Strains, planes, and EBSD in materials science

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1 Strains, planes, and EBSD in materials science Electron back scatter diffraction (EBSD) has made an impressive impact on the characterization of materials by directly linking microstructure and crystallographic texture to provide very rich and quantitative datasets which in many instances have forced us to rethink how microstructure should be defined and analyzed. In this article we try to first give a very basic idea of how an EBSD map is obtained and what the data produced is like. We then give a brief history detailing some of the more major steps in developing the technique to what it is today. Finally, we explore two advanced and exciting technique areas of strain mapping and 3D microscopy and demonstrate how the EBSD technique continues to evolve to tackle new applications and bolster our materials characterization toolbox. Angus J. Wilkinson* and T. Ben. Britton Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, UK * angus.wilkinson@materials.ox.ac.uk Electron backscatter diffraction (EBSD) allows crystallographic information to be obtained from small volumes of material in a scanning electron microscope (SEM) which provides versatility in mapping orientation, crystal type, and perfection over a wide range of step sizes making it a powerful microstructural characterization tool. EBSD maps are formed by moving a focused probe of electrons point by point across a grid of positions on the surface of a bulk sample in a scanning electron microscope. At each point, some of the electrons backscattered from the sample are collected by a detector comprising a scintillator screen coupled generally by a lens, but sometimes by a fiber optic bundle, to a photon sensitive imaging detector, typically a charge coupled device (CCD) camera, to form an electron backscatter diffraction pattern. The scintillator is generally 30 to 40 mm in size and held close enough to the sample so as to subtend a relatively large angle (60 to 70 ). The sample 366 is generally highly tilted (60 to 80 ) toward the detector, as is depicted schematically in Fig. 1, to increase the quality of the pattern obtained. Each pattern consists of many bands of raised intensity that span across the screen. The bands, termed Kikuchi bands, appear at first glance to have parallel straight edges but in fact the edges are slightly curved and are the hyperbola formed by the intersection of Kossel diffraction cones with the plane of the detector. An example pattern from a CCD based detector is shown and compared to examples from earlier technologies and simulations in Fig. 2. Most importantly the centers of the bands are straight lines and mark the projections onto the detector screen from the point-like volume illuminated by the incident electron beam of the diffracting planes within the crystal. Patterns are transferred from camera to the computer for indexing and determination of crystal orientation, as detailed in Fig. 3. Briefly, the ISSN: Elsevier Ltd 2012

2 Strains, planes, and EBSD in materials science REVIEW Fig. 1 Schematic diagram showing the experimental set-up for EBSD observations. Hough transform algorithm is used to convert the nearly straight bands from lines to points which can be more easily located. With knowledge of the experimental geometry, the peak locations can be converted to a table of interplanar angles and compared with look up tables of expected angles for the phases present within the sample. With modern systems, pattern capture and indexing can be performed very rapidly (many 100s of patterns per second) and when combined with precise scanning of the electron beam, a detailed mapping of the sample crystallography (crystal type, crystal orientation, pattern quality etc.) can be obtained. These maps provide rich measurements of the sample microstructure. Fig. 4 outlines the major stages in the process of characterizing a sample using EBSD. No technique provides suitable information without adequate specimen preparation. For EBSD, standard metallographic processes of sectioning, grinding and polishing are the starting point but additional care must be taken to ensure that the final polishing steps leave the sample surface free of any sectioning damage, as the EBSD pattern is generated from a very thin surface layer (~40 nm) of material. Polishing with colloidal silica, chemical etching, electro-polishing, ion milling, and plasma etching are all methods that have been shown to work in various material systems 1-3. If the sample is etched an assessment of microstructure uniformity using an optical microscope is often time well spent. Once the sample is in the SEM chamber, it is sensible to have a quick manual interactive point and click survey of the sample to assess the quality of patterns being obtained, as at this point if the patterns are of poor quality, the preparation steps may need to be revisited. Secondary and/or back scattered electron imaging can be used to guide selection of the initial area and step size to use. Furthermore, if the measured crystal orientations need to be related to some external macroscopic direction (e.g., extrusion direction, rolling direction, growth direction) then care needs to be taken to align the sample correctly with the axes of the microscope and EBSD detector. This may seem obvious but it is sometimes overlooked or rather poorly performed in the rush to get on to rather more interesting parts of the operation. In practice, there is no one way of correctly setting up an EBSD scan as the parameters used depend on many competing factors including the nature of the sample and the information that is required. For instance, if the main aim is to measure the overall crystal texture with little regard for the grain size and morphology, then it is sensible to use a relatively coarse step size so as to quickly asses many grains within the sample. In other situations such as an analysis of the path taken by a fatigue crack and assessing damage in the surrounding lattice, then it would be sensible to choose a smaller step size and a slower and more accurate use of the pattern capture and peak detection algorithms (i.e., increased resolution in the Hough transform and longer exposure times) to realize an increase sensitivity in the measurement of intragranular misorientation. For samples which are entirely unknown at the outset, it is generally useful to run a rather quick map with widely spaced measurement points, or a line scan, to get an estimate of the grain size and to visualize the microstructure morphology before deciding on settings for more detailed work. For all these applications, assessment of how representative a given dataset might be should be made. For example if the grain size distribution is known to be unimodal and the average grain size is the only requirement then we agree with Humphreys 4 and Randle s 5 guidance that a minimum of 200 grains should be sampled, with at least ~10 points across a grain, i.e., 100 points per grain so that a relatively modest map of points results, with the step size set at approximately a tenth of a first guess at the grain size. If the grain size distribution is required, rather than just the average, then a similar but slightly more elaborate assessment of the size of the required dataset can and should be made. Similar assessment of the size of datasets required to establish 367

3 REVIEW Strains, planes, and EBSD in materials science (a) (b) (d) (c) Fig. 2 Electron backscatter patterns: (a) High angle diffraction pattern from lead sulphide captured by Alam et al. 6 on film, (b) picture of monitor showing pattern obtained using SIT camera with BBC micro-computer graphics overlay indicating indexing 15, (c) EBSD obtained using a current day CCD-based EBSD detector, (d) kinematic and (e) dynamical simulations of EBSD patterns from Si 101. sub-grain size, texture, phase fractions in multiphase materials can also guide quantitative measurement of microstructure with EBSD 5, just as it does with other techniques. An example of the information available from an EBSD dataset is shown in Fig. 5, in this case from a Ti-15wt%Mo alloy. The first map (Fig. 5a) distinguishes regions of the high temperature retained bcc phase in blue, from the low temperature hcp phase in red. We find that ~20 % of the phase has transformed to. Some information concerning the crystal orientations is revealed in Fig. 5b in which the color of every point depends on the crystal pole along the surface normal direction, through the color-key provided for each phase. This makes it clear that there are several grains within the field of view and within a particular grain there are one or more colonies of lathes with similar orientations. Here mapping of the orientation data makes it clear that changes in lathe crystallography are linked to changes in the alignment of the long axis of the lathe (noting that we are looking at a 2D cross section from a 3D microstructure). We can also see that phase has formed on many of the grain boundaries. Looking in more detail at the crystal orientations of the in relation to the parent grains we can see that the Burger s orientation relationship is obeyed: This type of information can be obtained very quickly using EBSD and commercial EBSD software packages provide many of the analysis tools that are required. Repeating this process for a larger area with a finer step size could be used to examine quantitative metrics such as sample macro (e) and micro texture (separating alpha and beta phases automatically), beta grain size, lath morphology and intergranular misorientations. Two very useful reviews of strategies for EBSD analysis and quantitative analysis of microstructure have been given by Randle 5 and Humphreys 4 respectively. A brief history of EBSD In 1954 Alam, Pashley and Nicholson 6 recorded onto EM film patterns which we now call EBSD patterns (see Fig. 2a) and observed that the pattern contrast was greatest when the sample was inclined so that the beam was incident within ~20 30 of the surface plane. They also noted that the part of the pattern at low take-off angles gave the highest contrast which was at best 15 %. Today s EBSD experiments adopt geometries that are in accord with these earliest observations with 20 between the sample surface and incident beam routinely used. In the 1970s Venables and co-workers 7-9 implemented the technique on a VG STEM operated in conditions more usual for an SEM and recording patterns on film either directly exposed to electrons within the chamber or using an externally mounted film camera coupled to a scintillator screen within the microscope chamber. Significantly they showed how the patterns could be used to measure the orientations of micro-crystals selected with the scanned beam in the SEM and gave a detailed error analysis estimating the orientation accuracy to be 0.5 to 1 very similar to today s measurements 8. Dingley who had been working on micro-kossel diffraction picked up the EBSD technique and pushed it forward by using a low light level ISIT camera to view the scintillator and overlaying the video output from this with graphics from a BBC micro-computer allowing a significant increase in the rate of pattern indexing and orientation measurements An example pattern from this type of set up is shown in Fig. 2b. This is one of the very earliest attempts at integrating capture of video information at a microscope to enable quantitative on-line analysis. Pattern indexing methods were improved so that minimal user input of only 3 zone axes positions were required to index and calculate orientations for patterns from cubic crystals 14, non-cubic crystals 16 and full automation of the analysis set as a clear goal very early on. The main materials science challenge EBSD was aimed at in these early days was in grain boundary characterization, a theme that continues to this day, and in particular identifying any significant special properties associated with low CSL boundaries, e.g Other topics that were explored were possibilities for phase identification including combining EBSD with local chemistry from EDX 20. A further notable study by Baba-Kishi and Dingley attempted to distinguish between different space and point groups from symmetry elements and systematic reflections in EBSD, again a topic that has been returned to more recently with much greater image analysis and computing power available now 24. The next big advance in the method came with automation of the band detection step which finally allowed the whole process of pattern collection and indexing to be undertaken without user intervention. By adding in computer control of the SEM beam position it was then a relatively simple task to implement EBSD orientation mapping. The Yale group of Adams, Wright, and Dingley (on sabbatical from Bristol) 25,26 first implemented a Burns algorithm for band detection but moved to the modified Hough transform which the Risø group (Krieger Lassen, Juul 368

4 Strains, planes, and EBSD in materials science REVIEW Fig. 3 Overview of EBSD indexing procedure showing pattern capture through to determination of crystal orientation. Jensen and Conradsen) had shown to be successful Both groups had successfully implemented automated EBSD mapping by the early 1990s. Goehner and Micheal 30 showed that phase discrimination is possible by comparing measured interplanar angles to those expected from the known crystallography for each of a wide range of possible phases held in a database. The problem to be overcome here is in reducing the number of possible phases to a manageable level either through knowledge of local chemistry or by the primitive lattice volume. Application areas EBSD has now been used for many aspects of materials characterization including characterization of grain boundary types, establishing epitaxial relationships between layers on substrates in metal, semiconductor and superconductor systems, characterizing texture and its changes during deformation and annealing in metal alloys and geological samples, establishing links between grain size and texture components during deformation and annealing, contributing to determination of grain boundary energy through thermal grooving, and ex situ and in situ experiments on grain boundary mobility. Although long, this list is not exhaustive and so we have decided to explore in detail only the following two aspects of strain measurement and three dimensional characterization. We have selected these aspects as we feel they are currently undergoing considerable development (and of course are of significant interest to the authors). 369

5 REVIEW Strains, planes, and EBSD in materials science Strain measurement Early work with EBSD concentrated on annealed structures however there has always been interest in applying EBSD to deformation studies. Initial attempts followed earlier work with ECP patterns, e.g in using the blurring of the EBSD patterns to assess the level of cold work. These methods are not as well established as for peak broadening of XRD and/or neutron diffraction and results have not be quantified in terms of dislocation densities but instead calibration samples are used to read across pattern blurring parameters to equivalent plastic strains. Applications were to superalloys in creep 35, Al 36 and Al-SiC MMCs 37, 38, and distinguishing between deformed and recrystallized grains 29. Since automated EBSD mapping has been available pattern quality has not been used so much for deformation studies in any quantitative sense. Instead plastic deformation studies have concentrated on use of intragranular misorientations which result from the residual dislocations accumulated during plastic straining. Various empirical metrics have been suggested and again in some cases calibration samples have been used to read across from these parameters to equivalent plastic strain. Methods exist to estimate a lower bound on the dislocation density either by a physically motivated minimization of dislocation line energy or a computationally convenient minimization of the square of the densities of the different dislocation types 39,40. Being physically based this approach is also being used by the X-ray synchrotron 41,42 and extensively within the micromechanical modeling communities. Grand challenges within the materials science and engineering communities will benefit from the use of a common physically based framework such as the Nye tensor to compare and combine results across these differing and complementary techniques. Accurate analysis of elastic strain, or lattice parameters, from measurement of Kikuchi band edge positions though Bragg s law has largely proved unsuccessful, despite some success with ECP 46, primarily because Kikuchi lines of sufficiently high order are not present 47,48. Goehner and Micheal 49 have explored the use of HOLZ rings for lattice parameter determination but found limited sensitivity for strain measurement and these rings are quickly removed by plastic deformation and so the method would not be very general. The most successful form of elastic strain measurement to date has been performed by measuring changes in interplanar angles and therefore determination of the deviatoric components of the elastic strain tensor. This can be performed using cross-correlation functions to determine small shifts in the patterns compared to a reference pattern obtained from the crystal in a known strain state. The approach can be found in the early work of Troost et al. 50 and Wilkinson 48,51,52. The method was improved notably by Wilkinson Meaden and Dingley with the geometry altered from an initial cumbersome long camera length-low capture angle setup to the more conventional large capture angle set-up while retaining a sensitivity of ~10-4. Several other groups have now implemented this method or modifications of it or are using a commercial version *. In this approach one pattern is used as a reference and small shifts are measured for a number of regions of interest (ROI) dispersed across the wide capture angle of the EBSD pattern. In common with various other image analysis applications the shifts are determined automatically using cross-correlation analysis and sensitivities of a few hundredths of a pixel can be obtained, although this depends on the pattern quality. These pattern shift and their systematic variation across the screen can be related back to the magnitude and nature of lattice strain variation and lattice rotation relative to the reference pattern 51-55,60, The strain sensitivity of ~10-4 can be thought of as measurement of shifts to a few hundredths of a pixel compared to sample to screen distances of a few hundred pixels. Two of the most recent improvements in the method have been firstly to increase the number of ROIs used in the analysis and move to an robust iterative fitting analysis to reduce the effects of outlier shift measurements on the resulting strain and rotation analysis 67, and secondly to use a remapping of the test pattern to remove the larger lattice rotations which cause errors in the smaller elastic strains 68,69. The most significant remaining challenge for strain mapping is the so-called reference pattern problem. In many circumstances there is a location on the sample from which a strain free reference pattern can be obtained with the crystal in the required orientation (e.g., far field from the deformed area of interest). However there are many more where this is not the case and so the measured strains represent variations from an unknown strain state at the position at which the reference pattern was obtained. One route to overcoming this is to use simulated patterns for the reference as suggested by Kacher et al. 57, although many of the specifics in the approach used by Kacher et al. have been criticized mainly due to the lack of fidelity in the simple simulations used and the lack of certainty over the detector geometry and aberrations 70, 71. An alternative to cross-correlation analysis, that does not rely on a reference pattern, has been suggested by Maurice and Fortunier 72 who use the 3D-Hough transform as a means of increasing the precision of band center positions, and thus interplanar angles, compared to the standard Hough transform. Assessment of simulated patterns suggested a sensitivity of , but factors such as noise and asymmetry of the Kikuchi band profiles are likely to significantly increase errors for measurements on real patterns which have yet to be reported. Applications of the cross-correlation analysis have been to both functional and structural materials. Early measurements were reported for SiGe alloys grown as unrelaxed blanket films on Si substrates in plan view 48, 51, 52 and in cross-section 54, 55. Work on SiGe/Si systems patterned with mesas has provided good agreement between EBSD measurements and elasticity theory 60, 73, 74. Further validation of the EBSD method has been provided by the group at NIST who have compared EBSD results with micro-raman 65 and AFM 66 measurements near wedge indents in Si. They assessed the stress sensitivity of the EBSD measurements to be ~10 MPa. Good agreement between EBSD and micro-raman has also been given by Tomita et al. 64 for strained Si on insulator and SiN/Si systems. Ishido et al. 62 have examined cross-sections of GaN structures including a 5 nm AlN/25 nm GaN multilayer for which they give a line scan within which the 50 repeats of the multilayer can be distinguished indicating that good spatial resolution can be achieved. Speller et al. 75 have recently widened the scope of cross-correlation EBSD studies by using it to map changes in c/a ratio with chemistry obtained from EDX in the iron containing Fe y Se 1- Te superconductor. Applications to structural metallics began with single x x crystals including fatigue crack tips in superalloys 54, and tensile cracks in tungsten 76 or single grains of polycrystals including mapping strains and dislocation densities near indents in Fe 40 and Ti 45, phase transformation induced strains in martensitic steels 58,77 and thermally and mechanically 370

6 Strains, planes, and EBSD in materials science REVIEW Fig. 4 Flow chart indicating significant steps in a typical EBSD observation. induced strain localization near hard inclusions in a superalloy 78,79. The method has also been applied to polycrystalline Ti-6Al-4V deformed in uniaxial tension at room temperature 80 and by hot rolling 81 in studies aimed at determining dislocation densities using the Nye tensor. Ojima et al. 63 have recently reported the first in situ deformation of a polycrystal coupled with the cross-correlation EBSD method which successfully demonstrates that grains with <100> along the tensile axis tend to continue increasing in elastic strain beyond the applied stress level at which <110> aligned grains tend to show a saturated elastic strain. These generalities are in agreement with volume averaged behavior seen for the same alloy using neutron diffraction, but the EBSD shows significant grain to grain variation which presumably depends on the local neighborhood. To illustrate the data available from the cross-correlation based analysis we will examine the elastic strains and rotations measured near a Vickers hardness indent in (001) Si. Fig. 6 (upper left) shows the misorientations near the indent measured by conventional Hough transform analysis along with a wireframe showing the crystal orientation. The indent was made with a load of 50 gf, which was large enough to generate radial cracks which radiate out from the center along the indent diagonals which are aligned with the [110] and [1-10] direction corresponding to horizontal x 1 and vertical x 2 axes. EBSD measurements were made on a JEOL JSM 6500F FEG-SEM at a beam energy of 15 kev, a beam current of ~16 na and a sample tilt of 70. EBSD patterns were recorded at the full ~1k 1k pixel 12 bit deep resolution of the peltier cooled CCD camera and saved to hard disk for batch-wise off-line analysis using CrossCourt3 software. The data acquisition rate was approximately 1 pattern/sec with the camera gain kept low so as to achieve good signal to noise and the μm area was mapped at a step size of 1 μm in approximately half an hour. Two data quality parameters are used to assess the dataset (lower left 371

7 REVIEW Strains, planes, and EBSD in materials science (a) (b) Fig. 5 Example EBSD data obtained from Ti-15%Mo. Inserts show raw diffraction patterns which are successfully indexed to determine crystal orientation and phase (a). The resultant data set can be separated into maps showing alpha and beta phase orientations (b) shown here with respect to the sample normal. In this alloy, the Burgers orientation relationship is seen easily, as shown for the colony/parent beta grain insert, which relates the basal plane (0001) and an <11-20> type lattice direction in the hexagonal phase, with a {110} plane and a <111> type lattice direction in the beta phase. of Fig. 6). The geometric mean of the normalized cross-correlation peak heights shows low values for regions within the indent due to shadowing effects from the topography of the sample and pattern blurring from the extensive deformation. The mean angular error describes the difference between measured pattern shifts and back calculations of pattern shifts based upon the best fit solution for the strain and rotation tensor. There is generally strong correlation between regions with low cross-correlation peak height and large mean angular errors. Thresholds can be used to remove the poorer quality data from subsequent analysis. In this instance patterns generating a cross-correlation peak height of less than 0.3 or a mean angular error of greater than 10-3 rads were removed from other maps. All components of the strain and lattice rotations are determined, and these are shown in pictorial tensor layout in Fig. 6. The lower parts of the tensors are not shown as the strain tensor is symmetric (i.e., = mirror across lead diagonal) and the rotation tensor is antisymmetric Ij ji (i.e., = - mirror across lead diagonal and swap sign). ij ji The 11 strain along the horizontal axis is seen to be compressive above and below the indent and tensile to the left and right with the magnitude of the strains falling significantly with distance from the center of the indent. For the 22 strain this is swapped so that the compressive regions are to the left and right while the tensile strains occur above and below the indent. This is in accord with expected compressive radial and tensile hoop strains that should develop. The in plane 12 shear strains are also consistent with this and show clear positive and negative lobes at ±45 to the horizontal. The lattice rotation about the horizontal axis shows 23 positive and negative rotations above and below the indent that result from the uplift of material surrounding the indent, to account for the materials volume displaced from the indent impression itself. A similar effect is seen for the rotation about the vertical x axis. Abrupt changes 31 2 in lattice rotation are accommodated by opening displacements caused by the radial cracks; this is most clearly demonstrated in rotations 12 (about the surface normal) which are generally of smaller magnitude. This is expected for mode I cracks loaded in tension and has also been seen for cracks in single crystal tungsten 76. This relatively simple test case gives an indication of the completeness of the quantitative data available from EBSD strain mapping. 3D microscopy The development of automated data collection in three dimensions using EBSD has opened up an exciting field of materials characterization. Two 372

8 Strains, planes, and EBSD in materials science REVIEW (a) (b) (c) Fig. 6 Information obtained from a high angular resolution EBSD map of a 50gF micro hardness indent in single crystal silicon. Upper left shows the crystal misorientations with an overlay indicating the how the crystal is oriented. Lower left gives the two data quality parameters: mean angular error (lower is better) and cross-correlation peak height (normalized to between 0 and 1 with 1 best). To the right are shown the elastic strain (top) and lattice rotation (bottom) tensors. These are displayed as pictorial tensors with a map shown for each non-zero component in the upper part of the tensor with the symmetry operator needed to populate the lower part also indicated. dimensional information obtained from surface sections of materials, can be descriptive for an elegantly designed experiment. However, in many cases additional information regarding the structure and connectivity of microstructural units in the third dimension would add significant value by reducing our reliance upon assumptions required to extend our observations to describe microstructures completely. Data obtained with 3D EBSD can be used to populate models with realistic microstructural information, for example with finite element or fast Fourier transform based crystal plasticity modeling For these data sets, the advantage of EBSD over other methods of observation (e.g., optical or secondary electron image acquisition) is that crystalline materials can easily be segmented and characterized using orientation information. In many cases this provides greater contrast than simply relying on electron (or ion beam) channeling contrast or the use of etchants to reveal microstructural features. In addition, orientation information combined with simple rules regarding microstructural connectivity can be utilized to improve the fidelity of the 3D reconstruction. Furthermore, the EBSD analysis can easily be extended using energy dispersive spectroscopy 85. Production and successful exploitation of 3D EBSD involves three major steps: data acquisition; model generation; and quantitative analysis. Data acquisition is performed by successively removing layers from a block of material and observation of the newly revealed surface. Any preparation route that produces a surface suitable for the successful generation of high quality diffraction patterns can be used. Mechanical polishing and focused ion beam machining are the two leading routes. Mechanical routes utilize readily available equipment but require many man hours to observe multiple slices. Material removal rates are high, which limits the minimum slice thickness (>1 μm) but potentially allows sampling of large volumes of material. In addition, precise calibration of the thickness of the layer removed is difficult and can introduce uncertainty into the data reconstruction step. Time can be saved if orientation information is not required for every slice, instead recording optical micrographs of an etched surface for every slice and orientation maps for every n th slice can be used 86. Uchic and co-workers are currently developing a system which integrates mechanical polishing, SEM operation and EBSD acquisition with robotic interchange to aid automation 87. Such a system should make data acquisition using 373

9 REVIEW Strains, planes, and EBSD in materials science mechanical routes significantly less demanding and greatly increase the quality and size of the available 3D datasets. In contrast, dual beam SEM-focused ion beam (FIB) instruments are expensive but recent developments in automation and instrument stability have made data acquisition much simpler. Data is acquired by moving the sample into a position suitable for EBSD observation, scanning the top surface, moving the sample into a position suitable for milling and removing a thin layer. This is repeated for as many slices as the user requires (or time allows). Slices as thin as ~50 nm can be successively removed, making the analysis of submicron grain sizes possible 88. However, the sampling volume attainable by this route is significantly smaller due to limited material removal rates. Furthermore, as the EBSD camera capture angle is relatively large, the volume of material that must be removed for each slice typically must be larger than the area scanned (or else edges of the pattern can become shadowed). A specimen geometry used is a mechanically polished sharp right angle. This can be used either to cross section a bulk material or removal of material from a standard cross section. For example, Zaafarani and co-workers used this geometry to sample the deformation flow fields beneath nanoindention impressions in copper revealing the full 3D character of the deformation field, which compared well with their finite element prediction 89. Alternatively, if significantly large volumes are required, it may be more efficient to manufacture a protruding finger -like specimen, which can be gradually shortened to remove each slice 87, 90. This geometry reduces EBSD pattern shadowing, waterfall and re-deposition artifacts as each free surface remains as a protrusion. Knowledge of the microstructure and the eventual use for the data obtained is essential to make decisions regarding slice thickness and EBSD step size. For both of these acquisition routes, the choice of slice thickness is determined at the lower end by the limits of the sectioning technique and at the upper end by the speed (and accuracy) of the material removal process. The choice of EBSD step size is largely dependent on the data acquisition speed available; here the use of a fast camera capturing several hundred patterns per second can be desirable, either enabling larger areas to be scanned or a finer step size to be chosen. The combination of step size and slice thickness defines the size and shape of the unit voxel (volume pixel) in the final map. The area scanned combined with the thickness of each slice and the number of slices viewed defines the volume of material sampled. Choice of voxel size and shape and the volume of material sampled is dependent on the nature of the experiment performed. In general, this is a combination of both the amount of instrument time available, the fidelity of the data required, the nature of the problem studied and the amount of effort required. For example, in order to analyze the nature of grain boundary planes within a material it is necessary to obtain many slices within each grain in order to accurately trace the grain boundary plane region (as a general rule of thumb Groeber et al. suggest at least 10 slices per grain 86 which is similar to the suggestion of Humphreys et al. for 2D EBSD noted previously 4 ). Yet, if the distribution of grain orientations in a 3D volume or the generation of a mesh for finite element modeling is required, then a significantly lower sampling frequency is necessary, thus sampling a larger volume of material, which may ensure that a representative volume element is sampled. Once several slices have been obtained, reconstruction of the 3D model must be performed. Firstly, the data that has been acquired will not be a perfect representation of the sampled material: successive removal will not consistently reproduce rectangular sections (due to a misalignment during the mill step); there will be optical distortions in the electron microscope; each slice will be misaligned with respect to its neighbors; there will be mis-indexed points; and finally, we do not have a continuous description of the microstructure (i.e., approximating curved lines on grain boundaries as a staircase). Careful data acquisition will reduce the magnitude of the sample mis-alignment and optical distortions (yet they will always be present). Generally the use of a suitable fiducial marker of a known shape (i.e., a milled circle or cross for FIB polishing or a series of hardness indents for mechanical polishing) can be combined with image correlation to reposition the sample well between each slice. In addition, these features could be imaged to produce a distortion free micrograph (e.g., using a travelling optical microscope or normal incidence SEM) to assess the presence of optical distortions 91. Subsequently a suitable correction could be applied, e.g. using an affine transformation 86, to ensure that the appropriate data cube is reconstructed. Physical alignment of the fiducial markers results in close alignment of each successive slice. Typically, alignment of the slices prior to reconstruction of the data cube is still required. A high quality reconstruction can be performed by aligning not only microstructure features, such as grain boundary triple points, but also local crystal misorientations between voxels in neighboring slices. One strategy suggested by Groeber and colleagues, is to allow iterative realignment of the slices in the form of translations in x and y (but in theory it could also include any potential misalignment such as sample tilt) in order to reduce the total misorientation in the cube 86. Clearly, care must be taken in dealing with poorly indexed points and grain boundary regions. Correction of poorly indexed points can be performed in a similar fashion to convention 2D clean up routines, but now may include information gained from voxels in neighboring slices. At this point we have a data stack that consists of voxels which are well alignment spatially with respect to each other but they may not yet represent the microstructure as fully as our interrogation requires. For example if the morphology of the individual grain boundary planes is important, then the apparent stepped nature of the interface inherited from the discrete sampling strategy must be addressed. For this application, neighboring voxels of significantly different orientation could be segmented from the data stack. Subsequently for each neighbor voxel a marching cubes algorithm can be utilized to transform the rectangular faceted voxel into a series of triangular facetted polygons 92. Finally additional smoothing of the microstructure can be performed as required. One example of 3D-EBSD obtained from FIB-SEM tomography is shown in Fig. 7, courtesy of Groeber and co-workers (described in detail elsewhere 87, 90, ). Here a polycrystalline nickel superalloy sample has been examined with FIB-SEM tomography and 3D EBSD with voxel size of nm 3. Fig. 7a shows a reconstruction of the 3D data cube after 374

10 Strains, planes, and EBSD in materials science REVIEW initial alignment of consecutive slices, allowing for small shifts in the EBSD maps for each slice to minimize total misorientation between neighbors, and then application of a marching cubes algorithm to render triangular facets. In order to analyze the nature of grain boundary planes, the grain boundaries have been smoothed to reduce alias induced roughening caused by discreet nature of voxel sampling. Qualitative analysis via rendering of particular grains in the volume showing Fig. 7c hints at some of the quantitative metrics that can be explored with in such a data cube, such as grain volumes, misorientation and other metrics which have two dimensional counterparts 90. Data of this type can be used to measure five parameter grain boundary plane distributions, which includes not only four parameters from standard 2D EBSD, grain boundary misorientation (axis 2, angle 1) and surface trace (1) but in addition the subsurface grain boundary plane inclination 94. While FIB-SEM or mechanical section routes of 3D EBSD provides a wealth of data on volumes of material at an intermediate length scale, resolution of the technique is limited by the probe size (~20 nm) and slicing and reconstruction ability at smaller length scales. Analysis of truly nanocrystalline materials of very fine detail in microstructures is therefore difficult and TEM experiments on these materials may be more suitable 96 and are certainly complementary. At larger length scales the total analyzed volume of material and the sampling resolution is limited primarily by experiment time and instrument stability. Recent advancements in 3D X-ray diffraction (XRD) microscopy provide similar information non-destructively with limited resolution 97,98. One advantage with these techniques is that although 3D-XRD experiments are difficult to perform, the technique is fundamentally nondestructive and thus in addition to sampling larger volumes of material, in situ dynamical information can be obtained. Fig. 7 Three dimensional reconstructions of microstructure obtained from a nickel superalloy (IN100): (left) after alignment and application of marching cubes; (middle) after grain boundary smoothing; (right) selected grains from the 3D model. The material volume analyzed measured 50 μm by 50 μm by 50 μm, with EBSD maps acquired after 250 nm FIB slices. Figure courtesy of Groeber, Rollett and colleagues 86, 90. Summary and outlook EBSD has come from being a very specialist technique being used in a small number of physics laboratories to a mainstream materials characterization tool. Potential of the technique to solve real materials problems was recognized near the outset and these end goals have always driven its development. In this field, technique development had been strongly associated with two aims: (i) looking for general solutions so that the tool can be rolled out easily from a specific initial problem to wide range of related ones and (ii) automation so the statistically significant datasets can be obtained for quantitative assessment of material microstructure. This has led to the powerful tool we have today with a vast range of applications which continues to expand. We have picked strain mapping and 3D microscopy as two areas which demonstrate that technique development is currently very active and to demonstrate the pace at which substantial advances have been achieved. In addition, we note that the work of Winkelmann on development of dynamical diffraction simulations and detailed analysis of the energy distributions contributing to Kikuchi bands within EBSD patterns 102 is another on-going major contribution. Work by Geiss et al. 103 on transmission-ebsd also contributes to a better understanding of the physics of generating EBSD patterns. We hope that these advances may develop into methods of crystal structure determination direct from EBSD patterns. We may also see some developments in detector technology over the next decade. We already see two competing trends in EBSD either attempting to go faster which has driven down pattern resolution, or to obtain as much detail in the pattern as possible which drives down speed. More sensitive detectors would be of benefit in both cases. It seems very likely new detector strategies being developed for X-ray and TEM may also lead to improved EBSD detectors. EBSD has come a long way but the journey is far from over. Acknowledgements We gratefully acknowledge funding from EPSRC (EP/E044778/1, EP/ G004676/1, and EP/H018921/1). We have enjoyed continuing discussions of the EBSD technique with Prof David J Dingley (University of Bristol) and Dr Graham Meaden (BLG Productions Ltd). We are grateful to Prof Tony Rollett (Carnegie-Mellon University) and Dr Michael Groeber (Wright-Patterson Air Force Base) for sharing and discussing 3D EBSD data with us. We also thank Dr Aimo Winkellman for his insight into the physics of EBSD pattern formation and simulation code used for Fig. 2e. References * CrossCourt 3, BLG Productions Ltd, Bristol, UK ( 1. Koll, L., et al., Journal of Microscopy (2011) 243, Schwarzer, R. A., Proceedings of the 10th International Conference on Textures of Materials 157, Wynick, G. L. and Boehlert, C. J., Materials Characterization (2005) 55, Humphreys, F. J., Journal of Materials Science (2001) 36, Randle, V., Materials Characterization (2009) 60, Alam M. N., et al., Proceedings of the Royal Society A (1954) 221,

11 REVIEW Strains, planes, and EBSD in materials science 7. Venables J. A. and Harland C. J., Philosophical Magazine (1973) 27, Venables J. A. and bin-jaya R, Philosophical Magazine (1977) 35, Harland C. J., et al., Journal of Physics E: Scientific Instruments (1981) 14, Biggin, S. and Dingley, D. J., Journal of Applied Crystallography (1977) 10, Dingley, D. J., Scanning Electron Microscopy (1981) Dingley, D. J. and Ferran, G., Micron (1977) 8, Dingley D. J., Scanning Electron Microscopy (1984) 2, Dingley D. J., Inst Phys Conf Series (1989) 98, Dingley D. J., et al., Scanning Electron Microscopy (1987) 2, Dingley, D. J., et al., Textures and Microstructures (1991) 14, Randle V and Brown A Philosophical Magazine A (1989) 59, Randle V, The measurement of grain boundary geometry (1993), Inst. of Physics. 19. Randle V and Dingley D. J., Scripta Metall (1989) 23, Dingley, D. J., et al., Institute of Physics Conference Series (1990) Baba-Kishi K. Z. and Dingley D. J., Scanning (1989) 11, Baba-Kishi K. Z. and Dingley D. J., Journal of Applied Crystallography (1989) 22, Dingley D. J., et al., Atlas of backscattering Kikuchi diffraction patterns (1995), Inst of Phys. 24. Dingley, D. J. and Wright, S. I., Electron Backscatter Diffraction in Materials Science, (2009), , eds. Schwartz, A. J., et al., Springer. 25. Wright S. I. and Adams B. L., Metallurgical Transactions A (1992) 23A, Adams B. L., et al., Metallurgical Transactions A (1992) 24A, Juul Jensen D and Schmidt NH, Proc. Recrystallisation Krieger Lassen N. C., et al., Scanning Microscopy (1992) 6, Krieger Lassen N. C., et al., Materials Science Forum (1994) , Goehner RP and Michael JR, J. Res. National Institute of Standards and Technology (1996) 101, Davidson, D., International Metals Review (1984) 29, Ruff, A., Wear (1976) 40, Davidson, D., Journal of Material Science Letters (1982) 1, Crompton, J. and Martin, J., Metallography (1980) 13, Quested P. N., et al., Acta Metallurgica (1988) 36, Wilkinson, A. and Dingley, D., Acta Metallurgica Et Materialia (1991) 39, Wilkinson, A., et al., Journal of Microscopy-Oxford (1993) 169, Wilkinson A. J. and Dingley D. J., Acta Metallurgica Et Materialia (1992) 40, Arsenlis, A. and Parks, D. M., Acta Materialia (1999) 47, Wilkinson, A. J. and Randman, D., Philosophical Magazine (2010) 90, Field, D. P., et al., Philosophical Magazine (2010) 90, Wang, L., et al., Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science (2011) 42A, Nix, W. and Gao, H., Journal of the Mechanics and Physics of Solids (1998) 46, Kysar, J. and et al., Journal of the Mechanics and Physics of Solids (2007) 55, Britton, T. B., et al., Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences (2010) 466, Kozubowski, J., et al., Journal of Appllied Crystallography (1991) 24, Keller, R., et al., Microelectronics Engineering (2004) 75, Wilkinson, A., Materials Science and Technology (1997) 13, Michael, J. R. and Goehner, R. P., Advances in Materials Problem Solving with the Electron Microscope, (2001), 39-49, eds. Bentley, J., et al., Materials Research Society. 50. Troost K. Z., et al., Applied Physics Letters (1993) 62, Wilkinson, A., Ultramicroscopy (1996) 62, Wilkinson, A. J., Journal of Electron Microscopy (2000) 49, Wilkinson, A. J., Scripta Materialia (2001) 44, Wilkinson, A. J., et al., Materials Science and Technology (2006) 22, Wilkinson, A. J., et al., Ultramicroscopy (2006) 106, Wilkinson, A. J., et al., Electron Backscatter Diffraction in Materials Science, (2009), eds. Adams, B. L., et al., Kluwer Academic/Plenum Publishers. 57. Kacher, J., et al., Ultramicroscopy (2009) 109, Miyamoto, G., et al., Acta Materialia (2009) 57, Tao, X. and Eades, A., Microscopy and Microanalysis (2005) 11, Villert, S., et al., Journal of Microscopy-Oxford (2009) 233, Krause, M., et al., AIP Conference Proceedings (2010),1300, Ishido, T., et al., Ieice Electronics Express (2007) 4, Ojima, M., et al., Acta Materialia (2011) 59, Tomita, M., et al., Japanese Journal of Applied Physics 50, Vaudin, M. D., et al., Applied Physics Letters (2008) 93, Vaudin, M. D., et al., Ultramicroscopy (2011) 111, Britton, T. B. and Wilkinson, A. J., Ultramicroscopy (2011) 111, Britton, T. and Wilkinson, A., Ultramicrscopy (2012), 114, Maurice, C., et al., Ultramicroscopy (2012) 113, Maurice, C., et al., Ultramicroscopy (2010) 110, Britton, T. B., et al., Ultramicroscopy (2010) 110, Maurice, C. and Fortunier, R., Journl of Microscopy (2008) 230, Wilkinson, A. J., Applied Physics Letters (2006) 89, Wilkinson, A. J., et al., Superlattices and Microstructures (2009) 45, Speller, S. C., et al., Applied Physics Letters (2011) 99, Murphy, J. D., et al., IOP Conf Series: Materials Science and Engineering (2009) 3, Wilkinson, A. J., et al., Journal of Strain Analysis for Engineering Design (2010) 45, Dingley, D. J., et al., Journal of Electron Microscopy (2010) 59, S155-S Karamched, P. S. and Wilkinson, A. J., Acta Materialia (2011) 59, Littlewood, P., et al., Acta Materialia (2011) 59, Britton, T. B., et al., Scripta Materialia (2010) 62, Bhandari, Y., et al., Computational Materials Science (2007) 41, Prakash, A. and Lebensohn, R. A., Modelling and Simulation in Materials Science and Engineering (2009) 17,. 84. Raabe, D., et al., Acta Materialia (2001) 49, West, G. D. and Thomson, R. C., Journal of Microscopy-Oxford (2009) 233, Groeber, M., et al., Electron Backscatter Diffraction in Materials Science, (2010), eds. Schwartz, A. J., et al., Springer. 87. Uchic, M., et al., Microscopy and Microanalysis (2011) 17, Zaefferer, S., et al., Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science (2008) 39A, Zaafarani, N., et al., Acta Materialia (2006) 54, Groeber, M. A., et al., Materials Characterization (2006) 57, Nolze, G., Ultramicroscopy (2007) 107, Khorashadizadeh, A., et al., Advanced Engineering Materials (2011) 13, Bhandari, Y., et al., Computation Materials Science (2007) 41, Rohrer, G. S., et al., Materials Science and Technology (2010) 26, Uchic, M., et al., Scripta Materialia et Materialia (2006) 55, Liu, H. H., et al., Science (2011) 332, Jakobsen, B., et al., Science (2006) 312, Suter, R. M., et al., Review of Scientific Instruments (2006) 77, Winkelmann, A., Ultramicroscopy (2008) 108, Winkelmann, A., Journal of Microscopy (2010) 239, Winkelmann, A., et al., Ultramicroscopy (2007) 107, Winkelmann, A. and Vos, M., Physical Review Letters (2011) 106, Geiss, R. H., et al., Microscopy and Microanalysis (2011) 17,