section of the sample. A beamstop after the sample blocks transmitted X-rays on the detector to increase sensitivity towards the substantially weaker diffraction signals. The setup takes advantage of the fact that for a divergent point source of X-rays, a crystal grain diffracts the X-rays such that they are focused one-dimensionally in the Laue focal plane of diffraction at a sample-detector distance equal to the source-sample distance [12]. A high-resolution detector is placed at this distance and the Laue focusing effect makes the diffracted signals appear as line-shaped spots minimizing spot overlap and allowing to record larger volumes.
During the acquisition of LabDCT, two scans are taken. The first scan collects ACT projections at increments through a 360° rotation of the sample illuminated by the direct beam (without employing the beam defining aperture or the beamstop). From the ACT data, a 3D reconstruction of the absorption signal is automatically created, as in traditional X-ray tomography. Subsequently, beam defining aperture and beamstop of appropriate sizes are added to the setup in order to collect the LabDCT data. Diffraction spots appear on the outer part of the detector not covered by the beamstop. The diffraction contrast patterns are acquired, usually at 1–2° increments, through a 360° rotation of the sample. The DCT data is used to reconstruct the crystallographic orientations, positions, and morphologies of the individual grains within the sample. ACT and DCT data are automatically collected in one sequential batch of scans without user interaction.
LabDCT measurements are followed by a computational reconstruction using the proprietary fast geometric indexing algorithm implemented into GrainMapper3D [10]. Since the diffraction geometry exposes shape information within recorded diffraction spots, the spots are segmented and fed into the reconstruction algorithm. The algorithm maximizes the completeness in a given sample point, defined as the ratio between observed and forward projected signals, and successively traverses and refines solution space until a user-defined convergence criterion is matched. Grains and their grain boundary counterparts are afterwards defined through connected regions of similar crystallographic orientation.
The processing steps comprising the entire GrainMapper3D reconstruction workflow are illustrated in Fig. 2. These have been implemented into an intuitive graphical user interface (GUI) under the headlines circled in the center of Fig. 2. The GUI provides instant visual feedback on data quality and reconstruction progress—making a complex scientific method accessible for a non-expert user. The GrainMapper3D reconstruction workflow is as follows:
1.
Project: Load the relevant data, the ACT reconstruction, and raw DCT projections, as well as crystallographic information about the sample phase.
 
2.
Absorption mask: Use the ACT reconstruction to specify the ROI (solution space) of the indexing algorithm
 
3.
Detector mask: Specify the beamstop used. The part of the detector not covered by the beamstop defines the region for diffraction spots used for segmentation and reconstruction.
 
4.
Segmentation: Separate the diffraction signal from the background. The user has the choice between several segmentation algorithms and can interactively adjust segmentation parameters to the binarization best capturing the diffraction spots.
 
5.
Reconstruction: Create a grain map from a segmentation within a ROI. Start with predefined parameters, a small ROI and a coarse discretization of solution space and watch the reconstructed completeness map appear in the live preview within a few minutes. Successively adjust parameters until a satisfactory reconstruction result is achieved.
 
6.
Grains: Define grains based on a misorientation criteria within which adjacent crystallographic orientations of reconstructed regions should be considered as originating from the same grain and visualize the grains with respect to properties such as completeness and/or IPF color.
 
For scan volumes with an arbitrarily large extent along the rotation axis, GrainMapper3D results covering partly overlapping ROIs within a sample can be stitched together into one final grain map of a combined sample volume. Likewise, grain maps measured at different temporal states during for instance an annealing process can be registered, enabling the user to track the same grains through the evolving microstructure. Statistical measures such as grain size distributions or pole figures can easily be derived from the data. In addition, specific information for the individual grains, such as the number of faces, and grain boundary properties like misorientations, grain boundary normal distributions, and curvatures can be calculated using, e.g., DREAM3D® [13].
The following examples of employing LabDCT to materials science applications take advantage of the possibility to measure grain boundary properties in the volume as outlined above. Here, it is important to note that a grain boundary is essentially a 3D structure, and to fully describe it mesoscopically, five independent parameters are needed: three for the misorientation between the two grains defining the boundary and two for the inclination of the grain boundary plane [14]. Examining a 2D section of a sample can only reveal partial information for grain boundaries [15].

LabDCT Materials Science Applications

Correlation Between Liquid Metal Embrittlement and Grain Boundary Energy Revealed by Exploiting the Complimentary of ACT and LabDCT

Grain boundary wetting refers to the phenomenon that a liquid metal penetrates along the grain boundaries within polycrystalline solid metals. Replacement of the original grain boundary with the liquid layer generally causes intergranular brittle fracture in otherwise ductile metals and alloys. This is known as liquid metal embrittlement and causes serious problems for certain materials processing scenarios such as welding and galvanizing, as well as in nuclear reactors with a spallation target of liquid metal [16, 17].
A classic case of liquid metal embrittlement is the penetration behavior of liquid gallium in aluminum. Previous studies have shown that the penetration of liquid Ga proceeds non-uniformly in the 3D grain boundary network of Al. Such studies require that both the penetration of the liquid Ga into the Al matrix and the crystallographic character of the Al matrix grain boundaries can be measured. Typically, the liquid Ga network has been measured by synchrotron X-ray ACT, whereas several different techniques including synchrotron X-ray diffraction [18] and electron backscattered diffraction (EBSD) [19] have been applied to obtain the crystallographic information for the Al matrix.
While many of the earlier studies suffer from either poor statistics (investigations limited to bi-crystals) or insufficient information about the grain boundary character (due to crystallographic limitations of 2D techniques), this type of investigation lends itself perfectly to a combination of ACT and LabDCT. In a recent study, the polycrystalline microstructure of the Al matrix was characterized by LabDCT, including both morphologies and crystallographic orientations of the grains. The misorientations and grain boundary plane normals were extracted from the reconstructed 3D grain map, and finally, the Ga penetration path was revealed by ACT and correlated with the grain boundary properties [20].
For details on the sample size and preparation procedure, please refer to [20]. The ACT data was collected using an X-ray source voltage of 60 kV and a pixel size of 1.08 μm to achieve best possible contrast between Al and Ga as well as a high resolution in the characterization of the Ga network. To reduce the signal-to-noise ratio, 3601 projections with an exposure time of 4 s were collected. The DCT data was collected using an X-ray source voltage of 150 kV to enhance flux and hence limit data collection time. Three hundred diffraction contrast images with an exposure time of 300 s were collected. The data collection was performed for two partially overlapping ROIs, which were reconstructed separately using GrainMapper3D and subsequently stitched together to yield one final 3D grain map. The total experimental time was 8 h for ACT and 50 h for LabDCT.
Figure 3 shows the reconstructed sample containing 1000+ grains using both the ACT data to visualize the Ga network (a) and the LabDCT data to obtain the crystallographic orientations and shapes of the individual grains (b). For each grain in the 3D grain map, one can extract all of its faces, as exemplified in Fig. 4a, determine the misorientations between this grain and its neighbors, and color code the faces accordingly, as displayed in Fig. 4b. In addition, one can determine a mesh on each face and, for each triangular facet in the mesh, calculate both the grain boundary normal direction with respect to the crystallographic orientation of the grain and the corresponding IPF color. Color coding the faces of a grain with the IPF color equivalent of the grain boundary normal leads to Fig. 4c.
With the grain boundary properties, exemplified in Fig. 4, and the degree of Ga wetting for each grain boundary, which can be derived from the ACT reconstruction in Fig. 3a, the relevant information for a statistically significant study of the non-uniform penetration of liquid Ga into the 3D grain boundary network of Al is at hand. Analysis of 115 grain boundaries in the mapped sample suggests that it is the grain boundary energy, which determines the extent of Ga penetration in an Al boundary: low-energy boundaries are much more resistant to liquid Ga than higher energy ones [20].
Elaborating a bit further on this main result, it was found that unwetted grain boundaries are mostly low-angle grain boundaries with average misorientations less than 10°. For this category of grain boundaries, it is generally assumed that the grain boundary energy increases with increasing misorientation angle according to the Read-Shockley equation [21]. While most of the high-angle grain boundaries with misorientation angles larger than 15° were found to be wetted, a few unwetted grain boundaries were encountered among these. Figure 5 shows an example of one such unwetted high-angle grain boundary with a 58.9° misorientation around [0.59, 0.58, − 0.60], making it a Σ3 grain boundary according to the Brandon criterion [22]. In addition, Fig. 5b shows that for this particular grain boundary, the grain boundary normal distributions concentrate around (111) relative to both grain orientations. Previous MD simulations have shown that for Σ3 boundaries, those with planes closer to {111} have lower energies [23, 24], leading to the conclusion that the unwetted high-angle Σ3 grain boundary in Fig. 5 is a low-energy grain boundary.
The combined ACT and LabDCT approaches used for the above outlined liquid metal embrittlement study provide a complete 3D description of the grain boundary network, which can be used as input for and validation of grain boundary models. As a highlight, the LabDCT technique was demonstrated to readily yield both the grain boundary plane normals and the misorientation angles of a large number of grain boundaries non-destructively. This allows for subsequent processing of the sample material and enables studies of microstructural evolution as will be exemplified by the next case study on grain growth.

4D study of grain growth in Armco iron, looking at rare events in large data sets

While serial sectioning can yield 3D information about grain topologies in microstructures consisting of thousands of grains [25, 26], this is a destructive characterization tool, and hence the information that can be derived about microstructural evolution is limited. With LabDCT, the user has access to a non-destructive experimental technique offering grain boundary character information for large 3D sample volumes; thus, the microstructural evolution during grain growth is an obvious topic to study. Mapping out the 3D grain structure at several different stages of an annealing process and correlating the observed grain boundary character and growth offers a wealth of 4D information that can be used to both understand and predict grain growth. 3D grain maps based on synchrotron data measured at several annealing steps have previously been used to study grain growth phenomena [2729] as well as in comparison with, e.g., phase field simulations to predict grain growth [30].
The first 4D study of grain growth kinetics enabled by the use of LabDCT was recently conducted on an Armco iron sample [31]. The initial as-received sample material was obtained from a hot-rolled bar. A 75% cold rolling reduction in thickness and subsequent annealing at 880 °C for 4 days was carried out to refine the grain size to approximately 90 μm in the as-treated sample. A cylindrical specimen with diameter of 1 mm was prepared by electrical discharge machining for the LabDCT grain growth studies. The axis of the cylinder was taken along the rolling direction (RD) of the initial hot-rolled bar. A ROI in the as-treated sample, time step t0, was first scanned. Annealing treatment at 880 °C for 8 h was then carried out using an external furnace, and the same ROI was scanned again using the same experimental settings to track the microstructural evolution to time step t1. At each time step, 84 h of experiment time was spent to scan four volumes with a height of 440 μm and a relative displacement of 325 μm along the cylinder axis. The data was reconstructed using GrainMapper3D and subsequently stitched together to achieve the required grain statistics from a cylindrical ROI of diameter 1 mm and height 1.4 mm.
More than 1200 grains and 8000 grain boundaries were mapped in the Armco iron sample before and after annealing (see the 3D grain map of the as-treated state in Fig. 6). Highlighted in yellow in Fig. 6 is a grain within the bulk of the sample displaying abnormal grain growth, hereafter called the abnormal grain. The equivalent sphere diameter (ESD) of the abnormal grain is 500 μm at t1, while the average ESD of all grains is 92 μm. The number of faces of the abnormal grain is 139 at t0 and 156 at t1, as compared with an average prediction of 13.4 faces per grain. Abnormal grain growth is a relatively rare event, the observation of which normally requires statistics on thousands of grains, and the same holds for grains with only three faces [25, 26].
In the t0 grain map of the Armco iron sample, a grain with three faces was observed right next to the abnormal grain (Fig. 7a), while it has disappeared at t1. A closer look at the grain boundary between the two grains at t0 reveals that they share a low-angle grain boundary (Fig. 7b), and that the average Gaussian curvature of the boundary is very large as evidenced in Fig. 7c. It has long been known that low-angle grain boundaries are predicted to have low mobilities [32, 33], while the driving forces of high-curvature grain boundaries tend to be high [34]; hence, theoretically predicting the fate of this particular grain pair upon annealing requires the correct relationship between two opposing effects. However, the experimental results clearly show that the grain boundary in question does move in order for the abnormal grain to swallow up the small grain with only three faces at t1.
The above example has demonstrated that essential information for the study of grain growth, such as the grain shapes, sizes, crystallographic orientations, and boundary properties, can be obtained non-destructively at multiple temporal states using LabDCT. The approach provides access to the necessary 4D experimental evidence that is neither available using 2D techniques such as EBSD nor destructive 3D techniques such as serial sectioning.

Discussion

LabDCT gives access to crystallographic and grain morphology information for polycrystalline samples in 3D and offers a solid alternative to synchrotron grain mapping techniques with comparable quality. The fact that this can be accomplished non-destructively in a laboratory setting makes LabDCT particularly well suited for studies of microstructural evolution taking place over several days to weeks or even months, for instance, annealing or corrosion.
From a materials science applications point of view, the extensive grain statistics accessible by LabDCT is large enough to capture rare events such as abnormal grain growth and the presence and annihilation of grains with only three faces. This amount of grain statistics lends even greater promise to the study of other rare events, for instance, material failure, where the exact onset point is hard to predict both in space and in time. For such applications, the seamless integration of LabDCT with ACT will be a real advantage, as demonstrated, e.g., in the grain boundary wetting example.
The uncertainties of the grain boundaries derived from LabDCT data have previously been quantified based on comparison with ACT in an aluminum sample with copper-decorated grain boundaries [35]. When comparing the LabDCT reconstruction performed with a voxel size of 5 μm with the ACT data with a resolution of 1.6 μm, it was found that the average distance in grain boundary location between the two was 7.6 μm, whereas 90% of the grain boundaries were within 20 μm [10]. It could seem obvious to perform the same kind of comparison for the present grain boundary wetting case; however, there are a number of inherent aspects of this particular study that makes a one-to-one comparison of the grain boundary networks derived from LabDCT and ACT inadvisable. First of all, the LabDCT measurement of the Al grain structure was performed prior to the Ga wetting [20], and furthermore the grain boundaries were wetted to very different extents, if at all. In fact, investigating and understanding these differences were the exact purpose of the study. Considering the similarities in both sample material and experimental setup, it is fair to assume that the uncertainties of the grain boundaries in the Ga-wetted Al sample are comparable with those observed in the Cu-decorated Al. Hence, there may be local variations in the grain boundary normal distributions caused by measurement uncertainties, but as can be seen from Fig. 5b, the individual distributions show clear maxima, which can be interpreted as the grain boundary normals.
For investigations of microstructural evolution—something that often requires external stimuli such as temperature or force—LabDCT has proven a valuable experimental tool, for instance, in the study of copper particle sintering [9] and in the above reported study of 4D grain growth [31]. For both of these studies, the annealing was performed ex situ, but the LabDCT implementation leaves ample space around the sample (L in Fig. 1 typically of the order 12–20 mm) to enable introduction of sample environments (e.g., furnaces, load rigs), thereby taking full advantage of the non-destructive nature of LabDCT. For specific cases requiring very high time resolution (seconds to minutes) currently only accessible at synchrotron sources, the availability of a lab-based setup allows for thorough investigations of suitable samples and complementary studies prior to synchrotron beamtime, thereby maximizing the outcome of costly and limited synchrotron access.
The current implementation of LabDCT supports well-annealed microstructures with grain sizes down to 10–40 μm mainly limited by the lower brilliance of laboratory X-ray sources compared with synchrotron sources. Although the present reconstruction model does not account for lattice imperfections across grains, these can be tolerated at the expense of the quality of the reconstructed grain map up to a certain point, as long as the individual diffraction spots can be segmented.
Key focus areas in the continued effort to improve the LabDCT technique are the sensitivities towards both grain size and strain. This will broaden the application space to include more challenging samples sometimes seen in e.g. additive manufacturing, geological and pharmaceutical applications.

Conclusion

In the present paper, it has been demonstrated that LabDCT has become a routine method for non-destructive studies of the time evolution of grain structures. The data collection procedure is seamlessly integrated with conventional X-ray imaging methods, enabling correlation of the resulting grain map with complimentary information on, e.g., cracks, porosities, and inclusions. The GrainMapper3D reconstruction workflow comes with an intuitive GUI that provides instant visual feedback on data quality and reconstruction progress, allowing a non-expert user the utilization of this advanced imaging modality. For each grain, the size, orientation, number of faces, and interface curvatures are measured directly, opening up for many new applications within the fields of engineering, materials, and geosciences.

Acknowledgments

The authors would like to thank Yubin Zhang and Dorte Juul Jensen, DTU Mechanical Engineering, and Burton R. Patterson and Catherine A. Sahi, University of Florida, for providing samples and engaging in fruitful discussion during the process of the investigations documented in the present publication.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Literature
4.
go back to reference Ludwig W, Reischig P, King A, Herbig M, Lauridsen EM, Johnson G, Marrow TJ, Buffière JY (2009) Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis. Rev Sci Instrum 80:033905. https://doi.org/10.1063/1.3100200 CrossRef Ludwig W, Reischig P, King A, Herbig M, Lauridsen EM, Johnson G, Marrow TJ, Buffière JY (2009) Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis. Rev Sci Instrum 80:033905. https://​doi.​org/​10.​1063/​1.​3100200 CrossRef
10.
go back to reference Bachmann F, Bale H, Gueninchault N, et al (2019) 3D grain reconstruction from laboratory diffraction contrast tomography. J Appl Crystallogr in press Bachmann F, Bale H, Gueninchault N, et al (2019) 3D grain reconstruction from laboratory diffraction contrast tomography. J Appl Crystallogr in press
Metadata
Title
Non-destructive Characterization of Polycrystalline Materials in 3D by Laboratory Diffraction Contrast Tomography
Authors
Jette Oddershede
Jun Sun
Nicolas Gueninchault
Florian Bachmann
Hrishikesh Bale
Christian Holzner
Erik Lauridsen
Publication date
15-05-2019
Publisher
Springer International Publishing
Published in
Integrating Materials and Manufacturing Innovation / Issue 2/2019
Print ISSN: 2193-9764
Electronic ISSN: 2193-9772
DOI
https://doi.org/10.1007/s40192-019-00135-6

Other articles of this Issue 2/2019

Integrating Materials and Manufacturing Innovation 2/2019 Go to the issue

Thematic Section: 5th World Congress On Integrated Computational Materials Engineering

AixViPMaP®—an Operational Platform for Microstructure Modeling Workflows

Thematic Section: Additive Manufacturing Benchmarks 2018

Meshfree Simulations for Additive Manufacturing Process of Metals

Premium Partners