A v.u.„.i, L • <:.. L^A ' VW&^

STATES ENTOF ERCE

CATION y\

r"*TM*'

NBS TECHNICAL NOTE 709

An X-Ray

Diffraction Method for

Determining the Amount

of Austenite in an

Austenite-Ferrite Mixture
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and

technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and

Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates

that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics—Electricity—Heat—Mechanics—Optical Physics—Linac

Radiation2—Nuclear Radiation2—Applied Radiation2—Quantum Electronics3—

Electromagnetics3—Time and Frequency3 —Laboratory Astrophysics3—Cryogenics3

. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research lead- ing to improved methods of measurement, standards, and data on the properties of

well-characterized materials needed by industry, commerce, educational institutions, and

Government; provides advisory and research services to other Government agencies; and develops, produces, and distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials and the following divisions: Analytical Chemistry—Polymers—Metallurgy—Inorganic Materials—Reactor

Radiation—Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services to pro- mote the use of available technology and to facilitate technological innovation in industry and Government; cooperates with public and private organizations leading to the development of technological standards (including mandatory safety standards), codes and methods of test; and provides technical advice and services to Government agencies upon request. The Institute also monitors NBS engineering standards activities and

provides liaison between NBS and national and international engineering standards

bodies. The Institute consists of the following divisions and offices: Engineering Standards Services—Weights and Measures—Invention and

Innovation—Product Evaluation Technology—-Building Research—Electronic Technology—Technical Analysis—Measurement Engineering—Office of Fire Programs. THE CENTER FOR COMPUTER SCIENCES AND TECHNOLOGY conducts re- search and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition, and effective utilization of automatic data processing equipment; and serves as the principal focus within the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer languages. The Center

consists of the following offices and divisions: Information Processing Standards—Computer Information—Computer Services —Systems Development—Information Processing Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS and other agencies of

the Federal Government; promotes the development of the National Standard Reference Data System and a system of information analysis centers dealing with the broader

aspects of the National Measurement System; provides appropriate services to ensure

that the NBS staff has optimum accessibility to the scientific information of the world, and directs the public information activities of the Bureau. The Office consists of the following organizational units: Office of Standard Reference Data—Office of Technical Information and

Publications—Library—Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

- Part of the Center for Radiation Research.

3 Located at Boulder, Colorado 80302.
MAR 2 1972 tJ^aCC- UNITED STATES DEPARTMENT OF COMMERCE

(k C (OO Maurice H. Stans, Secretary

ntrrr^- NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

jVo. Vol

NBS TECHNICAL NOTE 709

ISSUED FEBRUARY 1972

Nat. Bur. Stand. (U.S.), Tech. Note 709, 15 pages (Feb. 1972) CODEN: NBTNAE

An X-Ray Diffraction Method for Determining the Amount of

Austenite in an Austenite-Ferrite Mixture

C. J. Bechtoldt

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office,Washington, D.C, 20402.

(Order by SD Catalog No. C 13.46:709). Price 30 cents.

CONTENTS

Page

Introduction 2

Theory 2

Measurement Method and Application 4

References 7

Appendix . 7

Table I 8

m

An X-ray Diffraction Method for Determining the

Amount of Austenite in an Austenite-Ferrite Mixture

by

C. J. Bechtoldt

Metallurgy Division

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

A method for determining the relative phase volume of austenite

in an austenite-ferrite mixture is described in detail. Results

obtained by applying this method to an austenitic-ferritic stainless

steel composite material are presented. The method can be extended to

other multi -phase materials.

Keywords: Austenite; computer; ferrite; phase measurement; quantitative

analysis; retained austenite and x-ray diffraction.
INTRODUCTION

In the characterization of alloys it is often important to determine

the volume fraction of certain phases. In the case of ferrous alloys it

is necessary to measure the amount of austenite retained after thermomechanical processing since it will affect important mechanical properties. Several different techniques have appeared in the literature

(see references in (1) and (2)) for determining the relative amount of

austenite, employing x-ray diffraction methods. This note will discuss

in detail the method in use in our laboratory, which differs in some

respect from these other techniques. Principally, integrated intensity

measurements from as many resolved, individual, diffraction lines as

possible are combined to determine a best value for the volume fraction

of austenite. Computer processing permits rapid collection of

data and calculation of results. An example of the application of this

method to a recent NBS standard reference material will be given.

THEORY

The theory concerned with the calculation of the volume fraction

of a phase in a mixture using a diffractometer has been summarized and

discussed by 0gilvie(2). That method assumes, as is done here, a

random orientation of the diffracting crystallites. Modifications of

the method to account for preferred orientation in, for example, rolled

material, have been proposed(3) and will not be considered here.
The integrated intensity of a reflection (hkl) is given by:

P hkl

= K.^T-L.p.j-A.V/^. (1)

where

K = scale factor (constant for a given experiment)

f = scattering factor

F = f-S, the structure factor (and F

2 = FF*)

-2B/4d 2 T = e '

, the temperature factor, where B is a constant and

d the interplanar spacing.

S = symmetry factor with S = 2 (body-centered-cubic)

S = 4 (face centered cubic)

L«p = (1 + Cos 2 2e)/(sin 2 0'cos0) , Lorentz polarization for

powder specimen

j = multiplicity factor

A = absorption factor (nearly constant for thick specimens)

V = volume fraction of the phase of interest, and

v = unit cell volume.

The known terms are collected into a quantity R so that eq (1) can be

written

P nkl

= K-R

hkl

-V (2)

hkl

where R = F

2 -T.L-p-j-A/v 2

Forming the ratio for two phases from eq (2), we have
P^1 = KRf

1 V

1 (3)

and if V-, + V

2 = 1 (two phase material) then

v

_ R hkl ph'k'l'

V 2

" R

1 P

2 (4)

R h'k'l'

p hkl ~Rhkl ph'k'l'

or

v

^

. , ,hkl

- 2 (vv

(Vp/

kl HVp/ri ' (5)

Letting I = R/P and averaging over all reflections in a phase, eqn. 5

becomes

2 J =- (6)

J

l + I 2 and the standard deviation is given by

s v

= v

2

(i - v

2 )[(s| /i

x

) 2 + (sj /i

2

) 2

] 1/2

. (7)

The method for determining the average volume fraction \L

from calculated values R. and measured values P. was programmed for

computer calculation and is described in the next section.

MEASUREMENT METHOD AND APPLICATION

The experimental conditions used with the application of the method

to an austenitic-ferritic stainless steel composite will be described.

Appropriate adjustments in, for example, radiation, stepping intervals

and so forth, can be made for studies of other materials. In the present

instance cobalt radiation (iron filtered) was obtained from a constant

potential x-ray generator operated at 35kV. The step-scanning diffractometer used a 1° scattering slit and a .024 inch receiving slit. Counting

A
periods of 50 to 100 s were chosen, with a 2e step interval of 0.05 deg

(this choice is determined in part by the sharpness of the peaks). For

the purpose of minimizing the effect of grain size, the specimen was

rotated in its plane at 117.8 rpm during measurement.

The scaler output was recorded directly on punched paper tape to

facilitate loading the data into a digital (time-shared) computer. Other

input information, such as the interval for background corrections, the

interval over which the peaks were integrated, appropriate hkl , multiplicity, and symmetry factor were supplied from a previously loaded

control file. Integration of the diffraction lines was accomplished

using Simpson's rule. The diffraction line center-of-gravity along the

20 axis was also determined and used to specify the angular position of

the line. The computer program (described in the Appendix) then

calculated the d-spacing, Lorentz polarization factor (with or without

monochromator) , unit cell volume, and temperature factor. The scattering

factor was calculated from the relation (4):

f hkl

= A exP(" B / 4d2 ) + c exp(-D/4d 2

) + E

where A, B, C, D, E are constants (see Appendix). A correction was made

to these calculated values in order to account for anomalous scattering.
The computer program provides for a linear correction of background

intensity. The theoretical relative intensity (R in eq 2) of the

principal diffraction lines of each phase is calculated and printed out

together with the observed integrated intensity and relative integrated

intensity for comparison. As a further check the multiplicity,

temperature factor, scattering factor correction, Lorentz polarization

factor, 2e angle, d-spacing and average lattice constant are also

printed out. To minimize systematic biases in the final calculated

phase volume fraction, the calculations are done for as large a number

of planes as possible and averaged together. In the austenite-ferrite

example, presented next, this involved 5 planes for the fee phase and

4 planes for the bec phase.

The output obtained from measurements on an austenitic-ferritic

stainless steel composite specimen is shown in table I. The average

volume percent austenite present is shown followed by

individual values obtained from pairs of diffraction lines. The

scatter shown indicates the need for caution in basing phase volume

determinations on only a few observed diffraction lines, particularly

at low relative values.

This program can be used with slight modification for other phases

with simple structure and can be extended to more complicated structures

with the introduction of the appropriate equations for the symmetry

factor. A modification of this program has also been used to study

preferred orientation resulting from the directional growth of crystals

on electrodeposited plates in various plating solutions.
REFERENCES

[1] Beu, K. E., Austenite Retained in Hardened Steels: Quantitative

Determination by X-Ray Diffraction Techniques", in the

Encyclopedia of X-Rays and Gamma Rays , George L. Clark, ed.,

Reinhold Publishing Corp., New York, pp. 71-77 (1963).

[2] Ogi 1 vie, R. E., Retained Austenite by X-Rays, Norelco Reporter,

p. 60-63 (1959).

[3] Morris, P. R., Measurement of Retained Austenite in PrecipitationHardening Stainless Steels, Trans. AIME, 239, pp. 1586-1589 (1967).

[4] Forsyth, J. B. and Wells, M., On an Analytic Approximation to the

Atomic Scattering Factor, Acta, Cryst. 12_, pp. 412-515 (1959).

APPENDIX

The computer program listed below is written in the BASIC

language and should execute on most time-shared computer terminals

accepting a BASIC language, except perhaps for minor changes in input

and output statements. This program has executed on four different

systems available in our laboratory.

Because of size limitations this program initially consisted of

three programs but they were recently combined. It should be possible

to subdivide again if necessary for a particular computer system.

The program permits greater details to be printed at execution

time or listed after execution. This was incorporated to "shake down"

the original program, facilitate transfer between time-sharing services,

and permit inspection of data used for background correction and data

over which the peaks were to be integrated.

A punched paper tape of this program can be provided on request to

the author. 7
Table I. Computer output showing calculated and observed integrated

diffraction line intensities, and relative phase volume

in a study of an austenitic-ferritic stainless steel composite.

XBASIC B RUN

DEFINE FILE

l=CONTRL

DEFINE FILE

2=HJL4

SPECIMEN DESIGNATION--! HICHO JL4

DETAILED PRINTOUT DESIRED? ENTER Y IF YES AND N IF NO! N

FOR LP* ENTER 1 IF MONOCHROMATOR

.

, 2 IF NOT. ! 2 ANOMALOUS SCAT. FACT. CORRECTION, ENTER IF NONE DESIRED.

TEMPERATURE CONSTANT R= .4

! 2.5

AUSTENITE

PLANE M SCAT.F TEMP.F LP F D-SPACING

111 8 16.36 .954 8.27 63.93 2.072

200 6 15.20 .940 5.82 58.93 1 .797

220 12 1 1 .82 • 883 2.83 44.42 1 .268

311 24 10.10 .844 2.94 37.12 1 .0 84

222 8 9.61 • 830 3.30 35.03 1 .037

RELATIVE RELATIVE OBSERVED

PLANE TWO-THETA CALCI OBSERVED I INTEGRATED

11 1 51 .190 100.00 100.00 156.60

200 59.771 44.84 32.68 51 .18

220 89.854 24.78 25.75 40.33

311 111 .325 35.97 33.56 52.55

222 119.436 11 .98 10.82 16.94

LATTICE CONSTANT= 3. 591
FERRITE

PLANE M SCAT.F TEMP.F LP F D-SPACING

110 12 16*18 .952 7.8J 31 .57 2.024

200 6 13.10 .90 7 3.44 24.96 1 .434

21 1 24 10.96 .864 2.73 20.3 8 1 .172

220 12 9.39 .824 3.56 17.03 1 .015

PLANE

110

200

211

220

RELATIVE RELATIVE OBSERVED

TWO-THETA CALCI OBSERVED I INTEGRATED I 52.493 100.00 100.00 4558.26

7 7.2 54 13.78 14.73 671 .23

99.628 29.12 31 .52 1436.58

123.684 13.28 13.80 629.12

LATTICE CONSTANT* 2.868

AVERAGE % AUSTENITE= 3.862 STD. DEV. = 501

95% CONFIDENCE INTERVAL IS 3.444 TO 4.279

RETAINED AUSTENITE BY PAIRS

PLANES

AUSTENITE FERRITE % AUSTENITE

1 11 1 10 4.37

200 110 3.22

220 110 4.53

311 110 4.09

222 1 10 3.96

1 11 200 4.10

200 200 3.02

220 200 4.25

311 200 3.83

222 200 3.72

111 211 4.05

200 211 2.99

220 211 4.20

311 21 1 3*79

222 211 3.67

111 220 4.21

200 220 3.11

220 220 4.37

311 220 3.94

222 220 3.82
100 FILES ***'PERMITS DESIGNATION OF CONTROL AND DATA FILES AT RUN TIME

110 FMT 14* I6*F9.2*F11 .3*F1 2 .2 *F12 .2 *F1 2 .3 120 DIM X(600)*Y(500 >* ZC500 )*HC2* 5 >*C <2* 5 ) *P (2* 5 )* 0(2* 5 >*U(2* 5) * MC2* 5)

130 DIM B(2*5)*NC2 >* A C2 ) * F C 9 >* G C 9 >* AS <2 > *T <2* 5 > * DC2 ) * U(2)

140 FMT //

150 FMT I4*F15.3*F12.2*F12.2*F14.2*F12.3

160 FMT "LATTICE CONSTANT=" F6.3*///

170 FMT "AVERAGE % AUSTENITE=" * F9 .3 > " STD. DEV. ="*F7«3*//

190 FMT "95% CONFIDENCE INTERVAL IS"*F9.3*" T0"*F9.3*//

200 FMT "RETAINED AUSTENITE BY PAIRS"//" PLANES"

210 FMT "AUSTENITE FERRITE % AUSTENITE"

220 FMT I6*I10*F12.2

230 FMT "TEMPERATURE CONSTANT R="*F4.1

240 FMT 18,15*15*15*15

2 50 READ #1*N(1 )* N<2 >* Ml * M2 * M3 * Wl *P 1 * T9* A ( 1 )*AC2)*A$C1 )*A$(2)

260 PR I NT* 140

270 PRINT"SPECIMEN DESIGNATION--";

280 INPUT T$ 'COMPUTER CALLS FOR SPECIMEN DESIGNATAON'

290 PRINT

300 PRINT "DETAILED PRINTOUT DESIRED? ENTER Y IF YES AND N IF NO";

310 INPUT T$

320 PRINT

330 PRINT"F0R LP* ENTER 1 IF MONCH.* 2 IF NOT. "; 340 INPUT Nl

3 50 PRINT

360 PR I NT" ANOMALOUS SCAT. FACT. CORRECTION* ENTER IF NONE DESIRED.

370 INPUT S9

3 80 PRINT

390 READ #2*0.9

400 * AT THIS POINT PROGRAM READS IN SCALER FILE AND SORTS DATA FOR

410 ^BACKGROUND CORRECTION* AUSTENITE PEAKS* AND FERRITE PEAKS.

420 *C0NTR0L IS EXERCISED FROM THE CONTROL FILE WHICH IS AMENDED FOR

430 *EACH RUN I F , NECESSARY . ALL ANGULAR DATA IS IN TERMS OF

440 *TW0-THETA TIMES 1000.

450 READ #1* A*S,T*A3

460 *A=STARTING ANGLE "AND A3=ENDING ANGLE OF D IFFRACTOMETER RUN

470 *S=STEPPING ANGLE AND T=COUNTING TIME INTERVAL.

480 A=A-S

490 READ #1*N*A1 *A2

500 *N=SORTING INSTRUCTIONS* 1 --BACKGROUND* 2--AUSTENITE PEAK

510 *3--FERRITE PEAK; Al AND A2 STARTING ANGLE AND ENDING ANGLE OF

520 *THE SCAN OF INTEREST.

530 A=A+S

540 READ #2* B 550 B=B+Q9

560 IF A<>A1 THEN 530

570 ON N GOTO 620*740*870

580 IF T$="N" THEN 600

590 PRINT*240*A;M1 ;M2;M3

600 IF A<>A3 THEN 490

610 GOTO 1030

620 M1=M1+1

630 XCM1 )=A1

640 M1=M1+1

650 XCM1 )=B

660 IF A<>A2 THEN 700

10
670 M1=M1+1

680 X<M1 ) = -l 690 GOTO 580

700 A=A+S

710 READ #2,B

720 B=B+Q9

730 GOTO 640

740 M2=M2 + 1 750 Y(M2)=A1

760 N(l )=N(1 ) + l 770 M2=M2 + 1 780 Y(M2)=B

790 IF A<>A2 THEN 830

800 M2=M2 + 1 810 Y(M2>=-1

820 GOTO 580

830 A=A+S

840 READ #2,B

850 B=B+Q9

860 GOTO 770

870 M3=M3+1

880 Z(M3)=A1

890 NC2)=N<2> + 1 900 M3=M3+1

910 Z(M3>=B

920 IF A<>A2 THEN 960

930 M3=M3+1

940 Z(M3)=-1

950 GOTO 580

960 A=A+S

970 READ #2,B

980 B=B+Q9

990 GOTO 900

1000 *END OF INPUT FROM SCALER FILE

1010 fCALCULATES CONSTANTS TO BE USED IN LINEAR CORRECTION OF BACK1020 *GROUND. ALSO READS IN HKL ' S AND MULTIPLICITY FACTORS.

1030 S1=S/1000

1040 READ #1*E9#M1 ,M2*M3

1050 FOR El =1 TO E9

1060 Y=0

1070 X1=0

10 80 X2=0

1090 Z=0

1100 N=0

1110 FOR E=l TO 2 1120 M1=M1+1

1130 A=X(M1 )/1000

1140 FOR E3=l TO 500

1150 M1=M1+1

1160 B=X<M1

)

1170 IF B<0 THEN 1250

1180 Y=Y+B

1190 X1=X1+A

1200 X2=X2+A*A

1210 Z=Z+A*B

1220 N=N+1

11
1230 A=A+S1

1240 NEXT E3

1250 NEXT E 1260 X4 = (X2*N-X1*X1 ) 1270 FCE1 >=<Z*N-Y*X1 >/X4

1280 GCE1 >=<X2*Y-X1*Z>/X4

1290 NEXT El

1300 FOR E=l TO 2 1310 FOR El =1 TO N<E>

1320 READ #1,N,H(E,E1 >,CCE,E1 >,P(E,E1 ) 1330 B(E,E1 )=G(N)

1340 MCE, El )=F(N)

1350 NEXT El

1360 NEXT E 137Q *PRINTS SAMPLE BACKGROUND CORRECTIONS IF DESIRED.

1380 READ #1,M1 ,M2,M3,M7,M8

1390 IF T$="N" THEN 1540

1400 FOR N=l TO 2 1410 FOR El=l TO N(N)

1420 READ A3

1430 PRINT A3

1440 PRINT, 150,HCN, El >,BCN,E1 >,MCN,E1 ) 1450 FOR A3=A3 TO A3+2

1460 B1=A3*M(N,E1 >+B(N,El > 1470 PRINT, 150, A3JB1

1480 NEXT A3

1490 PRINT

1500 NEXT El

1510 NEXT N 1520 DATA 50,59,88,110,118,52,76,99,121

1530 *DNTEGRATES PEAKS AND FINDS TWO-THETA ANGLES.

1540 PRINT, 230, T9

1550 FOR N3 = i TO 2 1560 A9=0

1570 PRINT, 140

1580 PRINT TABC22+N3>;A$(N3>

1590 PRINT, 140

1600 PRINT"PLANE M SCAT.F TEMP.F LP

1610 PRINT" D-SPACING"

1620 FOR El=l TO NCN3)

1630 IF N3<>1 THEN 1670

1640 M7=M7+1

1650 A1=Y(M7>/1000

1660 GOTO 1690

1670 M8=M8+1

1680 A1=Z(M8)/1000

1690 A3=A1

1700 FOR E=1T0500

1710 IF N3<>1 THEN 1750

1720 M7=M7+1

1730 M1=Y<M7)

1740 GOTO 1770

1750 M8=M8+1

1760 M1=Z(M8)

1770 IF MIO THEN 1820

1780 B1=M(N3,E1 )*A3+BTN3,E1

)

1Z
1790 A3=A3+S1

1800 X<E)=(M1-B1 )*S1/T

1610 NEXT E 1820 A2=A1

1830 M1=XU

)

1840 M2=A2*XC1 ) 1850 FOR Fl=3 TO E-2 STEP 2 1860 A2=A2+2*S1

1870 M1=M1+4*X<F1-1 >+2*XCFl

1880 M2=M2+4*<A2-S1 )*X(F1 -1 >+2*A2*X(Fl

)

1890 NEXT Fl

1900 F1=CA2+S1-A1 )/Sl

1910 T(N3*E1 >=M1+XCF1 > 1920 0CN3*E1 >=<M2+<A2+S1 )*X(F1 >>/T(N3*El > 1930 NEXT El

1940 *CALCULATES THEORETICAL RELATIVE PATTERN AND COMPARES WITH

1950 *OBSERVED INTEGRATED PATTERN.

1960 FOR E=l TO NCN3)

1970 D=W1/<2*SIN(P1*0(N3*E>>>

1980 A=D*SQR(CCN3*E>>

1990 X=1/(4*D*D>

2000 S=15.01*EXP(-4.958*X)+3.573*EXP(-46.50*X)+7.375 * FE SC . FACT.'

2010 S=S-S9

2020 L3=<SIN(P1*0<N3*E>>>»2*C0S<P1*0CN3*E>>

2030 ON Nl GOTO 2040*2060

2040 LI = C 1 + < C OS C 2 *P 1 * 52 • 7 8 > *C OS (2 *P 1 * < N3 * E > > > » 2 > /L3

2050 GOTO 2070

2060 L1=C1+<C0SC2*P1*0CN3*E>)>»2)/L3

2070 T1=EXP(-T9*X)

2080 F1=T1*A<N3>*S

2090 UCN3*E>=PCN3*E>*L1*F1*F1

2100 PRINT.

10*H(N3*E)*PCN3*E>*S*T1*T1*L1*F1*D

2110 A9=A9+A

2120 NEXT E 2130 A9=A9/N<N3)

2140 PR INT* 140

2150 PRINT TAB(25);"RELATIVE";TABC37>;"RELATIVE";TAB(51 >*" OBSERVED"

2160 PRINT"PLANE TWO-THETA CALC .OBSERVED I INTEGRATED 1 2170 FOR E=l TO NCN3)

2180 UCN3»E)=U(N3»E)/A9t6

2190 M2=U(N3*E>/U(N3*1 )*100

2200 A1=T<N3*E>/T<N3*1 >*100

2210 PRINT*150*H<N3*E>*0CN3*E>*M2*A1*T<N3*E>

2220 NEXT E 2230 PRINT

2240 PRINT* 160*A9

2250 NEXT N3

2260 FOR N3=l*2

2270 F(N3)=0

2280 GCN3)=0

2290 FOR E=l TO N(N3>

2300 *CALC AVERAGE* VARIANCES* CONFIDENCE INTERVAL

2310 M1=T(N3*E)/U(N3*E)

2320 F(N3)=F(N3)*M1

2330 G<N3)=G(N3)+M1*M1

2340 NEXT E

13
23 50 F(N3)=FCN3>/N<N3>

2360 D<N3)=<G<N3)-FCN3)*F(N3)*NCN3) )/(N(N3)-l ) 2370 NEXT N3

2380 V=l/(1 +F(2)/F(1 ))

2390 V3 = 100*V*U-V)*SQR<D(1 )/F(l ) t2+D<2 )/F(2 ) »2 ) 2400 V=V*100

2410 PRINT>170*V*V3

2425 V3=2.5*V3/SQR(NC1 )+N(2 )) 'VALID FOR APPROX. 5 TO 7 DEG. OF FREE.'

2430 PRINT* 190*V-V3*V+V3

2440 PRINT* 200

2450 PRINT* 210

2460 FOR E=l TO NC2)

2470 FOR F=l TO NCI ) 2480 R1=T<1*F>*U<2*E>/CTC1*F>*U<2*E>+TC2*E)*UU*F>>*100

2490 PRINT*220*H<1 *F)*H(2*E)*R1

2500 NEXT F 2510 NEXT E 2515 PRINT*140

2520 END

14 * U. S. GOVERNMENT PRINTING OFFICE :! 972--W1 -330/1 61
form NBS-114A (1-71) 2. Gov't Accession No.

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS-TN-7093. Recipient's Accession No.

4. TITLE AND SUBTITLE

An X-Ray Diffraction Method for Determining the Amount

of Austenite in an Austenite-Ferrite Mixture

5. Publication Date February 1972

6. Performing Organization Code

7. AUTHOR(S) 8. Performing Organization C. J. Bechtoldt

10. Project/Task/Work Unit No. 9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same as No. 9.

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) A method for determining the relative phase volume of austenite in

an austenite-ferrite mixture is described in detail. Results obtained

by applying this method to an austenite-ferrite stainless steel

composite material are presented. The method can be extended to

other multi -phase materials.

17. KEY WORDS (Alphabetical order, separated by semicolons) Austenite . computer . fe rrite; phase

measurement; quantitative analysis; retained austenite; x-ray diffraction.

18. AVAILABILITY STATEMENT

[%! UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

15

22. Price $.30

UScj0MM-DC 66244-P71

NBS TECHNICAL PUBLICATIONS

PERIODICALS NONPERIODICALS JOURNAL OF RESEARCH reports National Bureau of Standards research and development in physics, mathematics, chemistry, and engineering.

Comprehensive scientific papers give complete details of the work, including laboratory data, experimental

procedures, and theoretical and mathematical analyses. Illustrated with photographs, drawings, and

charts.

Published in three sections, available separately:

• Physics and Chemistry

Papers of interest primarily to scientists working in these fields. This section covers a broad range of physical and chemical research, with major emphasis

on standards of physical measurement, fundamental

constants, and properties of matter. Issued six times a year. Annual subscription: Domestic, $9.50; $2.25

additional for foreign mailing.

• Mathematical Sciences

Studies and compilations designed mainly for the mathematician and theoretical physicist. Topics in mathematical statistics, theory of experiment design, numerical analysis, theoretical physics and chemisty, logical design and programming of computers and computer systems. Short numerical tables. Issued

quarterly. Annual subscription: Domestic, $5.00;

$1.25 additional for foreign mailing.

• Engineering and Instrumentation

Reporting results of interest chiefly to the engineer and the applied scientist. This section includes many

of the new developments in instrumentation resulting from the Bureau's work in physical measurement,

data processing, and development of test methods.

It will also cover some of the work in acoustics, applied mechanics, building research, and cryogenic

engineering. Issued quarterly. Annual subscription

:

Domestic, $5.00; $1.25 additional for foreign mailing.

TECHNICAL NEWS BULLETIN

The best single source of information concerning the Bureau's research, developmental, cooperative, and

publication activities, this monthly publication is designed for the industry-oriented individual whose

daily work involves intimate contact with science and

technology

for engineers, chemists, physicists, re- search managers, product-development managers, and company executives. Annual subscription: Domestic,

$3.00; $1.00 additional for foreign mailing.

Applied Mathematics Series. Mathematical tables, manuals, and studies.

Building Science Series. Research results, test methods, and performance criteria of building materials, components, systems, and structures.

Handbooks. Recommended codes of engineering and industrial practice (including safety codes) de- veloped in cooperation with interested industries, professional organizations, and regulatory bodies.

Special Publications. Proceedings of NBS conferences, bibliographies, annual reports, wall charts, pamphlets, etc.

Monographs. Major contributions to the technical

literature on various subjects related to the Bureau's

scientific and technical activities.

National Standard Reference Data Series. NSRDS provides quantitative data on the physical

and chemical properties of materials, compiled from

the world's literature and critically evaluated.

Product Standards. Provide requirements for sizes, types, quality, and methods for testing various industrial products. These standards are developed co- operatively with interested Government and industry groups and provide the basis for common understanding of product characteristics for both buyers and

sellers. Their use is voluntary.

Technical Notes. This series consists of communications and reports (covering both other agency and

NBS-sponsored work) of limited or transitory interest.

Federal Information Processing Standards

Publications. This series is the official publication within the Federal Government for information on

standards adopted and promulgated under the Public Law 89-306, and Bureau of the Budget Circular A-86

entitled, Standardization of Data Elements and Codes

in Data Systems.

Consumer Information Series. Practical information, based on NBS research and experience, covering

areas of interest to the consumer. Easily understandable language and illustrations provide useful back- ground knowledge for shopping in today's technological marketplace.

NBS Special Publication 305, Supplement 1, Publications of the NBS, 1968-1969. When ordering, include Catalog No. C13. 10:305. Price $4.50;

$1.25 additional for foreign mailing.

Order NBS publications from: Superintendent of Documents Government Printing Office Washington, D.C. 20402
U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington. D.C. 20234

OFFICIAL BUSINESS

Penalty for Private Use, $300

POSTAGE AND FEES PAID

U.S. DEPARTMENT OF COMMERCE