The Snoek effect in iron specimens with high dislocation densities

The Snoek Effect in Iron Specimens with High Dislocation Densities J. C. SWARTZ E. C. Bain Laboratory for Fundamental Research, U. S. Steel Corporation Research Center, Monroeville, Pa. (U.S.A.) (Received April 30, 1969; revised July 8, 1969)

SUMMA R Y Experiments are described on deformed Fe(C) and Fe(N) solutions to determine the effects of the dislocation structure on the magnitude of the Snoek relaxation. For dislocation densities of the order of 10 lo cm - 2 the usual water quench is not sufficiently fast to retain all the interstitials in solid solution, When a high density of dislocations is formed at the

moment of quenching (as in the formation of lowcarbon martensite) large quantities ofinterstitialare absorbed by the dislocations during the quench. A subsidiary experiment demonstrates a technique for measuring by the Snoek effect the amount of interstitial trapped by the dislocations during an equilibration treatment.

RgSUM~, Les expdriences ddcrites sont relatives dl des solutions solides Fe(C) et Fe(N) ddformdes, elles ont pour but de ddterminer l'influence de la structure de dislocations sur l'amplitude de la relaxation de Snoek. Pour des densitds de dislocations de l'ordre de 1 0 1 ° cm -2, la trempe ~ l'eau habituelle n' est pas assez rapide et tons les interstitiels ne restent pas en solution solide. Lorsqu'un nombre dlevd de dislocations se

forme au moment de la trempe (comme lors de la formation des martensites d bas carbone), une proportion importante d'interstitiels est absorbde par lea dislocations au moment de la trempe. Une expdrience annexe montre comment on peut mesurer dl raide de l' effet Shock la concentration d'interstitiels pidgds par les dislocations dans un mdtal traitd dans les conditions d'dquilibre.

Z USA M M E N F A SS UNG Verformte Fe(C)- und Fe(N)-Lfsungen wurden untersucht, um den Einflufl der Versetzungsstruktur auf die Gr6J3e der Snoek-Relaxation zu bestimmen, Fiir Versetzungsdichten der Gr6flenordnung 10 l° cm- 2 ist das fibliche Abschreckverfahren in Wasser nicht schnell 9enug, um alle Zwisehengitteratome in fester L6sun9 zu halten. Wenn beim Abschrecken eine hohe Versetzungsdichte erzeugt wird (wie bei der

Bildung kohlenstoffarmen Martensits), werden viele Zwischengitteratome wdhrend des Abschreckens yon den Versetzungen absorbiert. In einem weiteren Experiment wird eine Methode gezeiot, mit der mit Hilfe des Snoek-Effekts die Zahl der wdhrend einer Gleichgewichtsbehandlung an Versetzunoen festgehaltenen Zwischengitteratome gemessen werden kann.

INTRODUCTION

tration of an interstitial component in the presence of a high dislocation density. To explore this upproach the effects ofthe dislocations on the measurement must be known. T w o effects are conceivable : (i), the dislocation stress fields may so strongly order

For certain studies, such as those of interstitialdislocation equilibria in b.c.c, metals, it is desirable to use the Snoek relaxation to measure the concen-

Materials Science and Engineering American Society for Metals, Metals Park, Ohio, and Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

31

SNOEK EFFECT IN IRON WITH HIGH DISLOCATION DENSITIES

the interstitials that their specific anelastic response is diminished ; and (ii), the short diffusion distance to dislocation traps may make it difficult to preserve an equilibrium state for measurement. The first effect has been treated in a separate report 1 which concludes that for carbon in iron the dislocation density must be very high (> 101a/cm 1) before any significant diminution of the relaxation strength per interstitial atom. The second effect is the subject of the present report. From the experiments to be described we conclude that quenching losses of interstitials in deformed iron wires become noticeable when the dislocation density is > 101°/ c m 2.

............... ~

1

i ~

z.~ Hz ~00

~ ,

,_ Z x ~ ~ ~ ~t ~ ~8

~

~' ~L ~ ~ •-

'

~

//x5

/

10

To estimate the quenching loss we compare the Snoek peak height of each deformed specimen with the range typical of undeformed specimens for the same interstitial content*. In addition a few tests were made of the sensitivity of the Snoek peak height to quenching speed. The techniques for controlling the interstitial content and for measuring the Snoek peak are described elsewhere 2'4. Estimates of the dislocation densities of the specimens were obtained from the transmission electron micrographs of thin samples. EXPERIMENTS

In one experiment six variously textured strips (Specimens la-lf) were cut from a 0.7 mm sheet of heavily cold-rolled iron containing 0.04~ dissolved nitrogen. A treatment at 400°C in an N H J H 2 atmosphere stabilized the dislocationstructureand adjusted the dissolved N concentration to 37 p.p.m, (by weight). The treatment was terminated by freefall into a water-CaC12 solution supercooled to _40oc. Metallography revealed that about 60~o of the specimen volume retained the cold-worked structure with about 10 l° dislocations/cm2 in cells 0.2 /~m wide (Fig. 1 insert). The remaining volume had recrystallized into grains averaging 6 #m wide. Figure 1 shows that the nitrogen Snoek peak of Specimen la is about 56 x 10 - 4 log decrement units during the initial warm-up and is several percent

* In our experience 2-4 the Snoek peak height (log decrement for 1 Hz torsional oscillations) per unit weight percent interstitial for undeformed iron specimens is in the range 2.0 to 4.6 for carbon and 1.5 to 3.5 for nitrogen,

-

J -5o

l 0 TEM~ATURE,*C

_ J ~0

Fig. 1. Internal friction spectrum of Specimen la after charging 37 wt. p.p.m. N in solution and quenching into - 4 0 ° C waterCaCl2 solution. Insert shows a typical microstructure viewed in a plane transverseto the rolling plane.

lower during cooling**. Similar tests of the other specimens established that the brief excursion (~ 10 min) above the peak temperature typically decreased the peak height about 15~o. Table 1 lists the height of the initial Snoek peaks of these six specimens. The scatter of these values presumably reflects the texture differences 4. The specimens were not sufficiently uniform in section to warrant inferences on texture from comparison of their resonant frequencies. To test the sensitivity to quenching speed, Specimens ld and If were requenched into oil*** from the same NH3/H2 mixture at 400°C. The initial peaks after the oil quench were 25 and 9 ~ lower than the respective peaks after the water quench. Since the interstitial distribution is undoubtedly frozen much more effectively by quenching in water rather than in oil, it seems safe to conclude that the fractional peak deficit due to trapping during the initial water quench was less than 25 ~. Note that an increase of the initial peak heights of

** The apparent temperature difference of the Snoek peak during heating and cooling results from thermal lag between the specimen and adjacent thermocouple in ceramic at a heating rate of about 3 degC/minute. *** Auxiliary measurements of cooling rates with an oscilloscope and thermocouple indicate that the quenching speed in oil is an order of magnitude slower than that in water.

Mater. Sci. Eng., 5 (1969/70) 3(~34

32

J . C . SWARTZ T A B L E 1 : SNOEKPEAKSOF DEFORMEDSPECIMENS

Specimen

la b c d e f 2a b c

Approx. _1_density 101 o cm- 2

N char#e wt. p.p.m.

1 1 1 1 1 1 22+ 2+

37 37 37 37 37 37 6l 56 7l

say 15 ~ would bring these data well within the range typical of undeformed specimens, An additional experiment on Specimen lc is worth recording since it demonstrates a method for measuring via the Snoek effect the equilibrium partition of the interstitial component between the dislocation sites and the normal lattice interstices, The total nitrogen (i.e. the sum of that in dislocation sites and the 37 p.p.m, in the normal lattice) absorbed by Specimen lc during the initial equilibration with the NH3/H 2 atmosphere at 400°C was determined as follows. First, the specimen was recrystallized 15 min at 689°C in an evacuated glass envelope and quenched. This put all the nitrogen in solution and yielded a Snoek peak (log dec.) of 99x 10 -4. Then, to measure the proportionality constant between Snoek peak height and dissolved nitrogen content, the specimen was equilibrated again at 400°C with the original ammonia/hydrogen mixture. This yielded a peak decrement of 83 × 10- 4 for 37 wt p.p.m. N, from which we deduce that the peak of 99 x 10-, indicates a total nitrogen content of 44 p.p.m., i.e. 7 p.p.m, in excess of that in the normal ferrite interstices. This excess amount is the nitrogen absorbed by the dislocations during the initial 400° equilibration of the deformed material, and quantitatively is roughly consistent with the results of the Wriedt-Darken 5'6 and Podgurski 7 experiments on pure iron. Several other specimens have been studied in conjunction with experiments of Podgurski 7. He cold-rolled zone-refined iron to sheets about 0.5 mm thick, charged these with about 50 p.p.m. N, then warm-rolled 5 0 ~ further at temperatures between 150 and 300°C. Specimens 2a, b and c are ribbons --~0.3 × 2 × 5 mm cut from such" sheet. Specimen 2a received a final equilibration with 2 atmosphere at 400°C whereas 2b and

an NHa/H

Snoek peak height (log dec. x 104) Observed

Typical of annealed spec.

56.0 81.2 63.9 55.8 54.6 63.8 146 49.1 88.6

57-130 57-130 57-130 57-130 57-130 57-130 91-214 84-196 106-248

2c were equilibrated at 300°C. From the anticipated recovery during these treatments we expect a lower dislocation density in 2a relative to 2b and 2c. The internal friction results subsequently presented are consistent with this expectation. The few available electron micrographs of these specimens (e.g. the inserts in Figs. 2 and 3) suggest densities ,-,2 × 101° cm- 2 but cannot be used to establish the density in 2a relative to 2c because the viewing planes are different. The equilibration of Specimen 2a at 400°C put 61 wt. p.p.m. N in solution. Figure 2 shows that the nitrogen peak is the same for an oil or water quench. Furthermore, the peak height is comparable with that of typical undeformed specimens (Table 1). Therefore, it seems that essentially all the 61p.p.m. N

....... ......

........ .

.

.

.

.

.

.

.

.

.

Fig. 2. Internal frictionspectra of Specimen 2a after charging 61 wt. p.p.m. N in solution and oil quenching, then requenching into - 4 0 ° C water-CaC12 solution. The micrograph shows the dislocation structure in a plane transverse to the rolling plane.

Mater. Sci. Eng., 5 (1969/70) 30-34

33

SNOEK EFFECT IN IRON WITH HIGH DISLOCATION DENSITIES

~oo zoo ........ ~oo0~

,c ~

~_ i0o~ ~ i

= -

z ~~~,

~

. ~27Hz

....

2L_.........

3I 10OO/T°K'' ,

Fig. 3. Internal friction spectra of Specimen 2c : (i)After filling the dislocation sites and removing the lattice nitrogen, and (ii) after re-equilibrating to put 71 p.p.m. N in solution, - 4 0 ° C waterCaC12 quench. The micrograph is a view of the dislocation structure in the rolling plane,

contributes to the relaxation despite the dislocation structure in the micrograph, In contrast the results on 2b and 2c suggest significant nitrogen loss during quenching. The warm-rolled sheet from which these specimens were obtained was equilibrated at 300°C with an NH 3/H 2 atmosphere which would put 56 p.p.m. N in solution, From the weight gain of the sheet and from Kjeldahl analysis of a sample, Podgurski determined that 84 p.p.m. N had been absorbed. Presumably, the extra 28 p.p.m, was absorbed by the dislocation sites. Specimen 2b was a strip cut from the sheet after this equilibration. The data in Table 1 show that the initial peak height of this specimen is substantially below the range expected for undeformed specimens. It seems that about half of the initial 56 p.p.m. N may have been trapped at dislocations during the quench. Podgurski treated the sheet further for nine days at 300°C in dry hydrogen. The weight change indicated the removal of 56 p.p.m. N, presumably the solution N, leaving the 28 p.p.m. N still trapped by the dislocations. Specimen 2c is a sample cut from the sheet in this reduced condition. Spectrum I of Fig. 3 shows that at this stage the height of the Snoek peak is z e r o , a s expected. Next, the specimen was equilibrated at 300°C with a different NH3/H 2

mixture. After quenching into a supercooled water solution, the Snoek peak in the internal friction spectrum (Curve II in Fig. 3) is still considerably below the expected range (Table 1). Hence both Specimens 2b and 2c with dislocation densities around 2 x 101°/cm 2 exhibited appreciable quenching losses. Summarizing the results so far, quenching losses have been investigated with two groups of specimens, all of which had estimated dislocation densities of the order of 101° cm -2. The results include cases of undetectable quenching loss (Specimen 2a), slight losses (Specimens la-f) and appreciable losses (Specimens 2b and c). In the last-named two cases the deficit in the Snoek peak indicates a quenching loss which seems to be roughly comparable with the amount of interstitial already absorbed by the dislocations at the equilibration temperature. In each of the preceding experiments the dislocations had acquired an equilibrium atmosphere before quenching. Now we describe a c a s e where the dislocations do not have their equilibrium a m o u n t s of C or N atoms before the quench. Such a case occurs in the formation of low-carbon martensite by rapid quenching of an austenitic iron-carbon alloy. In conjunction with experiments of Speich 8 we measured the Snoek peaks in several specimens of low-carbon martensite. Figure 4 contains a typical micrograph of 0.18 w/o C martensite obtained by Speich. He has concluded from resistivity measurements that the dislocation density is of the order of 10 ~~ cm- 2. At the concentration of l~

~~

~

:i'

-, ' -

b_

-4 -

.

~ toi ~ ~

_ 1.9Hz t0~-40J

........

o] . . . . . TEMPERATURE,o¢

L 40

Fig. 4. Internal friction spectrum of Fe 0.18 w t . ~ C martensite as quenched from 1000°C into 0°C brine. The insert shows a typical

microstructure. Mater. Sci. Eng., 5 (1969/70) 3(~34

34

J.C. SWARTZ

0.18 w/o C the critical temperature for spontaneous ordering is 175°K using the "internal stress approximation "3. Since the specimen was quenched to 273°K the carbon presumably is disordered, Figure 4 shows the Snoek peak in a strip (0.25 x 2 x 50 mm) of this martensite prepared by Speich. On cooling from the first warm-up the peak was found to have decreased about 45~o: Assuming that a similar decrease occurred between 0 and 40°C, the inherent Snoek peak (i.e., that before any aging loss) would be ~0.037 (log dec.). Then with an expected decrement between 2 and 4.6 per unit w/o C, the active carbon at the end of the quench would be (135_+50) p.p.m.; i.e., less than one-tenth of the initially dissolved carbon. Most of the missing carbon presumably was absorbed by the dislocations during the quench.

CONCLUDINGREMARKS The foregoing experiments on the efficiency of water quenching deformed iron wires show that : (i) quenching losses of interstitial atoms become apparent for dislocation densities of the order of 101° cm -2, and (ii) large amounts are lost from solution when about 101 ' f r e s h dislocations per ClTI2 are formed during the quench, as in the case of lowcarbon martensite. The possibility of studying interstitial-dislocation equilibria directly by Snoek measurements on equilibrated and quenched specimens is discouraged by the observation that the quenching losses are comparable with the equilibrium amount of interstitial in the dislocation sites. On the other hand another internal friction technique has been demonstrated (with Specimen lc) by which the amount of C or N absorbed by dislocations during an equilibration treatment can be measured. A subsidiary result worth noting is the strong temperature dependenceofthe dislocation damping in Spectrum I of Fig. 3 and its absence in Spectrum II. Recall that for both spectra the major dislocation sites were filled with nitrogen at the equilibration

temperature. Evidently the exponential rise of the dislocation damping culminating in a small "cold work peak ''9 at 195°C (27 Hz) somehow is suppressed when the "solution" nitrogen is added (Spectrum II). This large effect certainly needs more investigation. Finally, the fact that the Snoek peak (e.g. of Specimens 1 and 2a) is almost unaffected by average grain dimensions of 6/~m or dislocation cell widths of 0.2 #m contradicts the prevalent immobilization and segregation hypotheses for the "grain size dependence" ofthe Snoek peak. Reference 2 contains a detailed study of this subject.

ACKNOWLEDGEMENTS The author wishes to acknowledge the assistance of A. J. Schwoeble in obtaining many of the internal friction spectra. Thanks are due to H. H. Podgurski and G. R. Speich for their collaboration and permission to include data on their specimens. G. R. Langford and R. C. Glenn skillfully obtained some of the electron micrographs from which the late A.S. Keh estimated the dislocation densities. The author is also grateful for helpful discussions with these individuals, all of whom are members of this laboratory.

REFERENCES 1 J. C. SWARTZ, Scripta Met., 3 (1969) 359. 2 J. C. SWARTZ,Effects of microstructure on the Snoek relaxation, Aeta Met., in press.

3 J. c. SWARTZ,J. W. SHILLINGANDA. J. SCHWOEBLE,Aeta Met., 16 (1968) 1359. 4 J. C. SWARTZ,Trans. AIME, 245 (1969) 1083.

5 H. A. WRIEDTANDL. S. DARKEN,Trans. AIME, 233 (1965) 111 and 122. 6 L. S. DARKEN,Trans. Am. Soc. Metals, 54 (1961) 599.

7 H. H. PODGURSKI, U. S. Steel Corporation, unpublished research, 1966. 8 G. R. SPEICH,Tempering of Low-CarbonMartensite, Trans. AIME, in press. 9 H. I s o AND T. SUGENO, Acta Met. 15 (1967) 1197.

Mater. Sci. Eng., 5 (1969/70) 30-34