Diffraction signal (Kikuchi pattern) as intensity modulation on a comparatively huge background (BG) number of detected bands band positions in Hough ...
Materials properties revealed by EBSD Gert Nolze Federal Institute for Materials Research and Testing, Berlin
1. Introduction 2. Crystal orientation maps 3. Misorientation tools 4. Some advanced approaches
Capabilities of EBSD today 1.
Locally resolved orientation measurements orientation (texture) and misorientation analysis
2.
Microstructure characterization (post-processing) grain size, grain shape, and phase distribution, recrystallization, deformation, characterization of cracks, orientation relationships, grain- or phase boundaries, epitaxy, twinning, phase reconstruction, orientation gradients (GND) etc
3.
Phase analysis or phase separation characterization of multi-phase materials, phase identification, combination with other signals like EDS or BSE
4.
Microstrain analysis processing of HighRes-EBSD patterns (cross-correlation)
5.
„in situ“ experiments high temperature investigations like grain growth, phase transformation, micro-testing
6. 2
Special techniques like low-kV, 3D-EBSD, TKD
The major information
What does a typical EBSD pattern tell us today? If we are talking about typical… What is typical? For orientation maps commonly patterns are binned down to 80x60 pixels or less, …and binarised! The entire talk only deals with patterns of this image resolution. Kikuchi pattern of Cu 3
Information: without any indexing
Which kind of information we can get? Diffraction signal
(Kikuchi pattern) as intensity modulation on a comparatively huge background (BG)
number of detected bands band positions in Hough coordinates (ρ,θ) band widths (e.g. in fractions of the screen dimension) averaged band contrast (pattern or image quality): describes roughly the visibility of bands (peak amplitude) in Hough space.
averaged band slope: describes the peak shape (peak contrast) in Hough space.
Information: with indexing
Diffraction signal (Kikuchi pattern) …this requires the knowledge about the pattern centre position
Index of the crystallographic phase, crystal orientation, e.g. described by Euler angles (ϕ1,φ,ϕ2) Goodness of fit (CI, MAD, AFI, BMM etc.) of experimental and theoretically derived band positions And of course the assumed position (x,y,z), where the signal has been acquired
Image (pattern) quality, band contrast
• Without any indexing the patterns already can be evaluated by a parameter describing the visibility of bands: image quality (IQ) ➳ band contrast (BC) ➳ pattern quality (PQ)
• Their definitions are different, however the aim is always the same: Presentation of the detectability of bands in Hough space. However, BC, PQ and IQ maps of the same material will not look identical since the validation is based on different algorithms. All of them have unpredictable advantages, e.g. one perhaps displays better orientation differences, another expresses differences between phases. It is coded as a 8 bit number so that pattern quality maps are typically grey-scaled images.
Crystal size, orientation, defects… • Superimposition of two or more patterns reduces the signal quality, e.g. tiny grains, boundaries .
It is sometimes hard to decide which factor dominates the visible signal!
• The band distribution is responsible for the orientation contrast in image quality maps. • Diverse phases form different signalbackground ratios.
30µm Cu dross containing several phases
• Defects destroy lattice periodicity and cause a blurring of the diffraction signal. • Topography
Phase distribution map The main application of EBSD measurements is still the generation of crystal orientation maps. To this end, for each measurement point (x,y) the orientation gx,y of the locally existing crystal is determined, but…
First the phase needs to be known!
Phase distribution map The main application of EBSD measurements is still the generation of crystal orientation maps. To this end, for each measurement point (x,y) the orientation gx,y of the locally existing crystal is determined, but…
First the phase needs to be known! This happens already during “pattern indexing”.
Cassiterite (SnO2) – tetrag. Magnetoplumbite (PbFe12O19) – hex. Magnetite (Fe3O4) Cuprite (Cu2O) Copper (Cu) Lead(IV) oxide (PbO2) For the highlighted pattern quality map an information is used which does not need any indexing.
It selects this phase from a list of candidates which shows the best correlation between experimental and theoretical band positions. Using the phase index phase distribution maps can be derived where each phase is simply displayed by another colour, cf. map (left). For microstructures with several cubic phases the phase assignment is erroneous. In this case a parallel acquisition of EDS might help.
Orientation matrix G Any orientation can be described by three rotations around different axes. A de-facto standard is the rotation around Z(ϕ1), X(φ), and Z(ϕ2) which has been proposed by Bunge. Mathematically rotations are described by matrices:
so that a general orientation G is given by the product of three matrices:
Using the matrix components gij the three Euler angles can be derived from G and stored as orientation description measured at position (x,y).
Euler colouring of orientation maps • Since crystal orientations are exclusively stored in Euler angles (ϕ1, φ, ϕ2), they are directly used for orientation visualization. Advantage of Euler space: • In Euler space each orientation is only given by one point. For convenience, only for cubic phases the same orientation occurs as three points.
Disadvantages: • A meaningful interpretation of Euler-anglecoloured maps is practically impossible since the Euler space is highly distorted, and the orientation sensitivity of colours is quite low, cf. the legend (left). • Moreover, the Euler space is discontinuous which causes colour jumps (arrow) within a grain, although the grain orientation is practically everywhere the same.
Axis/angle description • Using G, a common rotation axis [r1, r2, r3] as well as the respective rotation angle θ can be derived. • Rotating the crystal by θ around the common axis r the coordinate system of the crystal (blue) ends up in the reference coordinate system of the sample (red) described by X, Y and Z. • Axis and angle can be calculated by:
For representations the angle θ but also r can be used. This tool is preferred for misorientation representations.
IPF colouring of orientation maps
Nowadays, as de-facto standard tool for orientation maps the Inverse Pole Figure (IPF) colouring is used. It displays the crystallographic indexing of a selected reference direction, e.g. the sample normal Z0 (ND), considering the crystal symmetry of the respective phase. Often it is overlaid by the pattern quality.
Z0 Y0
X0
Crystal orientation maps
However, also the IPF-colouring has certain pitfalls: • One needs more than a single map to get an impression about the entire crystal orientation. • Using standard colour keys not all crystal symmetries generate maps which are free of colour jumps. • In multiphase materials not all phases have the same symmetry so that different colour keys are used in the same map.
IPF maps: phase-specific colouring
SnO2 rods Recommendation: • If you have more than one phase, or if you have phases displayed by different colour keys, do not show them all together in a single map (as done in two of the previous slides). Such images are hard to interpret. • For a meaningful interpretation do not forget the colour keys as legend for the map.
Misorientation ∆G • Misorientation and orientation description are quite similar. Whereas an orientation describes the alignment of a crystal with respect to the reference coordinate system, the misorientation defines the alignment of one crystal related to another. • The misorientation between two orientations Gj and Gj is again described by a matrix: the misorientation matrix ∆G.
And because of the same character of ∆G all former tools can be used in a similar way, i.e. ∆G can be displayed like G. • The index i mainly expresses that there are many different reference coordinate systems Gi conceivable which offers a comparatively big amount of various misorientation types.
Grain recognition • The misorientation between adjacent measurement positions (same phase) is used to define grains. • The misorientation angle ∆θ commonly compared with the maximum deviation angle ∆θmax is defined in the same way as θ already described for orientations:
• As long as ∆θ = |θi−θi+1| < ∆θmax both pixels are assumed to belong to the same grain.
Conclusions: • Amount, size and shape of recognized grains depend on ∆θmax. • Since only adjacent points are considered, within grains angular differences much bigger than ∆θmax may occur, accumulated during infinitesimal but continuous lattice rotations.
Example: grain recognition ∆θmax=0.5°
∆θmax=1°
∆θmax=2°
∆θmax=3°
∆θmax=5°
Ni, directionally solidified The cross section of a bar shows thousands of grains with obviously very similar orientations so that the grain recognition only works really well for ∆θmax=0.5° . However then preparation artifacts appear.
Grain distribution maps for different ∆θmax overlaid by pattern quality
Grain boundaries • The misorientation line between grain A and B describes the trace of a grain boundary. • Along this line the misorientation angle ∆θ but also the rotation axis r can be described:
• Using ∆θ and r, grain boundaries can be classified, e.g. as small angle and large angle grain boundaries, twins, or more general as coincident site lattices (CSL) Please keep in mind that this only describes the misorientation but not really a grain boundary as plane. Necessary to that end are two additional parameters describing the plane (trace).
Grain boundaries in Cu dross Grain boundaries (red) in Cu2O only
Grain boundaries using different CSL Grain boundaries (black) and twins (red)
• The visualization tools of grain boundaries are comprehensive. Therefore, sometimes less is more, especially for multiple phase materials. • The definition of CSL boundaries for cubic phases is usually part of the EBSD software. • However, twin laws need to by defined manually.
Phase boundaries • A qualitative description of phase boundaries is simple and does not need any further data processing since the phase index already defines where which phase exists. Cu
Fe3O4 Cu2O
• For more than 2 phases it becomes challenging to keep the overview. • A general problem for all boundary descriptions are missing orientation determinations and misindexings caused e.g. by sample topography. • There are several approaches for the a proper handling of misinterpretations. One of the best is part of MTEX, a free and open-source Matlab toolbox for EBSD data.
Phase boundaries • A quantitative classification of phase boundaries is a bit more sophisticated. • Although the equation
is still correct, the link between two phases described by different crystal lattices is not that straightforward since the definition of noncubic crystal lattices needs to be to consider. • Because of the different metric of the described lattices CSL’s convert to NCSL’s, so-called near coincident site lattices. • The most easiest case is given if both crystal coordinate systems are only scaled to each other. However, this is fulfilled for cubic phases only. • Typical applications are phase transformations, epitaxy and topotaxy.
Phase transformations
• Phase transformations often follow very specific crystallographic rules since commonly not that much happens on the atomic scale. • Typically, the definition of common lattice planes and directions of both phases A and B is preferred:
• The related structural similarities also have specific effects on the Kikuchi patterns.
Topotaxy: Magnetite-Hematite
{110}
{110} {110}
{111}
{110}
{110} {110}
phase distribution map
• Hematite transforms from magnetite along certain crystallographic planes (foliation). • The transformation becomes visible as planes parallel to {110}M . • The transformation happens parallel to {111}M.
How does the diffusive transformation affect the Kikuchi patterns?
Pattern similarities The centered pattern is from a magnetite parent grain. The hematite patterns around appear in the same grain but already in transformed regions. In each of these patterns some bands and zone axes* of magnetite remain. bands with same width bands with different width
*
intersections of bands
Misorientations within grains
A reference orientation Gi can be also defined to be not variable: • Misorientation to a reference orientation Go (same phase)
• Misorientation within a grain to the averaged grain orientation (GAM). • Misorientation to adjacent pixels (kernel) within a grain (KAM).
The size of the considered neighborhood is given by n.
Misorientation: GAM and KAM • GAM describes the local orientation difference to the average orientation of the grain., i.e. GAM strongly depends on ∆θmax • Regarding the grain recognition within a grain clearly higher misorientation angles can appear (the Ni-DS-example shows for a ∆θmax =1° a maximum value of θ=7.8°) Ni-DS material (containing NbC fibers)
• Whereas GAM represents accumulated lattice rotations, KAM displays the local orientation gradient. • For KAM the maximum value is de-facto given by ∆θmax, i.e. also KAM somehow depends on ∆θmax.
Further misorientation tools Misorientation distribution (Mackenzie plot): • In order to get an impression about the statistical distribution of grain orientations and their positions the uncorrelated misorientation can be derived. To this end between a suitable number of arbitrarily selected pairs of orientation measurements the misorientation angle will be calculated and displayed as histogram.
Orientation noise: • Very often questions regarding the orientation precision (not accuracy) are of interest. Also here a correlated misorientation between pairs of measurements (of the same phase) will be calculated, however the selection of the second orientations takes place within the kernel of the arbitrarily selected primary orientation.
EBSD signal General information from plain image processing: • Overall brightness • Overall contrast • Centre of mass
Information from specific Kikuchi bands: • Position and width • Intensity (band contrast) • Contrast (band slope) • Blurring (anisotropy) • Symmetry
Relation between them: • Diffraction signal/background ratio
(how clear an image becomes visible?)
• Diffraction signal/noise ratio
(how noisy is the Kikuchi pattern?)
EBSD screen as multiple BSE detector
Definition of superpixels (here 10x10) The pixels can be combined in order to derive meaningful features of the microstructure. Up to now images of different contrasts are interpretable: • periodic number (Z) • orientation • topography
Periodic number contrast Scanning a sample, at each position the formed pattern allows the generation of super-pixel signals. Specific images can be derived. BSE image derived from the upper 2 rows of super-pixels.
Cu
Al
BSE imaging using hardware Cu dross
Cu
PbO2
Cu2O Fe3O4 30µm BSE image at 70° tilt
• Using a BSE detector mounted above the EBSD screen from tilted samples images can be collected displaying different phases. • The reason is a different backscatter coefficient η of phases if their chemical composition changes and so their averaged periodic number.
EBSD: BSE images Co dross
Cu
PbO2
Cu2O Fe3O4
Derived BSE image using Kikuchi patterns.
Non-corrected Kikuchi pattern (160x120 pixels)
• For each Kikuchi pattern the grey values in the yellow-marked part can be summarised. • Using these numbers as new image pixels an image results which looks like the former one collected by the detector. The derived image (left) is less noisy, and also higher resolving (passive energy filtering).
Orientation contrast & topography Co dross
Orientation contrast image from EBSD patterns
Topography image from EBSD patterns.
• Summarizing the intensity of three different pattern areas colour images can be derived which mainly display the orientation contrast (left). • Also the surface topography can be derived (right) if more than two fields are combined, cf. right.
Kikuchi pattern “misorientation” Similar to EBSD data which can be used for orientation but as well as for misorientation interpretations, a single Kikuchi pattern can be a) simply processed, but also b) compared with other Kikuchi patterns.
Comparison of Kikuchi patterns is possible by • Cross-correlation which is a suitable tool to evaluate the match between two patterns by a simple number. • The results are diverse and depend on the comparing reference Kikuchi pattern, i.e. - is it of experimental nature, - or is it of theoretical nature? • The applications cover a wide field of interesting issues, starting from a simple increase of the angular resolution (using the same data), up to a more reliable indexing (pseudo-symmetry, point-group sensitive interpretation, phase selection etc.)
Cross correlation (dot product) Quartz FSE image
Pattern quality
…to reference pattern Dot product X to next neighbor
IPF-Y + GB + TB
Misorientation by Schmidt factor Y Z
Schmidt factor presentation based on orientation data.
averaged raw patterns (ca. 50) Quartz - 175B_08, 16ms, 3frame, LV, 20kV
Phase verification by pattern averaging and simulation
Phases in Cu dross
Simulations
Cuprite (Cu2O) Cassiterite (SnO2) Magnetite (Fe3O4) Copper (Cu) Lead(IV) oxide (PbO2) Magnetoplumbite (PbFe12O19)
Simulations
Whatever people claim: A phase identification or verification only by band positions and widths without any appropriate intensity simulations is extremely poor.
Take home message • EBSD allows us to get a deep insights into the microstructure of materials using crystal orientation measurements. • There are standard and advanced tools for orientation and misorientation data presentation available which only need to be applied in a proper way. • For many applications the angular and also spatial resolution of EBSD maps is outstanding. • The post-processing of stored patterns delivers additional information and often a significantly higher precision. • Results derived from different analytical devices like BSE, EDS, EBSD are complementary but often help to cross-check conclusions made by only one technique.
