Unsupervised approval criteria for automated EBSP investigation of deformed metals

Unsupervised approval criteria for automated EBSPinvestigation of deformed metals

A. GODFREY & N. C. KRIEGER LASSEN*

Sandia National Laboratories, MS9405, Livermore, CA 94551, U.S.A.

*Materials Department, Risù National Laboratory, DK-4000, Roskilde, Denmark

Key words. Al, BKD, calibration, deformation, EBSP, rolling.

Summary

Unsupervised approval criteria have been investigated for

orientations gathered from cold deformed samples (medium

to high strain range) using the electron backscattering

pattern technique. For such samples, the dislocation cell-size

is on the order of the available step-size and pattern quality is

generally low. Approval criteria for assessing the validity of

measured orientations under these conditions were deter-

mined using, as a calibration, channel die cold deformed

single crystals of stable orientations. In all cases, approval

criteria based on an indexing con®dence measure are found

to be preferable. Different criteria are suggested, depending on

whether the orientation data are subsequently to be used for

texture analysis, or for a misorientation angle-based analysis.

The latter is illustrated by an investigation of the number of

deformation generated high angle boundaries introduced

during a 90% cold reduction of a polycrystalline sample.

1. Introduction

As the speed of electron backscattering pattern (EBSP) data

gathering increases, larger and larger data sets become

amenable to collection. Whilst for studies of annealed

samples a signi®cant fraction of the points gathered will

provide redundant information (all readings within a grain

interior for example), for materials deformed even to only

moderate strains (<30%), every measured orientation

within even a 1 mm step-size grid is likely to correspond

to a different orientation and to be of interest to the

researcher. The EBSP pattern quality is, however, expected

to decrease with increasing strain, due both to the

increasing likelihood of `double' (overlapping) patterns,

and to the increased incoherent scattering associated with

higher dislocation densities. Additionally, the small disloca-

tion cell-size, relative to the available investigation step-size,

limits in most cases the number of measurements to just

one point per dislocation cell. Thus, the correction

algorithms developed to account for incorrect points in

conventional grain orientation imaging microscopy studies

(where all points surrounding a point in a grain interior are

constrained to have the same orientation) cannot be used

for the examination of deformed microstructures. The case

where the maximum use can be made of EBSP data (every

point providing potentially useful differing information) is

therefore also one where the most demands are placed upon

the technique.

Although automation allows the rapid gathering of a

large amount of data, it presents the user with a list of

orientations that must be analysed blindly, without the

option of double-checking the measurements. In order to

assist in a critical analysis of the data it is common therefore

to store along with the orientation some measure of the

indexing con®dence, typically a measure of the pattern

quality (Wright et al., 1993; Krieger Lassen et al., 1994)

and/or a measure of the con®dence in the pattern indexing

based on the results of the pattern indexing procedures

(Adams et al., 1993; Kunze et al., 1993; Field et al., 1996).

In this study the effectiveness of two such measures in

removing incorrect orientations from medium to high strain

deformation microstructure investigations is assessed. As a

calibration channel die deformed single crystals of stable

rolling orientations are used. This method has the advantage

of providing the calibration data from samples with a range

of pattern qualities typical of cold deformed microstructures.

Whilst the results presented are speci®c to the particular

con®dence measures and class of materials investigated,

both the methodology and procedure are applicable to any

EBSP investigation of deformed microstructures, and can

readily be extended to include more sophisticated measures

of pattern quality, such as those based on the shape and

intensity of the Hough (image transform) space peaks.

Journal of Microscopy, Vol. 197, Pt 3, March 2000, pp. 249±259.

Received 18 May 1999; accepted 18 October 1999

q 2000 The Royal Microscopical Society 249

Correspondence to: A. Godfrey, Holly Cottage, The Walk, Wootton by Woodstock,

Oxon OX20 1ED, U.K. Tel: �45 46775791; fax: �45 46775758; e-mail: godfrey

@rishp1.risoe.dk

2. Methodology

A summary of the terms used in the following is provided for

reference in Table 1. To develop a set of orientation accept-

ance criteria based on indexing con®dence measures, one

ideally would obtain a data set of indexed patterns covering

a suitable range of pattern image qualities, where the subset

of orientations that were correct was known with certainty.

This could be achieved by manual supervision of the pattern

indexing routine, but obtaining a suf®ciently large data set

for analysis would take considerable user time. As an alter-

native deformed Al single crystals of stable orientations have

been used. Two crystals, chosen with orientations that are

known to develop a well de®ned texture spread during

deformation, were channel die deformed to a strain of e�1.5

(78% reduction). The texture spread was determined for

each sample from a large number of transmission electron

microscope (TEM) orientation measurements taken using

a fast semiautomatic technique (Liu, 1995). EBSP scans

were then also made on the samples. Orientations falling

within the expected (TEM determined) texture spread are

assumed to be correct, whilst those falling outside the

expected spread are assumed to be incorrect. Unsupervised

acceptance criteria based on an indexing con®dence

measure can then be tested by comparing the set of orien-

tations selected using a given acceptance criterion, with the

set of orientations falling within the expected spread.

During deformation of metals with medium to high

stacking fault energy, microstructural subdivision takes

place, leading to the development of nearly dislocation free

volumes separated from each other by dislocation walls,

where each of these volumes has an orientation differing

from those of its neighbours (Bay et al., 1992). For single

crystals of certain orientations, and under particular defor-

mation conditions (as for the samples used in this study),

the average orientation of the single crystal sample remains

unchanged (or changes by only a few degrees) whilst devel-

oping a well de®ned spread of orientations (Driver et al.,

1994; Godfrey et al., 1998a, b). A typical intermediate strain

cold deformed microstructure is illustrated in Fig. 1. Such

samples provide an excellent calibration data set as they

cover a range of both orientations and of EBSP pattern

qualities. In order to use such data for the development and

evalulation of unsupervised approval criteria it is only

necessary to make the assumption that all orientations

lying within a certain spread are correct, and all orienta-

tions lying outside this spread are incorrect. The general

validity of this assumption can be seen by considering the

two possible cases of errors: (i) a point is inside the orien-

tation spread but is assigned an incorrect orientation ± this

is very unlikely since incorrect orientations usually have a

large misorientation to the true orientation (this is discussed

further in section 3), or (ii) a point is outside the spread but

is nevertheless correct ± this is possible, but for the single

crystal samples used the orientation spread is very well

de®ned such that there is only a small group of points where

this error may hold.

The sequence of steps used to develop the unsupervised

approval criteria can be summarized therefore as follows:

(i) de®ne the expected spread for the orientation at the

strain level employed using TEM measurements, (ii) take a

large set of EBSP measurements and subdivide these into

two groups covering those that fall within the expected

orientation spread (assumed correct) and those that do not

(assumed incorrect), (iii) partition the EBSP data again

using indexing con®dence measures, and (iv) compare the

®t with the sets of correct/incorrect orientations based on

the expected orientation spread.

3. Experimental procedure

EBSP measurements were taken on samples of 99.993%

pure Al single crystals, of either {112} <111> or

{110} <112> orientation, channel die deformed to a strain

of e�1.5. Both these crystal orientations are `stable' under

these deformation conditions, i.e. they do not undergo any

large rotation during deformation or splitting into differing

orientation components. Three line scans were taken on the

{110} <112> sample (each taken from a different part of

the deformed single crystal), and one x±y map taken on the

{112} <111> sample. All samples were investigated in the

longitudinal section (de®ned by the elongation or rolling

direction, RD, and by the compression or normal direction,

ND). The line scans were taken parallel to RD, and the map

rectangular, taken parallel to RD and ND. In each case the

scan step-size was 1 mm. Patterns were indexed automati-

cally using a Hough transform based system (Krieger Lassen

et al., 1992). For each pattern two measures of indexing

con®dence are stored: (a) the signal-to-noise ratio (Q) for the

pattern, the speci®c calculation of which is described in

Krieger Lassen et al. (1994), and (b) the fraction of bands

located in the pattern that can be indexed consistent with the

estimated (measured) orientation (the fraction of indexable

bands, or FIB).

The signal-to-noise ratio is dependent upon the disloca-

tion substructure as well as a number of external variables

including focus height, ®lament quality, extent of sample

charging, sample orientation and sample preparation

quality. This measure has been successfully used elsewhere

for distinguishing between patterns arising from deformed

or recrystallised material (Krieger Lassen et al., 1994). In

general, for EBSP indexing, the lower the value of Q, the

lower the pattern quality and therefore the lower the chance

of a correct solution being found.

For the FIB measure, the indexing routine currently used

attempts to ®nd up to eight bands in any given pattern,

though in some cases fewer than eight bands are found.

From these the program determines its best estimate of the

250 A . GODFREY AND N. C . KRIE GE R LAS SE N

q 2000 The Royal Microscopical Society, Journal of Microscopy, 197, 249±259

orientation (the `measured orientation', see Table 1). Each

band is then regarded in turn and is considered indexable if

the crystal plane represented by the band deviates by no

more than 38 from the corresponding crystal plane for the

measured orientation.

Incorrect orientations are returned when the measured

orientation is based either on correctly localized bands but is

assigned an incorrect indexing, or on wrongly localized

bands. In both these cases the result is an orientation with a

large misorientation to the correct orientation. Although

the indexing procedure takes place in orientation space it is

useful here to think instead of the process as taking place in

image space (i.e. of matching the locations of the detected

bands to the predicted Kikuchi band positions for some

orientation). Obtaining an incorrect orientation nevertheless

close to the true orientation would mean that the predicted

Kikuchi band pattern for the measured orientation would be

rotated/translated by a small amount to the true (observed)

pattern. The effect of this can be simulated approximately by

taking two identical transparencies of a region of Kikuchi

space and then offsetting one to the other by a small rotation/

translation ± in general only one band will match between

the two. Wrongly localized bands (where the image analysis

routines locate a Kikuchi band where one does not exist)

could add to this number ± but even to obtain three

matching bands would mean that two false bands would

need to be found, and these would need to lie in very

particular locations in order for both to be regarded by the

analysing routines as indexable.

In this study the number of bands located (NBL) varied

only between six and eight. In this regime the likelihood of a

pattern being indexed correctly is nearly independent of


Fig. 1. TEM image showing a typical

deformed microstructure (longitudinal sec-

tion of {112}<111> orientation 99.993%

Al single crystal channel die cold deformed

to a strain of e�1.5).

EBSP INVESTIGATION OF DEFORMED SAMPLES 251

NBL. Values of FIB reported in this study are therefore

quoted simply as decimal fractions, without reference to the

number of bands located. Correct solutions for which FIB

are <1.0 are likely to arise from overlapping patterns, from

particles/inclusions or due to ghost images resulting from a

background subtraction procedure.

Three measures were considered to assess the ef®ciency of

the unsupervised approval criteria: X1, the fraction of mis-

classifed orientations (incorrect orientations selected plus

correct orientations not selected); X2, the fraction of the

total number of correct orientations selected; and X3, the

fraction of incorrect orientations within the selected data set

of points. De®nitions of these three measures are also given

in Table 2 for reference. The ®rst measure (X1) should

be minimized when it is important to limit the total fraction

of misclassi®ed orientations, for example when using the

EBSP data for quantitative texture evaluation. For some

purposes, however, (see section 5) it is desirable to place

more emphasis on minimizing the number of incorrect

orientations within the ®nal selected data set than on

minimizing the total number of classi®cation mistakes. In

such cases, one must decide on how to weight the trade-off

between selecting correct orientations and leaving gaps in

the data set.

The TEM orientation measurements, used for the calibra-

tion, were taken using a fast semi-automatic technique (Liu,

1995) on thin foils obtained from the deformed single crystal

samples. For the {112} <111> sample, 657 orientation

measurements were obtained and for the {110} <112>

sample, 253 orientation measurements were taken. It should

be noted that all misorientation measurements presented in

this paper are given as the minimum misorientation based

upon the cubic crystal symmetry (often referred to as the

disorientation).

4. Results

4.1. Determination of orientation spread criteria

Figure 2 shows {111} pole ®gures constructed from orien-

tation measurements taken from the TEM samples. For the

{110} <112> sample all orientations observed in the TEM

Table 1. De®nitions for the terms used to describe orientations.

True orientation The exact orientation of a particular volume.

Measured orientation An orientation returned by the indexing routines.

Correct orientation C A measured orientation, differing from the true orientation only by an amount due to limitations

in experimental precision.

Incorrect orientation I A measured orientation that does not represent the true orientation.

Within spread WS The orientation lies within an expected spread. These are assumed to be correct.

Outside spread OS The orientation lies outside an expected spread. These are assumed to be incorrect.

Classified correct CC Classified as being correct based on some pattern parameter (here either Q or FIB).

Classified incorrect CI Classified as being incorrect based on some pattern parameter (here either Q or FIB).

Table 2. Measures used to assess unsuper-

vised orientation determination approval

described using standard operators for set

intersection (Ç) and set union (È). Enclo-

sure in square brackets indicates the num-

ber of elements within the set described.

X1 ± the number of mistakenly classified orientations as a fraction of the total number of

orientations:

X1 ��CC Ç OS� È �CI Ç WS��

�WS È OS�;

��CC Ç I� È �CI Ç C��

�C È I�

X2 ± the number of true orientations selected as a fraction of the total number of true

orientations:

X2 ��CC Ç WS�

�WS�;

�CC Ç C�

�CC�

X3 ± the number of false orientations selected as a fraction of the number of orientations

selected:

X3 ��CC Ç OS�

�CC�;

�CC Ç I�

�CC�



are contained within a spread of 128 from the ideal orien-

tation. For the {110} <112> sample a check on this value

for the orientation spread can also be made directly from the

EBSP data. As described in section 3, incorrect orientations

are almost always associated with a high misorientation to

the true orientation. Thus, for samples with only a narrow

spread of orientations a histogram plot of misorientation to

the ideal orientation for EBSP data should exhibit an empty

region where there are neither any correct orientations nor

any incorrect ones. Figure 3 shows such histogram plots

for the three {110} <112> EBSP data sets. In each case a

separation between correct and incorrect orientations is

seen. In Fig. 3(a,b) unambiguous cut-offs are located at 78

and 128, respectively. A cut-off angle of 128 was therefore

decided upon to de®ne the orientation spread of this deformed

single crystal sample (note that extending the cut-off to 168,

to include the somewhat wider spread seen for the third

sample, Fig. 3c, made negligible difference to the unsuper-

vised approval criteria determination).

TEM orientation measurements reveal a larger spread

for the {112} <111> orientation sample, predominantly

about a single axis (in this case the transverse direction, TD)

and extending further in the direction of the ND-rotated

cube orientation {001} <110> than the Goss orientation

{110} <011>. In order to quantify this orientation spread

the misorientation of each crystallite to the ideal orientation

was partitioned into two successive rotations, the ®rst by an

angle a about TD, and the second by an angle b about some

other axis, where a was chosen to minimize the non-TD

rotation angle (Wert et al., 1997). In this way it was

determined that 95% of the TEM spread could be described

by the conditions of (i) a TD misorientation component to

the ideal orientation of ÿ108 # a # 258 and (ii) a non-TD

component of b # 118. The spread was de®ned to exclude


Fig. 2. {111} pole ®gures constructed from individual TEM orientation measurements; (a) {112} <111> sample (657 measurements),

(b) {110} <112> sample (253 measurements), (c) {112} <111> sample showing only data points within the misorientation angle criteria.

(Note that due a more homogeneous deformation microstructure, the misorientation angle criterion for the {110} <112> orientation

includes all the measured TEM orientations.)


the most extreme 5% of points, as it was known from TEM

investigations of the deformation structure (Godfrey et al.,

1998a) that these most extreme TD orientations were

associated with isolated very narrow dislocation cells inside

regions of localized glide, unlikely to give rise to indexable

EBSP patterns. Figure 2(c) gives the {111} pole ®gure for

just the data included within the above misorientation angle

criteria. On account of the larger orientation spread for

this sample the alternative EBSP method used for the

{110} <112> sample was not applicable in this case.

4.2. Selection of unsupervised approval criteria

For each EBSP data set (the three {110} <112> line scans

and the {112} <111>map) the relevant orientation spread

criteria determined as described in the previous section were

used to decide a priori the subsets of correct and incorrect

orientations. For the {112} <111> orientation this was

done as for the TEM data by expressing the misorientation of

each point to the ideal orientation as a combination of a TD

rotation followed by a non-TD rotation. Various unsuper-

vised approval criteria based upon Q or FIB were then

applied to each scan in turn. Initially, only simple single

criteria were applied, of the type `accept all scan points with

FIB $ x' or `accept all scan points with Q $ y'.

The results for measure X1 are shown in Fig. 4. Minima

are seen in the graph due to the trade-off between accepting

only the highest con®dence points (and rejecting many that

are correct but are of lower indexing con®dence) or accepting

all the points (giving, by de®nition, all the correct points, but

also many incorrect points). It can be seen that the minimum

for each data set is lower when using a FIB criterion than

when using a Q criterion, with the minimum occurring for

the FIB criteria at a cut-off of either FIB�0.5 or 0.625. The

values of these minima are summarized in Table 3. The

results for measures X2 and X3 are shown in Fig. 5. These

graphs illustrate the necessary trade-off between ®nding the

correct orientations, and limiting the number of incorrect

orientations selected. Choosing points with only the highest

Fig. 3. Histograms of misorientation angle to the ideal {110} <112> orientation for the EBSP scans on deformed samples of this orientation.

Table 3. Minima for X1 together with corresponding cut-off levels

for Q or FIB (simple criteria of the kind FIB $ x or Q $ y).

X1min (%) X1min (%)

Sample using Q (cut-off) using FIB (cut-off)

{112}<111> 11.6 (0.35) 8.8 (0.5)

{110}<112> I 16.1 (0.32) 12.2 (0.625)

{110}<112> II 7.8 (0.39) 4.8 (0.625)

{110}<112> III 11.3 (0.39) 8.1 (0.5)



con®dence index gives very few errors in the selected data

set, but at the expense of ®nding only a small fraction of the

correct orientations, thereby leaving large gaps in the data

set. Note also that the Q parameter does not show a mono-

tonic decrease in X3. This behaviour results from the fact

that some patterns with high values of Q may still be

incorrect (as may be the case with double or overlapping

patterns). Some examples of the selection trade-offs are

summarized in Table 4. The FIB measure always results in a

lower percentage of incorrect orientations selected (X3) for

a given percentage of the total correct orientations located

(X2). The criterion FIB $ 0.750 gives only a <1% error (X3)

whilst locating <70% (X2) of the total number of the

correct orientations. Accepting FIB $ 0.625 results in the

fraction of correct orientations located increasing to <90%

(X2), but at the cost of an increase in the error of up to

< 4% (X3). The graphs for measure X3 also highlight the

fact that without application of approval criteria, between

8% and 18% of the measured orientations are incorrect (the

far left-hand side of each graph corresponds to accepting all

the data points).

Combined criteria of the type `accept all points with


Fig. 4. Graphs showing variation of X1 (fraction of all classi®cation

mistakes) with selection criteria for the four data sets: (a) using Q,

(b) using FIB. In each case the minimum is lower for the FIB

criterion.

Fig. 5. Graphs showing the variation of measures X2 and X3 with

selection criteria based upon either Q or FIB.

Table 4. Trade-offs between X2 or X3 based either upon simple

FIB $ x or Q $ y criteria. The cut-off values for Q are chosen to

give comparable values of X2 to the FIB criteria.

Sample Criterion X2 (%) X3 (%)

{112} <111> FIB $ 0.750 75.5 1.3

FIB $ 0.625 93.2 4.6

Q $ 0.38 65.8 5.8

Q $ 0.36 92.5 8.7

{110} <112> I FIB $ 0.750 68.6 0.9

FIB $ 0.625 89.4 4.7

Q $ 0.34 59.3 5.1

Q $ 0.32 89.9 9.7

{110} <112> II FIB $ 0.750 78.9 0.3

FIB $ 0.625 96.1 1.3

Q $ 0.45 69.7 1.8

Q $ 0.42 93.7 4.7

{110} <112> III FIB $ 0.750 65.6 1.3

FIB $ 0.625 88.7 2.6

Q $ 0.42 61.0 3.1

Q $ 0.40 88.5 5.7


FIB $ x or Q $ y', were also investigated. These gave a small

improvement in X1, although only by less than 1% for each

for the data sets. Using such selection methods, it was

always possible to increase the percentage of correct orien-

tations located (X2), but invariably at the expense of a large

increase in the fraction of incorrect orientations selected

(X3). It should be noted that since Q does not explicitly

involve the average pattern quality (being affected by both

dislocation substructure and by external variables, see section

3), any generalized criterion involving this quantity would

need to also be related to the average value for each scan. To

illustrate the variation possible in Q the average value was

calculated for the four EBSP data sets above, considering

either all points, or just the set of points corresponding to

FIB�1.0 (i.e. only the best patterns). The values are given

in Table 5. The average value varies over a wide range of

0.11, both for the average over each entire scan, and over

just the FIB�1.0 points.

From the data analysis and the considerations above it

was concluded that simple FIB criteria provide the best

method for selecting correct orientations. For cases where it

is appropriate to minimize X1 (e.g. texture determination)

this criterion should be FIB $ 0.5 or $ 0.625 (it is suggested

that both be tried in each case and the results compared to

establish the extent of any difference). For cases where it is

more important to limit the fraction of error points in the

selected data set this criterion should be FIB $ 0.625 or

$ 0.750 depending on the accuracy required. The effect of

the latter criterion in cleaning up the EBSP data is illus-

trated in Fig. 6, which showing {111} pole ®gures for data

sets gathered from the {110} <112> and {112} <111>

samples.

5. Application: study of deformation-induced highangle boundaries

TEM investigations into the development of microstructure

during deformation suggest that high angle grain bound-

aries are formed within the original grains as a result of

continued microstructural subdivision. EBSP investigation

of this process has the advantage of allowing measurements

to be taken over a large number of grains, thereby smooth-

ing out any grain-to-grain variation in either orientation-

dependent grain break-up behaviour or in starting grain

size. The disadvantage of the EBSP technique, however, is

that at large strains, cell orientations can vary widely over

a very small distance (Hughes & Hansen, 1993, 1997;

Hughes, 1995). Since any recorded orientation could be

true, it is important to use reliable selection criteria to assess

critically the EBSP data and to analyse such data with

con®dence. For such studies it is important to minimize the

numbers of errors in the ®nal selected data set (i.e. measure

X3 of the previous section), as each error point will give rise

to two incorrect misorientations (one each to the orienta-

tions on either side of it). A lower limit on the number of

high angle grain boundaries encountered along a scan can

therefore be determined by assuming both such incorrect

misorientations to be high angle. Note that, as discussed

in section 3, by not selecting correct orientations we leave

gaps in the EBSP scan such that misorientations calculated

between now adjacent points correspond to misorientations

between cells separated by 1±3 mm. In the current context,

these will only give rise to additional incorrect high mis-

orientations if a cumulative orientation change occurs over

the region of the gap in the scan. TEM studies, however,

show that these structures usually exhibit alternating rather

than cumulative orientation changes, even over these small

distances.

A 300 mm long, 1 mm step-size EBSP scan was made

parallel to the compression direction on a sample of alu-

minium deformed by rolling to a 90% reduction (e�2.3).

The starting material possessed an equiaxed grain structure

with average grain diameter of d�100 mm. Subsequent to

the orientation data collection, the FIB $ 0.750 acceptance

criterion was applied to the gathered data set, resulting in

the elimination of 93 data points. Pole ®gures of the data set

before and after the application of this criterion are shown

in Fig. 7. From the deformed single crystal calibration data,

this criterion should give only < 1% of incorrect orienta-

tions in the selected data set. The misorientations between

the remaining scan points were then calculated. Rather

than choosing a ®xed arbitrary value to de®ne a high angle

grain boundary, the ratio of the number of misorientations

with an angle greater than a to the number expected on the

basis of a random grain orientation distribution was

determined, for all possible values of a. This was calculated

as follows: for an initial average grain size of 100 mm, a

reduction of 90% will produce pancake-shaped grains with

an average width of 10 mm. The EBSP scan direction was

parallel to the compression direction; therefore, a scan would

on average encounter one grain boundary every 10 mm.

Assuming a random initial texture, the fraction of these

boundaries with misorientation angle greater than a certain

value can be determined using a cumulative calculation

of the Mackenzie distribution for misorientation angles

Table 5. The variation in Q over the scans (the average in each case

is calculated for all points, and for just those points with FIB�1.0).

Sample Mean Qall Mean QFIB�1.0

{112} <111> 0.38 0.41

{110} <112> I 0.34 0.37

{110} <112> II 0.45 0.48

{110} <112> III 0.42 0.47



between randomly orientated crystallites of cubic symmetry

(Mackenzie & Thompson, 1957). The number of boundaries

along the scan expected to arise from original grain boun-

daries with a misorientation angle of $ a is then given by

NR; $ a ��1 ÿ f�X < a�� ´ scan length

average grain width

where f(X <a) is the cumulative Mackenzie distribution

(giving the probability that a grain boundary will have an

angle less than a). The results of this calculation are shown

in Fig. 8(a). This graph also plots, for comparison, values

calculated for the data set without application of the approval

criterion. It is seen that application of the approval criterion

greatly reduces the observed number of boundaries for all

values of a. In Fig. 8(b) the ratio of number of experimentally

observed boundaries with misorientation angle $ a to the

expected value is plotted. In the range 158 # a # 408 there

are about three times as many observed boundaries with

misorientation angle $ a than expected to arise from just

the original grain boundaries, increasing still further for

higher values of a. A ratio of three corresponds to two

deformation-induced high angle boundaries on average per

grain. The ratio is also much higher in the low angle regime

(0±158), as expected from the known development of

dislocation substructures. The scatter in the extreme high

angle region is most likely due to the small number

of misorientations in this region (as seen in Fig. 8(a), the

number of boundaries expected from the original grain

boundaries with angles $ a is less than 1).

In removing data points with FIB <0.750 the expected

number of error points is only <1%, or, for the case above, 2

points. These would give rise to at most four extra high

angle misorientations, making very little difference to the

calculation. The data selection procedure removes <1/3 of

the data points, such that misorientation measurements are

made across several dislocation cells. As an estimate of the

effect of `holes' in the EBSP data list, a further 50 points

were removed at random from the FIB<0.750 data set


Fig. 6. {111} pole ®gures illustrating the use of the FIB $ 0.750 criterion in cleaning up EBSP data: (a) {112} <111> all points,

(b) {112} <111> FIB $ 0.750 only, (c) {110} <112> all points, (d) {110} <112> FIB $ 0.750 only.


(leaving 157 of the original 300 data points) and the mis-

orientations between the remaining points recalculated.

This procedure was performed several times, and in each

case the number of misorientations with angle $ a was

observed to decrease, on average by < 15%. This shows that,

in this regime at least (1/2 to 2/3 of the initial data set), the

effect of increasing the number of holes in the EBSP data list

is to lower the number of high angle misorientations

observed, suggesting that the ®gure obtained of < two

high angle boundaries per grain is indeed a lower bound

estimate.

Summary and conclusions

Channel die deformed single crystal Al samples were used to

develop unsupervised acceptance criteria for automated

EBSP investigations of deformation microstructures. The

technique was illustrated using two simple indexing con-

®dence measures ± the fraction of indexable bands (FIB) and

the pattern signal-to-noise ratio. The method can be readily

extended however, to include more sophisticated measures

of pattern indexing con®dence. Of the two measures con-

sidered here the best method for selecting correct orien-

tations was a simple cut-off in the value of FIB. The value

of the cut-off should be different, however, depending on

whether one wishes to minimize the total number of mis-

classi®cations (FIB $ 0.5 or FIB $ 0.625), or whether one

wishes to minimize the fraction of errors in the ®nal selected

data set (FIB $ 0.750). From an application of this latter

criterion to a data set gathered from aluminium with an

initial equiaxed grain size of 100 mm rolled to a reduction of

90%, it was calculated that on average a minimum of two

high angle grain boundaries are developed in the compres-

sion direction within each grain as a result of microstructural

subdivision during the deformation process.

Fig. 7. {111} pole ®gures constructed from EBSP measurements of a 90% reduction polycrystalline Al sample: (a) all points, (b) after

application of FIB $ 0.750 criterion.

Fig. 8. Determination of the number of high angle boundaries

developed during deformation. Graphs show (a) the number of

boundaries expected assuming an initially random textured material

with an angle $ a (NR), and the experimentally measured number

(NM) with an angle $ a using either all data or just FIB $ 0.750

data; (b) the ratio of the values (NM/NR) (FIB $ 0.750 data only).



Acknowledgements

The authors would like to thank Drs D. Juul Jensen and

D. A. Hughes for useful discussions and comments, and for

provision of the polycrystalline aluminium material. Dr J.

Driver is thanked for provision of the channel die deformed

single crystal samples. Part of this work was supported in

part by the U.S. Department of Energy, Of®ce of Basic Energy

Sciences ± Division of Material Sciences, under contract

number DE-AC04-94AL85000.

References

Adams, B.L., Wright, S.I. & Kunze, K. (1993) Orientation imaging:

the emergence of a new microscopy. Met. Trans. A, 24A, 819±

831.

Bay, B., Hansen, N., Hughes, D.A. & Kuhlman-Wilsdorf, D. (1992)

Evolution of FCC deformation structures in polyslip. Acta Metall.

Mater. 40, 205±219.

Driver, J.H., Juul Jensen, D. & Hansen, N. (1994) Large strain

deformation structures in aluminium crystals with rolling texture

orientations. Acta Metall. Mater. 42, 3105±3119.

Field, D.P., Wright, S.I. & Dingley, D.J. (1996) Multi-phase texture

analysis by orientation imaging microscopy. Proceedings of the

11th International Conference on Textures of Materials ± ICOTOM

11 (ed. by Z. Liang, L. Zuo and Y. Chu), pp. 94±99. International

Academic Publishers, Beijing.

Godfrey, A., Juul Jensen, D. & Hansen, N. (1998a) Slip pattern,

microstructure and local crystallography in an aluminium single

crystal of copper orientation {112}<111>. Acta Mater. 46, 835±

848.

Godfrey, A., Juul Jensen, D. & Hansen, N. (1998b) Slip pattern,

microstructure and local crystallography in an aluminium single

crystal of brass orientation {110}<112>. Acta Mater. 46, 823±

833.

Hughes, D.A. (1995) The evolution of deformation microstructures

and local orientations. Proc. 16th Risù Int. Symp: Microstructural

and Crystallographic Aspects of Recrystallisation. (ed. by N. Hansen,

D. Juul Jensen, Y. L. Liu and B. Ralph), pp. 63±85. Risù National

Laboratory, Roskilde, Denmark.

Hughes, D.A. & Hansen, N. (1993) Microstructural evolution in

nickel during rolling from intermediate to large strains. Met.

Trans. A. 24A, 2021±2037.

Hughes, D.A. & Hansen, N. (1997) High angle boundaries formed

by grain subdivision mechanisms. Acta Mater. 45, 3871±3886.

Krieger Lassen, N.C., Juul Jensen, D. & Conradsen, K. (1992) Image

processing procedures for analysis of electron back scattering

patterns. Scanning Microsc. 6, 115±121.

Krieger Lassen, N.C., Juul Jensen, D. & Conradsen, K. (1994)

Automatic recognition of deformed and recrystallized regions

in partly recrystallized samples using electron back scattering

patterns. Mater. Sci. Forum, 149, 157±162.

Kunze, K., Wright, S.I., Adams, S.I. & Dingley, D.J. (1993) Advances

in automatic EBSP single orientation measurements. Textures

and Microstructures, 20, 41±54.

Liu, Q. (1995) A simple and rapid method for determining orien-

tations and misorientations of crystalline specimens in the TEM.

Ultramicroscopy, 60, 81±89.

Mackenzie, J.K. & Thompson, M.J. (1957) Some statistics associ-

ated with the random disorientation of cubes. Biometrika, 44,

205.

Wert, J., Liu, Q. & Hansen, N. (1997) Dislocation boundary

formation in a cold-rolled cube oriented Al single crystal. Acta

Mater. 45, 2565±2576.

Wright, S.I., Adams, B.L. & Kunze, K. (1993) Application of a new

automatic lattice orientation measurement technique to poly-

crystalline aluminum. Mater. Sci. Eng. A160, 229±240.



Unsupervised approval criteria for automated EBSP investigation of deformed metals

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