“Stage III” recovery in cold-worked iron

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relevant papers on dislocation intersections by Lomer, Cottrell, Friedel, Whelan and Saada. The present note is meant to clarify the position. The fact that the said two discussions took place, and the way in which they ended, shows that a rather widespread misconception exists, according to which the stability, and hence the frequency, of dislocation barriers increases with the width to which they are extended. According to this idea, those locks which are due to the least favorable reactions, i.e. yield the smallest reduction of dislocation energy, should be the most stable. Namely, all of the barriers considered are formed as reaction products of two extended $(llO> dislocations, meeting at the intersection of two (11 l> planes inf.c.c. metals. The resultant lockstherefore are all parallel to (1 lo), consisting of stacking fault ribbons, joined at their line of intersection by a stair-rod dislocation, and bordered by $(112) partials. The total reduction of dislocation energy through the formation of the said locks will be the higher, the smaller the Burgers vector of the resultant stair-rod dislocation is, and the greater the attraction of the two remaining +(112) partials. Actually, of all locks the Lomer-Cottrell barrier has the lowest possible energy and therefore is the least extended. Conversely, Hirth locks, reactions (10a) and (lla), arise from the interaction of $(llO) dislocations with perpendicular Burgers vectors. Correspondingly, they result in the smallest energy gain due to any of the barriers, yielding two mutually repelling &(112) partials, and a stair-rod dislocation of large Burgers vector which repels the remaining partials. In truth, for the following three reasons the most stable dislocation barriers are the Lomer-Cottrell locks, while Hirth locks must be quite rare, if they exist at all. Firstly, it stands to reason that locks, foremost among them the Lomer-Cottrell barrier, which are the result of dislocations strongly attracting at long range, must form much more frequently than locks that are due to dislocations which are nearly indifferent to each other as in the Hirth reaction No. (1 la), or have a mild long-range repulsion as in the Hirth reaction No. (lOa). In the latter cases, the two dislocations will have a tendency to simply by-pass each other, which is easily possible if they are parallel, or if both end points of one are on the same side of the other slip plane. Secondly, for barrier formation it is necessary that two extended dislocations with line orientations including sufficiently small angles intersect each other. Only then will the four-fold nodes at the point of intersection dissociate into two three-fold nodes, and a dislocation barrier of the discussed type will

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be drawn out between these; provided a favorable dislocation reaction is possible. Clearly, for any given angle of intersection, the length of the thus formed dislocation barrier will increase with increasing energy gain of the reaction; again with the result that a muoh greater total line length of Lomer-Cottrell locks are formed than of Hirth locks. Thirdly, while barriers formed from in&itely Eong parallel dislocations pose an important and interesting mathematical problem, and while their stability against dissociation due to applied stresses or piled-up dislocations was found by Hirth to rise with increasing width of extension, these do not exist in nature. Instead, the length of the barriers is always finite. For finite barriers, much smaller stresses are required to complete the dislocation intersections, and thereby break the barriers. This is no new idea. In particular, for example, Hirth (Ref. 3 footnote 20) noted for the case of non-parallel reacting dislocations, that the applied stress will tend to “unzip” the reacted barrier dislocation, to once again form the reactant dislocations. Thus, in summary we may say that Hirth locks will be formed infrequently and will be broken easily. The influenceof anisotropyon the stability of the locks, while not negligible, does not change these results.(5*6) The above conclusions should in no way detract from the important contributions made to the mathematical theory of dislocations by the quoted references. Stimulating remarks and discussions of Drs. L. D. Dyer, F. C. Frank, T. E. Mitchell, F. R. N. Nabarro, and particularly Drs. J. P. Hirth and L. T. Teutonic0 are gratefully acknowledged. The author thanks the AEC for the financial support of her research under Contract No. AT-(40-l)-3108. DORIS KWLMANN-WILSDORF

School of Engineering and Applied Xcience University of Virginia C?uwlottfmille, Virginia References 1. GGTTINQEN, Meeting of the Faraday Society, 1964. 2. DAYTON, Air Force Conference, Wright Patterson Air Force Base, Ohio, March 11th md 12th. 1965. 3. J. P. HIBTH,J. AmZ. Phye. 83, 700 (1961). 4. Z. S. BASINSKI, Disc. B’amday Sot. (1965) in press. 5. L. J. TEUTONICO, Phil. Msg. 10, 401 (1964). 6. T. J~SSANG, C. S. HAXTLEY and J. P. HIRTH, J. Appl. Phye. (1965) in press. * Received August 9, 1965.

“Stage

III” recovery in cold-worked

iron

Sharp stages of recovery of electrical resistivity observed during annealing of b.c.c. metals after cold

LETTERS

TO

THE

TABLE 1. Effect of incomplete removal of the contaminated surface on the resulting carbon content of pure iron

Batch

Depth of chemical polish (in.)

Carbon * in solution (ppm)

A B

.002 .006

19 0.8

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been purified by a series of twelve passes in controlled atmospheres in a vertical zone melter. The resulting iron was swaged to 0.037 in. dia., chemically polished to remove surface contamination from swaging, and recrystallized for 15 min at 550°C in He + 2% H,. The amount of material removed by the polish differed for two sets of specimens of the same iron. The resulting carbon contents in the recrystallized specimens are shown in Table 1. It is obvious from these data that the contaminated surface layer was not fully polished away in Batch A so that the remaining carbon diffused into the specimen during recrystallization. After recrystallization, the specimens were elongated 15% by drawing through a die under liquid nitrogen. Isochronal anneals were effected by immersing specimens into liquid baths controlled to f0.05”C for 10 min periods. Specimens were returned to liquid nitrogen for resistance measurements. Figure 1 shows the recovery spectra for typical samples from Batches A and B. It is seen that a “recovery stage” occurs only in the iron which has been contaminated with carbon. The activation energy associated with this stage is 0.87 eV, the value for the migration of carbon in alpha iron. Furthermore, this stage was reduced and the Snoek peak lowered when the contaminated specimens were wet-hydrogen annealed for 3 hr at 900°C prior to straining. Even so, an easily discernible stage was observed in iron with as little as 2.4 ppm carbon in solution. Only for iron with less than 1 ppm carbon was no recoverystageobserved. Finally, it is interesting to compare this strain-aging stage with the aging due to carbon observed by Fujitac6) after neutron irradiation of iron containing 0.01 wt.% C. As shown in Fig. 2, the two ooour at approximately the same temperature and at about the same rates even though the radiation-induced sinks

* From Snoek Peak. work or irradiation have been attributed by the investigators to stage III annealing of induced point defects.(l+ Rosenfielcl,(4) however, has demonstrated that the “reooveries” after cold work occur at temperatures and with activation energies very much like those which would be expected for strain-aging due to interstitial impurities in these metals. Apparent experimental proof that the mechanism of recovery is indeed strain-aging is provided by Gregory’sc5) observation that “stage III” recovery in cold worked Nb increases with increasing interstitial impurity content. Nevertheless, the former interpretation continues to be accepted, primarily on the basis of two arguments: (1) The interstitial-impurity content is too small (50-100 ppm) to produce an observable resistivity drop during aging. (2) The stage III recovery in b.c.c. metalsafter coldwork is remarkably similar to that after irradiation. Aging caused by interstitial impurities should not be similar in the two cases because of the differences in the sink types and distribution. Induced point defects, however, could agglomerate in much the same way after the two prooesses, as they do in f.c.o metals. This note demonstrates that neither of these arguments is a valid defense of the point-defect hypothesis in b.o.o. metals. The present study usedironwhiohhad

h_

B-0.8

-A

_5LLLLL-I 60

too

140

I 180

I 220

I

I

I

260

ANNEAL

I 300

I

I

I

340

TEMPERATURE,

I

PPM c

A-19 PPM C

I I I 380

420

I

I

---O I I I I I 460

500

540

“K

FIG. 1. I~ochronel annealing (10 min) of high-purity iron strained 16 % at 77’K.

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I

I

200

250

I

I

I

300 350 400 ANNEAL TEMP.,“K

METALLURGICA,

I

I

450

500

I

Fro. 2. Isochronal annealing of iron containing carbon. (a) After neutron irrad. Fe + 0.01% C. 5 min anneal. (Fugita.) (b) After 6% strain at 77’K. Fe + 0.002% C. 10 min anneal. (Present work.) for carbon differ in type and distribution from the dislocation sinks introduced by cold work. From these observations of the behavior of carbon in iron, we see that strain-aging of interstitial impurities can be observed even at levels as low as 2-3 ppm, and disappears only at levels of approximately 1 ppm. Further, this aging after straining may be remarkably similar to aging after irradiation. In view of these observations we feel that no definite cause can be assigned to “stage III” annealing in b.c.c. metals until investigations have been made with highly purified materials. The authors are grateful to B. F. Oliver for supplying the high-purity iron, and to J. C. Swartz for Snoekpeak determinations.

Edgar C. Bain Laboratory For Fundamental Research United &ate8 Steel Corporation Research Center Monroevilk, Pennsylvania

L. J. CUDDY J. C. RALEY

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Westlake(5) used the concept of zonal twinning dislocations to allow all necessary atom movements to be accomplished during the passage of a single dislocation. In developing such models one can always find one or more combinations of unit dislocations that might interact to result in the required twinning dislocation plus an integral number of unit dislocations in the twinned material.(67) We would like to suggest, however, that restricting atom motion so as to obtain a mirror image of every atom across the twin plane, as Thornton(7) has done for (10.1) twinning, may complicate the model, and may constitute a preternatural restriction. Westlake@) pointed out that the bonding across any twin interface is highly disturbed, relative to the bonding in the matrix. Even in models that are nearly perfect, geometrically, some atoms must move to positions of compromise in the interface. It is not unrealistic, then, to assume that all of the atoms at the twin-matrix interface will be displaced slightly from normal atom sites of the matrix lattice to produce the twin boundary of lowest energy. Let us say, for example, that the interface atoms of a (10.1) twin are displaced as shown by the arrows in Fig. 1. This creates a misfit with the plane of atoms just below the twin plane, shown as 0’s. In reality, this misfit would probably be spread over several planes, but for the moment, let us keep the misfit localized. Further, let us consider the motion of atoms in one plane at a time, first the plane of the interface, then the first plane above the interface, and so forth. The atom G is in contact with atoms A, B, C and D. If the passage of a twinning dislocation causes these latter four to shift toward A‘, B’, C’ and D’, respectively, then one could expect that atom G would be

References 1. D. E. PEACOCKand A. A. JOHNSON,Nature, Lond. 195,164 (1962); Phil. Maq. 8, 563 (1963). 2. J. NIHOUL, Radiation Damage in So&da, vol. I, pp. 309-322. International Atomic Energy Agency, Vienna (1962). 3. H. SCHULTZ, Acta Met. 12, 649 (1964). 4. A. R. ROSENFIELD,Acta Met. 12, 119 (1964). 6. D. P. GREGORY,Acta Met. 11, 465 (1963). 8. F. E. FUJITA and A. C. DAMASK, Acta Met. 12, 331 (1964). * Received July 2, 1965.

On {lO.l} twinning in the h.c.p. structure* During deformation twinning of h.c.p. metals, certain atoms are required to shuffle while others undergo the shift described by the observed shear.(l-7)

FIQ. 1. Projection of atoms on a (10.1) plane. O’s are in the plane that will become the interface between matrix and twinned material. n’s are in first plane beneath the interface. A’s, 0’s and O’s are in ii&, second and third planes above the interface, respectively.