mapping the mesoscale interface structure in polycrystalline materials

Ultramicroscopy 93 (2002) 99–109

Mapping the mesoscale interface structure inpolycrystalline materials

C.T. Wua,b, B.L. Adamsa,b, C.L. Bauera,b, D. Casasenta,b,*, A. Morawieca,b,S. Ozdemira,b, A. Talukdera,b

a Department Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USAb Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Received 3 July 2001; received in revised form 4 March 2002

Abstract

A new experimental approach to the quantitative characterization of polycrystalline microstructure by scanning

electron microscopy is described. Combining automated electron backscattering diffraction with conventional

scanning contrast imaging and with calibrated serial sectioning, the new method (mesoscale interface mapping system)

recovers precision estimates of the 3D idealized aggregate function GðxÞ: This function embodies a description of lattice

phase and orientation (limiting resolutionB11) at each point x (limiting spatial resolutionB100 nm), and, therefore,

contains a complete mesoscale description of the interfacial network. The principal challenges of the method,

achieving precise spatial registry between adjacent images and adequate distortion correction, are described. A

description algorithm for control of the various components of the system is also provided. r 2002 Elsevier Science

B.V. All rights reserved.

PACS: 60; 61.14.Bg; 61.72.Mm Subject index terms: 014

Keywords: Electron backscatter diffraction patterns; Triple junctions; Orientation imaging microscopy

1. Introduction

The purpose of this paper is to describe a newexperimental approach to the characterization ofmesoscale aspects of the internal structure ofpolycrystalline materials. Mesoscale refers here tothose aspects of internal structure described by the

idealized aggregate function [1]

GðxÞ ¼ ffðxÞ; gðxÞg; ð1Þ

where and denote the crystalline phase andorientation, respectively. As defined, GðxÞ carriesinformation about the size, shape and arrange-ment of grains, their phase and their crystal-lographic orientation. GðxÞ also contains partialinformation about the state of dislocation in theinternal structure [2].

Using the new method known as orientationimaging microscopy (OIM) [3], characterization of

*Corresponding author. Department of Electrical and

Computer Engineering, Carnegie Mellon University, Pitts-

burgh, PA 15213, USA. Tel.: +1-412-268-2464; fax: +1-412-

268-6345.

E-mail address: [email protected] (D. Casasent).

0304-3991/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 4 - 3 9 9 1 ( 0 2 ) 0 0 1 5 1 - 1

GðxÞ in the two-dimensional (2D) section planehas become routine. OIM simply involves scan-ning with the electron beam of a scanning electronmicroscope (SEM) over a regular grid ofpoints {x} restricted to the section plane of thesample ðxAR3Þ; and capturing and indexingthe electron back-scattered patterns (EBSPs) forthe phase and orientation at each grid point. (Theroutine application of OIM is for single-phasematerials, but two-phase systems have alsobeen studied [4].) The spacing of grid points mustbe selected with an eye towards the important scaleof information of interest to the investigator.Images formed from such data sets, calledorientation imaging micrographs (OIMs), containa wealth of geometrical, orientational (and phase)data.

An increasingly important application ofOIM has been the characterization of theinterfacial network exposed by the sectionplane. In some applications, the distribution ofinterfaces by type or character is of primaryinterest [5,6]. In other applications, the connectiv-ity of interfaces, such as at triple junctions,is the main focus [7,8]. For these applicationsOIM is rather inefficient since only the scanpoints that lie adjacent to the interfaces areused to determine interface character. Scan pointslying away from the interfaces have neg-ligible value in this setting. When the OIMgrid spacing is dictated by the precision withwhich the interfacial inclination parameters mustbe determined in the section plane, the efficiencywith which conventional OIM can harvest inter-facial data is rather poor. For example, it isestimated that at the current rate of EBSDrecovery and indexing, which is approximately100,000 per hour in ideal conditions, that recoveryof high-precision data on grain boundary crystal-lography and in-plane inclination could not beachieved more rapidly than E10 boundary seg-ments per hour; and, therefore, the recovery oflarge data sets by conventional OIM remainsinfeasible.

Furthermore, a complete mesoscale character-ization of interfaces and triple junctions requiressampling the three-dimensional (3D) aggregatefunction GðxÞ ¼ ðxAR3Þ. For example, in a

single-phase polycrystal we must be concernedwith five (macroscopic) parameters of grainboundary character: three of these specify themisorientation between adjacent crystal latticesacross the interfacial plane, and two are requiredto fix the inclination of the plane itself. Allfive parameters are believed to influence theintrinsic properties of the grain boundary (e.g.,excess free energy, mobility, etc.) [9,10]. IfOIM reveals GðxÞ only in the section plane,then only four of the five parameters are determin-able for the observed boundaries, all three para-meters of crystal misorientation, and one of thetwo parameters of interface inclination. Similarlimitations exist in terms of triple junctions, wherethe orientation of the triple line itself is obscuredby the electron-opacity of the polycrystallinesample.

In this paper, a new approach and system ofmicroscopy is described, called the mesoscaleinterface mapping system (MIMS). MIMS over-comes each of these challenges associated withconventional OIM. The efficiency of sampling themicrostructure for lattice orientation near inter-faces is overcome by directing the beam to thevicinity of interfaces that have been identified by amicrostructural contrast image. This also enablesefficient sampling near the interface to establishin-plane inclination with sufficient angular resolu-tion. The need for 3D characterization of bound-aries is met by a system of algorithms for achievinga precise spatial registry between adjacent micro-structural data sets. Here, the principal challengeis to achieve a high degree of parallelism betweenadjacent section planes, and an accurate registrybetween the 2D GðxÞ data. One recent approachto the problem of control of parallelism andaccurate registry involves embedding a siliconinternal metrology device in the sample prior toserial sectioning. This was described by King et al.[11].

The approach of this paper is to focus upon thedescription of MIMS as a novel system ofmicroscopy. Each of the individual componentsof MIMS comprises algorithms that are more-or-less familiar to practitioners of image analysis andanalytical microscopy. Thus, the emphasis here isupon the system itself.

C.T. Wu et al. / Ultramicroscopy 93 (2002) 99–109100

2. The mesoscale interface mapping system

(MIMS)

In that which follows the functionality of thevarious components of MIMS is described.

2.1. Integral components of MIMS

Fig. 1 shows the basic structure of the MIMS asit is applied to each individual scanned sector onthe section plane. A sector is defined as a 2Dregion of breadth specified by the operator of thesystem. Its dimension is selected such that theindividual boundaries in the section plane arecharacterized with sufficient angular resolution bythe microscope. Since this is dependent upon thegrain size and other characteristics of the sample,it must be selected by the operator after apreliminary examination of the grain structurehas been conducted. When characterization of awide field in the section plane is desirable, data forseveral overlapping sectors will be taken. Theseoverlapping data sets can subsequently be‘‘stitched’’ together (in-plane registration) in orderto form a wide-field (2D) mosaic of the micro-structure.

For the characterization of each 2D sector, threefunctional modules and a central control systemare employed as illustrated in Fig. 1.

(1) Microscope (digital SEM with appropriatedetectors for contrast formation and forrecording EBSPs),

(2) Image Processing (for morphological andgeometrical processing of scanning contrastimages),

(3) Automatic EBSP Indexing (automated latticephase and orientation determination), and

(4) Systems Control (for sequencing the opera-tions of the aforementioned modules, infor-mation transfer, and output).

The remaining function associated with the 2DMIMS pertains to the registry of multiple sectorsto form the wide-field mosaic image, where this isdesirable. This is described further below.

Fig. 1 also highlights the differences betweenconventional OIM and the 2D MIMS technology.

OIM requires the Automatic EBSP Indexingfunction in connection with the use of a 2Ddetector. (A typical example is a digital camerasystem such as the silicon intensified target (SIT)or a charge coupled device (CCD) televisioncamera. In these examples the EBSP is formedon a phosphor screen within the SEM, andinterrogated by the television camera.) This isillustrated by the schematic in Fig. 2. That portionof the Systems Control which directs the beam toselected grid points, either by beam deflection orby stage motion, is required by OIM.

2.1.1. Microscope

MIMS differs from OIM in its use of a seconddetector system in connection with the SEM toform contrast images of the microstructure in thesector. This second detector system is used to formintensity contrast images. One or more detectorsmight be involved in the system in order to obtainadequate contrast using the conventional SEMscan mode. In typical detectors employed sample,the back-scattered electron (BSE) and secondaryelectron (SE) emissions are stimulated by thefocused electron beam. A typical back-scatteringcontrast image obtained with a BSE detector isshown in Fig. 3. Contrast forms due to orientationand phase differences among the different grains.Fig. 4 shows a SE contrast image formed using theSE detector. In this image, the contrast isassociated with the topography of the surface,deliberately introduced by thermal grooving.

MIMSSystem

Controls

(FeatureDetection)

AutomaticEBSP Indexing

Image Processing

Microscope

SIT/CCDCamera

BSE/SEDetectors

: Conventional OIM

Fig. 1. Components employed in MIMS.

C.T. Wu et al. / Ultramicroscopy 93 (2002) 99–109 101

Since interface in-plane inclination and loca-tions desired to determine crystalline phases andorientations are directly obtained from micro-structural contrast images, any distortion willaffect the result. These distortions must also becorrected to provide accurate dihedral anglemeasurements at each triple junction. Moreover,

locations retrieved from distorted images cancause incorrect capturing and indexing of EBSPs.Thus, a distortion correction of contrast images isrequired when the employed SEM is insufficient toavoid any external influence to its image output.Since the distortion can vary from point to pointon any given contrast image, a combination of

Fig. 2. A typical configuration of a digital SEM. When used in scanning mode, BEI or SEI are produced. When used in spot mode,

EBSP images are formed.

Fig. 3. A back-scattering contrast image of 99.999% Al foil.

The average grain size is 100mm.Fig. 4. A SE contrast image of MgO.


simple rotation and translation is insufficient tocorrect the entire image. Thus, multidimensionalpolynomial rotation and translation are used toconvert each pixel coordinate in the originaldistorted image to the proper coordinate in aresultant corrected image. The parameters ofmultidimensional polynomial rotation and trans-lation are calculated based on calibration per-formed prior to the MIMS scan with selectedmagnification and working distance. Two contrastimages, correct (Fig. 5(b)) and distorted(Fig. 5(a)), of a standard grid sample are capturedat 01 sample tilt and a tilt angle selected toimplement a later MIMS scan. Image coordinatesof reference points are selected and recorded atlocations where the same object point appears inboth distorted and correct images.

Image coordinates are measured as ðxd ; ydÞ onthe distorted image and ðxc; ycÞon the correctedimage with gray scale values Iðxd ; ydÞ and Iðxc; ycÞ:By using least squares analysis, the coefficients adc

and bdc of the polynomial functions can bedetermined and

xc ¼X

d

adcIðxd ; ydÞ; ð2aÞ

yc ¼X

d

bdcIðxd ; ydÞ: ð2bÞ

Distorted images captured at 601 tilt then canbe transformed based on adc and bdc: Fig. 6illustrates a resultant corrected image using suchcoordinate transformations. This transformationis required for each contrast image captured from

current microscope with non-zero specimen tiltand is embedded into the Image Processingmodule.

2.1.2. Image processing

Contrast images are analyzed using the ImageProcessing module in order to extract geometricalinformation about the location and geometry ofinterfaces. A central component of the ImageProcessing module is edge detection. It is knownthat gradients in the intensity contrast images areoften associated with interfaces. The intensitysignature of these gradients, however, varieswidely, depending upon the type of contrast imageformed and the preparation of the sample surface.Thus, the Image Processing function requires abroad range of algorithms with sufficient flexibility

(a) (b)

Fig. 5. (a) SEI of a standard grid specimen obtained at 601 tilt, (b) same area obtained at 01 tilt.

Fig. 6. Corrected SEI. All mapped coordinates are rounded up

to integers and intensities are transferred to corresponding

pixels.


to be effective in locating interfaces from a varietyof contrast images.

More precisely, the boundaries in some contrastimages (secondary electron images—SEI) are lines

(bright, dark or a combination of bright and darklines), whereas in other cases (back-scatteringelectron images—BEI) the boundaries are moregradual transitions. Combinations of line andtransition boundaries also may occur in the samecontrast image. In these cases three different edge-detection methods are used. For transition bound-aries, imaginary Gabor filters are used. For lineboundaries, several approaches have been devel-oped, including the use of real Gabor filters andmedian filters [12,13]. The most promising methodfor line-boundary detection uses various combina-tions of Gaussian and median filters. For transi-tion boundaries, Gabor filters replace the medianfilters [13]. The other steps in both the casesinclude: blob coloring and morphological erosion(plus dilation) to remove isolated artifacts such asprecipitates, pits, etc., and morphological proces-sing to fill in gaps on grain boundaries [12,13]. Theselection of a particular approach to ImageProcessing is a matter of experience and selectionfrom among the set of available algorithms. Theimage-processing algorithm suite developed usesseveral Gaussian and median (or Gabor) filterswith different parameters. These results are thenfused. The choice of filter parameters and fusionused handles a range of situations and yields goodresults. Thus, the user need not have to concernhimself with selecting these parameters.

Having successfully detected edges in the image,the image is then thresholded to obtain a binaryimage. This image is then processed with newmorphological filters to reduce all boundaries to‘‘skeletonized’’ lines, which are only one pixel wide[14]. Skeletonized images for Figs. 3 and 4 areshown by superposition in Figs. 7 and 8, respec-tively. False ‘‘spurs’’ that occur in the skeletonizedimage are also removed.

Having obtained the skeletonized image of thecontrast pattern, the spatial coordinates forfeatures associated with the interfacial networkcan be determined with specific algorithms that aretuned to find the particular features of interest.From the identified coordinates of the salient

features, the electron probe can be directed (bybeam deflection using the magnetic lens system ofthe SEM) to specific points near the featuresthemselves. As an example, Fig. 9 illustrates themarked locations of specific points near triplejunctions in Fig. 7.

These points were obtained by first applying aline-following routine to the skeletonized image tofind the location of each identified triple junction.A set of three points lying in the interiors of thethree associated grains at each junction is thenlocated [12,14]. It should be clear that the auxiliarypoints required to characterize the triple junctionderive from a knowledge, not only of the location

Fig. 7. The skeletonized boundaries are superimposed onto

Fig. 3 as white curves.

Fig. 8. The skeletonized boundaries are superimposed onto

Fig. 4 as black curves.


of the triple junction, but also of the geo-metrical location (inclination) of each grainboundary associated with that junction. It isevident from Figs. 7–9 that the recovery ofboundary contrast information is imperfect, andthis constitutes a continuing challenge in thepresent approach. However, we note that in manyof the applications of interest to the authors, it isnot required to obtain complete fully connecteddata sets.

2.1.3. Automatic EBSP indexing

The final steps associated with MIMS in thesector include: the positioning of the beam at eachidentified point, the collection of an EBSP there,followed by the indexing of each EBSP todetermine local lattice phase and orientation.These operations are associated with the Auto-matic EBSP Indexing module. The indexingfunction of MIMS does not differ from conven-tional OIM. It is now a matter of routine that thecharacteristic bands of the EBSPs are detectedusing the Hough–Radon transform. After appro-priate corrections for the geometry of the phos-phor and detector, interband angles andbandwidths are then compared with the knowncrystallographic characteristics of the phase (orphases) present in the sample. Typically, four ormore non-coplanar bands are used to index eachEBSP. Once the indexing is complete, the orienta-tion of the local pattern is easily determined from

the geometry. The main ideas associated withpattern indexing are described in greater detail inthe article by Adams et al. [3].

2.1.4. Systems control

Sequencing and control of the operations ofMIMS are provided by the Systems Controlmodule. Fig. 10 provides a flow diagram for thesequencing of 2D MIMS operations. A simplifieddescription of the control sequence follows. TheSystems Control module directs the microscope,used in conjunction with one or more (point)detectors, to form an intensity contrast image overa sector of selected area. When this is completed,Systems Control passes the contrast image toImage Processing for analysis. After the image isfully processed, geometrical data is passed back toSystems Control. These data include the positionsfor EBSP analysis, and geometrical data on theinterface structure as required in the selectedcharacterization. Systems Control passes theidentified positions for EBSP analysis to theAutomatic EBSP Indexing module. This moduledirects the beam to each identified position,obtains an EBSP and analyzes it for image qualityand lattice orientation. Data is then passed back toSystems Control. When multiple sectors arerequired, Systems Control directs the microscopeto change its mechanical stage position to the nextsector, and the complete process is repeated again.Repetition continues until sufficient sectors havebeen analyzed.

2.2. Extension of MIMS to wide-field 2D imaging

A common application of MIMS is for thecharacterization of the interface structure of 2Dsurfaces; this employs a magnification, whichprovides adequate resolution of geometrical para-meters of the network (e.g., triple junctionlocations and their dihedral angles). This magni-fication will often limit the area interrogated byMIMS and the number of interfaces present in thefield of view. It is, thus, often necessary to expandthe field of view by examining many sectors. Thus,after data from each sector is passed back toSystems Control, the microscope is directed tochange its mechanical stage position (beam

Fig. 9. Black spots represent locations to which MIMS directs

electron probes.


Launch MIMS ScanLaunch Microscope Launch Image Processing

Save contrast image?NO

Request contrast image

Ready to save image?

NO

YES

YES

Save contrast image

Reply job done

Contrast image saved?NO

YES

Request image processing

Ready to process image?

NO

YES

Image distortion correction,Image processing

GB and TJ detection.

Reply job done

Request move stage to next sector

Image processing finished?NO

YES

Switch to EBSP indexing

Switch back to original scan mode

MIMS completed?

MIMS finished / Output data

YES

NO

Move stage to next sector

Launch EBSP Indexing

Ready to index EBSP?NO

YES

Move beam to identified location,Grab EBSP,

Hough/Radon transform,Orientation indexing.

Finish identified points?NO

YES

EBSP indexing finished?

Move stage?NO

YES

Reply job doneYES

NO

Application specific analysis(Identify EBSP locations)

Fig. 10. Flow chart of MIMS Control module.


deflection can also be used in some cases) to thenext sector, and the entire process outlined aboveis repeated again. Repetition continues untilsufficient sectors have been analyzed.

In such cases, it is necessary to mesh togetherthe data obtained from several adjacent sectors inorder to form a single wide-field mosaic imageof the entire sample. This meshing process iscalled stitching. In this case it is important thatadjacent sectors contain overlapping regions fromwhich the stitching can be implemented. Typicaloverlaps might be 10–20%. The algorithm em-ployed makes use of the mean square error of thecorrelation of the overlapping images to obtaintranslations and rotations needed to bring theadjacent images into the best possible registry.From Fourier transforms of the overlap region, theshape of the correlation peak is known. Thus, fromseveral samples of it, the registration can beobtained to sub-pixel accuracy. Normalized corre-lations are used.

3. Extension of MIMS to 3D imaging

The electron opacity of most crystalline materi-als provides a serious challenge to the completecharacterization of the interfacial network. Fullcharacterization of interfaces requires informationabout the inclination of the interfacial planes.Likewise, the full characterization of triplejunctions requires the description of the orienta-tion of the junction line itself. These data areinaccessible in a single-section characterization ofthe network.

In this section, we describe the application ofmethods of data registry to the 3D reconstructionsof the interfacial network by MIMS. Three-dimensional reconstruction refers to registry ofthe data in adjacent section planes obtained bycalibrated (parallel) serial sectioning. Differentsection planes are obtained by removing a smallslice from the top surface of the sample andrepeating the analysis for such different slices indepth of the material. Such characterizationdestroys the sample from which the data isobtained.

3.1. The registry algorithm

We consider the points x associated withfeatures in a specified 2D section; these pointsrepresent their ‘‘reference positions’’; their asso-ciated ‘‘variable positions’’ in the adjacent sectionplane are given by y: The relationship betweenreference and variable positions must be given bythe rigid body rotation O and the translationvector t according to

y ¼ Ox þ t: ð3Þ

It is assumed that the component of thetranslation vector perpendicular to the sectionplane is a known constant. It is also assumed thatan exact correspondence of the selected featurescommon to both planes is known.

Generally, several (or many) feature points aremeasured in their reference and variable positions.Each point in these reference and variable posi-tions is related by the same (O; t) transformation.Thus

yi ¼ Oxi þ t ði ¼ 1; 2;y;NÞ; ð4Þ

where N is the number of feature points deter-mined from the data. Due to experimental errors,the relations in Eq. (4) are only approximate, anda best fit for the transformation (O; t) is obtainedby the minimization of the function

c ¼X

i

oiðyi � ðOxi þ tÞÞ2; ð5Þ

where oi is a non-negative weight assigned to theith feature point.

There is an inherent physical assumption in theminimization problem expressed by Eq. (5). It isthat there is no directional anisotropy present inthe set of feature points examined by the analysis.For example, if common triple junctions are usedas feature points, the present analysis assumes thatthe triple junctions are randomly distributed in alldirections. In cases where this assumption isinvalid, knowledge of the distribution must beknown in order to conduct the registry analysis.

The minimization problem posed in Eq. (5) isone that has been widely applied for many years invarious fields. The solution for the translationvector is given as the difference between the


centroids of true and incorrect points according tothe expression

t ¼X

ioiðyi � OxiÞ

� �=X

ioi: ð6Þ

The rotation O is obtained from the polardecomposition of a matrix constructed from the xi

and yi vectors. Further discussion of the solution isavailable in standard works of linear analysis, andwill not be expounded on here.

3.2. Practical application

Two approaches have been taken in connectionwith the aforementioned analysis. (These can alsobe combined.) The first approach involves the useof ‘‘external markers’’ which are in commonbetween any two adjacent section planes. Acommon example is the use of several hardnessindentations which are observable on both planes.The centroid of the matching pairs of indentationson each plane can be used as the true and incorrectpositions in Eq. (6). The problem with externalmarkers is associated with the fact that thesemarkings are typically quite large relative to thefeatures of interest in the microstructure. Deter-mination of a precise location of the centroid ofthese features can be problematical, and thuserrors can be large.

When precise registry between adjacent sectionplanes is necessary, it is useful to employ ‘‘internalmarkers’’. These are features of the microstructureitself that carry over from one section plane to thenext. Examples include the orientations andphases of the grains themselves, the positions oftriple junctions and grain boundaries, twin bound-aries, etc. Usually, the use of internal markersrequires one or more additional assumptionsabout the statistical nature of the distribution ofthese markers in the microstructure. For example,it might be assumed that the orientation distribu-tion of the triple junctions is uniform (i.e., there isno preferred direction to the distribution of triplelines in the microstructure). The measured dis-tribution can then be compared with the uniformmodel distribution (with its associated geometricalweighting factors oi) through Eq. (6). In someinstances (e.g., when twin boundaries are present

in the microstructure), additional statistical as-sumptions may not be necessary.

New grain boundary energy and mobility datacan be obtained from 3D MIMS data [15]. Furtherresults will soon be forthcoming. Our presentpurpose is to note this ability that MIMS provides.

4. Summary

MIMS exploits a novel coupling of contrastimaging with phase and orientation determinationand with calibrated serial sectioning to obtaincharacterizations of what has been called the 3D

idealized aggregate function GðxÞ: This function

GðxÞ ¼ ffðxÞ; gðxÞg ð7Þ

describes the phase f and the lattice orientation g

of each point x in the 3D sample. GðxÞ contains acomplete description of the interfacial network.GðxÞ has many known connections to the proper-ties of polycrystalline materials (see Adams andOlson, [2]). Such functions have never before beenobtained, and the invention of MIMS constitutesan essential advance and coupling of contrast andorientation imaging microscopies required toobtain them.

Acknowledgements

This work was supported primarily by theMRSEC Program of the National Science Foun-dation under Award Numbers DMR-9632556 andDMR-0079996.

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mapping the mesoscale interface structure in polycrystalline materials

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