Accelerated stress relaxation caused by an alternating magnetic field

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TO

section varied from zero at the neutral axis to a maximum at the outer surfaces. Thus, no effect of strai~g was detected within the individual specimens. In addition, the measurements reported here for both strained and unstrained specimens are compared in Table 1 with values, D,, obtained by Dunlap for unstrained specimens; and these are in good agreement. The results reported here reveal no measurable effect of plastic straining on the diffusion of Sb in Ge. Two possible means of strain-enhanced diffusion are dislocation short circuiting and enhancement resulting from excess vacancies. The mechanism of diffusion of substitutional atoms in Ge has not been elucidated; however, Ileldt and Hobstetter were unable to detect any dislocation short-circuiting for the diffusion of Sb in Ge. We would expect that any enhancement observed in our experiments would have resulted from the production of excess vacancies during straining. If plastic straining causes enhancement of diffusion by the production of excess single vacancies and by this means only then D, and D,, the diffusivities in strained and unstrained material respectively, are related by(ll) D _S _ 12, -I- n, Ds_n,

(2)

where 12, is the concentration of vacancies in thermal equilibrium and n, is the steady state concentration of excess vacancies produced by plastic deformation. No enhancement was detected in the results reported here; thus, for the precision achieved in these measurements D e< D, and

1.5

n, < 0.5n,

THE

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in the form of divacancies, in contrast to the single vacancies expected to arise from bombardment or thermal treatments.(~3*1K)Further, it is likely that the mobility of the divacaney in Ge is considerably less than that of a single vaeancy.(13) In this case, the di-vacancies, produced by straining, would be difficult to detect in diffusion studies. This work was supported by Air Force Office of Scientific Research Grant #62-290. c. D. CALHOUN L. A. HELDT Department of Metallurgical Engineering Michigan Technological University ~o~g~n~ ~~~h~gan References 1. H. J. QUEISSER, K. HUBNER and W. SBOCKLEY, Phys. Rev. 123,1245 (1961). 2. F. KARSTENSEN, J. Electron. and Control 3, 305 (1957). 3. J. C. PFISTER and P. BARUCH, J. PAYS. Sot. Jqan 18, (Suppl. 3) 251 (1963). 4. P. BARUCH, C. CONSTANTIN, J. C. PFISTER and R. SMNTESPRIT, D&c. ~~r~uy Sot. No. 31, 76 (1961). 5. H. STRACK, BUZZ.Amer. Phys. Sot. 7, 543 (1962). 6. R. STRACK,J. AppZ. Phys. 34, 2405 (1963). 7. N. L. PETERSON and R. E. OQILVIE, Trans. Amer. Inst. Min. (Met&.) Engrs 215, 873 (1959). 8. L. A. HELDT and J. N. HOBSTETTZIR,Acta Met. 11, 1165 (1963). 9. H. WIDMER, Phya. Rev. 125, 30 (1962). 10. W. C. DUNLAP, P&a. Rev. 34, 1531 (1954). II. L. A. GIRIFALCO and H. H. GRIMES, KASA Teeha&& Report R-38 (1959). 12. R. A. LOGAN, phys. Rev. 101, 1455 (1956). 13. H. G. VAN BUEREN, Imperfections in C?y8taZs, p. 636. North-Holland Publishing Company, Amsterdam (1960). 14. J. N. HOBSTETTER, Semiconductora, Chapter 12, N. B. HANNAY, ed., Reinhold, N.Y. (1959). 15. J. N. HOBSTETTERand C. A. RENTON, J. AppZ. Phye. 33, 600 (1962). * Received Kovernber 1965.

19, 1964; revised February

16,

(4)

Measurements of D, are most sensitive to excess vacancies at low temperatures. Taking the energy of formation of a single vacancy in Ge to be 2.0 eV,(r2pi3) the concentration of vacancies in thermal equilibrium at 6OO”C., the lowest temperature employed in these experiments, is n, = 2.0 x 10n per cc. Thus, from equation (a), n, < 1On per cc. Accordingly, if straining o&uses diffusion enhancement in Ge through the production of excess single vacancies, the maximum concentration of such vacancies generated in these experiments is less than about lOi per cc. The results of electrical conductivity and Hall measurementso4,15) on deformed Ge specimens furnish strong evidence that vacancies and in~rstitials are introduced by plastic deformation, although an exact analysis of these measurements in terms of the concentration of defects is not feasible. It is likely, however, that vacancies introduced in Ge by deformation exist

Accelerated stress relaxation caused by an alternating magnetic field* The rate of stress relaxation, at constant strain, in nickel at room temperature can be increased by the application of a magnetic field alternating at 60 c/s. We first observed this effect in tension, but found it to be much more pronounced in bending. Figure 1 illustrates the experimental method and the nature of the observed effect. A ring of square section (8 x * in.), of 1.5 in. mean diameter, was machined from “A” nickel, which has a nominal total Ni + Co content of 99.4%, annealed for 30 min in vacua at 750°C, and furnace cooled. It was wound with a magnetizing coil as indicated and loaded in compression in an Instron machine of 200-lb capacity at a crosshead speed of 0.02 in./min. At a load somewhat above the proportional limit, the crosshead was

ACTA

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METALLURGICA,

Magnetic Field Crosshead

-

Turned On

stopped

I

--W.

\-

:

c

0

0 Def iection Fro.

Time

1. Effect of in altern&ing mragneticfield cm stress relaxation in a compressed nickel ring.

stopped. After normal stress relaxation had gone on for some S-10 see, an alternating current was turned on in the magnetizing winding. The rate of stress relaxation immediately increased, as indicated in Fig. 1. The size of the effect, as measured by the change in the slope d.Lldt of the relaxation curve, increases with increase in the intensity H of the applied magnetic field but not beyond a certain value of the field, about 11 oe. in these ex~riments. At this field the specimen is just beyond the knee of its ma~etization curve, and the magnetization is some 55 percent of the saturation value. The observed change in slope dL/dt is about 8 to 1, and the stress at the point A, the most highly stressed point in the ring, is 25,000 lb/in2 tension (17.6 kg/mm2). Relaxation tests in tension, compression, and torsion (of tubing) have also been made. The effect is small in tension and barely observable in compression and in torsion. That the effect is quite large in bending is presumably due to the fact that s fairly large change in deflection of the ring ~rres~nds to a small change in strain, and the indicated drop in load is actually

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1965

caused by a change in deflection, even though the crosshead is stopped. Bending experiments, however, have the disadvantage that the st,ress in the specimen is not uniform; the observed changes of load with time are therefore difficult to interpret in terms of more fundamental quantities. We ascribe the effect of an alternating field on stress relaxation to an interaction of moving domain walls with dislocations. Other phenomena which might cause the observed effect are: (1) Eddy-current heating. This causes thermal expansion, which in turn causes a decrease in load during a tensile relaxation test, but an increase in load during a test in axial compression or in compression of a ring. Thus, eddy current heating cannot be held responsible for the increased relaxation rate observed in the two latter kinds of test. Heating will also cause an increase in the rate of stress relaxation because this is a thermally activated process. However, if this were the only effect operating, one would have to invoke a temperature rise of several degrees to explain the observed eightfold change in relaxation rate, for any reasonable value of activation energy; this temperature rise would then produce, because of thermal expansion, an increase in the indicated compressive load more than sufficient to wipe out the decrease in load due to the increased relaxation rate. Since a decrease in load is observed (Fig. l), it cannot be due simply to a heating effect alone. (2) ~~e~~rnen ~~b~~t~~. Because of magnetostriction an alternating magnetic field will cause a specimen to alternately elongate and contract in a direction parallel to the field. Blaha and Langeneckero) have shown that ultrasonic vibrations can cause an abrupt stress relaxation in a tension test. It is therefore conceivable that magnetostrictive vibration of the specimen could accelerate stress relaxation, even though the frequency is far below ultrasonic. However, it is knownf2) that the ma~etostri~tion of nickel is increased in ma~itude by tension but decreased by compression; at a compressive stress of about 20,000 lb/in2 the magnetostriction becomes zero. These facts suggest that specimen vibration may have accelerated stress relaxation in the tension tests, but no such explanation can be advanced for the compression tests. The overall magnetostrictive deformation of a compressed ring cannot easily be predicted because the stress varies from tension to compression, not only across the section, but also around the eircumferenee. However, there is experimental evidence that the magne~strictive change in diameter of a Cornpressed ring is negligible: when a constant field was switched on, there was no change in the indicated load.

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We therefore believe that the observed effect is due, not to any magnetostriction of the specimen as a whole, but to the ma~etostrict~ve strain within domain walls. Because the magnetization changes direction within the wall, there must be a change in strain along any line passing through the wall. When the wall moves, this maximum, or minimum, of strain is oarried with it and can interact with the strain field of any waxy-pined dislocation the wall encounters. This interaction may be such as to relieve the stress which was pinning the dislocation. That dislocation then moves, making an extra contribution to the observed relaxation of applied stress. Although it seems intuitively evident that dislocations and domain walls must interact, the details of that interaction are far from clear. Vicenac3) ooneluded that there is an interaction and that it is due mainly to a change in the magnetoelastic energy. Scherpereel and Allenf4) considered the elastic, as well as the ma~etoelastic, energy of the system and concluded that there is no net interaction if the material inside the domain wall is free to deform magnetostrictively; if the material in the wall cannot deform freely but is held to the deformation of the adjoining domains, then there is an interaction. A real crystal presumably forms an intermediate case. If a magnetic field affects the rate of stress relaxation, it should also affect the creep rate. E’ranyuk(6) observed that the creep rate of nickel at 200% was increased by the application of an alternating or a ~n$~u~ magnetic field. Independently, we had tried to find an effect of an alternating field on the creep of mild steel and nickel, but with no clear-cut results. Part of this work was supported by the Office of Naval Research. B. D. CULLITY C. W. ALLEN Department of Metallurgical Engineering

and Materials Science UrGversity of Notre Dame Dame. Indiana

Natre

References F. BLAHA and B. LANGENICKER,Acta Met. 7, 93 (1969). H. KIRCHNER,Ann. Physik. 27, 49 (1936). (His date, we reproduced by RICHARD M. BOZORTH, Ferromqaetism, Fig. 13-53, Van Nostrand, N.Y., 1951). F. VICENA, Cm& J. Phys. 5, 480 (1964). of FerroDONALD E. SC~RPEREEL, “The In~r~tion magnetic Domain W&s and Disbcrstions”. Ph.D. thesis, directed by C. W. Allen. University of Notre D&me (1964). V. A. FRANYUK, DAN BSSR (Doklady, Academy of Sciences, BSSR), 8, 228 (1964). (Brief mention of these results is made by N. 6. AEULOV, PhiZ. Mug. 9, 767 (1964)). * Received January 28, 1965.

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recrystallization

in b.c.c.

metals*

Recently there has been an attempt to explain the preferred orientations occurring in cc uranium after transformation from ,8 at 660°C, by identifying the orientations which grow fastest with those in which strains due to vacancy collapse and/or dislocation climb can minimise the transformation stress.(r) It is of interest to see whether similar ideas can be applied to explain either primary recrystallization textures or the large grained secondary recrystallization textures which follow grain growth. In this context recrystallization is viewed simply as a phase change to a more dense structure. In a cold worked metal it is likely that vacancies will be removed largely by climbing edge dislocations. The assumption is that the removal of vacancies in this way is the rate-controlling step in the growth of new recrystallized grams (there is some evidence for this in the experiments of H@) and Walter.~3)) The orientations of recrystallization nuclei which will be best equipped to remove vacancies by climb will be those of highest edge dislocation density. Dislocation climb produces strain in the direction of the Burgers vector and since, in a thin sheet, strain normal to the sheet can most easily be accommodated, grains in which the total strain along all (111)‘s due to climb has a maximum resolved value normal to the sheet, oan be expected to be those in which climb is fastest. Thus orientations which satisfy this condition and also have a high dislocation density can be expected to be important in the recrystallization texture. It may be, therefore, that if sufficient were known about edge dislocation populations in cold worked b.c.c. metals, predictions of recrystallization textures according to this method would be possible. Some features of abnormal grain growth in silicon iron can now be qualitatively explained if this model is assumed. Precipitates of MnS or S&N4 are known to play an important part in producing the (110) [OOlJ orientation.(~*5) The vacancies supplied by solution of these precipitates will be most easily absorbed by climb in grains of favourable orientations which will be able to keep a low vacancy supersaturation. There will, therefore, be a driving force for their growth and because precipitates will dissolve preferentially in them, the movement of their boundaries will be relatively easy. This may explain why the solution and agglomeration of particles of MnS or S&N, have the same kinetics as grain growth.c6) Another unusual feature of the development of