T.E.M. STUDY OF THE TEXTURE AND PREFERENTIAL ORIENTATION OF GRAIN BOUNDARIES IN POLYCRYSTALLINE NiO PREPARED BY METAL OXIDATION

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T.E.M. STUDY OF THE TEXTURE AND PREFERENTIAL ORIENTATION OF GRAIN

BOUNDARIES IN POLYCRYSTALLINE NiO PREPARED BY METAL OXIDATION

M. Dechamps, A. Marrouche, Franck Barbier, A. Revcolevschi

To cite this version:

M. Dechamps, A. Marrouche, Franck Barbier, A. Revcolevschi. T.E.M. STUDY OF THE TEXTURE

AND PREFERENTIAL ORIENTATION OF GRAIN BOUNDARIES IN POLYCRYSTALLINE NiO

PREPARED BY METAL OXIDATION. Journal de Physique Colloques, 1985, 46 (C4), pp.C4-435-

C4-440. �10.1051/jphyscol:1985448�. �jpa-00224699�

T.E.M. S T U D Y O F T H E T E X T U R E A N D P R E F E R E N T I A L O R I E N T A T I O N OF GRAIN B O U N D A R I E S IN P O L Y C R Y S T A L L I N E N i O P R E P A R E D B Y M E T A L O X I D A T I O N

M. Dechamps, A. Marrouche, F. Barbier and A. Revcolevschi

Laboratoire de Chimie Appliquée, Université Paris-Sud, 91405 Orsay Cedex, France

Résumé - On a déterminé par diffraction électronique les relations d'orienta- tion, l'indice de coïncidence et le plan du joint de grains de 71 couples de cristaux adjacents dans de l'oxyde de nickel polycristallin.

Abstract - Orientation relations, coincidence index and Miller indices of grain boundary planes were determined by electron diffraction for 71 couples of adjacent crystals in polycrystalline NiO prepared by oxidation of Ni.

INTRODUCTION

Atkinson and Taylor, and Chen and Peterson have observed a significant intergranular diffusion in nickel oxide. The intergranular diffusion coefficients of Ni and Co in polycrystalline NiO prepared by oxidizing a foil of high purity nickel 25 ym in thickness at 1100°C have been determined by Atkinson and Taylor /l/ whereas Chen and Peterson have determined the intergranular diffusion coefficients of Co and Cr in po- lycrystalline NiO grown from the melt by the flame fusion technique 111. The results indicate a significant quantitative disagreement between the diffusion data relative to Co but, so far, no convincing reasons were found to explain it.

In order to clarify this discrepancy one of us (F. Barbier) has carried out experi- ments in which cobalt was diffused into bicrystalline NiO samples of known (Disorien- tation. Several bicrystals having a <001> or <011> symmetrical tilt axis were grown by the flame fusion technique 13/, then submitted to various thermal treatments in order to promote intergranular diffusion of Co. No preferential diffusion of cobalt at the grain boundaries has been observed. These results led us to characterize with more precision the nickel oxide which was used by Atkinson and Taylor and the bi- crystalline samples used in our laboratory, in order to explain the different beha- viour of the two materials. We present here the results of a T.E.M. characterization of the polycrystalline grain boundaries, our purpose being the determination of the orientation relationships existing between adjacent crystals and the precise crystal- lographic characterization of the grain boundaries (G.B.). Other data obtained during this study are presented, concerning, in particular, the oxidation texture of the polycrystalline samples.

I - METHOD OF CHARACTERIZATION AND RESULTS Specimen preparation

NiO polycrystalline samples were provided by Atkinson after being prepared by the procedure described in /l/. Taking into account the observations of Atkinson and Taylor, 3 mm NiO disks were polished on both faces then ion-milled for electron transparency. Various areas in each sample were examined yielding a total of 71 grain boundary characterizations. No significant difference between the various samples or between different areas of one sample was noticed, which seems to indicate that our results are representative of the NiO polycrystalline samples.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985448

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Orientation relationships

In order t o determine by T.E.M. the orientation re1 ationships existing between any two adjacent c r y s t a l s we have used the numerical method proposed by Fontaine and Rocher /4/, which i s only s l i g h t l y d i f f e r e n t from t h a t proposed by Karakostas e t a1

/5/,

both techniques using the matrix formal ism developed by Lange /6/. Basically the method consists of characterizing each crystal by 3 non coplanar crystallographic directionswhich define the transformation matrix MI from the <001> orthonormal t r i - hedron t o the experimental c r y s t a l l i n e trihedron. Simultaneously the 3 corresponding pairs of angles

a

and

B

read on the goniometer stage of the microscope give access to the spherical coordinates of each experimental direction in a fixed orthonormal trihedron, i . e . t o the transformation matrix M2 from the fixed trihedron t o the ex- perimental trihedron. Hence the matrix product o

=

(M2t)-'. ~ ~ where the exponent t , t stands f o r transposed matrix , defines the transformation matrix from the fixed orthonormal trihedron t o the crystal <001> trihedron.

Fig. 1 - Stereographic projection of a

Z =

7 bicrystal w i t h the plane of the thin f o i l as the plane of projection.

<001> directions of crystal 1.

<001> directions of crystal 2.

+ d i r e c t i o n s of the 24 possible axes of rotation.

0

pole of the G.B. plane. The G.B. i s represented by a s o l i d l i n e meridian.

If o ' i s the equivalent matrix f o r a second c r y s t a l , then the rotation matrix between both c r y s t a l s i s R

=

0 ' t . o . The rotation angle i s calculated from the t r a c e of R and the rotation axis i s an Eigen vector of R . The 24 equivalent descriptions associated with cubic symmetry may be obtained by permutation of the elements of a ' ,

o

remaining unchanged. As an example, t h e graphical expression of one calculation i s represented i n f i g . 1.

Coincidence indices

The previous r e s u l t s were used t o investigate the possible existence of a coincidence index

Z*

f o r each couple of adjacent c r y s t a l s . Two methods were used. F i r s t

C was

computed by t r i a l and e r r o r using the r e l a t i o n Y/X

=

tg ( 8 / 2 ) / f l , where N

=

h2+k2+12 and

C =

X2+N.y2

( Y

and X a r e integers r e l a t i v e l y prime

;

0 i s the misorientation angle and h k 1 a r e integer indices of the misorientation a x i s ) which was shown t o be v a l i d , if2 e 5 180°, only i f both c r y s t a l s a r e coincident /7,8/. I f e

=

180°, then z

=

h2+ k2+l. Secondly,C was a l s o found by d i r e c t comparison with the coincidence tables established by Mykura /9/ or others /e.q. l o / . B u t before assigning a bicrys- t a l a

C

value two problems had t o be solved. The f i r s t i s the choice of the upper l i m i t physically meaningful f o r

C.

The second i s the d e f i n i t i o n of the angular in- terval A0 allowed from the s t r i c t coincidence misorientation

8 .

Concerning the upper

*

^C

i s defined a s the r a t i o of the volume of the coincidence s i t e l a t t i c e u n i t c e l l

t o t h a t of the cr.ysta1 l a t t i c e unit c e l l .

70

a

50

-

10

5 ,

F i g . 2

-

Cumulative frequency o f b i c r y s t a l s c h a r a c t e r i z e d by a coincidence index, versus C. About 50 % o f t h e b i c r y s t a l s analyzed f i t t e d w i t h an index C 6 41, w i t h i n t h e l i m i t s o f Brandon's c r i t e r i o n . W i t h i n t h i s p o p u l a t i o n t h e r e i s no n o t i c e a b l e p r e f e r e n t i a l o r i e n t a t i o n r e l a t i o n s h i p .

l f m i t o f C, i t i s impossible t o d e f i n e a p r e c i s e v a l u e because o f t h e l a c k o f expe- r i m e n t a l o r t h e o r e t i c a l grounds. So f a r we have l i m i t e d our i n v e s t i g a t i o n , f o r most o f t h e samples, t o C ( 41, m a i n l y because, up t o now, secondary d i s l o c a t i o n a r r a y s have been observed up t o C = 4 1 i n some m a t e r i a l s /11/. However i t must be noted t h a t several b i c r y s t a l s f i t v e r y w e l l w i t h l a r g e r values o f C. As f o r t h e i n t e r v a l AB, v a r i o u s semi-empirical c r i t e r i a have been proposed, which a r e a l l formulated as Ae = Bo/Cn w i t h Bo = 15' o r 8" and n = 1 o r 0.5 /12-14/. F o l l o w i n g Warrington /13/ we have chosen t o apply t h e Brandon c r i t e r i o n A8 = 15/& /13/. F i g . 2 presents our r e s u l t s i n terms o f cumulative frequency o f t h e number o f b i c r y s t a l s versus C, i n o r d e r t o make e a s i e r a comparison w i t h f u r t h e r r e s u l t s .

Grain boundary plane

Each boundary was indexed using several micrographs taken a t v a r i o u s

R

t i l t angles measured along t h e m e r i d i a n perpendicular t o the m e r i d i a n r e p r e s e n t i n g t h e G.B. plane.

G B P L A N E

P P R O J E C T I O N P L A N E

F i g . 3

-

Schematic diagram o f a t h i n f o i l s e c t i o n c o n t a i n i n g a g r a i n boundary : W : a c t u a l w i d t h o f t h e G.B.

P : p r o j e c t e d w i d t h o f t h e G.B. on a h o r i z o n t a l plane.

R

: angle between the h o r i z o n t a l plane and the f o i l plane.

Y : angle between the f o i l plane and t h e G.B. plane.

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111

Fig. 4 - Distribution of the

G.B.

planes in a standard stereographic t r i a n g l e . i s no

G.B.

plane with a pole close t o [Oil]

;

t h e density of

G.B.

planes along 011/111 meridian i s r a t h e r poorer than elsewhere, except near the 111 pole.

There the

I t s pole, i n f i g . 1 , i s a t the end of the meridian representing the

G.B.

plane

;

t h i s pole corresponds t o the fixed horizontal direction defined by t h e i n t e r s e c t i o n of the

G.B.

plane and the f o i l plane when the l a t t e r i s horizontal. In such a manner the dihedral angles

f2

and

Y

defined i n f i g .

3

l i e i n the same plane and the r e l a t i o n between the actual width

W

of the

G.B.

plane and i t s projection P i s obvious. I t is of p a r t i c u l a r i n t e r e s t t o formulate t h i s r e l a t i o n as P/cos

f2 =

a.tg

f2

+ b, where a

=

- W.sin

Y

and b

=

W.cos

Y

a r e constants, because t h i s l i n e a r r e l a t i o n lends i t s e l f very well t o a l i n e a r regression. Although t h i s method needs a t l e a s t

3

o r 4 micro- graphs, t o be v a l i d , i t i s more accurate (within one degree) than t h a t proposed by Michaut /15/ or than the purely graphical ones.

Fig. 4 represents the graphical d i s t r i b u t i o n of the

G.B.

' s . I t i s obvious t h a t there i s no marked preferential orientation except f o r the f a c t t h a t there i s no

G.B.

close t o (0111 planes. One may a l s o note a r a t h e r poor density of (11R)

G.B.

planes

Fig. 5 - S t a t i s t i c a l orientation of the

G.B.

planes with respect t o the f o i l plane.

Two groups of

G.B.

planes appear

:

the f i r s t i s roughly perpendicular t o the f o i l

surface. The second i s t i 1 ted approximately 50°.

preferential diffusion was observed so f a r .

Another important feature of the boundaries appears i n f i g . 5 where the G.B.'s frequency i s plotted as a function of the angle formed by the G . B . plane and the surface of the t h i n f o i l assumed t o be parallel t o the i n i t i a l Ni sheet. As expected the G.B.'s i n the oxidized layer a r e strongly oriented and nearly half of them are closely perpendicular t o the surface. However we observe a puzzling gap between t h i s 1 s t group and a 2nd group f o r which the average angle with the surface i s about 50".

W e have so f a r no d e f i n i t i v e explanation f o r the existence of such a gap.

Texture

Although electron d i f f r a c t i o n i s not r e a l l y well suited f o r a texture study, some r e s u l t s a r e presented here since the data which were collected were in s u f f i c i e n t number to g e t some evidence of a marked c r y s t a l l i n e growth t e x t u r e , upon oxidation, along the approximate < I l l > , <123> and <011> directions ( f i g . 6 ) .

Fig. 6 - Distribution of the f o i l normals when indexed in r e l a t i o n t o each grain.

The oxidized specimen i s strongly textured.

CONCLUSIONS

I t appears t h a t despite the existence of an oxidation t e x t u r e , the crystallographic orientation of the nickel oxide G.B. planes in samples prepared by oxidation of nickel sheets i s random, except in the 011 area where thev a r e lackinq. Moreover.

nearly a l l the G.B. planes a r e t i l t e d more than 45' with respect t o the surface.

Lastly, although a major f r a c t i o n of the paired c r y s t a l s can be characterized with a

coincidence index, no intergranular preferential orientation relationships were ob-

served. Obviously these r e s u l t s do not allow the prediction of atomic G . B . structures

which could explain diffusion properties. They show however t h a t , a p r i o r i , these

oxidized specimensare very well suited t o obtain information on the average intergra-

nular diffusion since there i s almost no preferential crystallographic orientation

of the G.B. planes. Morevover these G.B.'s are well oriented with respect t o the

surface t o carry out intergranular diffusion experiments. Nevertheless, we shall note

t h a t the G.B.'s of our b i c r y s t a l l i n e samples are also well oriented f o r diffusion

experiments but have another diffusional behaviour. One possible cause of t h i s dis-

crepancy i s the preparation method of our b i c r y s t a l s which might induce a facettinq

of the boundaries.

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