Report on VAMAS Round Robin of 

ISO 13067: Microbeam analysis –

Electron backscatter diffraction –

Measurement of average grain size

Adam!Creuziger

Mark!Vaudin

NISTIR 7814
NISTIR 7814

Report on VAMAS Round Robin of 

ISO 13067: Microbeam analysis –

Electron backscatter diffraction –

Measurement of average grain size

Adam!Creuziger

Guest Researcher 

Metallurgy Division

Material Measurement Lab

Kent State University

Mark Vaudin

Ceramics Division

Material Measurement Lab

September 2011

U.S.$Department$of$Commerce

Rebecca&M.&Blank,&Acting&Secretary

National!Institute!of!Standards!and!Technology

Patrick&D.&Gallagher,&Under&Secretary&for&Standards&and&Technology&

and&Director
Abstract

NIST recently!participated in!a Versailles!Project!on!Advanced!Materials!and!

Standards!(VAMAS)!sponsored round!robin!evaluation!of!a!new!ISO!document!draft,!

ISO!13067:!Microbeam!analysis!– Electron!backscatter!diffraction!– Measurement!of!

average!grain!size.!!This!report!details!the!results!of!the!study,!some!of!the!

difficulties!encountered and!suggestions!to!improve the!ISO!document. The!average!

grain!size!measured!using!this!technique!was!internally!consistent!within!NIST and!

compared!well!to!the!preliminary!aggregate!round!robin!data!revealed!to!the!

authors.!The!methods!described!in!ISO!13067!to!modify!or ‘clean!up’!the!raw!data!

were!found!to!significantly!affect!the!average!grain!size!value.!

Background

In!April!of!2010,!the!authors!were!approached!about!participating!in!a!round!

robin!evaluation!of!a!draft!International!Organization!for!Standardization (ISO)!

document!created by!ISO!technical!committee!(TC)!202.!!This!document!is!ISO!

13067:!Microbeam!analysis!– Electron!backscatter!diffraction!– Measurement!of!

average!grain!size [1].!The!Versailles!Project!on!Advanced!Materials!and!Standards!

(VAMAS)!would!coordinate!the!round!robin!under!Technical!Working!Area!(TWA)

37,!Quantitative!Microstructural!Analysis.!An!alternate!standard!for!grain!size!

measurement!using!electron!backscatter!diffraction!(EBSD)!is!also!available!as!

ASTM!E2627:!Standard!Practice!for!Determining!Average!Grain!Size!Using!Electron!

Backscatter!Diffraction!(EBSD)!in!Fully!Recrystallized!Polycrystalline!Materials [2].

Prior!standard!methods!for!average!grain!size!measurement!using!light!

microscopy!are available. Standards!such!as!ASTM!E112:!Standard!Test!Methods!for!

Determining!Average!Grain!Size [3] have!been!published!since!the!1950’s and!are!

frequently!used!for!grain!size!analysis.!However,!there!are!difficulties!with!this!and!

similar!techniques.

Conventional!grain!size!analysis!requires!etching!of!a!polished!sample!to!

reveal!the!grain!structure.!!Finding!a!suitable!etchant!can!be!a!nonatrivial!task.!!The!

ideal etchant!would!evenly!etch all!grain!boundaries and!be!safe!for!the!user.!!Real!

etchant!solutions!typically only!attack!certain!types!of!grain!boundaries or are

otherwise!dangerous!to!use.!!There!is!also!the!difficulty!in!determining!the!type!of!

grain!boundary.!!There!are!many!different!types!of!grain!boundaries!that!can!have!

particular!properties:!high!angle,!low!angle,!twin,!coincident!site!lattices!(CSL).!

Usually!these!structures!cannot!be!distinguished!by!etching alone!and!may!be!types!

of!grain!boundaries!to!disregard!in!an!average!grain!size!measurement.

Grain!size!analysis!methods!based!upon!electron!backscatter!diffraction

(EBSD) can!be!used!to!overcome!some!of!these!difficulties.!One!of!the!most!

significant!is!that!the!sample!does!not!need!to!be!etched.!The!EBSD!method!provides!

crystallographic!orientation!data!at!a!series!of!points.!!The!orientation!difference!

between!adjacent!points!can!be!used!to!define!a!grain!boundary.!In!this!way!the!

definition!of!a!grain!boundary!is!applied!uniformly!throughout!the!sample.!

Crystallographic!and!sample!boundary!relations!can!be!used!to!determine!other!

grain boundary!types.!!The!crystallography!information!can!also!be!used!as!phase!

discrimination as!well.!!There!are!some!disadvantages!of!EBSD,!namely!the!
requirement!of!a!scanning!electron!microscope!(SEM)!with!EBSD!equipment!for!

automated!indexing.!!The!surface!preparation!is!also!more!stringent,!as!the!EBSD!

technique!requires!the!surface!50!nm!to!100!nm!to!have!diffracting!lattice!planes.!

This!often!requires!chemoamechanical!polishing!or!electrolytic!polishing!to!remove!

any!deformation!caused!by!mechanical!polishing on!the!surface.

Methods

Samples

Dr.!Kenneth Mingard!at!the!National!Physical!Laboratory!(NPL)!in!the!United!

Kingdom!provided!two!13!mm!diameter!commercial!purity!αaphase!(hexagonal)!Ti!

samples!for!our!investigations.!!The!samples!were!labeled,!sectioned,!polished!and!

electropolished prior!to!arrival.!!Two!microindents!were!made!in!the!surface!of!the!

sample,!one!on!the!edge!for!orientation!and!one!in!the!center.!!The!round!robin!

requested!that!the!authors!analyze!regions!within!5!mm!of!the!center indent,!and!

that!five!test!regions!should!be!scanned!on!each!sample.

Data(Acquisition

Two!different!scanning!electron!microscopes!(SEMs)!were!used!in!this!study:

a!Hitachi!Sa47001 and!a!JEOL!6400.!The!Hitachi!Sa4700!is a!cold!tip!fieldaemission!

gun!SEM!(FEGaSEM)!while!the!JEOL!6400!is a thermionic!emission!SEM!with!a LaB6

cathode.!Both!SEMs!are!equipped!with!an!Oxford!Instruments!Nordlys!II!detector!

and!an HKL Channel!5 software!package!for!EBSD!analysis (version!5.0.9.0).

As!per!ISO!13067,!the!SEM!magnification!was!calibrated!at!various!times!

during!the!study!according!to!ISO!16700:!Microbeam!analysis!– Scanning!electron!

microscopy!– Guidelines!for!calibrating!image!magnification [3], using!National!

Institute!of!Standards!and!Technology!(NIST)!Reference!Material!(RM)!8820 [4].

The!final!calibrations for!each!instrument are!recorded!in!Table!1.! In!working!with!

the!manufacturer,!the!authors determined!that!significant!scan!instabilities!could!

result unless!the Hitachi!SEM!was!set!to!a!‘slow!scan’!mode!during the!EBSD!data!

collection!process. These!results have underscored!the!need!to!check!the!

magnification!calibration!and!scan!generation!of!the!SEMs!before!collecting!data.

The!scan!employed!by!the!authors was!400!pixels x!400!pixels with!a!step!

size!of!2.5!μm.!At!each!point!in!a!scan,!the!software!automatically!obtained!an!

electron!backscatter!diffraction!pattern!(EBSP)!and!determined!the!position!of!

diffraction!bands.!From!the!band!location pattern!the!orientation!of!the!diffracting!

planes!at!the!analysis!point and!the!angles!between!the!diffracting!planes!were

determined.!From!the!interplanar!angles,!the!crystallographic!orientation!at!the!

analysis!point!was!determined. More!information!on!the!EBSD!technique!can!be!

found!in![5].

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1 "Certain!commercial!equipment,!instruments,!or!materials!are!identified!in!this!paper!in!order!to!specify!the!experimental!

procedure!adequately.!Such!identification!is!not!intended!to!imply!recommendation!or!endorsement!by!the!National!Institute!

of!Standards!and!Technology,!nor!is!it!intended!to!imply!that!the!materials!or!equipment!identified!are!necessarily!the!best!

available!for!the!purpose."
The!Hitachi!software!had!access!to!the!PDF2!database [6] and!the!NIST!

Structural!Database![7],!which!contained!a!variety!of!different!αaphase!Ti!lattice!

parameters.!!After!comparing!the!pattern!fits,!the!TiaJOMTAA![8] parameters!or!Tia

PPSOAU![9] parameters!were found!to!improve!the!hit!rate (ratio!of!successfully!

indexed!pixels!to!total!pixels!investigated)!by!approximately!5% over!the!

parameters in!the!HKL!database.!The!unit!cells!from each!of!these!files!are!given!in!

Table!2. The!JEOL!system!did!not!have!access!to!the!PDF2!database,!so!a database!

entry!was!generated using!the!HKL!software!program Twist!with!Wyckoff!positions!

of!(1/3,!2/3,!1/4)!and!space!group!194.!

Before!each!scan,!it!was!necessary!to!adjust!the!EBSD!calibration parameters!

in!the!HKL!EBSD!capture!software!(Flamenco) to!obtain!the!high!hit!rate (>90%)

required!by!ISO!13067.!If!the!steps described below were!not!carried!out!between!

data!scans!or if the!stage!were!moved!to!a!different!location!on!the!sample, the!hit!

rate!would!decrease!by!10%!to!30%.!The!sample!working!distance was!adjusted!

such!that the!highest!intensity spot!was in!the!center!of!the!phosphor!screen.!!A!new!

background!was!collected,!and!the!EBSD!geometry!was!adjusted!so!the!region!of!

interest!(ROI) circle!captured!the!welladefined!portion!of!the!Kikuchi!pattern.!!Then!

the!EBSD calibration!was!refined to!set the!detector!geometry!in!Flamenco.!!

After!calibrating!the!EBSD!system,!the!scan!parameters!were!varied!to!

determine!optimal!settings for!both!microscopes.!!The!scan!parameters!used!for!our!

analysis!are!listed!in!Appendix!A.!Most!of!these!parameters!were!determined!

iteratively!or!with!assistance!from!the!manufacturer. Increasing!the!maximum!

number!of!bands!from!5!to!6!lead!to!a!decrease!in!hit!rate,!as!did!low!or!normal!

divergence.!!The!authors also!wanted!to!minimize!the!time!it!took!to!acquire!the!

data!sets,!which!lead!to!our!choices!for!acquisition!time,!pattern!binning,!number!of!

frames!to!average,!Hough!resolution,!and!number!of!reflectors.!Using!a!single!frame!

was!too!noisy!for!reliable!indexing,!but!averaging!more!than!two!frames!did!not!

further!improve!indexing. The!data!collection!scan!was!160 000!pixels;!the!average!

duration!for!the!JEOL!SEM!was!3!h!22!min!and!for!the!Hitachi!it!was!1!h!40min.

Data(Analysis

Figure!1 shows!the!raw!data!from!a typical scan,!with!coloration!

corresponding!to!the!Euler!angles!of!each!pixel. After!acquisition!of!the!data,!data!

cleaning!operations!were!conducted!prior!to!determination!the!grain!size.!To!

summarize!ISO 13067,!there!are!three!parts!to!the!data!cleaning!operation:!removal!

of!small!grains;!filling!in!unindexed!pixels;!and!setting!a!minimum!grain!size!for!

grain!size!analysis. The!complete!procedure!the!authors used!for!data!cleaning!is!

listed!in!Appendix!B!and!includes!information!about!the!images!recorded!for!the!

VAMAS!report!sheets.!The!median!recommended!value!from!ISO!13067!for!smallest!

grains!(4)!was!used,!so!all!grains less!than!four!pixels!were!nullified!and!set!to!zero!

solution.!After!this,!a!threshold!of!5!nearest!neighbors!or!more!was!used for!cleanup!

of!the!dataset,!so!that!all!zero!solution!data!points!with!five!nearest!neighbors or!

more of!a!common!orientation!were!filled!in!with!the!average!orientation.!!This!

value!for!nearest!neighbors!was!chosen!from!the!constraints!in!the!ISO!document:!

that!the!number!of!pixels!modified!should!not!exceed!5%!of!the!data!set;!the!fill!
should!not!be!done!iteratively;!and!the!grains!should!not!have!obvious!holes!in!

them.!After!this,!grains!smaller!than!ten!pixels!were!removed!from!the!grain!size!

analysis.

A!consideration!in!determining!the!grain!size!in!these!samples!was!

pseudosymmetry,!defined!in!ISO!13067!as!the!potential!for!an!EBSD!pattern!to!be!

indexed!in!several!different!ways!due!to!internal!similarities!within!the!EBSD!

pattern that!are!not!caused!by!crystal!symmetry.!The!authors noted that in!the!Euler!

angle!maps some!regions!that!appeared!to!be!a!single!grain!would!have!a!number!of!

points of!a!different!orientation!within!the!apparent single grain. The!authors!

determined that!the only!difference!in!orientation!between!these!pixels was!that!the

c!and!a!axes!were!interchanged.!!These pseudosymmetries were!best!categorized by!

analyzing!the!misorientations!between!adjacent!pixels. Figure!2 is!an!example!of!a!

misorientation!angle!density!plot.!Each!spike!in!this!plot!is!an!overarepresentation!

of!a!specific!misorientation!angle.!!Misorientation!axes!corresponding!to!these!

misorientation!angles!were analyzed!by!plotting!in!an!inverse!pole!figure the!

misorientations!axes!for!a!small!range!of!angles!around!the!spike in!misorientation!

angle!density,!as!shown!in Figure!3.!!From!these!plots and!detailed!examination!of!

our!data!sets, ten!pseudosymmetry!operators!were!found,!as!listed!in!Table!3.!Only

four!pseudosymmetry!operators!were!found to!affect!the!grain!size!measurements;

the!other!pseudosymmetry!operators!did!not!occur!in!large!enough!groups!to!

remain!after data!cleaning!operations.

Equivalent!circle!diameter!and!grain!area!were!directly!calculated!in!Tango!

(the!HKL!EBSD!map!plotting!software). The!linear!intercept!values!requested!in!the!

VAMAS!report!were!not!calclated!by Tango.!A script!in!the!statistical!computing!

software, R, was!written!to!calculate!linear!intercept!values!and!relevant!statistics.!!

The!equation!to!calculate!the!linear!intercept!(LI)!value!is!given!in!ISO!13067![1].!

This!script!also checked the!average!values for!equivalent!circle!diameter!and!grain!

area from!Tango!against!those!calculated!in!R, and!they!were!found!to!be!in!

agreement.!

Results

Average!Grain!Size

Data!were!collected!from!five!areas!on!both!of!the!Ti!samples,!all!within!5!

mm!from!the!central!indent.!The!results!reported!to!the!VAMAS!round!robin!are!

summarized!in!Table!4 to!Table!7. Table!4 lists!the!mean!circle!equivalent!grain!size!

for!sample!23.!!Table!5 lists the!mean!linear!intercept!values!for!sample!23.!!Table!6

and!Table!7 respectively!describe!the!mean!circle!equivalent!grain!size!and!mean!

linear!intercept!values!for sample!24.!The!unweighted!average!and!standard!

deviation!are the!simple!averages of!the!mean!grain!size!and!standard!deviation!of!

the!average!grain!size!for!the!five!data!sets!recorded.!The!final!column!is!the!mean!of!

the!full!data!set,!which!creates!a!larger!set!from!each!of!the!five!individual!grain!size!

measurements,!and!the!mean!value!is!computed!from!the!large!dataset.!!There is!a!

discrepancy!between!the!mean!of!the!full!data!set!and!the!unweighted!average,!due!
to!the!different!number!of!grains in!each!data!set.!!However,!an average weighted!by!

the!number!of!grains matches!the!mean!of!the!full!data!set.

A!variety!of!different!data!cleaning!methods!was!investigated!before!

choosing!the parameters discussed!in!the!data!analysis!section.!Figure!4 and!Figure!

5 show!some!of!these!data!cleaning!methods!and!the!effect!they!had!on the!grain!

size!statistics. These figures!will!be!discussed!in!more!detail!below.

Uncertainty

As!currently!written,!ISO!13067!gives!very!little!guidance!as!to!uncertainty!

analysis.!ISO!13067!states,!“The!uncertainty!shall!be!determined!with!reference!to!

the!Guide!to!the!Expression!of!Uncertainty!in!Measurement.!ISO/TS!21748:2008.“!A!

few!factors!to!consider!follow!in!the!text!of!the!standard!(linear!calibration,!

resolution,!step!size,!postaacquisition!treatment!of!raw!data,!tilt,!specimen!drift),!but!

no references!or!guides!are!given!as!to!how!to!properly!account!for!them!for!EBSD!

methods or!integrate!them!into!an!aggregate!uncertainty!metric.!!At!this!time,!the!

authors!have!only!attempted!to!assess the!uncertainty!in specimen!drift,!tilt!error!

and!linear!calibration.!!

The!linear!calibration!errors!are!shown!in!Table!1.!!As!shown,!the!Hitachi!

may overestimate!the!grain!size!area!by!2.1%,!while!the!JEOL!may!underestimate!

the!area!by!4.1%.!The!tilt!was!assessed!by!measuring!RM8820!at!the!nominal!70°!tilt!

used!for!EBSD.!For!both!the!Hitachi!and!JEOL,!the!measured!value!was!69.8°. This!

0.2°!deviation results!in!a!shortening!perpendicular!to!the!tilt!axis!of!1%. To!assess

the!specimen!drift,!images!were!automatically!recorded!before!and!after!acquisition.!!

Image!subtraction!of!these!images!did!not!show!any!systematic!shifting!of!the!image!

within!the!resolution!of!the!SEM image,!which!was!1.76!μm!per!pixel.!

Noise!Reduction!Methods

Figure!4 shows!some!of!the!effects!of!noise!reduction!methods!and!the!initial!

minimum!grain!size!(section!6.3.1!in!ISO!13067).!!The majority!of!grains!in!the raw!

data set are individual!pixels!(5191!grains!of!the!6479!grains!detected!in!the!raw!

data!were!1!pixel!in!area).!!Removing!(removed!pixels!are!set!to!zero solution)!

single!pixels from!the!average!grain!size!calculation increases!the!circle!equivalent!

diameter!from!6.64!μm!to!23.4!μm.!!Increasing!the!initial!minimum!grain!size!up!to!

≤4!pixels!produces!more!modest!increases,!up!to!31.1!μm!for!≤4!pixels.!!At!this!

point, how!to!translate!the choice!of!initial!minimum!grain!size into!a!reasonable!

metric!for!uncertainty is!not clear,!but!the!effect!would!be!a!bias!error.

After!the!initial!minimum!grains!are!removed,!zero!solution!points!are!filled!

in!with!orientations!adjacent!to!the!point,!referred!to!as!noise!reduction.!ISO!13067!

recommends!avoiding!iterative!noise!reduction methods.!!For!the!noise!reduction!

methods!used!here,!points!that!have!no!solution!are!evaluated!to!determine!the!

number!of!nearest neighbors!(NN).!This!value!can!range!between!1!and!8,!since!the!

data!are recorded!in!a!rectilinear!grid.!!For!nonaiterative!noise!reduction,!one!value!

along!this!range!of!nearest!neighbors!is!chosen,!and!any!points!that!have!no!solution!

are!filled!if!they!have!that!value!of!nearest!neighbors!or!more.!!Three!different!NN!
values!were!investigated:!1,!5,!and!7. For!example,!in!the NN=7!case,!only!zero!

solution!points!that!had!7!indexed!points!surrounding!the!zero!solution!point!are

filled!in!with!the!average!orientation of!those!7!points.!The!grain!size!increased!as!

the!number!of!nearest!neighbors!decreased.! In!addition, a!sequential!iterative!

method!was!also!performed,!sequentially!decreasing!the!NN!value!from!8!to!4!while!

iterating!each!noise!reduction!step!until!there!were!no!more!points!with!that!

number!of!nearest!neighbors.!The grain!size!calculated!from!the iterative!sequential!

method!is!between!the grain!sizes!calculated!from!the 5!and!1!nearest!neighbor!

methods. Similar!to!the!effect!of!minimum!initial!grain!size,!the!authors are!not!sure!

how!to!translate!these data!into!a!reasonable!metric!for!uncertainty.!The!effects!of!

resolution!and!step!size!on!the!uncertainty!were!not addressed.

After!the!initial minimum!grain!size!and!the!noise!reduction!using!nearest!

neighbors,!an!additional!minimum!grain!size!of!10!pixels!is!applied!(ISO!13067!

section!6.3.4).!!All!grains!10!pixels!or!less!are!removed!from!the!average!grain!size!

measurement.!!While!this!step!may seem!redundant!to!the!initial!minimum!grain!

size!grain!size,!the!authors have!noted!that!after!noise!reduction,!grains!less!than!4!

pixels!are!created.!!The!10!pixels!cut!off!was!recommended!in!ISO!13067!due!to!

pixelation!errors.!!However,!as Figure!5 shows,!the!average!grain!size!increases!

nearly!linearly!for!each!pixel!in the!final!minimum!grain!cutoff,!introducing!the!

possibility!of!another!bias!error.!!

Discussion

The results!of!our!analysis!were selfaconsistent,!with!a!grain!size!average!of!

about!33!μm.!An!average!grain!contains!approximately!130!pixels,!calculated!from!

the!average!grain!size!and!step!size.!!Only!one!analysis!might!be!considered!an!

outlier (sample!24,!JEOL!area!1) leading!to!a!larger!standard!deviation!for!that!series!

than!the!other!three. The!other!three!data!sets!had!standard!deviations!of!about!1!

μm to!2!μm.!There!was!consistency!both!between!the!samples!and!between!the!

equipment!used.!!From!the!preliminary!aggregate!round!robin!data revealed!to!us,!

our!values!also!compare!well!with!the!mean!values!of!the!round!robin.

However,!it!is!the!opinion!of!the!authors!that!the!uncertainty!analysis!for!the!

ISO!needs!improvement.!!As!mentioned!in!the results,!several!contributions!to!the!

uncertainty!have!not!been!assessed, and!how!to!assess!them!is!not!clear.!!The!

choices!for!minimum!grain!size!cutoff!and!noise!reduction!methods!leave!the!final!

numbers!for!average!grain!size!dependent!on!these!choices and!may!create!bias!

errors.

Related!to!the!uncertainty!analysis,!different!noise!reduction!methods!can!

lead!to!different!values!for!the!average!grain!size.!For!the!noise!reduction!methods!

investigated,!different!numbers!of!nearest!neighbors!create!average grain!sizes!that!

differ!by!3!μm.!!In!addition, with!a!non!iterative!method, some!grains!in!the!sample!

have!regions!of!zero!solutions!interior!to!the!grain!boundary, even!after!noise!

reduction.!!The!authors have!also!noted!that!the!noise!reduction!method!can!create!

grains!smaller!than!the!initial minimum!grain!size. For!example,!often!1!pixel!square!

grains!are!created after!noise!reduction. It!is!not!clear!why!this!occurs.!!
Neither!ISO 13067 nor!ASTM!E2627 explicitly requires repeated!

measurements!such!as!those!performed!as!part!of!the!round!robin.!Without!

repeated!measurements,!the!uncertainty!can!only!be!determined!by!an!analysis!of!

the!scatter!in!the!data.!!A!typical!distribution!of!the!grain!size!is!shown!in!Figure!6,!

with!a mean!and!standard!deviation of!34.53!μm!±!15.83!μm.! As!written,!both!ISO!

13067!and!ASTM!E2627!base!the!uncertainty!on!the!dispersion!of!the!grain!size!in!a!

single!sample,!not!the!uncertainty!in!repeated!average!measurements.!Using!this!

definition, the!uncertainty!for!a!sample!from!this!data!set would!be!on!the!order!of!

15!μm,!which!does!not!seem!to!be!the!goal!of!either standard.!!

In!contrast,!the!method!in!ASTM!E112:!Standard!Test!Measurements!for!

Determining!Average!Grain!Size!provides!an!average!value!on!a!line!or!circle.!!These!

averages!are!then!used!to!calculate!the!uncertainty!on!the!average!value,!but!only!

the!average!value,!not!any!metrics!on!the!distribution!of!grain!sizes.!!A!similar!

metric!for!Gaussian!distributions!is!the!standard!deviation!of!the!mean,!which!is!the!

standard!deviation!divided!by!the!square!root!of!the!number!of!samples [10].!For!

the!distribution!shown!in!Figure!6 the!standard!deviation!of!the!mean!is!±0.51!μm.!

This!value!is!closer!in!magnitude!to!the!uncertainty!from!repeated!measurements

and!may!be!the!metric!intended.!A!further!question!is!the!applicability!of!a!mean,!

standard!deviation!and!standard!deviation!of!the!mean values on!a!distribution!that!

does!not!follow!a!Gaussian!distribution.!!Viewing!the!histogram!in!Figure!6,!it!is!

clear!that!this!is!not!a!normal!distribution,!but!possibly!closer!to!a!loganormal!or!

Weibull!distribution.!!Perhaps!metrics!that!describe!the!functional!form!of!the

distribution!would!be!more!useful!in!predicting!material!properties than!a!mean!

grain!size.

There!are!other!opportunities!for!the!EBSD!technique!that!are!not!currently!

utilized!in!ISO!13067.!!By!measuring!the!distribution!of!grain!sizes!in!the!test!area,!

not!just!a!simple!average!value,!there!is!more!information!in!the!data!set!than!an!

average!value.!!Often!the!largest!or!smallest!grains!dominate!some!material!

properties,!and!measurements!of!the!distribution!can!provide!information!about!

these!grain!sizes.!The!authors!recommend!that!any!subsequent!revisions!of!ISO!

13067!consider!reporting!the!distribution!in!grain!size!instead!of!focusing!on!an!

average!value.!These!and!other comments!to!improve!ISO!13067!will!be!provided!to!

the!ISO!TC!and!are!listed in!Appendix!C.!

Conclusions

ISO!13067:!‘Microbeam!analysis!– Electron!backscatter!diffraction!–

Measurement!of!average!grain!size’ advances!measurements!of!grain!size to!allow!

for!a!less!ambiguous!definition!of!a!grain.!Obtaining!EBSD!maps!of!high!enough!

quality!to!meet!this!standard!is!a!challenge,!and!may!be!very!difficult!for!novice!

users.!!A!revision!of!this!standard!or!a!new!standard!that!focuses!on!the!distribution!

of!the!grain!sizes!should!be!considered!to!utilize!the!discrete!grain!size!data

currently!recorded!by!the!EBSD!maps,!but!only!used!in!ISO!13067 to!calculate!a!

mean!value. The!uncertainty!analysis!section!of!ISO!13067 should!be!improved. As!

written,!it!is!unclear!if!the!uncertainty!is!to!be!estimated!by!repeated!measurements
or!a!single!measurement. More!details!on!how!to!integrate!data!cleaning!operations!

into!the!uncertainty!are!also!needed.

Acknowledgements

The!authors!would!like!to!thank!Dr.!Kenneth Mingard and!Dr. Peter!Quested

of!the!National!Physical!Laboratory!(NPL)!in!the!UK!for!inviting!us!to participate!in!

the!round!robin!and!for providing!the!Ti!samples; Dr.!John!Bonevich, Director!of!the!

Metallurgy/Ceramics Microscopy!Lab for!advice!and!assistance!with!the!

microscopes;!Scott!Sitzman of!Oxford!Instruments for!advice!and!assistance!with!the!

HKL!software!package;!and!William!Luecke!for!many!useful!discussions.

References

[1] ISO!FDIS!13067:!Microbeam!Analysis!– Electron!Backscatter!Diffraction!–

Measurement!of!average!grain!size.!2011.!!International!Organization!for!

Standardization.

[2] ASTM!E2627:!Standard!Practice!for!Determining!Average!Grain!Size!Using!

Electron!Backscatter!Diffraction!(EBSD)!in!Fully!Recrystallized!

Polycrystalline!Materials.!!2010.!ASTM!International.

[3] ASTM!E112:!Standard!Test!Methods!for!Determining!Average!Grain!Size.!!

2004.!ASTM!InternationalISO!16700:!Microbeam!analysis!– Scanning!

electron!microscopy!– Guidelines!for!calibrating!image!magnification.!

2004.!International!Organization!for!Standardization.

[4] National!Institute!of!Standards!and!Technology!Report!of!Investigation!

Reference!Materials!8820:!Scanning!Electron!Microscope!Scale!Calibration!

Artifact.!2009.!URL:!http://www.nist.gov/srm/index.cfm

[5] Introduction!to!Texture!Analysis!2nd Ed. O.!Engler!and!V.!Randle!CRC!Press!

2010

[6] Powder!Diffraction!File.!PDF2_2002 database.!International!Centre!for!

Diffraction!Data http://www.icdd.com/products/pdf2.htm

[7] NIST!Structural!Database.!National!Insitute!of!Standards!and!Technology!

http://www.nist.gov/srd/nist83.cfm

[8] H.!T.!Clark,!Jr.!“The!lattice!Parameters!of!High!Purity!Alpha!Titanium;!and!

the!Effects!of!Oxygen!and!Nitrogen!on!Them”!Journal!of!Metals (1949),!vol!

1,!p588

[9] R.!M.!Wood. “The!Lattice!Constants!of!High!Purity!Alpha!Titanium”!

Proceedings!of!the!Physical!Society,! London,!(1962),!vol.!80,!page!783

[10] Joint!Committee!for!Guides!in!Metrology.!“Evaluation!of!measurement!data!

– Guide!to!the!expression!of!uncertainty!in!measurement.”!!URL:!

http://www.bipm.org/en/publications/guides/gum.html
Figures

Figure(1:(Raw(Data(from(EBSD(map.((The(colors(correspond(to(the(Euler(angles listed(in(the(

key(above. Data(is(from(JEOL(data(set,(sample(24,(scan(1.
Figure(2:(Misorientation(angle(distribution(plot(showing(large(spikes(at(specific(angles.((The(

large(spikes(in(relative(frequency(correspond(to(systematic(misindexing(due(to(

pseudosymmetry. All(misorientations(5°(or(less(are(considered(grain(boundaries(and(are(not(

included(in(this(plot. Data(is(from JEOL(data(set,(sample(24,(scan(1.

0 20 40 60 80

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Misorientation Angle Distribution

Misorientation Angle

Relative Frequency
Figure(3 :(Misorientation(axes(plot.(The(misorientation(angle(ranges(corresponding(to(the(

spikes(shown(in(Figure(2 are(listed(above(each(of(the(inverse(pole(figures.((Dark(points(in(the(

inverse(pole(figure indicate(a(large(number(of(misorientations(at(that(location.((The(location(in(

the(inverse(pole(figures corresponds to(misorientation(axes.((Ten(misorientation(axes(are(

circled in(this(figure, with(the(colors(corresponding(to(the(colors described(in(Table(3. Data(is(

from(JEOL(data(set,(sample(24,(scan(1.
Figure(4:(Effect(of(minimum(grain(size(cutoff((red)(and(noise(reduction(methods((blue)(on(

Equivalent(Circle(Diameter.(The(grain(size(from(the(raw(data((black)(is(also(shown.((The(

minimum(grain(size(cutoff(values(indicate(the(size(grains(removed(in(pixels((px).(For(the(noise(

reduction(methods,(all(grains(four(pixels(or(smaller(are(removed(first.(The(description(7NN

indicates pixels(with(7(nearest(neighbors((NN)(were(filled((non(iteratively),(5NN indicates(

pixels(with(5(nearest(neighbors((NN)(were(filled((non(iteratively), 1NN(indicates(pixels(with(1(

nearest(neighbor((NN)(were(filled((non(iteratively), Seq(NR indicates pixels(with(8(NN(were(

filled(until(no(pixels(with(8(NN(were(left,(then(7NN(iteratively(up(to(4(NN. Data(is(from(JEOL(

data(set,(sample(23,(scan(2.

5 10 15 20 25 30 35 40

Mean Equivalent Circle Diameter [!m]

Raw

Data

!1 px !2 px !3 px !4 px !4 px 

 7NN

!4 px 

 5NN

!4 px 

 1NN

!4 px

Seq

 NR

Size of Small Grains Removed Noise Reduction Methods

Raw Data

Size of Small Grains Removed

Noise Reduction Methods
Figure(5:(Effect(of(Final(Minimum(Grain(Size(on(the(Average(Grain(Size.((The(average(grain(size(

increases(nearly(linearly(depending(on(final(minimum(grain(size. For(the(data(with(noise(

reduction,(the(equivalent(circle(diameter(increases(at(a(rate(of(approximately(.13(μm/pixel.

Data(is(from(JEOL(data(set,(sample(23,(scan(2.

0 10 20 30 40

20 25 30 35 40

Final Minimum Grain Size [pixels]

Mean Equivalent Circle Diameter [!m]

Raw Data

With Noise Reduction NN=5
Figure(6:(Histogram(of(the(Equivalent(Circle(Diameter [μm].((The(vertical solid blue(line(is(the(

mean,(the(vertical dashed red(lines(are bounds(placed one(standard(deviation on(either(side,(

and(the(vertical(dashed(orange lines(are(bounds(placed(at(one(standard(deviation(of(the(mean.

Data(are from(JEOL(data(set,(sample(23,(scan(2.

Equivalent Circle Diameter [!m]

Frequency

0 20 40 60 80 100

0

5 10 15 20 25

Mean

St. Dev.

St. Dev. of Mean
Tables

Table(1:(Calibration(measurements(for(both(microscopes(used(in(this(study at(the(working(

distances(and(magnifications(used(for(the(EBSD(grain(size(analysis.((Calibrations(were(

performed(in(accordance(with(ISO(16700(using(reference(material((RM)(NIST(8820.((Error(

remains(after(calibration(as(a(bias(error(due(to(a(number(of(factors(such(as:(coupling(of(x(and(y(

calibration(values(from(the(requirement(of(square(pixels,(truncation of(the(image(from(

pixelation,(drift(of(the(electromagnetic(lensing(system.

Hitachi!16 May!2011!Working!Distance!=!18.2mm!Magnification=90X

Horizontal Vertical

RM!value 1000 750

Mean 1012.6 756.23

Error 1.26% 0.83%

JEOL!!6!May!2011!Working!Distance!=!26mm!Magnification!=!70X

Horizontal Vertical

RM!value 1000 750

Mean 967.6 744.3

Error 3.29% 0.79%

Table(2:(Unit(cell(parameters(for(hexagonal(Ti.((b=a,(α=β=90°,(γ=120°

a c Reference

TiaHex 2.95 4.73 HKL!Software

TiaJOMTAA 2.94 4.68 [8]

TiaPPSOAU 2.951 4.684 [9]

Table(3:(Pseudosymmetry(operations(found(in(hexagonal(Ti(samples.((Active(designates(

whether(the(pseudosymmetry(operator(was(used(in(the(grain(size(analysis. Axis(and(angle(

describe(the(misorientation(axis(and(angle.((The(tolerance(is(the(angular(deviance(allowed(to(

axis(and(angle(pairs(to(still(be(considered(as(part(of(the(misorientation(axis(and(angle(set.((The(

tolerance(applies(to(both(the(axis(and(angle.((The(colors(correspond(to(the(circles(in(Figure(3.

Active Axis Angle Tolerance Color

Y 0001 30° 2° Red

N a1a120 90° 5° Yellow

Y a1010 90° 2° Orange

Y 16!6!3 92° 2° Green

N 2!a1!a1!0!! 72° 5° Aqua

N a8!1!2 33° 3° Blue

N a1!2!a1!0 30° 3° Purple

Y a1!2!a1!0 62° 2° Pink

N a1!a1!4 30° 3° Maroon

N a1!a3!1 45° 2° Olive
Table(4:(Sample(23(circle(equivalent(diameter(mean(grain(size((μm)

Area 1 2 3 4 5 Unweighted!

Average

Standard!

Deviation

Mean!of!

full!

dataset

JEOL 34.08 34.53 33.32 33.65 32.93 33.70 0.63 33.69

Number!of!grains 749 768 787 748 805 Total= 3857

Hitachi 36.64 34.25 36.08 34.94 34.43 35.27 1.05 35.21

Number!of!grains 614 724 653 686 713 Total= 3390

Table(5:(Sample(23(mean(linear(intercept((μm)

Area 1 2 3 4 5 Unweighted!

Average

Standard!

Deviation

Mean!of!

full!

dataset

JEOL 30.20 30.60 29.23 29.82 29.19 29.81 0.61 29.86

Number!of!grains 749 768 787 748 805 Total= 3857

Hitachi 32.47 30.36 31.98 30.97 30.51 31.15 0.93 31.15

Number!of!grains 614 724 653 686 713 Total= 3390

Table(6:(Sample(24(circle(equivalent(diameter(mean(grain(size((μm)

Area 1 2 3 4 5 Unweighted!

Average

Standard!

Deviation

Mean!of!

full!

dataset

JEOL 40.29 34.59 33.59 35.74 35.86 36.01 2.56 35.77

Number!of!grains 531 711 740 675 672 Total= 3329

Hitachi 34.08 36.51 34.04 33.68 35.39 34.74 1.18 34.56

Number!of!grains 664 666 735 768 684 Total= 3589

Table(7:(Sample(24(mean(linear(intercept((μm)

Area 1 2 3 4 5 Unweighted!

Average

Standard!

Deviation

Mean!of!

full!

dataset

JEOL 35.70 30.65 29.77 31.68 31.78 31.92 2.27 31.70

Number!of!grains 531 711 740 675 672 Total= 3329

Hitachi 30.20 35.36 31.36 30.17 29.85 31.39 2.29 30.63

Number!of!grains 664 666 735 768 684 Total= 3589
Appendices

Appendix(A Scan!parameters!(*!indicates!these!were!adjusted!before!each!scan)

[ProjectionParameters]

VHRatio=0.77800

*PCX=0.49800

*PCY=0.86900

*DD=0.43800

[AOI2DHough]

*X0=97

*Y0=62

*R=61

[AOI3DHough]

*Left=36

*Top=1

*Right=158

*Bottom=123

[Band!Detection]

Detect=0!(band!centers)

Divergence=2!(high)

Min=4

Max=5

HoughRes=80

[Discriminators]

BC=0

BS=0

MAD=5.00000

[Live!EBSP]

MinTimePerFrame=9

BackgroundMode=0

AutoBackgroundLevel=10

NoFramesBackGround=50

NoFrames=2

BackgroundCorrOn=True

AutoBackgroundOn=True

AutoStretch=True

Binning=8x8!superfast

Gain=Low

Magnification=70

kV=30.00

TiltAngle=70.00

TiltAxis=90.00

GridDistX=2.5000

xCells=400

yCells=400
Appendix(B Data!Analysis!Methods!&!Clean!up!procedure

1) Open!data!file!in!Project!Manager!using!Grainsize_ISO!profile

a) Export!as!.ctf

2) Open!data!file!in!Tango

a) Export!Euler!Map!to!results!directory

b) Export!Limited!Band!Contrast!Special!Boundaries!Map!to!results!directory

3) Detect!Grains

a) Sort!by!area

b) Select!grains!4!pixels!or!less!(0um2 to!25um2)

c) RClick!in!selected!grains!a>!Into!current!subset,!selected!grains

d) Name!‘4px!or!less’

4) Nullify!4px!or!less!subset!

a) Click!on!‘4px!or!less’!subset!in!project!manager!!(PM)

b) On!subset!tab,!click!nullify!a does!operation!6.3.1

c) Click!on!‘complete’!subset!in!PM

d) Refresh!tango!!(ctrlaR)

5) Perform!Noise!Reduction

a) Extrapolate!using!5!nearest!neighbors!(once)!a does!operation!6.3.2

b) Click!apply

6) Detect!Grains

a) Sort!by!area

b) Select!grains!10!pixels!or!less!(0um2 to!62.5!um2)

c) RClick!in!selected!grains!a>!Into!current!subset,!selected!grains

d) Name!‘10px!or!less’

7) Nullify!10px!or!less!subset

a) Click!on!‘10px!or!less’!subset

b) On!subset!tab,!click!nullify!a does!operation!6.3.4

c) Click!on!‘complete’!subset!in!PM

d) Refresh!tango

8) Export!Maps!w/!“_cleaned”!to!filename

a) Euler!Map

b) Limited!Band!Contrast!Special!Boundaries!Map

9) Detect!Grains!

a) Select!grain!size!statistics

b) Rclick!in!windowa>!“Range!to!subset”

c) Name “no!border”

d) Click!on!“no!border!subset”

e) Refresh!tango

10) Export!Maps!w/!“_noborder”!to!filename

a) Make!sure!‘antiasubset’!is!checked

b) Euler!Map

c) Limited!Band!Contrast!Special!Boundaries!Map

11)Detect!Grains

a) RClick!a export!all!cells!to!file

b) Comes!out!as!a!tab!delimited!text!file

c) TRUE/FALSE!indicates!if!the!grain!is!a!border!grain

12) Grain!size!statistics

a) Choose!size!parameter!d[um]

b) Record!Ex,!N
Appendix(C Comments!for!revising!ISO!13067!

General!comments:

The!high!hit!rate!required!means ISO!13067!users!must!know!how!to!optimize!their!

SEM for!this!measurement. The!authors needed!to!work!closely!with!our!application!

support!specialist!to!get!the!90%!to!95%!hit!rate required!by!ISO!13067,!even!with!

optimal!sample!preparation performed!prior!to!sample!arrival.

In!our experience!both!SEMs!needed!about!1a2!hours!of!warm!up!time!before!it!was!

stable!enough!to!record!data.!!The!JEOL!would!remain!stable!for!long!periods!(days),!

while!the!Hitachi!would!start!to!become!unstable!again!after!6a10!hours.

We!were!not!able!to!set!the!grain!size!measurement as!an!array!of!measurements!

(i.e.!automatic stage!mapping!without!attempting!to!overlap!the!images),!we!found!

there!were!little!tweaks necessary in!the!EBSD!geometry,!SEM!focus!or!EBSD!

calibration!that!if!not!performed!for!each area!of!interest!would!decrease!the!hit!

rate!between!5%!to!10%.

There!is!a!lot!of!dispersion!in!the!grain!size,!so!calculation!of!the!uncertainty!in!the!

average!grain!size!seems!to!require!repeated!measurements,!which!aren’t!stated!as!

being!required!in!ISO 13067.!Section!5.5.3!alludes!to!repeated!measurements,!but!

does!not!explicitly!require!it. Metrics!such!as!standard!deviation!of!the!mean!may!be!

useful as!an!alternative!to!repeated!measurements.

When the histograms!for!frequency!vs.!grain!size are!examined,!it’s!pretty!obvious!

that!the!plot!is!nonaGaussian.!!Terms!like!‘mean’!and!‘standard!deviation’!may!not!

have!the!meaning!expected!from!Gaussian!statistics. Better!metrics,!like!those!used!

for!loganormal!or!weibull!distributions!may be!more!appropriate.!!

The!EBSD!technique!allows!measurement!of!the!distribution!of!grain!sizes,!not!just!

the!average!value.!!The!distribution!data!can!give!much!more!information!than!an!

average,!the!authors believe ISO 13067 should!be!revised!or!a!new!standard written!

to!measure!the!distribution!of!grain!sizes.

It may!be!worth!noting!in!ISO!13067!that!the!average!linear!intercept!cannot!be!

calculated!from!the!mean!average!area,!the!linear!intercept!needs!to!be!calculated!

separately!for!each!area!and!then!averaged.!!

As!written,!Section 8: Reporting of analysis!results, does!not!explicitly require!any!

mention!of!the!average!grain!size!result, and!reporting!the!data!cleaning!operations

appear!to!be!optional to!report.
Specific!comments:

3.3.3!– The!EBSD!patterns!are!in!the!SEM reference!frame; it’s!up!the!user!to!get!

them!in!the!sample!reference!frame.

5.1.1!– This!section!discusses!a!threshold!of!10%!misindexed!points,!but!6.3.2!states!

only!5%!should!be!altered.!!This!implies!that!we!will!not!correct!5%!of!the!

misindexed!points.

6.1.3!– The!authors do not!think!the!qualifier!‘easily’!should!be!included!with!the!

description!of!defining!twin!boundaries,!particularly!after!our!difficulties!with!

pseudosymmetry!in!this!sample.

6.3.2!a Is!the!increase!in!hit!rate!stated!here!relative!to!the!raw!data!or!after!step!

6.3.1!where!small!grains!are!removed? The!authors!have!taken!it!to!be!relative!to!

the!raw!data!set,!as!the!small!grain!removal!caused!the!hit!rate!to!decrease!from!

near!90%!to!approximately!80%.

6.3.2!a Examples!of!data!with!excessive!artifacts!in!the!index!would!be!helpful.

6.3.4!a This!step!seems!like!a!repeat!of!6.3.1.!!After!doing!the!procedure,!the!authors

can!see!that!isn’t!the!case,!but!seems!like!a!likely!place!where!someone!would!merge!

the!two!steps!to!save!time.!!A!note!on!why!this!is!a!twoastep!procedure!would!be!

good.

6.5!a Should!we!use!geometric!mean!or!arithmetic!mean!values,!since!the!

distribution!is!nonaGaussian?!Arithmetic mean!is!tacitly!implied,!but!geometric!

mean!might!be!more!applicable.