ELECTRON BACKSCATTER DIFFRACTION (EBSD) THE METHOD AND ITS APPLICATIONS IN MATERIALS SCIENCE AND ENGINEERING

Transcription

1 ELECTRON BACKSCATTER DIFFRACTION (EBSD) THE METHOD AND ITS APPLICATIONS IN MATERIALS SCIENCE AND ENGINEERING P. Cizek UNIVERSITY OF OXFORD, Department of Materials, Parks Road, Oxford OX1 3PH, GB Abstract The present work gives a brief overview of the current status of the electron backscatter diffraction (EBSD) technique. The fundamentals of the production of Kikuchi patterns are first discussed. An experimental set-up for the automated obtaining and processing EBSD patterns in scanning electron microscopy (SEM) is subsequently described and the relevant calibration and automatic Kikuchi pattern recognition procedures are briefly discussed. The derivation of both a crystallite orientation and a misorientation between two crystallites from an EBSD pattern is also described and various ways of the graphical representation of these characteristics are summarised. Several practical examples of the application of the EBSD technique in the field of metallic materials science and engineering are finally presented. 1. INTRODUCTION Electron backscatter diffraction (EBSD) technique, utilising Kikuchi patterns produced in scanning electron microscopy (SEM), represents a modern tool for the crystallite orientation determination [1-3]. This technique has a number of advantages over other diffraction methods, such as those used in the transmission electron microscopy or X-ray diffractometry [1,3], while its spatial resolution of approximately 200 nm coupled with an agular precision of about 1 are sufficient for a wide range of applications. The recently introduced fully automated EBSD systems [2], requiring a minimal amount of the operator involvement, allow the measurement of large numbers of crystallite orientations to be performed in a rather short time frame. The aim of the present work was to give a brief overview of the current status of the EBSD technique with emphasis on its applications in the field of metallic materials science and engineering. 2. KIKUCHI PATTERN FUNDAMENTALS Kikuchi patterns are essentially projections of the geometry of lattice planes in a crystal [1]. They arise as a result of the divergence of the electron beam in all directions as it penetrates the specimen. This means that all atomic planes in the crystal will interact elastically with the scattered beam and there will always be some electrons which impinge on lattice planes at the Bragg angle which is given by 2d.sinθ = n.λ (1) where d is the interplanar spacing for a family of planes, λ is the electron wavelength, n is the order of reflection and θ is the Bragg angle. In addition to these elastic scattering events, many electrons are scattered inelastically and give rise to a diffuse background in the pattern. When the Bragg condition (1) is satisfied, electrons which are incident on a lattice plane are reflected through the Bragg angle. After diffraction this results in two cones of electron radiation, from - 1 -

2 a single set of lattice planes, with generally unequal transfer of electrons along each cone surface. Consequently, if a flat surface of a phosphor screen is allowed to intercept the cones (Fig. 1), one conic section will appear darker and the other lighter than the background. Since Bragg angles are generally very small (typically about 0.5 ), the apex angle of the reflected cones is so large that a section through them approximates to a pair of parallel straight lines known as Kikuchi lines. electron beam cone 2 cone 1 crystal L screen 2θ hkl 000 dark K line light K line Figure 1. Three-dimensional schematic illustration showing the formation of two radiation cones during electron diffraction on a crystal lattice plane (hkl). The cones intersect the screen and are visible as a pair of parallel Kikuchi lines. Hence each pair of Kikuchi lines represents a plane in the crystal, the actual trace of the plane lying equidistant between the pair. It also follows from the Bragg equation (1) that the interplanar spacing is inversely proportional to the Kikuchi line spacing. The complete Kikuchi pattern is a product of the interaction of the scattered electron beam with all the lattice planes in the crystal. Important directions in the crystal occur where several planes intersect. These directions are called zone axes and appear in the Kikuchi pattern as prominent intersections of Kikuchi line pairs. The Kikuchi map is essentially a map of angular relationships in a crystal, as distances on the pattern are equivalent to angles. The total angular range of a single Kikuchi pattern will depend on the distance between the specimen and the camera. For EBSD, performed in SEM, the position of the camera with respect to the specimen is such that about 80 of the pattern is typically visible [1]. 3. EBSD PATTERN ACQUISITION 3.1 Hardware Configuration The current hardware configuration for automatic obtaining and processing EBSD patterns in SEM [1,2] is shown schematically in Fig. 2. A bulk specimen is placed to the scanning electron microscope chamber in a highly tilted position. The angle of incidence between the primary electron beam and the specimen surface normal needs to be high so that a highquality Kikuchi pattern was obtained on a fluorescent screen, which is placed typically at about 25 mm from the specimen. An optimum contrast is usually achieved at tilt angles between 70 and 80. The EBSD pattern visible on the screen is viewed using a high-gain fiber-optic camera, which removes any image distortions inherent to conventional camera lenses. The video images are processed by the camera control unit that is capable of subtracting a background. A background image is obtained when the microscope is in the - 2 -

3 image mode. The sample holder with a specimen in a tilted position is fixed on a piezoelectric x-y stage. Since the specimen surface is aligned parallel to the plane of the stage movement, translations of the sample within this plane keep the electron beam in focus. Small variations in the surface morphology do not influence the calibrated beam geometry noticeably. The camera control unit and the stage control unit are interfaced to a mini-supercomputer and, thus, the computer becomes the central control unit for both the stage and the video camera units. The computer has a frame capture board installed to capture the video images from the camera control unit and also contains a set of software programs for an analysis of the EBSD patterns. The computer controls the automatic EBSD investigation in the following manner. First, it tells the specimen stage (stage control) or the electron beam (beam control) to move to a given position on a pre-selected grid; second, it tells the camera control unit to process an image; third, it captures the processed image through the video digitiser board and fourth, it analyses the pattern and records the orientation data, the (x,y) position and an image quality parameter. This procedure is automaticaly repeated for all points on the grid. electron beam SEM SEM control unit phosphor screen camera mini-supercomputer move stage start image processing x-y stage fiber with specimen optics stage control unit camera control unit image digitiser capture image obtain orientation from image Fig. 2. Schematic of the hardware configuration of the fully automated EBSD system 3.2 Calibration Procedures There are three reference parameters which have to be measured in order to calibrate the geometry of an EBSD system. These are the position of the pattern source point SP on the specimen, the position of the pattern centre PC on the phosphor screen and the distance L from SP to PC. These parameters might be obtained by the known orientation method where a single crystal of, usually, silicon having surface normal [001] is used to provide the reference orientation [3]. The single crystal is mounted in a precision pre-enclined holder such that the beam strikes the specimen at an angle of 70.6 ± 0.5, with respect to the surface normal. Thus, the specimen tilt is fixed. The rotation about the surface normal is fixed by mounting the calibration crystal so that [011] is parallel to the horizontal direction in the microscope, the X M axis (Fig. 3). We define the orthogonal reference axes of the calibration crystal (specimen) as X S, in the plane of the surface parallel to X M (that is parallel to left-right microscope stage traverse); Y S, also in the plane of the surface; and Z S, the direction normal to the surface. For the calibration crystal X S is [110], Y S is [1-10] and Z S is [001]. The source point SP and the position of the specimen reference axes with respect to the microscope axes are the same as for the calibration crystal, provided the specimen holder geometry is invariant between the two. The specimen coordinate system system then has to be related to the screen coordinate system via a set of axes which is common to both of them, namely the microscope axes. Figure 3 illustrates the three sets of reference axes: those for the specimen (S), screen (F) and - 3 -

4 microscope (M). Since the angle between [001] and [114] for the cubic calibration crystal is 19.4, which corresponds to the tilt of the specimen, Y M axis is parallel to [114]. If the phosphor screen is mounted so that it is normal to Y M, then the position of the [114] zone axis on the screen is the pattern cetre PC. The specimen to screen distance, L, can be calculated using the relationship [3] L = N/tan(19.4 ) (2) where N is the distance between poles [001] and [114] on the EBSD pattern of the calibration crystal, corresponding to an angle of 19.4, as shown in Fig. 3. electron beam Z M X S Z S X M [001] Z F X F N 19.5 L SP specimen Y S Y F PC = [114] Y M SEM stage 70.5 phosphor screen EBSD pattern Figure. 3. Schematic of the geometry of the EBSD system showing the sample (S), screen (F) and microscope (M) reference frames. Also illustrated is the calibration procedure utilising an oriented silicon single crystal giving rise to the Kikuchi pattern on the screen (see text). Another calibration method, which does not use a silicon crystal, requires movement of the phosphor screen relative to the specimen [1]. During movement of the screen, the only point in the EBSD pattern whose coordinates remain unchanged is the pattern centre PC. Thus, lines connecting the locations of at least three zone axes, obtained before and after movement of the screen and overlapped on one common pattern, should intersect in one point, corresponding to the pattern centre. The error in the beam normal can then be directly estimated. Having defined the PC, the specimen to screen distance L can then be found from the location of two or more zone axes in any diffraction pattern of a known crystal structure [1]. 3.3 Automatic Pattern Recognition and Indexing Modern fully automated EBSD systems are based on the automatic recognition and indexing of diffraction patterns [2]. The first step in an automated analysis of EBSD patterns consists of automatic detecting of the Kikuchi line positions by a computer. It is now generally agreed that the Hough transform [2,3] provides a reliable and robust procedure to accomplish the above task. In this procedure, the intensity of each pixel of the filtered image of an EBSD pattern is first determined. The Hough transform then maps each pixel onto a curve in Hough space, each point on the curve being assigned an intensity equal to that of the pixel. The equation of the curve is ρ = x i.cosθ + y i.sinθ (3) where x i and y i are the coordinates of the ith pixel in the image and θ takes all values from 0 to π. Thus, there is a different curve for each pixel in the image. The property of the transform - 4 -

5 is that the curves, ρ, for co-linear pixels in the image, such as those comprising a Kikuchi line, all intersect in Hough space at the same point. When an EBSD pattern is so mapped, each Kikuchi line will be transformed to a single point having an intensity greater than the background, by an amount equal to the sum of the intensities of the pixels along the length of the original Kikuchi line. It is now relatively easy to find such points. Once found, the position of the original Kikuchi line can be determined from the value of ρ and θ of the corresponding point. The relevant property of the Hough transform is that ρ is equal to the length of the normal, constructed from the origin of the coordinate axes, to the line and θ is the angle between this normal and the x axis [2,3]. The intensity difference between a Hough peak and the background gives a measure of sharpness of the Kikuchi pattern and, thus, can serve as a parameter reflecting an image quality. The angles between the crystal planes giving rise to the Kikuchi lines are then found, together with the Kikuchi band widths which are inversely proportional to the corresponding interplanar spacings, as follows from the Bragg equation (1). Using the calibrated value of the distance L (see Section 3.2), these spacings can thus be determined. Computer programs, performing indexing of the Kikuchi patterns, are based on the comparison of measured interplanar (or interzonal) angles and spacings with theoretical values calculated for the current crystal structure [4] 4. ORIENTATION INFORMATION DERIVED FROM EBSD PATTERNS 4.1 Determination and Representation of a Crystallite Orientation Once the Kikuchi pattern has been indexed, it is possible to determine an orientation of the crystallite, giving rise to this pattern, using a dedicated computer software. The objective of the diffraction pattern analysis is to express the crystallite lattice coordinates in terms of three orthogonal directions in the specimen (S), which is a definition of the orientation matrix [1,5]. This is a matrix, whose first column is given by the cosines of the angles between [100] and X S (α 1 ), [100] and Y S (β 1 ), and [100] and Z S (γ 1 ). Similarly for the second and third columns with [010] and [001] respectively. Thus the orientation matrix R CS desribing the rotation from the crystallite lattice frame (C) to the specimen reference frame (S) is cosα 1 cosα 2 cosα 3 R CS = cosβ 1 cosβ 2 cosβ 3 (4) cosγ 1 cosγ 2 cosγ 3 For the calculation it is convenient to use an intermediate reference frame (R), which might be identical to the screen frame (F), and also to the scanning electron microscope frame (M) for the screen position parallel to the electron beam, as depicted in Fig. 3. There are several ways how to derive the matrix R CS from a Kikuchi pattern [1,6]. In the following, the method based on that presented in [7], which is illustrated in Fig. 4, will be briefly decribed. In this method, the rotation matrix R CR, describing the rotation from the crystal frame (C) to the reference frame (R), is first set up using a two-step process. In the first step, the crystallographic indices of the direction normal to the screen (ND) are obtained by a triangulation procedure [6]. This procedure involves setting up three simultaneous equations based on the scalar product between the vectors defining three zone axes [u i v i w i ] on the Kikuchi map and the vector defining the normal direction ND (see Fig. 4). The angles between the zones and ND are known from the map, the three unknowns are then the direction cosines (crystallographic indices) of the normal direction that are calculated. Consequently, a pattern frame (P) is - 5 -

6 defined with the Y P axis parallel to ND and X P axis parallel to a vector product between ND and one of the plane normals hkl present in the Kikuchi pattern. The rotation matrix R CP which describes the rotation from the crystal frame (C) to the pattern frame (P) is given by ND hkl R CP = ND (5) (ND hkl) ND The pattern frame (P) and the reference frame (R) differ only by a rotation of γ around ND, where γ is the angle between X P and X R (see Fig. 4). The corresponding rotation matrix is cosγ 0 sinγ R PR = (6) -sinγ 0 cosγ The combined rotations (6) and (7) are equivalent to the rotation from the crystal frame (C) to the reference frame (R), represented by the matrix R CR R CR = R PR R CP (7) γ Y P,Y R [u 2 v 2 w 2 ] X R XP (h3 k3 l3 ) [u 1 v 1 w 1 ] (h 2 k 2 l 2 ) screen [u 3 v 3 w 3 ] Ζ P Z R (h 1 k 1 l 1 ) ND [100] [001] crystal [010] h 1 k 1 l 1 Figure 4. Schematic illustration of the derivation of a crystallite orientation from the Kikuchi pattern (see text for details). The reference frame (R) used is identical to both the screen (F) and microscope (M) frames (after their rotation to the vertical position), shown in Fig. 3. In order to obtain the orientation matrix R CS, relating the sample and crystal frames, it is only necessary to premultiply the matrix R CR by an appropriate rotation matrix R RS, describing the rotation from the reference frame (R) to the sample frame (S). The concrete form of this matrix depends on the experimental set-up (eg. see Fig. 3). The orientation matrix, calculated for each EBSD pattern analysed, is stored in the computer memory and the computer software also provides a number of options for representation of the crystallite orientations, based on the above matrix [1-3,6]. In the representation using the ideal orientation concept, a crystallite orientation is expressed using the nearest Miller indices of planes, parallel to the principal specimen surface, and the nominated reference direction in that plane. This nomenclature has been widely used in the traditional texture research to denote significant texture components [5]. The orientation may be plotted on a direct pole figure which represents the stereographic projection of the poles of the chosen family of lattice planes, displayed with respect to the sample macroscopic axes. Alternatively, an inverse pole figure can be used, representing a stereogram in which each sample axis is plotted separately with respect to the crystal lattice coordinates. Because of the - 6 -

7 symmetry of the crystal, it is common to plot a unit triangle from the overall projection, as it contains all of the relevant information without repetition. Also, a crystallite orientation can be expressed in terms of three Euler angles and plotted, conveniently, as a single point in the corresponding Euler space. The mathematical expressions converting the orientation representations based on Miller indices to those based on Euler angles are given in [1,5]. Thus, the results of the EBSD investigation can be directly related to those obtained by X-ray texture analysis, represented by the orientation distribution function (ODF) utilising the Euler space [5]. Orientations of a large number of crystallites, obtained from the EBSD investigation, might be plotted on the pole figures or in the Euler space either directly as discrete points (density plots) or appropriate contouring routines can be applied to obtain corresponding contour plots [1-3]. For a graphical representation of grain orientations, the three orientation parameters, such as triplets of Miller indices defining an inverse pole figure or triplets of Euler angles, may be assigned to three basic colours, that are red, green and blue. Each grain in a micrograph may thus be stained by a unique colour, which can in turn be interpreted in terms of the orientation parameters by a comparison with a colour legend [8]. The computer software, utilising a digitised micrograph of a sample region together with the measured grain orientations, constructs an orientation image of the sample, showing the microstructure morphology in conjunction with the corresponding orientation distribution of grains. This is the basis of the crystal orientation mapping (COM) [2] Misorientation Between Two Crystallites The concept of the orientation matrix is also utilised for the calculation of a misorientation between two crystallites [1-3,6,7]. The orientation matrices corresponding to the two crystallites 1 and 2, R 1S and R 2S, are first set up utilising the common reference frame, the most convenient choice being the sample frame (S). The rotation from the crystal lattice frame 1 to the lattice frame 2, represented by the misorientation matrix R 12, can be then expressed as R 12 = (R 2S ) -1 R 1S (8) From the misorientation matrix R 12, the corresponding misorientation angle/axis pair can be readily obtained from the eigenvectors of the matrix and from its trace [1,6,7]. When the matrix R 12 is calculated using equation (8), the concrete indices of the axes of the second crystallite are fixed with respect to those of the first one. However, the crystal symmetry dictates that the axes of the second crystallite may be chosen in a number of crystallographically equivalent ways. This means that, in the case of the cubic crystal system, the misorientation matrix R 12 can be described in 24 crystallographically equivalent ways, which in turn gives 24 different solutions of the angle/axis pair. The symmetry-related forms of R 12 are generated by systematic premultiplying the original matrix by the matrices T i, representing the symmetry operations for a given crystal structure [6]. By convention, the solution associated with the smallest value of the misorientation angle is chosen to represent the misorientation. The calculated misorientation characteristics may be presented as a frequency distribution of misorientation angles, accompanied by a distribution of misorientation axes expressed either in a unit triangle of the stereogram or with respect to the sample coordinates using the direct pole figure representation. Alternatively, a misorientation angle/axis pair may be plotted in the Rodrigues-Frank (RF) space [1-3,6]. The corresponding Rodrigues-Frank vector R is calculated as R = L.tan(ϕ/2) (9) - 7 -

8 where L is a unit vector in the direction of the misorientation axis [uvw] and ϕ is the misorientation angle, representing the magnitude of the vector. The R-vector is then plotted in the RF space which has axes chosen parallel to either the axes of the specimen or the axes of the crystal [1,3,6]. The RF space is the only practicable way of showing misorientations in a single space, without a need for separate angle and axis diagrams. Furthermore, the locations of R-vectors corresponding to the prominent coincidence site lattice (CSL) orientation relationships [6] between crystallites can be very clearly visualised. From the measured data, the computer software also allows to plot the positions of the intercrystalline boundaries, thus constructing a misorientation map of an ivestigated specimen region [2], in analogy to the COD map mentioned in Section 4.1. The boundary segments, whose misorientation angles correspond to differing pre-selected ranges of values, may be plotted on the misorientation map using a different colour and thus be clearly distinguished from each other. Also, those boundary positions corresponding to the prominent CSL orientation relationships [6] may be selectively highlighted. 5. EXAMPLES OF PRACTICAL APPLICATION OF EBSD EBSD technique has been extensively used for the determination of both microtexture and mesotexture (misorientation texture) in a wide range of metallic materials, processed in a variety of ways. In the case of materials, subjected to extensive plastic deformation at low temperatures, the quality of EBSD patters generally becomes degraded proportionally to the amount of imposed strain. The amount of pattern diffuseness can be quantified and related to the strain level [3]. EBSD patterns of acceptable quality can frequently be obtained even after very high levels of cold work or, alternatively, an improvement in the pattern quality may be achieved by a preliminary low-temperature anneal to bring about some recovery of the microstructure without recrystallisation or grain rotation. EBSD technique has proven to be particularly useful in the studies of deformation banding, see eg. [9]. It has also been extensively used in the recovery and, in particular, recrystallisation studies in a range of materials, see eg. [3,10-12]. In the latter case, the above technique allows to determine a microtexture corresponding to early stages of the recrystallisation process together with the locations of the recrystallised grains, which brings a significant advantage over the recrystallisation texture studies performed using X-ray diffractometry. EBSD technique has frequently been utilised in the determination of mesotextures corresponding to grain boundaries in various materials, subjected to differing processing treatment, as part of the research into grain boudary design for achieving optimum mechanical and physical properties, see eg. [3,6,13]. Apart from the misorientation angle/axis pairs, the above technique, in conjunction with either a two-surface trace analysis or serial sectioning method, also facilitates the determination of boundary plane orientations [3,6]. EBSD method has also been applied in the phase transformation studies, where it facilitates the determination of both micro- and mesotextures, the latter in relation to the crystallographic orientation relationships between the phases, see eg. [14]. REFERENCES 1. RANDLE, V. Microtexture determination and its applications. London: The Institute of Materials, 1992, 174pp. ISBN Crystal orientation mapping - guide book series. High Wycombe, GB: Oxford - 8 -

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