Preferred orientations in alpha uranium

PREFERRED

ORIENTATIONS

J. J.

STOBOt, G.

IN

ALPHA

C. C. ROBINSON? H. MAY t

URANIUM and

With an Appendix by W.

S. BLACKBURNt

The orientations of grains in fibre-textured rods of a phase grown by slow cooling transformation of uranium of various purities and histories have been determined by a Laue back-reflection technique. These results show that growth directions are always more than 60” from [ 1001,are around [OlO] in pure uranium and move towards [OOl] with increasing impurity content (such as Fe, Al, C). A theory which predicts growth directions and which is based on the relief of transformation stress by vacancy collapse or climb is proposed and is shown to fit the results if (010) and (001) are the planes on which collapse or climb occurs. Since collapse on (001) produces a stacking fault the effects of impurity content on orientation are then due to changes in stacking fault energy. There is discussion of the importance of these ideas to fuel element technology. ORIENTATIONS

PREFERENTIELLES

DANS

L’URANIUM

ALPHA

Les auteurs ont determine les orientations des grains dens des batonnets 8,texture fibreuse de phase do form&s par transformation par refroidissement lent d’uranium de differentes puretes et de differentes h&edit&, en utilisant une technique de LAUE en rayons en retour. Lea result&s obtenus montrent que les directions de croissance sont toujours a plus de 60” de [loo], se situent aux environs de [OlO] dans l’uranium pur et tendent vers [OOl] quand la teneur en impuretes (telles que Fe, Al, C) augmente. Les auteurs proposent une theorie qui predit les directions de croissance et qui est be&e sur une diminution des contraintes associQs a la transformation, par disparition de lacunes ou par montee; ils montrent que cette theorie est en accord avec les resultats experimentaux si (010) et (001) sont les plans dans lesquels se prod& la disparition des lacunes ou la montee. Comme une disparition de lacunes dans un plan (001) conduit 8. une faute d’empilement, l’influence de la teneur en impure&s sur l’orientation est alors due a une modification de l’energie de faute d’empilement. Les auteurs discutent ensuite l’importance de ces id&esau point de vue technologique. VORZUGSORIENTIERUNGEN

IN ALPHA-URAN

Mit Hilfe einer Laue-Rtickstrahltechnik wurden die Orientierungen van KGrnen bestimmt, die in Stiiben mit Faser-Textur aus cc-Uranverschiedener Reinheit und Vorgeschichte durch Umwandlung bei langsamem Abktihlen gewachsen waren. Diese Ergebnisse zeigen, daB die Wachstumsrichtungen mit der [loo]-Richtung stets einen Winkel van mehr als 60” bilden, in reinem Uran bei etwa [OlO] liegen und mit zunehmender Verunreinigung (z.B. Fe, Al, C) gegen [OOI] wandern. Es wird eine Theorie zur Vorhersage der Wachstumsrichtungen vorgeschlagen, die auf der Entfernung van Umwandlungsspannungen durch Zusammenfall van Leerstellen oder durch Klettern beruht. Sie entspricht den obigen Resultaten, wenn (010) und (001) die Ebenen sind, in denen Zusammenfall und Klettern auftreten. Da ein Zusammenfall in der (001)Ebene einen Stapelfehler erzeugt, sind die Einfliisse van Verunreinigungen auf die Orientierung folglich auf Veranderungen der Stapelfehlerenergie zuriickzufiihren. Die Bedeutung dieser Vorstellungen fur die Technologie van Brennelementen wird diskutiert.

1. INTRODUCTION

A

study

has

been

made

of

Soaking the

fibre

textures

times were 24 hr at the top temperatures.

These details are repeated

obtained as the result of slow cooling transformations to a in uranium specimens of various purities and

tion showing the elongated

histories

more equiaxed

(Table

1).

This paper describes

and offers explanations 2.

the results

for some of their features.

EXPERIMENTAL

AND

specimen

RESULTS

,6 phase, and of 112”C/cm from 890°C in the y phase. * Received September 25, 1964. t International Research and Development Fossway, Newcastle-upon-Tyne.

4

VOL.

13, JUNE

1965

Co.

specimen

Ltd.,

(Fig.

on Fig. 1 with a drawing

macroetched

after transforma-

a grains and the smaller,

u grains at the leading (i.e. cooler) end.

On a transverse

5 cm x 5 mm dia. uranium specimens have been transformed by pulling them at 0.25 cm/hr through temperature gradients of 62”C/cm from 760°C in the

ACTA METALLURGICA,

of a typical

section 2 cm from the end of the

l(b))

back-reflection

Laue

patterns

have been solved for between 2 and 6 grains from each specimen.

The crystallographic

directions

of these

grains along the long axes of the specimens (which are their growth directions) are plotted on stereographic triangles in Figs. 2(a), (b), (c). On no specimen the spread of orientation greater than 35”; average 629

spread was 20”.

Included

was the

as Fig. 2(d) are

ACTA

630

13,

VOL.

METALLURGICA,

1968

TABLE 1. Details of specimens

As-cast

Condition Cooled from

B-quenched

BYB

1’

33

No. of specimens

12

No. of Law films solved -._

8

-Unadjusted*

Adjusted*

Composition

&quenched and rolled to 50% R of A at 300°C. Y

B

As-cast

Pure*

B-quenched

BYB

As-cast

Y@Y

3

3-

3

3

3

3

12

11

12

9

8

9

p-quenched B

1

1

-3

3

1

2

4

14

14

3

* Analyses (ppm) of uranium were as follows: N

0 Pure

30

5

Unadjusted

-

-

Adjusted

-

35

Fe

Si

30

15

10

5

175

90

20

295

20

c

-.

some results of similar experiments reported by Butcher and Williamson(i); these were obtained on “American uranium of unknown purity”. The main trends revealed by Fig. 2 are as follows. (i) The orientations are close to [OlO] in pure metal (Fig. 2(a)) ; with increasing impurity level through unadjusted (Fig. 2(b)) to adjusted (Fig. 2(c), orientations close to [OOl] appear as well as those close to [OlO] ; in Butcher and Williamson’s material (Fig. 2(d)) there are no orientations close to [OlO]. It only requires the assumption that Butcher and Williamson’s material was more impure than adjusted to allow the generalisation that increasing impurity level favours [OOl] orientations at the expense of [OlO]. (ii) Within the adjusted results (Fig. 2(c)) there is a

‘A

(b)

SPECIMEN

AFTER

TRANSWfiMATON

FIG. 1

Al

Xi

Cr

Cu

-

-

-

150

50

-

-

665

35

15 --

Mn

5

F

._.-‘ 8

5

tendency for specimens transformed from the /3 phase to have orientations close to [OlO] and for those transformed from the y phase to have orientations close to [OOl]. (iii) All orientations are more than 60’ from [loo]. 3. DXSCUSSION

A mechanism which explains many of these observations is outlined in the following paragraphs. The central idea is in adaption of Buckley’s proposalc2) for a mechanism of irradiation growth (amplified by Makin eEaZ.c3)and discussed by Crocke#) . Buckley explains shape changes by the condensation of vacancies and interstitials on different planes under the action of a stress system imposed by the anisotropic expansion of the a uranium crystal. There is a stress system acting on the M:phase whilst it forms from the /3 phase at a plane interface(5*6); this can be described as tension in all directions in the interface. While there is no mechanism operating to produce interstitials, vacancies are present in the u phase at least in their equilibrium number. If vacancy discs are formed in planes near the plane of the interface their collapse will give a macroscopic strain tending to relieve the transformation stress. Their collapse will occur in a direction coincident with the Burgers vectors of the dislocation loops created, and if dislocations climb by absorbing rows of vacancies the strain will also be along their Burgers vectors. Thus collapse of vacancy discs and dislocation climb can shorten an element of CEin one direction without changing its other dimensions. In those orientations in which this direction is normal to tensile stresses there will be maximum relief of these stresses. Therefore, the most energetically favoured orientations (and

STOBO,

ROBINSON

MAY:

AND

PREFERRED

ORIENTATIONS

reasonable

IN

CC-U

631

because (001) is the most densely packed

flat plane and (010) the most densely packed gated

plane in the u uranium

probable

Burgers

vectors

vectors

at >60”

lattice

(i.e.

the

to the planes)

(Fig. 3). shortest

The

lattice

are the 3(110)

3.236 A at 26” to the [OlO], and vectors

of

of the kind

labelled XY on Fig. 3. XY is close to [012] and is at

AQUENCHED TRAwmmiED %ml THEA PHASE TR,XVSFXb’ED FROM I THE X PHASE

l

26” to [OOl]. The XY distance is 2.784 8.

t

i

corru-

The effectiveness

a) FURE URANIUM

of the two systems

of collapse

can be compared

by calculating

for each, the product

of the component

of the collapse vector normal to the

plane and the area occupied by one atom in the plane. (001) collapse along (012) is 1.02 times more effective than (010)

collapse

along

(110)

in this basis;

this

difference is neglected in what follows. The fibre textures removal vector

are labelled

favoured Contours :xf

strain

(b) UNADJUSTED URANIUM

most favoured

energetically

by

of a (010) plane with collapse along a (110) A on Fig. 4, while those

by removal joining

energy

most

of a (001) plane are labelled B.

orientations

are drawn

of equal

as thin

Fig. 4. These are the projections

decrease

dotted

lines

in on

of cones of contained

angle 28 where cos2 0 = y and where y is the decrease in strain energy in arbitrary units between 100 and 0. (The appendix

to this paper gives the derivation

of

the cos2 form of this expression.) Each set of concentric

thin dotted

collapse along one lattice vector. crystallographically two B points together, collapse

A points as there are

and since collapse

further

orientations

equivalent contours

circles refers to

Since there are two

can

can occur on both be

drawn

joining

of the same strain energy change when

is on both

equivalent

vectors.

shown on Fig. 4, the full lines being

These

are

(001) collapse

contours and the dashed lines (010) collapse contours. Then,

since both

(001) and (010) collapse

can pre-

sumably occur together in a specimen, these have to be

i

LISO~ Cd) URANIUM OF W4MOWN

PURITY

FIG. 2. Stereographic projections of crystal directions along the long &xes of specimens. therefore the fastest growing orientations)

will be those

for which the Burgers vectors of dislocations, which are either formed by vacancy collapse or which climb, are normal to the transformation interface. The experimental results are consistent

with this

theory if (010) and (001) are assumed to be the planes on which vacancy

collapse occurs and from which the

half planes are removed by climb.

This assumption

is

FIG.

3. The a-uranium lattice.

032

ACTA

METALLURGICA,

VOL.

13,

1965

------INDIVIDUAL (001) ----

L (010) COLLAPSE COMBINED (010) COLLAPSE COMSlNED too0 COLLAPSE

FIG. 4. Construction of strain energy change contours. The faint dotted lines are circles joining points of equal strain energy change for collapse only along the vector at their centre. Each A and B point has its own set of these and each line has a number (although these are not shown). The sums of the two numbers at each intersection of circles round A, and separately of circles round B have been found and the heavy lines we contours through these. Thus the heavy dashed lines are contours of strain energy chmge for (010) collapse along ~lpossiblev~tors, whilethe heavy full lines are the same for (001) collapse. The numbers on these contours represent strain energy decrease in arbitrary units.

added; but they can be added to give different contour shapes depending on the ratio: No. of vacancies collapsing on (001) No. of vacancies collapsing on (010) ’ hereafter called the (001) ratio (010) To each intersection of (001) and (010) contours (the thick full and dashed lines of l?ig. 4) a number 8, can be ascribed to represent the strain energy change at the orientation represented by the intersection. If 4soI, and 5’010, are the values of strain energy change on the full and dashed contours of Fig. 4 and Q is the (OOl)~(OlO)ratio, then 8, = Q * 4001, + %1,,~ A set of such contours, drawn through points of equal X,, is shown as Fig. 5(a) ; single contours at different values of Q are on Fig. 5(b).

A contour representing a different ratio of (OOl)/(OlO) can now be selected (Fig. 6) to enclose the points shown in Figs. 2(a), (b), and (d) but the points representing adjusted uranium on Fig. 2(c) are difficult to surround with a contour chosen from Fig. 5. The adjusted uranium points of Fig. 2(c) can be surrounded by contours only if they are divided into two groups, those transformed from the 6 phase being separated from those transformed from the y phase. Then, as shown on Fig. 7, they fall well within contours of Q values 1.3 and 3. Figures 6 and 7 show that, according to these ideas, the history of the specimen affects the (OOl)/(OlO) ratio as follows : Uranium history Pure, all conditions Unadjusted, all conditions Adjusted, /i cooled 1 Adjusted, y cooled Butcher and Williamson(i) 1 -_______

& 0.3 1.3 3

STOBO,

ROBINSON

PREFERRED

MAY:

AND

ORIENTATIONS

the element principally of stacking

IN

cc-U

responsible for the stabilisation

faults then a qualitative

Gittus’ observation transforming

633

explanation

for

is forthcoming.

Assuming that the interface is of the form shown in Fig. 8,

the rim of a bar, with its preponderence

of axial

[OlO]‘s will grow while the core will certainly grow less and may shrink due to the axial component [lOO]‘s. some b-&RAIN ool 7~I

ENERGY CHANGE CONKIJRS _~ IOU)1

w ’

FOR Q-I.3

High Fe concentration

of the axial

[OlO]‘s in the rim by [OOl]‘s SO

lessening rim growth and hence end-inch growth; less rim growth the bar’s overall contraction

with will be

greater.

e

17

5. CONCLUSION 13

The experimental

results have been well explained

on the basis of a mechanism collapse of vacancy on (010) This

impurity

o0o1(b) THE ‘LARIATION OF CONTOUR SHAPE WITH Q

to by

an

relieve

transformation

interesting

purity

elements

which proposes that the

discs and the climb of dislocations

and (001)

leads

specimens FIG.

of the

will tend to replace

and

in some

stresses.

classification

to

the

way

of

suggestion stabilise

stacking

Combined strain energy change contours (taking account of (001) and (010) collapse together).

5.

The fact that this classification for the proposition

can be made argues

that strain energy has a controlling

part to play in deciding favoured

orientations.

Because of the corrugations in (OlO), vacancies collapsing on (001) in LXuranium will produce stacking faults,

while vacancies

collapsing

on (010) will not.

There is therefore evidence : (a) that increasing impurity level stabilises stacking faults, and (b) that

the impurities

rendered faults

more

in adjusted

potent

uranium

in stabilising

are

stacking

after 24 hr in the y field and cooling

through both the y + ,!l and b +

a transforma-

tions, than after 24 hr in the /? field prior to the p -+ a transformation. The mechanisms and heat-treatment metallographic

leading to these effects of purity are not yet understood nor has

examination

of the specimens

suggested an explanation.

It may be, however,

precipitate-stacking

interactions

described

fault

by Honeycombe’s)

P

so far

ma (b) UNADJUSTED URANIUM

that

of the kind

in stainless

steels can

occur. 4.

APPLICATION TO FUEL TECHNOLOGY

ELEMENT

Recently GittusP has described the effects of varying Fe and Al concentrations on the preferred orientations of fuel rods. He notes that increasing Fe content leads to an increase in the overall contraction of the bars due to irradiation localised end-inch

expansion.

and a decrease in the If Fe is assumed to be

FIG.

the that

6. Fitting contours to experimental points.

ACTA

634

METALLURGICA,

VOL.

13, 1965

3. M. J. MAKIN, W. H. CHATWIN, J. H. EVANS, B. HUDSON and E. D. HYADI, The study of irradiation damage in uranium by electron microscopy. Inst. of MetalsSymposium on Uranium and Chuphite. London 20 and 21 March 1962. p. 45. 4. A. G. CROCKER,J. Inst. Met. 91, 242 (1963). 5. 8. N. BUCKLEY, A. G. HARDING and M. B. WALDRON, J. Inst. Met. 87, 150 (1959). 6. J. J. STOBO.J. ivucl. Mat. 2, 97 (1960). 7. J. H. GITTUS, J. Brit. Nucl. Ewrgy Sac. 8, 106 (1964). 8. R. W. K. HONEYCOMBE,J. S. T. ASWE~EN and D. H. WARRINOTON,The role of stacking faults in precipitation processes. N.P.L. Symposium Xo. 15, 1963. H.M.S.O. k--&i

(a) ADJUSTED URANIUM CTRANSrORMED FROM UWNOW_ PURITY -MARKED X

8)

APPENDIX SIMPLIFIED

THEORY OF VACANCIES

W.

COLLAPSE

OF

S. BLACKBURN

It is assumed that an element of p transforms in two stages.

to tl

Firstly it changes its crystal structure

with no volume

change,

and secondly

collapse to give a fractional

the vacancies

density increase E. It is

also assumed that there is no strain in the plane of the 1,001 (b) ADJUSTED Fm.

7.

URANIW (TRANSFW.IED

FR0h4

4)

Division of adjusted points according to condition of transformation.

interface so that the only strain is --e normal to the interface. If the vacancies

t

OF FUEL

ROD

collapse to give normal strains of

amounts &s in directions longitude

&r -

with angles of latitude and

Bi and CJ$relative to an axis normal

to the interface and the remaining strain is elastic with Young’s

modulus E and Poisson’s ratio v then Cli = 1

and the total elastic energy is

B + *(C& sin2

4

\

+ (Cili sin2 ei

-4 RADIAL

on (001).

element

doing

this,

an explanation

of Fe on the preferred

orientation

traverse

p

for

the effect

in fuel rods is

sin2 &)”

di

sin Q2 + (C& sin

ei

co9

cos

ei)S)

i&i&

strain is taken

and considerable

who financed the work.

REFERENCES 1. B. R. BUTCHERand G. K. WILLIAMSON,unpublished work. 2. S. N. BUCKLEY,Irradiation growth. AERE R-3674 (1961).

For simplicity

sv{$(I +

ei cos

t$J2

to be perfectly to the square

interactions

will

izi2) - cili co~2ei)

This has been calculated on two assumptions

in each

of which the first term is fixed so that the energy depends

ACKNOWLEDGEMENTS

Harwell, for his patience

8,

+

be neglected so that the energy reduces to

to be the main

The authors’ sincere thanks go to Mr. B. R. Butcher help, and to the UKAEA

ei

co9

root of this quantity.

possible.

of AERE,

sin

sin2

+i)2

plastic the rate of work is proportional

during

If Fe is assumed

(C&

cos2

If the remaining

OWANCE

FIG. 8. Transformation interface quenching.

faults

+

ei

only

on Z;ili cos2 Bi.

Firstly

it is assumed

that the whole collapse is on that plane which gives rise to the least energy, but this was found not to give such good agreement

with experiment.

Secondly,

it

was assumed that the ratio of the li is fixed from prior requirements, given system.

e.g. it is the same for all planes of a