APPLICABILITY OF SIMS IN THE STUDY OF GRAIN BOUNDARY DIFFUSION

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APPLICABILITY OF SIMS IN THE STUDY OF GRAIN BOUNDARY DIFFUSION

W. Gust, M. Hintz, A. Lodding, R. Lučik, H. Odelius, B. Predel, U. Roll

To cite this version:

W. Gust, M. Hintz, A. Lodding, R. Lučik, H. Odelius, et al.. APPLICABILITY OF SIMS IN THE

STUDY OF GRAIN BOUNDARY DIFFUSION. Journal de Physique Colloques, 1985, 46 (C4), pp.C4-

475-C4-482. �10.1051/jphyscol:1985452�. �jpa-00224703�

APPLICABILITY OF SIMS IN THE STUDY OF GRAIN BOUNDARY DIFFUSION

W. Gust, M.B. Hintz , A. Lodding , R. Lucie, H. Odelius , B. Predel and U. Roll

Max-Planck-Institut ftir Metallforschung and Institut ftir Metallkunde, Seestrasse 92, D-7000 Stuttgart 1, F.R.G.

^Michigan Technological University, Houghton, Michigan, MI 499S1, U.S.A.

++

Chalmers University of Technology, S-41296 Gothenburg, Sweden

Résumé - Nous avons mis au point une technique qui permet d'étudier de façon quantitative 1'hêtérodiffusion intergranulaire de soluté sans 1'aide de radio- isotope. Cette technique utilise la spectrométrie de masse d'ions secondaire

(SIMS) pour déterminer les profils de concentration en soluté; elle exploite les deux possibilités de l'instrumentation SIMS: l'imagerie (pour positionner et aligner l'échantillon) et le mode analytique. Les mesures expérimentales permettent de calculer de façon simple le triple produit sêDj^ qui caractérise vie transport de matière au joint, en utilisant l'équation de Le Claire relative

aux méthodes de sectionnement. Cette technique est spécialement adaptée aux études d'hêtérodiffusion le long de joints de grains individuels parfaitement définis du point de vue géométrique; elle est donc particulièrement utile pour des études détaillées dans des échantillons bicristallins. Nous présentons ici un ensemble d'expériences faites sur des bicristaux de structure CFC; les ré- sultats présentés sous la forme de droites d'Arrhénius log (sôDj-,) = f (1/T) montrent une très faible dispersion expérimentale.

Abstract - A technique has been developed which allows the diffusion of impurities along grain boundaries to be quantitatively studied without the use of radioisotopes. The technique employs secondary ion mass spec- trometry (SIMS) for evaluation of the impurity concentration distributions, and exploits both the imaging (for specimen alignment) and analytical modes of SIMS instrumentation. The measurements allow convenient evalu- ation of the grain boundary diffusion triple product, s6Dj-,, using Le Claire's equation for serial sectioning experiments. The procedure is especially well suited for studies of impurity diffusion along individual grain boundaries of well defined geometry, and is thus particlarly useful for detailed

investigations involving bicrystal specimens. Pilot studies of impurity diffusion along grain boundaries in fee bicrystals have been performed, and have resulted in straight Arrhenius lines with very low experimental scatter.

1. Introduction - Bicrystal studies of grain boundary diffusion have hitherto yielded relatively few quantitative experimental data. This is largely due to the unavailabi- lity of convenient measuring techniques and due to the experimental difficulties to produce oriented bicrystals of macroscopic thickness (several mm or more). Most

existing data have been obtained on polycrystalline materials, and express only the average behavior of differently oriented grain boundaries. It is, however, well known that individual grain boundaries may exhibit widely varying diffusivities, dependent on the geometric orientation not only of the neighboring crystallites but also of the boundary itself in relation to the crystallites /l/.

Mass transport via grain boundaries is important in many technical processes; thus the study of grain boundary diffusion is of considerable practical as well as scientific interest. Detailed knowledge of interfacial diffusion behavior can also provide valuable information regarding interfacial structure / 2 / and the opperative diffusion mechanism(s) /3/. Characterization of interfacial diffusion kinetics in detail, however, requires that the orientation relationships between the Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985452

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boundary p l a n e and t h e a d j o i n i n g c r y s t a l l i t e s a r e known. O r i e n t e d b i c r y s t a l s a r e t h u s i d e a l specimens f o r such s t u d i e s . Following t h e development of a technique f o r producing o r i e n t e d b i c r y s t a l s with f l a t boundary s u r f a c e s some 1 cm2 i n a r e a /4/, a t t e n t i o n was focused upon f i n d i n g an a n a l y t i c a l method s u i t a b l e f o r e v a l u a t i n g t h e b i c r y s t a l d i f f u s i o n p r o f i l e s . Because of i t s h i g h s e n s i t i v i t y t o many elements and e x c e l l e n t i n d e p t h s p a t i a l r e s o l u t i o n , t h e technique of secondary i o n mass s p e c t r o - metry (SIMS) was chosen /5,6/. I n t h e f o l l o w i n g , i t w i l l be shown t h a t t h e technique i s w e l l s u i t e d f o r t h e measurement of i m p u r i t y d i f f u s i o n k i n e t i c s a l o n g i n d i v i d u a l g r a i n boundaries. The methods developed were f i r s t a p p l i e d t o t h e Ni-In and Cu-In b i n a r y systems, which a r e of p a r t i c u l a r i n t e r e s t i n connection w i t h t h e d i s c o n t i n u o u s p r e c i p i t a t i o n r e a c t i o n /7/.

2. Fundamentals

-

For t h e e v a l u a t i o n of t h e measured t r a c e r c o n c e n t r a t i o n p r o f ? l e s , t h e e q u a t i o n given by Le C l a i r e /8/ was u t i l i z e d , formulated f o r t h e geometry o f t h i n s e c t i o n s p e r p e n d i c u l a r t o t h e boundary,and hence p a r t i c u l a r l y s u l t a b l e f o r t h e p r e s e n t s t u d i e s . The r e s u l t a n t e n t i t y i s t h e t r i p l e p r o d u c t of t h e i n t e r g r a n u l a r d i f f u s i o n c o e f f i c i e n t Db, t h e boundary width 6 and t h e s e g r e g a t i o n f a c t o r s, according t o

where c i s t h e mean i m p u r i t y c o n c e n t r a t i o n i n a t h i n l a y e r p a r a l l e l to,and a t ' a d i s t a n c e z from,the b i c r y s t a l s u r f a c e on which t h e t r a c e r was f i r s t d e p o s i t e d . _D i s t h e bulk d i f f u s i o n c o e f f i c i e n t of t h e t r a c e r and t i s t h e d i f f u s i o n a n n e a l time. The s e g r e g a t i o n f a c t o r h a s been d e f i n e d /9/ a s s = xb/xv, i . e . t h e r a t i o n of t h e concen- t r a t i o n i n t h e boundary t o t h a t i n t h e bulk. I n t h i s p a r t i c u l a r c a s e t h e d e f i n i t i o n of s must be somewhat modified, a s t h e t r a c e r c o n c e n t r a t i o n xv i s near-zero every- where e x c e p t i n t h e immediate neighborhood of t h e boundary.

E q . ( l ) i s v a l i d w i t h t h e following c o n d i t i o n s :

and

The above s o l u t i o n r e s u l t s i n e s s e n t i a l l y i d e n t i c a l v a l u e s f o r b o t h extremes of d i f f u s a n t source behavior, i . e . t h e c o n s t a n t c o n c e n t r a t i o n source

/lo/

^and

t h e t h i n f i l m ( i n s t a n t a n e o u s ) source /11/. The s o l u t i o n i s t h u s independent of i m p u r i t y source c o n d i t i o n /8/. T h i s i s of c o n s i d e r a b l e p r a c t i c a l advantage, a s t h e a c t u a l c h a r a c t e r i s t i c s of e x p e r i m e n t a l d i f f u s a n t s o u r c e s a r e d i f f i c u l t t o d e f i n e and/or monitor. For a given i s o t h e r m a l a n n e a l l i n g h i s t o r y , t h e t r i p l e p r o d u c t , s60b, i s a c o n s t a n t , a s a r e t h e l a s t two terms of ~ q . ( i ) . A l o g a r i t h m i c p l o t of c ( o r , f o r t h e c a s e of SIMS measurements, t h e measured i m p u r i t y i o n i n t e n s i t y , I ) v e r s u s 2615 t h e r e f o r e r e s u l t s i n a s t r a i g h t l i n e . The s l o p e of t h e l i n e can t h e n be determined and used t o e v a l u a t e s6Db i n an i t e r a t i v e f a s h i o n v i a E q . ( l ) s i n c e t h e r i g h t hand term of ~ q . ( 1 ) i s a v e r y weak f u n c t i o n of s 6 ~ ~ . ~t should be k e p t i n mind t h a t t h e r e s u l t s y i e l d t h e t r i p l e p r o d u c t , and n o t any of i t s terms s e p a r a t e l y . I n l i t e r a t u r e o f t e n only t h e v a l u e s of Db a r e given, b u t any comparison should be made by means o f t h e s6Db v a l u e s . Therefore it i s n e c e s s a r y t o make some reasonable assumptions f o r s and 6, i f n o t s t a t e d i n t h e o r i g i n a l paper.

3 . Experimental Procedure

-

The b i c r y s t a l s u r f a c e , on which t h e t r a c e r (In) was d e p o s i t e d i n high vacuum, was p r e p a r e d p e r p e n d i c u l a r t o t h e boundary between t h e c r y s t a l s . The t r a c e r l a y e r was 20 t o 100 nm t h i c k . The d i f f u s i o n a n n e a l s took p l a c e e i t h e r i n a p r o t e c t i v e atmosphere o f streaming A r o r i n h i g h vacuum. A s t h e p e n e t r a - t i o n d e p t h a l o n g t h e boundary was t o o g r e a t t o allow d e t e r m i n a t i o n of t h e concentra- t i o n p r o f i l e with a s i n g l e SIMS s p u t t e r c r a t e r , a low a n g l e b e v e l (lo-4O) was ground i n t o t h e specimen s u r f a c e ( c f . F i g . 2 a ) . This was accomplished u s i n g a s p e c i a l l y con- s t r u c t e d g r i n d i n g f i x t u r e which allowed t h e b e v e l a n g l e t o be c o n t r o l l e d t o w i t h i n f 0. lo.

symmetrical g r a i n boundaries, t o avoid t h e SIMS a r t i f a c t of d i f f e r e n t s p u t t e r r a t e s i n d i f f e r e n t l y o r i e n t e d c r y s t a l s . The SIMS i n s t r u m e n t employed (Cameca) had t h e advantage of being o p e r a b l e i n an imaging mode ( i o n microscope /5/) which made it p o s s i b l e t o i d e n t i f y and a d j u s t t h e analyzed f i e l d w i t h c o n s i d e r a b l e p r e c i s i o n . Fig. 1 shows SIMS images of t h e g r a i n boundary and i t s v i c i n i t y i n a copper b i c r y s t a l , v i a t h e Cu+ and 1n+ i o n s i g n a l . I n t h e Cu image ( l a ) one may n o t e t h a t t h e primary i o n beam was i n t e n t i o n a l l y mis-aligned, t o i l l u s t r a t e t h e s p u t t e r r a t e d i f f e r e n c e between t h e two c r y s t a l s . From t h e I n image it can be c l e a r l y seen t h a t a t s m a l l d e p t h s t h e t r a c e r has s i g n i f i c a n t l y p e n e t r a t e d i n t o t h e bulk ( I b )

,

while a t g r e a t e r d i s t a n c e s from t h e s u r f a c e t h e indium i s found n e a r l y e x c l u s i v e l y i n t h e g r a i n boundary i t s e l f

z 1 0

v m

1 1 5 1 n + z = 1 0 0

urn

F i g . 1

-

SIMS images ( i o n micrographs) of a Cu b i c r y s t a l i n which I n has been d i f f u s e d .

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Fig. 2a

-

Schematic diagram o f t h e measurement procedure. GB g r a i n boundary of a b i c r y s t a l , OS o r i g i n a l s u r f a c e , a b e v e l a n g l e , C c r a t e r , BG d e t e r m i n a t i o n o f t h e background s i g n a l , BP d i s t a n c e e n r i c h e d w i t h I n by b u l k p e n e t r a t i o n , z d i r e c t i o n o f mass t r a n s p o r t .

F i g . 2b

-

I n t e r f e r e n c e photograph. On b o t h s i d e s of t h e g r a i n boundary t h e f l a t c r a t e r s produced d u r i n g t h e d e t e r m i n a t i o n of t h e background s i g n a l can be recognized. 48O < l o o > tilt boundary, 18.25 h a t 923 K /12/.

The d i r e c t i o n a l l y a d j u s t e d b i c r y s t a l i n t h e SIMS specimen h o l d e r i s s u b j e c t e d t o t h e primary i o n beam a t s u c c e s s i v e p o i n t s of a n a l y s i s stepwise a l o n g t h e g r a i n boundary on t h e beveled s u r f a c e , a s schematized i n F i g . 2a. The c r a t e r 3 shown a d j a c e n t t o t h e boundary a r i s e from c o n t r o l measurements o f t h e background s i g n a l . On each analyzed s p o t t h e primary i o n beam d e n s i t y . (05) g e n e r a l l y amounted t o 1

-

5 m ~ / c r n ~ , which w i t h i n a moderate s p u t t e r i n g p e r i o d r e s u l t e d i n a c r a t e r s i m i l a r t o t h a t shown i n t e r - f e r o m e t r i c a l l y i n Fig. 2b.

4. R e s u l t s and Discussion

-

For e a c h analyzed s p o t t h e s i g n a l was r e c o r d e d i n numerous counting c y c l e s , d e s i g n a t e d w i t h o r d e r number N i n a s p u t t e r p r o f i l e ( s e e

39'

<

110> Tilt GB 4 2 h 967K -2

c l i c a l l y measured secondary i o n s i g n a l s . I n t e n s i t y I, a s a f u n c t i o n of t h e measurement c y c l e number N on a given l o c a t i o n of t h e i n c l i n e d p o l i s h e d s u r f a c e .

Fig. 3b

Semi-logarithmic p r e s e n t a - t i o n o f t h e I / I ; - Z ~ / ~ r e - l a t i o n s h i p . I i s t h e back- ground c o r r e c t e d i n t e n s i t y of t h e 1151n+ s i g n a l and I{ i s t h e measured i n t e n s i t y o r a m a t r i x s i g n a l ( 6 0 ~ i + ) 1131.

F i g s . 3 and 4 ) . The p r o f i l e s s e r v e d a s c o n t r o l of t h e s t a b i l i t y of t h e s p u t t e r i n g and i o n i z i n g c o n d i t i o n s . The u t i l i z a t i o n of t h e combined s i g n a l o f s e v e r a l channels made it p o s s i b l e t o minimize t h e s t a t i s t i c a l e r r o r . For t h e p r o f i l e s i n F i g s . 3a and 4a t h e e a r l i e s t c y c l e s , recorded b e f o r e t h e a t t a i n m e n t of a c c e p t a b l e s t a b i l i t y , were omitted. The t r a c e r i o n s i g n a l (1n+) i n t h e l a t e r c y c l e s was c o r r e c t e d f o r s p e c t r a l background and i n t h e c a s e of t h e Ni-In system normalized t o t h e measured s i g n a l of a m a t r i x i o n ( 6 0 ~ i + ) . I t may b e seen from t h e constancy o f t h e s e s i g n a l s t h a t t h e depth o f each s p u t t e r e d c r a t e r ( - 3 um) was n e g l i g i b l y s m a l l i n comparison with t h e p e n e t r a t i o n depth o f t h e t r a c e r ( - 600 v m ) . By t h e use o f t h e normalized averaged i n t e n s i t i e s I/I{ (which a r e p r o p o r t i o n a l t o t h e average i m p u r i t y concen- t r a t i o n of t h e s e c t i o n s i n q u e s t i o n ) , s m a l l d i f f e r e n c e s i n i n s t r u m e n t f o c u s i n g between one l o c a t i o n and t h e next a r e canceled.

The e f f e c t i v e measuring depth z can be e a s i l y determined from t h e b e v e l a n g l e a and

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Fig. 4b

Semi-logarithmic resen-

t a t i o n of t h e 1-zg/5 r e - l a t i o n s h i p .

'5=cu+

o o ~ O O O O O O O O O O O O O O O O D O O O O O O O O O O O

-

-

"51,,+

~ o o o * ~ ~ o o o ~ ~ ~ ~ ~ o ~ ~ o ~ o ~ ~ ~ o o o ~ o o o ~

t h e d i s t a n c e v from t h e i n t e r s e c t i o n l i n e between t h e o r i g i n a l s u r f a c e and t h e b e v e l p l a n e :

F i g . 4a

I n t e n s i t y Im a s a f u n c t i o n of t h e measurement c y c l e number N on g i v e n l o c a t i o n of t h e i n c l i n e d p o l i s h e d s u r f a c e ( z = 118 u m ) .

-

Cu 1 In -

45" <100> Tilt GB

-

. ^{Diff. 11} <100>

m

39" < 1 1 0 > ^{Tilt GB}

Diff. 11 <110>

-20 -

9 10 11 12 13

IO~IT (K-')

F i g . 5 - Arrhenius p l o t of t h e e x p e r i m e n t a l l y determined g r a i n boundary d i f f u s i v i t i e s f o r t h e d i f f u s i o n of I n a l o n g symmetric tilt boundaries i n N i and Cu /6,14/.

The e r r o r b a r s i n d i c a t e f o r t h e h i g h e s t and lowest temperature t h e maximum of t h e e s t i m a t e d e x p e r i m e n t a l e r r o r r e s u l t i n g from t h e u n c e r t a i n t i e s of t h e in-depth c o o r d i n a t e , t h e background v a l u e and t h e s c a t t e r i n a s p u t t e r p r o f i l e .

- F i g u r e s 3b and 4b show t h e l i n e a r i t y of t y p i c a l log I

-

z6I5 and l o g I/I: - z 6 l 5 p l o t s , r e s p e c t i v e l y . The s l o p e s of t h e s e p l o t s were used t o determine s 6 ~ b . According t o t h e Arrhenius r e l a t i o n (Fig. 5 )

(where Q~~ i s t h e e f f e c t i v e a c t i v a t i o n e n t h a l p y of i n t e r g r a n u l a r d i f f u s i o n and R t h e g a s c o n s p a n t ) , one h a s o b t a i n e d t h e f o l l o w i n g parameters f o r a symmetrical 45O<100>

tilt boundary i n t h e =/In system. The d i f f u s i o n a l f l u x was p a r a l l e l t o t h e tilt a x i s .

+

8.36

( s S D ~ ) ~ = (4.93 - 3. e f

x m 3 / s and Qb = (203.2

+

7.1) kJ/mol

T h i s may be compared t o t h e bulk d i f f u s i o n d a t a /15/

Do ⁼ 2.19 x m 2 / s and Q = 178.0kJ/mol

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It i s a s u r p r i s i n g , b u t a w e l l e s t a b l i s h e d e x p e r i m e n t a l f a c t t h a t f o r t h e Cu-In system t h e measured a c t i v a t i o n e n t h a l p y ,

Qgf,

of g r a i n boundary d i f f u s i o n i s h i g h e r t h a n t h e corresponding e n t i t y of volume d i f f u s i o n /14/. Here it should be taken i n t o account t h a t

gf

i s an e f f e c t i v e ( a p p a r e n t ) e n t i t y e x p r e s s i n g t h e temperature dependence o f t h e t r i p l e p r o d u c t ~ 6 % . A simple i n t e r p r e t a t i o n of t h e

sf

v a l u e a s t h e sum of Qb+Qs, where Qb i s t h e ' r e a l ' a c t i v a t i o n e n t h a l p y of g r a i n boundary d i f f u s i o n and Qs i s t h e a c t i v a t i o n e n t h a l p y of g r a i n boundary s e g r e g a t i o n , i s n o t p o s s i b l e because t h e e n t i t y

%

i t s e l f (and consequently Qb) i s i n any c a s e i n f l u - enced by t h e s e g r e g a t i o n p r o c e s s . Such an i n t e r p r e t a t i o n would l e a d t o a Qb v a l u e which i s even l a r g e r t h a n Q E f , because Qs i s a n e g a t i v e q u a n t i t y f o r s e g r e g a t i n g systems.

For a symmetrical 39°<110> tilt boundary i n s / I n one has determined

( s S D ~ ) ~ = (5.4 4::i) x 10-l1 m 3 / s and

Q E ~

^{= (161}

+

19) kJ/mol t o compare with t h e bulk d i f f u s i o n d a t a /16/

-4 2

Do ⁼ 1.1 x 10 m /s and Q = 250 kJ/mol

These r e s u l t s , o b t a i n e d from Arrhenius l i n e s w i t h very low s c a t t e r of t h e i n d i v i d u a l d a t a p o i n t s , i n d i c a t e t h a t t h e above d e s c r i b e d t e c h n i q u e s a r e very s u i t a b l e f o r t h i s c l a s s o f s t u d i e s . We s h o u l d p o i n t o u t t h a t s u c h i n v e s t i g a t i o n s can be r e l a t i v e l y time consuming, even under o p t i m a l c o n d i t i o n s , and t h a t t h e e x p e r i m e n t a l t e c h n i q u e s a r e f a i r l y involved. The t e c h n i q u e s a r e , however, e x p e c i a l l y w e l l s u i t e d f o r performin s y s t e m a t i c s t u d i e s of t h e r e l a t i o n s h i p s between g r a i n boundary d i f f u s i v i t y and i n t e r - U g c r y s t a l l i n e m i s o r i e n t a t i o n , and t h u s have t h e p o t e n t i a l t o become an i m p o r t a n t t o o l f o r e x t e n d i n g our knowledge of i n t e r f a c i a l p r o p e r t i e s .

We a r e i n d e b t e d t o t h e Deutsche Forschungsgemeinschaft and t o t h e S t y r e l s e n f b r Teknisk Utveckling f o r f i n a n c i a l s u p p o r t . We a l s o wish t o acknowledge t h e s k i l l of M r F. E c k s t e i n i n t h e p r o d u c t i o n of s i n g l e c r y s t a l s .

References

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