Quantification of mineral behavior in four dimensions: Grain boundary and substructure dynamics in salt

Authors

  • V. E. Borthwick,

    1. Department of Geological Sciences, Stockholm University, Svante Arrhenius väg 8C, Stockholm SE-10691, Sweden
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  • S. Schmidt,

    1. Research Division, Risø DTU, Technical University of Denmark, Frederiksborgvej 399, PO Box 49, DK-4000 Roskilde, Denmark
    2. Department of Physics, DTU, Technical University of Denmark, Building 307-309-311-312, DK-2800 Kongens Lyngby, Denmark
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  • S. Piazolo,

    1. Department of Geological Sciences, Stockholm University, Svante Arrhenius väg 8C, Stockholm SE-10691, Sweden
    2. Australian Research Council Centre of Excellence for Core to Crust Fluid Systems/GEMOC National ARC Key Centre, Department of Earth and Planetary Sciences, Macquarie University, New South Wales 2109, Australia
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  • C. Gundlach

    1. European Synchrotron Radiation Facility, 6 Rue Jules Horowitz, F-38043 Grenoble CEDEX 9, France
    2. MaxLab IV, Lund University, PO Box 118, Lund SE-22100, Sweden
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Abstract

[1] Here we present the first four dimensional (time and three dimensional space resolved) experiment on a strongly deformed geological material. Results show that even complicated microstructures with large continuous and discontinuous changes in crystallographic orientation can be resolved quantitatively. The details that can be resolved are unprecedented and therefore the presented technique promises to become influential in a wide range of geoscientific investigations. Grain and subgrain scale processes are fundamental to mineral deformation and associated Earth Dynamics, and time resolved observation of these processes is vital for establishing an in-depth understanding of the latter. However, until recently, in situ experiments were restricted to observations of two dimensional surfaces. We compared experimental results from two dynamic, in situ annealing experiments on a single halite crystal; a 2D experiment conducted inside the scanning electron microscope and a 3D X-ray diffraction experiment. This allowed us to evaluate the possible effects of the free surface on grain and subgrain processes. The extent to which surface effects cause experimental artifacts in 2D studies has long been questioned. Our study shows that, although the nature of recovery processes are the same, the area swept by subgrain boundaries is up to 5 times larger in the volume than observed on the surface. We suggest this discrepancy is due to enhanced drag force on subgrain boundaries by thermal surface grooving. Our results show that while it is problematic to derive absolute mobilities from 2D experiments, derived relative mobilities between boundaries with different misorientation angles can be used.

1. Introduction

[2] Bulk material behavior and material properties in terms of rheology and dominance of deformation processes are governed by behavior at the grain and subgrain scale. This includes deformation and annealing behavior, but also reactions and phase transitions [Ashby, 1970; Means and Xia, 1981]. During deformation and post-deformational annealing crystal defects rearrange into arrays of dislocations, tilt walls and subgrain boundaries forming the substructure. In particular, post-deformational annealing is important as it can significantly change the substructure by the reorganization of boundaries and nucleation of new, strain-free grains [Beck, 1954; Bever, 1957; Hobbs, 1968; White, 1977; Covey-Crump, 1997; Heilbronner and Tullis, 2002; Barnhoorn et al., 2005]. This process is also often termed “recovery” [Humphreys and Hatherly, 2004]. Developments in the quantitative treatment of recovery related processes have allowed advances in both the material [Nes, 1995] and geoscience [e.g., Piazolo et al., 2002] fields.

[3] Our knowledge of relevant grain and subgrain scale processes has significantly advanced due to investigations utilizing in situ experiments. Such time-resolved experiments are ideal for observations of microstructural dynamics and their quantification through accurate knowledge of the spatial and crystallographic relationships [Le Gall et al., 1999; Seward et al., 2004; Piazolo et al., 2005; Bestmann et al., 2005; Mirpuri et al., 2006; Piazolo et al., 2006; Field et al., 2007; Borthwick and Piazolo, 2010]. The major drawback of the aforementioned types of in situ experiments is that the area of analysis is restricted to a 2D surface which may introduce artifacts. For example, at a free surface the evolution of the grain boundary topology may not be representative of bulk behavior as it is impossible to rule out that behavior may be influenced by surface effects [Frost et al., 1990, and references therein]. In particular, thermal grooving has been suggested to have an effect on boundary migration [Mullins, 1958; Gottstein and Shvindlerman, 2010, and references therein]. The groove acts as a surface defect and moving this requires mass transport and thus energy dissipation. These factors exert a drag force on the migrating boundary, and the boundary can be temporarily “pinned” at the groove tip. Experimentally this manifests as “jerky” grain boundary motion on the surface [Babcock and Balluffi, 1989]. Thermal grooving has been mainly investigated in high-angle grain boundaries with fewer studies on low angle subgrain boundaries. The full extent of such surface effects on 2D experimental results has yet to be established. Thus, ideally, for the development of quantitative physically based models for grain and subgrain scale processes, in situ experiments allowing real-time observations in three dimensions within a volume of material are needed. Such investigations will have to be non-destructive to allow viewing of the dynamics of a system through time.

[4] Recently, 3D X-Ray Diffraction (3DXRD) microscopy [Poulsen et al., 2001] has been introduced in materials science as a tool to perform in situ time resolved 3D studies of crystalline materials, primarily metals [Lauridsen et al., 2001; Nielsen et al., 2001; Fu et al., 2003; Schmidt et al., 2004; Gundlach et al., 2004; Poulsen, 2004; Poulsen et al., 2004; Lauridsen et al., 2006; Baruchel et al., 2008; Schmidt et al., 2008]. This technique seems well-suited to address the shortcomings just listed, but requires the use of a synchrotron. However, experimental and computational difficulties restricted such analysis to highly annealed microstructures, where individual grains are well defined and exhibit negligible internal deformation. In this contribution, we not only show that the 3DXRD technique can now be utilized to study processes operative at the subgrain level, but also present a first application of 3DXRD to a geological material: a study of the microstructural evolution during annealing of a deformed rock salt single crystal. The results are directly compared to a published in situ EBSD (Electron Backscatter Diffraction Analysis) study performed within a Scanning Electron Microscope (SEM) on the same material [Borthwick and Piazolo, 2010]. Our study shows that complicated microstructures, as commonly seen in geological materials, can be sufficiently resolved to allow quantitative process orientated research. In addition, the direct statistical comparison of 2D and 3D subgrain scale behavior is crucial for deciding how to approach and interpret time-resolved in situ studies in geosciences in the future.

2. Experimental Method

[5] The 0.5 × 0.5 × 1.2 mm3specimen was cut from a single crystal, which initially had been uniaxially compressed at 453°C to 16.5% strain. SEM based EBSD analyses performed on the surface show that this material contains subgrains of an average cross-sectional area of ∼1200μm2 and with an internal misorientation variation of ∼6 degrees [Borthwick and Piazolo, 2010].

[6] The four dimensional experiment was conducted at beamline ID11 at the European Synchrotron Radiation Facility (Grenoble, France). The 3DXRD experimental configuration is sketched in Figure 1. The sample was held in place with dried silver paint, which also served to increase thermal conductivity between the sample and the heated copper rod, which housed a thermocouple. A small nickel flake was glued to the top of the halite sample in order to increase the ease with which the top surface could be found during experiments. A fitted glass casing around the copper rod and sample was flooded with Argon gas to keep the sample at a constant temperature.

Figure 1.

Schematic diagram illustrating the setup for 3DXRD. The figure is adapted from Poulsen [2004] for the case in which the monochromatic beam has a linear focus. The diffracted beam is emitted from the sample as it is rotated around the ω axis and has a direction defined by Bragg angle 2θ and azimuthal angle η. The diffraction pattern is collected simultaneously by two detectors positioned at different distances from the sample. The coordinates of the laboratory system are also shown. Inset shows the analysis volume which was composed of 20 layers of ∼0.5 by 0.5 mm size.

[7] A monochromatic beam was passed through the specimen, illuminating the sample and generating diffracting beams in any parts of the structure that fulfill the Bragg condition. The beam was constrained to a suitable cross-section using focusing and absorbing slits. The sample was rotated around a vertical axis perpendicular to the beam direction with a rotation angleω constrained to two rotations, each 45° in 0.25° steps (Figure 1). This rotation was necessary to determine the orientation of the substructural elements of the TL1 crystal. The diffraction patterns for each rotation step was collected by one or more 2D detectors placed at varying distances from the center of rotation.

[8] Full crystallographic orientations within the sample were mapped as a vertical sequence of x-y layers, with a spatial resolution in x and y of 5μm and a 10 μm vertical resolution between layers in the z direction. The diffraction pattern was collected simultaneously by two detectors positioned at different distances from the sample. The semi-transparent detector close to the sample gave spatial information with a resolution of 5μm on the distribution of misorientation within the subgrains at each point, while the second low-resolution detector provided the full crystallographic analysis of the crystal. 3D maps of 20 layers were acquired before and after a heating procedure (Figure 2) similar to that used in 2D in situ SEM experiments on the same crystal [Borthwick and Piazolo, 2010]. Specifically, the sample was heated at 280°C for a duration of 221 min, then cooled to a temperature of 100°C for complete mapping.

Figure 2.

3D reconstruction images. (a and b) Stacked reconstructed x-y layers with subgrains shown in random colors before Figure 2a and after Figure 2b heating. Some subgrains increase in size e.g., subgrain colored light blue (see gray arrows), while others decrease in size e.g., subgrain colored purple (see white arrows). To highlight the size change the light blue subgrain with before heating internal misorientation of 1–2.5° and surrounding 1–4° boundaries has been isolated and is shown before Figure 2c and after Figure 2d heating. This subgrain has significantly increased in size during annealing. We deliberately did not crop the sides where the data was more difficult to reconstruct in order to show that the size of the overall area increased after heating. This shows that successful annealing with reduction in the orientation spread occurs allowing greater accuracy of reconstruction for the more recovered structure. Scale for all images is shown in Figure 2d.

[9] For this work we succeeded in generalizing and improving the Grainsweeper program [Schmidt et al., 2008] in order to be able to reconstruct, for each layer, a 2D orientation map of the highly deformed microstructure (cf. Figures 3a and 3b). The GrainSweeper [Schmidt et al., 2008] is a standalone program for reconstructing both undeformed and deformed microstructures in materials, i.e., the crystallographic orientations as well as the grain morphologies are extracted simultaneously. The current resolution, which is limited by detector resolution, is 5 microns. Once the geometric (also called the global) parameters of the experimental setup are determined (beam energy, distance and tilt of the detector) the GrainSweeper program runs in a fully automatic mode. Data are collected using a planer beam shape thus illuminating a layer with thickness of typically 5 microns.

Figure 3.

Changes in orientation and subgrain boundaries during annealing and validation of data reconstruction technique. (a and b) Maps show the relative angular deviation in gray scale from the orientation at the red cross. A gray scale bar in Figure 3b shows the angular variation. Subgrain boundary misorientations are shown in an interpolated colorscale, where light blue indicates 1°, dark blue 1–2° and green to yellow >2° misorientation. Figures 3a and 3b are horizontal layers and Figures 3c and 3d are vertical cross sections which have a spacing of 10 μm between rows which translates as 2 pixels. The black dashed lines show the location where cross-sections were taken. Figures 3a and 3c were taken before heating and Figures 3b and 3d after. White arrows show examples of substructures that can be followed before and after heating and are sensibly reproduced in the vertical cross section also; note also the slight change in subgrain boundary misorientation angle; black headed arrows point to a newly formed subgrain boundary; gray headed arrows indicated a subgrain boundary whose misorientation angle decreased during annealing; the black stars mark a subgrain which shows substantial crystallographic rearrangement resulting in distinct areas of similar orientation. (e) A schematic 3D cross-section of the sample showing the approximate location of the horizontal maps (Figures 3a and 3b) shaded in gray with red outline and vertical layers (Figures 3c and 3d) shaded in brown with blue outline. The location of the black dotted line is the same as for the 2D images Figures 3b and 3d. The scale bar for all images is shown in Figure 3c and is equivalent to 25μm.

[10] For each voxel a rough orientation distribution function (ODF) is obtained by adding all signals on the detector, which could originate from the voxel in question, to the Rodrigues space (each signal is a geodesic in the Rodrigues space). Afterwards, the orientation space is searched for local maxima and a forward projection onto the detector estimates the completeness of candidate orientations (the completeness being the ratio of measured reflection over number of reflections expected). The orientation with the maximal completeness is chosen as the final orientation for the voxel in question.

[11] Following the reconstruction, a 2D voxel grid with crystallographic orientations is obtained (i.e., the output data format is similar to a grain map obtained by the electron backscattering method). Hence, post-processing of both the 2D SEM based EBSD and the 3DXRD data could be performed by the same commercial software (HKL Channel 5, Oxford Instruments). 3D maps are obtained by translating the sample vertically. At the ID11 beamline the GrainSweeper runs on a computer cluster where the layers are reconstructed in parallel.

[12] For our analysis as well as data representation we restrict used and shown data to data of high confidence as determined by the Grainsweeper data reduction software. This resulted in data gaps within the volume investigated; however, it ensured the necessary data quality. To ensure validity of our results we reconstructed cross-sections perpendicular to each other through the sample from our data (cf.Figure 3).

3. Results

[13] Orientation maps before and after annealing are shown as 3D composite images in Figures 2a and 2b, respectively. Perpendicular cross-sections show that data reconstruction using Grainsweeper was successful. It is evident that subgrains can be followed between layers (Figures 2a and 2b). A number of subgrains disappear after heating, and some increase in size (Figure 2b). One of such growing subgrains is shown in Figures 2c and 2d. During annealing crystallographic orientations within individual subgrains rearrange to form distinct areas of similar orientation (e.g., subgrain marked with star in Figures 3a and 3b). Furthermore, the misorientation angle of subgrain boundaries decreases (gray headed arrow, Figures 3a and 3b) or new subgrain boundaries form (black headed arrow, Figures 3c and 3d).

[14] To assess the influence of a free surface on subgrain boundary migration we compared the swept area from boundary migration for five 2D layers in the 3D experiment and one large 2D area in the results from 2D in situ annealing on the same crystal [Borthwick and Piazolo, 2010] (see Figures 4b and 4c). Low-angle boundary (LAB) movement was clearly more extensive within the 3DXRD volume, with LABs between 4 and 28 times more likely to move than for a 2D surface (Figure 4a). We compared the distribution of fractional swept area to boundary misorientation angle to the total fraction of boundaries present in the before heating map for 2D and 3D. This comparison shows that for the 3D experiment, the original boundary length percentage is similar to that of the swept area. This indicates that boundaries present move, generating swept areas. For the 2D experiment the proportion of swept area is far less than that of total boundary length. This indicates that a smaller fraction of the boundaries present in the 2D sample move. For both experiments a similarly shaped distribution was seen for swept area fraction, though the relative frequency of moving boundaries in 2D is significantly lower than in the 3D experiment (Figure 4a).

Figure 4.

Comparison between the percentage of area swept by moving LABs and boundary lengths in the 3D and 2D annealing experiments. (a) The swept area is displayed as columns and the original total boundary length as lines, both as a function of misorientation angle, and both as a percentage of total area. It is clear that movement occurs much more frequently in the 3D experiment; note that boundaries with misorientation of >4° are rare and therefore data is not statistically representative. Error was calculated based on a minor rotation of the 3D sample and mapping in slightly different positions. (b and c) 3DXRD maps of one x-y layer before (Figure 4b) and after (Figure 4c) heating. The greyscale represents the angular deviation from the Euler angle orientation at the red cross. LABs are shown in an interpolated color scale from 1 to 8°. Scalebar for Figures 4b and 4c is shown in Figure 4b and is equivalent to 40μm. The boundary outlined in red in Figures 4b and 4c moved during annealing. In Figure 4c the original position of the boundary is shown by a dashed line. The swept area is shaded. Blue arrows point to a boundary which has moved.

4. Discussion and Conclusion

[15] Our results show that it is possible to accurately reconstruct highly deformed microstructures in three dimensions. As in 2D SEM-EBSD experiments [Borthwick and Piazolo, 2010] annealing of a highly deformed microstructure resulted in both growing and shrinking or disappearing subgrains. Furthermore, Borthwick and Piazolo [2010] reported subdivision of subgrains into areas of like orientation, and increase and decrease of subgrain boundary misorientation angles. All of these features are also observed within the body of the crystal, demonstrating that the general microstructural behavior observed in 2D reflects behavior throughout the crystal. However, significant differences are seen in the absolute values of subgrain boundary migration rates, which we suggest arises from a significant influence on boundary migration from thermal grooving of LABs. Investigation of the surface topography, before and after heating, show that on the surface, topographic grooves form in the location of subgrain boundaries at high temperatures (Figure 5). The LABs experience drag at the groove tip which retards migration rate [Mullins, 1958; Brokman et al., 1995; Gottstein and Shvindlerman, 2010]. In the 3D experiment the boundaries are internal and as such not affected by this process; thus the boundary length corresponds to the boundaries that move. In the 2D experiment, even though boundaries have the same characteristics in terms of dislocation types as those in the 3D case, they extend to the surface. Therefore, these boundaries must overcome the added drag force exerted by the groove on the surface in order to move. As a consequence, many boundaries cannot move at all and are pinned. Caillard and Martin [1982]predict that the drag effect on subgrain boundaries will be less than that for grain boundaries, because of the greater surface tension of high-angle misorientation boundaries. Consequently, the drag effect on grain boundaries is anticipated to be greater than for LABs; however, a comparative 2D–3D experiment on a polycrystalline sample is required to confirm this prediction. Based on our results we predict that relative migration rates will be similar while absolute rates will not accurately describe behavior in the body of the crystal.

Figure 5.

Comparison of surface properties of 2D sample and location of low angle boundaries; (a) secondary electron (SE) image taken before heating where difference in gray scale signifies topographic differences (bright spots are minor charging which disappeared upon heating to 100°C). It is not possible to distinguish the subgrain boundaries. (b) SE image of the same area after heating for ∼6 h; subgrain boundaries are clearly seen due to extensive thermal grooving at the boundary sites. (c) EBSD band contrast map showing in different gray scale slight differences in orientation; subgrain boundaries are shown in white. Arrows show that corresponding boundaries can be seen in both images. Scale bar in Figure 5a is equivalent to 500 μm.

[16] The presented experiment demonstrates that the 3DXRD technique is applicable for crystalline materials with complex internal subgrain structure commonly observed in geological materials. Future experiments utilizing the quantification techniques presented here and existing high-temperature and/or high-pressure set–ups [Duffy, 2005, 2008; Bass and Parise, 2008] open up new avenues of mineral investigation with which changes in mineralogy and microstructure can be tracked in space and time. Possible applications include the study of phase transformation and nucleation of new phases with time while having complete spatial control. 3DXRD studies will be complementary to more traditional experiments such as bulk experiments and two dimensional, in situ experiments.

[17] Results of our study confirm those derived from 2D experiments. However, even though relative mobilities are reliable from 2D experiments, surface effects (thermal grooving) at an exposed surface do markedly influence the development of the substructure by pinning subgrain boundaries and halting or slowing migration. Similar studies looking at the dynamics of complex microstructures in terms of crystallography and phase promise significant advances in the understanding of grain scale processes crucial for eliciting macroscopic behavior.

Acknowledgments

[18] We would like to thank H. F. Poulsen, T. J. M. van der Linden, C. Peach, N. Walte, G. Pennock, P. Bons, M. Jessell and A. Griera for their part in the development of this manuscript. Gratitude is expressed for the funding of the 6 day experiment by the European Synchrotron Radiation Facility. VB and SP acknowledge the financial support of the European Science Foundation under the EUROCORES Programme, EuroMinSci, MinSubStrDyn, ERAS-CT-2003-980409 of the European Commission, DG Research, FP6. SS gratefully acknowledges the Danish National Research Foundation for supporting the Center for Fundamental Research: Metal Structures in Four Dimensions. This is contribution 47/812 from the Australian Research Council National Key Centre for the Geochemical Evolution and Metallogeny of Continents (http://www.gemoc.mq.edu.au).