Standard Practice for X-Ray Determination of Retained Austenite in Steel with Near Random Crystallographic Orientation

SIGNIFICANCE AND USE
Significance—Retained austenite with a near random crystallographic orientation is found in the microstructure of heat-treated low-alloy, high-strength steels that have medium (0.40 weight %) or higher carbon contents. Although the presence of retained austenite may not be evident in the microstructure, and may not affect the bulk mechanical properties such as hardness of the steel, the transformation of retained austenite to martensite during service can affect the performance of the steel.
Use—The measurement of retained austenite can be included in low-alloy steel development programs to determine its effect on mechanical properties. Retained austenite can be measured on a companion sample or test section that is included in a heat-treated lot of steel as part of a quality control practice. The measurement of retained austenite in steels from service can be included in studies of material performance.
SCOPE
1.1 This practice covers the determination of retained austenite phase in steel using integrated intensities (area under peak above background) of X-ray diffraction peaks using chromium Kα  or molybdenum Kα  X-radiation.
1.2 The method applies to carbon and alloy steels with near random crystallographic orientations of both ferrite and austenite phases.  
1.3 This practice is valid for retained austenite contents from 1 % by volume and above.
1.4 If possible, X-ray diffraction peak interference from other crystalline phases such as carbides should be eliminated from the ferrite and austenite peak intensities.
1.5 Substantial alloy contents in steel cause some change in peak intensities which have not been considered in this method. Application of this method to steels with total alloy contents exceeding 15 weight % should be done with care. If necessary, the users can calculate the theoretical correction factors to account for changes in volume of the unit cells for austenite and ferrite resulting from variations in chemical composition.
1.6 Units—The values stated in inch-pound units are to be regarded as standard. No other units of measurement are included in this standard.
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E975 − 03(Reapproved 2008)
Standard Practice for
X-Ray Determination of Retained Austenite in Steel with
Near Random Crystallographic Orientation
This standard is issued under the fixed designation E975; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The volume percent of retained austenite (face-centered cubic phase) in steel is determined by
comparing the integrated chromium or molybdenum X-ray diffraction intensity of ferrite (bodycen-
tered cubic phase) and austenite phases with theoretical intensities. This method should be applied to
steels with near random crystallographic orientations of ferrite and austenite phases because preferred
crystallographicorientationscandrasticallychangethesemeasuredintensitiesfromtheoreticalvalues.
Chromium radiation was chosen to obtain the best resolution of X-ray diffraction peaks for other
crystalline phases in steel such as carbides. No distinction has been made between ferrite and
martensite phases because the theoretical X-ray diffraction intensities are nearly the same. Hereafter,
the term ferrite can also apply to martensite. This practice has been designed for unmodified
commercial X-ray diffractometers or diffraction lines on film read with a densitometer.
Other types of X-radiations such as cobalt or copper can be used, but most laboratories examining
ferrous materials use chromium radiation for improved X-ray diffraction peak resolution or
molybdenum radiation to produce numerous X-ray diffraction peaks. Because of special problems
associated with the use of cobalt or copper radiation, these radiations are not considered in this
practice.
1. Scope necessary, the users can calculate the theoretical correction
factors to account for changes in volume of the unit cells for
1.1 This practice covers the determination of retained aus-
austenite and ferrite resulting from variations in chemical
tenite phase in steel using integrated intensities (area under
composition.
peak above background) of X-ray diffraction peaks using
chromium K or molybdenum K X-radiation.
α α
1.6 Units—The values stated in inch-pound units are to be
1.2 The method applies to carbon and alloy steels with near regarded as standard. No other units of measurement are
included in this standard.
random crystallographic orientations of both ferrite and aus-
tenite phases.
1.7 This standard does not purport to address all of the
1.3 This practice is valid for retained austenite contents
safety concerns, if any, associated with its use. It is the
from 1 % by volume and above.
responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica-
1.4 If possible, X-ray diffraction peak interference from
bility of regulatory limitations prior to use.
other crystalline phases such as carbides should be eliminated
from the ferrite and austenite peak intensities.
2. Significance and Use
1.5 Substantial alloy contents in steel cause some change in
peak intensities which have not been considered in this
2.1 Significance—Retained austenite with a near random
method. Application of this method to steels with total alloy
crystallographic orientation is found in the microstructure of
contents exceeding 15 weight % should be done with care. If
heat-treated low-alloy, high-strength steels that have medium
(0.40 weight %) or higher carbon contents. Although the
1 presence of retained austenite may not be evident in the
This practice is under the jurisdiction of ASTM Committee E04 on Metallog-
raphy and is the direct responsibility of Subcommittee E04.11 on X-Ray and
microstructure, and may not affect the bulk mechanical prop-
Electron Metallography.
erties such as hardness of the steel, the transformation of
Current edition approved June 1, 2008. Published September 2008. Originally
retained austenite to martensite during service can affect the
approved in 1984. Last previous edition approved in 2003 as E975 – 03. DOI:
10.1520/E0975-03R08. performance of the steel.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E975 − 03 (2008)
A
TABLE 1 Calculated Theoretical Intensities Using Chromium K Radiation
α
2 B 2
hkl Sinθ/λθ f ∆f8 ∆f9 /F/ LP P T N R
(α iron, body-centered cubic, unit-cell dimension a = 2.8664Å):
o
B C
110 0.24669 34.41 18.474 −1.6 0.9 1142.2 4.290 12 0.9577 0.001803 101.5
B C
200 0.34887 53.06 15.218 −1.6 0.9 745.0 2.805 6 0.9172 0.001803 20.73
B C
211 0.42728 78.20 13.133 −1.6 0.8 534.6 9.388 24 0.8784 0.001803 190.8
(γ iron, face-centered cubic, unit-cell dimension a = 3.60Å):
o
B C
111 0.24056 33.44 18.687 −1.6 0.9 4684.4 4.554 8 0.9597 0.0004594 75.24
B C
200 0.27778 39.52 17.422 −1.6 0.9 4018.3 3.317 6 0.9467 0.0004594 34.78
B C
220 0.39284 64.15 14.004 −1.6 0.8 2472.0 3.920 12 0.8962 0.0004594 47.88
A
Data from “International Tables for X-Ray Crystallography,” Physical and Chemical Tables, Vol III, Kynoch Press, Birmingham, England, 1962, pp. 60, 61, 210, 213;
Weighted K and K value used (λ = 2.29092Å).
α1 α2
B −2M 2 2
Temperature factor (T =e ) where M=B(sin θ)/λ and 2B = 0.71. Also N is the reciprocal of the unit-cell volume.
C
Calculated intensity includes the variables listed that change with X-ray diffraction peak position.
2.2 Use—The measurement of retained austenite can be
r = radius of the diffractometer,
includedinlow-alloysteeldevelopmentprogramstodetermine
c = velocity of light,
its effect on mechanical properties. Retained austenite can be λ = wavelength of incident radiation,
measured on a companion sample or test section that is A = cross sectional area of the incident beam,
v = volume of the unit cell,
includedinaheat-treatedlotofsteelaspartofaqualitycontrol
/F/ = structure factor times its complex conjugate,
practice. The measurement of retained austenite in steels from
p = multiplicity factor of the (hkl) reflection,
service can be included in studies of material performance.
θ = Bragg angle,
3. Principles for Retained Austenite Measurement by LP = Lorentz Polarization factor which is equal to
(1 + cos 2θ)/sin θ cos θ for normal diffractometric
X-Ray Diffraction
2 2 2
analysisbutbecomes(1 + cosθ 2αcos 2θ)/(sin θ
3.1 A detailed description of a retained austenite measure-
cos θ) (1 + cos 2α) when a monochromator is used
ment using X-ray diffraction is presented by the Society
2 in which diffraction by monochromator and sample
ofAutomotive Engineers. Since steel contains crystalline
take place in the same plane; 2α is the diffraction
phases such as ferrite or martensite and austenite, a unique
angle of the monochromator crystal. If diffraction
X-ray diffraction pattern for each crystalline phase is produced
by the monochromator occurs in a plane perpen-
when the steel sample is irradiated with X-irradiation. Carbide
dicular to the plane of sample diffraction,
phases in the steel will also produce X-ray diffraction patterns. 2
2 2 2
then LP = (cos 2α + cos 2θ)/sin θcos (1 + cos
3.2 For a randomly oriented sample, quantitative measure-
2α),
−2 M
ments of the relative volume fraction of ferrite and austenite
e = Debye-Waller or temperature factor which is a
2 2 2
can be made from X-ray diffraction patterns because the total
function of θ where M=B( sin θ)/λ , B =8π
2 2
integrated intensity of all diffraction peaks for each phase is
(µ ) , where µ is the mean square displacement of
s s
proportional to the volume fraction of that phase. If the
the atoms from their mean position, in a direction
crystalline phase or grains of each phase are randomly
perpendicular to the diffracting plane, and
oriented, the integrated intensity from any single diffraction
V = volume fraction of theα -plane.
α
peak (hkl) crystalline plane is also proportional to the volume
K is a constant which is dependent upon the selection of
fraction of that phase:
instrumentation geometry and radiation but independent of the
hkl hkl
I 5 KR V /2µ
α α α nature of the sample. The parameter, R, is proportional to the
theoretical integrated intensity. The parameter, R, depends
where:
upon interplanar spacing (hkl), the Bragg angle, θ, crystal
e 2 4 3
K 5 I /m c 3 ~λ /32πr!
~ !
o A structure, and composition of the phase being measured. R can
be calculated from basic principles.
and
2 22M 3.3 For steel containing only ferrite (α) and austenite (γ)
1 /F/ pLPe
~ !
hkl
R 5
2 and no carbides, the integrated intensity from the ( hkl) planes
α
v
of the ferrite phase is expressed as:
where:
hkl hkl
I 5 KR V /2µ
α α α
hkl
I = integrated intensity per angular diffraction peak
α
3.3.1 A similar equation applies to austenite. We can then
(hkl)inthe α-phase,
I = intensity of the incident beam,
write for any pair of austenite and ferrite hkl peaks:
o
µ = linear absorption coefficient for the steel,
hkl hkl hkl hkl
I /I 5 @~R /R !~V /V !#
α γ α γ α γ
e,m = charge and mass of the electron,
3.3.2 The above ratio holds if ferrite or martensite and
austenite are the only two phases present in a steel and both
Retained Austenite and Its Measurement by X-ray Diffraction, SAE Special
phases are randomly oriented. Then:
Publication 453, Society ofAutomotive Engineers (SAE), 400 Commonwealth Dr.,
Warrendale, PA 15096-0001, http://www.sae.org. V 1V 5 1
α γ
E975 − 03 (2008)
3.3.3 The volume fraction of austenite ( V ) for the ratio of metallographic sample preparation. Standard chromic-acetic
γ
measured integrated intensities of ferrite and austenite peak to acid for electropolishing 0.005-in. from samples ground to 600
R-value is: grit or specific chemical polishing solutions for a particular
grade of steel polished to a 6-µm finish can be used to verify
V 5 I /R / I /R 1 I /R (1)
~ !
@ ~ !#
γ γ γ α α γ γ
the metallographic polish. Hot-acid etching is not recom-
3.3.4 For numerous ferrite and austenite peaks each ratio of
mended because of selective etching of one phase or along a
measured integrated intensity to R-value can be summed:
preferred crystallographic direction.
q P q
4.1.5 Sample size must be large enough to contain the Xray
1 Iγj 1 1
V 5 / Iαi/Rαi 1 Iγj/Rγj (2)
FS D S D S DG
γ ( ( (
beam at all angles of 2θ required for the X-ray diffraction
q Rγj P q
j51 i51 j51
analysis to prevent errors in the analysis. In most cases, a 1- in.
3.3.5 If carbides are present:
square area is sufficient, but sample size depends upon the
V 1V 1V 5 1 dimensions of the incident X-ray diffraction. When using
α γ c
molybdenumradiation,selectpeaksintherangefrom28to40°
3.3.6 Then the volume fraction of austenite ( V ) for the
α
2θ for best results.
ratio of measured ferrite and austenite integrated intensity to
4.2 X-Ray Equipment:
R-value is:
4.2.1 A standard X-ray diffractometer with a pulse height
V 5 1 2 V I /R / I /R 1 I /R (3)
@ ~ ! ~ !#
γ ~ c! γ γ ~ α α! γ γ
selector circuit is preferred for the measurement, but an X-ray
3.3.7 For numerous ferrite and austenite peaks the ratio of
camera plus densitometer readings of the film may be used.
measured integrated intensity to R-values can be summed:
X-ray film and adequate photographic development techniques
q p
are required to assure a linear response of the film to the X-ray
1 2 V 1/q Iγj/Rγj /1/P I i/R i
~ !S ~ !D ~ !
c a a intensity.
( (
j51 i51
V 5 (4)
q
γ 4.2.2 A chromium X-ray source with a vanadium metal or
3 4
11/q I j/R j
~ !
( γ γ compound filter to reduce the K radiation is recommended.
β
j51
ChromiumradiationproducesaminimumofXrayfluorescence
3.4 The volume fraction of carbide, V , should be deter-
c
of iron. Chromium radiation provides for the needed X-ray
mined by chemical extraction or metallographic methods.
diffraction peak resolution and allows for the separation of
Adequate X-ray diffraction peak resolution for the identifica-
carbide peaks from austenite and ferrite peaks.
tion of carbide peaks is required to avoid including carbide
4.2.3 Other radiation such as copper, cobalt, or molybde-
peaks in the retained austenite measurement.
num can be used, but none of these provide the resolution of
chromium radiation. Copper radiation is practical only when a
4. Procedure
diffracted-beam monochromator is employed, because iron
4.1 Sample Preparation:
X-ray fluorescence will obscure the diffracted peaks.
4.1.1 Samples for the X-ray diffractometer must be cut with
4.2.4 A molybdenum source with a zirconium filter is used
a minimum amount of heat effect. Since most steels containing
to produce a large number of X-ray diffraction peaks.
retained austenite are relatively hard, abrasive cutoff wheels
4.3 X-Ray Method—X-ray diffraction peaks from other
arefrequentlyused.Ifadequatecoolingisnotused,heateffects
crystalline phases such as carbides must be separated from
from abrasive cutoff wheels can be substantial and, in some
austenite and ferrite peaks. The linearity of the chart recorder
cases, can transform retained austenite. Saw cutting rather than
or photographic film shall be verified prior to utilizing this
abrasive wheel cutting is recommended for sample removal
method.
whenever it is practical.
4.3.1 Entire diffraction peaks minus background under the
4.1.2 Rough grinding using a milling tool or high-pressure
peaks shall be recorded to obtain integrated peak intensities.
coarse grinding can deform the surface and transform some of
Peaks without carbide or second phase interference can be
the retained austenite to a depth that is greater than the surface
scanned, and the total peak plus background recorded. Back-
depth analyzed. Final milling or rough grinding cuts limited to
ground counts are obtained by counting on each side of the
a depth of 0.010-in. or less should reduce the depth of
peak for one-half of the total peak counting time. Total
deformation.
background is subtracted from peak plus background to obtain
4.1.3 Standard metallographic wet-grinding and polishing
the integrated intensity. Alternatively, software supplied with
methods shall be used to prepare samples for X-ray analysis.
the diffractometer can be used. In general, a diffractometer
Grit reductions of 80, 120, 240, 320, 400, and 600 silicon
scanning rate of 0.5°2θ/min or less is recommended to define
carbide or alumina abrasives may be used but other valid grit
the peaks for austenite contents of less than 5 %.
combinations may also be used.Afinal surface polish of 6-µm
diamond or an equivalent abrasive polish is required. Sample 4.3.2 Where carbide or other phase X-ray diffraction peak
etching, observation for heat effects, and repolishing is a interfer
...


This document is not anASTM standard and is intended only to provide the user of anASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation:E975–00 Designation:E975–03 (Reapproved 2008)
Standard Practice for
X-Ray Determination of Retained Austenite in Steel with
Near Random Crystallographic Orientation
This standard is issued under the fixed designation E975; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The volume percent of retained austenite (face-centered cubic phase) in steel is determined by
comparing the integrated chromium or molybdenum X-ray diffraction intensity of ferrite (bodycen-
tered cubic phase) and austenite phases with theoretical intensities. This method should be applied to
steelswithnearrandomcrystallographicorientationsofferriteandaustenitephasesbecausepreferred
crystallographicorientationscandrasticallychangethesemeasuredintensitiesfromtheoreticalvalues.
Chromium radiation was chosen to obtain the best resolution of X-ray diffraction peaks for other
crystalline phases in steel such as carbides. No distinction has been made between ferrite and
martensite phases because the theoretical X-ray diffraction intensities are nearly the same. Hereafter,
the term ferrite can also apply to martensite. This practice has been designed for unmodified
commercial X-ray diffractometers or diffraction lines on film read with a densitometer.
Other types of X-radiations such as cobalt or copper can be used, but most laboratories examining
ferrous materials use chromium radiation for improved X-ray diffraction peak resolution or
molybdenum radiation to produce numerous X-ray diffraction peaks. Because of special problems
associated with the use of cobalt or copper radiation, these radiations are not considered in this
practice.
1. Scope
1.1 Thispracticecoversthedeterminationofretainedaustenitephaseinsteelusingintegratedintensities(areaunderpeakabove
background) of X-ray diffraction peaks using chromium K or molybdenum K X-radiation.
a a
1.2 The method applies to carbon and alloy steels with near random crystallographic orientations of both ferrite and austenite
phases.
1.3 This practice is valid for retained austenite contents from 1% by volume and above.
1.4 Ifpossible,X-raydiffractionpeakinterferencefromothercrystallinephasessuchascarbidesshouldbeeliminatedfromthe
ferrite and austenite peak intensities.
1.5 Substantial alloy contents in steel cause some change in peak intensities which have not been considered in this method.
Application of this method to steels with total alloy contents exceeding 15 weight% should be done with care. If necessary, the
users can calculate the theoretical correction factors to account for changes in volume of the unit cells for austenite and ferrite
resulting from variations in chemical composition.
1.6 Units—The values stated in inch-pound units are to be regarded as standard. No other units of measurement are included
in this standard.
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Significance and Use
2.1 Significance—Retained austenite with a near random crystallographic orientation is found in the microstructure of
heat-treated low-alloy, high-strength steels that have medium (0.40 weight%) or higher carbon contents. Although the presence
of retained austenite may not be evident in the microstructure, and may not affect the bulk mechanical properties such as hardness
This practice is under the jurisdiction of ASTM Committee E04 on Metallography and is the direct responsibility of Subcommittee E04.11 on X-Ray and Electron
Metallography.
Current edition approved July 10, 2000. Published October 2000. Originally published as E975–84. Last previous edition E975–95.
Current edition approved June 1, 2008. Published September 2008. Originally approved in 1984. Last previous edition approved in 2003 as E975–03.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E975–03 (2008)
A
TABLE 1 Calculated Theoretical Intensities Using Chromium K Radiation
a
2 B 2
hkl Sinu/lu f Df8 Df9 /F/ LP P T N R
(a iron, body-centered cubic, unit-cell dimension a = 2.8664Å):
o
B C
110 0.24669 34.41 18.474 −1.6 0.9 1142.2 4.290 12 0.9577 0.001803 101.5
B C
200 0.34887 53.06 15.218 −1.6 0.9 745.0 2.805 6 0.9172 0.001803 20.73
B C
211 0.42728 78.20 13.133 −1.6 0.8 534.6 9.388 24 0.8784 0.001803 190.8
(g iron, face-centered cubic, unit-cell dimension a = 3.60Å):
o
B C
111 0.24056 33.44 18.687 −1.6 0.9 4684.4 4.554 8 0.9597 0.0004594 75.24
B C
200 0.27778 39.52 17.422 −1.6 0.9 4018.3 3.317 6 0.9467 0.0004594 34.78
B C
220 0.39284 64.15 14.004 −1.6 0.8 2472.0 3.920 12 0.8962 0.0004594 47.88
A
Data from “International Tables for X-Ray Crystallography,” Physical and Chemical Tables , Vol III, Kynoch Press, Birmingham, England, 1962, pp. 60, 61, 210, 213;
Weighted K and K value used (l = 2.29092Å).
a1 a2
B −2M 2 2
Temperature factor (T =e ) where M=B (sin u)/l and 2B = 0.71. Also N is the reciprocal of the unit-cell volume.
C
Calculated intensity includes the variables listed that change with X-ray diffraction peak position.
of the steel, the transformation of retained austenite to martensite during service can affect the performance of the steel.
2.2 Use—The measurement of retained austenite can be included in low-alloy steel development programs to determine its
effect on mechanical properties. Retained austenite can be measured on a companion sample or test section that is included in a
heat-treated lot of steel as part of a quality control practice. The measurement of retained austenite in steels from service can be
included in studies of material performance.
3. Principles for Retained Austenite Measurement by X-Ray Diffraction
3.1 AdetaileddescriptionofaretainedaustenitemeasurementusingX-raydiffractionispresentedbytheSocietyofAutomotive
Engineers. Since steel contains crystalline phases such as ferrite or martensite and austenite, a unique X-ray diffraction pattern
for each crystalline phase is produced when the steel sample is irradiated with X-irradiation. Carbide phases in the steel will also
produce X-ray diffraction patterns.
3.2 For a randomly oriented sample, quantitative measurements of the relative volume fraction of ferrite and austenite can be
made from X-ray diffraction patterns because the total integrated intensity of all diffraction peaks for each phase is proportional
tothevolumefractionofthatphase.Ifthecrystallinephaseorgrainsofeachphasearerandomlyoriented,theintegratedintensity
from any single diffraction peak ( hkl) crystalline plane is also proportional to the volume fraction of that phase:
hkl hkl
I 5 KR V /2µ
a a a
where:
e 2 4 3
K 5 ~I /m c ! 3 ~l /32pr!
o A
and
2 22M
1~/F/ pLPe !
hkl
R 5
a 2
v
where:
hkl
I = integrated intensity per angular diffraction peak (hkl)inthe a-phase,
a
I = intensity of the incident beam,
o
µ = linear absorption coefficient for the steel,
e,m = charge and mass of the electron,
r = radius of the diffractometer,
c = velocity of light,
l = wavelength of incident radiation,
A = cross sectional area of the incident beam,
v = volume of the unit cell,
/F/ = structure factor times its complex conjugate,
p = multiplicity factor of the (hkl) reflection,
u = Bragg angle,
2 2
LP = Lorentz Polarization factor which is equal to (1+cos 2u)/sin u cos u for normal diffractometric analysis but
2 2 2 2
becomes (1+cosu 2a cos 2u)/(sin u cos u) (1+cos 2a) when a monochromator is used in which diffraction by
monochromator and sample take place in the same plane; 2a is the diffraction angle of the monochromator crystal.
If diffraction by the monochromator occurs in a plane perpendicular to the plane of sample diffraction,
2 2 2
thenLP=(cos 2a+cos 2u)/sin ucos(1+cos 2a),
Retained Austenite and Its Measurement by X-ray Diffraction , SAE Special Publication 453, SAE, Warrendale, PA 15096., SAE Special Publication 453, Society of
Automotive Engineers (SAE), 400 Commonwealth Dr., Warrendale, PA 15096-0001, http://www.sae.org.
E975–03 (2008)
−2 M 2 2 2 2 2
e = Debye-Waller or temperature factor which is a function of u whereM=B( sin u)/l , B =8p (µ ) , where µ is
s s
the mean square displacement of the atoms from their mean position, in a direction perpendicular to the diffracting
plane, and
V = volume fraction of thea -plane.
a
K is a constant which is dependent upon the selection of instrumentation geometry and radiation but independent of the nature
of the sample.The parameter, R, is proportional to the theoretical integrated intensity.The parameter, R, depends upon interplanar
spacing (hkl), the Bragg angle, u, crystal structure, and composition of the phase being measured. R can be calculated from basic
principles.
3.3 For steel containing only ferrite (a) and austenite (g) and no carbides, the integrated intensity from the ( hkl) planes of the
ferrite phase is expressed as:
hkl hkl
I 5 KR V /2µ
a a a
3.3.1 A similar equation applies to austenite. We can then write for any pair of austenite and ferrite hkl peaks:
hkl hkl hkl hkl
I /I 5[~R /R !~V /V !#
a g a g a g
3.3.2 The above ratio holds if ferrite or martensite and austenite are the only two phases present in a steel and both phases are
randomly oriented. Then:
V 1 V 51
a g
3.3.3 The volume fraction of austenite ( V ) for the ratio of measured integrated intensities of ferrite and austenite peak to
g
R-value is:
V 5[I /R /~I /R ! 1 ~I /R !# (1)
g g g a a g g
3.3.4 For numerous ferrite and austenite peaks each ratio of measured integrated intensity to R-value can be summed:
q P q
1 Igj 1 1
V 5 / Iai/Rai 1 Igj/Rgj (2)
g FS ( D S ( D S ( DG
q Rgj P q
j 51 i 51 j 51
3.3.5 If carbides are present:
V 1 V 1 V 51
a g c
3.3.6 Then the volume fraction of austenite ( V ) for the ratio of measured ferrite and austenite integrated intensity to R-value
a
is:
V 5[~1 2 V !~I /R !/~I /R ! 1 ~I /R !# (3)
g c g g a a g g
3.3.7 For numerous ferrite and austenite peaks the ratio of measured integrated intensity to R-values can be summed:
q p
V 5 @~1 2 V !~1/q ~Igj/Rgj!!/1/P ~I i/R i!
( (
g c a a
j 51 i 51
q
11/q ~I j/R j!# (4)
(
g g
j 51
3.4 The volume fraction of carbide, V , should be determined by chemical extraction or metallographic methods. Adequate
c
X-raydiffractionpeakresolutionfortheidentificationofcarbidepeaksisrequiredtoavoidincludingcarbidepeaksintheretained
austenite measurement.
4. Procedure
4.1 Sample Preparation:
4.1.1 Samples for the X-ray diffractometer must be cut with a minimum amount of heat effect. Since most steels containing
retained austenite are relatively hard, abrasive cutoff wheels are frequently used. If adequate cooling is not used, heat effects from
abrasive cutoff wheels can be substantial and, in some cases, can transform retained austenite. Saw cutting rather than abrasive
wheel cutting is recommended for sample removal whenever it is practical.
4.1.2 Rough grinding using a milling tool or high-pressure coarse grinding can deform the surface and transform some of the
retained austenite to a depth that is greater than the surface depth analyzed. Final milling or rough grinding cuts limited to a depth
of 0.010-in. or less should reduce the depth of deformation.
4.1.3 Standard metallographic wet-grinding and polishing methods shall be used to prepare samples for X-ray analysis. Grit
reductions of 80, 120, 240, 320, 400, and 600 silicon carbide or alumina abrasives may be used but other valid grit combinations
mayalsobeused.Afinalsurfacepolishof6-µmdiamondoranequivalentabrasivepolishisrequired.Sampleetching,observation
for heat effects, and repolishing is a recommended safeguard.
4.1.4 Since deformation caused by dull papers or over-polishing can transform some of the retained austenite, electrolytic
polishing or chemical polishing of initial samples of each grade and condition should be used to verify proper metallographic
sample preparation. Standard chromic-acetic acid for electropolishing 0.005-in. from samples ground to 600 grit or specific
chemicalpolishingsolutionsforaparticulargradeofsteelpolishedtoa6-µmfinishcanbeusedtoverifythemetallographicpolish.
Hot-acid etching is not recommended because of selective etching of one phase or along a preferred crystallographic direction.
E975–03 (2008)
4.1.5 Sample size must be large enough to contain the Xray beam at all angles of 2u required for the X-ray diffraction analysis
to prevent errors in the analysis. In most cases, a 1- in. square area is sufficient, but sample size depends upon the dimensions of
the incident X-ray diffraction. When using molybdenum radiation, select peaks in the range from 28 to 40° 2u for best results.
4.2 X-Ray Equipment:
4.2.1 AstandardX-raydiffractometerwithapulseheightselectorcircuitispreferredforthemeasurement,butanX-raycamera
plus densitometer readings of the film may be used. X-ray film and adequate photographic development techniques are required
to assure a linear response of the film to the X-ray intensity.
4.2.2 A chromium X-ray source with a vanadium metal or compound filter to reduce the K radiation is recommended.
b
Chromium radiation produces a minimum of Xray fluorescence of iron. Chromium radiation provides for the needed X-ray
diffraction peak resolution and allows for the separation of carbide peaks from austenite and ferrite peaks.
4.2.3 Otherradiationsuchascopper,cobalt,ormolybde-numcanbeused,butnoneoftheseprovidetheresolutionofchromium
radiation.Copperradiationispracticalonlywhenadiffracted-beammonochromatorisemployed,becauseironX-rayfluorescence
will obscure the diffracted peaks.
4.2.4 A molybdenum source with a zirconium filter is used to produce a large number of X-ray diffraction peaks.
4.3 X-RayMethod—X-raydiffractionpeaksfromothercrystallinephasessuchascarbidesmustbeseparatedfromausteniteand
ferrite peaks. The linearity of the chart recorder or photographic film shall be verified prior to utilizing this method.
4.3.1 Entire diffraction peaks minus background under the peaks shall be recorded to obtain integrated peak intensities. Peaks
withoutcarbideorsecondphaseinter
...

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