STRUCTURAL AND MECHANICAL STUDY OF CREEP IN Al2O4Mg SINGLE CRYSTALS

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STRUCTURAL AND MECHANICAL STUDY OF CREEP IN Al2O4Mg SINGLE CRYSTALS

N. Doukhan, R. Duclos, B. Escaig

To cite this version:

N. Doukhan, R. Duclos, B. Escaig. STRUCTURAL AND MECHANICAL STUDY OF CREEP IN Al2O4Mg SINGLE CRYSTALS. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-379-C9-387.

�10.1051/jphyscol:1973965�. �jpa-00215441�

JOURNAL DE PHYSIQUE Co//oque C9, supplkment au no 11-12, Tot?lcl 34, Nouet?lbre-Dkcetlibre 1973, page C9-379

STRUCTURAL AND MECHANICAL STUDY OF CREEP IN AI,O,Mg SINGLE CRYSTALS

N.

D O U K H A N ,

R.

DUCLOS and

B. ESCAIG

Physique des Dkfauts d e 1'Etat Solide, Equipe Associte a u

CNRS

no 374, Universite des Sciences et Techniques de Lille, BP 36, 59650 Villeneuve-d'Ascq, France

RbsumC. - Le fluage de rnonocristaux (A120s)~.rMg0 a CtC etudie en compression selon I'axe

<

100

>

entre I 300°C et 1450°C. 11 suit une loi :

5.3

=

0,5 eV

- ,,lu1,cJ;0,3 e=p ^.-

(.

^--

-~-)

lc T

coherente avec un fluage de glissen~ent contrble par la montee des dislocations. Nous avons observt aussi la structure cellulaire de fluage, par topographie de Berg-Barrett et microscopic klectronique a 1 MV et 100 kV, a la fois a l'echelle de I'echantillon et

a

celle de la dislocation. Cette sous-struc- ture est ensuite discutee en fonction de la loi de fluage trouvee.

Abstract.

-

The creep law of (A1203)1 8MgO single crystals has been experimentally derived from usual

<

100

>

compression creep tests in the temperature range I 300 "C-1 450 OC. It obeys a so called dislocation creep equation :

;

⁼ a.3 ^{q.0 3} exp ^-

(K

/c T

which is consistent whit11 a glide creep controlled by dislocation climb. A well defined cell struc- ture develops during creep, which is observed by Berg-Barrett topography. 1 MV and 100 k V electron n~icroscopy both at [he sample scale and at the dislocalion scale. The features of this creep substructure is discussed in relation with the obscrved creep law.

1.

Introduction. - Little is known about the mechanical properties of crystals with the spinel structure, although of increasing technical i ~ n p o r t a ~ l c e in the field of high performing ceramics. On the other hand, magnesium aluminate spinels offer

a

unique example of a whole range of solid solut~on withalumina,

i.

e,

a

whole serie ofcrystals (A120,),, MgO with the stoichiometry 17 ranging from I to 5. This system allows to study the mechanical influence of widely different contents of empty sites in the cation sublattice w11icl1 exist in large number

i n

crjstals with different 17's. This can possibly influence three aspects of mechanical properties :

(i)

Transit1011 from the metallic

: ^{I I}

^{I )} slip planes for n =

I .

to the ~ o n i c

.(

l I0

j

ones for 11 >

1

[8].

(ii) The nature of an eventual Peierl5 frict~on at temperature below 0.5 T,,, (synchro-shear mecha-

I

450 (JC (0.65-0.71 T,,,), and under a constant resolved shear stress of 5 kg/mm2 2: 0.4

x

l o p 3 p, where ji

is the shear modulus.

The creep law is experimentally derived from usual

<

¹⁰⁰

>

conlpression tests ; these results are confront- ed with a n extensive observation of the steady stare substructure which develops into the sample during creep. Berg-Barrett topography, 1 MV and 100 kV electron microscopy observations are used to follo\v the substructure both at the sample scale and at the dislocation scale.

The creep law observcd is consistent with a glide creep controlled by dislocation climb. We also obtained some evidences about the questionable dissociation of disloca~ions in that structure and about the possible stoichiometry defecis which exist when heating up the sample in vacuum inside the microscope.

nism) [14].

(iii)

The

diflusivities

of ion species

alld

climb 2.

Experimental techniques. -

2 I

MATERIALS A N D

process of dislocations

temperature lligher ^CR~:" PIPPARATUS. - Large single crystal boules

0.5 T,. of aluminium spinel have been bought from Cris-

taltec

(LETI,

Grenoble). They are Verneuil grown We started a program of study of creep properties with n stoichiometry (AI20,),,MgO, 11 = I

.8. A

for single crystals wit11 stoichiometries 17 = 1 and spectrographic analysis gives an impurity content n =

1.8

in order to elucidate these points. We report of a few 10 ppm. mainl)

Ca"

and F e + ' + .

in this paper on preliminary results obtained for Creep samples are then cut from a bogle with a the stoicl~iometry ,I = 1.8 betueen 1 300 "C and boron carbide sau into a

1

/

2

x 6 mm3 cube.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973965

C9-380 N. DOUKHAN, R. DUCLOS A N D B. ESCAIG

This cube is oriented by Laiie back reflection into tlie [OOl] direction, i. e. the compression axis, with longitudinal faces along { 100 ) planes. These faces are polished until a 1 pm diamond paste, and the ends of each specimen are carefully ground perpen- dicular t o the [OOI] axis.

All specimens are tested in air inside a furnace with a S i c heating element, with the temperature measured right at the sample. Compression creep is performed between two alumina rams. Ram inden- tation is easily avoided, provided that single crystal alumina buttons are placed in between sample and rams, having their c-axis parallel to the rams. A thin (10

pm) platinum sheet protects the sample

from alumina. The strain was measured by one sapphire rod which impinges into the alumina button, just above one face of the specimen, and is connected t o a linear voltage differential transformer and recorder in such a way that any change in the rams length, either thermal or elastic, is eliminated from the measurement. During each test tlie temperature is maintained constant t o an estimated + ^{4 OC.}

If now we have some equilibrated dislocation wall (as much of one sign as the other), then the reflected beam images on the film a typical cusp featuring this kind of micro-kink band (the so-called displa- cetnent contrast

;

see for ex. Fig. 4).

The other

R component in tlie reflecting plane, y,

lies perpendicular to the incidence plane

;

it gives rise to an equal change

y

in the incidence angle which is brought out of the Bragg conditions as soon as

y

is larger than A0

;

then there is no more X-ray reflection and this causes a white band to appear on the image film, featuring the misorienta- tion

y

(tlie so-called ot.ioltatiotl contrast). Finally the third R component is normal to the reflecting plane, so that it let be it unchanged and is neutral for tlie X-ray reflection.

In preparing samples for BBT, care has t o be taken t o avoid any misleading surface markings originated from sawing or mechanical polishing.

This is achieved by dissolving surface regions of tlie crept specimen with orthophosplioric acid during half

a n

hour at 300 "C for { 100

)

faces or at 350 OC for { I10 ) ones.

2 . 2 SUBSTRUCTURE

OBSERVATIONS. -

The creep ~ i ~

two

~ radiations have been used in this l l ~

substructure of each sample is observed at both two work

:

(i) ~ 1 K~ radiation with a vanadium ~ ~ ~ ~ i ~ ~ scales

:

a t the sample scale first, by Berg-Barrett filter for reflections of the type < 440 > on { 100 }

topography (BBT) and at

a

microscopic scale by or ( 110 ) faces

;

and (ii) copper Kg radiation with transmission electron microscopy (TEM). a nickel filter for reflexions < 800 > on

{

100

)

2 . 2 .

1

Berg-Barrett toj~ogra/)li!..

^-

BBT is an X-ray reflection topography. We used it following the method described by Wilkens [I]. Two main types of contrasts occur

:

(i) extinction contrasts. Because of lattice dis- tortions, the primary extinction is decreased in those regions where dislocations lie so that more X-rays are locally reflected than it should be if there was no dislocations at all at the place. This causes a local enhancement in the reflected intensity wliicli allows imaging the defects.

(ii) Rotation contrasts. These contrasts originate from local lattice rotations R. It allows t o separate in a given dislocation wall those dislocations whicli equilibrate their signs from those dislocations whicli are in excess and give rise to a misorientation between the two neighboring subgrains. This is readily seen if R is decomposed into its three orthogonal compo- nents.

One is lying both in the reflecting plane and in

or ( 1 10 ) faces and < 444 > on {

l

10 ) faces. Emul- sions films are either H R P Kodak plates, or 10 pm llford nuclear plates. Exposure time needs t o be about a day.

2 . 2 . 2 TEM.

-

From the crept specimens, longi- tudinal { 100 ) lamella are sawed and mechanically thinned with carborandum until being a few thenth of millimeter thick. Then a chemical thinning with orthopliosphoric acid at 300 OC [2], working at a dissolution rate of about 250 pm per hour, allows us to obtain a

5 000

A thick lamella which is enough in the case of spinel because it does not absorb very mucli. After washing in boiling water then in ethylic alcliool, the lamella is mounted between two grids inside tlie microscope. Botli 100 kV (Philips EM 300) and 1 000 kV (in the Laboratory of Electronic Optics in Toulouse) images have been observed. Good diffraction conditions for imaging are

g =

{ 440 1,

{ 400 }, { 131

),

{ 151 ). We used also

g =

{ 220

)

for caracterizing extended defects [2].

the X-ray incidence plane. let be called it P

: then

3, Experimental results. Only preliminary results it can be shown that /? makes the incidence angle ,re reported below. specimens have been

crept

change by about p2/2

;

it means that wit11 an usual i n the temperature range 1300-1450 IIC under

a

Bra!% width

A 0 of

about

^{' ' 7}

the plane const;lnt applied stress

of

10 ( i e.

8

resolved still remains in Bragg position until /? is not larger shear stress of 5 kg/mm2 on the active ( 1 10

)

slip than a few degrees

;

however tlie reflected beam is plilnes),

deflected through an angle 2

/I

sin

0 normally to the

incidence plane, causing its image point t o be 3 .

1

CREEP

^{L A W .} -

Figure In shows a typical

displaced on the emulsion film by 2 Pel sin 0 if

tl

creep curve obtained at T

= 1

412 OC and a resolved

is the spacing between reflecting plane and film. shear stress of 5 kg/mm2. After some hours of tran-

STRUCTURAL AND MECHANICAL STUDY OF CREEP IN AlrOjMg SINGLE CRYSTALS C9-381

FIG. 1. - a ) Creep curve at a temperature T = 1 412 OC and under a resolved shear stress CT = 5 kglrnrn?. b) Creep rate (logarithmic scale) versus l / k T , for the constant resolved shear stress a = 5 kglmrnr. The slope gives the creep activation

energy.

sient creep, a quasi steady state creep is reached which obeys the usual equation :

= Aa" exp - - U kT

where A is constant, a is the stress and n a constant stress exponent, U is the creep activation energy and

IC

the Boltzmann factor and

E'

is the creep rate.

The creep activation energy :

has been determined from the creep rates observed a t two different temperatures under the same stress and the same creep substructure. This is achieved either by conventionnal, or differential tests.

Conventionnal tests consist in plotting the steady state creep rate (in logarithmic scale) versus T - I

for different samples. Figure Ih shows that a straight line results. the slope of which gives :

Differential tests consist in temperature jumps performed 011 the same specimen while i t is creeping

at the steady state creep rate E , . With jumps T , -

T,

=

L-

15 (IC, it takes about ten minutes to reach a new steady state creep rate

l,.

This gives a value :

in a good agreement with conventionnal tests.

The stress exponent

n

is measured in a similar way by the stress jump method :

. .

where E , , are again the steady state creep rate before and after the jump. Using a , - a , = f 1 kg/

mm2 we found n = 3.9

+

0.3 in the whole tempe- rature range.

A wider stress range would have t o be investigated in order to establish if the creep rate depends on the stress through a power law as assumed here, o r through an exponential law as it would follow from a stress dependence of the activation energy (giving rise t o an actual activation volume).

3 . 2 CREEP SUBSTRUCTURE. - 3 . 2 . 1

Slip

systems. - After a few percent strain, birefringence observations show clearly that slip occurs on

(

110

) <

110

>

systems for the present stoichiometry. The four systems expected from the [001] compression axis are effectively seen to be active at least in the first few percent strain.

BBT confirm this point, as does also measuring the sample cross-section before and after the creep.

However, once about four percent strain is reached.

only two perpendicular slip planes really work making the sample to become flat-barrel1 shaped at the creep end.

3 . 2 . 2 Substructure c)r!ollctio17. - The substructure evolution as a whole has been followed versus strain, at 1-3-7-9-12 percent strain. Mainly BBT and some high voltage microscopy

( 1

MeV) observations have been used. All the BBT pictures shown here (Fig. 2 and

4)

are topographies of the (100) face under the g = [440] reflection. A more complete report of the topographic work is given elsewhere [3].

Dependent on the strain. some remarks are to be noted :

3 . 2 . 2 . 1 Loll s f / . n i / ~ , tru~r.ri~/lt creep. - Figure 2a gives a typical view of the as-grown bulk crystal.

Only a few dislocations are seen ; there are some subgrains, about 500 pm in size, bounded by subgrain boundaries the misorientation of which is around half a degree. Of course dislocations are probably more numerous near the surf'ace regions in the speci- mens which are mechanically polished prior to creep test. Figures 2h. c.. (/show the bulk creep substructure.

once the damaged superficial regions have bccn chemically rcmovcd.

C9 382 N. D O U K H A N , R. D U C L O S A N D R. ESCAlG

FIG. 2. - Berg-Barrett topographies of the (100) face of spinel single crystals with thc g

-

^[440] reflection : n ) as-grown : b) loaded only a few minutes ; c) one percent creep strain at T = 1 450 "C ; r l ) thrcc percent crcep strain at T ^-- 1 300 "C.

On figure 2b, the specimen has been loaded during only a few minutes. In the part shown there, slip lines are visible in the two (01

1 )

and (01 I) directions

;

in some other parts traces of the two other ( 110 ) slip planes are also found.

Figure

2c and ti

show that dislocations at

I

o r

3

percent strain are still concentrated in glide bands nearly parallel to the < I10 > directions. The crossing

of

a

band by another one seems to be a difficult process

:

many bands are seen stopping against each others

;

no real cell structure is formed.

This view is precised by the high voltage microscopy observations (Fig. 3) performed on a I percent creep strain specimen. On the (001) lamella observed, two different features are apparent

:

( i ) Fine subgrain boundaries. probably already

S T R U C T U R A L A N D MEC'HANICAL S T U D Y 01' C R E E P IN AlzOjMg S I N G L E C R Y S T A L S C9-383

F I G . 3. - 1 M V electron micrograph of a one percent creep strain specimen : (031) lamella : the edge dipole seen in A is cnlarged ; note an as-grown s ~ ~ b - b o ~ l n d a r y on the right a n d num:rous lo:ig edge dislocations parallel to [100].

n tlie as-grown crystal, formed by two dislocation families and not in any of the .( 110

i

planes (see on the riglit part, Fig. 3).

(ii) Long edge dislocations, parallel to [100]:

whicli seem t o stari clustering in a more o r less loose way. More random, steeply inclined dislocations are also visible : they are of a nearly edge character and belong to tlie

( 1

10) [I 101 system, showing that this later has to be activated in the first creep stage.

3 . 2 . 2 . 2 F o l ~ ~ l l a t i o ~ l ( ? / ' ( I . S ~ C C I I / I ~ stcite cell sh.lic.ture. -

As tlie strain increases. a well defined cell structure takes place. At a seven percent strain this is clearly seen from figure 4rr and 0. but the cell size is not yet liomogeneous everywhere as figure 40 and 4h give a n exemple. Some equilibrium size develops however more and more as the strain goes on increas- ing : at

9

percent strain it is practically achieved everywliere tliroughout the whole sample and does not vary much at 12 percent (Fig. 4c and (1). Thus the steady state S L I ~ S ~ ~ L I C ~ L I I - ~ appears to be set in the sample not before about 0.1 creep strain.

Once i t is set up. this cell size is no more dependent on temperature o r strain. How i t varies with stress is

n o w

being planned to be investigated in a furtlier work.

3 . 2 . 2 . 3 S I I . L I ~ ~ I I I . C of' (.(.I/ II.LI//.Y. - Analysis of Berg-Barrett contrasts allows to obtain informations about the lattice rotations associated with a cell wall. On the othel- hand, TEM gi\.es direct pictures of walls. The two methods agree to represent :I cell wall as a simple tilt boundary. tlie boundal-y plane being either (01 I) or (01

1 ) .

i. e. the two prevailing slip planes and tlie t i l t axis lying at their intel-section.

i. e. along [I001 : i n addition the boundary sllould contain

a

lot o f opposite dislocations ~vithout efrect on the t i l t angle.

No orientatidn contrast is seen when [OOI], i. e.

tlie compression axis is set normally to the incidence plane. This is the case figure

4

where cell valls are imaged only by extinction contrast. Thus the lattice rotation axis,

R

lies in tlie (001) plane. On the otlier hand, these extinction contrast lines are cusped by crossing each otlier, whicli is very typical of a displa- cement contrast (see

4

2 . 2 . 1 ) . In the geometry of figure

4,

it stems from a [I 101 component of S2 but

it

sliows chiefly some kink band cllaracter around that axis within the cell walls, i. e. that cell walls contain

a

lot of those opposite dislocations which give rise to these typical cusps.

Further topographic work on 9 percent creep strain specimens allows a precise determination of R,

\vhicli is found mninly along [I001 [3]. When setting the [I001 axis normal to the incidence plane, a stronF orientation contrast is observed ; with [OIO] normal to this plane. the orientation contrast is much weaker but still n o n zero. We think this slight [OIO] compo- lielit of

R

is due to a residual contribution of tlie two others weak d i p planes. (101) and (101) the intersection of \vhich is [010] ; indeed that [010]

rotation component is clearly stronger in

I

or 3 percent creep strain specinie~is than it is in the

9

percent ones. i . e. 9 is mel-ely shifting from the [I001

+

[010] = [I 101 direction to mainly the [I001 one when s t e a d state creep is setting up in the sample.

Finally. when topogrupliying the (100) face with the symmetrical reflection g = [I001 any contrast from the t\vo main slip systems vanishes (extinction.

orientation and Jisplaccmcnt) and only residual ccntributions of the otlicl- ones are imaged.

Quantitative e\,aluation of

R

sliows that. while tlie t i l t angle does not exceed n few ~niriutes the kink angle is seen from the cusp i~mplitudcs to be about ten times larger. i . e. cell \valls contain about ten

C9-384 N. DOUI<HAN, R . DUCLOS A N D B. ESCAIG

FIG. 4. - Berg-Barrett topographies of the (100) face of spinel single csyslals after creep ; g - [440] : on thcse topogral~hics, orientation contrasts w o ~ ~ l d be given by [001] lattice rotation component, a ~ i d displacement contrasts by [I 101 components : rr) and b) 7 %crept specimens at I 350 lJC, two regions showing different s i ~ e s of cell 5~ruct~ll-e ; (.) 9

pi,

1 412 "C ; ( i ) I Z P,,.

1 450 "C, crept specimens : the cell size is hornogeneo~~s everywhere.

times more of opposite dislocations than of excess as ciln be seen it is mainly u wall of edge dislocations.

dislocations. pat-allel to [I001 ; Burgers vector determination givcs

T E M

fully agrees with these observations. 9 percent the same [OI

11

vector for all the wall, arid its plane creep strain speciniens reveal several tilt subgrain is observcd to be neat- (01 l j , perpendicular to thc boundaries formed witti only one edge dislocation cotnmon

(01

^{1 )} slip plane. The dislocation density family. Figure

5

shows one of these boundaries ; in the wall is about

2 x

10' c m - l , which would

S T R U C T U R A L A N D M E C H A N I C A L S T U D Y 01' C R E E P IN A120,Mg S I N G L E CRYSTALS 0 - 3 8 5 The few edge dipole still visible in 1 percent strain specimens (Fig. 3 and 6) have evaporated, probably by pipc dilrusion as seen in A , figure

3

and are comple- tely absent at further strain.

t

i

FIG. 5. - 100 kV clcclron micrograph of a 9 ", creep strain specimen : (001) laniclla, g = [440].

correspond to

a

misorientation of about half .I degree A& it!%@ if all dislocations were of the same sign (which we

kllow

is

tile

case from tile

preceding

BBT

obser- FIG. 6. - I MV c l e c t l ~ n mlclogla1711 o f a 1 "/: crept specinlcn ; weak beam c o n d ~ t ~ o n s .

vations). All these features are quite consistent with the above picture.

3 . 2 . 3 TEM locul ohsrruutions. - T E M allows to co~nplete the substructure picture w ~ t h more local observations, i. e. at the dislocation scale. We report below some of these features, particularly on the questionable dissociat~on of dislocations in our spinel crystal.

3 . 3 . 3 .

1

Defort cotit~nt ~~'itliiti ~ I I C cell.\. - Between cell walls dislocation density is observed to be about 10' ~ m - ~ , rather random as is sl~own figure 5 from one side to the other of the ~maged \\tall. They are almost only edge dislocations in the

9

percent speci- mens, belonging to the two ~ u a i n slip $!\terns : parti- cularly, no screw disloc:~tion has been found there.

Apart from slip dislocations, some secondary defects have been observed, probably not essential to the creep itself. Figure

7

shows some small black dots which are seen sometimes decorating edge dislocations after creep. I t is difficult to identify them precisely (vacnncylintel-stitial loops or precipitates), but we I-iave been able to create

a

large number of similar ones when irradiating the sample inside the microscope (in removing the condensor dia- phragms for a while).

3 . 2 . 3 . 2

Di.r.rociutiotl c!j' tli.vlocations. - The large value obtained for the quantity /1b3 =

135

eV, where p = 1.2 x 10'".

G.

S. is the shear n~odulus and

" a .

Flc;. 7. - ( 1 ) 100 kV clectrc~n ~liic~-ogl.nph o f \mall hlack cloi\ cicco~.a[~ng cclgc. di\locotiorl\ after creep. I n

1 7 ) ~ l i \ I o c : i ~ i o ~ i cc?1~11 :I\[ \ L l ~ i i 4 ~ c \ .

C9-386 N. DOUKHAN, R. DUCLOS A N D B. ESCAlG

b

⁼

5.7 A is the smallest lattice period ( I ) , strongly suggests that perfect dislocations sl~ould be disso- ciated a t some extent.

In fact, contrary to Lewis observations [2], [4], we have never seen widely extended dislocations.

Weak beam images show thin and non double contrasts (Fig. 6). Bright field images may often be found thick or doubled depending on diffraction conditions. Such a case is shown figure 8, where two

FIG. 8. - 100 kV electron micrograph of a double dislocation image. Note the zig-zag eontl-ast in phase on the two half-

images. The spacing is a b o ~ r t 100 .\.

steeply inclined dislocations are imaged. However, even in this case the spacing between the two contrast peaks is slightly smaller than

d =

100 A. This means that. assuming the reaction

:

and the dislocation to be edge, the stacking fault energy

y =

pb2/6

nci

should not be smaller than 3 x

{ib

-- 210 ergs/cm2.

3 . 2 . 3 . 3

Remmk. -

We have incidentally observed tliose extended defects which appear in the foil while heating it up inside the microscope. Figure 9 gives their typical staircase shape.

I t

is interesting to note that fault planes are there alternatively ( I 10)

FIG.

^{9. -} Stoichiometry defects after heating u p the specimen inside the microscope : n ) the foil is alrnost perpendicular to the beam ; b) the foil is inclined t l i r o ~ ~ p h a 0 0 ~ 1 t 25" relatively to a ) ; note the contrast vanishes for the defect I in 11).

(1) We have c o m p ~ ~ t e d jc froni the e q ~ ~ a t i o n / I - c4, - 0.7 H, with H = 2 c44 .I- C I- ~ C I I . as ;1 Voigt average [I I]. The cii's are taken from ultrasonic measurements of Lewis [12]

for a stoichiometry I, and Sch~.cibcr [I 31 for stoichionictrics

11 = 7.6 and 3.5. Comparing thcre measurements shows that the stoichiometry infl~rences only a little ( 5

q;)

the clas~ic constants. The same kind of average gives the Poisson ratio.

v

-

^0.25.

and (TI I), as seen in the figure (the defect on (1 10) is seen edge-on figure 6a, the (001) foil being nearly perpendicular to the electron beam). The fault vec- tors have been determined following Lewis [2].

In figure 9, these are

:

R

⁼

+ [IOI], defect I .

R

=

g [ l o l l , defect 2 . R

= $ [Ol I], defect 3 .

None of them are in fault planes. We think of them as stoichiometry defects which accommodate the preferential evaporation of one of the ion species, presumably the oxygen, when heating up in vacuum.

This type of fault is different from the one attributed

by

Lewis to dissociated dislocation ribbons in samples of stoichiometry

n

ranging from 1.5 to 3.5 [4].

None of these defects exist in the as-crept crystals.

4.

Discussion. -

I n order t o give a reasonable interpretation of creep properties, seveval theoritical problems have t o be first answered

:

(i) How have to be mixed up the fluxes of different ion species, i. e. the different diffusivities, in order to make sure that the transported matter be elec- trically neutral

'?

This problem has to start from a defect structure model in spinel (Frenkel versus Schottky pairs), which has not be investigated up t o now.

(ii) How is the rate of ion evaporation/condensation at the dislocation core, compared with the rate of volun~e diffusion, i. e. are the dislocation jogs vacancy saturated

?

This problem deals with a kinetic theory of climb in ionic crystals. The situation is different froni what has been elucidated in metals [5] because once a jog jumps and emits a vacancy, it changes its electrical nature and energy, so that it changes also its ability to absorb or eniit further vacancies at least under thermal equilibrium conditions.

( i i i ) How does the dislocation dissociation influences the climb process

?

Some of these problelns will be discussed in a forth coming paper [6]. For the time being, we restrict ourselves to some conclusions which can be deduced from preceding observations

:

( i ) The creep ~ ~ c t i v a t i o n energy (5.3 eV) falls in the same range as sintering energies measured by Bratton

[7] i n a

MgAI20, powder

( n =

I ) for the initial and intermediate stage. This sintering energy is believed to be a volume diffusion energy but our stoichiometry is different

( 1 1 =

1.8) and stoichiometry effects

^-

although non negligible [8]

-

are not precisely known.

(ii) Spinel single crystal investigated in the range

0.65-0.71 T,,, creeps following a so-called dislocation-

creep law

:

STRUCTURAL AND MECHANICAL STUDY O F CREEP IN AI2O4Mg SINGLE CRYSTALS C9-387

The stress exponent value, the activation energy and the numerous evidences of slip we have observed allow to classify the present creep mechanism as a climb-controlled glide creep.

(iii) The steady state creep substructure consists of a well defined cell structure. Cell walls are merely tilt sub-boundaries containing a lot of opposite dislocations and a slight excess of one sign disloca- tions. This structure is essential for the creep process.

For exemple, decreasing suddenly the stress by a half makes the strain rate going almost to zero, an observation which can only be explained if the controlling step occurs within the cell walls and not in between where dislocation density should be high enough to give some finite extra-strain [9].

So we end up with the view that the controlling climb should be an in-wall process, as it has been proposed for a number of metallic or non-metallic crystals

[lo].

Further work is in progress to enlarge the inves- tigated temperature and stress range and to test in parallel single crystals of stoichiometry n nearly 1.

Acknowledgment. -

It is a pleasure for the authors to thank Dr. Jouffrey, from the Laboratoire d'optique Electronique de Toulouse, for providing the facilities of the 1 MeV electron microscope. Also the support of CNRS is gratefully acknowledged (Action ThC- matique Programmte, PropriCtks MCcaniques des Solides).

References

[I] WILKENS, M., C U I I . J . P/~)Js. 45 (1967) 1101.

[7] LEWIS, M. H., Plril. Mug. 14 (1966) 1003.

[3]

Duc~os,

R., These 3C Cycle, Universite de Lille, a paraitre (1 973).

[4] LEWIS, M. H., Plril. Mug. 17 (1968) 481.

[5] FRIEDEL, J., D i ~ t o ~ ~ t i o l l s (Pergamon-Press) 1964, p. 11 1.

[6] BOUQUIN, A. M., ESCAIG, B., a paraitre.

[7] BRATTON, R. J., J. Amer. Ceram. Soc. 54 (1971) 141.

[8] RADFORD, K. C., NEWEY, C. W. A., Proc. Brit. Ceram.

SOC. 9 (1967) 131.

[9] MUCHERJEE, A. K., BIRD, J. E., DORN, J. E., Trans. ASM 62 (1969) 155.

[lo] BLUM, W., P/I).s. Stat. Sol. ( b ) 45 (1971) 561 ;

POIRIER, J. P., These d7Etat de 1'Universite de Paris-Sud, 1971.

[I I] HIRTH, J. P., LOTHE, J., T/ICOI.Y of dislocations (McGraw- Hill) 1968, p. 404.

[12] LEWIS, M. F., J. Acoust. Soc. Amer. 40 (1966) no 3.

1131 SCHREIBER, J. Appl. Phys. 38 (1967) 2508.

[14] HORNSTRA, J., J. Phys. Chem. Sol. 15 (1960) 311.