COMPARISONS BETWEEN OBSERVED AND COMPUTED GRAIN BOUNDARY STRUCTURES AND ENERGIES IN CERAMICS

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COMPARISONS BETWEEN OBSERVED AND COMPUTED GRAIN BOUNDARY STRUCTURES

AND ENERGIES IN CERAMICS

M. Rühle

To cite this version:

M. Rühle. COMPARISONS BETWEEN OBSERVED AND COMPUTED GRAIN BOUNDARY STRUCTURES AND ENERGIES IN CERAMICS. Journal de Physique Colloques, 1985, 46 (C4), pp.C4-281-C4-292. �10.1051/jphyscol:1985431�. �jpa-00224681�

JOURNAL DE PHYSIQUE

Colloque Ck, supplément au n°», Tome 46, avril 1985 page C4-281

COMPARISONS BETWEEN OBSERVED AND COMPUTED GRAIN BOUNDARY STRUCTURES AND ENERGIES IN CERAMICS

M. Ruhle

Max-Planak-Institut filv Metallforschung, Institut fiXv Werkstoffwissensohaften, Seestrasse 92, D-7000 Stuttgart 1, F.R.G.

Résumé': Une discussion critique des résultats expérimentaux et théoriques de structures et énergies de joints de grains dans les céramiques est faite .- Les difficultés expérimentales rencontrées ainsi que les ambignitês dans l'interprétation des résultats sont décrites.

Abstract: Experimental and theoretical results on the structure and energies of grain boundaries in ceramics are discussed critical. The difficulties for experimental studies and the ambiguities in the interpretation of the experimental results are described.

Introduction

Grain boundaries in ceramics possess an important influence on many properties of the materials. Especially the mechanical properties (strength, toughness, deformation and high temperature creep resistance) depend strongly on the morphology of the grain boundaries, impurities at grain boundaries and on the presence of interphase interfaces.

Recently, new theoretical and experimental efforts shed some light on the open questions concerning the structure of grain boundaries. The relation between structure and properties is, however, not yet understood. Kingery [1] pointed out that from a poorly phenomenological point of view, grain boundaries in metals and non-metals, respectively, should have many similarities. Grain boundaries of all materials possess an interfacial energy, they have a mobility (at high temperatures) which can be influenced by impurities, diffusion is usually more rapid along grain boundaries, deformation may occur by grain boundary sliding, segregation of solutes happens at grain boundaries, grain boundaries act as sinks and sources for point defects, electrical and electronic properties are often determined by grain boundaries. However, there exist important differences [1]

between metals and ceramic oxides which influence strongly the structure and properties of grain boundaries: (i) The charges of the ions in ionic materials influence the stability of grain boundaries, (ii) The ionic bonding of oxides leads to the formation of an electrostatic potential on grain boundaries which depends strongly on defect structure, impurities, and temperature [2, 3 ] . There is no analogy to the charging for grain boundaries in metals, (iii) The impurity content in binary oxides is usually much higher than in (pure) metals in which basic studies on structure and properties of grain boundaries are performed, (iv) In many oxides the energy of formation of point defects is very high (up to 6_eV).

This results in a very low concentration c of intrinsic defects (c = 10 at 1800 C for MgO), factors lower than the impurity level in the pure binary oxide sample, (v) Deviations from stoichiometry occur in oxides of the transition metals. This leads to a temperature and oxygen pressure dependence of the composition. Those oxides may possess a large concentration of vacant lattice sites.— From these differences Kingery [1] concluded that arguments by analogy for metals and ceramic oxides are often dangerous and unconvincing , even since many similarities in the structure and properties of grain boundaries in metals and ceramics exist.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985431

C4-282 JOURNAL DE PHYSIQUE

G r a i n boundaries a r e c h a r a c t e r i z e d by ( i ) t h e s t r u c t u r e . ( i i ) t h e energy of t h e g r a i n boundary and ( i i i ) t h e chemical composition a t t h e g r a i n boundary and/or t h e formation of an i n t e r p h a s e i n t e r f a c e . Experimental a s w e l l a s t h e o r e t i c a l r e s u l t s on t h e s e t h r e e p r o p e r t i e s of g r a i n bonndaries w i l l be summarized and compared i n t h i s paper. Emphasize i s p u t on t h e s t u d i e s i n magnesium oxide (MgO) and n i c k e l oxide (Ni 0 ) . The d i s c u s s i o n of g r a i n bonndaries of t e c h n i c a l l y r e l e v a n t multiphase g r a h y b o u n d a r i e s a r e summarized i n Clarke's paper [41 of t h e s e proceedings. It should a l s o be noted t h a t proceedings of o t h e r c o n f e r e n c e s summarize t h e r e s u l t s concerning t h e s t r u c t u r e and p r o p e r t i e s of g r a i n boundaries i n ceramics 15, 61.

Comvuter S i m u l a t i o n of G r a i n Boundarv S t r u c t u r e s

Recently, Wolf 171 and Tasker e t a l . 18. 91 performed molecular s t a t i c c a l c u l a t i o n s on t h e s t r u c t u r e of t w i s t and t i l t boundaries i n MgO and N i O . The s i m u l a t i o n s were performed f o r c e r t a i n i n t e r a t o m i c p o t e n t i a l s and o t h e r assumptions (e.g. e x a c t s t o i c h i o m e t r y f o r a l l b i n a r y o x i d e s , u s u a l l y no p o i n t d e f e c t s ) . Wolf [7, 101 demonstrated t h a t t h e e x a c t shape of t h e i n t e r a t o m i c p o t e n t i a l i n f l u e n c e s t h e s t r u c t u r e and energy of t h e bonndaries. U s u a l l y e m p i r i c a l p o t e n t i a l s a r e used and i o n i c p o l a r i z a t i o n was included f o r NiO by t h e s h e l l model [121. T h e o r e t i c a l r e s u l t s f o r d i f f e r e n t p o t e n t i a l s a r e summarized by Duffy and Tasker [Ill.

T h e o r e t i c a l R e s u l t s f o r Twist Boundaries

S t r u c t u r e and e n e r g i e s of <001> t w i s t boundaries were c a l c u l a t e d by Wolf 17, 101 and Tasker and Duffy [8, 111. Wolf o b t a i n e d a r a t h e r h i g h boundary energy which c o n t i n u o u s l y i n c r e a s e d w i t h i n c r e a s i n g t w i s t a n g l e . An i n s p e c t i o n of t h e g r a i n boundary s t r u c t u r e showed t h a t n o t o n l y c o i n c i d e n c e s occur where i o n s of d i f f e r e n t charges oppose a c r o s s t h e g r a i n boundary, b u t a l s o a n t i c o i n c i d e n c e s where l i k e i o n p a i r s a r e p r e s e n t a t t h e boundary. These a n t i c o i n c i d e n c e s d e s t a b i l i z e t h e boundary, due t o t h e long range Coulomb f i e l d s of t h e i o n s and r e s u l t i n a high v a l u e of t h e g r a i n boundary energy. S i m i l a r r e s u l t s were o b t a i n e d by Tasker and Duffy 181. However, t h e a u t h o r s 181 demonstrated t h a t f o r a =5 t w i s t boundary a v e r y s t a b l e s t r u c t u r e c a n be reached by t h e i n t r o d u c t i o n of Schottky d e f e c t s i n t o t h e boundary plane. The s t a r t i n g p o i n t of t h e i r s t u d i e s i s t h e usual a n t i c o i n c i d e n c e c o n f i g u r a t i o n which h a s l i k e i o n s f a c i n g e a c h o t h e r a c r o s s t h e boundary. A l l o t h e r ions a r e reasonably c l o s e t o t h e i o n s of t h e o p p o s i t e charge. The a n t i c o i n c i d e n c e ions i n one p l a n e a r e t h e n removed and t h e remaining i o n s r e l a x e d t o e q u i l i b r i u m . I n P i g . 1 t h e r e s u l t i n g s t r u c t u r e i s shown, where t h e s o l i d l i n e s r e p r e s e n t t h e r e c o n s t r u c t e d boundary p l a n e and t h e broken

F i g . 1: S t r u c t u r e of t h e s t a b l e 36.9' [0011 coincidence t w i s t boundary i n NiO.

The broken l i n e s i n d i c a t e t h e v s t r u c t u r e of t h e lower g r a i n . Tasker and Duffy [8, 91.

'\ ^,-7' '

':.'

l i n e s a r e t h e p l a n e s above and below t h e boundary. The r e l a t i v e r o t a t i o n between t h e p l a n e s r e p r e s e n t e d by t h e broken l i n e s i s 36.9' (corresponding t o a C = 5 boundary), b u t t h e bonndary p l a n e h a s a n i n t e r m e d i a t e angle. The d i l a t a t i o n of t h e c r y s t a l a c r o s s t h e i n t e r f a c e i s n e g l i g i b l e which i s an i n d i c a t i o n of t h e s t a b i l i t y of t h i s c o n f i g u r a t i o n . Duffy and Tasker 1111 s t a t e t h a t t h e introduced Schottky d e f e c t s have a n e g a t i v e energy of f o r m a t i o n (- 1.4

ex)

T h e o r e t i c a l R e s u l t s f o r Larne Anale T i l t Boundaries

The r e l a x e d s t r u c t u r e s and e n e r g i e s of 7 c o i n c i d e n t symmetric t i l t boundaries, w i t h r o t a t i o n axes o r i e n t e d along t h e 10011 d i r e c t i o n and of 6 <011> symmetric

t i l t boundaries have been c a l c n l a t e d by Duffy and Tasker [Ill. The g r a i n boundary p l a n e s were f i x e d on d i f f e r e n t p l a n e s s o t h a t t h e Z=37 (610), E=13 (510), E=17 (4101, Z =5 (310). =5 (210). s = 1 3 (320) andZ=25 (430) were considered f o r a [OOll t i l t a x i s a n d r = 1 9 (133). C = 9 (1991, C=3 (111). 2 = 3 ( 2 1 1 ) , E = l l (311) and t = 9 (411) f o r a <011> t i l t bonndary.

F i g . 2 r e p r e s e n t s r e s u l t s f o r a [OOl] p r o j e c t i o n of t h e c a l c n l a t e d s t r u c t u r e of t h e 2 = 5 (310) t i l t boundary ( t i l t i n g angle 36.9'). There e x i s t s n e a r l y no d i f f e r e n c e i n t h e c a l c u l a t e d s t r u c t u r e f o r N i O and MgO, r e s p e c t i v e l y . Large gaps i n t h e boundary p l a n e a r e observed. The c o n f i g u r a t i o n i s much l e s s dense t h a n t h a t of t h e corresponding g r a i n bonndary i n m e t a l s 171. It i s p o s s i b l e t o r e s o l v e t h e s t r u c t u r e i n t o an a r r a y of 11001 d i s l o c a t i o n s . S i m i l a r r e s n l t s a r e o b t a i n e d f o r t h e o t h e r l a r g e angle g r a i n bonndaries, however, t h e s t r u c t n r e may a l s o be r e s o l v e d by an a r r a y of [I101 d i s l o c a t i o n s .

The g r a i n boundary e n e r g i e s v a r y between 1.8 and 2.1 J m -2 where t h e ( d p ~ b l e d ) energy of t h e d i f f e r e n t f r e e s u r f a c e s i s i n t h e range of 2.5 t o 2.8 J m

.

t h e c a l c u l a t i o n i t cannot y e t been concluded t h a t t h e e n e r g i e s of t h e boundaries v a r y smoothly w i t h i n c r e a s i n g angle of m i s o r i e n t a t i o n s , s i n c e t h e s i m u l a t i o n s were o n l y performed f o r g r a i n boundaries w i t h s h o r t p e r i o d l c i t i e s ( l o w z v a l u e s ) . F u r t h e r s i m u l a t i o n s f o r long range p e r i o d i c b o a n d a r i e s must r e v e a l i f cusps i n t h e energylangle of m i s o r i e n t a t i o n r e p r e s e n t a t i o n a r e p r e s e n t .

S i m i l a r r e s u l t s a r e o b t a i n e d f o r t h e <011> t i l t boundaries 18, 111. The e n e r g i e s of t h e s e boundaries a r e h i g h e r t h a n t h o s e of t h e <001> boundaries6 There is, of c o u r s e , a very deep cusp i n t h e energy m i s o r i e n t a t i o n curve a t 70.5

.

o r i e n t a t i o n corresponds t o a (111) 10111 c o h e r e n t twin s t r u c t u r e I l l ] . I n t h e boundary p l a n e of such a coherent twin boundaries a l l n e a r e s t neighbour d i s t a n c e s a r e very c l o s e t o t h e i d e a l c r y s t a l l i n e s t r u c t u r e b u t t h e l o c a l environment of t h e i o n s a r e a l t e r e d . This r e s u l t s i n a small i n t e r f a c i a l energy.

Enerxies of D e f e c t s Near Grain Boundaries

The s t r u c t u r a l d i s o r d e r around g r a i n bonndaries i n b i n a r y o x i d e s i n t r o d u c e s a change of t h e formation energy of d e f e c t s . The r e s u l t i n g d e f e c t d i s t r i b u t i o n

P i x . 2: The r e l a x e d s t r u c t u r e of t h e (310) [0011 t i l t bonndary, drawn w i t h p a u l i n g s r a d i i . Duffy and Tasker 18. 91.

C4-284 J O U R N A L DE PHYSIQUE

m o d i f i e s a l s o t h e d i f f u s i o n a l o n g t h e g r a i n boundary w i t h r e s p e c t t o t h e b n l k c r y s t a l . The d i f f u s i o n c o e f f i c i e n t i s u s u a l l y s t r o n g l y enhanoed a t t h e g r a i n boundary. Duffy and T a s k e r [8, 111 c a l c u l a t e d t h e f o r m a t i o n and bonding e n e r g i e s f o r d i f f e r e n t p o i n t d e f e c t s a t d i f f e r e n t b o u n d a r i e s . The e n e r g i e s o f f o r m a t i o n v a r y s u b s t a n t i a l l y from t h o s e i n b n l k m a t e r i a l and i t i s observed t h a t a t 1000 K t h c o n c e n t r a t i o n of c a t i o n and a n i o n v a c a n c i e s i s enhanced by a f a c g y r of 1.2 10' w i t h r e s p e c t t o t h e b u l k and t h e c o n c e n t r a t i o n o f h o l e s ( N i i o n s ) i s enhance$, by ~ ~ 0 . 8 1 0 3

.

1.9 1 0 e m and t h e d i f f e r e n c e s between t h e p o t e n t i a l a t t h e boundary and t h e b u l k i s 0.34 eV. Thus t h e low e n e r g y s i t e s f o r d e f e c t f o r m a t i o n a t c o i n c i d e n c e s g r a i n b o u n d a r i e s i n t r o d u c e space c h a r g e l a y e r s s i m i l a r t o t h o s e formed a t g e n e r a l g r a i n b o u n d a r i e s and s u r f a c e s i n i o n i c c r y s t a l s due t o t h e t h e o r e t i c a l p r e d i c t i o n s .

Furthermoret+ t h e s e g r e g a t i o n e n e r g 4 t s o f i m p u r i t i e s were c a l c u l a t e d 19.

1ii.

N e u t r a l , (Co ) s i n g l e charged (A1 ), a s w e l l a s d o u b l e charged (C ) s u b s t i t u t i o n a l i m p u r i t i e s p o s s e s s a n e g a t i v e s e g r e g a t i o n e n e r g y a t t h e i o n i c s i t e s f o r a l l t i l t b o u n d a r i e s [ 8 , 111. Thus, a l l i m p u r i t i e s w i l l t e n d t o s e g r e g a t e t o g r a i n b o u n d a r i e s i n i o n i c c r y s t a l s . The d i s t r i b u t i o n o f d e f e c t s i n t h e s p a c e c h a r g e r e g i o n depends on t h e boundary c h a r g e which i s , o f c o u r s e , a f u n c t i o n o f t e m p e r a t u r e .

E x ~ e r i m e n t a l D e t e r m i n a t i o n o f G r a i n Boundarv Energp

The g r a i n boundary e n e r g y c a n be measured by t h e r m a l grooving e x p e r i m e n t s . B i c r y s t a l s ( c o n t a i n i n g a w e l l d e f i n e d g r a i n boundary) were f a b r i c a t e d and a n n e a l e d t o e q u i l i b r i u m . A groove i s formed i n t h e a r e a where t h e g r a i n boundary i n t e r s e c t s t h e s u r f a c e . The r a t i o of g r a i n boundary e n e r g y and s u r f a c e e n e r g y c a n be d e t e r m i n e d from t h e a n g l e s ( o f t h e groove) between s u r f a c e and g r a i n boundary.

Dhalenne e t a l . [13. 141 measured t h e r e l a t i v e f r e e e n e r g y o f <001> and <011>

symmetrical t i l t b o u n d a r i e s i n N i 0 a t e l e v a t e d t e m p e r a t u r e s ( P i g s . 3 and 4 ) . The r e s u l t s show ( F i g . 3 ) a c o n $ ~ E u o u s i n c r e a s e i n g r a i n boundary e n e r g y a s a f n n c t i o n of t h e a n g l e o f m i s o r i e n t a t i o n f o r <001> b o u n d a r i e s . There e x i s t

.

D 50 heures '

i

A 20 heures

I Readey et Jech

i

F i g . 3: Measured r a t i o o f g r a i n boundary f r e e P i p . 4: Measured r a t i o o f energy, yb, t o s u r f a c e f r e e e n e r g y , ys, f o r g r a i n boundary f r e e energy,

<001> symmetry t i l t b o u n d a r i e s i n N i 0 a t yb, t o s u r f a c e f r e e energy.

1 5 2 0 ~ ~ a s a f u n c t i o n o f m i s o r i e n t a t i 6 ~ ~ 0 . y

.

1 5 2 0 ~ ~ a s a f a n c t i o n l o f m i s - o r i e n t a t i o n O h a t a from Dhalenne e t a l . C141.

d e f i n i t e l y no c u s p s i n t h i s c u r v e . The e n e r g y c u s p s a r e found f o r symmetrical

<011> b o u n d a r i e s ( F i g . 4 ) f o r a n g l e s of m i s o r i e n t a t i o n c o r r e s p o n d i n g t o C = 3 , 9 and 11. Thereby, t h e 3 boundary c o r r e s p o n d s t o t h e c o h e r e n t t w i n boundary.

One problem remains d u r i n g t h e c o u r s e of t h e d e t e r m i n a t i o n of g r a i n boundary e n e r g y . The grooves formed i n N i 0 a r e s t r o n g l y f a c e t e d 113, 141, p r o b a b l y due t o a n a n i s o t r o p i c s u r f a c e enera;? The e v a l u a t i o n s of t h e d a t a assume. however, t h a t t h e s u r f a c e e n e r g y i s i s o t r o p i c . An a n i s o t r o p i c s u r f a c e e n e r g y may modify t h e r e s u l t s of F i g . 6 and 7.

E x ~ e r i m e n t a l O b s e r v a t i o n s on t h e S t r u c t u r e o f G r a i n Boundaries

R e c e n t l y , s e v e r a l c o n f e r e n c e s on g r a i n boundary phenomena i n c e r a m i c s 15, 6, 1 5 , 161 emphasized t h e importance of t h e e x p e r i m e n t a l d e t e r m i n a t i o n of t h e s t r u c t u r e o f g r a i n b o u n d a r i e s i n o x i d e s and o t h e r c e r a m i c s . Only few s y s t e m a t i c s t u d i e s were performed u n t i l now, t h e s t u d i e s were m a i n l y done by t r a n s m i s s i o n e l e c t r o n microscopy. I n t h i s p a p e r r e s u l t s on MgO. Ni 0 and A1203 a r e

summarized. 1-Y

R e s u l t s o n Ma0

Twist b o u n d a r i e s on (0011 p l a n e s have b e e n s t u d i e d by u s i n g s m a l l c u b i c MgO c r y s t a l s which were produced by b u r n i n g magnesium i n a i r . Chaudhari and Matthews 1171 found t h a t t h e s m a l l c r y s t a l s i n t h e smoke s t u c k t o g e t h e r t o form b i c r y s t a l s c o n t a i n i n g <001> t w i s t b o u n d a r i e s , w h i l e Mykura e t a l . 1181 d e p o s i t e d t h e s m a l l s i n g l e c r y s t a l s on a <001> p l a n e o f a MgO s i n g l e c r y s t a l t o form a l s o <001> t w i s t b o u n d a r i e s . A subsequent e x a m i n a t i o n of t h e d i s t r i b u t i o n o f t w i s t a n g l e s showed a marked p r e f e r e n c e f o r h i g h d e n s i t y CSL o r i e n t a t i o n a s s e e n i n F i g . 5 ( f o r t h e d e f i n i t i o n of a CSL l a t t i c e , s e e e.g. 1191). T h i s r e s u l t p r o v i d e s f i r s t e v i d e n c e t h a t h i g h d e n s i t y CSL o r i e n t a t i o n s a r e o f low energy.

Sun and B a l l u f f i 1201 p r e p a r e d b i c r y s t a l s by welding two m i s o r i e n t e d s i n g l e c r y s t a l s o f MgO t o g e t h e r under h i g h p r e s s u r e and h i g h t e m p e r a t u r e . The t w i s t m i r o r i e n t a t i o n of t h e b o n n d a r i e s was c l o s e t o h i g h - d e n s i t y CSL m i s o r i e n t a t i o n s . S t a b l e g r a i n b o u n d a r i e s were o n l y o b t a i n e d when t h e welding p r e s s u r e and t h e

Orientation angle

.

F i n . 5: R e l a t i v e f r e q u e n c y o f o c c u r r e n c e o f t w i s t a n g l e , 8, f o r 10011 t w i s t b o u n d a r i e s produced by d e p o s i t i n g MgO smoke p a r t i c l e s on a MgO 10011 s i n g l e c r y s t a l s u b s t r a t e (from Mykura e t a l . 1191).

-

F i : .mist aounaary i n N i 0 . D i r e c t i o n ofnin:oming beam p a r a l l e l t o l ~ ~ O O 1 d i r e c t i o n of b o t h c r y s t a l s . A s q u a r e network i s observed.

Normal of SAGB p l a n e l i e s p a r a l l e l t o a < I l l >

d i r e c t i o n .

C4-286 JOURNAL DE PHYSIQUE

temperature were r a t h e r h i g h (Sun 1211). The g r a i n boundaries were examined by TEM. Square networks of screw g r a i n boundary d i s l o c a t i o n s were analyzed i n a l l those boundaries. The measured s p a c i n g s of t h e g r a i n boundary d i s l o c a t i o n s accommodate t h e m i s f i t of t h e t w i s t angle t o high d e n s i t y CSL o r i e n t a t i o n s (low v a l u e s ) . The o b s e r v a t i o n s of Sun and B a l l u f f i suggest t h a t t h e r e s u l t s on l a r g e angle g r a i n boandary s t r u c t u r e s i n MgO a r e v e r y s i m i l a r t o those o b t a i n e d i n metals.

Moriyoshi e t a l . 1221 produced n a t u r a l small angle g r a i n boundaries (SAGB) i n MgO by deformation and subsequent annealing of s i n g l e c r y s t a l s of MgO. TEM s t u d i e s demonstrated t h a t t h e SAGBs e x i s t of a network of l a t t i c e d i s l o c a t i o n s . Twist boundaries around [I001 a r e found and show a square network of d i s l o c a t i o n s i f t h e d i r e c t i o n of t h e incoming e l e c t r o n beam i s p a r a l l e l t o t h e [I001 d i r e c t i o n . The SAGB plane was n o t determined by Moriyoshi e t a l . 1221. It was assumed t h a t it i s p e r p e n d i c u l a r t o t h e d i r e c t i o n of t h e r o t a t i o n a x i s by which t h e t w i s t boundary was formed.

Black and Kingery 1231 determined w i t h a n a l y t i c a l e l e c t r o n microscopic s t u d i e s t h a t i m p u r i t i e s s e g r e g a t e on a l l g r a i n boundaries i n MgO. Black and Kingery 1231 used w e l l c h a r a c t e r i z e d MgO, t h e p u r i t y of t h i s m a t e r i a l was much b e t t e r t h a n t h a t used i n t h e o t h e r s t u d i e s [20-221. The r e s u l t s of t h e a n a l y t i c a l s t u d i e s imply t h a t a l l g r a i n boundaries i n MgO a r e d e c o r a t e d w i t h i m p u r i t i e s .

The o b s e r v a t i o n s on MgO s u g g e s t t h a t t h e s t r u c t u r e of small angle g r a i n bonndaries a s w e l l a s of l a r g e a n g l e g r a i n boundaries a r e very s i m i l a r t o t h o s e observed i n m e t a l s . However, a l l l a r g e angle g r a i n bonndaries seemed t o be d e c o r a t e d w i t h i m p u r i t i e s .

R e s u l t s on N i 0 1-Y-

Schmid e t a l . 1241 s t u d i e d by TEM small ankle g r a i n bonndaries (SAGB) which were formed by p l a s t i c deformation and subsequent annealing of s i n g l e c r y s t a l s of N i 0. T i l t boundaries a s w e l l a s t w i s t boundaries (Fig. 6 ) were found. The g e h Z t r q of t h e t w i s t boundaries w i t h t w i s t a x i s w p a r a l l e l t o a [I001 d i r e c t i o n was analyzed i n d e t a i l s . The normal q of t h e SAGB p l a n e i n F i g . 6 does not c o i n c i d e w i t h a. The normal g d i r e c t e d p a r a l l e l t o a < I l l > d i r e c t i o n . The v e c t o r q was p a r a l l e l t o a <110> d i r e c t i o n f o r o t h e r s e c t i o n s of t h e 11001 t w i s t SAGB.

never d i r e c t e d p a r a l l e l t o [1001. T h i s s u r p r i s i n g o b s e r v a t i o n c a n be explained w i t h t h e assumption t h a t a n t i c o i n c i d e n c e s must be avoided on t h e n a t u r a l l y grown SAGB. I f a t w i s t component would e x i s t on a (100) p l a n e , t h e n i o n s of l i k e charges would l i e i n c l o s e proximity a c r o s s t h e SAGB ( " a n t i c o i c i d e n c e s " ) . These c o n f i g u r a t i o n s a r e extremely u n s t a b l e , s i n c e t h e r e p e l l i n g Coulomb f o r c e s of l i k e ions i n c r e a s e s t r o n g l y t h e energy of t h e boundary. The t w i s t SAGBs w i t h g 1 1 [I001 change t h e i r p l a n e p r e f e r e n t i a l l y t o a {111) p l a n e t o p r e v e n t t h e a n t i c o i n c i d e n c e s

.

a n t i c o i n c i d e n c e s a r e not p o s s i b l e . I f t h e SAGB s t a y s on a (1101 plane, t h e i n f l u e n c e of a n t i c o i n c i d e n c e s i s reduced by t h e i n t r o d u c t i o n of extraneous d i s l o c a t i o n s i n t o t h e network and a l s o by o t h e r r e l a x a t i o n p r o c e s s e s .

T i l t g r a i n boundaries i n N i 0 were i n v e s t i g a t e d s o t h a t t h e normal of t h e boundary was p e r p e n d i c u l a r t o t h e B ~ g n e . Very t h i n f o i l s ( w i t h small wedge a n g l e s ) were prepared by an extremely c a r e f u l p o l i s h i n g procedure and subsequent i o n t h i n n i n g . The specimens were a l i g n e d i n t h e microscope s o t h a t t h e d e f e c t s ( d i s l o c a t i o n s ) a s s o c i a t e d w i t h t h e g r a i n boandary were e r a c t l y p a r a l l e l t o t h e incoming e l e c t r o n beam. Fig. 7 i s a TEM micrograph taken under s l i g h t l y overfocussed c o n d i t i o n . The micrograph shows a 12.4' t i l t boundary i n Ni 0 when viewed along t h e t i l t a x i s . The t i l t a x i s i s p a r a l l e l t o t h e 11041 d i r e c % i 8 n . The boundary i s c l e a r l y f a c e t e d along t h e 11001 d i r e c t i o n and d i s p l a y s image c o n t r a s t i n t h e form of b l a c k s p o t s of d i f f e r e n t i n t e n s i t i e s surrounded by f a i n t white r i n g s . The s p o t spacing c a n b e measured, i t i s between 1.2 nm a n d 2 nm and t h e s p o t diameter i s a s small a s 0.6...0.7 nm. It was demonstrated from t i l t i n g experiments t h a t each of t h e s p o t s i n Fig. 7 corresponds t o a d i s l o c a t i o n which i s being viewed end on 125-271. F i g . 7 a l s o shows t h a t t h e image c o n t r a s t is low i n

F i a . 7: Orain boundary ( 1 2 ~ t i l t boundary) i n N i 0 . The d i s l o c a t i o n s of t h e boundary a r e p a r a l l e l t o t h e incoming e l e c t r o n b k a ~ . Kinematical, well d e f i n e d d i f f r a c t i o n c o n d i t i o n s . Defocusing d i s t a n c e 1; = 198 nm.

t h e t h i n p a r t of t h e f o i l and i n c r e a s e s w i t h i n c r e a s i n g f o i l t h i c k n e s s . Prom t h e dependence of t h e c o n t r a s t on t h e o r i e n t a t i o n a s w e l l a s on t h e f o i l t h i c k n e s s ( P i g . 7 ) i t could be concluded t h a t t h e observed c o n t r a s t was not caused by a r t i f a c t s , e.g. e t c h p i t s .

The Burgers v e c t o r s of t h e d i f f e r e n t d i s l o c a t i o n s were determined C261. It was found t h a t t h e p l a n e of t h e g r a i n boundary i s a plane w i t h a h i g h d e n s i t y of coincidence l a t t i c e s i t e s , t h e s i t e s of t h e d i s l o c a t i o n s concur w i t h t h e r e g i o n s of worst matching. F o r t h e e v a l u a t i o n i t was assumed t h a t t h e d i s l o c a t i o n s i n t h e small angle g r a i n boundary p o s s e s s a Burgers v e c t o r b_ ( o r m u l t i p l e of b) of a l a t t i c e d i s l o c a t i o n which i s b_ = a12 <110> ( a = l a t t i c e parameter). It i s found t h a t t h e d e f e c t s p o s s e s s i n g a s t r o n g c o n t r a s t ( l a r g e d o t s ) a r e d i s l o c a t i o n s w i t h b = a <loo>, whereas t h e weak c o n t r a s t s a r e d i s l o c a t i o n s w i t h Burgers v e c t o r s of

t k e type a12 (110) 1263.

The d i s l o c a t i o n s were imaged under d i f f e r e n t focusing c o n d i t i o n s . t h a t means, t h e imaging plane of t h e o b j e c t i v e l e n s of t h e TEM does n o t c o i n c i d e w i t h t h e lower s u r f a c e of t h e f o i l . I n focus c o n d i t i o n i s reached when t h e lower f o i l

F i a . 8: Grain bc

a )

5

5

Dependence of c o n t r a s t on defocusing d i s t a n c e r .

= 0 nm;d)

I=

T =

C4-288 JOURNAL DE PHYSIQUE

surface is exactly imaged with the objective lens. A plane which lies closer to the objective lens than the lower foil surface is imaged for > 0 (overfocussed).

the reverse is true for 5 < 0 (underfocussed). I n order to illustrate the behaviour of the image contrast with change in focus, images for 5 selected focus values are shown in Fig. 8a-e. The complete focus serie exists of 6 0 similar micrographs. Fig. 8 demonstrates that o n going from the overfocussed t o the underfocussed condition the image appearance changes from black spots surrounded by white rings t o white spots surrounded by black rings. For a certain defocusing distance the contrast of the dislocations disappears nearly for a limited region of the grain boundary corresponding to a certain thickness of the foil.

F o r the interpretation of the observations a model is assumed where the mean inner potential V along a tube (radius r ) parallel to the dislocation line is changed compared to the mean inner potentiaf V of the perfect crystal. so that V

= Vo + AV

.

-(0.09.. .O.l!?)vo and r = (0.32.. .0.25)nm result in calculated contrast profiles which approach best theoobservations.

The defects observed in the boundary are dislocations 125-271. Therefore, the results have to be related to the atomic structure of the grain boundary dislocations in Ni 0. The dislocations of the boundary possess Burgers vectors of lattice disloca$igns. The core structure of edge dislocations (Burgers vector a12 11101) was calculated by Puls and Norgett 1281 for MgO. The results show (Fig.

9) that a dilatation exists underneath the additional semiplane of the dislocation which is essentially larger than the dilatation expected from linear theory of elasticity (Volterra dislocation). Equivalent computations for stoichiometric NiO

Distance from grain boundary (nm)

-

Fig. 9: Atomic structure of the Fia. 10: Concentration profiles across [I101 edge dislocation in MgO grain boundaries in polyurystalline Ni 0 calculated b y computer simulation specimens. The two specimens were dopea-aith (Puls and Norgett 129, 301). The a different amount of Cr203 and the seg- dilatation in the marked region regation of Cr203 at the boundary is ob- underneath the additional semiplane served. The probe size of the electron beam:

of the dislocation is essentially 2 0 nm. The strongest defocusing contrast is larger than the dilatation expected observed for large Cr segregations.

from linear theory of elasticity.

by P u l s C301 r e v e a l t h a t t h e d i l a t a t i o n f i e l d h a s a d i a m e t e r o f 6 nm and t h a t t h e r e s u l t a n t n o n l i n e a r d i l a t a t i o n c a u s e s a r e d u c t i o n i n mean i n n e r p o t e n t i a l of o n l y AV = - 0.05 Vo. T h i s d i l a t a t i o n i s , t h e r e f o r e , n o t s u f f i c i e n t t o e x p l a i n t h e obzerved changes i n mean i n n e r p o t e n t i a l . The r e s i d u a l change o f V c a n be e x p l a i n e d e i t h e r by ( i ) t h e i n f l u e n c e of a s p a c e c h a r g e [ I ] , ( i i ) cgange i n c o m p o s i t i o n of N i 0 a t t h e g r a i n boundary upon c o o l i n g o r ( i i i ) by i m p u r i t i e s which s e g r e g a t e a t

$%g

The N i 0 p o l y c r y s t a l s a r e f a b r i c a t e d a t t e m p e r a t u r e 2 of 1 5 0 0 ~ ~ under a i r . The off-stoic&8metry a t t h a t t e m p e r a t n r e i s y

-

^.

R e c e n t l y . TEM s t u d i e s were performed on specimens which c o n t a i n e d Cr 0 (0.5 and 0.8 wt.%) 1301. The w i d t h of t h e d e f o c u s i n g c o n t r a s t s i n c r e a Z e 3 w i t h i n c r e a s i n g Cr203 c o n t e n t . A n a l y t i c a l TEM s t u d i e s ( d i a m e t e r of probe: 20 nm) showed t h a t C r was s e g r e g a t e d a t t h e g r a i n bonndary ( s e e F i g . 1 0 ) . The s e g r e g a t e d Cr i o n s i n f l u e n c e t h e change i n mean i n n e r p o t e n t i a l n e a r t h e bonndary.

Large a n g l e b o u n d a r i e s were a l s o s t u d i e d by TEM, F i g . 11. No d i s l o c a t i o n s could be observed. However, a s t r o n g dependence of t h e c o n t r a s t on t h e d e f o c u s i n g c o n d i t i o n was a l s o o b s e r v e d f o r t h o s e l a r g e a n g l e b o u n d a r i e s (mixed t y p e ) . Those o b s e r v a t i o n s i n d i c a t e a g a i n t h a t a r a t h e r extended d i l u t e d zone e x i s t s c l o s e t o t h e g r a i n boundary. D i f f r a c t i o n s t u d i e s a t l a r g e a n g l e t w i s t b o u n d a r i e s i n NiO by Lamarre e t a l . C311 a l s o show t h a t t h e extended d i l u t e d zone i s p r e s e n t a t a t w i s t bonndary. A q u a n t i t a t i v e e v a l u a t i o n of t h e d i f f r a c t i o n d a t a [311 shows f a i r l y good agreement w i t h t h e c a l c u l a t e d e x p a n s i o n n e a r t h e boundary b y Wolf 1321.

R e s u l t s o n Alumina

Coble 1331 r e p o r t e d t h a t s m a l l a d d i t i o n s of MgO i n h i b i t e x a g g e r a t e d g r a i n growth i n A 1 0 and a l l o w n e a r t h e o r e t i c a l d e n s i t y t o be a c h i e v e d . T h e r e f o r e . p o l p c r y s t a l l in: 3 ~ 1 2 0 3 c o n t a i n s f r e q u e n t l y s m a l l amounts of MgO. There remains s u b s t a n t i a l l a c k o f agreement on t h e mechanisms which s u p p r e s s t h e g r a i n growth, d e s p i t e e x t e n s i v e s t u d i e s . It i s , however, w e l l e s t a b l i s h e d t h a t MgO c o n c e n t r a t e s a t g r a i n b o u n d a r i e s i f t h e s o l u t i o n l i m i t w i t h i n A1203 i s p a s s e d .

C a r t e r e t a l . 134, 351 i n v e s t i g a t e d t h e s t r u c t u r e of s m a l l a n g l e [341 and l a r g e a n g l e 1351 g r a i n b o u n d a r i e s i n A 1 0 b y e l e c t r o n d i f f r a c t i o n and TEM s t u d i e s . A p e r i o d i c a r r a y of c l o s e l y spaced f a q t i c e d i s l o c a t i o n s c a n be found i n SAGB. The p e r i o d i c d i s l o c a t i o n a r r a y c a u s e s e x t r a s t r e a k s i n t h e d i f f r a c t i o n p a t t e r n . The l e n g t h o f t h e e x t r a s t r e a k s i s a measure of t h e s t r u c t u r a l w i d t h of t h e g r a i n

P i n . 11: Large a n g l e g r a i n boundary i n Ni 0. T i l t a n g l e a b o u t 43.3'. A d e f o c u s i n g c o n t r a s t b e h a v i o u r i s observed s u g g e s t i n g l t ~ a t a t t h e g r a i n boundary t h e d e n s i t y of t h e m a t e r i a l (mean i n n e r p o t e n t i a l ) i s lowered. a ) Defocusing

5

+

C4-290 JOURNAL DE _PHYSIQUE

boundary. The d i s t a n c e between t h e d i s l o c a t i o n s e q u a l s t o t h e observed s t r u c t u r a l width of t h e small angle g r a i n boundary - a r e s u l t which is i n agreement w i t h t h e o r e t i c a l p r e d i c t i o n s . Large a n g l e g r a i n boundaries a r e q u i t e f r e q u e n t l y f a c e t e d where many f a c e t s were f i r s t - o r d e r twin boundaries w i t h 100011 d i r e c t i o n s being common f o r t h e a d j a c e n t g r a i n s . C a r t e r e t a l . 1351 were a b l e t o show by a d e t a i l e d thoroughly done TEM a n a l y s i s t h a t t h e observed p r e f e r r e d i n t e r f a c e p l a n e and t h e secondary d i s l o c a t i o n s a r e i n agreement w i t h p r e d i c t i o n s based on t h e CSLIDSC g r a i n boundary model.

An enrichment of MgO can b e analyzed on l a r g e angle g r a i n bonndaries, v i t r e o u s phases were observed i f more t h a n 0.2 w t . 5 MgO were added 1321. Mechanical measurements imply t h a t t h e presence of a g r a i n boundary phase r e s u l t s i n good mechanical p r o p e r t i e s .

Discussion

The e n e r g i e s of g r a i n bonndaries i n metal o x i d e s were c a l c u l a t e d and t h e c a l c u l a t e d dependency of t h e g r a i n boundary energy on t h e angle of m i s o r i e n t a t i o n showed a r a t h e r smooth and s l i g h t i n c r e a s i n g behaviour. An energy cusp was c a l c u l a t e d f o r a twin boundary. The grooving experiments 113, 141, however, r e s u l t i n t h r e e well d e f i n e d cusps i n t h e energy m i s o r i e n t a t i o n diagrams f o r <011>

symmetric t i l t boundaries. It may w e l l be t h a t t h e two observed a d d i t i o n a l cusps a r e missed i n t h e c a l c u l a t i o n s i n c e o n l y f i v e s h o r t p e r i o d i c <001> symmetric boundaries were s t u d i e d by t h e t h e o r e t i c a l i n v e s t i g a t i o n s . F u r t h e r t h e o r e t i c a l work could demonstrate i f t h o s e cusps, observed by energy measurements, can a l s o be p r e d i c t e d .

The t r a n s m i s s i o n e l e c t r o n microscopy s t u d i e s i n MgO suggest t h a t t h e low 2

t w i s t boundaries on (100) p l a n e s p o s s e s s a l s o a low energy. T h i s r e s u l t i s s u r p r i s i n g s i n c e t h e t h e o r e t i c a l s t u d i e s showed t h a t a pure t w i s t boundary has a v e r y h i g h energy. Two models may e x p l a i n t h e o b s e r v a t i o n s . ( i ) The model proposed by Tasker and Duffy 181 i s r e l e v a n t . I n t h i s model, i t i s assumed t h a t a h i g h d e n s i t y of Schottky d e f e c t s i n t h e g r a i n boundary p l a n e s avoids t h e

" a n t i c o i n c i d e n c e s " , however, r e s u l t s i n a charge l a y e r . ( i i ) I m p u r i t i e s which a r e p r e s e n t a t t h e boundaries i n MgO smoked p a r t i c l e s may s t a b i l i z e t h e boundary.

The d i f f e r e n t o b s e r v a t i o n s i n N i 0 show t h a t t h e s t r u c t u r e of t h e g r a i n b o u n d a r i e s and of t h e g r a i n b o u n d a r y l d ~ s l o c a t i o n s a r e s t r o n g l y dependent on t h e c o n c e n t r a t i o n of i m p u r i t i e s and a l s o on annealing c o n d i t i o n s . It was expected and e x p e r i m e n t a l l y observed t h a t i n t r i n s i c d e f e c t s a s w e l l a s i m p u r i t i e s s e g r e g a t e a t g r a i n boundaries and produce a d i l u t e d l a y e r c l o s e t o t h e boundary. I f more t h a n one atomic l a y e r of t h e i m p u r i t i e s s e g r e g a t e s a t t h e boundary, t h e n t h e formation of an i n t e r p h a s e s t a r t s . The i n v e s t i g a t i o n s of g r a i n boundaries a r e t h e n changed t o s t u d i e s of i n t e r p h a s e i n t e r f a c e s . I f t h i s i n t e r p h a s e i s amorphons, a s i t i s f o r many commercial ceramics ( s e e Clarke 141), and q u i t e f r e q u e n t l y i n o t h e r ceramic m a t e r i a l s , t h e n an amorphous f i l m e x i s t s on t h e g r a i n boundary which should

i n v a l i d a t e b o t h t h e CSL and t h e DSC l a t t i c e c o n s t r u c t i o n .

7 . References

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a

a

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[I91 Smith, D.A. and Pond, R.C., I n t . Met. Rev. 205 (1976) 61.

1201 Snn, C.P. and B a l l n f f i , R.W.. P h i l . Mag. & (1982) 49; & (1982) 63.

1211 Sun, C.P.. Ph. D. Thesis. Cornell U n i v e r s i t y . I t h a c a , NY. 1980.

I221 Moriyoshi. Y., Ikegami, T., Matsnda. S., Bando. Y.. Sekikawa, Y. and S h i r a s a k i , S.. 2. Phys. Chem. Nene Folge 118 (1979) 187.

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1241 Scbmid, H.. R6hle. M and Peterson, N.L.. i n r e f . 1161, p. 177.

I251 Riihle, M. and Sass. S.L.. Proc. 1 0 t h I n t . Congress E l e c t r o n Microscopy 2

(1982) p. 99.

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1341 C a r t e r , C.B., K o h l s t e d t , D.L. and Sass, S.L., J . Amer. Ceram. Soc.

a

1351 Morrissey. K.J. and C a r t e r , C.B.. i n r e f . 151, p. 85.

1361 Eansen, S.C. and P h i l l i p s . D.S., P h i l . Mag. (1983) 209.

DISCUSSION

Y.Vitek: Very c l e a r secondary d i s l o c a t i o n s a t n e a r t = 5 twist boundaries i n MgO a r e seen. I wonder i f a cusp a t Z = 5 is found i n c a l c u l a t i o n s . I f n o t , then t h e same problem a r i s e s i n both ceramics and metals and it i s , t h e r e f o r e , u n l i k e l y t h a t t h i s problem can be r e l a t e d t o t h e l a c k o f understanding t h e i n t e r a t o m i c f o r c e s . M. Riihle: Indeed, secondary d i s l o c a t i o n s a r e seen n e a r t = 5 t w i s t boundaries i n MgO and it should be p o s s i b l e t o determine t h e Burgers v e c t o r o f t h e s e secondary d i s l o c a t i o n s unequivocally by t h e g - b = O r u l e . Cusps i n t h e energy V S .

m i s o r i e n t a t i o n curve a r e n o t found f o r twist boundaries i n t h e c a l c u l a t i o n s . This may have two reasons: ( i ) The c a l c u l a t i o n s a r e done only f o r r a t h e r small Values o f Z

,

C4-292 JOURNAL DE PHYSIQUE

J.T. Klom~: I n your paper observed and computed GB s t r u c t u r e s and e n e r g i e s were compared f o r ceramics. T h i s was done i n t h e preceding paper f o r metals. How a r e t h e p r o s p e c t s t o do computations on ceramic-metal systems?

M. Ruhle: Geometrical models o f heterophase boundaries were developed, e.g. by H.

G l e i t e r and co-workers ( s e e t h e papers i n t h e proceedings o f t h i s conference).

However, we a r e s t i l l f a r away from doing c a l c u l a t i o n s f o r t h e s t r u c t u r e of ceramic/metal i n t e r f a c e s . Those c a l c u l a t i o n s a r e very d i f f i c u l t s i n c e t h e bonding changes from one p a r t ( m e t a l l i c ) t o t h e o t h e r (ceramic) a t t h e i n t e r f a c e . Quantum mechanical & initio c a l c u l a t i o n s a r e required f o r an understanding o f t h e s t r u c t u r e and bonding mechanisms a t i n t e r f a c e s .

A. Revcolevschi: Have t h e sphere-rotation t y p e experiments been c a r r i e d o u t i n t h e c a s e o f oxides, t o determine p r e f e r e n t i a l x l s ? How a r e t h e s e r e g u l a r s i z e spheres prepared f o r oxides?

M. Ruhle: The sphere-rotation t y p e experiment was t r i e d f o r N i O by Peterson e t a l . (Adv. i n Ceramics l ( 1 9 8 1 ) 101). The experiment could n o t g i v e information on t h e e x i s t a n c e o f low-energy g r a i n boundaries s i n c e excessive sphere evaporation occurred b e f o r e r o t a t i o n o f t h e sphere could b e d e t e c t e d . The NiO spheres (

-

M. Schliiter: What is known about t h e e l e c t r i c a l p r o p e r t i e s o f oxide GBs and i n t e r f a c e ? Can we make d e v i c e s using them?

M. Ruhle: Oxide ceramics a r e a l s o used a s e l e c t r o n i c components and t h e e l e c t r i c a l p r o p e r t i e s o f t h e g r a i n boundaries, e s p e c i a l l y t h e i n f l u e n c e o f segregated along a t g r a i n boundaries, were s t u d i e d ( f o r r e f e r e n c e s e e e.g. M.F. Yan and A.H. Heuer ( e d t

.

^,

7 ( 1983) )

.