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Materials Science and Engineering A

journal homepage: www.elsevier.com/locate/msea

Diffraction study of the retained austenite content in TRIP steels

T. Gnäupel-Herolda,b,∗, A. Creuziger c,d

a NIST Center for Neuron Research, 100 Bureau Dr., Gaithersburg MD 20899-6102, USA

b University of Maryland, Department of Material Science and Engineering., College Park MD 20742-2142, USA

c NIST Metallurgy Division, 100 Bureau Dr., Gaithersburg MD 20899-8553, USA

d Kent State University, Kent, OH 44242, USA

article info

Article history:

Received 3 August 2010

Received in revised form 2 December 2010

Accepted 13 January 2011

Available online 19 January 2011

Keywords:

Austenite

Neutron diffraction

Texture

Steels

Deformation

abstract

The results of a study of using neutron diffraction for determining the retained austenite content of TRIP

steels are presented. The study covers a wide area of materials, deformation modes (uniaxial, biaxial and

plane strain), strains, and the retained austenite content as a result of these variables. It was determined

using basic principles of statistics that a minimum of two reflections (hkl) for each phase is necessary to

calculate a phase mass fraction and the associated standard deviation. Texture from processing the steel

is the largest source of uncertainty. Through the method of complete orientation averaging described

in this paper, the texture effect and with it the standard deviation of the austenite mass fraction can be

substantially reduced, regardless of the type or severity of the texture.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Steel typically may contain three different phases: austenite,

ferrite, and martensite. The relative mass fractions of austenite and

martensite have been of interest for a long time [1–14]. For new

high performance steels such as transformation induced plasticity

(TRIP) steels, accurate measurement of the austenite mass fraction

is key. The measurement of the retained austenite content down to

very low levels (less than 1% austenite) is a challenge for all suitable methods, and diffraction is no exception. However, with the

established theoretical principles of diffraction, accurately measured composition, and suitable signal to noise ratios the actual

detection limit could be significantly lower than 1%. The achievable accuracy is limited by several factors, with texture being the

most significant.

So far the difficulties associated with texture, and there is virtually no steel without texture, have been dealt with in a heuristic

manner by issuing recommendations to use procedures for weakly

textured samples [1] or for untextured samples [2]. In [1] Jatczak

focuses entirely on X-ray diffraction and recommendations are

made for dealing with texture using a scheme of partial orienta-

∗ Corresponding author. NIST Center for Neuron Research, 100 Bureau Dr. stop

6102, Gaithersburg, MD 20899-6102, USA, Tel.: +1 301 975 5380;

fax: +1 301 921 9847.

E-mail addresses: tg-h@nist.gov (T. Gnäupel-Herold),

adam.creuziger@nist.gov (A. Creuziger).

tion averaging of multiple reflections through rotation and limited

tilt but without regard to the different statistical weight of -tilts

and the effect of the missing tilt range. The error analysis presented

in [1] uses either the counting statistics or repeated measurements

with remounting of the same sample. Both methods have serious

limitations because they largely miss the texture effect and they

tend to produce unrealistically small uncertainties. To our knowledge, there has been no systematic study of the effects of texture

on the calculation of retained austenite mass fraction.

Good agreement in the measured retained austenite content

was achieved in an X-ray diffraction round-robin [3]. However, the

standard reference samples used there have since been withdrawn.

In a recent round robin, different characterization techniques were

used to measure the retained austenite in TRIP steel[4,5]. There was

significant scatter in the mass fractions calculated, both between

the different methods used and between the same methods, indicating there can be a significant bias error associated with different

methods or labs. At the same time, the standard deviations given by

each measurement were unrealistically low, thus indicating a real

lack of consistency in calculating both of mass fractions and their

uncertainties.

This paper focuses on the use of neutrons and schemes for orientation averaging to measure austenite mass fractions on TRIP

steels. Neutron diffraction has many advantages over some of the

other techniquesmentioned and employed in[4]; for example, each

measurement takes place over volumes of 10–100 mm3 and the

methods for determining phases by diffraction methods are well

developed. In this paper, a suitable orientation averaging proce0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved.

doi:10.1016/j.msea.2011.01.030
dure that permits the effect of texture to be largely suppressed is

discussed. These methods allow for precise measurement of the

austenite mass fraction and the standard deviations.

2. Experimental

2.1. Diffraction method

The estimation of the volume fractions in a polycrystalline

specimen containing different phases and with a random grain

orientation distribution by means of diffraction is based on the relationship of the calculated integrated intensity R(i)

hkl of a diffraction

line (hkl) for phase i and the volume fraction Vi of that phase in the

specimen. The expression used here can be written as [6–8,15]

R(i)

hkl = KVi

j3F2

hkl

v2

i sin  sin 2

e

−B sin2 

2 Ahkl (1)

where K: constant specific for the experiment; j: multiplicity of the

plane (hkl); : wavelength; F2

hkl: structure factor of the plane (hkl);

vi: unit cell volume of phase i; B: Debye–Waller factor; : Bragg

angle; Ahkl: absorption factor. The absorption factor depends on the

linear absorption coefficient and the specimen shape. It was found

to be negligible in this investigation. The theoretical structure factors Fhkl were calculated using the widely available Powder Cell[16]

program; for B the value 0.35 was used as quoted in [17]. If all intensities are measured on the same equipment, and under the same

conditions, the term K may be dropped, as it will for subsequent

discussion.

The steel specimens investigated here contain ferrite ( ̨),

retained austenite () and martensite (m). Bainite, which is typically encountered in TRIP steels, is a particular structure of ferrite

with austenite laths. Due to the alloying in TRIP steels, excess

carbon is partitioned to the austenite instead of forming cementites as in conventional bainite. The martensite peaks cannot be

resolved from the ferrite peaks [18]; thus, only the austenite ()

and the ( ̨+ m) volume fractions can be determined. The austenite

mass fraction value is not affected by the presence of the martensite phase because the sum of the structure factors of overlapped

martensite and ferrite peaks is practically identical to that of the ferrite peak with the martensite replaced by ferrite. Also, the austenite

peaks are unaffected by martensite. As these phases are the only

constituents in a TRIP steel, the volume fractions of each phase must

add to one (V ̨ + Vm + V = 1) and the volume fraction of the austenite phase can be correlated to the measured integrated intensities

I

()

l and I

( ̨+m)

l by

V =



1

n

n

l=1

I

()

l

R()

l





1

m

m

l=1

I

( ̨+m)

l

R( ̨+m)

l

+ 1

n

n

l=1

I

()

l

R()

l

 =  ̄I

()

 ̄I() +  ̄I( ̨+m) (2)

where (n) and (m) are the number of diffraction peaks for each

phase. The mass fraction is obtained from the densities () of each

phase:

f =



V





V + V ̨+m ̨+m

 (3)

Eq.(2) contains averages of integrated intensities normalized by

theoretical intensities. It is reasonable to use a longer counting time

for weak reflections, thus requiring time normalization as well. In

order to allow for the statistical nature of the intensities in Eq. (2)

one must consider the effects of individual standard deviations as

well as the averages calculated in Eq. (2). The standard deviation

of the measured integrated intensity of a peak (P) is derived fro

the counting statistics through:

P =



2

T + 2B (

with T = 0.675IT as standard deviation of the total intensity 

of the peak including background, and B = 0.675IB as standa

deviation of the background [19]. In principle, through sufficient

long counting times P could be reduced to arbitrary small valu

and, through error propagation in Eq.(2), a similarly small standa

deviation could be achieved for V . In reality this is not the ca

First, the averages in Eq. (2) need to be modified to allow for t

different individual P as weights:

 ̄I =

n

l=1

Il/



Rl2

l





n

l=1

1/2

l

(

Second, the normalized intensities I/R for each phase imp

that they are equal after the various normalizations for structu

factor, multiplicity, polarization, etc. This is usually not fulfill

because of counting statistics, texture, imperfect diffraction geom

etry, specimen shape and insufficient knowledge of specim

material parameters such as the precise elemental distribution 

constituent elements over phases and crystallographic sites. It 

assumed that all these influences combined act as one individu

uncertainty for each reflection. Thus, the variance of the avera

normalized intensities is

2

 ̄I = 1

n − 1

n

l=1



 ̄I − Il

2 (

The counting statistics still plays a role for 2

 ̄I as a contribut

to the scatter. Note that the factor (n-1) allows for the fact tha

was determined from the average of the Il. The standard deviati

of the volume fraction becomes

V =

	

2

 ̄I()


 ∂V

∂ ̄I()

2

+ 2

 ̄I( ̨+m)


 ∂V

∂ ̄I( ̨+m)

2

=



2

 ̄I()



 ̄I( ̨+m)

2 + 2

 ̄I( ̨+m)



 ̄I()

2



 ̄I() +  ̄I( ̨+m)

4 (

which can be converted to a mass fraction using the known de

sities. From Eqs. (5), (6), (7) it follows that the measurement 

only one single peak for austenite and ferrite does not allow t

proper calculation of a mass fraction or its standard deviation. Fro

equation (6) the factor 1/(n-1) requires at least two peaks. Phy

cally speaking, at least a second peak is necessary to compare t

normalized intensities and to calculate an uncertainty; with on

one peak one has to assume an ideally random sample, a conditi

that is rarely fulfilled. By having at least a second reflection ava

able (more are desirable) one has in essence an internal measu

of scatter through the differences in I/R for a particular phase in E

(2).

Eq. (2) is also the basis for the standard procedure in [2] whi

explicitly states that specimens should be texture free. It is w

known that in steels some preferred grain orientation is alwa

present, thus making the intensity dependent on the specim

orientation. If left uncorrected, textured samples produce a ve

large scatter in diffraction-based estimates of phase fractions. 

correction can be performed in two ways: (1) By averaging ov
Table 1

Chemical composition (wt %) of the TRIP samples investigated.

Sample Material C Mn Al Si Thickness

(mm)

A TRIP 700 0.23 1.49 2.02 0.04 1.0

B TRIP 590 0.10 1.48 0.059 1.19 1.6

C TRIP 780 0.16 2.07 2.04 0.03 1.0

sufficiently many, and suitably different specimen orientations and

(2), by using the orientation distribution function (ODF) for the

calculation of the integrated intensity with texture effect.

For the purpose of volume/mass fraction determination the first

approach, here called complete orientation averaging, is preferable

because it requires far less measurement time. In that case, a summation of peaks measured at different specimen orientations is

performed and the average intensity of the peak used to determine

the phase fraction. Method (2) requires a known ODF from which

one can calculate the multiples of random density numbers (m.r.d)

for the combinations of (hkl) and specimen orientations used in the

measurement.

Method (1) is used extensively as the basis for the neutron

diffraction texture measurements where individual measurements

are taken for (φ ) values obtained by a reverse equal-area projection from a plane onto the pole sphere. The locations on the plane

are the central points of equal-sized hexagons, which, through areapreservation of the projection, yield directions with nearly constant

angular distance between neighboring points [20,21]. This is realized in the meshes shown in Fig. 1.

The orientation mesh in Fig. 1 left represents a nearly ideal case:

how well the orientation average is achieved depends only on the

angular width of intensity poles with respect to the spacing of orientations. When averaging the intensities of different reflections

(hkl) this effect is a contributor to the variance in Eq. (6). With the

complete orientation averaging each sample orientation has equal

weight; a non-equidistant spacing could be used instead but would

require the introduction of weight factors to correct for over/underrepresentation of some orientations.

2.2. Samples

Three different grades of commercially produced TRIP steels

were investigated: TRIP590, TRIP700 and TRIP780. The numbers

following TRIP indicate the nominal ultimate tensile strength in

MPa. These samples are sheet stock; their chemical compositions

and as received thickness are given in Table 1.

The deformation modes included uniaxial deformation parallel to the rolling direction (RD), uniaxial deformation parallel to

the transverse direction (TD), in plane-strain deformation (ε2 = 0)

with the straining direction parallel to the rolling direction (PS-RD)

plane-strain deformation parallel to the transverse direction (PSTD), and balanced biaxial deformation (BB) (ε1 = ε2). TRIP700 was

investigated only in the undeformed state. TRIP590 samples were

measured in the undeformed state and at nominal deformations of

2%, 5%, 10%, 15%, 20% and 25% engineering strain with the exception

of a PS-TD sample that failed before reaching 25% strain. TRIP780

samples were measured in the undeformed state and at nominal

deformations of 2%, 5% and 10% engineering strain. The equipment

used to deform the samples is described in more detail in [22]. In

order to create sufficient scattering volume, reduce data acquisition

times and produce an equal-axial sample shape, the sheet material was sheared into small plates and glued together into cubes

(6 mm × 6 mm × 6 mm) while maintaining the plate orientations.

The densities used here were obtained by Rietveld analysis of neutron diffraction patterns measured on the undeformed samples B

( ̨+ m = (7.749 ± 0.002) g/cm3 and  = (7.765 ± 0.018) g/cm3) and

C ( ̨+ m = (7.591 ± 0.004) g/cm3 and  = (7.668 ± 0.016) g/cm3).

For sample A (TRIP700), the values for sample C were used because

of the similar composition.

2.3. Diffraction measurements

The integrated intensities, averaged over all orientations were

determined from the fit of a gaussian with linear background function. Values of the standard deviation () were obtained from the

respective standard deviation of the peak height and the width.

The neutron measurements of individual, non-overlapping

peaks were done at the BT8 residual stress diffractometer at NCNR

using a full-circle Euler cradle for specimen orientation [23]. The

steel samples are fully bathed in the neutron beam at all orientations. Because of the low attenuation of neutrons, the entire sample

contributes almost uniformly to the diffracted beam. Absorption

effects were found to be negligible for the specimens used in this

work.

A total of six reflections – three for austenite, three for ferrite –

were used for mass fraction estimation. A Si (3 1 1) monochromator

produced a wavelength of = 0.1637 nm without /2 contamination, thus putting the three austenite reflections: A200, A220 and

A311 at values of 2 of (54◦, 79◦, 96◦) and for ferrite F200, F211

and F220 at values (69◦, 88◦, 107◦), within the available 2-range

of 45◦–110◦. The composition given in Table 1 was used to calculate

the structure factors.

The method of complete orientation averaging represents the

measurement of a complete pole figure, albeit not necessarily at

counting times or φ -mesh resolution required to calculate the

ODF. A minimum of 127 orientations in φ -mesh resolution was

used for the calculation of retained austenite content (see Fig. 1).

Control measurements were done using five different powders (Fe,

Mo, Cu, Al, Ni). Orientation averaging was not carried out on the

control powder measurements because the cylindrical shape of the

sample container did not allow that a constant volume of sample

material be illuminated by the beam at all orientations.

Selected X-ray measurements were performed using filtered

Mo-Kradiation in a partial averaging scheme up to 45◦ -tilt (see

pictograms in Fig. 3, right).

3. Results

The determination of mass fractions based on the comparison

of orientation averaged peaks as laid out in Eq. (1)–(7) is largely

limited by the signal/noise ratio which decreases with decreasing

austenite content. However, all austenite peaks were well behaved,

and no constraints for the peak position or the width were used. The

ferrite peak shapes were symmetric without indication of martensite peaks.

Measurements of peaks from the various control powder materials were used to demonstrate the effect of insufficient orientation

averaging even for samples deemed to be random. This is shown

in the normalized intensities vs. 2 (Fig. 2). As mentioned, sample container geometry precluded using orientation averaging

while measuring the powder materials. For the random orientation assumption, the normalized intensity should not depend on

2. However, the relative differences up to 30% in the normalized intensities in Fig. 2, left, are most likely caused by texture

from the settling of the powder particles. Thus, it provides an

excellent illustration of the difficulties that can arise from the

assumption of random grain orientation even for powder samples that are typically assumed to be untextured. The normalized

intensities are shown only as a representative example for two

TRIP590 samples, one sample as undeformed and one sample

strained to 20% in the PS-TD strain state in Fig. 2, right. The
a d b c f e

Fig. 1. Specimen orientations in spherical polar coordinates (φ ) plotted in equal-area projection. The circles represent the azimuth angle φ (sample rotation); the rad

distance is the tilt angle . At the center is zero and the φ-axis is parallel to the bisector of incident and diffracted beam (scattering vector). The mesh resolutions are (l

to right, with 
φ =90◦ in brackets) a: 469(5◦), b: 331(6◦), c: 217(7.5◦), d: 127(10◦), e: 61(15◦), f: 19(30◦).

Normalized Intensities from Powders

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

40 50 60 70 80 90 100 110

2θ [°]

Fe Mo Al Cu Ni

I/R [a.u]

I/R (ferrite) [a.u]

TRIP590, PSTD, Normalized Peak Intensities

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

50 60 70 80 90 100 110

2θ [°]

0.00

0.02

0.04

0.06

0.08

0.10

undef. (F) 20% (F) undef. (A) 20% (A)

I/R (aust.) [a.u]

Fig. 2. Left: Normalized intensities (I/R) for peaks from various powders. The following peaks were measured: Cu, Ni:(111), (200), (220), (311), (222); Al: (200), (220), (31

(222), (400); Fe: (110), (200), (211), (220); Mo: (200), (211), (220). Right: Normalized integrated intensities for TRIP 590, undeformed and 20% strain PS-TD with ferrite pea

(200), (211), (220) and austenite peaks (200), (220) and (311). In the right graph the -values are of the size of the markers or smaller.

I/R (2) for all other samples displayed a very similar behavior.

For the TRIP steel the I/R both for ferrite and austenite have small

slopes over 2. Through measurements with different mesh resolutions in complete and partial orientation averaging it was found

that imperfect orientation averaging together with the particular

combination of reflections (hkl) used here could cause this behavior. However, one should note that overall the differences between

normalized intensities over 2 are much smaller (max × 7%) for

the TRIP sample with complete orientation averaging than for

the powder samples (max ± 17%) without comparable orientation

averaging.

Instead of a complete orientation average with varying point

density one can also consider a partial average limited by tilt. Such

a case arises if the tilt angle ( ) range is restricted as it is the case in

X-ray diffraction. These data were created by partitioning of existing data sets from complete orientation averaging. At ≈0 one has

the case of a –2 scan at one orientation. Consequently, the ma

fractions derived from these measured intensities deviate signi

cantly from the result obtained with complete orientation averag

As larger values are included, the calculated values conver

again. However the trends prior to the convergence are not co

sistent between different samples, showing the need to measure 

higher angles to improve accuracy.

Fig. 3 demonstrates the effect of the number of orientations 

the mass fraction value. As the number of orientations increa

there is convergence in the mass fraction measurement. The ma

fractions do not show a strong dependence on the number of o

entations beyond 100 orientations measured.

The effects of φ -mesh densities (see Fig. 1) or limited tilt cap

bility are clearly reflected in the dependence of relative standa

deviation shown in Fig. 4. Values for rel increase steeply belo

100 orientations per measurement (complete averaging schem

or for averaging in a -range less than 30◦ from the sample no

fe d c b a

Fig. 3. Effect of different numbers of individual orientations on the calculated austenite mass fraction. Left: complete orientation averaging with different mesh densit

with letters a–f referring to the meshes in Fig. 1. Right: Partial orientation averaging with limited -tilt. The grey area in the pictograms indicate the tilt range used with t

x-axis as the cut-off. A value of = 0 would be the equivalent of a –2 scan with only one contributing orientation per reflection. TRIP 700 set 1 refers to A(220), A(31

A(420) and F(211), F(220), F(321). Set 2 refers to A(200), A(220), A(311) and F(200), F(211), F(220).
0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 100 150 200 250 300 350 400 450 500 50

number of orientations

rel

0 20 30 40 50 60 70 80 90 100 10

highest ψ-value used

PS-RD 5%

TD 5%

TRIP 700

partial average PSRD 5%

partial average, TRIP700, set 1

partial average, TRIP700, set 2

σ

Fig. 4. Relative standard deviations for the complete averaging scheme (bottom axis) and for partial averaging in limited -tilt (top axis). Low values on the top axis mean

fewer orientations just as on the bottom axis.

mal. Beyond that, the relative standard deviation values are stable

at 10–20%.

Larger fluctuations in the calculated value of the mass fraction are observed if different combinations of orientation averaged

reflections (hkl) are used. Fig. 5 illustrates very effectively the reason why mass fraction calculations based on single reflections are

unreliable. First, the calculation of the standard deviation is not possible with Eq. (6), and second, the effects of insufficient orientation

average are amplified leading to relative minimum/maximum differences of up to 50% in the mass fraction. The standard deviations

 calculated from the counting statistics (1A/1F combinations)

are too small as evident from the comparison with the  values

for f from combinations of multiple reflections (Fig. 5, left). Due

to instrumental restrictions the pool of simultaneously accessible

reflections is restricted to ferrite (110), (200), (211), (220) with

austenite (111), (200), (220), (311) and (222). However, the austenite (111) and (222) reflections are difficult to measure for small

mass fractions due to their low multiplicity and some overlap with

neighboring ferrite reflections. Therefore the undeformed TRIP700,

which had the largest austenite mass fraction, was chosen to investigate a large number of different combinations of reflections (Fig. 5,

right).

The 2A/2F combination requires fewer measurements than

3A/3F or 5A/4F but comes at the expense of a larger  expressed

through the larger scatter than 3A/3F. This uncertainty is not related

to the counting statistics but stems from the previously discussed

effects of insufficient orientation average and limited knowledge

of the phase specific chemical composition. The 5A/4F combination represents the maximum available data with a total of 2979

individual intensity measurements but it does not come with a significant reduction in . In effect, the relative standard deviation for

the data in Fig. 4 has a lower limit of approximately 10%. A similar

threshold for  exists for TRIP590 and TRIP780, both of which have

much lower contents of retained austenite.

The mass fractions for different deformation regimes and strains

are shown in Fig. 6 for TRIP780 and TRIP590. They are plotted in

terms of effective strain, which is the Von Mises average of the true

strains:

εeff =

√

2

3



(ε11 − ε22)

2 + (ε22 − ε33)2 + (ε331 − ε11)2 1

2 (8)

This allows different strain states to be compared directly. The

austenite mass fractions measured follow a similar curve for all

three strain modes explored, similar to results shown in [5].

For the purpose of comparison selected X-ray measurements

were performed on three undeformed samples with results shown

in Table 2. The austenite weight fractions are comparable to the

neutron results when using the X-ray standard deviations. However, this is not always the case when considering the much smaller

standard deviations from neutron diffraction measurements. Two

main reasons for this discrepancy were identified: the generally

low X-ray signal/noise ratio (≤1/10) and the “missing orientations”

from the -tilt limited to values ≤45◦. The wider effects of the

averaging scheme in connection with different textures on weight

fractions derived from X-ray diffraction is currently under investigation.

4. Discussion

The values of retained austenite measured for the TRIP steels

investigated here are comparable to the range of retained austenite measured by Jacques et al. [4] as part of round robin. As noted

previously, the round robin data shows a great deal of scatter, and

ranges from 2% to 36% austenite. While the TRIP 590 and TRIP 780

steels are on the low end of this range, they are commercially produced alloys. The TRIP 700 steel falls into the middle of the range

of retained austenite with a value of 15%. From the composition

data, there does not seem to be a strong effect from alloying alone,

the thermo-mechanical processing plays a strong role in the final

austenite value. Similarly, comparing the retained austenite value

alone of the TRIP steels does not give an indication to the strength

and ductility of the different steels.

Comparing the retained austenite as a function of applied strain

and strain state in Fig. 6 shows some differences and commonality between the TRIP 590 and TRIP 780 alloys. Neither alloy shows

a strong effect from stress triaxiality, as predicted previously [5].

In both materials the lowest retained austenite value occurs near

failure in the balanced biaxial strain state, and appears to reach

Table 2

Austenite mass fractions for three different TRIP steels (undeformed) as obtained

from complete orientation average (neutron diffraction) and partial average/X-ray

diffraction.

Sample Wt.

fraction

(X-ray)

 Wt.

fraction

(neutron)



TRIP 700 0.156 0.038 0.135 0.016

TRIP 590, undeformed 0.053 0.045 0.058 0.006

TRIP 780, undeformed 0.039 0.032 0.051 0.003
fγ

TRIP700: Combinations of different austenite and ferrite reflections

0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

(combination)

2A/2F 5A/4F 3A/3F

TRIP780, PSRD 5%: different (hkl) combinations

0.012

0.014

0.016

0.018

0.020

0.022

0.024

0.026

A:(200),(220),(311)

F:(110), (200), (211), (220)

A:(200), (220), (311)

F:(200), (211), (220)

A:(200), (220), (311)

F:(211), (220)

A:(200), (220), (311)

F:(211), (220)

A(220) / F(211)

A(220) / F(200)

A(200) / F(220)

A(200) / F(211)

A(220) / F(220)

A(311) / F(200)

A(311) / F(211)

A(311) / F(220)

A(200) / F(200)

fγ

Fig. 5. Effect of (hkl)-combinations on the mass fraction f Left: TRIP 780 sample strained in PS-RD 5%. Right: TRIP 700, undeformed. 2A/2F and 3A/3F use different combinatio

of (hkl) out of 5A/4F (Austenite: (111), (200), (220), (311), (222) with Ferrite: (110), (200), (211), (220)). The -values for combinations of single reflections are calculat

from the counting statistics. Each reflection was measured with 331 orientations.

a plateau value before reaching failure. In contrast the uniaxial

deformation samples follow the plane strain and balanced biaxial for the TRIP 590 samples, while in the TRIP 780 alloy there is

more retained austenite for both uniaxial samples, with the TD oriented sample having a higher austenite value for higher levels of

strain. This will be investigated further in the future, but may be

due to differences transformation potential due to crystallographic

orientation discussed in [24].

The method of complete orientation averaging provides a precise method for measuring the retained austenite mass fraction.

With this method, the retained austenite mass fractions can be

measured to levels less than 1% with standard deviations on the

order of 10%. This overall precision of 10% (Fig. 4) was found for the

entire range of austenite mass fractions (from 0.01 to 0.14), even if

significantly more orientations contribute to the average.

It is difficult to compare this precision with other published

results, mostly due to the lack of detail about the error estimation

procedures. The twomethods given in[1] should be seen in a critical

light because both methods do not take texture into account, and,

compared with the results presented here, bothmay underestimate

 by a significant amount. For example, for all samples where  is

estimated solely based on the count rate, the standard deviation is

over 10 times smaller than the values given here from Eq. (7). Such

a low value clearly does not reflect the observed scatter.

The results presented here on the role of texture and orientation averaging can offer some explanation of the large variability

in the X-ray results of the round-robin in [4]. The results listed in

the round-robin presumably follow the SAE [1] or ASTM [2] guidelines, while no details are given. As shown in this paper an austen

mass fraction f derived from a partial orientation average is su

ject to a large relative deviation. A necessary condition to obtain 

meaningful value for f – which includes a meaningful uncertain

– is that a minimum of two diffraction lines from both ferrite a

austenite are needed to accurately determine f . Neither of the

criteria are stated in the ASTM standard [2] and the requireme

on the tilt axis is not explicitly stated in the SAE publication 

Jatczak [1]. The statement in [1] that if tilt and rotation are pe

formed, only one line pair is needed is also incorrect because 

meaningful uncertainty can be given for f . The assumption of 

random orientation distribution is hard to justify, given the scatt

of intensities of powder samples investigated here. The latter resu

in particular (Fig. 2) demonstrates that at least for the purpose 

mass fraction determinations a sample cannot be assumed to ha

no or negligible texture. The recommendation of four (hkl) pa

if the sample is not rotated or tilted is also insufficient becau

each additional reflection (hkl) improves the average only by t

multiplicity of that particular (hkl).

The retained austenite content determined from partial ave

aging schemes such as X-ray diffraction is susceptible to ‘missin

orientations from limited -tilt (Fig. 3, left). Complete orientati

averaging schemes require a minimum density of orientations 

order to yield stable results. That number depends on the type a

strength of the underlying texture. Fig. 3 indicates that number 

be >100 for the samples investigated here. This underscores som

of the advantages of neutron diffraction: superior grain statisti

(103 more contributing grains than X-ray diffraction), and easi

Fig. 6. Austenite mass fractions f for TRIP 590 (left) and TRIP 780 (right). The deformation modes are uniaxial in RD and TD, in plane-strain deformation (ε2 = 0) parallel 

RD and TD (labeled as PS-RD and PS-TD), and balanced biaxial deformation (BB)(ε1 = ε2).
complete orientation averaging. In comparison, X-ray diffraction is

limited by its low penetration and tilt angle restrictions.

5. Conclusions

Amethod of austenitemass fractionmeasurement, termed complete orientation averaging has been demonstrated. If an unknown

texture is present then averaging over sufficiently many (over 100)

specimen orientations is necessary in order to reduce the influence

of texture. Additionally, the measurement of at least two peaks

for each phase are necessary to calculate the standard deviation

and thus a minimum requirement for reliable measurement of the

austenite mass fraction. Within the range of results obtained here

the relative accuracy of neutron diffraction with complete orientation averaging is remarkably stable, and even austenite mass

fractions down to values <0.01 were determined with good precision (rel = 10%).

6. Disclaimer

Certain commercial firms and trade names are identified in this

report in order to specify aspects of 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.

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