HAL Id: jpa-00220700
https://hal.archives-ouvertes.fr/jpa-00220700
Submitted on 1 Jan 1981
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
PLASTIC DEFORMATION OF SLIGHTLY
REDUCED RUTILE
M. Vrinat, M. Blanchin
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C3, supplément au n°6, Tome 42, juin 1981 page C3-79
PLASTIC DEFORMATION OF SLIGHTLY REDUCED RUTILE
M. Vrinat and M.G. Blanchin
Département de Physique des Matériaux (*), Université Claude Bernard Lyon I 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
Résume.- Des monocristaux de rutile ont été réduits à la température de 1323 K sous faible pression partielle d'oxygène à différentes compositions dans l'intervalle H O 2 0000 - ^*~® 1 • 9965 Pui-S déformés plastiquement en
com-pression uniaxiale à la même température, tout en maintenant la composition. La variation de la limite élastique en fonction de l'écart à la
stoechiomé-trie montre qu'il existe deux régimes dans le comportement mécanique de TiÛ2_x en fonction de la valeur de x. Dans le premier régime c'est à dire pour de faibles degrés de réduction (O/Ti > 1,9985), la limite élastique diminue quand l'écart à la stoechiométrie augmente. Pour des degrés de ré-duction plus important (O/Ti < 1,9985), on observe un fort effet de dur-cissement : la limite élastique augmente quand l'écart à la stoechiométrie augmente.
Des mesures du volume d'activation dans ces deux régimes suggèrent que le comportement mécanique du rutile réduit à 1323 K peut être analysé en termes d'interaction entre dislocations et défauts ponctuels : défauts ponc-tuels intrinsèques (titane interstitiel) aux forts degrés de réduction et impuretés extrinsèques pour des compositions se rapprochant de TiO„.
A b s t r a c t . - Rutile single c r y s t a l s were reduced at the temperature of 1323 K under low oxygen pressure to d i f f e r e n t compositions in the range T1O2.0OOO ~ TiOj 9965 and p l a s t i c a l l y deformed under uniaxial compression a t the same temperature while maintaining the composition. The dependence of the flow s t r e s s on the departure from stoichiometry suggests t h a t two regimes of mecha-nical behavior e x i s t for Ti02_x depending on the value of x. In the f i r s t r e
-gime, i . e . for s l i g h t degrees of reduction (O/Ti > 1.9985), the flow s t r e s s decreases when O/Ti decreases. For l a r g e r degrees of reduction (O/Ti £ 1.9985) a marked hardening effect i s observed and the flow s t r e s s increases as the departure from stoichiometry i n c r e a s e s . Measurements of the a c t i v a t i o n volume in these two regimes suggest t h a t the p l a s t i c behavior of r u t i l e reduced a t 1323 K could be explained in terms of i n t e r a c t i o n between d i s l o c a t i o n s and point d e f e c t s , i . e . i n t r i n s i c point defects (titanium i n t e r s t i t i a l s ) a t the l a r g e s t departures from stoichiometry and e x t r i n s i c impurities for composi-tions close to TiO„.
I n t r o d u c t i o n . - R u t i l e i s t h e s t a b l e form of T i O?, t h e h i g h e s t o x i d e of
t h e Ti - 0 s y s t e m . The c r y s t a l s t r u c t u r e of t h e o x i d e s i n t h e composi-t i o n range Ti,0,- - TiO- h a s been e x composi-t e n s i v e l y s composi-t u d i e d i n composi-t h e p a s composi-t composi-t o i d e n t i f y t h e d e f e c t s accomodating n o n - s t o i c h i o m e t r y of r u t i l e .
I t h a s been shown t h a t t h e s t r u c t u r e of t h e Magneli p h a s e s which c o r r e s p o n d t o t h e g e n e r i c formula Ti O _ . w i t h 4 < n < 3 6 , can be d e -s c r i b e d i n term-s of t h e p e r i o d i c a l i g n m e n t of " c r y -s t a l l o g r a p h i c -s h e a r " p l a n e s (CSP) whose o r i e n t a t i o n i s w e l l d e f i n e d b u t v a r i e s from {011}
(*') Associe au C.N.R.S. (LA 172)
C3-80 JOURNAL DE PHYSIQUE t o {132) and t h e n t o ( 1 2 1 ) depending on t h e v a l u e o f n ( s e e B l a n c h i n e t a l . /1/ i n t h i s i s s u e ) . On t h e o t h e r hand, t h e n a t u r e o f d e f e c t s i n s l i g h t l y reduced r u t i l e may b e s t i l l r e g a r d e d a s a m a t t e r o f d e b a t e and t h i s i s d i s c u s s e d f u r t h e r by B l a n c h i n e t a l . /1/ i n t h e p r e s e n t i s s u e .
P h y s i c a l p r o p e r t i e s o f Ti02-x o x i d e s i n t h e composition range Ti01.960
-
T i 0 2 . 0 0 0 have been s t u d i e d a s a f u n c t i o n o f t h e d e p a r t u r e x from s t o i c h i o m e t r y under e q u i l i b r i u m c o n d i t i o n s , i . e . c o n t r o l l e d p a r -t i a l p r e s s u r e o f oxygen a t e l e v a t e d t e m p e r a t u r e s 1000
-
1800 K . The r e s u l t s o f t h e r m o g r a v i m e t r i c /2/,
e l e c t r o m o t i v e f o r c e /3,4/ and e l e c - t r i c a l c o n d u c t i v i t y /5/ measurements show t h r e e d i s t i n c t r e g i o n s o f be- h a v i o r . The f i r s t r e g i o n c o r r e s p o n d s t o t h e h i g h e s t t e m p e r a t u r e s and t h e l o w e s t v a l u e s o f x ; i t h a s been i n t e r p r e t e d ( s e e f o r i n s t a n c e r e - f e r e n c e / 5 / ) , a s due t o t h e e x i s t e n c e of a homogeneous s o l i d s o l u t i o n Ti02-x of i s o l a t e d p o i n t d e f e c t s i n t h e p e r f e c t r u t i l e m a t r i x and it was a r g u e d t h a t t h e p o i n t d e f e c t s a r e t i t a n i u m i n t e r s t i t i a l s , r a t h e r t h a n oxygen v a c a n c i e s /5/. A t l o w e s t t e m p e r a t u r e s and l a r g e s t v a l u e s o f x , o r d e r e d s t r u c t u r e p h a s e s Tin02n-l r e p r e s e n t t h e minimum f r e e e n e r g y whereas t h e i n t e r m e d i a t e r e g i o n i s r e g a r d e d a s a d i p h a s i c one, c o r r e s p o n d i n g t o t h e e x i s t e n c e o f b i n a r y compounds T i 0 n 2n-1-
Ti02-x. R e s u l t s o f s t u d i e s /2/ t o /5/ a l l o w t o d e t e r m i n e a n a l y t i c a l equa- t i o n s i n v o l v i n g t h e d e p a r t u r e x , t h e t e m p e r a t u r e and t h e oxygen p r e s - s u r e . From t h e s e d a t a we have c a l c u l a t e d t h e s o l v u s c u r v e s s e p a r a t i n g t h e t h r e e r e g i o n s d e s c r i b e d above. The c u r v e s a r e p l o t t e d i n f i g u r e 1, i n terms o f 0 t o T i r a t i o v e r s u s t e m p e r a t u r e , d e f i n i n g a p o s s i b l e s o l i d p h a s e diagram.The d e f e c t s t r u c t u r e o f s l i g h t l y reduced r u t i l e Ti02-x w i t h x 5 0.003 was s t u d i e d by B l a n c h i n e t a l . /6/ by means o f t r a n s m i s s i o n e l e c - t r o n microscopy (TEM). CSP
w e r e
n o t o b s e r v e d i n c r y s t a l s quenched from t h e r e d u c t i o n t e m p e r a t u r e o f 1323 K b u t a p p e a r e d o n l y i f t h e quenched c r y s t a l s had been m e c h a n i c a l l y deformed b e f o r e t h e r e d u c t i o n p r o c e s s .s o l i d s o l u t i o n T i O , _
\
B i n a r y compoundk
ZADOR Tin02.. - BLUMENTHAL P ICARD BAUMARD BAUMARD\
F i g , 1.- Phase diagram f o r t h e Ti-0 system n e a r Ti02. Data c a l c u l a t e d from t h e r e - s u l t s o f k ~ a d o r / 4 / , # Blumenthal and Whitmore / 3 / , * ~ i c a r d and Gerdanian / 2 / ,
Baumard / 5
/
,
Baumard (thermogravimetric measurements).2. Experimental.- S i n g l e c r y s t a l b o u l e s o f undoped r u t i l e grown by t h e V e r n e u i l flame f u s i o n method were p u r c h a s e d from D j e v a h i r d j i a n Co. These b o u l e s had been a n n e a l e d a f t e r growth a t 1973 K i n oxygen f o r s e v e r a l h o u r s and t h e n s l o w l y c o o l e d t o room t e m p e r a t u r e : t h i s i n s u r e d t h a t t h e c r y s t a l s were s t o i c h i o m e t r i c /6/. S p e c t r o g r a p h i c a n a l y s i s o f t h e b o u l e s r e v e a l e d a t o t a l i m p u r i t y c o n t e n t o f a b o u t 500 ppm, t h e main i m p u r i t y b e i n g aluminum. Specimens were c u t from t h e b o u l e s /6/ a s pa-
3
r a l l e l e p i p e d s ( 2 . 8 x 2 . 8 x 6
rnrn
) o r i e n t e d s o t h a t t h e [001] a x i s was p a r a l l e l t o t h e l a r g e s t dimension.R e d u c t i o n a n d d e f o r m a t i o n o f t h e c r y s t a l s under u n i a x i a l compres- s i o n p a r a l l e l t o [001] a x i s were performed i n a s t a n d a r d I n s t r o n machine equipped w i t h a f u r n a c e a l l o w i n g t e m p e r a t u r e up t o 1 3 5 0 K. The needed oxygen p a r t i a l p r e s s u r e s p02 were o b t a i n e d by u s i n g t h e h i g h tempera- t u r e e q u i l i b r i u m p r o p e r t i e s o f CO
-
C 0 2 g a s m i x t u r e s d i s s o l v e d i n N2.The g a s e s were p u r i f i e d by f l o w i n g t h r o u g h a copper column a t 650 K
C3-82 JOURNAL DE PHYSIQUE
a p p a r a t u s and f u r t h e r d e t a i l s o f t h e e x p e r i m e n t a l p r o c e d u r e have been r e p o r t e d by V r i n a t /7/.
S t a n d a r d c a l c u l a t i o n s /2/ a l l o w e d t o d e t e r m i n e t h e v a l u e o f p02 c o r r e s p o n d i n g a choosen v a l u e o f t h e O/Ti r a t i o . Due t o t h e i n c e r t i t u d e on t h e v a l u e of t h e t e m p e r a t u r e ( + 5 K ) and p r e s s u r e r a t i o pCO/pC02
( + 4
x
t h e O / T i r a t i o was f i n a l l y d e t e r m i n e d y i t h a n i n c e r t i t u d e o f+
3x
T h i s was checked by means o f t h e r m o g r a v i m e t r i c measure- ments d u r i n g r e o x i d a t i o n o f some o f t h e reduced c r y s t a l s t o t h e s t o i - c h i o m e t r i c c o m p o s i t i o n .The c r y s t a l s were a n n e a l e d 24 h o u r s a t 1323 K b e f o r e t h e d e f o r - mation t e s t , i n o r d e r t o i n s u r e thermodynamic e q u i l i b r i u m o f t h e de- f e c t s . A t t h e end of t h e compression t e s t , t h e samples were c o o l e d i n
-6
a dynamical vacuum o f 10 t o r r . T h i s was shown t o p r e s e r v e t h e compo- s i t i o n o f t h e c r y s t a l s /6/.
Thin f o i l s o f d i f f e r e n t c r y s t a l l o g r a p h i c o r i e n t a t i o n s were prepa- r e d from t h e b u l k specimens f o l l o w i n g t h e p r o c e d u r e d e s c r i b e d by Blan- c h i n e t a l . /6/. They were examined i n a P h i l i p s EM 300 microscope a t 100 kV.
3. R e s u l t s . - 3 . 1 . Mechanical b e h a v i o r . - Regarding t o t h e r e s u l t s o f p r e - v i o u s s t u d i e s / 6 / , t h e p r e s e n t c r y s t a l s were reduced a t t h e t e m p e r a t u r e o f 1323 K t o c o m p o s i t i o n s r a n g i n g from Ti02.0000 t o Ti01.9965 (10-l5 atm. < p02 < 1 a t m . ) A l l t h e compression t e s t s were c o n d u c t e d a t t h e
-5 -1
t e m p e r a t u r e o f r e d u c t i o n and a t a s t r a i n r a t e o f 5.65 x 10 s 181. Due t o t h e compression o f t h e specimens a l o n g t h e [001] a x i s , t h e e q u i - v a l e n t {101} < i 0 1 > s l i p systems were a c t i v a t e d /8/. 3.1.1. S t r e s s - s t r a i n c u r v e s . - Depending OQ t h e v a l u e o f t h e O/Ti r a t i o , f o u r c h a r a c t e r i s t i c t y p e s o f s t r e s s - s t r a i n c u r v e s were r e c o r d e d which a r e reproduced i n f i g u r e 2 ( p l o t t e d i n r a t i o n a l c o o r d i n a t e s ) . A l l t h e c u r v e s e x h i b i t e d an e l a s t i c r e g i o n f o l l o w e d by a p l a s t i c r e g i o n w i t h an i n i t i a l l i n e a r p a r t . Curve ( a ) c o r r e s p o n d s t o t h e s t o i c h i o m e t r i c composition T i 0 2 . S e v e r a l t e s t s l e d t o d e t e r m i n e a mean v a l u e o f t h e flow s t r e s s which
2
was a b o u t 6.5 daN/mm
,
i n agreement w i t h r e s u l t s o f p r e v i o u s i n v e s t i - g a t i o n s /8,9/. A d i s t i n c t i v e f e a t u r e o f t h e c u r v e s were marked s t e p s j u s t a f t e r y i e l d i n g , which i n v o l v e d 6s o f % 0.01-
0.03 d a ~ / m m ~ and6~ o f % ( S O t h a t t h e s e s t e p s c o u l d n o t b e reproduced a t t h e s c a l e o f f i g u r e 2 ) . T h i s s e r r a t e d f l o w was shown t o b e due t o a dynamic s t r a i n a g e i n g (DSA) e f f e c t /9/.
( a ) 2.00000
-
( b ) 1.99940-
( c ) 1.99745 ( d ) 1.99655 F i g . 2.- I n f l u e n c e o f t h e d e p a r t u r e from s t o i c h i o m e t r y on t h e form of t h e s t r e s s - s t r a i n c u r v e s . For 1.9980<O/Ti<1.9970 ( F i g . 2c) a y i e l d d r o p o f r e l a t i v e l y s m a l l a m p l i t u d e was o f t e n o b s e r v e d and t h e flow s t r e s s was found t o i n c r e a s e markedly. The work-hardening r a t e a p p e a r e d t o b e l a r g e r t h a n i n Ti02 immediatly a f t e r y i e l d i n g , b u t was found t o d e c r e a s e and t e n d t o z e r o-2 f o r v a l u e s o f s t r a i n E e x c e e d i n g 2 x 10
.
For 1.9970 5 O/Ti < 1.9960 ( P i g . 2 d ) , t h e flow s t r e s s c o n t i n u e d t o i n c r e a s e ( u p t o t h r e e t i m e s t h e v a l u e i n T i 0 2 ) b u t t h e y i e l d d r o p and t h e s e r r a t e d flow were n o t observed anymore. The work-hardening r a t e was l a r g e immediately a f t e r y i e l d i n g b u t became n u l l and even n e g a t i v e
( w o r k - s o f t e n i n g ) f o r s t r a i n v a l u e s E > 2 x Such a w o r k - s o f t e n i n g e f f e c t had n e v e r been o b s e r v e d d u r i n g p l a s t i c d e f o r m a t i o n of s t o i c h i o - m e t r i c T i 0 2 even a t h i g h e r t e m p e r a t u r e s and l a r g e r s t r a i n s /8,9/.
3 . 1 . 2 . Dependence o f t h e flow s t r e s s and o f t h e work-hardening r a t e on t h e d e p a r t u r e from s t o i c h i o m e t r y . - a ) V a r i a t i o n o f t h e flow s t r e s s . - I n f i g u r e 3 i s p l o t t e d t h e va- r i a t i o n o f t h e flow s t r e s s t a k e n a s t h e s t r e s s oe a t t h e b e g i n n i n g of t h e l i n e a r work-hardening r e g i o n /9/ a s a f u n c t i o n o f t h e c o m p o s i t i o n e x p r e s s e d i n t e r m s o f O/Ti r a t i o ( a q u i t e s i m i l a r v a r i a t i o n c o u l d b e o b s e r v e d on t h e p l o t o f t h e y i e l d s t r e s s t a k e n a t t h e d e p a r t u r e o f t h e s t r e s s - s t r a i n c u r v e from t h e e l a s t i c s l o p e / 7 / 3 .
Two r e g i o n s can b e d e l i n e a t e d i n f i g u r e 3. For c o m p o s i t i o n s c o r r e s - ponding t o O/Ti
>
1.9985, t h e flow s t r e s s d e c r e a s e s a t i n c r e a s i n g de- p a r t u r e from s t o i c h i o m e t r y . I n t h e second r e g i o n i . e . O/Ti < 1.9985, t h e flow s t r e s s i n c r e a s e s a s t h e d e g r e e of r e d u c t i o n i n c r e a s e s .JOURNAL DE PHYSIQUE
F i g . 3 . - Flow s t r e s s v e r s u s O / T i r a t i o ( t h e d i f f e r e n t s e t s of measurements f o r e a c h composition were done on specimens randomly c u t from t h e same b o u l e ) .
c o u l d b e d e t e c t e d i n t h e e l a s t i c r e g i o n o f t h e c u r v e s . On t h e o t h e r hand t h e work-hardening r a t e a f t e r y i e l d i n g , t a k e n a s t h e s l o p e o f t h e i n i t i a l l i n e a r p a r t o f t h e p l a s t i c r e g i o n , d i d e x h i b i t a s i g n i f i c a n t h a r d e n i n g e f f e c t f o r v a l u e s o f O/Ti < 1.9980 ( F i g . 2 ) : t h e work-harde- n i n g r a t e i n t h i s r e g i o n was found t o b e a b o u t 1.8 x
l o 2
d a ~ / r n m ~ com- p a r e d t o a mean v a l u e o f 0 . 6 xl o 2
daEJ/mm2 f o r c o m p o s i t i o n s r a n g i n g fromTi02.000 Ti01.998.
F i g . 4 a
F i g . 4 b
F f g . 4.- M i c r o s t r u c t u r e o f n o n - s t o i c h i o m e t r i c r u t i l e a t i n c r e a s i n g d e g r e e o f reduc- t l o n a s shown by b r i g h t - f i e l d (BF) e l e c t r o n micrographs qf f o i l s c u t from samples
deformed up t o a s t r a i n E : ( a ) T i 0 .99895> E = 4 - I x 10- ; (b) ~ i 0 E = ~ . ~ ~ ~ ~ ~ ~
c3-86 JOURNAL DE PHYSIQUE
F i g . 5 a
F i g . 5 b
3.2. T r a n s m i s s i o n e l e c t r o n microscope s t u d i e s - M i c r o s t r u c t u r e o f t h e TiOZ-x c r y s t a l s a f t e r d e f o r m a t i o n was t h u s s t u d i e d by means o f TEM ob- s e r v a t i o n s r e g a r d i n g t o t h e d i f f e r e n t a s p e c t s o f t h e mechanical beha- v i o r .
I n f i g u r e 4 a r e shown micrographs t a k e n from c r y s t a l s deformed up t o a b o u t t h e same s t r a i n b u t f o r i n c r e a s i n g d e g r e e s o f r e d u c t i o n whereas f i g u r e 5 shows t h e m i c r o s t r u c t u r e of Ti01.99655 c r y s t a l s a t
i n c r e a s i n g s t r a i n s . A l l t h e m i c r o s t r u c t u r e s were found t o b e v e r y s i - m i l a r . No i s o l a t e d d i s l o c a t i o n was s e e n b u t a r o u g h l y c o n s t a n t d e n s i t y o f f r i n g e c o n t r a s t s was observed and c o n t r a s t e x p e r i m e n t s showed t h a t t h e s e f r i n g e s were c h a r a c t e r i s t i c o f e x t e n d e d p l a n a r d e f e c t s . The t r a - c e s o f t h e p l a n e s of t h e f a u l t s when i n t e r s e c t i n g a {010} p l a n e were found c l o s e t o e q u i v a l e n t <132> d i r e c t i o n s ( F i g . 4b) and some f a u l t s c o u l d b e p u t edge on p e r p e n d i c u l a r t o 132 d i f f r a c t i o n v e c t o r s when ima-
-
g i n g f o i l s w i t h t h e e l e c t r o n b e a m p a r a l l e l t o a <112> zone a x i s ( F i g . 5 b ) .I t was t h u s concluded t h a t t h e mean o r i e n t a t i o n o f t h e f a u l t p l a n e s was c l o s e t o (1321, which i s i n d e e d a CSP o r i e n t a t i o n . ( O n e d i d n o t ob-
s e r v e any e v i d e n c e f o r f a u l t p l a n e s c l o s e t o (1211 o r i e n t a t i o n s ) . Higher r e s o l u t i o n TEM o b s e r v a t i o n s and f u r t h e r d i s c u s s i o n o f t h e o r i e n - t a t i o n of t h e CS d e f e c t s p r e s e n t i n t h e c r y s t a l s a r e r e p o r t e d l a t e r i n t h i s i s s u e / I / .
F i g . 6 . - CS p l a n e s r e v e a l e d by a BF micrograph of a f o i l from a non-deformed
Ti0
c3-88 JOURNAZ. DE PHYSIQUE
Micrographs o f f i g u r e s 4 and 5 s u g g e s t t h a t n e i t h e r t h e composi- t i o n , r e g a r d i n g t o t h e t w o r e g i m e s o f mechanical b e h a v i o r p r e v i o u s l y d i s c u s s e d , n o r t h e v a l u e o f t h e s t r a i n r e g a r d i n g t o t h e s h a p e o f t h e s t r e s s - s t r a i n c u r v e s (compare, f o r i n s t a n c e , f i g u r e s 5a and b w i t h f i - g u r e 2d) do n o t seem t o have any s i g n i f i c a n t i n f l u e n c e on t h e micro- s t r u c t u r e observed a t room t e m p e r a t u r e .
T h e r e f o r e non-deformed c r y s t a l s reduced and c o o l e d i n t h e d e f o r - mation a p p a r a t u s f o l l o w i n g t h e same e x p e r i m e n t a l p r o c e d u r e were a l s o s t u d i e d 6 y TEM and C S p l a n e s o f mean o r i e n t a t i o n c l o s e t o (132) were a l s o o b s e r v e d i n many a r e a s o f s u c h non-deformed specimens, a s shown i n f i g a r e 6 .
B l a n c h i n e t a l . /6/ d i d n o t o b s e r v e any C S P i n non-deformed r u -
t i l e c r y s t a l s reduced up t o Ti01.9965 a t 1 3 2 3 K and t h e n quenched from t h i s t e m p e r a t u r e . Such a r e s u l t was r e g a r d e d a s c o n s i s t e n t w i t h t h e diagram drawn i n f i g u r e 1. Compared t o t h e quench r a t e o b t a i n e d by
Blanchin e t a l . / 6 / , t h e c o o l i n g r a t e i n t h e p r e s e n t c a s e ( F i g . 7 ) a p p e a r s s l o w e r , e s p e c i a l l y f o r t e m p e r a t u r e s below 1000 K . A demixtion' i n two p h a s e s c o r r e s p o n d i n g t o t h e d i p h a s i c r e g i o n o f t h e diagram ( F i g . l ) , c o u l d t h u s o c c u r d u r i n g c o o l i n g . A l l t h e s e r e s u l t s t a k e n t o g e t h e r s u g g e s t t h a t t h e m i c r o s t r u c t u r e s o b s e r v e d a t room t e m p e r a t u r e i n t h e p r e s e n t c a s e might b e n o t r e p r e s e n - t a t i v e o f t h e s t r u c t u r e o f t h e c r y s t a l s a t t h e t e m p e r a t u r e o f r e d u c t i o n T~me ( h )
and d e f o r m a t i o n a s f a r
as
t h e o b s e r v e d C S P c o u l d have S e e n n u c l e a t e d from t h e d i s l o c a t i o n s (produced by t h e defor.mation) d u r i n g t h e c o o l i n g o f t h e samples /6/.4 . D i s c u s s i o n . - I n o r d e r t o i d e n t i f y t h e d e f o r m a t i o n mechanisms ope- r a t i n g i n reduced r u t i l e a t 1323 K , f u r t h e r i n v e s t i g a t i o n s o f t h e mechanical b e h a v i o r were made, e s p e c i a l l y t h r o u g h measurements o f t h e a c t i v a t i o n volume.
4.1. yGi_riation o f t h e a c t i v a t i o n volume.- Assuming t h a t a t h e r m a l l y a c t i v a t e d d e f o r m a t i o n mechanism may o p e r a t e i n t h e p r e s e n t c a s e , appa- r e n t a c t i v a t i o n volumes were measured a t 1323 K u s i n g s t r e s s - r e l a x a t i o n e x p e r i m e n t s a t s m a l l p l a s t i c s t r a i n s . The r a t i o of t h e a c t i v a t i o n vo-
+
lume
%
t o b 3 , w i t h b = < i 0 1 > b e i n g t h e B u r g e r s v e c t o r o f t h e g l i s s i l e d i s l o c a t i o n s i n t h e a c t i v a t e d s l i p s y s t e m s / 9 / , i s p l o t t e d a g a i n s t t h e c o m p o s i t i o n i n f i g u r e 8. Again two r e g i o n s c a n be c l e a r l y d i s t i n g u i s h e d i n t h i s p l o t , which c o r r e l a t e w e l l w i t h t h e t.wo regimes o f b e h a v i o r p r e v i o u s l y d e s c r i b e d i n 5 3 . 1 . 2 . m n'
LO- >m F i g . 8.- R a t i o og t h e a c t i v a t i o n volume 0 t o b3 ( b = 5.46 A) v e r s u s O / T i r a t i o . Two1 9 9 9 0 1 ~ 9 8 0 1.9970 measurements were done on each specimen a t very n e a r v a l u e s of the s t r a i n . For
O / T I some compositions, measurements were re-
C3-90 JOURNAL DE PHYSIQUE
c o r r e l a t e d With t h e i n c r e a s e i n t h e flow s t r e s s and i n t h e work-harde- n i n g r a t e observed i n t h e same r a n g e o f c o m p o s i t i o n . The c o r r e s p o n d i n g
3
o r d e r o f magnitude of t h e a c t i v a t i o n volume (Va < 4 0 b ) may be r e g a r - ded a s p o s s i b l y s i g n i f i c a n t o f a p o i n t d e f e c t
-
d i s l o c a t i o n i n t e r a c t i o n( s e e f o r i n s t a n c e
/ l o / ) .
Such a c o n c l u s i o n seems t o b e c o n s i s t e n t w i t h t h e p h a s e diagram p r e s e n t e d i n f i g u r e 1, where it can b e s e e n t h a t t h e e x p e c t e d e q u i l i b r i u m p h a s e a t 1323M
f o r O/Ti 2 1.9960i s
t h e s o l i d s o l u t i o n of t i t a n i u m i n t e r s t i t i a l s i n t h e r u t i l e m a t r i x . The y i e l d i n g mechanism i n reduced r u t i l e c o u l d t h u s b e governed by t h e i n t e r a c t i o n between t h e g l i s s i l e d i s l o c a t i o n s and t h e t i t a n i u m i n t e r s t i t i a l s ( " i n - t r i n s i c " r e g i m e ) , s i n c e f o r O/Ti < 1.9985 t h e atomic c o n c e n t r a t i o n o f t i t a n i u m i n t e r s t i t i a l s e x c e e d s 750 p.p.m. compared t o t h e v a l u e o f a b o u t 500 p.p.m. f o r t h e t o t a l c o n c e n t r a t i o n o f c a t i o n i m p u r i t i e s . The c o n c e n t r a t i o n o f p o i n t d e f e c t s c o r r e s p o n d i n g t o a g i v e n v a l u e o f t h e a c t i v a t i o n volume may b e r e a d i l y e s t i m a t e d s i n c e it i s w e l l known/ l o /
t h a t where R i s t h e mean d i s t a n c e of t h e o b s t a c l e s , i . e . t h e p o i n t d e f e c t s , i n t h e g l i d e p l a n e o f t h e d i s l o c a t i o n s , and X i s t h e w i d t h o f t h e ob- s t a c l e s , Assuming t h a t t h e d i s l o c a t i o n s o n l y i n t e r a c t w i t h p o i n t d e f e c t s l o c a t e d i n t h e i r s l i p p l a n e , it f o l l o w s t h a t where ni i s t h e c o n c e n t r a t i o n ( p e r u n i t of volume) of t h e p o i n t d e f e c t s , i . e . h e r e t h e t i t a n i u m i n t e r s t i t i a l s . Regarding t 6 t h e composition r a n g e i n v e s t i g a t e d , t h e o r d e r of magnitude o f ni i s s m a l l i n t h e p r e - s e n t c a s e , s o t h a t t h e t i t a n i u m i n t e r s t i t i a l s can b e assumed t o remain i s o l a t e d i n t h e r u t i l e m a t r i x and t h e n/ l o /
T o n i c o r r e s p o n d s a n a t o m i c c o n c e n t r a t i o n o f t i t a n i u m i n t e r s t i -
t i a l s
w i t h V b e i n g t h e v o l u m e o f t h e u n i t c e l l , a n d t h e c o r r e s p o n d i n g d e g r e e C o f r e d u c t i o n c a n b e e x p r e s s e d i n t e r m s o f O / T i r a t i o O / T i = 2-
n . V 1 C F o r e a c h v a l u e o f Va m e a s u r e d i n t h e i n t r i n s i c r e g i m e , we h a v e t h u s c a l c u l a t e d t h e e x p e c t e d v a l u e of O / T i , a l o w e r l i m i t o f t h e i n - c e r t i t u d e o n t h i s v a l u e b e i n g e s t i m a t e d f r o m s e v e r a l m e a s u r e m e n t s o fVa
a t t h e s a m e c o m p o s i t i o n . C o m p a r i s o n of t h e c a l c u l a t e d v a l u e s of O / T i w i t h t h e n o m i n a l ( e x p e r i m e n t a l ) v a l u e s ( T a b l e I ) s h o w s t h a t t h e agree- m e n t b e t w e e n t h e t w o s e t s i s r a t h e r g o o d .Table I.- Nominal and c a l c u l a t e d values of t h e O / T i r a t i o r e g a r d i n g t o t h e a c t i v a t i o n volume. Nominal v a l u e s of O/Ti are known w i t h i n an i n c e r t i t u d e f 3 x 1
o - ~ .
c3-92 JOURNAL DE PHYSIQUE
p u r e TiOZ c o u l d b e e s t i m a t e d e q u a l t o a b o u t 4 d a ~ / m m ~ , what a l l o w s t o c a l c u l a t e a * ( y ) f o r Ti02-x i n t h e i n t r i n s i c regime. I n f i g u r e 9 , we have p l o t t e d l o g a * ( y ) a g a i n s t l o g y . Regarding t o e q u a t i o n ( l ) , t h e v a l u e o f
m
which was computed from t h e p l o t by l i n e a r r e g r e s s i o n i s m = 1 . 8 . T h i s v a l u e i s h i g h e r t h a n t h o s e commonly observed i n m e t a l s where 0.5 5m
<
1 /11/. Such a r e s u l t may b e r e g a r d e d a s n o t s u r p r i s i n g b e c a u s e o f t h e i o n o - c o v a l e n t c h a r a c t e r of t h e bonding i n T i 0 2 .0 0.5 1 1.5
1
l o g 10
xY
Fig.9.- Log a * versus log y .4.3. E x i s t e n c e o f an " e x t r i n s i c " behavior-g_eyime- For c o m p o s i t i o n s c o r r e s p o n d i n g t o O / T i > 1.9985, t h e p l a s t i c b e h a v i o r o f Ti02-x i s v e r y s i m i l a r t o t h a t o f T i 0 2 , a s r e p o r t e d above, i n t h a t t h e p e r s i s t e n c e of t h e s e r r a t e d f l o w e f f e c t i s observed. -5 -1 S e r r a t e d flow o c c u r r i n g a t 1323 K ( f o r E = 5 . 6 5
x
10 s ) i n s t o i c h i o m e t r i c r u t i l e was i n t e r p r e t e d by Blanchin e t a l . /9/ a s s i g n i - f i c a n t o f a DSA e f f e c t p r o b a b l y due t o t h e main a l i o v a l e n t i m p u r i t i e s( e s p e c i a l l y At) whose m o b i l i t y i s n e a r t h e a v e r a g e m o b i l i t y of t h e g l i s s i l e d i s l o c a t i o n s .
For O/Ti
>
1.999, t h e a t o m i c c o n c e n t r a t i o n o f t h e non-stoichiome- t r i c d e f e c t s , i . e . t h e t i t a n i u m i n t e r s t i t i a l s , becomes o f t h e same o r - d e r a s t h e t o t a l c o n c e n t r a t i o n of c a t i o n i m p u r i t i e s d e t e c t e d i n t h e p r e - s e n t c r y s t a l s , s o t h a t one may t h i n k t h a t t h e y i e l d i n g b e h a v i o r o f s l i -d e p a r t u r e s from s t o i c h i o m e t r y u n t i l t h e y r e a c h a minimum a f t e r which t h e y i n c r e a s e a s t h e composition t e n d s t o T i 0 2 . T h i s i n c r e a s e was i n t e r - p r e t e d a s due t o t h e i m p u r i t i e s p r e s e n t i n t h e c r y s t a l s ( I ) and t h e
m i -
nimum o c c u r r e d f o r O / T i = 1.99995 a t 1323 K .The e n e r g y of i n t e r a c t i o n between t h e d i s l o c a t i o n s and t h e impu- r i t i e s g i v i n g r i s e t o DSA i n s t o i c h i o m e t r i c T i 0 2 was found t o b e o f s h o r t - r a n g e w i t h t h e main c o n t r i b u t i o n a r i s i n g from e l e c t r o s t a t i c e f f e c t s . Due t o DSA, t h e flow s t r e s s o f commercially a v a i l a b l e c r y s t a l s of T i 0 2 i s f a r h i g h e r t h a n t h a t e x p e c t e d f o r p u r e Ti02 /9/. But t h e d i s s o l u t i o n of a l i o v a l e n t i m p u r i t i e s i n Ti02 l e a d s t o t h e f o r m a t i o n of charge-compensating d e f e c t s i n v o l v i n g i n t r i n s i c p o i n t d e f e c t s /9/ s o t h a t t h e c h a r g e of t h e d e f e c t s i n t e r a c t i n g w i t h d i s l o c a t i o n s i s expec- t e d t o change a s t h e c o n c e n t r a t i o n o f i n t r i n s i c p o i n t d e f e c t s i n c r e a s e s . T h i s could e x p l a i n t h e p r o g r e s s i v e d i s a p p e a r a n c e o f DSA and hence t h e d e c r e a s e i n t h e flow s t r e s s o b s e r v e d a t i n c r e a s i n g d e p a r t u r e from s t o i - chiometry i n t h e e x t r i n s i c regime. S i n c e t h e m o b i l i t y o f t h e i n t r i n s i c p o i n t d e f e c t s i s d i f f e r e n t from t h a t o f t h e " a c t i v e " i m p u r i t i e s / 9 / , DSA i s e x p e c t e d t o d i s a p p e a r c o m p l e t e l y i n t h e i n t r i n s i c regime.
5 . C o n c l u s i o n . - The r e s u l t s of t h e p r e s e n t work s u g g e s t t h a t t h e mecha- n i c a l b e h a v i o r o f r u t i l e reduced up t o t h e c o m p o s i t i o n T i 0 1.9965 a t 1323 K c o u l d be e x p l a i n e d i n terms o f i n t e r a c t i o n between d i s l o c a t i o n s and p o l n t d e f e c t s , i . e . i n t r i n s i c p o i n t d e f e c t s ( t i t a n i u m i n t e r s t i t i a l s ) a t t h e l a r g e s t d e p a r t u r e s from s t o i c h i o m e t r y and e x t r i n s i c i m p u r i t i e s f o r c o m p o s i t i o n s c l o s e t o T i 0 2 . Regarding t o t h e f a c t t h a t t h e t e m p e r a t u r e o f 1323 K i s above h a l f t h e m e l t i n g p o i n t , t h e s t r o n g h a r d e n i n g e f f e c t o b s e r v e d a t t h e flow s t r e s s l e v e l i n t h e i n t r i n s i c regime h a s t o be emphasized f o r s o f - t e n i n g e f f e c t , a c c o m p a n i e d by w o r k - s o f t e n i n g a t l a r g e s t r a i n s , h a s been e x t e n s i v e l y r e p o r t e d i n n o n - s t o i c h i o m e t r i c o x i d e s a t e l e v a t e d tempera- t u r e s / 1 4 / . T e c h n i c a l improvements o f t h e a p p a r a t u s a r e needed t o i n c r e a s e t h e r a t e of c o o l i n g from t h e r e d u c t i o n t e m p e r a t u r e f o r c o n c l u s i v e TEM m i c r o s t r u c t u r a l o b s e r v a t i o n s . These s h o u l d a l l o w a b e t t e r u n d e r s t a n d i n g o f t h e d e f e c t s t r u c t u r e a t t h e d e f o r m a t i o n t e m p e r a t u r e and of t h e work- s o f t e n i n g e f f e c t o b s e r v e d a t l a r g e s t r a i n s . E x t e n s i o n of t h e r a n g e o f c o m p o s i t i o n s and t e m p e r a t u r e s i n v e s t i g a t e d i s a l s o n e c e s s a r y t o c o n f i r m t h e y i e l d i n g mechanism. A l l t h e s e s t u d i e s a r e p r e s e n t l y under way. Acknowledgements.- We a r e v e r y g r a t e f u l t o C. Pi.card ( L a b o r a t o i r e d e s Composss Non-Stoechiom6triques, U n i v e r s i t g P a r i s Sud, 0rsay)who k i n d l y
( ' 1
The concentration of the aliovalent impurities in the specimens studied byc3-94
JOURNAL DE PHYSIQUEmade t h e t h e r m o g r a v i m e t r i c measurements on o u r samples. W e wish t o t h a n k P. F a i s a n t f o r h i s h e l p when d e s i g n i n g and b u i l d i n g t h e e x p e r i - m e n t a l d e v i c e . We a r e a l s o i n d e b t e d t o G. F o n t a i n e and C . P i c a r d f o r h e l p f u l d i s c u s s i o n s d u r i n g t h i s work. R e f e r e n c e s
--
/1/ B l a n c h i n , M . G . , B u r s i l l , L . A . , Hutchison, J.L., Gai, ?., (1981) t h i s volume /2/ P i c a r d , C . , Gerdanian, P . , J . S o l i d S t a t e Chem.14
(1975) 66 /3/ Blumenthal, R . N . , Whitmore, D.H., J . E l e c t r o c h e m . Soc.110 (1963) 92
-
/4/ Zador, S . , E l e c t r o m o t i v e f o r c e measurements i n h i g h tempera- t u r e s y s t e m s , ( I n s t i t u t e o f Mining and M e t a l l u r g y , London) 1968, p . 145
/5/ Baumard, J . F . , P a n i s , D . , Anthony, A.M., J . S o l i d S t a t e Chem.
20
(1977) 43/6/ B l a n c h i n , M . G . , F a i s a n t , P., P i c a r d , C . , Ezzo, M., F o n t a i n e , G . , Phys. S t a t u s S o l i d i ( a )
60
(1980) 357/7/ V r i n a t , M., ThSse Docteur-Inggnieur (1980) Lyon
/8/ B l a n c h i n , M . G . , F a i s a n t , P . , Revue Phys. Appl.
