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HIGH-TEMPERATURE DEFORMATION OF CUBIC OXIDES
J. Routbort
To cite this version:
J. Routbort. HIGH-TEMPERATURE DEFORMATION OF CUBIC OXIDES. Journal de Physique
Colloques, 1981, 42 (C3), pp.C3-59-C3-66. �10.1051/jphyscol:1981306�. �jpa-00220697�
HIGH-TEMPERATURE DEFORMATION OF CUBIC OXIDES*
J.L. Routbort
Materials Seienoe Division, Argonne National Laboratory, Argonne, IL 60439 USA
Résumé.- Les courbes contrainte-déformation de MgO et NiO ont un tauxd'écrouis- sage 8 qui décroît linéairement quand la contrainte augmente jusqu'à un état stationnaire (6=0) alors que la courbe pour CoO présente un crochet de traction et un taux d'écrouissage négatif qui augmente jusqu'à s'annuler quand l'état stationnaire est atteint. Ces résultats prédisent des formes de courbes de fluage similaires pour NiO et MgO, différentes de celle obtenue pour CoO.
Finalement, la contrainte T de l'état stationnaire divisée par le mo- dule de cisaillement est très semblable pour les trois oxydes, NiO présentant la plus grande valeur. La dépendance en température de T est donnée pour les trois oxydes par la loi : log T = B - T/A, où A et B sont des constantes.
A b s t r a c t . - The s t r e s s - s t r a i n curves for MgO and NiO have a work-hardening r a t e 6 t h a t decreases l i n e a r l y with increasing s t r e s s to a steady s t a t e (8=0) while the curve for CoO has an upper yield point and a work-hardening r a t e that
i s negative but increases to zero when steady s t a t e i s achieved. These r e s u l t s p r e d i c t t h a t the shapes of the creep curves for NiO and MgO are s i m i l a r , and
different from those obtained for CoO. F i n a l l y , the s t e a d y - s t a t e s t r e s s T divided by the shear modulus i s very similar for a l l three oxides, with NiO having the l a r g e s t value. The functional dependence of Tg on temperature T for a l l three oxides i s given by log T = B - T/A, where B and A are c o n s t a n t s .
1 . I n t r o d u c t i o n . - H i g h - t e m p e r a t u r e s t r e s s v e r s u s s t r a i n m e a s u r e m e n t s y i e l d i n f o r m a t i o n on t h e m e c h a n i s m s of work h a r d e n i n g a n d r e c o v e r y . I n a d d i t i o n , i f t h e m e a s u r e m e n t s a r e p e r f o r m e d t o s u f f i c i e n t l y l a r g e s t r a i n s , t h e c o m p e t i t i o n b e t w e e n h a r d e n i n g and r e c o v e r y b a l a n c e s a n d t h e w o r k - h a r d e n i n g r a t e becomes z e r o . At t h i s p o i n t t h e s t e a d y - s t a t e s t r e s s T , w h i c h i s d e v e l o p e d u n d e r c o n d i t i o n s of n e a r l y c o n s t a n t s t r a i n r a t e ( c o n s t a n t c r o s s h e a d v e l o c i t y ) , c o r r e s p o n d s t o t h e s t r e s s t h a t m u s t b e a p p l i e d t o g e n e r a t e t h e same s t r a i n r a t e i n a c r e e p t e s t . The r e s o l v e d . s h e a r s t r e s s v e r s u s t o t a l s h e a r s t r a i n (x v s . y) m e a s u r e - ment p r o v i d e s a d d i t i o n a l i n f o r m a t i o n on t h e b e h a v i o r o f t h e w o r k - h a r d e - n i n g r a t e a n d p o s s i b l y on t h e m e c h a n i s m s o f h a r d e n i n g a n d r e c o v e r y .
E x t e n s i v e m e a s u r e m e n t s h a v e b e e n p e r f o r m e d on MgO s i n g l e c r y s t a l s o v e r a w i d e t e m p e r a t u r e r a n g e o f 0 . 4 T t o 0 . 7 - T , , , u s i n g s t r a i n r a t e s
- 7 - 1 - 4 - 1
from 3 x 1 0 s t o 3 x 10 s / l / . The r e s u l t s o f t h e s e m e a s u r e -
* Work supported by the U.S. Department of Energy
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981306
c3-60 JOURNAL DE PHYSIQUE
ments can be d e s c r i b e d by t h e same formalism t h a t was developed t o de- s c r i b e deformation i n f c c m e t a l s , which p r e d i c t e d a s t r e s s - d e p e n d e n t , a c t i v a t i o n - f r e e e n t h a l p y and a t e m p e r a t u r e - d e ~ e n d e n t s t e a d y - s t a t e s t r a i n - r a t e s e n s i t i v i t y .
This n o t e w i l l r e p o r t on t h e r e s u l t s of measurements of T vs.y f o r two n o n s t o i c h i o m e t r i c oxides, N i l - x O and C 0 ~ - ~ 0 . ' T h e o b j e c t i v e o f t h i s work i s t o compare t h e deformation behavior of t h e s e two o x i d e s , which l i k e MgO e x h i b i t p l a s t i c i t y a t low t e m p e r a t u r e s , w i t h t h a t of MgO i n o r d e r t o determine whether t h e formalism e s t a b l i s h e d i n t h e MgO work can be extended t o t h i s e n t i r e c l a s s of oxides. An i n v e s t i g a t i o n of t h e e f f e c t of t h e d e v i a t i o n from s t o i c h i o m e t r y on t h e deformation of COO i s c u r r e n t l y under way /2/.
Cree? d a t a from d i f f e r e n t l a b o r a t o r i e s f o r COO s i n g l e c r y s t a l s of nominally t h e same p u r i t y a r e n o t i n agreement. Two s t u d i e s /3,4/ on COO s i n g l e c r y s t a l s r e p o r t sigmoidal c r e e p , w h i l e t h e o t h e r /5/ r e p o r t s normal c r e e p b e h a v i o r , e . g . , a d e c e l e r a t i n g c r e e p r a t e l e a d i n g t o a c o n s t a n t ( s t e a d y - s t a t e ) r a t e . Measurements of t h e
r
v s . y behavior of COO could r e s o l v e t h i s discrepancy, s i n c e t h e shape of t h e c r e e p curve( s t r a i n v s . time a t c o n s t a n t a ) can be deduced from t h e s t r e s s v e r s u s s t r a i n d a t a . I t should be mentioned t h a t Cabrera-Cano e t a l . / 6 / have r e p o r t e d normal c r e e p behavior f o r N i O s i n g l e c r y s t a l s ; t h e c r e e p d a t a f o r MgO s i n g l e c r y s t a l s a r e a l s o normal /7/.
2. Procedures
.-
Compression t e s t s were performed using an a p p a r a t u s d e s c r i b e d p r e v i o u s l y /1/. MgO s i n g l e c r y s t a l s of v a r i o u s o r i e n t a t i o n s were t e s t e d i n an i n e r t atmosphere. The N i O c r y s t a l s were compressed w i t h t h e l o a d i n g a x i s p a r a l l e l t o< l o o >
I n an argon-oxygen atmosphere.\
(Po2 % 10-3 atm. ) The COO was compressed along
< l o o >
a s w e l l , b u t t e s - t e d using a modified a p p a r a t u s i n which t h e oxygen p a r t i a l p r e s s u r e could be v a r i e d from 1 0 - l 3 t o 1 atm. a t up t o 1500°C. The compression rams f o r t h i s a p p a r a t u s a r e made from A1203 and P t f o i l s a r e used a s a d i f f u s i o n b a r r i e r . A boron n i t r i d e spray i s used t o reduce f r i c t i o n . The MgO c r y s t a l s were purchased from v a r i o u s s o u r c e s , while t h e N i O and COO were grown from 99.999% powder by t h e Verneuil process using a c a r - bon arc-image furnance. The MgO and COO c r y s t a l s a r e approximately5 x 5 x 12 mm i n s i z e while t h e N i O c r y s t a l s , which were used f o r an- o t h e r purpose a f t e r t e s t i n g , were approximately 10 mm i n diameter x 1 0 mm long.
3. Results.- A T v s . y curve o b t a i n e d on MgO a t T = llOO°C and 8 = 3 x shown i n f i g u r e 1 (reproduced from / 1 / ) . The s t r e s s and s t r a i n have been r e s o l v e d on t h e s l i p system ( 1 1 0 ) [110]
,
which i s t h e primary system f o r a l l t h r e e c u b i c o x i d e s . The work-hardening r a t ev a l u e o f T when 8 = 0. Although t h e l l O O ° C (T = 0.45 T ~ ) r e s u l t s r e - q u i r e d an e x t r a p o l a t i o n t o d e f i n e T ~ ,d a t a o b t a i n e d a t h i g h e r tempera- t u r e s o r lower s t r a i n r a t e s r e q u i r e d none. The s h a p e o f t h e T v s . y c u r v e f o r MgO i s s i m i l a r t o t h a t measured i n s t a g e I11 f o r fcc m e t a l s .
Fig. 1.- Resolved s h e a r s t r e s s v e r s u s t o t a l s t r a i n f o r a < 100 > MgO c r y s t a l a t
i 100°c and
<
= 3 x 1 0 - ~ s - l (reproduced from / 11).Data measured f o r N i l - x 0 a t t e m p e r a t u r e s from 1 1 0 0 t o 1 4 0 0 ° C , = 1 . 8
x ~ o - ~ s - ' ,
and Po2 a atm. a r e shown i n f i g u r e 2 . I t s h o u l d be mentioned t h a t s i n c e t h e oxygen p a r t i a l p r e s s u r e was c o n s t a n t , t h e d e v i a t i o n from s t o i c h i o m e t r y x v a r i e d w i t h t e m p e r a t u r e . The s h a p e o f t h e r v s . y c u r v e i s s i m i l a r t o t h a t o b t a i n e d f o r MgO. The work-harde- n i n g r a t e d e c r e a s e s l i n e a r l y w i t h i n c r e a s i n g s t r e s s . S t e a d y s t a t e i s e a s i l y a c h i e v e d a t h i g h e r t e m p e r a t u r e s .Fig. 2.- Resolved s h e a r s t r e s s . v e r s u s t o t a l s h e a r s t a i n a t v a r i o u s t e m p e r a t u r e s f o r a < l o o > Nil-,O c r y s t a l a t E. = 1.8 x 1 0 - ~ s - l and an oxygen p a r t i a l p r e s s u r e o f
atm.
c3-62 JOURNAL DE PHYSIQUE
The d e f o r m a t i o n b e h a v i o r o f C O ~ - ~ O a t 100O0C, x =
7
x and= 5 x 1 0 - ~ s - l i s shown i n f i g u r e 3 . The d a t a show a l a r g e upper y i e l d p o i n t f o l l o w e d by a n e g a t i v e work-hardening r a t e , p r o b a b l y t h e r e s u l t o f d i s l o c a t i o n m u l t i p l i c a t i o n , which r e a c h e s z e r o when t h e s t e a d y - s t a t e stress i s a c h i e v e d . The v a l u e o f -rs depends on x and / 2 / . However, t h e s h a p e o f t h e s t r e s s v s . s t r a i n c u r v e i s i n d e p e n d e n t o f t e m p e r a t u r e and d e v i a t i o n from s t o i c h i o m e t r y .
Fig.3.- Resolved shearestress ve sus total shear strain for a < l o o > Co crystal at 1 0 0 0 ' ~ and E = 10 - 5 3 0.993'
4. D i s c u s s i o n . - I t i s c l e a r from a compariscn o f f i g u r e s 1-3 t h a t t h e t h r e e c u b i c o x i d e s N i O , flgO, and COO do n o t e x h i b i t t h e same high-tem- p e r a t u r e d e f o r m a t i o n b e h a v i o r . MgO and NiO behave i n a s i m i l a r manner, showiAg a p o s i t i v e work h a r d e n i n g r a t e which d e c r e a s e s l i n e a r l y w i t h i n c r e a s i n g s t r e s s u n t i l s t e a d y s t a t e i s approached. T h i s i s shown sche- m a t i c a l l y i n f i g u r e 4 ( l e f t ) a s s o l i d l i n e s . Creep c u r v e s ( a = c o n s t a n t ) o b t a i n e d on m a t e r i a l s t h a t e x h i b i t normal c r e e p b e h a v i o r ( a d e c r e a s i n g
Fig.
4.-
Schematic drawing showing the relation between stress versus strain curves( E = constant) and strain versus time curves ( 0 = constant). Solid lines show normal behavior exhibited MgO and NiO while dashed lines indicate the inverse behavior of coo.
ved) a r e a l s o shown s c h e m a t i c a l l y a s s o l i d l i n e s i n t h e E v s . t i m e ( t ) p l o t o f f i g u r e 4 . T h i s b e h a v i o r i s i n d e e d obser'ved i n s i n g l e c r y s t a l s o f N i O / 6 / and MgO / 7 / .
On t h e o t h e r hand, t h e T v s . y b e h a v i o r f o r COO i s q u i t e d i f f e r - e n t from t h a t o f MgO and N i O . T h i s i s shown a s a d a s h e d l i n e i n f i g u r e 4 ( l e f t ) . C o n s t r u c t i o n o f t h e E VS. t c u r v e s ( a t c o n s t a n t o ) g i v e s t h e c r e e p c u r v e s . shown a s dashed l i n e s i n f i g u r e 4 ( r i g h t ) . I n t h i s c a s e t h e c r e e p r a t e i n c r e a s e s w i t h i n c r e a s i n g s t r a i n u n t i l a c o n s t a n t s t r a i n r a t e i s a c h i e v e d . T h i s r a t e may n o t r e p r e s e n t a s t e a d y s t a t e i n t h e s e n s e of a c o m p e t i t i o n between p r o c e s s e s a s o b s e r v e d i n t h e normal cu- b i c o x i d e s b e c a u s e a t r u e minimum r a t e i s n e v e r r e a c h e d .
Sigmoidal c r e e p would be m a n i f e s t e d i n t h e T v s . y c u r v e a s a d d i t i o n a l h a r d e n i n g . T h i s i s n o t o b s e r v e d w i t h i n e x p e r i m e n t a l e r r o r up t o E = 0.2, a s t r a i n h i g h e r t h a n t h a t used by C l a u s e r e t a l . /3/
b u t s l i g h t l y lower t h a n t h a t ( E c 0 . 3 ) used by Nehring e t a l . / 4 / .
~ o t h groups c l a i m t h a t c r e e p i s s i g m o i d a l . C l o s e e x a m i n a t i o n o f t h e c r e e p c u r v e s of C l a u e r e t a l . /3/ r e v e a l t h a t ( w i t h t h e e x c e p t i o n o f a s l i g h t d e c r e a s e i n
k
f o r E c 0.06) t h e y h a v e t h e i n v e r t e d s h a p e shown by t h e dashed l i n e s i n f i g u r e 4 , which a r e p r e d i c t e d from t h e T v s . y d a t a . The s l i g h t d e c r e a s e i n E may b e due t o f r i c t i o n a l e f f e c t s o r t o b a r r e l i n g , b o t h o f which a r e m a g n i f i e d a s d e f o r m a t i o n i n c r e a s e s . T h e i n - t z r y ~ r e t a t i o n r ~ i v e n by N e h r i r ~ g e t a l . / B / c a n n o t b e d i s c u s s e d b e c a u s e t h e i r c r e e p d a t a a r e oi?ly p r e s e n t e d s c h e n a t i c a l 1 y : T h e s h a p e o f t h e F. v s . t c u r v e s r e p o r t e d by Krishnamachari and J o n e s /5/ a r e normal and a r e i n c o n s i s t e n t w i t h t h e o t h e r two c r e e p s t u d i e s and t h e r v s . y r e s u l t s r e p o r t e d h e r e . I t i s n o t e d t h a t t h e s t r e s s e s t h e y used i n o r d e r t o a c h i e v e t h e same s t r a i n r a t e used i n t h e s h o r t - t e r m t e s t s were c 2 t i m e s l a r g e r t h a n T ~ .I t i s p o s s i b l e t h a t i f t h e s t r e s s - s t r a i n e x p e r i m e n t s were performed t o h i g h e r s t r a i n s , a d d i t i o n a l h a r d e n i n g would b e o b s e r - ved. 3n t h e o t h e r hand, d i f f e r e n c e s i n khe c r e e p b e h a v i o r of COO c o u l d b e a c c o u n t e d f o r by v a r i a t i o n s i n oxygen p a r t i a l p r e s s u r e o r a c t u a l i m p u r i t y c o n t e n t .A comparison o f t h e s t e a d y - s t a t e s t r e s s r s f o r t h e t h r e e c u b i c o x i d e s a s a f u n c t i o n of t e m p e r a t u r e ( n o r m a l i z e d by t h e m e l t i n g p o i n t , T ~ ) i s shown i n f i g u r e 5 . The d a t a were accumulated a t n e a r l y c o n s t a n t and e q u a l s t r a i n r a t e s . I t s h o u l d be mentioned a g a i n t h a t whereas t h e lug0 c r y s t a l s were s t o i c h i o m e t r i c , t h e d a t a f o r N i l - x O were o b t a i n e d a t po2 c 10-3 a t m . , c a u s i n g t h e d e v i a t i o n from s t o i c h i o m e t r y x t o v a r y w i t h t e m p e r a t u r e . The T, d a t a f o r COO a r e shown a t x =
l o e 4 .
P r e l i m i n a -c3-64 JOURNAL DE PHYSIQUE
ry experiments indicate that the
Tof COO may vary by approximately
S
a factor of
3at 1000°C depending on x, and may indeed have
aplateau between T
=1000 and 1200°C for x
%10-3. The composition closest to stoichiometry is shown in figure
5because the behavior of stoichiomet- ric samples may be expected to be more intrinsic and thus comparable to that of 14gO.For these reasons, a comparison of absolute magnitudes of
T,
should be viewed with caution. Furthermore, the rs/p ratio (where
u
=the shear modulus for screw dislocations) is more fun- damental. The high-temperature moduli for NiO and COO have not been measured, but if du/dT is assumed to be the same for all oxides, and
p
values of 6.7 x lo4, 6.7
xlo4, and 12.3 x lo4 Mpa at 300
Kare used for NiO, COO, and MgO, respectively, the ~,/p values for COO and MgO are comparable while that of NiO is approximately three times larger at T
= 0.6TM. The high-temperature yield stress of NiO is higher than that of COO
/8/;this is consistent with the
T,measurements. The low- temperature (T
<0.3
Tbl)strengths are reversed; COO is stronger than NiO, which is stronger than MgO, but this is probably related to se- cond-phase precipitation of Co304.
Fig.5.- Comparison o f t h e s t e a d y - s t a t e s t r e s s a t n e a r l y c o n s t a n t and e q u a l s t r a i n r a t e s f o r Nil-,O, MgO, and Coo.gggg0 a s a f u n c t i o n o f t e m p e r a t u r e n o r m a l i z e d by t h e m e l t i n g p o i n t .
s t a c k i n g - f a u l t e n e r g y /1/, a c c o r d i n g t o t h e c r o s s s l i p t h e o r y o f s t a g e 111 d e f o r m a t i o n o f f c c m e t a l s /11/. I t c a n b e s e e n from f i g u r e 5 t h a t w i t h i n e x p e r i m e n t a l e r r o r , t h i s t e m p e r a t u r e dependence i s a l s o found f o r n e a r l y s t o i c h i o m e t r i c COO and N i O . F u r t h e r m o r e , s i n c e t h e s t a c k i n g f a u l t e n e r g y o f b o t h o x i d e s /9/ i s lower t h a n t h a t o f MgO, f o r which no d i s l o c a t i o n d i s s o c i a t i o n has e v e r been r e p o r t e d , it would b e expec- t e d t h a t t h e In T, v s . T p l o t s f o r COO and N i O would n o t b e a s a s t r o n g a f u n c t i o n of T a s t h e p l o t s f o r MgO. T h i s i s a p p a r e n t l y observed. I t i s i n t e r e s t i n g t o n o t e t h a t C a s t a i n g
/ l o /
h a s r e p o r t e d t h a t t h e y i e l d s t r e s s i n A l 2 O 3 e x h i b i t s t h e same l o g a r i t h m i c r e l a t i o n between T S and T o v e r a v e r y wide t e m p e r a t u r e range.5 . C o n c l u s i o n s . The h i g h - t e m p e r a t u r e s t r e s s - s t r a i n b e h a v i o r i s s i m i l a r f o r MgO and N i O ; b o t h show a work-hardening r a t e t h a t d e c r e a s e s w i t h i n c r e a s i n g s t r e s s , and s t e a d y s t a t e i s a c h i e v e d a t 0 = 0. T h i s b e h a v i o r c a n b e used t o p r e d i c t n o r n a l c r e e p b e h a v i o r , which i s o b s e r v e d . The
T v s . y d a t a o b t a i n e d f o r COO show a n upper y i e l d p o i n t f o l l o w e d by a n e g a t i v e work-hardening r a t e which e v e n t u a l l y becomes z e r o . T h i s r e s u l t s i n an i n v e r s e c r e e p . The s t e a d y - s t a t e stress i s g i v e n by l o g
-rS
= B-
T/A f o r a l l t h r e e c u b i c o x i d e s , and t h e s h e a r ~nodulus-compensated s t e a d > - - s t a t e s t r e s s f o r N i O i s h i g h e r t h a n t h e c o r r e s p o n d i n g s t r e s s e s f o r COO and MgO, which a r e a p p r o x i m a t e l y e q u a l .
6 . Acknowledgments.- The a u t h o r i s g r a t e f u l t o G . T a l a b e r and C . Wiley, who grew t h e COO and N i O s i n g l e c r y s t a l s , and t o N. Mecking and U . F . Kocks f o r v e r y u s e f u l d i s c u s s i o n s .
JOURNAL DE PHYSIQUE
R e f e r e n c e s
/1/ R o u t b o r t , J . L . , A c t a M e t a l l ,
2
( 1 9 7 9 ) 6 4 9/ 2 / R o u t b o r t , J . L . , presented a t Second W o r k s h o p o n t h e i n t e r - a c t i o n s B e t w e e n D i s l o c a t i o n s and D e f e c t s i n O x i d e s , L y o n , F r a n c e ( 1 9 8 0 )
/3/ C l a u e r , A . H . , S e l t z e r , M . S . and W i l c o x , B . A . , J M a t e r . S c i .
6
( 1 9 7 1 ) 1 3 7 9/ 4 / N e h r i n g , V.W., S m y t h , J . R . a n d M c G e e , T . D . , J. Am. C e r a m . S o c . 60 ( 1 9 7 7 ) 3 2 8
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/ 5 / K r i s h n a m a c h a r i , V . and J o n e s , J . T . , J . Am. C e r a m . Soc.
5 7 ( 1 9 7 4 ) 5 0 6 -
/ 6 / C a b r e r a - C a n o , J . , D o m i n q u e z - R o d r i g u e z , A . , M a r q u e z , R . and C a s t a i n g , J . P h y s i q u e L e t t .
2
( 1 9 7 8 ) L 4 5 1/ 7 / S e e f o r e x a m p l e , C l a u e r , A.H. and W i l c o x , B . A . , J . A r n . C e r a m . Soc.
59
( 1 9 7 9 ) 8 9/8/ C a s t a i n g , J . , S p e n d e l , M. and P h i l i b e r t , J . , R e v u e P h y s . A p p l .
12
( 1 9 8 0 ) 2 7 7/ 9 / K r i s h n a m a c h a r i , V. and N o t i s , M . R . , A c t a M e t a l l .
5
( 1 9 7 7 ) 1 3 0 7
/ l o /
C a s t a i n g , J . , p r e s e n t e d a t S e c o n d W o r k s h o p on t h e I n t e r - a c t i o n s B e t w e e n D i s l o c a t i o n s and P o i n t D e f e c t s i n O x i d e s , L y o n , F r a n c e ( 1 9 8 0 )/11/ K o c k s , U . F . , J . E n g . I v l a t e r . T e c h n o l .
