Dislocation substructures in deformed uranium dioxide single crystals

Dislocation substructures in deformed uranium dioxide single crystals

JOURNAL OF NUCLEAR DISLOCATION MATERIALS S~STRU~TUR~ 31 (1969) 121-137. 0 NORTH-HOLLAND IN DRFO~D Cl S. YUST ~NIUM PUBLISHING DIOXIDE CO., ...

3MB Sizes 6 Downloads 42 Views

JOURNAL

OF NUCLEAR

DISLOCATION

MATERIALS

S~STRU~TUR~

31 (1969) 121-137. 0 NORTH-HOLLAND

IN DRFO~D

Cl S. YUST

~NIUM

PUBLISHING

DIOXIDE

CO., AMSTERDAM

SINGLE CRYSTALS”

and C. J. McHARGUE

Metals and Ceramice Division, Oak Ridge National Labomtoty, Oak Ridge, Tenlzessee 37830, USA

Single crystals of umnium dioxide were deformed in compression to nominal strains of 1 and 5%. The crystals were oriented to promote slip on only one slip system of the family { lOO} (110). The strain rate and temperature rcmges studied were 10-s to 10-I min snd 750 to 1400 “C, respectively. The dislocation density of the as-grown crystals was 2 x loS/cms. Sections of the deformed specimens were examined by transmission electron microscopy, indicating that the dislocation substructuresat a strain of 1*h consist of numerous dipoles and dipole loops, the edge componentsof the dipoleslying &long directions. At 5 y0 strain, extensive dislocationtangles are present in addition to the dipole configumtions. Particnlar features are noted in the dislocation arrangements which can be related to several of the theories of dipole formation. The critical resolved shear stress on the (100) (I IO> slip system is reported as a function of tern~~&t~, ss is the variation in the appearance of the loaddeflection curve with tempemture level. Of particular interest is the markedly sermted load-deflection behavior observed at 1150 ‘C, and the minimum in the shear stress curve at 950 “C. The dislocation density as & function of stmin has been ev&&ed, and dislocation velocities &re estim&ed.

~r&ct~~stiqu~ particuli&es sont not&s dans lee arrangementsde dislocations, qui peuvent &re reliees B,de nombreuses theories de la formation de dipales. La oission critique du systeme de glissement (100) est etudiee en fonction de la temp&ature, cission determinee par la variation de I’aspect de la courbe charge-d$fo~tion fonction de la temp&&.rre. 11 est prtrticuli6rementimportant de noter le oomportement de la courbe de deformation qui presente le phcnomene observe & 1150 “C, et le minimum dans la courbe d’effort de cisaillement 8.950 “C. La densite des dislocations en fonction de le deform&ion a et6 BvaJueeet les vitesses de dislocation ont et& e&m&s.

Einkristalleaus Urandioxid wurden unter Druck einer nominalen Verformung von 1 und 5% unterworfen. Die Kristalle waren so orientiert, dw ein Gleiten nur in einem System der Art (109) erfolgen konnte. Die Verformungsgeschwind.igkeitenlagen zwischen 10-e und lo-l/min, die Temperaturen zwischen 750 und 1400 “C. Die Versetzungsdichteder gewachsenen Kristalle betrug 2 x 108/cm*. Teile der verformten Proben wurden elektronemnikroskopiseh im D~c~chtverf~en untersucht. Es zeigte sich, doss die Substndrtur der Versetzungen bei der Verformung von 1% aus zahlreichenDipolen und Dipolringen bestand, wobei die Randkomponenten der Des monocristaux de bioxyde d’uranium ont et& Dipole in . La vitesse de deforsetzungen wurden beobschtet. Sie k&men mit vermation et la domaine de temp&ature etudies titaient schiedenen Theorien der Dipolbildung in Beziehung compris respectivement entre 10-3 A 10-r min-1 et gebraoht werden. 750 b 1400 “C. Ltt densite des disloccttionsdes oristaux Die kritische Schubspannungim (100) (llO>-Gleitbrut de croissance et&t de 2 x 106 cm-z. Les sections system wird als Funktion der Temperatur angegeben. des ~chantillo~ deform& ont 6t& examinees par la Diese Funktion ent~rioht dem We&se1 in der Gestalt transmission par microscopic Bleotroniquequi revele der Last-Auslenkungskurven mit dem Temperaturque la sous-structure des dislocations, pour une disniveau. Von besonderemInteresseist der ausgepriigte location de 1% consist%en de nombreux dipoles, les siigezahnartige Charakter dieser Kurve bei 1150 “C composantes-coindes dip&s sont autrement disposces und das Minimum der Sahubspamnmg bei 950 “C. le long des directions
122

1.

C.

S.

YUST

AND

Introduction The intent

by

the

J.

iMCHARGUE

microscopy,

of this study

is to extend

the

knowledge of the deformation processes in ceramics having the fluorite structure, principally

C.

use

of

transmission

electron

2.

UOz single Internal

directed

developed

with this structure

to those with the rock salt structure,

than

undoubt-

edly because the least complex systems are studied first. With the background obtained from studies on such ceramics as NaCl, MgO and LiF, several ~vestigators have undertaken studies of fluorite structure materials. Phillipsl) studied the deformation crystals of CaFs from

during the performance

proof

Materials and experiment

microscopy to study deformed single crystals of uranium dioxide. Much less attention has been to materials

along with some mechanical

perty data derived the experiments.

crystals

Centrifugal

as-grown

were

Zonal

at Oak National dislocation

grown

Growth

by

Laboratory

density

the

technique 8). The

of these crystals

is typically 2 x 10s/cm2, determined by both etch-pitting techniques and electron microscope observations. A typical electron photomicrograph in fig. 1.

of an as-grown

specimen

is shown

and fracture of single room temperature to

1000 “C, reporting resolved shear stress data and evaluating the operative slip systems from the analysis of slip traces. Rapperport and Huntress 2) used slip trace analysis the operative glide systems in crystals; Ashbee 3) has noted the stacking faults in UOs and reported

to identify UOs single presence of the princi-

pal slip system on the basis of electron microscope observations. More recently, Evans, Roy and Pratt 4) discussed the deformation of single crystal and polycrystalline CaFs, relating the single-crystal deformation characteristics to the poly~rystalline behavior. The influence of impurities

on

the

deformation

of

CaFs

single

crystals has been reported by Urusovskaya and Govorkov 5), and Blank and Amelinckx 6) have used transmission electron microscopy to study defects in irradiated UOs. The literature however, does not contain a comprehensive report of electron microscope observations of dislocation configurations in deformed fluorite structure materials or their variation with deformation conditions. In addition, Nabarro et a1.7) have pointed out that ionic crystals may frequently vary markedly in behavior even within one structural group, SO that for these types of materials a detailed investigation of each specific compound is desirable. This paper will present observations of the dislocation substructure in deformed UO2 single crvstals as determined bv transmission electron

Fig.

1.

Typical

dislocation distribution

uoz

crysts;l.

in as-grown

x 6000

The total cation impurity content of the specimens is approximately 300 ppm, with the principal contaminants being iron, silicon, chromium, copper and calcium. The growth technique effects some degree of zone refining, so that the chemical composition within a single specimen rod is not homogeneous. As a consequence, samples cut from different regions of a specimen rod .may vary in properties due to the variation of impurity content. Deformation samples were cut from the

DIBLOCATIOI

123

SUBSTRUOTURZS

RELATIVE POSlTlON OF SPECIMEN

TABLE Summq

1

of deformation experiments. Deformation

Specimen

variables

l?emp.

Strain rate

Total strain

(“C)

(min-1)

(%I

110-l

1360

1.7 x 10-a

3.4

110-3

1360

1.5 x 10-a

110-5

1360

1.40 x 10-s

14.7 1.0

110-11

1360

1.60 x 10-s

15.2

110-2

1360

1.5 x 10-l

4.5

110-10

1360

1.60 x 10-l

16.6

130-6

1180

1.4 x 10-s

0.9

130-3

1150

1.8 x 10-3

5.0

135-4

1150

5.6 x lo-*

4.7

135-2

1150

5.6 x 10-s

1.0

135-1

1150

3.0 x 10-n

5.0

135-3

1150

3.1 x 10-a

1.1

110-8

940

1.5 x 10-3

4.5

110-4

940

1.5 x 10-3

1.5

130-4

950

5.9 x 10-3

4.9

130-7

950

6.1 x 10-a

0.9

would maximize the shear stress on one of the slip systems, promoting single slip at the start of deformation. The stereographic projection presented in fig. 2 shows the orientation of the primary slip system, the secondary systems, and the direction of the applied stress. This

110-12

940

1.7 x 10-Z

4.7

110-9

940

1.6 x 10-l

36.2

130-L

750

1.4 x IO-3

1.1

130-2

750

1.6 x 10-a

5.1

orientation

115-1

550

1.4 x 10-l

0.8

115-4

550

1.4 x 10-l

1.6

122-2

550

1.6 x 10-l

2.1

122-3

550

1.6 x 10-l

7.4

122-4

550

1.6 x 10-l

1.3

Fig.

2.

Relationship

between specimen position, slip

plane orientation,

single-crystal

specimens

and applied

stress.

in an orientation which

is about halfway between the [iil]

and [ii-21 orientations.

The specimens were cut

with a diamond wheel and ground on 600 grit paper so that they would have flat, parallel, and orthogonal sides and ends. The aides of the specimens were chemically polished to remove the surface damage and to facilitate the detection of slip traces. Specimens were deformed in compression in an argon-4% hydrogen atmosphere on an Instron test machine. This atmosphere maintained the O/U ratio of the crystals at 2.00. The range of test variables was 750 to 1400 “C, cross-head speeds of 0.0013 to 0.025 cm /min, and deformations of about 1 and 5%. The specific tests performed are summarized in

table 1. The small variations in strain rate are due to the variations in specimen length. The deformed specimens were sectioned parallel to the slip plane, and in some cases, perpendicular to the slip plane. Slices approximately 0.25 mm thick were cut from the sample, and were then thinned chemically to electron transparency by the technique of

124

C. 5.

AND

YUST

Manley a). The electron photomicrographs made

on a Hitachi

UH-11

microscope

accelerating voltage of 100 kV. Dislocation density measurements

were at an

and

es-

timates of the dislocation velocity were obtained from

the

deformed

electron structures.

photomicrographs

of

Quantitative

determina-

the

C.

J.

3.

MCHARC+UE

Results

The principal slip system and the Burgers vector of the active dislocations are by now well established for the fluorite structure, R apperport and Huntress 2, have reported tlhe principal slip system in UOs to be {loo) (110)

The sections of UOs examined on the electron microscope were also viewed in reflected monochromatic light on an optical microscope. A pattern of extinction contours is seen under these conditions, each contour corresponding to a thickness

of material

the wavelength

of the incident

light.

Since the wavelength

was about

equal

to one-half

monochromatic

of the light used

6000 A, the thickness

of the foil at

the first extinction contour was about 3000 A. It is estimated that most of the electron photomicro~aphs were made between the edge of the foil and the first contour, so that a foil thickness of approximately 2500 A is a reasonable estimate. Blank and Amelinckx 7) note that transmission in UOc is possible for foils thicker than 2000 A, especially if anomalous transmission is used. On the basis of the various estimates made in this study, an average foil thickness of 2500 A was adopted for the calculation of dislocation density.

Fig.

3.

View of slip plane in specimen 135-4.

x 10 000

a. Diffraction vector is g= [020] ; b. Diffraction vector is g= [BO], and dislocation contrast is weak. Burgers vector is perpendioular to the diffraction vector, and of the type 4 .

DISLOCATIQW

Fig.

4.

View of the slip plane in specimen

125

SUBSTRUCTURES

130-l

Fig.

5.

View

of the slip plane in specimen

130- 7

deformed 1.1 y0 at 750 ‘C. The arrows indicate an open

deformed 0.9%

dipole

dipole having unequal leg lengths (A), an open dipole

(A), aligned lengths of dislocation

an edge trapping impurity

Fig.

0.

View

mechanism interaction

(B), (C).

suggesting

and dislocation-

of the slip plane in specimen

deformed

1.6%

at 940 “C.

(B), probable

X 10 000

x

10 000

at 950 “C. The arrows indicate an open glissile jogs (C), and aligned portions

of dislocation

110-4,

Fig.

7.

View

(D).

x

10 000

of the slip plane in specimen

deformed

0.9%

at 1180 ‘C.

x 10 000

130-6,

iP6

Fig. 8. deformed

‘2.

View 1.0%

S.

YUST

of the slip plane in specimen

AND

135-2,

at 1150 “C. A possible expanding loop

is shown at (A).

x

10000

C.

J.

BIlleRARGUE

Fig. 9. deformed aligned

View

of the slip plane

1.196 lengths

at of

1150 “C. dislocation

forming on a screw dislocation having

with the (1 lo} and (11 l> planes becoming active at higher temperatures. The Burgers vector of the active slip dislocations was found by Ashbee a) to be i(110) by means of transmission

electron

microscopy.

Blank

and

Amelinckx ‘3) also concluded that the observed di~raotion contrast effects were consis~nt with a ${llO) Burgers vector. These results are also in agreement with the work of several other investigators showing that the principal slip system in CaFz is (100) (1 lo}. The specimens of this study were therefore oriented for single slip on the (100) (110) system, and a single set of slip traces corresponding to the orientation of this plane in the specimen was observed after the deformation. Fig. 3 shows the dislocations on the slip plane in specimen 135-4. In part (a) of the Ggure, the d~a~ion vector, g, is [OZO], and the dislooations in the slip plane are visible. In part (b), the difiaction vector is [2zO] and the dislocations in the siip plane do not show diffraction contrast. The

a variable width

in specimen

The (A).

arrows

135-3,

indicate

several

dipoles

(B), and a dipole loop (C).

x 10 000

direction of the Burgers vector of the dislocations in the slip plane is therefore as indicated, since the Burgers vector must lie in the plane perpendioular to the operating diffraction vector for that condition for which contrast is not obtained. As shown in the figure, the Burgers

vector

is of

the type 9 (IlO}.

The

specimen orientation is such that the slip direction concides with that of the Burgers vector. At a strain of about l*& many long dislocation lines of mixed character are evident. Dislocation dipoles are numerous, both as dipoles continuous with the dislocation line and as elongated loops. These features are seen in figs. 4, 5, 6, 7, 8 and 9 which show the variation with test conditions of dislocation arrangements in UOZ deformed 1o/o. The long axis of the dipoles and dipole loops lie along (llO> directions. The extended sides of the dipole loops lie on different, but parallel, slip planes, and have been observed after deformation in a variety of materials 7911-14)” Dif-

DISLOCATION

Fig.

10.

View

perpendicular

specimen 135-3, deformed 1.1%

Fig.

to

the

slip plane

at 1150 “C.

in

Fig.

130-4,

fraction contrast effects at the extended sides of the loops indicate that the opposing sides are edge dislocations of opposite sign. The fact that these dislocation segments lie in parallel planes is seen by reference to sections

11.

View of the slip plane in specimen

deformed

x 10 000

12. View of the slip plane in specimen x 10 000 deformed 4.9% at 950 “C.

127

SUgSTRUOTURES

Fig.

13.

5.1%

at 750 “C.

View of the slip plane in specimen

deformed

4.5%

at 940 “C.

130-2,

x 10 000

x

110-8,

10 000

perpendicular to the slip plane, fig. 10, where the sides of complete loops and pairs of dislocation lines are seen to be parallel in the edge view of the slip plane. At a strain of about 5%, distinct tangling

128

Fig.

C.

14.

S.

YUST

View of the slip plane in specimen

deformed

5.07;

at

indicakd

1150 “C. at, (A).

A

subsidiary

AND

130-3, loop

is

x 10 000

C.

J.

Fig.

BWHARGUE

IS.

View of the slip plane in specimen

deformed at (A),

5.Oo/b ut 1150 “C. Y-shaped

and aligned lengths at (B).

135-i.

loops indicated

of dislocation

indicated

x 10000

regular configurations. The long individual dislocations continue to exist in the regions between the tangles. Certain individual features which reappear consistently in the dislocation arrangements should be noted. The long dislocations tend to lie along (loo} directions and are of mixed character. firequently, they abruptly ehange from one (100) direction to another, forming a cusp, for example, at A in fig. 15. Many

Fig.

15.

View of the slip plane in specimen

deformed toward

4.7%

135-4,

at 1150 “C. Rotation

edge orientation

of dislocations

of dislocations x IO 000 is shown at (A).

has occurred, figs. 11, 12, Many dislocation loops found within the tangles and appear to interacting, forming complex and highly 14,

15

and

16.

13,

are be ir-

variations of cusp size and density exist along the dislocation lines. Many loops can also be seen which display configurations that Bre repeated frequently, for example, Y-shaped loops, seen at A in fig. I6 and subsidiary loops, seen at A in fig. 14. In some instances, loops appear to be opening under the influence of stress, as at A in fig. 8. These consistently repeat,ed features may be related to the mechanism of multiplication of dislocations in the IJO2 lattice. At the completion of a deformation test the stress was removed from the specimen before the temperature was lowered. The configura-

DISLOCATION

tions are therefore

representative

129

of a “stress-

relaxed”

condition.

The rate of cooling

relatively

rapid, e.g., cooling to less than 600 “C

from test temperature

SUBSTR’UCTURES

was

was usually accomplished

in less than 15 min, and the degree of entanglement of the dislocations is such that appreciable modification would

of

the

dislocation

not be expected

arrangement

to occur.

shape of some of the dislocation

The specific

lines, however,

might be expected to vary slightly. Observations of more extensively deformed specimens show that many of the features of the structure noted above are present over a wide range of deformation variables. Dislocation dipoles and dipole loops persist in a specimen deformed at 950 “C and a strain rate of 1.6 x lo-l/min to a total strain of 16.2%, fig. 17. At this degree of deformation, an extensive cellular network is beginning to form, although cusps, dipoles, and dipole loop configurations can still be observed throughout the structure. At 1350 “C, deformation to a total strain of 14.7% at a strain rate of 1.5 x lo-a/min results in extensive network formation, fig. 18, and subdivision of the lattice into cells. Some

Fig. 17. View of the slip plane in specimen 110-9, deformed 16.2% at 940 “C. x 10 000

loops can still be observed in such a structure. Load-deflection curves were recorded for each deformation experiment. Generally, a distinct

yield point was observed, but the response after yield varied with the test conditions. At the highest temperature studied, 1350 “C, yielding was followed by essentially no work-hardening 15%.

At

lower

for quite large strains, e.g., temperatures,

a very

short

easy-glide region was followed by a region of decreasing work-hardening. Macrosoopioally only one set of slip lines was observed on the specimen surfaces; hence, although some cross slip occurred multiple slip did not. The yield behavior as a function of temperature is summarized in fig. 19 where schematic representations of the typical appearance of the load-deflection curves are shown. A prominent feature of the load-deflection curves is the very irregular response to stress after a small amount of deformation, principally in tests at 1150 “C, although this effect is present to a

Fig. 18.

View of the slip plane in specimen 110-3, deformed 14.7% at 1360 “C.

lesser degree in some of the tests at 950 and 1350 “C. Typically, the irregular portion of the curve begins at about 2*0/O strain. The critical-resolved shear stress was calculated for each crystal and the data are presented in fig. 20. Some of the scatter may be attributed

130

C.

S.

YUST

AND

0.

J.

MCHARGUE

to variations 1150°C

75OOC

in the initial

condition

of each

specific specimen! since the original crystals are

1350°C

ihfl!

known to be not fully homogeneous

with respect

to ingrown defects and chemical purity. Des+

950°c

z i:

the scatter however,



and the limited

a minimum

shear stress at about The dislocation

number

of test,s,

in the critical-resolved

950 "C is indicated.

density as a fun&ion of st’rain

was measured by lineal analysis of the electron photomicrographs. The density was evaluated by t’he method suggested by Hirsch, Howic,

DEFLECTION

Fig.

19.

Schematic

curves

representation

as a function

Nicholson, expression

of load-deflection

of temperatlwe.

TEMPERATURE

Fig.

lo+

2

20.

5

Critical

16’

2

COMPRESSIVE

Fig.

21.

Dislocation

density

resolved

5

IO“

(“C)

shear stress as a function

2

5

100

STRAIN

as a function

of strain.

Pashley, and Whelan Is), using the Q= 2N/(Lt), where Q is density of

of deformation

temperature.

dislocations, N/L is the number of intersections of dislocations with a line of length L, and t is the foil thickness. The number of intersections of the dislocation lines was evaluated with a series of concentric circles according to the method of Steeds, as reported by Hirsh et al. Although the dislocations are not uniformly distributed in the specimen, the use of concentric circles should minimize the effects of such a distribution. The dislocation density as a function of strain is shown in fig. 21 and can be represented by the relationship Q= 3.73 x 109~~0.39. There was no systematic

DISLOCATION

variation

in dislocation

density with tempera-

ture and/or strain rate, Dislocation velocities can be estimated the measured dislocation

from

densities. Such calcu-

lated velocities cannot be considered to be more than order of magnitude are the minimum

estimates and, indeed,

average velocities.

they will be of interest deriving

the

However,

dislocation

location

density.

The velocity

estimates

are

plotted as a function of reciprocal yield stress. The data derived from these experiments, however,

are too limited

and too dispersed to

permit the drawing of the appropriate isotherms, but do allow the distinction and a region

incorporating

of a 950 “C region the data at 750,

some

1150, and 1350 “C, fig. 22. The dashed line in

The expression for

the figure serves only to separate the data at

in interpreting

of the current observations.

131

SUBSTRUCTURES

velocity

is due

to

950

“C from

that at the other

temperatures.

Cottrell ia), and is developed by Gilman 17) to yield the relation p = [email protected], where y is the plastic

This diagram indicates that for a given shear stress a higher average dislocation velocity can

strain rate, B is the average dislocation velocity, b is the Burgers vector, and Q is the dislocation density. Gilman is) has also shown that the

temperatures.

be anticipated

at 950 “C than at the other test

stress dependence of dislocation velocity is best described by the relation v = vo exp ( -D/z) where vo is a limiting velocity near the velocity

4.

of sound, D is a characteristic drag stress, and t is the appropriate shear component of the applied stress. A plot of log v versus reciprocal shear stress should therefore yield isotherms showing the relationship between applied stress and dislocation velocity. The average dislocation

are the large numbers of elongated loops, the cusps on long dislocation lines, and at least

velocity was calculated from the density of dislocations at 0.1% strain which was determined by extrapolating the observed dis10’

Discussion

The characteristic features of the dislocation configurations illustrated in figs. 4-9 and 11-16

two types of dislocation

dipoles. There are few

long segments of pure screw character. Examples of one type of dipole are shown in A in fig. 4, B in fig. 5, and B in fig. 9. In these cases, long, continuous dislocations are extended into several short dipoles; most of the dipoles are composed of pure edge oomponents. This configuration suggests a dipole formation mechanism involving the formation of jogs along the dislocation line. Jogs at the closed end of the open dipole pairs were observed in photographs of sections taken perpendicular to the slip plane, for example, fig. 10. However, dipoles

are also formed in other as at B in fig. 16.

than

edge

orientation,

I

50

fO-2 0

0.1

0.2 I/r,

Fig.

22.

\

*

O\ 0.3

0.4

RECIPROCAL

CRSS

Dislocation

velocity

0.5

0.6

as a function

procal CRSS.

0.7

(md/kg)

of reci-

A second type of dipole configuration contains long dislocation segments as at D in fig. 5, and at A in fig. 9. These arrays suggest an edgetrapping mechanism. A possible third type of dipole is shown at A in fig. 5. In this case, a loop appears to be nearly pinched off by dipole segments of mixed character. The configuration is suggestive of the pinching-off process observed by Price 19) in zinc. The loop is larger than the separation between the dipole legs, indicating that some cross slip has occurred.

C. S. PUS’2

132 The appearance

of more

dipole suggests the operation

than one type

for their formation.

models

dipole

formation

of

of more than one

mechanism for

AND

Some will

be

Gilman

and Johnston 12) proposed

that di-

in front of the slowly moving

formed by the interaction of two mixed dislocations crossing on parallel slip planes. If the Burgers vectors are equal but have opposite signs, a reduction in energy can be accomplished by a reorientation of a segment of each in their respective glide plane to form a parallel pair, i.e., dipole. Two requ~ements of this model are often seen in the microstructure of UOz: aligned portions of dislocations on parallel planes, as at A in fig. 9, at I) in fig. 5, and at B in fig. 4; and dipoles having legs of unequal length, A in fig. 5. Fourie 13) proposed mechanisms for the

they

of dipoles and dipole loops in copper. he found few examples of open i.e., dipoles

are very

structures,

closed

readily

for example,

at only

observed

of glissile-sessile

jog pairs. The glissile jog can

causing isolation

presence of dipoles in orientations other than pure edge corresponds to Tetelman’s objection to this model 20). According to Tetelman 20921) dipoles can be

dipoles,

dipoles into isolated loops involves the formation

briefly

jog. W%ile some of the features of the dipoles in IJOZ are consistent with such a model, the

formation Although

IvICHAROUE

glide

by the jogging of moving screw with the resultant dragging out of

edge components

J.

of the

discussed in terms of the foregoing observations. poles form dislocations

C.

one end,

in the UOz

A in fig. 4 and B in

fig. 5. Fourie’s photomicrographs are similar to those for UOZ showing that the open dipoles do not exist as single dipoles, but are usually close to other jogs in the screw dislocation. Fourie established the direction of the shear stress and the direction of motion of the screws and thus showed that the dipoles trailed behind the screw dislocations, while other closely associated jogs were evidently glissile under the influence of the applied stress. Such jogs are seen at C in fig. 5. Upon release of the applied stress, the glissile jogs become immobilized, and the w-shaped configurations result. Fourie’s mechanism for closing of the

conservatively

Washburn’s loops

requires

on

a

of prismatic

cross-slip

plane,

loops.

22) model for dipoles and dipole the accumulation

cusp in a moving

of jogs

screw dislocation.

at a

A dipole

is formed in front of a large, slow-moving

jog,

and a closed loop is formed whenever the total number of positive and negative jogs collected on the dipole become equal. certainly the dislocations in UOz contain large numbers of cusps and jogs. The process of collecting jogs on dipoles can give loops having variable widths; the loop at C in fig. 9 is an example of such a condition. Although only one set of slip traces, corresponding to the primary slip system, was observed on the surfaces of the deformed crystals, the electron photomicrographs suggest that widespread cross slip, for relatively short distances, has occurred. Hirsch and iMitchell 23) have noted that a small amount of cross slip can accompany deformation in which only slip traces attributable to the primary slip system are produced, and that the proportion of the total deformation due to the operation of cross-slip systems is very small. Nominal stressstrain curves prepared from the load-deflection traces indicate that easy glide (or stage 1) occurred only for a short period in the specimens tested at 750 and 950 “c). There was no indication in the stress-strain curves of a0 linear strain-hardening region (stage II) ; an immediat,e transition to a recovery or decreasing rate of work hardening (stage III) was observed. Specimens tested at 1150 “C exhibited stage 1x1 behavior from the onset of plastic flow. The stage III characteristics of the 750 Ltnd 950 “C specimens persisted up to strains of about 5(;/,, at which point the specimens were unloaded. On the other hand, at 1150 “C. stage III deformation was replaced by discontinuous yielding after about 2.5% strain. The discontinuities in the stress-strain curves are reminiscent of the Portevin-Lo Chatelier effect.

DISLOCJATION

SUBSTBUUTUBES

133

A significant aspect of deformation in ionic restraining effects of the lattice. But at the solids is the influence of electrostatic charge on temperature at which the dislocationa are the behavior of dislocations. Numerous studies electrioally neutral, a force is not required to have been made on charge effects on dis- overcome electrostatic effects and the yield locations, almost exclusively on NaCl. A recent stress should be a minimum. The yield stress paper by Brantley and Bauer 24) analyzes the minimum observed in the UO2 single crystal geometry of charged dislocations in NaCl and results reported here are considered to reflect points out that straight dislocations, regardless the existence of an isoelectric temperature in of character, are electrically neutral, but both UO2 at about 950 “C. Urosovskaya and screw and edge dislocations may acquire a Govorkov 5) have also observed a minimum of virtual electrostatic charge due to the formation the type described here in CaF2, and attribute of half-jogs. Eshelby, Newey, Pratt and it to the isoelectric temperature effect. The theoretical analysis indicates that the Lidiard 25) pointed out some years ago that a charge on dislocations in NaCl at room temperasurplus of one type of vacancy would be likely to form in an ionic crystal, producing a potential ture should be negative. Several experimental between the surface and the interior of the determinations contim this, for example, studies crystal, and that since dislocations could form by Caffyn, de Freitas, and Goodfellow 22); vacancies, they too might be expected to be Kishsh 27) and by Davidge 28). Davidge also charged. The dislocations would contain an noted a change in dislocation sign when anion excess of one type of vacancy and should be rather than cation doping was used. The surrounded by a sheath of vacancies of opposite theoretical explanation of the isoelectric temperature is therefore supported by these findings. sign. Eshelby et al. also discussed the effects of The electrostatic effects associated with disimpurities on the sign of the charge on the locations in UO2 have not been discussed in dislocation. At low temperatures, where the detail in the literature, but results qualitatively thermal equilibrium concentration of vacancies similar to those reported for NaCl can be is relatively low, the majority of vacancies expected. The existence of an apparent isowould exist due to the presence of cation electric temperature in UO2 suggests that at impurities having a different valence than the low temperatures sign&ant interaction between host cation. In NaCl, cation impurities would dislocations and cation impurities might be cause dislocations at low temperatures to be expected, while at elevated temperatures the negatively charged, while at high temperatures, predominant interaction might be between where the thermal equilibrium concentration of dislocations and vacancies. Some of the disvacancies would be much greater than the location images in fig. 4, e.g., at C, suggest concentration of vacancies due to impurities, the interaction of the dislocation with imthe dislocations would be positively charged. purities. Differences in the appearance of the At some intermediate temperature, called the dislocations in figs. 4 and 9 may also reflect isoelectric temperature, the number of positive impurity interaction at low temperatures and and negative jogs is equal, and the dislocations the effect at high temperatures of cation are electrically neutral. vacancies and extensive cross slip. A minimum observed in the yield stress Other effects discussed by Eshelby et al. and versus temperature curve for NaCl reported by associated with the presence of the charge Eshelby et al. can be explained in terms of the cloud near a charged dislocation were (1) a isoelectric temperature. When the dislocations maximum in the yield stress curve, (2) the are charged, a force must be applied to free appearance of serrations in the stress strain them from the surrounding charge cloud, as curve in a particular temperature range, and well as to move them against the other (3) the tendency for screw dislocations to turn

134

C. S. YUST AND C. J. McHARUUE

toward the edge orientation, stress data of this study sufficiently

high temperature

conclusion,

the

temperature will

and

similar

The maximum

the yield

to provide

expectation

exceeds

decrease,

maximum

Although

are not carried to a is

that

a firm as

1400 “C the yield the

curve

to that

observed

in the yield

to be due to the fact

will

that

the

stress

exhibit

a

in NaCl.

stress is thought the charge

field

s~rroun~g the dislocation becomes more mobile with ~ereasing temperat~e, so that finally the charge cloud follows the dislocation readily and electrostatic

the force required effects disappears.

to overcome As the force

flow. The struotures of figs. 13-16 were produced by deformation response

in which a serrated stress-strain

is evident,

and reflect the conditions

that gave this dynamic Some

of the spread

stress data reported

were

taken.

1350 “C yield

here for UOz may be due

to the inhomogeneous in the specimen

instability. in the

distribution

of impurity

rod from which

the samples

The

technique

by

which

the

specimens were grown affects a zone-refining of the material, and samples taken from higher positions in the rod are apt to carry a greater impurity content. In addition, the relative amounts

of the various

impurities

may vary

overcoming the influence of charge fields diminishes so does the yield stress, resulting in s, yield stress maximum. At a somewhat lower temperature, a condition will exist where, according to the analysis of

from sample to sample, so that the effect of temperature on impurity solubility will not be t,he same in every sample. The relative strengths of the samples at 1350 “C can be correlated with the position of the sample in the specimen

Eshelby et al. the charge cloud can barely keep up with t#he moving dislocation, resulting in a serrated stress-strain behavior. It was also noted by Eshelby that Classen-Nekludowa observed jerky flow in rock salt in 1929. The serrated stress-strain behavior observed in this

rod. At the lower test temperature, the agreement of the data is close enough to negate any attempt to correlate the result with the position of the sample in the specimen rod. Screw dislocations tend to rotate toward the

study is very likely due to the ability of charged ,vacancies to diffuse to and form charge clouds around dislocations. In this view of the process, dislocations may break away from the surrounding charge cloud, but once the dislocation stops, nearby vacancies of opposite sign can readily diffuse to it, reformil~g the surrounding charge cloud from which the dislocation must break away again. The periodic reconstitution of restraining charge clouds results in the serrated stress-strain curve. The marked differences in the dislocation arrays seen in figs. 11 and 12 as compared to figs. 13-16 may have some connection with impurity and dislocation charge effects. Most of the deformation that gave the structures of figs. 11 and 12 occurred during stage III, and is characterized by dynamic recovery or profuse cross slip. Hence, tangling of the dislocations has occurred and the beginning of cell walls is apparent. Most impurity-dislocation interaction affected only the initial portion of the

edge orientation, as seen, for example, in fig. 15 at A. Eshelby has suggested that this might be due to lack of charge on screws. and their effort to turn toward edge orientation to pick up a charge and a balancing cloud of charged vacancies. However, Brantley and Bauer a*) have shown that charge is due only to the presence of unequal numbers of charged jogs, so that there is nothing about a particular orientation, per se, that would create the desired charge. In the screw orientation, the jogs that form can glide conservatively along the disaccumulating to form large jogs, location, dipoles, and dipole loops, freeing much of the pure screw dislocation of charge effects. These relatively uncharged screws can move readily. but are anobored at the large jogs along t,heir length and are therefore forced to rotate toward an edge orientation. As they become more edge in character, jogs formed on them are less able to glide along their length, and the charge remains more uniformly distributed along the dislocation. Such a process might explain the

DISLOCATION

apparent preference of many of the dislocations in UOz to lie along (100) directions, intermediate between the screw and edge orientations. The temperature range of the deformation tests is at a sufficiently of

the

absolute

high level (0.38 to 0.53

melting

point)

so that

the

influence of diffusion on the structures observed should

be

determining

considered.

Using

a

model

135

SUB%TRUUTURES

for

the rate of climb of a dislocation

TABLE 2

Summmy of data for dislocation climb calculations. Temp. W)

4 (omz/seo)

GZZ (psi)

V

(cm/set)

10-18

3000

10-16

3675

1.9 x 10-10

1350

10-15

4430

2.0 x

b(UOa)=3.87

)

1.8 x IO-12

950 1150

10-Q

x 10-e cm.

and available diffusion data, the maximum distance of climb for the total time under stress may be calculated. According to Hirthe and Lothe zg), the diffusion-controlled velocity of climb of a straight dislocation is given as v M D,vaF/(be2kTL), where

Da is the volume self-diffusion coeffioient ; F/L is the force per unit length on the dislocation ; va is the atomic volume ; be is the Burgers vector of the edge com-

ponent. For F/L substitute o,,b, where csZ is the normal stress on the dislocation, taken to be equal to the applied resolved normal stress. Approximating v, M be?, v m Dsb20zz/(kT). A similar expression is obtained for the rate of climb of a jogged dislocation with DJ, the diffusion

rate

for

pipe

diffusion

substituted

for D,. The data of Auskern and Belle 30) were extrapolated to give self-diffusion coefficients for uranium in UOa of 10-l*, lo-16 and lo-l5 om2/seo at 950, 1150 and 1350 “C, respectively. Since Reimann and Lundy 31) have shown that these values are almost certainly due to short circuit or pipe diffusion, any climb velocity calculated on the basis of the chosen diffusion coefficients represents an upper limit of climb velocity. The results are summarized in table 2. For the test times imposed, the calculated velocities would permit a climb distance of less than one Burgers vector for all specimens tested at

950 “C. Specimens at temperature 2 min or less at 1150 “C would also be restricted to less than one Burgers vector of dislocation climb. A test time of 7 min at 1150 “C (specimen 130-6, fig. 7) would permit a climb distance of about 3b, and 30 min at 1150 “C (specimen 130-3, fig. 14) yields about 9b. It is therefore unlikely that annealing or recovery produced observable changes in the .dislooation configurations at 1150 “C or lower. At 1350 “C, a climb distance of approximately 20b is calculated for specimen 110-5, while for specimen 110-3 (fig. 18) a possible climb of 300b is calculated. The electron photomiorographs indicate that only fig. 18 shows obvious annealing effects. In this specimen, rearrangements in the tangled cell boundaries have occurred to give some segments of a dislocation net. The presence of many loops of a variety sizes has been

noted

in the

deformed

of

UOa

structures. The loops are prismatic dipole loops, lying at a steep angle to the slip plane, rather than perpendicular

to it, because of the slight

displacement of the edge components of the dipole by elastic interaction. The separation between the dislocation lines comprising the elongated sides of the loops, as projected in the (100) plane, is equal to the height displacement of the elements of the dipole. The longer sides of the prismatic loops lie in their slip plane, and could move under the application of a sufficiently high stress. The shorter sides of the loop are edge dislocations lying on (110) planes. Any significant enlargement of the loop in its own plane requires nonconservative motion of these short-edge com-

136

C.

which may the The

not

the loop

of

which to the Since the

planes,

are

Previous investigators

of some the prismatic by slip either or of the of the is therefore It has been noted loop configurations observed in which imply

of the The prospect more than slip system involved in growth of loops leads many possibilities formation of complex shapes Some of possible steps which these loop shapes be attained indicated in 23. In observed to cusps in

respects the processes this work UOs are similar noted in The formation dislocations,

Fig.

dipoles,

Possible

loops all processes have been in many and alloys. formation tangles

dipole

steps

substructure is

leading is

degrees

of

particular factors,

so

influenced

is no

in

a

and

metals. The required

structures

of

to noted in

common observation

compare

reported slip high temperatures the (1 plane, and Roy, and 4) have that (1 slip in is readily at sufficiently temperatures. Enlarge-

formed UOs

MCHARGIUE

promote

the plane

(100)

0.

is

as

a shear loops, fig.

sides lie

AND

deformation

manner

but does of the

potentially

at

shear stress, in such

enlargement it

permissible

temperature

ditions.

YUST

to by

in attempting

the

UOa

with

specific

and alloy Some genemay be however. Data iron (bee) Keh and as) indicate above 100 (0.2 absolute point) cell occurs at low degrees deformation, in UOZ, 1000 “C absolute melting extensive deformation, to 15% Work

required for formation on metals summarized

to Swann 33)

that for single crystals cells not yet an observation is comparable the behavior here in The dislocation reported for single crystals Swarm: lOa/cm2 the end stage I, also comparable that observed UOa single at 1 5% deformation. is also to note extended dislocations stacking faults not observed the deformed structures. 10%

the enlargement

prismatic

loops.

DISLOCATION

5.

SUBSTRUCTURES

8) H. Blank and S. Am&n&x,

Summary The dislocation

substructure

of UOs single

in compression

to strains of crystals deformed 1 and 5% at various temperatures and strain rates

have

been

examined

by

electron

mi-

croscopy. The structures consist of dislocations of the (100) (110) slip system. Dislocation dipoles and dipole loops are formed at an early stage of deformation,

and tangles are formed

at a later stage. The initial stages of deformation involve the relatively free motion of dislocations through the lattice, which gradually begin to interact, forming tangled dislocation clusters. Subsequent deformation is accomplished by motion of dislocations between the tangles and an increase in the complexity of the tangled regions. The dislocation density as a function of strain was evaluated by measurements from the electron micrographs. The yield stress versus temperature curve has a minimum at 950 “C, and the load-deflection curve shows serrations after approximately 28% strain at 1150 “C. The dislocation velocity as a function of applied shear stress has been estimated and shows that dislocations move most rapidly at 950 “C for a given stress, which supports observed minimum in the yield stress.

the

References 1) W. L.

Phillips, Jr., J. Am. Ceram. Sot. 44 (1961) 499 ? E. J. Rapperport and A. M. Huntress, Nuclear Metals (USA) Report, NMI-1242 (Sept. 1960) 9 K. H. G. Ashbee, Proc. Roy. Sot. (London) Ser. A 280 (1964) 37 4) A. G. Evans, C. Roy and P. L. Pratt, Proc. Brit. Ceram. Sot. 6 (1966) 173 5) A. A. Urusovskaya and V. G. Govorkov, Soviet Phys.-Crystall. 10 (1966) 437, in English translation

137

J. Appl. Phys. 34 (1963) 2200 7) F. R. N. Nabarro, Z. S. Basinski and D. B. Holt, Adv. Phys. 13 (1964) 193 9 A. T. Chapman and G. W. Clark, J. Am. Ceram. Sot. 48 (1966) 494 A. J. Manley, J. Nucl. Mat. 15 (1965) 143 7 loI C. L. Formby, Phil. Mag. 13 (1966) 621 11) J. R. Low, Jr. and A. M. Turkalow, Acta Met. 10 (1962) 215 12) J. J. Gilman and W. G. Johnston, J. Appl. Phys. 31 (1960) 687 13 J. T. Fourie, Phil. Meg. 10 (1964) 1027 1 14 K. Ogawa, Phil. Mag. 14 (1966) 619 1 P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. 15) Pashley and M. J. Whelan, Electron Microscopy of Thin Crystals (Plenum Press, New York, 1965) p. 422 A. H. Cottrell, Dislocations and Plastic Flow in l5) Crystals (Oxford Press, London, 1953) J. J. Gilman, in Progress in Ceramic Science 1 9 (Pergamon Press, 1961) p. 179 18 J. J. Gihnan, J. Appl. Phys. 36 (1965) 3196 1 P. B. Price, Phil. Mag. 5 (1960) 873; 6 (1961) 449 9 A. S. Tetehnan, Acta Met. 10 (1962) 813 2O) 21 A. S. Tetelman, Phil. Mag. 7 (1962) 1801 22 J. Washburn, in Electron Microscopyand Strength I of Crystals (Interscience, 1963) p. 301 23 P. B. Hirsch and T. E. Mitchell, Can. J. Phys. 45 1 (1967) 663 W. A. Brantley and C. L. Bauer, Phys. Stat. Z4) Sol. 18 (1966) 465 25 J. D. Eshelby, C. W. A. Newey, P. L. Pratt and ) A. B. Lidiard, Phil. Mag. 3 (1958) 75 26 J. E. Caffyn, J. C. de Freites and T. L. Good1 fellow, Phys. Stat. Sol. 9 (1965) 333 I. Kishsh, Soviet Phys.-Crystall. 10 (1966) 740, 27) in English translation 22 R. W. Davidge, Phil. Mag. 8 (1963) 1369 ) J. P. Hirthe and J. Lothe, Theory of Dislocations 22) (McGraw-Hill, 1968) p. 510 A. B. Auskern and J. Belle, J. Nucl. Mat. 3 29 (1961) 311 D. Reimann and T. S. Lundy, J. Nucl. Mat., 21) to be published 82 A. S. Keh and S. Weissmann, in Electron Micro) scopy and Strength of Crystals (Interscience, 1963) p. 231 ss) P. R. Swarm, ibid. p. 131