Stacking Fault Energies of Austenitic Stainless Steels

Seven Commercial

R. E. SCHRAMM AND R. P. REED

The stacking fault energies of seven commercial austenitic Fe-Cr-Ni, Fe-Cr-Ni-Mn and Fe-Mn-Ni alloys have been determined by X-ray diffraction line profile analysis. From comparison with existing data on laboratory alloys with similar compositions, it is con- eluded that both Ni and C increase 7 while Cr, Si, Mn, and N decrease ~. Regression analysis of data produced in this study provides an expression relating ~ to commercial alloy composition in terms of Ni, Cr, Mn, and Mo alloy concentrations.

THE stacking fault energy (~) is of both practical and theoretical interest and is reported here for a series of commercial austenitic steels. The defect properties of alloys are known to affect mechanical behavior and the stacking fault energy is essential to any fundamen- tal understanding of the defect structure. Stacking fault energy influences dislocation cross slip and climb, which are dominant factors in metal work hardening and creep behavior. The stacking fault energy also affects susceptibility to stress corrosion cracking. 1 In austenitic steels the influence of the stacking fault energy on hydrogen embrittlement must be considered, since Fe-18 Cr-8 Ni (AISI 304) alloys are known to be more susceptible to embrittlement than the more stable Fe-25 Cr-19 Ni (AISI 310) grades, z'3

The stacking fault energy has been previously deter- mined for several Ni-base and some Fe-base alloys, mostly binary systems. 4'S The ternary system Fe-Cr- Ni is important because it is the basis for austenitic stainless steels. Most of the measurements that have been made 6-2~ (Fig. 1) for Fe-Cr-Ni alloys have been on high-purity laboratory melts with carefully con- trolled compositions. Nickel, 8,%n'~%~r carbon, s' ~ nitrogen,8,,7 and chromium 9 have been varied to deter- mine their effect on 7. We are unaware of any mea- surements on commercial austenitic steels except a few on AISI 304 (Table I).

The stacking fault energy of the austenitic (fcc) phase of the Fe-Cr-Ni alloys depends on the exact composition of the steel and generally ranges from 10 to 100 mJ /m 2 (1 mJ /m z = 1 erg/cm~). Measure- ments of this parameter reported over the last 17 years are collected in Table I. Various methods for measuring Z have been developed 4 and applied to these materials, q~ne most frequently used method is the measurement of extended dislocation nodes by trans- mission electron microscopy. Resolution in the elec- tron microscope restr icts this method to cases where ;J ~< 50 mJ /m z, except where one measures weak-beam ribbon images. Values reported over the years are in reasonable agreement with each other when some of the earlier ones are corrected according to Brown's suggestion 23 for an improved theoretical treatment of dislocation line tension. Recently it was shown that the technique of analyzing X-ray diffraction profiles by

R. E. SCHRAMM is Physicist, and R. P. REED is Supervisory Metal- lurgist, Cryogenics Division, Institute for Basic Standards, Boulder, Colorado 80302.

Manuscript submitted November 4, 1974.

Fourier analysis can be apptied with relative ease and accuracy. ~4 The use of X-ray stacking fault energy measurements insures that energies higher than 50 mJ/m 2 can be determined; so this method seemed the best approach to measure the expected wide stacking fault energy range of these austenitic steels.

X-ray line profile analysis was used to obtain ~, for seven commercial grade alloys. These include AISI 304L (Fe-18 Cr-8 Ni), AISI 305 (Fe-18 Cr-12 Ni), AISI 310S (Fe-25 Cr-19 Ni), AISI 316 (Fe-17 Cr-t3 Ni-2 Mo), grade 21-6-9 (Fe-21 Cr-6Ni-9 Mn), grade 22-13-5 (Fe-22 Cr-13 Ni-5 Mn-2 Mo) and Hadfield steel (Fe-16 Mn-4 Ni). Commercial steels contain significant quan- tities of other elements that could possibly influence alloy behavior. Our data on commercial alloys are compared with data obtained from better composition controlled austenitic Fe-Cr-Ni alloys (Table I).

MATERIALS

Melt analyses of seven austenitic steels are listed in Table II. Two melts of the 21-6-9 alloy were avail- able (melt no. 1 is the same material examined by Vandervoort ~ for susceptibility to hydrogen embrit- tlement).

With a single exception noted below, specimens for X-ray examination consisted of powders obtained by filing from the bulk at room temperature (~24~ and sifting through a 150 mesh screen. Filing was done slowly to avoid heating the bulk metal. Half this pow- der from each alloy was annealed at 1000~ for 1/2 h at 5 x 10 -5 torr. Annealed and cold-worked powders

Cr O Previous Measurements

i~90 (Table I) 9 This Report

}h/ AAAso

Fe ] O 20 30 40 50 60 70 80 90 Ni

Fig. l--Fe-Cr-Ni ternary diagram indicating alloys for which the stacking fau]t energy has been measured.

METALLURGICAL TRANSACTIONS A VOLUME 6A, JULY 1975-1345

Table I. Stacking Fault Energy of Fe-Cr-Ni Alloys

Reference

Stacking Fault

Energy (mJ/m 2)

Composition, Pet

Cr Ni Others Method, Variables

Whelan, et al, (1957) I5-20 18-20 8-11

Table I (Contd)

Stacking Fault

Energy Reference (mJ/m 2) Cr Ni Others Method, Variables

LeCroisey, Thomas 45 17.8 14. l 0.01C Extended nodes, b = 1.46 A, (1970) 24 15.9 12.5

faults inc reases , Le . , as the stacking fault probabi l i ty , a, i nc reases , the degree of l ine shift ing increases . This can be calculated from: 2~

h20 = (20zo o - 20~)CW- (20~o o - 2Ore)AN N

45C3- - .z [tan 02o o + 89 Om]a , [1]

where the 2O's a re the l ine posi t ions in degrees . F rom these micros t ra in and stacking fault p robab i l -

ity calculat ions, it is poss ib le to determine the s tack - ing fault energy 7, f rom thei r rat io by ~

gm wo G (m) ao A-~ ( C~o) 111 = [2]

where

K m r 6.6 = proport iona l i ty constant, G(u~ shear modulus in the (111) fault plane,

= + c l l - c1 ),

a o = unit cel l edge d imension A = Zener an isot ropy = 2c,, , , / (c~ - c~2) , and

ci j = elast ic st i f fness coeff ic ients.

The value of 6.6 for the proport iona l i ty constant, Kll~Wo, and the an isotropy correct ion , A -~ were determined for the e lements Ag, Au, Ni, Cu, and A1 by compar ison of accurate e lect ron microscopy mea-

2 surements with our (%o),11/~ X- ray data for the same e lements , z4

EXPERIMENTAL PROCEDURE

The equipment and approach used here were bas ic - a l ly the same as repor ted prev ious ly , z4 F ixed- t ime point data were col lected for the (111) and (222) pro - f i les and the (111) and (200) peak posi t ions with a com- merc ia l X - ray d i f f rac tometer and monochromated CoK(~ radiat ion (~ = 1.79021A). In this instance, Eq. [1] reduces to A20 = -- 6.5 (~. Publ ished procedures and computer p rograms z8-31 provided the needed cor - rect ions and ana lyses .

For the present measurements , a s tepper motor re - p laced the synchronous e lec t r i c motor to dr ive the d i f - f rac tometer X - ray detector for s t r ip -char t record ing. This change and the dig i ta l output a l ready avai lable f rom the sca le r made it poss ib le to automate the data col lect ion process with a min icomputer having an 8K memory . The software program (in BASIC) requ i red the in i t ia l and final angular l imi ts , angular step incre - ment, and t ime of count for each prof i le . With the en- t ry of these parameters , no further intervent ion was necessary and the computer recorded al l data on mag- netic tape for subsequent process ing at a centra l com- putation faci l i ty . Severa l advantages to this automation are obvious, but one is fo remost here - - fo r the f i r s t t ime, it became pract i ca l to obtain mult ip le measure - ments on each spec imen. Col lect ing three separate sets of data for each al loy al lowed better p rec is ion est imat ions .

EXPERIMENTAL RESULTS

To calculate the stacking fault energy f rom Eq. [2], it is necessary not only to measure the X - ray param- e ters but to know the e las t i c st i f fness coeff ic ients and

the unit cel l d imension. Very l i t t le of this type of data exists in the l i te ra ture for these a l loys, but it is enough to proceed if some assumpt ions are made. E last ic data on three al loys with composit ions s imi la r to the s tee ls studied here are l i s ted in Table IIL 3z'33 While c l l and c 12 vary with composit ion, the shear modulus and an iso - t ropy are re la t ive ly constant. Therefore, average va l - ues of these parameters were used for a l l of the s tee ls repor ted on here, i .e . ,

G(111) = 0.65 1011 N/m 2. [3]

and

A = 3 .43 . [4]

The latt ice parameter of AISI 304 is 3.589/~ 3a and was also assumed to be constant through the a l loy compos i - tion range of in terest . Eq. [2] then reduces to

2

7 = 17.8 l0 s (%o)1,1 (mj/mZ). [5] Cg

The exper imenta l parameters and the ca lcu lated stacking fault energ ies a re l i s ted in Table IV. The values presented are the ar i thmet ic averages of the three sets of data col lected f rom each spec imen. The numbers in parentheses indicate the data scat ter found within each set of three. For these eight a l loy spec i - mens, the scat ter of the y value averages about 20 pct of the stated value. The AISI 304L and Hadfield s tee l have the lowest V's of about 20 mJ /m z while the high al loy content AISI 310S has the h ighest :e of this group.

Table I I I. Elastic Parameters

10 ~l N/m 2

G(t ll) A Reference and Alloy c1~ c,2 c~ Shear Modulus Anisotropy

Salmutter, Stangler (1960) Fe-12Cr-12Ni 2.332 1.626 1.235 0.647 3.50

Mangalick, Fiore (1968) Fe-18.1Cr-14.1Ni 1.98 1.25 1.22 0.650 3.34 Fe-I 8.2Cr- 19.1Ni 1.91 1.19 t.24 0-653 3.44

Table IV. X-Ray Parameters and Stacking Fault Energy of Commercial Stainless Steels, Numbers in Parentheses are the

Total Spread of Three Measurements

Stacking Fault 2

Alloy 106(e~o>lll l03 103 (eso)ut Energy, a 7, (mJ/m:)

AISI 304L 6.1 (1.4) 7 (2) 1.0 (0.1) 18 (2) AIS1305 28.6 (7.7) 15 (5) t.9 (0.4) 34 (7) AtSI 310 S 66.9 (11.6) 13 (2) 5.3 (0.8) 94 (14) AISI 316 27.9 (15.0) 6 (3) 4.4 (0.2) 78 (6) 21-6-9(melt 1) 112.1 (5t.7) 31 (9) 3.6 (0.6) 65 (t2) 21-6-9(melt 2) 68.1 (13.8) 29 (4) 2.3 (1 A) 41 (20) 22-13-5 49.7(26.I) 14(3) 3.6(1.1) 64(20) Hadfield 38.9 (5.1) 34 (0) t.2 (0.1) 21 (2)

In the absence of Cr (Hadfield steel) the stacking fault probabi l i ty data scat ter is cons iderab ly reduced, compar ing favorably with peak posit ion deviat ions of pure e lements . ~ Again, with the presence of Cr f luo- rescence , it was not poss ib le to obtain the same re - peatabi l i ty of peak posit ion.

1348-VOLUME 6A, JULY 1975 METALLURGICAL TRANSACTIONS A

As noted above, the AISI 304L, AISI 305, and Had- field steel part ial ly t ransformed martensi t ica l ly ; this could possibly be a source of systemat ic e r ro r due to some line overlap. Since the AISI 304L bulk specimen was lightly cold worked rather than a powder, the ex- istence of residual s t resses (not present in the ran- domly oriented powders) could introduce shifts in the line positions, Assuming a rather high residual s t ress of 30,000 psi (2.1 108 N/m 2) and a Young's modulus of 30 10 ~ psi (2,1 101~ N/m~), one dimensional residual s t ress calculations resul t in a =e 3 10 "s possible change of ~, leading to an est imated 50 pct e r ro r of the stack- ing fault probabil ity.

DISCUSSION

It has been demonstrated (Table I) that Ni raises the stacking fault energy of Fe-Cr'Ni alloys and this has been associated with its influence on dislocation cross slip. High Ni alloys display a cellular structure of dis locations in the austenite phase, {.e., cross slip is easy. a'35 Several workers have examined quantitatively the dependence of T on Ni concentration in Fe-Cr-Ni austenitic alloys. Swarm, 8 Douglass, et al, I~ and Dulieu and Nutting, 11 holding the Cr concentration at 18 to 20 pct, reported an almost linear dependence on Ni con- centration in the range 8 to 27 pct Ni,

-~ 2(pct Ni) (mJ/m~). [6]

with the Douglass data slightly at var iance with the other data. Eq. [6] was adjusted by a factor of two from the reported data following Brown. a3 More recently, Fawley, et al , ~7 have var ied both Cr and Ni concentra- tion. At 20 pct Cr, their results agree quite well with Eq. [6] until Ni concentrations in excess of about 20 pct are reached; at higher concentrations y decreased.

Gatlagher, 4 including some of the above results a'~~ plus more recent measurements , 4'6' ~2, ~, ~4 performed a least squares fit of available data with Cr concentra- t ions of 15 to 20 pct and found that

7 ~- 2.8 (pct Ni) (mJ/m~). [7]

It is of interest to note that all of the above analyses imply that Fe-18 pct Cr in the austenitic phase would have y = 0.

With increasing Cr, dislocation ar rays have been shown to become more planar.l~ Measurements11,~ confirm that, while holding Ni constant at about 10 pct, an increase of Cr concentration from 10 pct to 15 pot Cr rapidly reduces ), f rom about 50 to 20-40 mJ /m 2. Larger Cr concentrations (15 to 20 pct) produce little significant change of ~.

The C content is very important to the mechanical propert ies of steels. Carbon also stabi l izes against martensit ic t ransformat ion from fcc to bcc and to hcp phases, s6 Carbon is known to promote a cel lular d is- location arrangement. ~7 Although also an interstit ial, N has the opposite effect on the dislocations. Like Cr, N tends to reduce dislocation tangles and to encourage planar ar rays . 8''~ However, like C, it has been re - ported to have little or no effect on 7. a'1~ Because of an affinity for Cr, N is thought to introduce shor t - range order into these al loys 1~ which may be re - sponsible for the observed planar dislocation ar rays , a

Small quantit ies of both Si and Mn are common in

steels. While Si depresses 7 in an Fe-18 Cr-14 Ni al- loy, ~4'15 there are no available data on the influence of Mn.

To corre late the stacking fault energy of stainless steels with their composit ion, Neff, et a l . 37 plotted equal energy l ines on an Fe -Cr -N i ternary diagram. Toward this same goal, we attempted some simple multidimensional l inear least squares regress ion fits of the data in Table I. Six elements (Cr, Ni, C, N, Si, Mn) were chosen since there were available in Table I sufficient data for simple four-dimensional l inear re - gress ion fitting (e. g., see Hoe138). Goodness of fit 39 was measured by the X z test and, after an initial fit, a few of the points with greatest deviations were re - jected to assure that k2 was not signif icant for a cr i t i - cal region of 0.05 or greater . The remaining points subsequently gave the resul ts in Figs. 2 and 3 and the expressions:

7 = 4 + 1.8 (pct Ni) - 0.2 (pct Cr) + 410 (pct C), [Sa]

= 34 + 1.4 (pctNi) - 1.1 (pctCr) - 77 (pctN), [8b]

7 = 34 + 2.2 (pctNi) - 1.1(pctCr) - 13 (pctSi), [8c]

y = 32 + 2.4 (pct Ni) - 1.2 (pct Cr) - 1.2 (pct Mn)

(mJ/m~). [8d]

Only data f rom di rect measurements were used to ob- tain Eq. [8a] to [Sd] and these are identified in Table I, using [a], [b], [c], and [d] superscr ipts . For the N i -Cr -C line of Eq. [8a] Ca in Fig. 2 and Table I), only data were

100 --

90

80

70 c~

"~ 60

50 Z

~ 40

,<

30

20

10

0

0

O

I l I ....... I J .......... l 20 40 60 80 100 120

WEIGHT PERCENT COMPOSITION EQUIVALENT

a: [4+I,8(%~i)-0.2(%Cr) b:[34+I.4(%N~)-I.O(%Cr)-76(%N)]

I 140

Fig. 2- -L inear regress ion analys is of data in Table I for Fe - N i -Cr -C and Fe-N i -Cr -N .

METALLURGICAL TRANSACTIONS A VOLUME 6A, JULY 1975-1349

90

80

OQ

/

70 --

E

60 --

u~ z

~- 50 --

40 m

~o

30 --

20

I0

I00

O C

9 d

o l 1 ,, t I . . . . . . . . t ....... I l 0 20 40 60 80 I00 120 140

WEIGHT PERCs COMPOSITION EQUIVALENT

c: [34 d: [32+2.4(gMi)-l.3(%Cr)-1.3(%Mn)]

Fig. 3 - -L inear regress ion analys is of data in Table I for Fe - Ni -Cr -S i and Fe -N i -Cr -Mn.

selected where the N content was low and reasonably constant (0.003 to 0.006 pct); Cr content varied from 10 to 30 pct, Ni varied from 10 to 20 pct. The data for the Ni-Cr-N fit, expressed in Eq. [Sb], were chosen so that C content was confined to the range 0.010 to 0.15 pct; Cr varied from 10 to 20 pct, Ni varied from 10 to 20 pct. For Ni-Cr-Si and Ni-Cr-Mn analyses Cr con- tent was limited from 8.5 to 22 pct, while Ni varied only from 9 to 11 pct.

Eqs. [8], for the most part, have two similarities; nickel increases 7 approximately 2 mJ /m e per wt pct, while chromium decreases y approximately 1 mJ /m 2 per wt pct. The effects of the other constituents, which are present in smaller concentrations, are much more tenuous. Any process such as precipitation or small- scale segregation would reduce the effective composi- tion in solution, which would not be reflected in the chemical analyses. Furthermore, variations of depen- dence in some cases can be obtained by changing data selection procedures. For instance, if high nitrogen concentration alloys are used in the Ni-Cr-C fitting, then a negative dependence of ~, on C content is ob- tained. Also, a significantly different constant, corre- sponding theoretically to the ~ of pure fcc iron at room temperature, is obtained in Eq. [8a] for the low N, Fe- Ni-Cr-C quaternary alloys. This difference of constant value (4 compared to 32 to 34) lends less credence to Eq. [Sa]. Such results strongly imply that there exists considerable interdependence among alloying elements on their influence on V. Nonetheless, the indications are that C tends to increase V at low N concentrations,

and that N, Si, and Mn tend to lower 7 in Fe, 10 to 20 pct Cr, 10 to 20 pct Ni alloys.

It is also of interest to analyze the dependence of on the composition of the principal solute alloying ele- ments in our commercial alloys, some of which have large concentrations of Mn and Mo. Using five-dimen- sional regression analysis for the 7 dependence on Ni, Cr, Mn, and Mo contributions, the following expression was obtained:

7 = - 53 + 6.2 (pct Ni) + 0.7 (pct Cr) + 3.2 (pct Mn)

+ 9.3 (pct Mo) (mJ/m ~) [9]

For this analysis only major alloying elements were considered, since the minor elements either were thought to influence y negligibly or had relatively con- stant concentration. The results from this analysis conflict considerably with those presented earl ier in Eq. [Sa] to [Sd]. The addition of Cr and Mn make a slightly positive contribution to ~ in Eq. [9] in contrast to their contribution in lowering y of Eq. [8a] to [Sd]. Furthermore, the dependence of y on Ni concentration is greater by about a factor of 3 than shown in Eq. [8a] to [8d]. Compared to the positive values of the constant in Eq. [Sa] to [Sd], the constant of Eq. [9] is negative; this perhaps represents tile influence of the other im- purities (C, N, Si, P, S, Co, etc.) contained in the com- mercially available alloys. There is little hope of com- pletely resolving these compositional dependencies. It seems that each elemental dependency is affected by concentrations of other elements, producing a large second order effect on y-composition dependence.

However, it is desirable to obtain a composition :v dependence expression that works best for austenitic steels. For this reason Fig. 4 (and Eq. [9]) are in- cluded. Notice that there is a reasonable correlation between our alloys, measured using the X-ray tech- nique, and the electron microscopy node data of Table I. All node data that produced ~ values higher than 60 mJ /m ~ and nickel concentrations higher than 20 pct were omitted. The resolution of node radii for higher

alloys is very difficult and subject to greater error. At nickel concentrations at higher than 20 pct the stack- ing fault energy tends to decrease with increasing Ni concentration (Table I, Ref. 5).

In applications where the stacking fault energy signif- icantly influences mechanical or chemical properties, it should be possible to select a steel composition to fit the requirements and to estimate 7 for the alloy in use. When trying this, it is necessary to consider the major elements present (Cr, Ni, Mn, Mo). Carbon and nitro- gen must also be considered if their compositions de- viate from approximately 0.3 to 0.8 pct C and greater than about 0.01 pct N. In general, the trend in Eq. [9] can only be considered indicative of the influence of composition. A lengthly comprehensive and systematic study is required to make more quantitative predictions.

CONC LUSIONS

A series of commercial austenitic steels has been examined, using X-ray measurements of line broaden- ing and line shifts, to obtain their stacking fault ener- gies. From this study the following was concluded:

1) The stacking fault energy results, obtained using X-ray techniques, agree quite well with the measure-

1350-VOLUME 6A~ JULY 1975 METALLURGICAL TRANSACTIONS A

100

90

80

70

c~

~0

50

~ 40

30

0 ~

% o

e

0

0

0 0

20 0

II Our Work

I0 0 Electron Microscopy, Literature Data.

0 V , I 1 I I ..... I ........... I 1 0 20 40 60 80 I00 120 140

WEIGHT PRECENT COMPOSITION EQUIVALENT

[-53+6.2(%Ni )+0.7(%Cr)+3.2(%Mn)+9.3(%Mo)]

F ig . 4 - -Re la t ionsh ip between s tac ldng fau l t energy and Fe - N i -Cr -Mn-Mo compos i t ion in austen i t i c s ta in less s tee ls .

ments of node radii f rom t ransmiss ion e lectron mi - croscopy. However, a greater range of 7 (12 to 94 mJ /m z) can be success fu ly measured with X - rays .

2) Simple regress ion analyses of previous data indi- cate that Ni and C additions tend to increase V while Cr, Si, Mn and N tend to decrease V in Fe -Cr -N i aus - tenit ic a l loys.

3) An attempt was made to establ ish a relat ionship between stacking fault energy and composi t ion of major al loying e lements for commerc ia l -g rade austenit ic Fe - Cr-Ni , Fe-Mn-Ni , and Fe -Cr -N i -Mn s tee ls . The re - sulting express ion V = - 53 + 6.2 (pct Ni) + 0.7 (pct Cr) + 3.2 (pct Mn) + 9.3 (pctMo), obtained using regress ion analyses of our data, cor re la tes reasonably wel l with previous stacking fault energy data.

ACKNOWLEDGMENT

The authors wish to thank the Lawrence L ivermore Laboratory of the Atomic Energy Commiss ion , par- t icularly Drs. P. R. Landon and R. R. Vanderwoort,

for sponsor ing part of this research and for providing the al loys and their chemica l analyses. We are espe- cial ly thankful to Dr. A. Tench who ass i s ted in some X-ray measurements and data analyses. We also ap- preciate the cr i t ica l readings of the manuscr ipt by Dr. H. M. Ledbetter and by Dr. A. W. Ruff, Jr.

REFERENCES

1, S. Bamartt, R, Stickler, and D. van Rooyen: Corros. Sci., 1963, voL 13, pp. 9-16.

2, M. L Holzwor~h: Corrosion-NACE, 1969, vol. 25, pp. t07-15. 3. R. B. Benson, R. K. Dann, and L. W. Roberts: Trans. TMS-AIME, 1968, voI.

242, pp. 2199-2205. 4. P. C. J. Gallagher: Met. Trans., 1970, rot. 1, pp. 2429-61. 5. R. P. Reed and R. E. Schramm: National Bureau of Standards, Boulder,

Colorado, unpublished research, 1975. 6. M. J. Whelan, P. B. Hirsch, R. W. Home, and W. Bollmann: Proc. Roy. Soc. A,

1957, vol. 240, pp. 524-38. 7. M. J. Whelan: Proc. Roy. Soc. A, 1959, vol. 249, pp. 114-37. 8. P. R. Swarm: Corrosion, 1963, vol. 19, pp. 102t-112t. 9. J. F. Breedis: Trans. TMS-AIME, 1964, vol. 230, pp. 1583-96.

10. D, L. Douglass, G. Thomas, and W. R. Roser: Corrosion, 1964, vol. 20, pp. 15t-28t.

11. D. Dulieu and J. Nutting: Metallurgical Developments in tfigh-Alloy Steels, pp, 140-45, Special Report 86, The Iron and Steel Institute, 1964.

t2. J. M. Silcock, R. W. Rookes, and J. Barford: J. Iron SteetlnsL, 1966, vol. 204, pp. 623-27.

13. A. Clement, N. Clement, and P. Coulomb: Phys. Status. Solidi, 1967, voL 2l, pp. K97-K98.

14. B. Thomas and G. Henry: Mere. Sci. Rev. Met., 1967, vol. 64, pp. 625-36. 15. B. J. Thomas: Metaux, Corrosion, lndustrie, 1969, no. 532, pp. 405-38. 16. O. Vingsbro: A cta Met., 1967, vol. 15, pp. 615-21. 17. R. Fawley, M. A. Quader, and R. A. Dodd: Trans, TMS-AtME, 1968, voL 242,

pp. 771-76. 18. R. M. Latanision and A. W. Ruff, Jr.: Jr. Appl. Phys., 1969, vol. 40, pp.

2716-20. 19, L. E. Murr: Thin Solid Films, 1969, vol. 4, pp, 389-412. 20. F. LeCroisey and B, Thomas: Phys. Status. Solidi (a), 1970, vol. 2, pp.

K217-K20. 21. R, M. Latanision and A. W. Ruff, Jr.: Met. Trans., 1971, vol. 2, pp. 505-09. 22. E, D. Butakova, K. A. Malyshev, and N. 1. Noskova: Fiz. Metal. Metalloved.,

1973, vol. 35, no. 3, pp. 662-64. 23. L. M. Brown: Phil Mag., 1964, vol. 10, pp. 441-66, 24. R. P. Reed and R. E. Schramm: J. AppL Phys., 1974, vol. 45, pp. 4705-1 h 25. R. R. Vandervoort: Metals Eng. Quart., 1972, voL 12, pp. 10-16. 26. C. J. Newton and A. W. Ruff, Jr.: J. AppL Phys., 1966, vol. 37, pp. 3860-68. 27. B. E. Warren: Prog. MetalPhys., 1959, vol. 8, pp. 14%202. 28. R. E. Schramm: National Bureau of Standards Tech. Note 600, t971. 29. C. P. Gazzara, J. J. Stiglich, Jr., F. P. Meyer, and A. M. Hansen: Advances in

X-Ray Analysis, vol. 12, pp. 257, Plenum Press, New York, 1969. 30. R. L. Rothman and J, B. Cohen: Advances in X-Ray Analysis, vol. 12, p. 208,

Plenum Press, New York, 1969. 31. Residual Stress Measurement by X-Ray Diffraction, SAE J 784a, p. 51, Society

of Automotive Engineers, New York, 1971, 32. K, Salmutter and F. Stangler: Z. Metallk., 1960, vol. 51, pp. 544-48. 33. M~ C. Mangalick and F. Fiore: Trans. TMS-AIME, 1968, vol. 242, pp. 2363-64. 34. R. P. Reed: Acta Met., 1962, vol. 10, pp. 865-77. 35. G. Thomas: Acta Met., 1963, vol. 11, pp. 1369-71. 36. R. P. Reed and J. F. Breedis: Behavior of Materials at Cryogenic Temperatures,

ASTM/STP 387, p. 60, Am. Soc. Testing Mats., 1966. 37. D. V. Neff, T. E. Mitchell, and A. R. Troiano: Trans. A&M, 1969, vol. 62,

pp. 858-68. 38. P. G. Hod: Introduction to Mathematical Statistics, p. 172, John Wiley and

Sons, Inc., New York, 1962. 39. P. G. Hoel: ibid., p. 244.

METALLURGICAL TRANSACTIONS A VOLUME 6A, JULY 1975-1351