OXYGEN SELF-DIFFUSION IN SUBBOUNDARIES OF ALUMINA SINGLE CRYSTALS

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OXYGEN SELF-DIFFUSION IN SUBBOUNDARIES OF ALUMINA SINGLE CRYSTALS

D. Prot, M. Miloche, C. Monty

To cite this version:

D. Prot, M. Miloche, C. Monty. OXYGEN SELF-DIFFUSION IN SUBBOUNDARIES OF ALU- MINA SINGLE CRYSTALS. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-1027-C1-1033.

�10.1051/jphyscol:19901160�. �jpa-00230266�

COLLOQUE D E PHYSIQUE

Colloque Cl, supplement au n o l , Tome 51, janvier 1990

OXYGEN SELF-DIFFUSION IN SUBBOUNDARIES OF ALUMINA SINGLE CRYSTALS

D. PROT, M. MILOCHE and C. MONTY

C.N.R.S., Laboratoire de Physique des Materiaux, 1, Place A. Briand, Bellevue, F-92195 Meudon Cedex, France

A b s t r a c t - Oxygen s e l f - d i f f u s i o n has been s t u d i e d i n alumina s i n g l e c r y s t a l s i n t h e temperature range 1520-1750°C by means o f t h e g a s - s o l i d i s o t o p e exchange technique.

A f t e r d i f f u s i o n anneal ing, p r o f i l e s o f oxygen-18 were determined by Secondary I o n Mass Spectrometry. Results i n d i c a t e t h a t two d i f f u s i o n mechanisms are involved: a b u l k d i f f u s i o n mechanism and a subboundary one. The b u l k d i f f u s i o n mechanism can be described by: D(cmz/s) = 99.6 exp ( - 626(kJ/mol)/RT) w h i l e subboundary c o e f f i c i e n t s obey: D' (cmZ/s) = 3 X 1013 exp (-877(kJ/mol)/RT). The l a r g e value o f t h e a c t i v a t i o n energy obtained f o r t h e subboundary d i f f u s i v i t y ( l a r g e r than those r e l a t e d t o the volume one) i s a t t r i b u t e d t o t h e segregation o f an i m p u r i t y along t h e subboundaries.

1

-

Owing t o i t s remarkable p r o p e r t i e s ( h i g h m e l t i n g p o i n t , low e l e c t r i c a l c o n d u c t i v i t y ) alumina i s a w i d e l y used ceramic m a t e r i a l . To understand t h e k i n e t i c s o f many processes occuring a t h i g h temperatures o f t h e use o f t h i s oxide such as s i n t e r i n g , g r a i n growth and creep i t i s necessary t o e x p l a i n how oxygen d i f f u s e s w i t h i n t h e s o l i d . Though several oxygen s e l f d i f f u s i o n s t u d i e s i n a-Al,03 have already been c a r r i e d out, t h e r e i s an important spread i n t h e d a t a and t h e d i f f u s i o n mechanisms i n v o l v e d i n t h i s system a r e n o t y e t f u l l y understood.

I n t h e present study, new oxygen s e l f - d i f f u s i o n c o e f f i c i e n t s are determined by means o f a Secondary I o n Mass Spectrometer equipped t o analyse i n s u l a t i n g samples, and t h e importance o f t h e s h o r t - c i r c u i t d i f f u s i o n i s p o i n t e d out.

2

-

S i n g l e c r y s t a l s grown by t h e Verneuil method were supplied by t h e Bai'kowski Chimie Company. The p r i n c i p a l i m p u r i t i e s were as f o l l o w s : 50 ppm Si, 40 K, 15 Ca, 10 Mg.

A f t e r o r i e n t a t i o n using t h e b a c k - r e f l e c t i o n Laue d i f f r a c t i o n technique, p l a t e s were c u t from t h e boules so t h a t t h e i r l a r g e faces correspond t o a (0001) plane. These faces were then mechanically p o l i s h e d u s i n g successive grades o f diamond pastes down t o 2

m.

2.2

-

A l l samples were f i r s t preannealed i n an oxygen-16 atmosphere d u r i n g a t l e a s t 12 hours a t t h e same temperature as was l a t e r used f o r t h e d i f f u s i o n treatments. The l a t t e r were c a r r i e d o u t by t h e gas-sol i d i s o t o p e exchange method u s i n g 180-enriched gas a t a pressure p = 20 kPa i n t h e temperature range 1520-1750°C.

2.3

-

Analysis o f the d i f f u s i o n p r o f i l e s were performed by SIMS, u s i n g a CAMECA IMS4F. The primary beam was made o f p o s i t i v e cesium i o n s ; i t s i n t e n s i t y was o f t h e o r d e r o f 100 nA o r l e s s . I n order t o prevent t h e storage o f e l e c t r i c a l charges on t h e surface o f t h e samples, they were coated w i t h about 20 nm o f Au metal and a c o a x i a l e l e c t r i c gun was used t o n e u t r a l i z e r e s i d u a l charges.

Two d i f f e r e n t k i n d s o f a n a l y s i s were performed :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19901160

COLLOQUE DE PHYSIQUE

- depth p r o f i l i n g f o r samples annealed a t low temperatures (T < 1600°C) f o r a few ("small p e n e t r a t i o n s " , down t o 1 m).

- l i n e scan f o r samples annealed a t h i g h temperatures ( " l a r g e p e n e t r a t i o n s " , 1 m). I n t h i s case, a b e v e l l e d s e c t i o n o f t h e samples was prepared befot a n a l y s i s (angles o f t h e o r d e r o f 30').

C r a t e r depths o r bevel angles were measured by means o f a Talystep roughness meter, I n t h e case o f depth p r o f i l i n g , p e n e t r a t i o n s c o u l d be deduced from t h e c r a t e r depi t h e t o t a l s p u t t e r i n g t i m e assuming t h e amount o f oxygen secondary ions e m i t t e d d u r i n g a time t o be p r o p o r t i o n a l t o t h e amount o f m a t e r i a l s p u t t e r e d d u r i n g t h e same time. I n thc scan method, t h e h o r i z o n t a l d i s t a n c e analysed had t o be converted i n t o a depth.

The c o n c e n t r a t i o n s o f oxygen-18 were c a l c u l a t e d from t h e measured i o n i c i n t e n s i t i e !

a f t e r c a l i b r a t i o n o f a background ( c a l i b r a t i o n on t h e n a t u r a l i s o t o p e abundance: 0.2 l 8 0 ) .

3 - ^RESULTS

An example o f a S I M S p r o f i l e i s g i v e n i n F i g u r e 1. The c o n c e n t r a t i o n - p e n e t r a t i o n ^I p l o t t e d from such p r o f i l e s e x h i b i t two d i f f e r e n t p a r t s : a f a s t decrease o f 180-concent~

f o r s h o r t p e n e t r a t i o n s (50 t o 150 nm) f o l l o w e d by a second p a r t w i t h a slower (Figure 2). I t can be deduced from these p l o t s t h a t two mechanisms a r e i n v o l v e d : ^c d i f f u s i o n mechanism and a s h o r t - c i r c u i t mechanism.

UJRS-HNDOEI DEPTH P R O F I L E

re' ~ 1 2 0 3 MPS CRRT I

1-

I - - - 4

i

F i g . 1 - D i f f u s i o n p r o f i l e o b t a i n e d b y SIMS f o r a sample s u b j e c t e d t o d i f f u s i o n a n n e a l i t = 3h and T = 1550°C.

Fig.,? -

concentration as a function of penetration (sample sub.iected to diffusion annealing for t

and

1630°C).

3.1

- Bulk diffusion mechanism

In the case of constant surface concentration, the solution of Fick's second law is

where

is the penetration

C

is the measured 180-concentration CS is the superficial concentration

C m

is the natural abundance of the tracer t is the annealing time

D is the bulk diffusion coefficient.

The first part of the concentration-penetration plots leads to profiles in Argerf

Cs)/x coordinates which fit this solution properly (Figure 3). From the slope

C m

- CS

of each of these l inear plots, a bulk diffusion coefficient

is deduced.

The expression of these coefficients as a function of the temperature T can be written

(

^(::/moll)

D

(cm2/s)

exp

COLLOQUE DE PHYSIQUE

Fig.3

- Argerf (Cis--CL) ) as a function of penetration ( t

and

3.2

- Short-circuit mechanism

The existence of two parts in the concentration-penetration profiles suggest thi diffusion experiments were performed in the so called "B" kinetic regime

The

segment must then be related to short-circuit defects. Assuming they were disloci arranged as subboundaries, the diffusion tails were analysed using the solution establ by Whipple /3/ and developed by Le Claire

for grain-boundary diffusion in the ci constant superficial concentration conditions

dLog C(x)

BD' =

0.66 [F] _(- ^dx6I5 1

where

is the grain-boundary thickness and

the bulk diffusion coefficient

From the slopes of the profiles obtained in log C/x6I5 coordinates, subbou diffusion coefficients were deduced. Taking on effective thickness

1 nm, they obey

( ^{877 ( ) ) l ?}

D'

(cm2/s)

3

10' exp

Figure 4 shows diffusion profiles in log C/x6I5 coordinates obtained for se diffusion experiments performed at the same annealing temperature but during diff annealing times

the linearity of the curves and the dependence of their slope o annealing time are to be noticed.

Both bulk and subboundary diffusion coefficients are collected in the table

Fig.4

-

-

Table l : D and D' values f o r d i f f e r e n t annealing temperatures and d i f f e r e n t annea7ing times.

D.P. stands f o r Depth P r o f i l e . L.S. stands f o r Line Scan.

Bulk diffusion coefficient

D (&/S)

5.1 X ]OS'7 1.0 X 10-16 2.1 X 10-l6 3.7 X 10-l6 2.0 X 10'l6 1.9 X 10'16 3.5 X 10-16

9.4 X 10-16 6.1 X 10-l6 5.4 X 10-l6 Analysis

D.P.

L.S.

D.P.

D.P.

D.P.

D.P.

D.P.

D.P.

D.P.

L.S.

D.P.

D.P.

D.P.

L.S.

L.S.

L.S.

L.S.

Annealing temperature

T ( ' C )

1521 1550 1570 1570 1577 1577 1600 1603 1630 1630 1630 1650

1675 1707 1751

Subboundary diffusion coefficient (6

-

D' (&/S)

9.1 X 10-l=

2.3 X 10*12 1.05 X 10-l1

6.2 X 10-l2 3.6 X 10'l2 2.85 X 10-l2

6.8 X 10'12 3.4 X 10-l1 1.2 X I0'l1 1.4 X 10'11 6.0 X 10'l1 5.0 X 10-U 3.2 X 10-U 2.3 X 10-to 1.5 X 10-9 Annealing

time t (h)

5.5 3 3 6 2 6 24

94.25 5 24 84 80 118 72 67

COLLOQUE DE PHYSIQUE

4

- DISCUSSION

Several authors have already measured oxygen s e l f - d i f f u s i o n i n a-AlzO,. The main r are r e p o r t e d w i t h t h e present d a t a i n an Arrhenius diagram (Figure 5 ) . I t must be n o t f the r e s u l t s t h a t we have obtained f o r t h e volume d i f f u s i o n mechanism, especial a c t i v a t i o n energy a r e i n s a t i s f a c t o r y agreement w i t h those o f o t h e r authors. Most 01 data suggest t h a t oxygen d i f f u s i o n takes p l a c e by a vacancy mechanism b u t t h e v a l u e a c t i v a t i o n energy s t i l l remains d i f f i c u l t t o explain. As a m a t t e r o f f a c t , t h e a c t i energy f o r an i n t r i s i n c mechanism would be :

where AH, i s t h e f o r m a t i o n enthalpy o f a Schottky q u i n t e t and AHmV..the o m i g r a t i o n ene an oxygen vacancy.

T h e o r e t i c a l estimates o f d e f e c t formation energies i n alumina /9,10,11,12/ l e a d t a Q

-

.

Assuming the mechanism d i f f u s i o n t o be an e x t r i n s i c mechanism r u l e d by an impur higher valancy than A1 such as s i l i c o n (which appears t o be t h e major i m p u r i t y i n U

samples), t h e a c t i v a t i o n energy would be

/7/:

Q = N,/3 t AHm 1000 kJ/mol

.

I t must be noted t h a t t h e a c t i v a t i o n energy we have measured i s i n b e t t e r agreemer~

the t h e o r e t i c a l c a l c u l a t i o n s i f d i f f u s i o n takes place by an i n t r i n s i c mechanism, bu c o n t r a d i c t s t h e . v a r i a t i o n i n t h e d i f f u s i o n c o e f f i c i e n t w i t h t h e i m p u r i t y content obser several authors /7,8,13/.

l o f and a l . /8/

Present d a t a ( b u l k )

Fig.5

-

A particularly striking result here is the evidence for a short-circuit diffusion mechanism in the single crystals. The linearity of the curves log C

f(x6I5) and the dependence of their slopes on the annealing times imply that the short-circuit paths are rather subboundaries than isolated dislocations /14/. Enhanced diffusion because of dislocations has already been observed in a-Al,03 single crystals in the case of impurity diffusion iron /15/ and silver /16/ can be mentioned. In such cases, the activation energies Q irelated to bulk diffusion) and Q' (related to short-circuit diffusion) were found to have about the same value.

Generally the increase in diffusivity along short-circuits is l inked to a corresponding decrease in activation energies obtained in the case of impurity diffusion in A1,03 . in metals, for example, Q'/Q was explained by the segregation of the - 0.5.The ratio Q'/Q - ¹

diffusion species /16/.The large value (Q'

877 kJ/mol) leading to a ratio Q'/Q - ^1.4

obtained in our case may not be related to the segregation of the diffusing species, as we were studying self-diffusion. Nevertheless the impurity content of our samples is large enough to be responsible for segregation effects dependent on the temperature. Segregation can modify the subboundary structure and chemistry and induce a diffusion mechanism different from the bulk one.

REFERENCES

/l/ Adda,Y. and Philibert,J., La diffusion dans les solides Ed. PUF Paris (1966).

/2/ Harrison,L.G., Trans. Faraday Soc. 51 (1961) 1191.

/3/

Whipple,R.T.P., Phil. Mag. 45 (1954) 1225.

/4/ Le Claire,A.D., Br. J. Appl. Phys. 14 (1963) 351.

/5/ Oishi,Y. and Kingery,U.D., J. chem. Phys. 33 (1960) 480.

/6/ Reed,D.J. and Wuensch,B.J., J. Am. Ceram. Soc. 63 (1980)

/7/ Reddy,K.P.R. and Cooper,A.R., J.

Ceram. Soc. fi (1982) 634.

/8/ Lagerlof,K.P.D., Pletka,B.J., Mitchel1,T.E. and Heuer,A.H., Radiat. Eff. H (1983) 87.

/9/ Dienes,G. J., Welch,D.O., Fischer,C.R., Hatcher,R.D., Lazareth,D. and Samberg,M., Phys.

Rev.

11 (1975) 3060.

/10/ Catlow,C.R.R., James,R., Mackrodt,W.C. and Steward,R.F., Phys. Rev. B 3 (1982) 1006.

/11/ Mackrodt,W.C., Solid State Ionics 12 (1984) 175.

/12/ El Aiat,M.M. and Kroger,F.A., J. of the Am. Ceram. Soc. 65 (1982) 162.

/13/ Haneda,H. and Monty,C., J.

Ceram. Soc. 72 (1989) 1153.

/14/ Le Claire,A.D. and Rabinovitch,A., J. Phys. C: Solid State Phys. 14 (1981) 3863, 15

(1982) 3455.

/15/ Lesage,B., Hunt2,A.M. and Petot-Ervas,G., Radiat. Eff. 75 (1983) 283.

/16/ Badrour,L., Moya,E.G., Bernardini,J. and Moya,F., J. Phys. Chem. Solids 50 (1989) 551.