Features of Transmission EBSD and its Application

SEIICHI SUZUKI1,2

1.—TSL Solutions KK, #SIC2-401, 5-4-30, Nishihashimoto, Midori-Ku, Kanagawa, Sagamihara252-0131, Japan. 2.—e-mail: info@tsljapan.com

Features of transmission electron backscatter diffraction (EBSD) observationwith a standard EBSD (s-EBSD) detector are surveyed in this study. Heavilydeformed Al and 8Cr tempered martensite transmission electron microscope(TEM) specimens were used for this study. It is shown that a specimen tiltangle of �30�–40� in the opposite direction of the usual 70� and a smallerworking distance in the range 4 mm–5 mm are recommended when using as-EBSD detector. Specimen thickness and accelerating voltage (Acc.V) have astrong affect on the quality of transmission EBSD patterns and orientationmaps. Higher Acc.Vs are generally recommended to get good quality orien-tation maps. In case of very thin specimens, lowering the Acc.Vs will givebetter results. In the observation of a thin film of an 8Cr tempered martensitesteel specimen, it is confirmed that t-EBSD can provide images and detailedquantitative orientation data comparable with that obtained by TEM. It is alsoshown that small precipitates of Cr23C6 with sizes around 30 nm could bedetected and their orientations measured.

INTRODUCTION

The transmission electron microscope (TEM) isgenerally considered the tool of choice for themicrostructural analysis of materials at the nano-scale. Atomic scale resolution is becoming routinefor modern high-resolution TEMs. Electron diffrac-tion can be used to analyze the crystal structure andcrystallographic orientation on a point-by-point ba-sis in the TEM. Spot diffraction, Kikuchi diffraction,and convergent beam diffraction are all viabletechniques for performing such analysis. However,one of the major difficulties that remains is themapping of orientations in an automated and robustmanner. Such capabilities are beginning to emergeusing automated indexing for spot diffraction pat-terns. Combining these automated indexing tech-niques with the nanobeam diffraction capability ofthe TEM, the spatial resolution of orientationmapping in the TEM can reach a 2 nm to 3 nmscale.1 But the accuracy of measured orientations isstill limited compared with the results of electronbackscatter diffraction (EBSD) in the scanningelectron microscope (SEM). The achievable spatialresolution of standard EBSD (s-EBSD) is still at the20 nm–30 nm level when combined with fieldemission SEM, although its orientation accuracy is

stable and it is generally a range of 0.5�. The auto-mated EBSD technique has made it nearly routineto quantitatively analyze the microstructure ofmaterials available based on crystallographic ori-entation. However, achieving spatial resolutionsbetter than 20 nm–30 nm with EBSD continues tobe difficult even with the most modern EBSD sys-tems and SEMs. A great advance would be to marrythe routine quantitative capability of automatedEBSD with the spatial resolution of the TEM—to beable to achieve EBSD spatial resolutions measuredin the nm instead of in the tens of nm of s-EBSD.1

In 2012, Keller and Geiss demonstrated thatEBSD patterns could be acquired from a thin filmspecimen by transmitted electrons in the SEM.2

They used a s-EBSD detector mounted on theirSEM and a thin film specimen (TEM specimen) wastilted in the opposite direction of the standardreflection EBSD configuration to enable a geometrywhere a transmitted electron can hit the phosphorscreen of the EBSD detector in the standard posi-tion as shown in Fig. 1. They showed that EBSDpatterns formed by these transmitted electronscame from very small volumes of the specimen.They suggested that this technique could improvethat spatial resolution of EBSD. Following theirpaper, Trimby showed that this high-resolution

JOM, Vol. 65, No. 9, 2013

DOI: 10.1007/s11837-013-0700-6� 2013 The Author(s). This article is published with open access at Springerlink.com

1254 (Published online July 27, 2013)

EBSD image can be acquired by using this tech-nique.3 In this paper, the basic features of theEBSD patterns formed by transmitted electrons aresurveyed, and an application of the technique toanalyze the microstructure of a 8Cr temperedmartensite specimen is described.

Keller and Geiss termed this technique ‘‘trans-mission EBSD (t-EBSD).’’ There are some argu-ments about whether it is correct to refer to thistechnique as t-EBSD. The term ‘‘backscatter’’ is nottruly valid. Therefore, the term ‘‘transmissionKikuchi diffraction’’ is suggested instead. However,since the name of EBSD is already recognized widelyas a method for analyzing microstructure using Ki-kuchi electron diffraction patterns in the SEM, theterm of t-EBSD is also used in this articles out ofrespect for the initial work of Keller and Geiss.

EXPERIMENTS

The effects of specimen tilt angle, working distance(WD), and accelerating voltage (Acc.V) were studiedto determine the optimal conditions for t-EBSD. Allt-EBSD patterns and map data were obtained by useof a JEOL JSM-7001F SEM (JEOL Ltd., Akishima,Tokyo, Japan) with EDAX-TSL OIM EBSD system(EDAX Inc. (Ametek), Mahwah, NJ) equipped with aDigiView 1612 high-speed charge-coupled devicecamera. Special specimen holders were made to setthe specimen at tilt angles of 20�, 40�, and 60� fromthe horizontal plane in a direction opposite to thes-EBSD tilt direction as shown in Fig. 1. An exami-nation of the effects of WD and the Acc.V were testedby varying the WD to values of 5 mm, 10 mm, and15 mm and Acc.V of 15 kV and 25 kV. A captureangle of s-EBSD patterns at a 15-mm WD is �75�with this geometry. The capture angle variesdepending on WD and becomes about 65� at a 5-mmWD. A thin film specimen of annealed Al after heavydeformation and a thin film sample of 8Cr temperedmartensite steel were used for these experiments.These specimens were prepared originally for TEMobservation by electro-chemical etching, which has ahole near the center of the specimen. The samplethickness around the hole is thin, and it becomesthicker away from the hole.

RESULTS

Heavily Deformed Al Thin Film

Effects of Specimen Tilt Angle and WD

The effects of specimen tilt angle and WD ont-EBSD patterns with these experimental settingsare shown in Fig. 2. These patterns were collectedfrom the same position of the specimen under aspecified condition. A portion of the pattern is ob-scured when the specimen at a lower tilt angle isused along with a longer WD. These results suggestthat a shorter WD and higher tilt angle are betterfor acquiring t-EBSD patterns for this specificEBSD detector geometry. Figure 3 shows inversepole figure (IPF) orientation maps overlaid on imagequality (IQ) maps (top half) and IQ maps (Sidebot-tom half) obtained at different specimen tilt anglesby t-EBSD from the Al specimen. IPF maps aremaps colored according to the crystal plane normaldirection (ND) aligned with a specified sampledirection (in this case the sample normal). The colorscheme used has red for (001), green for (101), andred for (111). This scanned area is thick at the leftside and becomes thinner at the right. The WD wasset at 5 mm based on the results of Fig. 2. Thesharpness of the IQ maps became better at lower tiltangles (20�). This is more apparent in the thickerarea on the left-hand side of the maps. This can beexplained by the fact that the electron beam path inthe specimen becomes longer with increased tilt ofthe specimen. This results in increasing beamspreading in the specimen leading to poor spatialresolution. Thus, the spatial resolution will be bet-ter with decreasing specimen tilt. On the otherhand, IPF orientation maps look better with highertilt. The average Confidence Index that shows thereliability of indexing results had 0.08, 0.14, and0.31 for the IPF maps with a tilting angle of 20�, 40�,and 60�, respectively. As shown in Fig. 2, the con-trast of bands at the upper part of the detector be-comes very weak with decreasing tilt. It becomesdifficult for the automated band detection of thebands to correctly detect bands from this area of thet-EBSD pattern resulting in poor indexing.

Effects of Specimen Thickness

The quality of t-EBSD patterns is very muchdependent on the thickness of the specimen. Thisdependence also has a strong effect on the spatialresolution of the t-EBSD map. Figure 4 showsexamples of how the pattern changes with specimenthickness. The specimen is 8Cr tempered martens-ite, and one grain occupies the full thickness of thesample. These patterns are acquired at 25 kV. Itshows that if the specimen is very thin, the patternbecomes weak and noisy as shown in Fig. 4a. As thespecimen becomes thicker, the patterns start to losetheir sharpness starting at the outer edges of thescreen as shown in Fig. 4c and d. Then as the

TEM SpecimenEBSDDetector

Primary Electron Beam

SEM Objective Lens

WD

Specimen Tilting Angle

Fig. 1. TEM specimen setting arrangement for t-EBSD.

Features of Transmission EBSD and its Application 1255

sample becomes thicker, the band contrast reversesas shown in Fig. 4f.4 It should be noted that all ofthese patterns can be indexed by the computer

algorithms, but it is easy to understand thatthe algorithms will struggle to achieve high-precision orientation measurements especially for

Tilt: 20° Tilt: 40° Tilt: 60°

WD

: 5

WD

: 10

WD

: 15

Fig. 2. Changes in t-EBSD patterns depending on specimen tilting angle and WD. Specimen was Al thin film, and Acc.V was set at 25 kV.

Fig. 3. Effects of specimen tilting angle to t-EBSD maps. Spatial resolutions is better in lower tilting angle, but indexing result is better in highertilting angle.

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the patterns within the thicker region of the sample.Figure 5 shows t-EBSD IPF orientation maps of theAl specimen near the hole at Acc.V of 15 kV and25 kV. The specimen thickness is thin at the left-hand side and becomes thicker at the right-handside of the maps. The sharpness of the mapsobtained from the thicker regions of the sample(right sides of the maps) are obviously better in themap obtained at 25 kV than that obtained at 15 kV.But the quality of the left side of the map (corre-sponding to the thin region of the sample) obtainedat 15 kV is obviously better than that obtained at25 kV. The quality of the map data clearly dependson both specimen thickness and Acc.V. The thickerthe sample, the higher Acc.V that should be used toachieve good t-EBSD results.

Next, the effect of overlapping grains through thethickness of the sample was investigated. If thespecimen thickness stays within a reasonable range(estimated as 100 nm to 400 nm) for t-EBSD, over-laid grains do not appear to seriously hamper theformation of t-EBSD patterns. Figure 6 comparesIPF maps overlaid on IQ maps acquired by boths-EBSD and t-EBSD. Once again, the specimen isthe heavily deformed Al thin film and the observa-tion area was set near the hole. Figure 6a and b aremaps acquired by s-EBSD from the front and backsurfaces of the same area of the specimen, respec-tively. The back surface map is reversed left to rightfor comparison with the front surface map. Thegrains highlighted by blue arrows are examples ofgrains extending through the full thickness of thesample. Note that the maps are similar for the thinregions of the sample area near the edge of the hole

(near left bottom corner), whereas regions of themap from the thick parts of the sample (near the topand right) are very different. The dissimilarity ofthe maps in the thick regions is due to grains thatoverlap in the thickness direction of the sample.Figure 6c is an orientation map acquired by t-EBSDfrom the same area of the specimen. This t-EBSDimage was acquired directing the electron beam onto the front surface of the sample. The IPF mapsFig. 6b and c are very similar. This shows thatt-EBSD patterns are primarily formed at the bottom(or exiting) surface layer of the specimen. This isfortunate, as grains that overlap in the thicknessdirection do not detrimentally affect the formationof t-EBSD patterns as long as the total thickness ofthe specimen stays within a reasonable range fortransmission. The lower part of the t-EBSD mapshown in Fig. 6c is particularly good, but it becomesnoisier at the upper right, which is the thicker partof the specimen.

Cr Tempered Martensite

TEM Bright Field versus t-EBSD IQ Map

Figure 7shows the microstructure of temperedmartensite of 8Cr steel for the same area observedby both TEM and t-EBSD. Figure 7a is a bright fieldimage obtained by TEM at 200 kV. The magnifica-tion was set at 15 kx. Figure 7b is an IQ mapobtained by t-EBSD in the SEM at 25 kV at amagnification of 10 kx. Figure 7c is an IQ mapobtained by s-EBSD in the SEM at 15 kV. Figure 7dis a SEM image obtained by SEM at 25 kV. Theimages of Fig. 7b–d were obtained at tilt condition,

Fig. 4. Example of how pattern changes depending on specimen thickness. These patterns are acquired at the position shown above of 8Crtempered martensite specimen. Position (a) is very close to the edge of the hole.

Features of Transmission EBSD and its Application 1257

15kV

25kV

Specimen thicknessThin Thick

2µm

Fig. 5. Effects of specimen thickness and Acc.V on the quality of t-EBSD maps. IPF maps overlaid on IQ map acquired at Acc.V of 15 and 25 kVwith Al thin film specimen. Yellow arrows show the same part of the specimen at a thin area.

Fig. 6. The comparison of IPF maps overlaid on IQ maps acquired by s-EBSD and t-EBSD. (a) and (b) are images of s-EBSD acquired from frontsurface and back surface of same area, respectively. White arrows show same grains. (c) is also an IPF map acquired by t-EBSD from the samearea of the specimen. It was acquired illuminating electron beam to the front surface and getting t-EBSD patterns from the back surface.

Fig. 7. (a) is a bright field image obtained by TEM at 200 kV, and (b) is an IQ map obtained by t-EBSD at 25 kV. The specimen was a thin film oftempered martensite of 8Cr steel.

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and these are tilt-corrected images. These imagesare from the exact same area, and Fig. 7a and b, aswell as Fig. 7c and d, look relatively similar,respectively, even though the mechanism of imageformation is completely different.

TEM bright field images exhibit a diffractioncontrast image formed by elections penetratingthrough the specimen. The specimen shows a lot ofsmall orientation changes in the field of view mak-ing the contrast of the bright field image appearquite complex.

The IQ map by EBSD is created using the sum ofintensities of the bands in the EBSD patterns asdetermined by the band detection computer algo-rithm (Hough transform5). The contrast in the IQmap reflects the sharpness of the bands in theindividual EBSD patterns obtained at each point inthe map. If there is no damage by specimen prepa-ration, contamination, or oxides formed on the sur-face of the specimen, the IQ map shows the qualityof the crystal of the specimen. The sharpness ofEBSD is reflective of the degree of disorder of thecrystal in the diffracting volume. Grain boundariescan be considered regions where the atoms in thecrystal lattice are highly disordered. The differencesin the IQ maps in Fig. 7b and c arise from the dif-ference in the diffracted electrons, transmittedversus backscattered electrons, and the specimentilt angle. The t-EBSD patterns used in constructingthis IQ map are formed by diffracted electronstransmitted through crystals at the bottom layer ofthe specimen. They are not the results of informa-tion integrated in the thickness direction. Thus, theIQ map appears less complicated relative to theTEM bright field image. The s-EBSD patterns usedfor the IQ map are formed by diffracted electronsscattered in the backward direction. The sampleneeds to be tilted more to acquire these backscat-tered electrons effectively. This actually causeslarger beam spreading in the specimen resulting inpoor spatial resolution.3 It is also affected more bysample surface topography than t-EBSD. The SEMimage mainly reflects the surface topography of thespecimen, which is why the images of Fig. 7c and dlook relatively similar.

One question that arises in an inspection of theseresults is whether the fine and faint lines observedwithin the grains in the IQ map as highlighted byred and blue arrows in Fig. 7b are dislocations. Themisorientations between both sides of the clearerlines shown by black arrow as an example are 4�–5�or more, and they are small angle boundaries. Themisorientations between both sides of these fine andfaint lines highlighted by the red arrow are gener-ally <1�, or within the fluctuation of orientationmeasurement. The misorientations between a littlebit thicker lines highlighted by the blue arrow are alittle bit larger. Given the magnification used inthese images, it is difficult to imagine a sourcefor these very fine lines except dislocations.

Dislocations disorder the crystal lattice and thusaffect the pattern quality leading to darker points inthe IQ map. Thus, it can be thought that very finelines are potentially individual dislocations and theslightly thicker lines having slightly larger misori-entations indicate a tangle of dislocations or thepresence of a dislocation wall. However, this has notbeen confirmed in this experiment.

Orientation Analysis

Figure 8 shows an IPF orientation map from themartensite structure obtained by t-EBSD. Detailedorientation information can be gleaned from thequantitative data from which these maps arereconstructed. The small changes in color betweenthe areas labeled as A, B, C, and D in the IPF mapcorrespond to small differences in orientation as isevident in the unit cell overlays in Fig. 8a. Thereare about 6�–7� differences between points Aand C, as well as B and D, and 1�–2� differ-ences between A and C, as well as B and D.These misorientations correspond to orientationrelations between variants in the martensitetransformation.6,7

Figure 9 a shows a (001) pole figure from theorientation data obtained from the observed area.The orientation data were rotated to bring the ori-entation cluster marked by the red circle to thecenter of the pole figure. The rotation about the NDwas also adjusted. After these rotations, the orien-tations of upper side grains were highlighted andplotted in the (001) pole figure as shown in Fig. 9cusing the same coloring as in the map. The polefigure shows the part of martensite variant orien-tation relations. Then two small spots shown byblue and light blue color arrows are two spots thatwere part of eight spots that would be createdaround the (001) pole of prior austenite after mar-tensite transformation. The blue and light bluecolors in the map of Fig. 9b are highlighted again byusing these two variant spot in the pole figure ofFig. 9c. It shows clearly the orientation relationsexplained in the previous paragraph regardingFig. 8a.

Figure 10 shows the distribution of misorienta-tions for the map data. The colored ranges of thechart are highlighted on the IQ map. Blue bound-aries correspond to general boundaries or twinboundaries of the original austenite phase beforemartensite transformation. Green boundarieshighlight the boundaries between matrix and chro-mium carbide. Yellow boundaries indicate variantorientation relations for the martensite transfor-mation. Red boundaries show the boundaries withthe twin orientation relation.

All these analyses based on orientation maps,which are not practically available with TEMobservation, can be done now relatively easily byt-EBSD.

Features of Transmission EBSD and its Application 1259

Analysis of Chromium Carbide Precipitates

Figure 11 shows an IPF map and an IQ map fromdifferent areas of the same specimen. Small grainshighlighted in green on the IQ map are chromiumcarbides (Cr23C6) that have a cubic structure. Thesedata were taken with a step size of 10 nm at anAcc.V of 25 kV. The magnification was set at 15 kx.The minimum size of chromium carbide that wasdetected reasonably well was about 30 nm indiameter. However, the ability to count these smallprecipitates will depend on where those precipitatesare located. If they are located on the back surface,they will produce clear patterns. If they are on theinside of the specimen, the patterns will be noisy orcompletely missing. Figure 12 shows examples oft-EBSD patterns taken from the chromium carbide

precipitates and the ferrite matrix. Both of thesetwo phases have a cubic crystal structure with dif-ferent structure factors. They were easily differen-tiated from each other. Chromium carbides areprecipitated along small angle grain boundaries,and most of them have the same orientation,although they were precipitated separately. Anexample of the orientation relation between theferrite matrix and the chromium carbide precipi-tates is shown in the (001) pole figure in Fig. 11c.The two unit cells show the orientation of ferritematrix and carbide precipitate, respectively. This isa typical example of misorientation between chro-mium carbide and ferrite matrix, that is, a 45�rotation around a near<001> axis with either sideof the ferrite matrix. The common rotation axis is

IPF map (RD) IPF map (TD) IPF map (ND)

A

B

C

D (a) (b) (c)

2 µµm

Fig. 8. IPF orientation maps of RD, TD, and ND sample directions.

Fig. 9. (a) is a (001) pole figure of the whole scan area. (c) is a pole figure of selected area colored in map (b) after rotating the orientation data tobring the cluster marked by a red circle to the center and rotation around the ND axis is adjusted.

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Fig. 10. Misorientation chart of orientation map data. The colored range of the chart is highlighted on the IQ map. The boundaries of thesemisorientation angles show some specific features.

Fig. 11. (a) IPF map overlaid on IQ map, and (b) IQ map where chromium carbides are highlighted with a green color. (001) Pole figure thatshows typical misorientation relation between chromium carbides and ferrite matrix.

Fig. 12. Examples of t-EBSD patterns from chromium carbide and ferrite matrix.

Features of Transmission EBSD and its Application 1261

near <001>, but it is always tilted from exact<001> by about 9�.

SUMMARY

Specimen Tilt Angle and WD

It is concluded that the optimum specimen tiltangle for t-EBSD with the system used for theseexperiments is to be �40�. Figure 3 shows that asmaller tilt angle gives better spatial resolution re-sults. A higher tilt angle increases the practicalspecimen thickness for electron beam travel verti-cally in the specimen. However, lower indexing re-sults are obtained at decreasing specimen tilt due tothe loss of information at the upper part of thephosphor screen. This is due to the EBSD detectorposition, which is relatively high with respect to thespecimen position. It is very opportune that ans-EBSD detector can be used for t-EBSD data col-lection without any modification. However, thetypical s-EBSD position is not the ideal detectorposition for t-EBSD. If the detector can be set at alower position with a higher elevation angle, asmaller specimen tilt angle can be used that wouldimprove the quality of t-EBSD patterns and thespatial resolution.

Specimen Thickness

Specimen thickness has a significant effect on thequality of t-EBSD patterns; hence, it also stronglyaffects the collection of the t-EBSD orientation mapdata as Trimby discussed in his paper.3 One featureof the t-EBSD pattern is that band contrast becomesinverted if electrons are diffracted from a thickerpart of the sample with the same lattice orientation,namely, a single though-thickness grain or a largegrain. This can be explained by the travel length ofdiffracted electrons along some crystal planes. Thebands in EBSD patterns are projections of crystalplanes within the diffracting crystal lattice. If dif-fracted electrons travel longer distance along thecrystal plane, they are scattered by atoms existingalong the electron travel direction. As a result, thenumber of electrons traveling in the original dif-fracted direction decreases considerably leading to aloss of intensity. Thus, the contrast becomes in-verted. Present EBSD software is programmed todetect bright peaks in the Hough transform used forautomated band detection, and thus, these invertedcontrast bands will not be correctly detectedresulting in poor indexing. This also depends onAcc.V; when a higher Acc.V is used, the invertedcontrast is minimized. However, the quality of theresults from the thinner areas of the sample willdiminish. This means a balance between the speci-men thickness and Acc.V must be achieved to obtaingood t-EBSD results.

Overlapping Grains

The observations made in this study show thatoverlapping grains do not pose a particular problemto t-EBSD. This is a big advantage over TEM-basedapproaches to the collection of orientation datawhere overlapping grains can lead to ambiguousresults. Diffraction patterns from t-EBSD areformed only from the bottom surface (exiting sur-face) of the sample. Grains that are bigger and ex-tend through the thickness of the sample areactually more problematic for t-EBSD as they canproduce patterns with an inversion in the bandcontrast.

Spatial Resolution

There is still some discussion regarding the spa-tial resolution of the t-EBSD method. It is clear fromthe results presented in this work that the spatialresolution depends very much on specimen thick-ness and Acc.V. It is assumed that the resolutiondepends on probe size too. Grain boundaries tend toappear more clearly than in s-EBSD maps as far asthe specimen thickness is in a reasonable range. Butthe clarity still depends on the inclination of thegrain boundary relative to the surface plane.Assuming optimal conditions for both t-EBSD and s-EBSD, t-EBSD is capable of spatial resolutions onthe order of the probe size, which is considerablybetter than s-EBSD.

CONCLUSIONS

Specimen thickness and Acc.V have a strong af-fect on the quality of t-EBSD patterns and orienta-tion maps. Higher Acc.Vs are generallyrecommended to get good quality orientation maps.In case of the very thin specimens, lowering Acc.Vwill give better results. A spatial resolution of the10-nm level can be achieved by t-EBSD, but it de-pends on specimen thickness and Acc.V.

An existing EBSD detector can be used fort-EBSD. However, a specimen holder that allows fortransmission of the electron beam is required. Whenusing a s-EBSD detector, it is recommended that aspecimen tilt angle of �30� to 40� in the oppositedirection of the usual 70� be used. A smaller WDshould also be used: in the range 4 mm–5 mm.

In this study, a thin film of an 8Cr temperedmartensite steel specimen was observed by t-EBSD.It is confirmed that t-EBSD provides images anddetailed quantitative orientation data comparablewith that obtained by TEM. A study of small pre-cipitates of Cr23C6 was also undertaken. Precipi-tates with sizes around 30 nm could be detected andtheir orientations measured. It was shown thatCr23C6 precipitations appeared along small angleboundaries with strong orientation relations to theferrite matrix. Very fine lines were observed in IQ

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images of 8Cr tempered martensite steel specimen,which were acquired with very small step sizes suchas 20 nm or less. These fine lines are thought to bedislocations, or arrays or tangles of dislocations, butthis has not been confirmed in this experiment.

ACKNOWLEDGMENTS

The author expresses his appreciation to Dr.Hiroki Tanaka of Sumitomo Light Metal IndustryKK and Prof. Soumei Ohnuki and Mr. TomokiKubota of Hokkaido University for providing TEMspecimen for this research work. The author alsoexpresses his appreciation to Dr. Stuart Wright ofAMETEK/EDAX division for very fruitful discus-sions to complete this article. Furthermore, theauthor acknowledges the Japan Institute ofMetals and Materials for granting use of the data ofFigs. 1, 5, 6, and 7, which were originally used inthe author’s article to be published in Journal ofJapan Inst. Metals 7, 2013.

OPEN ACCESS

This article is distributed under the terms of theCreative Commons Attribution License which per-mits any use, distribution, and reproduction in anymedium, provided the original author(s) and thesource are credited.

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