SmallAngle Scattering of XRays from Neutron Irradiated CopperH. H. Atkinson, R. E. Smallman, and K. H. Westmacott Citation: Journal of Applied Physics 30, 646 (1959); doi: 10.1063/1.1735208 View online: http://dx.doi.org/10.1063/1.1735208 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/30/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Smallangle xray scattering from amorphous polycarbonate J. Appl. Phys. 44, 4288 (1973); 10.1063/1.1661953 SmallAngle Scattering of XRays by NeutronIrradiated Germanium J. Appl. Phys. 39, 4509 (1968); 10.1063/1.1655794 SmallAngle XRay Scattering from Glassy Carbon J. Appl. Phys. 39, 1840 (1968); 10.1063/1.1656439 SmallAngle XRay Scattering from Rods and Platelets J. Math. Phys. 7, 1295 (1966); 10.1063/1.1705032 SmallAngle Scattering of XRays and Neutrons from Deformed Metals J. Appl. Phys. 30, 637 (1959); 10.1063/1.1735207

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JOURNAL OF APPLIED PHYSICS VOLUME 30, NUMBER 5 MAY, 1959

Small-Angle Scattering of X-Rays from Neutron Irradiated Copper

H. H. ATKINSON,* Crystallographic Laboratory, Cavendish Laboratory, Cambridge, England

AND

R. E. SMALLMANt AND K. H. WESTMACOTT, Mettalurgy Division, Atomic Energy Research Establishment, Harwell, England

The scattering of x-rays at small angles from polycrystalline copper is found to increase when the recrystal­lized metal is bombarded with fast neutrons. The observed effects above 2° are due to double Bragg reflec­tions; below about 1!0 they can be explained in terms both of double reflections and "true" small-angle scattering. The results indicate that either small coherent regions (of diameter about 100 A) or severe strains are present in the irradiated meta!' The results are consistent with other measurements (particularly of mechanical properties) on irradiated metals.

1. INTRODUCTION

WHEN a piece of metal, e.g. copper, is bombarded with fast neutrons in a nuclear reactor, its prop­

erties are altered. The metal becomes harder (see Fig. 1), may show a

yield phenomenon, and has a large dependence of yield stress on temperature. The slip lines become of the coarse, sharply defined, and clustered type and the deformation texture characteristics change from those typical of pure copper to those of a low alloy content brass. Large changes also occur in the electrical resis­tivity and internal friction properties. (For review see Cottrell.l)

The nature of the damage is as yet incompletely understood but all explanations arise from the excess of point defects (both vacancies and interstitials) created by the bombardment. Other defects such as "thermal" and "displacement" spikes have been suggested but evidence, at least in nonfissile metals, has not been forthcoming so far. It seems reasonably well established that some of these defects migrate to and pin disloca­tions resulting in suppression of dislocation damping. However, the extent of defect clustering in metals is still unknown. Consequently, it was considered worth­while to study neutron irradiated metals using a small­angle scattering technique.

2. X-RAY SMALL-ANGLE SCATTERING

The small-angle scattering from pile-irradiated poly­crystalline metals has been examined using both the point-focusing and line-focusing instruments described by Atkinson and by Smallman and Westmacott,2 respectively, elsewhere in these proceedings. In all cases the metals were recrystallized before being irradiated

* Now at the Atomic Energy Research Establishment, Harwell England. '

t ~o~ at the D.ep~rtment of Physical Metallurgy, University of Blrmmgham, Blrmmgham, England.

I A. H. Cottrell, Institute of Metals Monograph Rept. Ser N 23 (1957). ' . .

2 R. E. Smallman and K. H. Westmacott J. App!. Phys 30 603 (1959). ,. . ,

in the Harwell BEPO (low dose) or DIDO (high dose) reactors.

The first specimens examined were copper, nickel, and aluminum foils (thickness 30 Ji,) which had been subjected to an integrated flux of 1019 neutrons cm-2•

The scattering from the recrystallized control and the irradiated samples was found to be the same over the angular range 10 to 6° within the experimental error, 40 electrons per atom. This result enables a lower limit to be set for the product of size and concentration of defects introduced by the radiation damage. If the defects are voids each about 100 atomic volumes in size, then the concentration is less than 5 X 1017 cm-s. If the size is smaller than this, then a much greater con­centration of defects would have gone undetected.

However, the scattering from copper irradiated to a higher dose (8X1019 n cm-2) is observable and is shown in Fig. 2(a) (exposure in this and all succeeding photo­graphs, 24 hours). The grains of this metal have strong preferred orientations and examination of the single Bragg reflections occuring shows that the small-angle streaks are due to double Bragg reflections. It appears

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02301234 % ELONGATION

FIG. 1: Effect of irradiation on strength of polycrystalline copper (unpublished work M. A. Adams and P. B. Higgins). 1. Unirradi­ated poly crystalline copper. 2. Irradiated (2X 1018 n cm-2)

polycrystalline copper.

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SMA L L - A N G L ESC A T T E R I N G FRO M N E U T RON I R R A D I ATE D C u 647

(a) (b)

FIG. 2. Small-angle scattering from irradiated polycrystalline copper with strong preferred orientations. Orientation of foil in (al is a few degrees different to that in (b).

that the radiation damage, by giving rise to some physical broadening of the reflections, greatly increases the probability of double Bragg reflections compared to that from the original recrystallized specimen which, in the same orientation, showed (in photograph not re­produced here) only one or two sharp spots due to double reflections in the same general region as the streaks.

The double reflections contributing to any particular streak occur from one grain to another in the same preferred direction, different pairs of grains giving rise to the different "blobs" which can be seen on the streaks. This explanation has been confirmed by chang­ing the orientation of the foil by a few degrees to shift most of the grains from reflecting positions: the double reflections to a large extent disappear, as can be seen in Fig. 2(b). In this orientation the only scattering above the smallest observable angle, It°, consists of a few blobs obviously due to double reflections.

Further observations have been made with the point­focusing instrument re-adjusted so that measurements could be made down to 50' (the intensity of the direct beam was halved by this modification). Copper with a more random grain orientation was used. The scattering from recrystallized and irradiated (8X 1019 n cm-2)

specimens of this material is shown in Figs. 3(a) and (b).

(a)

It is seen that substantial small-angle scattering occurs from the irradiated metal. To see that this effect was not due to mishandling of the specimen, a control un­irradiated sample was deliberately bent several times and its surface abraded, introducing much more defor­mation than could possibly have occured mechanically to the irradiated specimen. The scattering from this specimen [Fig. 3(c)] is considerably less than that from the irradiated metal. Therefore it appears that most of the small-angle scattering from the latter resulted from the neutron irradiation.

However, it is more difficult to determine whether the effect is due to true small-angle scattering or double Bragg scattering. The texture of this particular foil makes it unlikely that double reflections occur from one grain to another at smaller scattering angles; in fact only one such reflection (at about 4° at A) can be seen in these pictures. Thus, if the scattering is due to double reflections, they must occur within a single grain.

On the other hand, the approximately cylindrically symmetrical scattering observed is also consistent with true small-angle scattering from randomly oriented defects. If this interpretation is accepted, the size and number of defects can be deduced from the shape of the scattering curve. This curve has been measured for scattering angles !o to 6° using a Geiger counter, for a specimen of the same type of copper, damaged by 1021 n cm-2, and is shown in Fig. 4. Negligible scattering is observed above 2°. On low-temperature annealing (100-200°C) the scattering increased slightly, but on further annealing to 450-500°C it disappeared completely.

3. INTERPRETATION

The various forms of defect which might have been introduced by the irradiation may be summarized as (a) dislocations, (b) aggregates of point defects, and (c) disturbed regions in which the density is different to the surrounding crystal.

Since intensity scattered into the small-angle region may arise either from differences in electron density or

(e)

FIG. 3. Small-angle scattering from polycrystalline copper with randomly orientated grains; (a) recrystallized, (b) irradiated, and (cl mishandled.

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648 ATKINSON, SMALLMAN, AND WESTMACOTT

50-

>-I-U1 Z w I-~ l!) 0

'0 ..J

0

! 5 -- 10

(2 x 104 (RADIANS) 15

FIG. 4. Log I versus E2

plot for irradiated poly­crystalline copper.

by the mechanism of double Bragg reflections the source of scattering for both processes must be examined. Considering first true small-angle scattering, it is un­likely from the magnitude of the scattered intensity that "jogged" dislocations or dislocation loops, formed by the collapse of aggregated vacancy disks, could be responsible. One of the more obvious sources of radia­tion hardening would be the formation, by point defect diffusion, of groups of vacancies or interstitials, dis­tributed randomly throughout the lattice. Analysis of the scattered intensity curve shows that the radius of gyration of the scattering groups is about 24 A. If these are spherical cavities then the scattering observed for the most heavily irradiated specimen could be accounted for by a concentration of about 1015 per cma• A group of interstitials would scatter less and a greater concentration would be required in this case. The observations could also be accounted for by one of the more complex pictures of damage as envisaged by Brinkman3 or Seeger.4 Brinkman pictures the main feature of the damage to be a displacement spike created by a fast knock-on particle. In its early stages this consists of three regions, one containing an excess of vacancies, a surrounding shell of undisturbed metal, followed by a further region containing an excess of interstitials. Under the pressure exerted by the inter­stitials the cavity created by the vacancies is filled up with atoms and the original lattice is to some extent restored. The final size of the disturbed region is not known but could well be of the order of 10 to 100 A in diameter. In Seeger's picture the central hole is replaced by a region of approximately the same size, or somewhat smaller in which a considerable fraction of the atoms (20 to 30%) are missing. The disturbed region in this case is produced by atoms being "shot-out" as dynamic crowdions and therefore could not be restored as easily as the disturbed regions envisaged by Brinkman.

If we now consider that the scattering arises from double Bragg reflections these could originate either

3 J. A. Brinkman, J. App\. Phys. 25, 961 (1954). 4 A. Seeger, "Theory of radiation damage and radiation

hardening" (to be published).

from misorientations introduced into the lattice or by the formation of small regions (or strains) which pro­duce physical broadening of each reflection. From Fig. 3 (b) the magnitude of the effects can be estimated. In this case, the result of pile irradiation must be such as to produce, within one grain, either lattice misorien­tation of up to 1° or damage giving rise to a physical broadening (at each reflection) of about 1°.

The jogging of dislocations will not produce much increase in double Bragg scattering but newly formed dislocations in the form of loops, etc., could. :Moreover, groups of aggregated point defects formed by diffusion of vacancies or interstitials, and small regions of dis­turbed lattice, if they are of diameter about 100 A, could give rise to physical broadening of reflections, resulting in scattering at angles up to about 1°.

Thus the interpretation both in terms of true smaIl­angle scattering and double Bragg reflection processes leads to the conclusion that the irradiated metal con­tains small aggregates (or disturbed regions), although the possibility of double reflections resulting from strains associated with groups of interstitials or newly created dislocations is not ruled out. An unambiguous interpretation is only possible using suitably orientated single crystals.

4. ADDITIONAL EVIDENCE

Although the x-ray experiments done so far do not allow conclusions as to the exact nature of irradiation damage, it is worthwhile considering them in conjunc­tion with other evidence. For example the existence of newly formed dislocations should be evident using thin film transmission electron microscopy. However, in the preliminary observations made so far on copper no obvious changes had occurred on irradiation. It was noticed, however, that etching and contamination rates in the microscope were very much altered after irradia­tion. This together with poor resolution of the instru­ment prevented any decision being made on the existence of regions 100 A or less. Newly found dislocation loops have been observed in irradiated aluminum.2

1\1 uch work has been done to study the effects of irradiation on mechanical properties and consideration of this as made by Seeger4 might eliminate certain models of damage. For example, the observation of Blewitt and co-workers5 that the increase in shear stress is apparently independent of the temperature of irradia­tion (down to 200K) would seem to rule out the possi­bility of groups of vacancies or interstitials formed by diffusion being responsible. The formation of cavities on dislocations as proposed by Coulomb and Friedel6 is also eliminated for this reason and also because this mechanism is expected to cause hardening which is virtually independent of the temperature of testing.

6 T. H. Blewitt (private communication). 6 P. Coulomb and J. Friedel, Dislocations and Mechanical

Properties of Crystals (John Wiley & Sons, Inc., New York, 1957), p.555.

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SMA L L - A N G L ESC A T T E R I N G FRO M N E U T RON I R R A D I ATE D C u 649

However, this observation requires verification but nevertheless it does not eliminate the formation of "zones" of disturbed lattice as proposed by Brinkman or Seeger to account for the major portion of the irradia­tion hardness. This view is enhanced by recent mechani­cal property measurements made at Atomic Energy Research Establishment (Harwell) (see previous paper by R. E. Smallman and K. H. Westmacott,2 Sec. 6). From an examination of the variation in lower yield stress with grain size in irradiated copper specimens it seems that a definite lattice "friction" hardening (im­pedance by groups of defects or disturbed zones, to dislocations moving across slip planes) does occur.

5. CONCLUSIONS

The scattering of x-rays at small angles from poly­crystalline copper is found to increase when the re­crystallized metal is bombarded with fast neutrons. At angles above about 2°, the observed scattering is clearly due to double reflections from one grain to another. However, between 30' and 1tO considerable-approxi-

JOURNAL OF APpLIED PHVSICS

mat ely circularly symmetrical-scattering occurs even from specimens of texture such that grain-to-grain reflections do not occur at small angles. Interpretation of the latter effect in terms of true small-angle and double Bragg scattering both lead to the conclusion that irradiation results in small coherent regions of diameter about 100 A. The effect could also be due to double Bragg reflections resulting from large lattice strains; these strains may be associated with newly formed dislocations or clusters of interstitials. Further experiments, using single crystals, are being carried out to eliminate the possibility of double Bragg reflections.

ACKNOWLEDGMENTS

The authors wish to thank Professor N. F. Mott, Dr. H .. M. Finniston, and Professor A. H. Cottrell, for continued interest in this work, and, especially, Dr. P. B. Hirsch for suggesting the problem to one of us (H.H.A.) and for many valuable discussions. One of the authors (H.H.A.) also wishes to thank I.e.I. for the award of a maintenance grant.

VOLUME 30. NUMBER 5 MAV. 1959

Study of X-Ray Scattering from Fatigued Metals

K. THOMAS AND A. FRANKS

National Physical Laboratory, Metallurgy Dh'ision, Teddington, Middlesex, England

Various explanations have been put forward to account for the low angle x-ray scattering from cold worked metals. The experimental results obtained by an examination of individual grains of polycrystalline fatigue specimens indicate that double Bragg reflection plays an important role in this phenomenon. The fatigue process resulted in the formation of subgrains, the misorientations within a grain amounting to 15°.

I. INTRODUCTION

T HE low angle x-ray scatt.ering from ~old worked metalsl- 6 has been ascnbed to vanous causes,

which have been outlined in a previous paper.7 It is important to decide experimentally whether or not sub­microscopic cavities are formed in the bulk of the metal. Various dislocation models have been put for­ward for the production of vacancies which could then aggregate to form cavities; this process would be most likely to occur in fatigued specimens. To investigate this a detailed study has been made of individual grains of fatigued polycrystalline metal foils using an optically focusing low angle scattering camera. 8

I J. Blin and A. Guinier, Compt. rend. 233, 1288 (1951). 2 A. Franks and J. Holden, Nature 176, 1022 (1955). a Y. Y. Li and R. Smoluchowski, J. App!. Phys. 26, 128 (1955). 4 W. W. Beeman et al., Handbuch der Physik (Springer-Verlag,

Berlin, 1957), Vo!' 32, p. 440. S J. Blin, Acta Met. 5, 528 (1957). 6 A. Seeger, Acta Met. 5, 24 (1957). 7 A. Franks and K. Thomas, Proc. Phys. Soc. (London) 71,

861 (1958). 8 A. Franks, Brit. J. App!. Phys. 9, 349 (1958).

In Sec. II the experimental technique is outlined. In Sec. IlIA it is shown that the earlier results were ex­plicable by either the presence of cavities or a process of double Bragg scattering. The discussion of the cavity model could have more general application to other problems. In the consideration of double Bragg scattering two possible forms are mentioned besides that applying to the present work. In Sec. IIIB further experiments are described which showed that double Bragg scattering, not cavities, was the explanation of the low angle scattering observed. Further experimental work is considered in Sec. IIIe. Short discussions of low angle scattering, and of the fatigue process at high stresses, conclude the paper.

II. EXPERIMENTAL TECHNIQUE

A. Specimen Preparation

Specimens were prepared from foils of spectroscopi­cally pure copper and aluminum, supplied by Johnson Matthey and Company, Ltd. The copper was 0.005 cm thick and the aluminum 0.0025 em. Specimens of the

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