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FROM THE ATOMIC STRUCTURE OF INTERFACES TO THEIR PHYSICAL AND
CHEMICAL PROPERTIES
A. Bourret
To cite this version:
A. Bourret. FROM THE ATOMIC STRUCTURE OF INTERFACES TO THEIR PHYSICAL AND CHEMICAL PROPERTIES. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-1-C1-10.
�10.1051/jphyscol:1990101�. �jpa-00229996�
COLLOQUE D E PHYSIQUE
Colloque Cl, suppl6ment au n 0 l , Tome 51, janvier 1990
FROM THE ATOMIC STRUCTURE OF INTERFACES TO THEIR PHYSICAL AND CHEMICAL PROPERTIES
A. BOURRET
Dkpartement d e Recherche Fondamentale, Service d e Physique, Groupe Structure, CEN-Grenoble, F-38041 Grenoble Cedex, France
Resume
-De nouveaux resultats experimentaux ont ete obtenus recemment sur la structu- re atomique des joints de grains et des interfaces. Les differentes techniques donnant des renseignements l'echelle atomique sont exposees
:la microscopie electronique haute resolution, la microscopie a emission de champ, la microscopie tunnel et la diffraction de rayons-X. La comparaison de ces resultats avec les modelisations sur ordinateur et le lien avec les propriktes des joints ont et6 menes a bien dans quel- ques cas particuliers. C'est un des enjeux majeurs des prochaines annees que de gene- raliser ces comparaisons dans l'etude des interfaces.
Abstract
-In the recent past years experimental new results have been obtained on the atomic structure of grain boundaries and interfaces. The different techniques for recording atomic-scale information at boundaries, either topological or chemical, are critically reviewed. These include high resolution electron microscopy, atom-probe field-ion microscopy, scanning tunneling microscopy and X-ray diffraction. The con- frontation with computer modelling as well as the link with the boundary properties has been carried out in few cases. It is emphasized that such a comparison is one of the major issue of the interface studies in the next future.
1
- INTRODUCTION
The study of grain boundaries and recently of more general interfaces has been the subject of many experimental as well as theoretical works. For some recent reviews see for instance
/1,2/.A continuous progress of our understanding of intergranular and interphase boundaries properties is evident when one follows the litterature on the subject. However the recent years seem to be characterized
bythe development and the proper use of new techniques at atomic scale. Among others the most advanced are
i)the high resolution electron microscopy (HREM)
/3/, i i )the field ion microscopy with the associated atom-probe
/4/,iii)the very recent appl ications of tunnel ing microscopy to interfaces
/5/.Thanks to these various techniques the experimentalist has now in principle direct access to atomic positions in the lattice, to the atom chemical species and/or to the electronic structure via the electron density of states. In addition X-ray diffraction techniques could give the atomic positions at periodic interfaces with a small unit cell. This recent trend towards atomic-scale probing is likely to be even more developed in the near future. The reason is that simulta- neously the last few years have seen an intensive use of the computer simulation. More sophisticated interaction potentials as well as larger computer capabilities have boosted large amount of information on the structures and the properties of various boundaries.
These informations should now be confronted to the experience, hence demanding more experi- mental results from the techniques at atomic scale. As this confrontation is likely to be one of the major issue of the next decade it seems important to review the main recent expe- rimental results obtained with the atomic-scale,technique and their impact in the understan- ding of the main physical properties of intergranular and interphase boundaries.
2 - PROGRESS IN THE ATOMIC SCALE TECHNIQUES
The advantages and limitations of the different methods are critically described with speci- fic examples on different kinds of boundaries. Some of their characteristics are summarized on Table 1.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990101
CL-2 COLLOQUE DE PHYSIQUE
Technique
H R E M
R e s o l u t i o n ( s t r u c t u r a l i n f o r m a t i o n )
Atom-probe F I M
Specimen Requirements R e s o l u t i o n
(chemical i n f o r m a t i o n ) 0.16 t o 0.2nm
I L I I
I
a t few 10 nms J X-rayd i f f r a c t i o n
Table 1
-
Main c h a r a c t e r i s t i c s o f t h e atomic-scale s e n s i t i v e techniques : h i g h r e s o l u t i o n e l e c t r o n microscopy (HREM), atom-probe f i e l d - i o n microscopy (FIM), scanning t u n n e l i n g micro- scopy (STM) and X-ray d i f f r a c t i o n .Probed t h i c k n e s s direct1y:none
indirect1y:l-2nm, 0.4nm i n very f a v o r a b l e case 0.3 t o 0.4nm
S T M
2.1. Hiqh
resolution electron microscopv
Materi a1 l i m i t a t i o n s
Surface method ( p e e l i n g l a y e r
by l a y e r p o s s i b l e ) 0.4nm (atomic
s e n s i t i v i t y )
0.2nm l a t e r a l 0.005nm normal
0.2-0.3nm
0.002nm l a t e r . 0.0061yn normal
The l a t e s t g e n e r a t i o n o f i n t e r m e d i a t e - v o l t a g e h i g h r e s o l u t i o n e l e c t r o n microscopes g i v e s the e x c i t i n g prospect o f r e s o l u t i o n l i m i t s below 0.2nm. Moreover under s p e c i f i c w e l l - d e f i n e d c o n d i t i o n s i t i s even p o s s i b l e t o deduce u s e f u l s t r u c t u r a l d e t a i l s down t o small f r a c t i o n s o f t h e r e s o l u t i o n l i m i t .
I n t e g r a t e d over 10-20nm
The p r i n c i p l e o f any i n t e r f a c e observations i s t o observe a t l e a s t one b u t p r e f e r a b l y both c r y s t a l s a t each s i d e o f t h e boundary, along a zone-axis w i t h t h e boundary seen end-on. This geometry assures t h a t atomic columns w i l l be w e l l a l i g n e d on e i t h e r s i d e o f t h e boundary g i v i n g an i n t e r p r e t a b l e 2-D p r o j e c t i o n o f a 3-D c r y s t a l . The i n f o r m a t i o n i s always i n t e g r a - t e d along t h e o b s e r v a t i o n axis, z, over t h e specimen thickness. The i n t e r p r e t a t i o n even i n t h i s case i s r a r e l y d i r e c t and a comparison w i t h computer simulated images i s u s u a l l y necessary. A t t h e boundary i t s e l f several cases should be considered as t h e 2-D medium i s p r o j e c t e d t o a l - D image :
i ) a l l displacements are confined i n t h e plane perpendicular t o t h e o b s e r v a t i o n a x i s and does n o t depend on t h e z coordinate : t h e r e l a x a t i o n a t t h e boundary c o u l d be u n i q u e l y determined by one observation a x i s /6/. I t i s a l s o necessary i n order t o g e t atomic-scale information, t h a t t h e distances between atomic columns a r e l a r g e r than t h e r e s o l u t i o n l i m i t . This i s t h e case, f o r instance, f o r pure t i l t g r a i n boundaries (GBs) along low index zone-axi S.
ii) I f t h e displacements along t h e z - d i r e c t i o n a r e non zero b u t remain independant o f z, several HREM images taken along d i f f e r e n t observation axes c o u l d be taken /7/.
i i i ) When t h e displacements a r e more general and v a r i e i n any d i r e c t i o n (case o f a t w i s t g r a i n boundary) atomic-scale i n f o r m a t i o n i s much more d i f f i c u l t t o o b t a i n . A s e r i e s o f p r o - j e c t i o n s along d i f f e r e n t observation axes combined w i t h a 3-D r e c o n s t r u c t i o n scheme would be necessary. It i s i n p r i n c i p l e p o s s i b l e but i t would r e q u i r e a r e s o l u t i o n l i m i t s m a l l e r than t h e one p r e s e n t l y a v a i l a b l e . However HREM images, i n t h i s case, g i v e already i n t e r e s t i n g i n f o r m a t i o n about t h e p e r i o d i c i t y a t t h e i n t e r f a c e and t h e presence o f a d d i t i o n a l d e f e c t s (steps, ledges, f a c e t s and d i s l o c a t i o n s . . .) /8/.
Best i n n o n - d u c t i l e
m a t e r i a l s
Surface method
i n d i r e c t l y p o s s i b l e
I n t h e most f a v o r a b l e cases a complete c r y s t a l l o g r a p h i c a n a l y s i s has been performed i n c l u - d i n g t h e 2-0 space group d e t e r m i n a t i o n as w e l l as t h e atomic coordinates o f several atoms i n t h e b a s i c u n i t c e l l o f t h e boundary i t s e l f . The accuracy o f t h e r i g i d - b o d y t r a n s l a t i o n determination i s o f t h e order o f O.Olnm and t h e atomic coordinates are measured w i t h i n -e 0.02nm (about one t e n t h o f t h e r e s o l u t i o n l i m i t ) /g/. A l l these s t u d i e s a r e s t a t i c s t r u c t u r e determinations. Two p o i n t s should deserve more a t t e n t i o n i n t h e f u t u r e : i) t h e i n f l u e n c e of t h e atomic v i b r a t i o n s a t t h e boundary and i i ) t h e everitual o b s e r v a t i o n o f dynamic f e a t u r e s d i r e c t l y i n - s i t u . Concerning t h e f i r s t p o i n t , up t o now t h e atomic v i b r a t i o n s were neglected i n t h e image i n t e r p r e t a t i o n a p a r t from t h e usual Debye-Waller f a c t o r a t t e n u a t i o n i n the atomic s c a t t e r i n g . However i n a boundary some bonds c o u l d be weakened enough so as t o a f f e c t t h e amplitude o f atomic v i b r a t i o n s even c l o s e t o t h e room temperature. Concerning t h e second
R a d i a t i o n damage i n i o n i c m a t e r i a1 S
Wire w i t h t i p r a d i u s 10-100nm High d e n s i t y o f boundaries 20nm t h i n f o i l w i t h
boundary end-on
I n s u l a t o r s a r e i n a m r o - 2 5nm
F l a t and clean surface w i t h p r i a t e
none
boundary end-on
boundary
-
r u n n i n g p a r a l l e l t o t h e surface
p o i n t , i t i s now f e a s i b l e t o use a h o t stage a t h i g h temperature w i t h a good r e s o l u t i o n /11/. Results a r e s t i l l q u i t e scarce b u t should appear i n t h e n e x t f e a t u r e .
I n a d d i t i o n t o s t r u c t u r a l i n f o r m a t i o n , some chemical i n f o r m a t i o n i s a l s o a v a i l a b l e from HREM images. That t y p e o f a n a l y s i s i s becoming q u i t e popular although i t r e l i e s on r e l a t i v e l y i n d i r e c t i n f o r m a t i o n : m a i n l y t h e atomic r a d i u s d i f f e r e n c e s and/or some Z - c o n t r a s t due t o the d i f f e r e n c e between atomic s c a t t e r i n g f a c t o r s . The method which i s employed, assumes a l a r g e amount o f a - p r i o r i i n f o r m a t i o n : i ) t h e atomic species which a r e i n v o l v e d a r e already known b u t t h e i r exact l o c a t i o n i s t o be found ; i i ) t h e r e l a t i o n s h i p between t h e l a t t i c e constant and t h e composition i s supposed t o be known o r has been measured independantly ; i i i ) t h e image p a t t e r n should be u n i q u e l y and i f p o s s i b l e l i n e a r l y dependant on t h e chemical composition. Although l i m i t e d , t h i s technique has been s u c c e s s f u l l y employed i n m u l t i l a y e r s t r u c t u r e s /12,13,14,15/.
The main l i m i t a t i o n o f t h e HREM technique r e l i e s on t h e p r o j e c t i o n problem. The i n f o r m a t i o n i s always averaged ( i n a n o n - l i n e a r manner) over t h e specimen thickness. As a consequence t h e r e i s a r e d u c t i o n by one dimension i n t h e a v a i l a b l e i n f o r m a t i o n which i s n o t simply over- come. The end-on geometry i s t h e most popular way o f overcoming i t , b u t i t should be asso- c i a t e d w i t h a t l e a s t two o r more p r o j e c t i o n axes. Several t r i a l s o f p l a n a r geometry, i n which t h e boundary i s observed p e r p e n d i c u l a r t o i t s h a b i t plane, a r e n o t completely convin- cing. The main d i f f i c u l t y here i s due t o t h e l a r g e c o n t r i b u t i o n t o t h e image o f t h e upper and lower p a r t s . Two o t h e r l i m i t a t i o n s should deserve some a t t e n t i o n although l e s s serious : the r e l a x a t i o n a t b o t h surfaces o f t h e t h i n l a y e r obtained a f t e r specimen p r e p a r a t i o n and the r a d i a t i o n damage. The r e l a x a t i o n i s o n l y s e r i o u s i n s t r a i n e d boundaries such as those produced i n m u l t i l a y e r s . On t h e o t h e r hand t h e r a d i a t i o n damage c o u l d be s e r i o u s : low-Z specimens o r c r y s t a l w i t h an important i o n i c bonding are g e n e r a l l y more s e n s i t i v e . However each specimen i s a s p e c i f i c case and a general assessment i s d i f f i c u l t t o p u t forward.
In
summary t h e main a p p l i c a t i o n s o f t h e HREM technique concern i ) t h e p e r i o d i c i t i e s a t t h e i n t e r f a c e , i i ) t h e coherency o r t h e l o s s o f coherency w i t h o r w i t h o u t i n t e r f a c i a l d i s l o c a - t i o n s , i i i ) t h e atomic modeling and p o s i t i o n n i n g a t t h e i n t e r f a c e , i v ) t h e roughness o f t h e boundary and t h e presence o f steps, f a c e t s o r chemical g r a d i e n t s .2.2. F i e l d i o n m i c r o s c o ~ y (FIM) and atom-orobe FIM
With t h e FIM i t i s p o s s i b l e t o form an image o f t h e arrangement o f i n d i v i d u a l atoms on t h e surface o f a small rounded t i p and i n c o n j u n c t i o n w i t h a t i m e - o f - f l i g h t mass spectrometer t o i d e n t i f y them c h e m i c a l l y /4/. However i t should be r e a l i z e d t h a t t h e atomic imaging i s r e s - t r i c t e d t o k i n k o r ledge s i t e s a t t h e boundary as w e l l as i n t h e two c r y s t a l s on e i t h e r side o f t h e boundary. C o n t r o l l e d f i e l d evaporation, atomic l a y e r by atomic l a y e r , extends t h i s i n h e r e n t s u r f a c e technique t o a b u l k technique : i t enables t o e x p l o r e an i n t e r f a c e
alonq
the boundary plane. The l a t e r a l r e s o l u t i o n i s t h e o r e t i c a l l y determined by t h e t i p tempera- t u r e and t h e t i p r a d i u s which should be as low as p o s s i b l e . I t i s o f t h e o r d e r o f 0.3nm i n the optimum case (tungsten) and t h e r e f o r e does n o t a l l o w t o make a c r y s t a l l o g r a p h i c a n a l y s i s o f t h e boundary s t r u c t u r e . The r e s o l u t i o n normal t o t h e surface i s s u b s t a n t i a l l y b e t t e r and o f t h e o r d e r o f 0.03nm. However any q u a n t i t a t i v e measurement i s h i n t e r e d by unknown surface r e l a x a t i o n under t h e a p p l i e d e l e c t r i c f i e l d . As a consequence although t h e d e t e c t i o n o f GBs geometry i n very small g r a i n s i z e specimens i s easy t o perform, t h e boundary s t r u c t u r e has never been determined by FIM. Nevertheless i n t e r e s t i n g parameters such as t h e m i s o r i e n t a - t i o n , t h e GB p l a n e and t h e presence o f a d d i t i o n a l d e f e c t s c o u l d be deduced from an FIM p i c t u r e . T h i s method c o u l d be a p p l i e d t o a general g r a i n boundary ( t w i s t as w e l l as t i l t ) i n a random o r i e n t a t i o n and i n m a t e r i a l s c o n t a i n i n g a v e r y h i g h d e f e c t d e n s i t y /17/. The same i s t r u e f o r an i n t e r p h a s e i n t e r f a c e although i t s range o f a p p l i c a b i l i t y i s r e s t r i c t e d t o t h e few cases where b o t h phases e x h i b i t a r i n g s t r u c t u r e a t t h e same a p p l i e d voltage. These l i m i t a t i o n s combined w i t h t h e f a c t t h a t GB-migration c o u l d be induced i n n o n - r e f r a c t o r y metal S and t h a t f i e l d evaporation occurs p r e f e r e n t i a l l y a t boundaries, has impeded extensive use o f t h e
F I M
f o r s t r u c t u r a l i n v e s t i g a t i o n o f boundaries i n t h e l a s t decade.F o r t u n a t e l y t h e f a c i l i t y f o r i d e n t i f y i n g t h e chemical n a t u r e o f atoms a t near atomic l e v e l has renewed t h e i n t e r e s t f o r t h e atom-probe FIM. This c o n s i s t o f t h e chemical i d e n t i f i c a t i o n of a s i n g l e i o n e m i t t e d from a s e l e c t e d area o f t h e t i p by small f i e l d evaporation pulse.
The c o u n t i n g being atom per atom t h e s t a t i s t i c a l s i g n i f i c a n c e o f atom-probe d a t a has t o be improved by data accumulation which i s sometimes cumbersome b u t y i e l d s t o unique data on i m p u r i t y segregation a t g r a i n boundaries /10,16,19/ i n t e r f a c e s /20/ o r s t a c k i n g f a u l t s /21,22/.
Cl-4 COLLOQUE DE PHYSIQUE
Despite i t s p o t e n t i a l i n t e r e s t , s p e c i a l l y w i t h t h e simultaneous use o f FIM imaging and atom- probe chemical c a p a b i l i t i e s , these techniques have n o t a t t r a c t e d very much a t t e n t i o n and i t ought t o be more w i d e l y e x p l o i t e d .
2.3. Scannina Tunnelins M i c r o s c o ~ v ISTM)
The STM i s an h i g h - r e s o l u t i o n instrument capable o f s t r u c t u r a l i n f o r m a t i o n as w e l l as e l e c - t r o n i c and spectroscopic imaging. T h i s provides a unique v e r s a t i l e t o o l b u t a l s o sometimes i t s r a t h e r s u b t l e image i n t e r p r e t a t i o n . The t u n n e l i n g c u r r e n t probes t h e e l e c t r o n i c d e n s i t y o f s t a t e s (occupied o r unoccupied depending o f t h e a p p l i e d v o l t a g e ) o f t h e s u b s t r a t e convo- l u t e d by those o f t h e t i p . I f t h e t i p wave f u n c t i o n i s supposed t o be known, t h e tunnel current, I , c o u l d be r e l a t e d t o t h e topology ( p o s i t i o n i n t h e space) as w e l l as t o t h e e l e c - t r o n i c s t a t e o f one p a r t i c u l a r atom a t the surface. The r e s o l u t i o n i s 0.2nm l a t e r a l l y and 0.005nm normal t o t h e surface. Topographic images are g e n e r a l l y taken w i t h scans a t constant t u n n e l i n g c u r r e n t m o n i t o r i n g t h e change i n t h e d i s t a n c e between t i p and s u b s t r a t e and e l e c - t r o n i c o r spectroscopic images are performed a t steady t i p on a p a r t i c u l a r atom by measuring t h e I ( V ) c h a r a c t e r i s t i c /5/. The combination o f a17 these s i g n a l s by a c l e v e l e l e c t r o n i - c a l l y - d r i v e n b i a s i n g may p r o v i d e d i r e c t and s e l e c t i v e imaging o f atomic species p a r t i c u l a r l y on semiconductor m a t e r i a l s where t u n a b l e - l a s e r e x c i t a t i o n i s a1 so p o s s i b l e /23/.
The observation o f an i n t e r f a c e i s l i m i t e d t o t h e edge-on geometry, o n l y t h e surface atoms being probed. Very few a p p l i c a t i o n s are y e t published t h e technique being s t i l l i n i t s infancy. However one c o u l d envisage t o l o o k a t a v a r i e t y o f i n t e r g r a n u l a r and interphase boundaries w i t h t h e exception o f i n s u l a t i n g m a t e r i a l s . The chemical i n f o r m a t i o n through some recognizable f e a t u r e i n t h e d e n s i t y o f s t a t e s i s r a t h e r i n d i r e c t when compared w i t h t h e atom-probe FIM, b u t t h e r e i s a unique c a p a b i l i t y o f combination between t h e s t r u c t u r a l information and t h e e l e c t r o n i c i n f o r m a t i o n . T h i s should a t t r a c t many new developments i n employing t h i s technique t o study s p e c i f i c segregation s i t e s i n a boundary a t an atomic scale, o r t o recognize t h e l o c a t i o n o f d i f f e r e n t species a t a boundary s p e c i a l l y i n a l l o y s . U n f o r t u n a t e l y t h e p r e c i s e d e t e r m i n a t i o n o f t h e atomic coordinates a t t h e i n t e r f a c e i s d i f f i - c u l t owing t o p o s s i b l e s u r f a c e r e l a x a t i o n as w e l l as t o s p a t i a l d i s t o r s i o n due t o t h e d r i f t . Recently t h i s instrument has been extended t o probe a b u r i e d i n t e r f a c e w i t h lnm s p a t i a l r e s o l u t i o n through b a l l i s t i c e l e c t r o n spectroscopy measurement /24/. T h i s appl i e s t o metal - semiconductor i n t e r f a c e s .
2.4. X-rav d i f f r a c t i o n
Q u a n t i t a t i v e X-ray d i f f r a c t i o n techniques c o u l d be used d i r e c t l y o r through standing-wave, t o study i n t e r f a c e s . S t r i c t l y p e r i o d i c i n t e r f a c e s such as those produced i n a commensurate g r a i n boundary c o u l d g i v e r i s e t o measurable r e f l e c t i o n s i n r e c i p r o c a l space : t h e i n t e r f a c e r e f l e c t i o n s a r e found t o be modulated rods o f i n t e n s i t y extended p e r p e n d i c u l a r t o t h e i n t e r - face /25/. The a v a i l a b i l i t y o f h i g h f l u x X-ray sources a t synchrotron f a c i l i t i e s has enable t o measure t h e i n t e n s i t y o f t h e GBs r e f l e c t i o n s . The atomic s t r u c t u r e can then be obtained by t e s t i n g model s t r u c t u r e s w i t h a
2
a n a l y s i s . The number o f r e q u i r e d r e f l e c t i o n s increases w i t h t h e number o f atoms i n c l u d e d i n t h e u n i t c e l l determined by t h e coincidence s i t e l a t t i - ce (50 were measured f o r 8 independant atomic p o s i t i o n s i n Z=13 GB /26/. The r e s o l u t i o n i s very good being 5 0.006nm normal t o t h e i n t e r f a c e and 0.002nm p a r a l l e l t o t h e i n t e r f a c e . Care should be taken i n o r d e r t o e l i m i n a t e c o n t r i b u t i o n s from double d i f f r a c t i o n as w e l l as o r d i n a r y f o r b i d d e n r e f l e c t i o n s appearing i n t h i n l a y e r s . I n t e g r a t e d i n t e n s i t i e s o f t h e 1=0 plane g i v e t h e p r o j e c t e d l o c a t i o n onto t h e GB plane w h i l e t h e r e l r o d i n t e n s i t y p r o f i l e along each s p e c i f i c r o d g i v e s an information i n t h e p o s i t i o n perpendicular t o t h e GB plane. Such experiments were l i m i t e d up t o now t o t h e transmission case i n which t h e i n t e r f a c e plane runs p a r a l l e l t o t h e surfaces o f a t h i n specimen. That type o f geometry i s t h e r e f o r e l i m i t e d t o h o t pressed boundaries. A g r e a t advantage o f t h i s technique i s t h e a v a i l a b i l i t y t o solve any p e r i o d i c s t r u c t u r e i n p a r t i c u l a r t w i s t g r a i n boundaries which are more d i f f i c u l t t o study by HREM. However i t should be generalyzed t o l e s s s p e c i f i c sample geometry. For instance a g r a z i n g incidence i n t h e r e f l e c t i o n mode c o u l d broaden t h e a p p l i c a t i o n s t o near surface i n t e r f a c e s such as those produced a f t e r surface r e a c t i o n o r d e p o s i t i o n . Another method i s t h e X-ray standing waves which c o u l d g i v e s t r u c t u r a l i n f o r m a t i o n w i t h a z - r e s o l u - t i o n l o r 2% of t h e d-spacing. This method may be used t o l o c a t e a t i n t e r f a c e s s p e c i f i c atoms recognized by fluorescence y i e l d measurement /27,28/. T h i s method can be a p p l i e d t o m u l t i l a y e r i n order t o l o c a t e a s p e c i f i c species and make extended X-ray a b s o r p t i o n f i n e s t r u c t u r e measurement /29/ : i n such a case t h e r e s o l u t i o n i s l i m i t e d t o t h e dimension normal t o t h e m u l t i l a y e r i n t e r f a c e s and i s o f t h e o r d e r o f 10% o f t h e m u l t i l a y e r p e r i o d .3 - POSSIBLE COMPARISON WITH COMPUTER MODELLING OF STATIC STRUCTURE
The comparison between experimental results at atomic level and the computer modelling has been made on few examples. This comparison has itself several degrees of complexity
:one may compare the rigid body translations at grain boundaries as a first overall parameter
;then one may compare the most stable structures when multiple structures are possible and finally one may compare the atom coordinates. The comparison has been so far limited to the first two points with the HREM technique and includes all these points with the X-ray tech- nique. The first example considered is the 2=3 (211) twin boundary in Ge (and Si), a tetra- coordinated structure. This GB was shown /30/ to be reconstructed forming a cm (2x2) struc- ture and having an important rigid-body translation (RBT). Several types of interatomic potential were tried. The simplest is the modified Keating potential used by Mauger et a1 /31/ which already agrees with the measured RBT in the direction parallel to the GB plane, but has a smaller expansion (by a factor 2) than the measured one. However the accuracy in this experimental determination is not good enough to decide if this discrepancy is meaning full or not.
Amore stringent test is given by identifying the lowest energy configuration among the five different reconstruction scheme. In silicon the use of semi-empirical tight binding /32/ as well as Keating-type /33/ potential has shown that indeed the cm (2x2) structure was the lowest in energy. It is worthwhile to note that the energy difference is extremely small and this agreement between experimental and calculated results is a remarka- ble achievement.
As a further example recent results on <001> pure tilt GB in germanium were compared with computer relaxed configurations using two types of empirical interatomic potential
:the Keating-type potential and the Tersoff potential /34/ (Fig. 1). For a large number of GBs the agreement on the final configuration (state of the lowest energy) is good
:this is the case for (310)2=5, (320)2=13 and remarkably for (11,3,0)Z=65 which has a large variety of possible unit mixing. Differences as small as a few per cent in energies are calculated and at least hierarchy in energy agrees with the observation. However in the case of (510)2=13 multiple structures are observed
:one of the observed configuration is not directly predic- ted from computer simulated static calculation. The same is true for (710) Z=25 and (910)2=41 GBs for which the observed structure presents an extremely variable core with con- figurations having relatively high static energy. It has been proposed /35/ that the confi
-gurational entropy term could explain thi
Sdiscrepancy.
Fig.1.
-Experimental images of a (130)Z=5 tilt GB in Ge as compared with the computer relaxed structures along two projection axes. From
/7/.In metals although a large variety of computer simulated structures are available since
twenty years only few comparison with experimental results were made. For the case of
(331))3=19 tilt in gold, Krakow et a1 /36/ showed that a close agreement between observed and
computer relaxed structures exists. The RBT and the large expansion agrees well with the
calculated ones. Unfortunately two very dissimilar structures have the same [l101 projection
and could not be distinguished by HREM. In molybdenum the (810)
Z=65HREM images were compa-
red with relaxed structures using Mie-type potential /37/. The calculated energies for two
variants of a (013) structural unit (empty or non empty core) are extemely close to each
other and multiplicity is predicted J38/. This is confirmed experimentally although the
empty form with a capped triangular prism is the most frequently encountered. However the
analysis is made questionable because of the possible oxygen segregation at GB which is
likely in molybdenum.
Afurther example of a qualitative comparison between experiment and
computer relaxed structures is given in NiO by Merkle and Smith
/39/.Large amount of open
space was observed as predicted in symmetric section of (210) Z=5, similarly the (320) z=13
aqrees quite well with the calculated structure. However asymmetric facets with low index
Cl-6 COLLOQUE DE PHYSIQUE
g r a i n boundary plane a r e present i n t h e same (320) Z=13. These s t r u c t u r e s are more compact than t h e symmetric ones and may have lower energies. T h i s i s c l e a r l y an example where new c o n f i g u r a t i o n s , which were n o t p r e v i o u s l y thought o f , have been suggested by t h e experimen- t a l observations and should be i n c l u d e d i n computer r e l a x a t i o n s t u d i e s .
The most p r e c i s e comparison i s undoubtedly t h e one performed on Z=5 [ O O l ] t w i s t GB i n gold, as i t a p p l i e s d i r e c t l y t o t h e atomic coordinates. I t has evidenced d i s t o r t e d octahedra and t e t r a h e d r a associated w i t h atomic rumpling o f t h e atoms a t d i f f e r e n t distances from t h e GB plane /25/. This. s t r u c t u r e was n o t p r e d i c t e d by computer s i m u l a t i o n although some o v e r a l l parameters l i k e t h e t o t a l expansion and t h e rumpling are q u a l i t a t i v e l y i n agreement. More r e c e n t l y t h e same a n a l y s i s was performed on Z=13 [001] t w i s t GB i n g o l d /26/. I t confirms t h e e a r l i e r hypothesis t h a t computer r e l a x a t i o n i s unable t o p r e d i c t t h e exact atomic l o c a - t i o n i n t h e f i r s t and even t h e second atomic plane from t h e GB plane. Absolute d i f f e r e n c e s have an average value o f 0.024nm and c o u l d be as l a r g e as 0.042nm. One p o s s i b l e explanation f o r t h i s l a r g e discrepancy i s t h e u n r e l i a b i l i t y o f e m p i r i c a l p a i r p o t e n t i a l i n regions where t h e d e n s i t y f a l l s down by more than 8%. Some authors have suggested /40/ t h a t a m i x t u r e o f d i f f e r e n t s t r u c t u r e s ( m u l t i p l i c i t y model) c o u l d e x p l a i n t h e X-ray data. However t h e r e l i a b i - l i t y f a c t o r i s n o t improved by such a mixture. Recently B a l l u f f i e t a l . have questioned t h e z=5 [ O O l ] l a r g e displacements /18/ and found r e s u l t s much c l o s e r t o t h e computer r e l a x e d s t r u c t u r e . Therefore i t i s u r g e n t l y necessary t o c o n f i r m these r e s u l t s on d i f f e r e n t mate- r i a l s and see i f t h i s behaviour can be generalized.
4 - ATOMIC SCALE INFORMATION AND BOUNDARIES PROPERTIES
The understanding o f t h e c o r r e l a t i o n between t h e atomic s t r u c t u r e and p h y s i c a l p r o p e r t i e s o f boundaries has been one o f t h e major goal o f t h e p a s t s t u d i e s . However although t h e d i s l o c a - t i o n approach has been v e r y successful i n t h e p h y s i c a l understanding o f low angle g r a i n boundaries, t h e r e i s n o t y e t u n i f y i n g concepts which c o u l d be a p p l i e d t o more general i n t e r - faces. Some new ideas a r e emerging i n d i f f e r e n t f i e l d s b u t they are s t i l l r a t h e r l i m i t e d due t o t h e formidable t a s k which c o n s i s t s o f making a l i n k between one s p e c i f i c d e f e c t o f the c r y s t a l a t atomic s c a l e w i t h an o v e r a l l p r o p e r t y depending on many body i n t e r a c t i o n s . Various f i e l d s w i l l be r a p i d l y reviewed : thermodynamical p r o p e r t i e s , i m p u r i t y segregation e l e c t r o n i c p r o p e r t i e s and some mechanical p r o p e r t i e s a t s p e c i f i c boundaries f o r which a l i n k w i t h atomic s t r u c t u r e s has been a t l e a s t tempted t o be established.
4.1.
Thermodynamical properties
Although i n t e r e s t i n t h e thermodynamical p r o p e r t i e s o f boundaries has r e c e i v e d wide spread a t t e n t i o n from t h e o r e t i c i a n s , o n l y few experimental r e s u l t s were obtained a t an atomic scale. The phase t r a n s i t i o n between faceted and a rough asymmetric GB was d i r e c t l y observed b u t a t a s c a l e which i s n o t t h e atomic scale /41/. Moving g r a i n boundaries i n g o l d as w e l l as n u c l e a t i o n o r decomposition o f e x i s t i n g ones have been recorded /11/ showing t h a t phase t r a n s i t i o n c o u l d be observed i n - s i t u by HREM o r STM. S i m i l a r l y t h e evidence obtained by Leroux e t a1 /42/ o f a w e t t i n g o f antiphase boundaries by t h e d i s o r d e r e d phase i n CoPt, although n o t y e t a t an atomic scale i s r e l e v a n t t o t h e techniques discussed here.
M u l t i p l e s t r u c t u r e s were evidenced i n Ge /35/ a t an atomic s c a l e and a core s t r u c t u r e which contains several s t a b l e p o s i t i o n s w i t h many v a r i a n t s can be b u i l t . Therefore i t has been emphasized t h a t t h e t o t a l s t a t i c energy can be misleading i f t h e entropy term i s n o t i n c l u - ded. T h i s c o u l d e x p l a i n why t h e s t a t i c energy c o n f i g u r a t i o n seems t o be n o t t h e r i g h t para- meter. These atomic s c a l e observations suggest t h a t phase t r a n s i t i o n s w i t h o r d e r - d i s o r d e r transformation c o u l d occur, although t h e y were n o t y e t observed.
The measurement o f t h e boundary X-ray r e f l e c t i o n s as a f u n c t i o n o f temperature /43/ has been used t o e v a l u a t e t h e thermal expansion c o e f f i c i e n t s o f t h e Z=13 [001] t w i s t GB i n gold, and t h e mean square displacement. The thermal expansion c o e f f i c i e n t p a r a l l e l t o t h e GB i s equal t o t h e b u l k value, w h i l e i t i s t h r e e times l a r g e r perpendicular t o t h e GB. The mean square displacement i s found t o be 40% l a r g e r i n t h e GB than i n t h e b u l k a t room temperature.
Although t h i s experimental r e s u l t i s v e r y important i t remains now t o make t h e connection o f t h i s behaviour w i t h t h e form o f t h e i n t e r a t o m i c p o t e n t i a l , a work which has r e c e n t l y been t a c k l e d by S u t t o n /57/.
As a m a t t e r o f f a c t t h e r e s u l t s are s t i l l very scarce and n o t f u l l y e x p l o i t e d : however although o f t e n q u a l i t a t i v e , t h e experimental r e s u l t s p o i n t t o an important d i r e c t i o n . The atom a t t h e GBs have d i f f e r e n t p r o p e r t i e s when compared t o t h e b u l k : t h e mean square displacement i s h i g h e r and probably v e r y a n i s o t r o p i c , and t h e entropy term i s m o d i f i e d by new c o n f i g u r a t i o n a l as we1 l as v i b r a t i o n a l terms.
4.2. Impurity seureuat
i o n andchemical uradient
The most clear atomic scale studies of interface segregation has been obtained by the atom probe FIM
:on a stacking fault in CO-Nb and CO-Fe alloys /21/ or at GBs in austenitic stainless steel /10/ and in MO-Re alloy /16/. Solute atom segregation of Nb or Fe is surpri- singly high and limited to the SF plane. A tendancy to form Co,Fe plane composition is evidenced associated with an order-disorder transformation within the plane of the fault.
This work demonstrates very conclusively that the elastic strain energy does not play as major role in the driving force and that interactions up to the third near neighbor atoms should be taken into account. In stainless steel boron was demonstrated to segregate at general GBs but not at coherent twins. The binding energy of boron to the GB was estimated at 0.65 + 0.04eV. Experimental results were so rich that a detailed diffusion model has been proposed /10/.
In molybdenum the HREM observations on pure GB have motivated the search for specific sites for oxygen segregation /38/. It was predicted that several sites were possible
:intersti- tially in the open core or substitutionnally with different interaction enthalpy. These pre- dictions could have important impli.cations in the theoretical modelling of interface segre- gation, although they have not yet been confirmed experimentally.
There is
anumber of HREM observations of interphase boundaries. See for instance th systems such as
:Al/Ge /44/, Cu/Au /45/, Al-Cu-Li /13/, superalloys
/G/,MgO/Al /47/, Nb?
A1 0, /48/, Cu/ A1203 /49/, and all the silicon-silicide interfaces, multilayers, quantum weTls (for a review see
/3/and /50/). Chemical gradients close to the interfaces were also directly evidenced in few cases. Kazmerski
/23/in highly doped (B on Al) polycristalline silicon was able to show directly by STM that
Band A1 atoms were attracted close to the GB in a region - lOnm wide with no special segregation at the GB plane (here an asymmetrical t110> 28" tilt). As expected B and A1 are substitutionaf. The addition of hydrogen (also made visible by spectroscopic means) introduces Si-H bonds and AI-H bonds but no direct interaction with B atoms. A similar study in CuInSe polycristal shows a very clear oxygen segregation at the grain boundary, the oxygen bin%ing being preferential l y at the indi urn sites. In mu1 til ayers structure which are frequently highly thermodynamical unstable sys- tems, chemical gradients at interfaces could be produced either during the crystal growth or during post-annealing. In the HgCdTe/CdTe multilayer system Kim et a1 were able to study the low temperature interdiffusion o f Hg at an atomic scale /51/. These authors used the digital pattern recognition to chemically map the mercury content on HREM images /12/ and demonstra- te that the stability of a specific layer may depend sensitively on its depth from the sur- face, with a higher diffusivity close to the surface. In addition non-linear diffusion was necessary to introduce in order to explain the profiles. In the Fe/Ti system a chemical gradient at the interface was also evidenced by d-spacing measurement at a lnm scale /52/
(Fig. 2). A marked asymmetry between the two sides of a given layer is measured, which is explained by the growth process inherent to ion-sputtered deposited layers.
Fig.2 - Atomic image of a Fe/Ti multilayer with a 47nm period, and the chemical profiles at different reduced period (L=26 corresponds to 47nm).
Finally such chemical gradients are also evidenced at precipitates /53/. Fujita et a7 have
shown that
8 'phase in AI-Cu dilute alloys is surrounded by a buffer layer. In addition the
composition tends to vary slowly when crossing the interface. It is suggested that the
intermediate layers are.reminiscent of the GP-2 zones composition. Therefore contrary to the
usually invoked denuded zone, an enriched layer could be stabilized in order to relax some
of the elastic strain in a precipitation process.
Cl-8 COLLOQUE DE PHYSIQUE
The above examples show how important will be the atomic scale observations with chemical mapping in order to understand and modelized correctly the segregation and the precipitation as well as the diffusion processes in highly metastable conditions.
4.3. Electronic ~ r o ~ e r t i e s and atomic structures
From the atomic structures deduced by
HREMseveral electronic structures were calculated in semiconductors /31,32,33/. They all agree on the following points (Fig. 3)
:- The density of states at grain boundaries does not contain deep levels inside the band gap in fully reconstructed structures.
-
No localised states above the minimum of the valence-band and below the maximum of the valence band are calculated.
L ENERGY lcVl
Fig.3
-Atomic model of a (211)2=3 tilt GB in Ge deduced from
HREMobservations and the calculated total density of states in the perfect lattice (solid curve) and in the GB (dashed curve). From /31/.
These results however appear to be in disagreement with experimental measurements of the tail states /58/ and the most plausible explanation is that most of the GB electrical acti- vity is due to impurity segregation or possibly to additional point or line defects. Such an impurity effect was clearly demonstrated on copper segregated GBs in silicon by DLTS measu- rement /54/. In semiconductor polycristalline oxides (Mn-Fe ferrites) the correlation between the GB structure and the in-situ voltage drop-off has been measured /55/. In parti- cular the presence of a lnm glassy film double the voltage drop-off when crossing the barrier but most remarkably the general boundary are much more resistive than particular twin orientations.
As a consequence the correlation between the atomic structure
o fboundaries and the electronic or electric properties, is far from being understood. The sensitivity of the electrical measurement is so high that a direct correlation with atomic models at a scale close to a point defect is, for the moment, unrealistic.
4.4. Mechanical Droperties
The hardening role of the GB and the mechanism by which dislocations could be incorporated at a GB has been investigated recently by Elkajbaji and Thibault-Desseaux /56/. It is shown that intrinsic dislocatiuns enter the GB where they decompose into discrete GB dislocations
:these residues can migrate and react along the interface giving rise to macroscopic rotation of the adjacent grains and new residues. These mechanisms are observed at atomic scale in silicon by
HREM.Although not made in-situ but by a frozen-in method, they provide a good basis for describing the absorption and the reemission of dislocations by GBs and could be in the future correlated with bulk mechanical properties.
5
-CONCLUSION
The development in parallel of experiments at atomic scale and of computer simulation is certainly one of the major issue of the next years. The first examples of such a comparison which have been carried out so far, have always shown the mutual benefit it can bring.
On one hand the experimental results have given surprising results which were not envisaged
before. One may mention several examples
:-
The bond r e c o n s t r u c t i o n w i t h s u p e r c e l l formation a t p e r i o d i c i n t e r f a c e s . - The presence o f disordered s t r u c t u r e s i n a " p e r i o d i c " s t r u c t u r e .- The segregation a t s t a c k i n g f a u l t s i n d i l u t e a l l o y s .
-
The p e c u l i a r d i f f u s i o n p r o p e r t i e s o f m u l t i l a y e r s .I t i s , o f course, necessary t o c o n f i r m and extend these observations. The atomic scale tech- niques are g e n e r a l l y h i g h l y s o p h i s t i c a t e d and t h e i n t e r p r e t a t i o n i s o f t e n r a t h e r elaborate.
The degree o f confidence i s sometimes r e l y i n g on a s o p h i s t i c a t e d i n t e r p r e t a t i o n and progress should be made p a r t i c u l a r l y i n t h e case o f STM i n t h e understanding o f t h e atomic images.
Another severe l i m i t a t i o n s o f a l l these atomic-scale techniques i s t h e i r l a c k o f a b i l i t y t o be a p p l i e d t o a l a r g e v a r i e t y o f m a t e r i a l o r t o general boundaries. This g e n e r a l l y prevent from mutual c o n t r o l by two o r more d i f f e r e n t techniques.
On t h e o t h e r hand computer r e l a x a t i o n s have given many new ideas which were confirmed l a t t e r by atomic-scale experiments. T h i s was t h e case f o r :
- The presence o f m u l t i p l e s t r u c t u r e s .
- The p r e d i c t i o n o f several low energy i n t e r f a c e s .
-
The e x i s t e n c e o f phase t r a n s i t i o n .- The presence o f several s p e c i f i c s i t e s f o r segregation a t g r a i n boundaries.
The development i n t h e computers c a p a c i t y and speed w i l l c e r t a i n l y tend t o improve the q u a l i t y o f t h e i n t e r a t o m i c p o t e n t i a l s . A check, even on a b - i n i t i o c a l c u l a t i o n s , w i l l be however always necessary and atomic-scale experimental methods w i l l be h i g h l y d e s i r a b l e . As a conclusion i t should be added t h a t w h i l e i t can be foreseen t h a t t h i s mutual confronta- t i o n i s t h e f u t u r e major development on s t u d i e s o f a l l k i n d o f i n t e r f a c e s , i t w i l l be necessary t o develop u n i f i e d models and concepts. They have t o g i v e simple and i n s i g h t f u l d e s c r i p t i o n o f t h e p h y s i c a l p r o p e r t i e s o f boundaries from microscopic mechanisms.
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