Recovery of cold-work in extruded Zr-2.5 wt% Nb

Journal of Nuclear Materials 59 (1976) 234-242 0 North-Holland Publishing Company

RECOVERY OF COLD-WORK IN EXTRUDED Zr-2.5 WT% Nb R.A. HOLT Atomic Energy of Canada Limited, Chalk River Nuclear Laboratories, Fuels and Materials Division, Chalk River, Ontario, Canada

Received 25 June 1975 Revised form received 8 December 1975

X-ray line broadening measurements and electron microscopy have been used to characterize the dislocation substructures in extruded. cold-worked and stress relieved Zr-2.5 wt% Nb pressure tube materials. Variation in dislocation substructure deduced from the X-ray line broadening measurements give good agreement with thin film observations. Recovery of cold-work occurs in three “stages” in Zr-2.5 wt% Nb. Between 575 and 725 K the dislocation density decreases from -1 .5-l .8 X 10” mm2 to 23-4 X 1014 m-’ with little change in sub-grain size or dislocation arrangement below 725 K. From 725 K to 875 K the sub-grain size increases from < 100 nm to -400 nm while the dislocation density decreases slowly to = 1.4-1.7 X lOI rne2. Above 875 K the sub-grain size increases to 2800 nm, some grain growth occurs and only a few well defined dislocation networks remain. As-extruded Zr-2.5 wt% Nb has a. sub-grain size of m600 nm and a dislocation density of =8 X 1013 rne2. The implications of the measurements are discussed. Des mesures d’&rgissement de pits de diffraction X et la microscopic 6lectronique ont it& utilisees pour caractiriser les sous-structures de dislocations dans les matiriaux pour tubes de force en alliage Zr-Nb i 2,5% (en poids) extrud6, &roui i froid et soumis i des recuits de d6tente. Les modifications subies par la sous-structure de dislocations d6duites des mesures d’klargissement des pits de diffraction X sont en bon accord avec les observations de films minces en microscopic ilectronique. La restauration de l’6tat Bcrouise produit en trois “stades” dans l’alliane Zr-Nb 2,5%. Entre 575 et 725 K la densit de dislocations diminue de = 1,5-1,8 X 10” m-’ i =3-4 X 1014 me2 avec un faible changement dans la taille des sousgrains ou dans l’arrangement des dislocations en dessous de 725 K. De 725 K i 875 K la taille des sousgrains augmente de < 100 nm i a400 nm, tandis que la densit& des dislocation diminue lentement jusqu’h atteindre 1,4-l ,7 X 1014 m-‘. En dessus de 875 K la taille des sous-grains augmente jusqu’i > 800 nm, il se produit une croissance du grain et il subsiste seulement quelques r& seaux de dislocations bien dbfinis. L’alliage Zr-Nb 2,5% brut d’extrusion a une taille de sous-grains de 13600 nm et une densit de dislocations de = 8 X 1013 m-*. Les cons&+ences de ces mesures sont discutees. An stranggepressten, kaltverformten und spannungsfrei gegliihten Zr-2,5% Nb-Druckriihren wurden die Versetzungssubstrukturen elektronenmikroskopisch und durch Messung der Rijntgenlinienverbreiterung bestimmt. VerInderungen der Versetzungssubstrukturen, die sich aus Messungen der R6ntgenlinienverbreiterung ergeben, stehen in guter ubereinstimmung mit den Beobachtungen an diinnen Schichten. Die Erholung der Kaltverformung in Zr-2,5% Nb erfolgt in drei Stufen. Zwischen 575 und 725 K nimmt die Versetzungsdichte von 1,s bis 1,8 X 10”/m2 auf 3 bis 4 X 1014/m2 ab; dabei lndert sich die SubkorngrGsse oder Versetzungsanordnung unterhalb 725 K nur wenig. Zwischen 725 und 875 K steigt die Subkorngrijsse von < 100 nm auf etwa 400 nm an, wlhrend die Versetzungsdichte langsam auf 1,4 bis 1,7 X 1014/m2 ‘abrdlt. Oberhalb 875 K nimmt die Subkorngrasse auf > 800 nm zu, betrIchtliches Kornwachstum tritt auf und wenige, gut definierte Versetzungsnetzwerke bleiben iibrig. Stranggepresstes Zr -2,5% Nb hat eine SubkorngrGsse von etwa 600 nm und eine Versetzungsdichte von etwa 8 X 1013/m2. Die Folgerungen aus diesen Messungen werden diskutiert.

1. Introduction

of extruding tube shells at 1120 K, air cooling, cold drawing about 20-30% and stress relieving for 24 h at 675 K. Recent experiments have shown that cold-work is detrimental to in-reactor creep at 575 K [2]; asextruded material creeps more slowly than cold-worked and stress-relieved material. Cold-work enhances irra-

Zr-2.5 wt% Nb was selected as a strong creep resistant alloy to replace Zircaloy-2 for pressure tubes in CANDU * reactors [ 11. The fabrication route consists

* CANada Deuterium Uranium 234

R.A. Holt 1 Recovery of cold-work in extruded Zr-2.5 wt%Nb

diation growth of zirconium alloys and dimensional changes occur during recovery [3]. These effects are probably related to the density and distribution of dislocations, and thus characterization of dislocation substructures in these materials is important. Previous studies of recovery of cold-work in Zr-2.5 wt% Nb have dealt with material with a larger grain size than is found in pressure tube extrusions [4,5]. The workers have relied extensively on mechanical property measurements. They have concluded that recovery occurs simultaneously with aging and thus the detail of the recovery process is masked. Aldridge and Cheadle studied the aging process separately using extruded and annealed materials [6]. In the present work the recovery process has been isolated by the use of X-ray line broadening measurements and thin film electron microscopy.

2. Experimental 2. I. Material

The material used in this study was taken from an extruded Zr-2.5 wt% Nb pressure tube shell (2.3-2.7 wt% Nb, 1000-1400 ppm 0). The material was coldworked 20 and 40% by rolling flat in the longitudinal direction. Cold-worked specimens were given isochronal anneals for 2 h at temperatures between 575 K and 975 K at 50 K intervals (cumulative treatments). After each stage the specimens were examined by X-ray line broadening.

235

the Stokes method [8] using the UOiO) and 12020) peaks from well annealed crystal bar zirconium sheet. Fourier strains and particle size coefficients were calculated by the method of Warren and Averbach [9]. 2.3. Thin films Thin slices were cut in transverse section from the 20% cold-worked material and after heating at 725, 825,875,925 and 975 K. These were thinned by standard techniques and examined in a Hitachi 200 kV electron microscope.

3. Results The coherent diffracting domain size can be determined directly from the (lOi peaks of hexagonal metals since these are not affected by stacking fault broadening [7]. The coherent diffracting domain sizes were determined as the negative slope of the plot of Fourier particle size coefficients against lattice distance after the ‘hook effect’ had died out “s recommended by Wagner [7] (fig. 1). The Fourier lattice strains sometimes showed low values at small lattice distances and fluctuations at large lattice distances (fig. 1). These effects can be attributed to difficulties in resolving the long tails of broadened peaks and peak asymmetry [7, lo]. The lattice strains at 15 and 20 nm were averaged to obtain a representative value for each specimen which would be least affected by these errors.

2.2. Line broadening measurements The extrusion and cold worked materials had a (1 OiO) fibre texture with a high density of El030) poles in the longitudinal direction. This allowed strong second order I20101 reflections to be recorded. A GE diffractometer was used with CuK radiation and a scanning speed of 0.1” (20) per minute. The output was recorded on charts and intensity values were read at intervals and then analyzed by computer. Corrections were made for background, polarization, and K,r/K,, asymmetry by the methods described by Wagner [7]. Fourier coefficients were calculated for the peaks and corrections for the contribution of instrumental broadening to peak width were made by

Y

LATTICE DISTANCE nm

Fig. 1. Particle size coefficient and lattice strain vs distance for 20% cold-worked material, after heating 2h at 775 K, showing, 1) The “Hook effect”, 2) Low values of lattice strain at small distances, and 3) Fluctuations in lattice strain at large distances.

236

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R.A. Holt /Recovery

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AS-EXTRUDED

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900

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600

700

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600

900

TEMPERATURE.

K

’

1000

Fig. 2. Variation in lattice strain with annealing temperature in Zr-2.5% Nb alloy.

20% IO0

COLD

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A AS-COLD l

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WORKEO

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A

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700

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900

1000

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WORK WORKED

0 AS-EXTRUDED

TEMPERATURE.

K

Fig. 3. Variation in coherent diffracting domain size with ing temperature in Zr-2.5% Nb alloy.

anneal-

Zr-2.5 wt% Nb

The values of lattice strain and coherent diffracting domain size are plotted as a function of annealing temperature in figs. 2 and 3. The lattice strain and coherent diffracting domain size of the as-extruded material are also given in figs. 2 and 3. After heating at 925 K the 40% cold-worked material showed negative strains at all lattice distances. This can only result from experimental error and the lattice strain for this treatment has been taken to be zero within the limits of experimental error. The coherent diffracting domain size for this treatment was calculated from the Fourier coefficients of both { lOi and (2020) peaks assuming that broadening was entirely due to small particle size. These lattice strains and coherent diffracting domain sizes are for the longitudinal direction. Since the material has a strong crystallographic texture this represents a large sample of grains. Lattice strain and coherent diffracting domain size are approximately isotropic (~25% variation) with respect to crystallographic direction in o-zirconium fillings [ 1 l] and anisotropy of these quantities is generally small (less than a factor of two) even for materials with much greater elastic anisotropy than o-zirconium [ 121. Thus it is reasonable to assume that the measurements reported here are representative of the bulk. Electron micrographs of representative areas of the 20% cold-worked material after various treatments are shown in figs. 4 and 5. The cold-worked material had a high dislocation density with the dislocations arranged in tangled cell walls (fig. 4A). The dark phase at the alpha grain boundaries is retained pZr. After heating at 725 K the dislocation density appeared to be reduced within the cells and the cell walls were more clearly defined. A few regular networks and some decomposition of the retained /3Zrwas observed (fig. 4B). After heating at 825 K the sub-boundaries were better defined with more regular networks. The pZr had decomposed to discrete particles at the grain boundaries (fig. 4C). After heating at 875 K a small proportion of the grains were almost strain-free. The second phase had coalesced at the grain corners and the OL grains had become much more equiaxed (fig. 5A). Heating at 925 K resulted in some grain growth and a large reduction in the number of subgrain boundaries. Many of the grains still contained some dislocations, however, mostly in the form of well defined networks (fig. 5B). After heating at 975 K the structure looked

Fig. 5. Electron micrographs of 20% cold-worked Zr-2.5 wt% Nb. A, heated for 2 h at 875 K showing coalescence of beta phase at grain corners and substructure-free subgrains; B, heated for 2 h at 925 K showing grain growth and a few well defined dislocation networks; C, heated for 2 h at 975 K showing grain growth. Reduced 1.6 times in reproduction.

Fii. 4. Electron micrographs of 20% cold-worked Zr-2.5 wt% Nb. A, as cold-worked showing retained beta Zr (dark phase at w grain boundaries) and non-uniform distribution of dislocations; B, heated for 2 h at 725 K showing formation of cell boundaries; C, heated for 2 h at 825 K showing well defined sub-boundaries and decomposition of beta phase. Reduced 1.6 times in reproduction.

238

R.A. Holt j Recovery of cold-work in extruded Zr-2.5 wt% Nb

similar with further increase in grain size and reduction in the number of dislocation networks (fig. SC).

4. Discussion 4.1. Grain structures and phase distribution The (Ygrain structures are typical of those observed in transverse sections of Zr-2.5 wt% Nb pressure tubes and pressure tube extrusions. In longitudinal sections the (Ygrains are much elongated as shown in fig. 6. The changes which occur in the &r phase on heating have been reported by Cheadle and Aldridge [ 131. Below the monotectoid temperature the &r phase eventually breaks down to (Yt f&, and the &, phase occurs as discrete particles at the (Ygrain boundaries. As observed in fig. 3C this process is almost complete after heating at 825 K. 875 K is above the monotectoid for this material and after heating at this temperature the (II+ f3m has reverted to &r which has coalesced at the grain corners. This allows some movement of the LY grain boundaries and the grains start to grow and become more equiaxed. 4.2. Dislocation structures The dislocation density can be calculated from the lattice strain or from the coherent diffracting domain

Fig. 6. Electron micrograph of a Zr-2.5 wt% Nb pressure tube extrusion showing elongated alpha grains and well defined sub-boundaries.

size [14] by pg = 3n/D2

p, = K(e2)/d2

,

where p. is the dislocation density calculated from domain size, pE is the dislocation density calculated from the lattice strain, n is a geometric factor, D is the coherent diffracting domain size, K is a geometric factor, E is the latticestrain, d is the interplanar spacing of the lattice. The value of K was taken as 10 after Aqua and Owens [14]. This assumes that the dislocation strain fields have a spatial distribution between Cauchy and Gaussian, that the strain fields extend about 50 nm and that the radius of the dislocation core is about 1 nm [ 1.51. The value of n was taken as 1 after Williamson and Smallman [ 151. Both these calculations assume a random spatial distribution of dislocations and if this is true will give approximately equal values for the dislocation density. When p, > pg, a piled up configuration exists and if p, < PD a polygonized cell structure exists [ 161. The values of pD and pE are given in table 1. For the 40% cold-worked material heated’at 925 K a maximum possible value of lattice strain was taken as 0.0002 for the purposes of estimating an upper limit for dislocation density. The increase in lattice strain observed in both 20 and 40% coldworked materials after heating at 975 K is obviously not due to an increase in dislocation density. It may result from volume changes due to the redistribution of phases on heating and cooling through the lower part of the two phase field. Thus the values of pE for the final heat-treatment are upper limits. The conclusions are in good agreement with the electron microscope observations. These are: The as-extruded material has a highly polygonized sub-structure. The dislocation distribution in the cold-worked materials is not random but some form of cell structure exists in which the strain fields of the dislocations cancel one another. After heating at 725 K the dislocation distribution becomes more polygonized and further polygonization occure between 775 and 875 K. The substructure is highly polygonized with well defined networks after heating at 925 K. When the dislocation substructure is polygonized the dislocation strain fields cancel each other and thus p, underestimates the true dislocation density by a factor of ln (r,/r,-,) + In (r/ro) where r is the di-

R.A. Holt /Recovery of cold-work in extruded Zr-2.5 wt% Nb

239

Table 1 Calculated dislocation densities for Zr-2.5 wt% Nb alloy Condition

P, Cm -*

Asextruded 20% cold-worked 40% cold-worked 20% cold-worked 20% cold-worked 20% cold-worked 20% cold-worked 20% cold-worked 20% cold-worked 20% cold-worked 20% cold-worked 20% cold-worked 40% cold-worked 40% cold-worked 40% cold-worked 40% cold-worked 40% cold-worked 40% cold-worked 40% cold-worked 40% cold-worked 40% cold-worked

0.6 11 12 8.7 8.5 6.2 2.4 1.7 1.8 1.3 0.3 < 0.6 11 9.1 6.1 2.8 2.5 1.0 1.1 < 0.1 < 0.4

+ 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at + 2 h at

515 625 675 125 175 825 875 925 975 515 625 615 725 115 825 875 925 975

K K K K K K K K K K K K K K K K K K

x

10_14)

mension previously assumed for the extent of the dislocation strain field (50 nm), r. is the radius assumed for the core of the dislocation (1 nm), and rc is the radius at which the strain fields cancel [ 151. Taking D as the mean spacing of dislocations [12] the true dislocation density, p, can be estimated by m (r/r,) ’ = ‘c In (D/2ro)

’

The values of p are given in fig. 7. Assuming that most of the dislocations are in cell walls and that the sub-grains are equiaxed then the sub-grain size, d, is: d= -?-

phtA

’

where h is the spacing of dislocations in the cell walls, is the area of grain boundary per unit volume and must be included when the subgrain size approaches the grain size since many subgrains will be bounded by grain boundaries. With flat elongated grams

A

A-

wltwtl wlt

’

PD cm -*x 22 31 36 36 25 21 18 20 20 14 10 4.5 44 23 20 20 20 19 17 14 2.5

10_14)

PDlPe 31 2.8 3.0 4.1 2.9 3.4 1.5 12 11 11 33 > 1.5 4.0 2.5 3.3 7.1 8.0 19 15 >140 > 6.3

where w and 1are the aspect ratios of the grains in the width and length directions respectively and t is the thickness. Values of w and 1 for extruded Zr-2.5 wt% Nb are 2-6 and 16-40 respectively [2] and t was measured for this material as 0.8 pm. This gives values of A between 1.5 and 2.0 X lo6 m-l. To estimate the subgrain size it was assumed that A = 1.7 X lo6 m-l and that h is approximated by D, the coherent diffracting domain size. Since the grain growth is relatively slow up to 925 K (compare figs. 5B and 4A) the error in A, the grain boundary area per unit volume, should be small up to 925 K. The subgrain sizes are shown in fig. 8. Subgrain sizes measured from thin films for a typical extrusion and the 20% cold-worked material after heating at 825 and 925 K are included. The recovery process has three stages. At low temperatures (575-725 K) a large reduction in dislocation density occurs, with little change in the dislocation arrangement. At intermediate temperatures (725-875 K) the dislocations rearrange with only a small decrease in dislocation density. Above 875 K sub-grain growth is rapid leaving a few well defined dislocation networks. Below 875 K recovery takes

R. A. Holt /Recovery

240

I4

20%

12

l

COLD

o.f cold-work in extruded

Zr-2.5 wt% Nh

WORK 20%

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WORK

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A

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400

A

A

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A 200

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0

100

I AS

I

600

RECEIVED

I

700

I

800

TEMPERATURE.

1

J

900

1000

K

Fii.8. Variation in subgrain size with annealing temperature in Zr-2.5% Nb alloy.

5. Implications TEMPERATURE.

K

Fig. 7. Variation in dislocation density with annealing temperature in Zr-2.5% Nb alloy.

place within the existing a-grains as defined by the grain boundary &phase and must occur entirely by climb and glide processes. Due to the shape of the grains the dislocation motion is limited to two dimensions. This may contribute to the relative stability of the partially recovered substructure up to 875 K much in the same way as the grain size in thin sheets becomes stable when it approaches the sheet thickness. At 875 K the grain boundary phase reverts to /3Zr which coalesces at the grain corners. This allows some grain boundary migration, and recovery proceeds again more rapidly. It is not clear whether the transformation temperature is coincident with an increase in dislocation mobility or whether the increased rate results entirely from the coalescense of the grain boundary network.

The Zr-2.5 wt% Nb pressure tubes currently used in CANDU reactors are cold drawn in the range 20-30% and subsequently stress-relieved at 675 K for 24 hours. The present work suggests that this wiI1 result in dislocation densities ~3-8 X 1014 mW2,i.e. the levels observed between 675 K and the beginning of the plateau of the recovery curve at 725 K. This is higher than the level observed in extruded material, i.e., 0.8 X 1014 mB2. The relationship between yield and dislocation density is [ 171: oY = o. + mcuGb& , where u,, is the yield stress, u. is the yield stress at zero dislocation density, m is an orientation constant taken as 2 after Aqua and Owens [ 141, OLis a geometric factor taken as 0.28 after Aqua and Owens [ 141, G is the shear modulus taken as 27 GN/m2 at 575 K after Northwood et al. [ 181, p is the total dislocation density. The yield stress of fully annealed sponge zirconium at 575 K can be estimated from the work of Coleman

R.A. Hoit /Recovery of cold-work in extruded Zr-2.S wt% Nb Table 2 Longitudinal yield stresses for extruded, cold-worked, and cold-worked and stress-relieved Zr-2.5 wtO/cNb pressure tube materials at 575 K Calculated from dislocation density MN/m’

Yield stress at 573 K (8 tubes) (3 tubes) MN/m2 MN/m2

As-extruded

321

As cold-worked

455

464

340 _

Stress-relieved

355-405

370

384

and Hardie [I91 as about 230 MN/m2 at 575 K with a grain size of 0.7 pm. The solution strengthening effect of niobium in zirconium levels off at about 0.4 w% Nb at room temperature and 775 K 1203and is estimated by interpolation as about 45 MN/m2 at 575 K. The calculated contributions of dislocation density to yield strength of extruded, cold-worked and coldworked and stress relieved materials are 46, 180, and 80-130 MN/m2 respectively. The yield strengths estimated by summ~g these three components give good agreement with measured values (table 2). The present results show little difference in dislocation density between 20% and 40% cold worked materials. Thus little variation would be expected in properties of Zr-2.5 wt% Nb pressure tubes for CANDU reactorsas a result of differences in d~location substructure arising from variations in cold work between 20 and 30%. The low in-reactor creep rate of extruded Zr-2.5 wt% Nb compared with cold worked and stress relieved materials (21 is probably due to the lower dislocation density and larger subgrain size of the extrusion since other microstructural factors are similar. Quantitative characterization of dislocation substructure will allow such hypotheses to be tested against theoretical models for in-reactor creep, for example the “irra~ation-enhanced climb” model which has recently received strong experimental support [21]. The present results suggest that it would be difficult to obtain a dislocation substructure in cold-worked material similar to that of an extrusion by recovery at temperatures below =825--875 K. Treatments at such high temperatures would rapidly overage the p phase (below the monotectoid temperature) or coalesce the fl phase and increase the a! grain size (above the monotectoid temperature). Both would

241

reduce short-term strength [6]. As-extruded material has a fine Q grain size and an unaged network of fl phase (fig, 6) and thus extrusion without subsequent cold-work appears to be the most attractive fabrication route to produce pressure tubes with low dislocation densities. Fidleris [3] has observed shrinkage in the longitudinal direction in cold-worked Zr-2.5 wt% Nb pressure tube material of the order of O.OS--0.1%during the initial stages of recovery at 675 K. After 2 h at 675 K the dislocation density in 20% coldworked material has been reduced from = 16 X 1014 rt-2 to 8 X lOI rne2. In order to annihilate each other the dislocations must move distances of the order of their own separation. The strain produced by moving dislocations can be expressed by e=pbF

f

where e is the strain produced, p is the number of dislocations involved in the motion per unit volume, Sis the mean distance moved, b is the Burgers vector. During the recovery then de = bF dp , where de is an increment of strain caused by annihilation of dp dislocations moving a mean distance S. If the dislocation motion during recovery were random then S would be equal to zero. If the dislocation motion were biased such that all dislocation motion produced strain in the same direction S would be approximately equal to the mean separation of the dislocations i.e. S = (31~)~‘~ and the maximum strain available would be approximated by % &=fib

j

p-‘12dp=2fib

[p;f2-p;i2]

,

PO

where p. is the initial dislocation density, pr is the recovered dislocation density. This gives maximum strain available of = 1% after 2 hours at 675 K. Thus only a small directional bias is required to produce the strains observed. This could arise from macroscopic residual stress fields or from a bias in the dislocation structure itself as a result of the working proCeSS.

6. Summary and conclusions

References

The changes in distocation density and distribution during recovery in extruded and cold worked Zr-2.5 wt% Nb pressure tube material have been examined by X-ray line broadening techniques and thin film electron microscopy. The X-ray observations with respect to dislocation density and arrangements give good qualitative agreement with the thin film observations and subgrain sizes calculated from the X-ray results were similar to those measured from thin films. A rapid reduction in dislocation density occurs without much change in dislocation arrangement between ‘725 K and 815 K and a rapid increase in subgrain size and decrease in dislocation density occur above 87.5 K. The results suggest that it would be difficult to produce cold worked and stress relieved material with dislocation structures similar to as-extruded material without substantial loss of strength. Quantitative calculations of dislocation density from the X-ray line broadening measurements have been used to calculate variations in yield strength between extruded, cold worked and cold worked and stress reiieved materials and to demonstrate that variations in cold work between 20 and 40% should have little effect on the properties of stress relieved material. These results agree with reported experimental data. Calculations also show that dimensional changes during stress relieving can be explained by a small bias in the motion of dislocations during recovery.

W. Evans, P.A. Ross-Ross, J.E. LeSurf and HE. Thexton, Atomic Energy of Canada Limited Report AECL-2982 (1971). 121 C.E. Coleman, A.R. Causey and V. Fidleris, Atomic Energy of CanadaLimited Report AECL-5042 (1975). 131 V. Fidleris, Atomic Energy Review 13 (1975) No. 1, 141 K.P. Steward, Atomic Energy of Canada Limited Report AECL-2250 (1965). 151 C.E. Ells, and B.A. Cheadle, J. Nucl. Mat. 23 (1967) 257. [61 S.A. Aldridge and B.A. Cheadle, J. Nucl. Mat. 42 (1972) 32. I71 C.N.L. Wagner, Local Atomic Arrangements Studied by X-ray Diffraction, A.1,M.E. Met. Sot. Conf. 36 (1966) 219. 181 A.R. Stokes, Proc. Phys. Sot. B, 61 (1948) 382. 191 BE. Warren, and B.L. Averbach, J. Appl. Phys. 21 (1950) 595. [lOI R.J. De Angelis, Locai Atomic Arrangements Studied by X-ray Diffraction, A.I.M.E. Met. Sot. Conf. 36 (1966) 271. IX11 J.H. Mogard and B.L. Averbach, Acta. Met. 6 (1958) 552. 1121 D.E. Mikkola, J.B. Cohen, Local Atomic Arrangements Studied by X-ray Diffraction, A.I.M.E. Met. Sot. Conf. 36 (1966) 289. 1131 B.A. Cheadle and S.A. Aldridge, J. Nucl. Mat. 47 (1973) 255. I141 E.M. Aqua and C.M. Owens, Trans. Met. Sot. A.I.M.E. 239 (1967) 1.55. 1151 G.K. Williamson and R.E. Smallman, Phil. Mag. 1 (1956) 34. 1161 M.A. Clegg and J.A. Lund, Met. Trans. 2 (1971) 2495. 1171 D. Kuhlmann-Wilsdorff, Work Hardening, A.I.M.E. Met. Sot. Conf. 46 (1966) 97. 1181 D.O. Northwood, L.E. Bahen and I. London, J. Nucl. Mat. 155 (I 975) 299. iI91 C.E. Coleman,and D. Hardie, J.I.M. 94 (1966) 387. D.L. Douglass, J. Nucl. Mat. 9 (1963) 252. WI 1211 S.R. MacEwan and V. Fidleris, Phil. Mag. 31 (1975) 1149.

Acknowledgements I would like to thank S.A. Aldridge, R.J. Dudzik and F.G. Elder for their able technical assistance and B.A. Cheadle and C.E. Coleman for helpful discussions.