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PROGRESS IN UNDERSTANDING ATOMIC STRUCTURE OF THE ICOSAHEDRAL PHASE
A. Melmed, M. Kaufman, H. Fowler
To cite this version:
A. Melmed, M. Kaufman, H. Fowler. PROGRESS IN UNDERSTANDING ATOMIC STRUCTURE OF THE ICOSAHEDRAL PHASE. Journal de Physique Colloques, 1986, 47 (C7), pp.C7-35-C7-40.
�10.1051/jphyscol:1986707�. �jpa-00225896�
JOURNAL DE PHYSIQUE
Colloque C7, supplement au n o 11, Tome 47, Novembre 1986
PROGRESS IN UNDERSTANDING ATOMIC STRUCTURE OF THE ICOSAHEDRAL PHASE
A.J. MELMED, M.J. KAUFMAN and H.A. FOWLER
National Bureau of Standards, Gaithersburg, MD 20899, U.S.A.
RBsum6
L f a n a l y s e par d i f f r a c t i o n e l e c t r o n i q u e de l a phase i c o s a k d r a l e ( p h a s e i ) d e s a l l i a g e s AlMn (I-AlMn) montre c l a i r e m e n t que, o u t r e l e s maxima de d i f f r a c t i o n t r h s marques de l a phase i , e x i s t e une q u a n t i t e c o n s i d e r a b l e d f i n t e n s i t e s d i f f u s e s i n d i q u a n t l a p r e s e n c e d'un c e r t a i n d e s o r d r e h l t i n t 6 r i e u r de c e t t e phase. Ce r e s u l t a t confirme b i e n l e s 6 t u d e s
p r e c e d e n t e s o b t e n u e s h l a f o i s p a r d i f f r a c t i o n n e u t r o n i q u e e t m i c r o s c o p i e i o n i q u e 2 champ (M.I.C.), e t permet de r e d u i r e l e nombre de modhles
s t r u c t u r a u x p o s s i b l e s pour l a phase i. L ' a n a l y s e d'images p a r M.I.C. r e v k l e l a p r e s e n c e de p l u s i e u r s t a i l l e s de " c l u s t e r s n a y a n t de nombreuses
c a r a c t d r i s t i q u e s q u i q u a l i t a t i v e m e n t p a r a i s s e n t e n a c c o r d a v e c d e s modkles proposes recemment. Une d e s c r i p t i o n q u a n t i t a t i v e complhte de l a s t r u c t u r e de l a phase i e s t p o u r s u i v i e e n comparant l e s m o t i f s atomiques o b s e r v e s
experimentalement a v e c l e s s u r f a c e s modgles s i m u l e e s p a r o r d i n a t e u r . Les r C s u l t a t s p r C l i m i n a i r e s de c e t t e e t u d e s o n t p r e s e n t e s .
A b s t r a c t
E l e c t r o n d i f f r a c t i o n a n a l y s i s o f t h e i c o s a h e d r a l phase ( i - p h a s e ) i n AlMn a l l o y s (i-AlMn) i s p r e s e n t e d which shows c l e a r l y t h a t , i n a d d i t i o n t o t h e s h a r p d i f f r a c t i o n maxima from t h e i-phase, t h e r e is a c o n s i d e r a b l e amount o f d i f f u s e i n t e n s i t y i n d i c a t i n g t h e p r e s e n c e o f a c e r t a i n amount o f d i s o r d e r i n t e r s p e r s e d w i t h i n t h i s phase. T h i s r e s u l t c o r r e l a t e s w e l l w i t h p r e v i o u s r e s u l t s from b o t h n e u t r o n d i f f r a c t i o n and f i e l d i o n microscopy s t u d i e s and h e l p s t o r e d u c e t h e number o f p o s s i b l e s t r u c t u r a l models o f t h e i-phase.
A n a l y s i s o f FIM images i n d i c a t e s t h e p r e s e n c e o f a h i e r a c h y o f c l u s t e r s i z e s w i t h numerous f e a t u r e s which appear t o a g r e e q u a l i t a t i v e l y w i t h r e c e n t l y proposed models. A complete q u a n t i t a t i v e d e s c r i p t i o n o f t h e s t r u c t u r e o f t h e i-phase is b e i n g pursued by comparing e x p e r i m e n t a l l y observed atomic m o t i f s w i t h computer-simulated model s u r f a c e s , and p r e l i m i n a r y r e s u l t s a r e pre- s e n t e d .
The o r i g i n a l ( 1 ) and subsequent r e p o r t s o f t r a n s m i s s i o n e l e c t r o n microscopy (TEM) o f t h e i c o s a h e d r a l phase ( i - p h a s e ) o f Al6Mn show e l e c t r o n d i f f r a c t i o n p a t t e r n s w i t h o n l y s h a r p d i f f r a c t i o n maxima, c o n s i s t e n t w i t h a n atomic s t r u c t u r e having long-range o r i e n t a t i o n a l ( i c o s a h e d r a l ) o r d e r and no t r a n s l a t i o n a l symmetry. However, weak-beam d a r k - f i e l d TEM images r e v e a l a n assembly o f p a t c h e s w i t h a b o u t 5 nm dimensions ( 2 ) . F i e l d ion microscopy
(FIM) h a s shown a t o m i c s t r u c t u r a l f e a t u r e s which a r q c o n s i s t e n t w i t h t h e s e TEM r e s u l t s , and a d d i t i o n a l l y some a p p a r e n t d i s o r d e r ( 3 ) . We p r e s e n t h e r e t h e r e s u l t s o f f u r t h e r TEM s t u d i e s , some a n a l y s i s o f t h e FIM micrographs o f t h e i-phase o f A16Mn and o u r i n i t i a l e f f o r t s t o computer s i m u l a t e t h e FIM images.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986707
JOURNAL DE PHYSIQUE
Specimens f o r t h i s work were prepared as described previously (3,U).
Figure 1 shows a s e l e c t e d a r e a d i f f r a c t i o n p a t t e r n taken along a minor zone a x i s . I n a d d i t i o n t o t h e sharp d i f f r a c t i o n maxima, a s i g n i f i c a n t d i f f u s e r i n g is evident, i n d i c a t i n g t h e presence of disordered m a t e r i a l within t h e i-phase. Dark-field images were obtained using a small p o r t i o n of t h e d i f - f u s e r i n g t o i l l u m i n a t e t h e i-phase; t h i s showed t h a t t h e d i f f u s e s c a t t e r i n g o r i g i n a t e d from very small r e g i o n s , usually 1 nm or l e s s i n dimension, uni- formly dispersed throughout t h e i-phase (M.J. Kaufman and A.J. Melmed, unpub- l i s h e d r e s u l t s ) . Also, a s i m i l a r background occurs i n d i f f r a c t i o n p a t t e r n s taken along t h e major 2-, 3- and 5-fold
zone axes, a s expected from t h e above r e s u l t s , although it is l e s s i n t e n s e r e l a t i v e t o t h e i n t e n s i t i e s of t h e sharp maxima and t h e r e f o r e o r d i n a r i l y is not obvious. F u r t h e r , s i m i l a r d i f f u s e i n t e n s i t y has been observed f o r o t h e r i-phase m a t e r i a l s a s well.
This c o r r e l a t e s well with t h e FIM o b s e r v a t i o n s o f d i s o r d e r ( 3 ) and a l s o with evidence f o r d i s o r d e r seen i n neutron d i f f r a c t i o n p a t t e r n s from t h e i-phase (8. Mozer, unpublished r e s u l t s ) .
We a r e t h u s l e d t o s p e c u l a t e t h a t only those s t r u c t u r a l models of t h e i-phase which c o n s i s t of b u i l d i n g blocks, o r s t r u c t u r a l u n i t s , packed t o g e t h e r with a profusion of small spaces ( t h a t is, i n t e r s p e r s e d with small disordered
r e g i o n s ) a r e v i a b l e . - We a r e aware of two Fig. 1 S e l e c t e d a r e a d i f f r a c t i o n such models which a r e promising candidates p a t t e r n obtained from a i n terms of t h e degree t o which they agree minor a x i s near a 5-fold with t h e TEM observations. These a r e a x i s of t h e i-phase. Note I ) packing of a Mackay-like 54 atom ico- t h e s i g n i f i c a n t d i f f u s e sahedron ( 5 ) v i a 3-fold symmetry f a c e s , i n t e n s i t y i n a d d i t i o n t o a model o f Cahn and G r a t i a s (CG) and t h e sharp d i f f r a c t i o n 2 ) packing of a s i m i l a r s i z e , b u t l e s s maxima.
dense 24 atom icosahedron v i a o c t a h e d r a l
connecting l i n k s s i m i l a r t o ( b u t s l i g h t l y d i s t o r t e d from) t h e packing of icosahedra i n t h e c r y s t a l l i n e a-AlFeSi s t r u c t u r e , proposed by Audier and Guyot (AG) ( 6 ) . The AG icosahedron c o n s i s t s o f a small hollow-centered icosahedron of 12 A 1 atoms, decorated with 12 Mn atoms a t t h e corners. Thus, it can be d i s s e c t e d i n t o planar pentagons normal t o any 5-fold r o t a t i o n a l symmetry a x i s , g i v i n g l a r g e r e g u l a r pentagons of 5 Mn atoms and smaller r e g u l a r pentagons o f 5 A 1 atoms. The CG icosahedron has 30 a d d i t i o n a l A 1 atoms packed around t h e o u t s i d e of t h e small icosahedron. Dissection of t h e CG icosahedron i n t o p l a n e s , a s above, g i v e s small r e g u l a r A 1 pentagons, l a r g e r e g u l a r pentagons of 10 ( 5 A 1 and 5 Mn) atoms with Mn atoms a t t h e c o r n e r s , and a l s o a l a r g e r i n g o f 10 A 1 atoms. Thus, t h e models d i f f e r with r e s p e c t t o t h e s t r u c t u r e of t h e b a s i c icosahedron b u i l d i n g block and t h e manner i n which t h e . i c o s a h e d r a a r e interconnected. AG a l s o suggest t h a t a l a r g e r u n i t , a triacontahedron, is an i n t e g r a l p a r t of t h e i-phase. Both of t h e s e models a r e incomplete a t p r e s e n t , and t h e a b s o l u t e dimensions a r e u n c e r t a i n .
We have begun a d e t a i l e d a n a l y s i s of FIM image f e a t u r e s f o r i-AlMn; a complete a n a l y s i s a w a i t s computer s i m u l a t i o n s of FIM images based on t h e d i f f e r e n t models. F i r s t , we consider images of t h e 5-fold r o t a t i o n a l symme- t r y p o l e ; t h u s f a r , we have found e s s e n t i a l l y t h r e e types o f atomic a r r a y s i n t h a t region. These a r e ( s e e f i g u r e 2 ) 1 ) a small incompletely resolved pentagon ( P I ) , a l i g n e d with o r r o t a t e d 36 deg. r e l a t i v e t o t h e o v e r a l l
i-phase o r i e n t a t i o n , 2 ) a l a r g e r pentqgon, s i m i l a r l y a l i g n e d , which h a s e i t h e r a vacant c e n t e r o r an atom i n t h e c e n t e r (P2) and 3 ) apparently disordered o r non-dsscript a r r a y s o f atoms. We note t h a t t h e g e n e r a l atom r i n g system seen arcr'lnd t h e 5-fold pole is s i g n i f i c a n t l y smaller than around t h e 2- or 3-fold symmetry p o l e s , u s u a l l y i n d i c a t i n g a smaller i n t e r p l a n a r spacing perpendicular t o t h e 5-fold pole ( 7 ) . We have observed a l s o many o t h e r completely o r incompletely resolved pentagons of various s i z e s l o c a t e d some d i s t a n c e from t h e 5-fold symmetry a x i s .
We can a s s i g n dimensions t o image f e a t u r e s based on
magnifications determined from t h e measured image v o l t a g e s ( 7 ) . Due t o t h e u n c e r t a i n t i e s i n t h i s determination and t h e measurements of image spot p o s i t i o n s , we e s t i - mate c o n s e r v a t i v e l y t h e p o s s i b i l i t y o f + 15%
u n c e r t a i n t y i n t h e s e dimensions. The edge- atom spacings f o r pentagons PI (estimated by using one h a l f t h e measured t o t a l width of t h e p a r t i a l l y resolved pentagon s i d e ) and P2 a r e 0.35 and 0.78 nm, r e s p e c t i v e l y . These a r e l a r g e r t h a n s i m i l a r pentagons within t h e icosahedra of t h e CG and
AG models. I n t e r e s t i n g l y , Fig. 2 Neon f i e l d ion micrographs of however, i f we i n c r e a s e t h e 5-fold r o t a t i o n a l symmetry s c a l e o f t h e models by a poles. The upper and lower f a c t o r o f (1+/5)/2 = 1.62 l e f t micrographs a r e o r i g i n a l ( t h e Golden mean) t h e small r e s u l t s ; t h e upper and lower
pentagon o f t h e model r i g h t micrographs have been
icosahedra becomes 0.41 nm photographically dodged ( 3 ) t o
and t h e l a r g e one becomes suppress t h e i n t e n s i t y o f t h e
0.83 nm. which agree with images around t h e pentagonal
t h e dimensions we have found. f e a t u r e s ( n e a r c e n t e r ) . Scale However, we have not observed markers r e p r e s e n t 2.5 nm.
two f e a t u r e s o f t h e CG
icosahedron, s p e c i f i c a l l y a l a r g e r ( o u t e r s h e l l ) pentagon having f i v e Mn atoms a t t h e corners and f i v e A 1 atoms, each halfway between t h e Mn atoms, and a l a r g e r i n g o f t e n A 1 atoms.
The next FIM image f e a t u r e we consider is a l a r g e r , seemingly d i s t i n c t s t r u c t u r a l u n i t appearing a t t h e s u r f a c e a s a recognizable patch having a s u r f a c e cross-section s i z e o f about 2-7 nm, and sometimes having a pentagonal, although not n e c e s s a r i l y r e g u l a r , shape (examples o f t h e s e can be seen i n f i g u r e s 3 and 4 ) . Thusfar, we have i d e n t i f i e d 20 patches having about 4.5-5.5 nm maximum width. The atomic arrangements o r m o t i f s seen a t t h e s u r f a c e of t h e s e u n i t s , d e s p i t e t h e i r appearances, a r e not random.
Rather, we have found examples of considerable s i m i l a r i t y i n t h e atomic m o t i f s .
C7-38 JOURNAL DE PHYSIQUE
The i r r e g u l a r penta- gonal a r r a y o f atoms seen s l i g h t l y off-center on a 3-fold symmetry pole plane i n f i g u r e 4 is r a t h e r i n t e r e s t i n g . I t is about 5.1 nm a c r o s s its widest p a r t and has a shape which r e l a t e s c l o s e l y t o t h e AG t r i a c o n t a h e d r o n i n t h e three-fold p r o j e c t i o n of t h a t f i g u r e ( a g a i n , t h e s c a l e s do not a g r e e (even i f we s c a l e by about 1.62 a s discussed above).
The very ragged edges of t h e atomic r i n g s seen i n t h e FIM micrographs (3) a l s o is a f e a t u r e which is ex- p l a i n e d by a c l u s t e r model, such a s t h e two described above. The f i e l d evaporation process ( 6 ) r e s u l t s i n such r i n g s due t o t h e i n t e r s e c t i o n of planes with t h e n e a r l y
hemispherical specimen apex. Fig. 3 Neon f i e l d ion micrographs In terms o f a c l u s t e r model, o f s e l e c t e d s u r f a c e a r e a s , such r i n g s would be expected not l o c a t e d on poles o r zone t o be discontinuous, o r broken l i n e s . The upper and lower up, a s t h e i n d i v i d u a l b u i l d i n g l e f t micrographs a r e o r i g i n a l blocks and t h e i r i n t e r s p a c e s r e s u l t s ; t h e upper and lower a r e c u t through by f i e l d r i g h t micrographs have out- evaporation. I n t e r e s t i n g l y , l i n e s added t o h e l p t h e i n a survey of 21 micrographs, reader l o c a t e t h e l a r g e
no seemingly continuous r i n g patches. S c a l e markers
segment having a chord longer r e p r e s e n t 2.5 nm.
t h a n about 8 nm was found,
and most l a r g e segments had chords about 4.5-6.5 nm long; many smaller seg- ments were a l s o observed. This o b s e r v a t i o n t e n d s t o support a model with a hierachy o f s t r u c t u r a l u n i t s . The segments would r e s u l t , i n such a model, from t h e d i s r u p t i o n o f atom chains whenever some s e p a r a t i o n between b u i l d i n g
s i m u l a t e FIM micrographs Fig. 4 Neon f i e l d ion micrographs o f f o r comparison t o t h e 3-fold r o t a t i o n a l symmetry poles.
experimental images ; S c a l e markers r e p r e s e n t 2.5 nm.
t h u s f a r , we have simulated
s m a l l a r e a s corresponding t o v a r i o u s s i n g l e p l a n e s . One of t h e s t r i k i n g f e a - t u r e s of t h e computer-simulated f i e l d - e v a p o r a t i o n o f t h e s e p l a n e s , a t l e a s t i n t h e CG model which we a r e computing, i s t h e f r e q u e n t appearance of l o c a l l y non-symmetric atomic a r r a y s ( f i g . 6 ) . This happens a l s o f o r t h e 5-fold ole and, of c o u r s e , r e s u l t s from t h e l a c k o f s h o r t - r a n g e symmetry i n h e r e n t i n t h e model. This computer r e s u l t a g r e e s q u a l i t a t i v e l y , a t l e a s t , with t h e FIM images ( 3 ) . Local symmetry i s o f t e n l o s t a s f i e l d e v a p o r a t i o n produces con- s e c u t i v e s u r f a c e c u t s through t h e specimen, because t h e i n d i v i d u a l b u i l d i n g b l o c k s ( i c o s a h e d r a i n both models) a r e n o t s t a c k e d o r a r r a n g e d p e r i o d i c a l l y i n any d i r e c t i o n .
F i g . 5 Neon f i e l d i o n micrographs of 2-fold r o t a t i o n a l symmetry p o l e s . S c a l e markers r e n r e s e n t 2 . 5 nm.
The d i r e c t comparison of FIM images and computer model s t r u c t u r e s is made d i f f i c u l t by t h e confluence o f s e v e r a l f a c t o r s . F i e l d e v a p o r a t i o n o f b i n a r y a l l o y s g e n e r a l l y is d i f f i c u l t t o s i m u l a t e a c c u r a t e l y ( 8 ) ; t h e f i e l d e v a p o r a t i o n of binary a l l o y s is o f t e n l e s s o r d e r l y and l e s s r e l i a b l y under- s t o o d t h a n f o r e l e m e n t a l m e t a l s ; and aluminum-based a l l o y s a r e n o t known t o be a s well imaged i n t h e FIM, compared t o more r e f r a c t o r y m a t e r i a l s . Here, we n o t e t h a t a t p r e s e n t we cannot d i s t i n g u i s h images of A 1 and Mn atoms s o l e l y by image c o n t r a s t . We b e l i e v e t h a t a t l e a s t some o f t h e atoms imaged a r e A 1 atoms, because atcm p a i r s p a c i n g s a s s m a l l a s 0.28 nm a r e s e e n , and a l s o t h a t a t l e a s t some of t h e atoms imaged a r e Mn atoms, because t h e i-phase images and f i e l d e v a p o r a t e s a s a more-refractory c o l l e c t i o n o f atoms than does t h e e x c e s s A 1 phase ( 3 ) . F i n a l l y , we note t h a t t h e a p e r i o d i c i t y o f t h e i-AlMn phase makes FIM image a n a l y s i s non-routine. Thus, it seems reasonable t o assume t h a t t e r n a r y i-phase m a t e r i a l s w i l l p r e s e n t an even g r e a t e r c h a l l e n g e .
We conclude t h a t t h e i-phase c o n t a i n s very s m a l l r e g i o n s of d i s o r d e r i n t e r s p e r s e d w i t h i n t h e phase and t h a t t h e phase c o n t a i n s a h i e r a c h y o f s i z e s o f b u i l d i n g b l o c k s . Also, a l l of t h e main f e a t u r e s of t h e AG icosahedron have been seen i n t h e FIM images, although t h e r e remain dimensional s c a l i n g d i f f e r e n c e s , w h i l e two major f e a t u r e s of t h e CG icosahedron have n o t y e t been seen. I n a d d i t i o n , t h e r e is some evidence f o r t h e e x i s t e n c e o f a l a r g e r s t r u c t u r a l u n i t . The FIM a n a l y s i s p r e s e n t e d h e r e is based on micrographs o b t a i n e d a f t e r random amounts of f i e l d e v a p o r a t i o n ( 3 ) . More d e c i s i v e r e - s u l t s , e s p e c i a l l y with r e g a r d t o t h e s t r u c t u r e of t h e b a s i c s t r u c t u r a l b u i l d - ing blocks, should be o b t a i n a b l e i n t h e f u t u r e from c a r e f u l l y c o n t r o l l e d f i e l d e v a p o r a t i o n and imaging sequences.
JOURNAL D E PHYSIQUE
Fig. 6 Computer s i m u l a t i o n s of small a r e a s of FIM s u r f a c e s (7).
a : f o u r s u r f a c e s normal t o a 5-fold p o l e , b: four s u r f a c e s normal t o a 2-fold pole, and c: four s u r f a c e s normal t o a 3-fold pole. A s p h e r i c a l s h e l l of r a d i u s 60 nm and t h i c k n e s s 0.156 nm was c u t through 5 t o 8 icosahedra composed and connected a s described i n r e f e r e n c e 4.
Each s u r f a c e a r e a has a width o f about 3 nm, based on t h e c u r r e n t model ( 4 ) .
(The s u r f a c e generating program i s due t o Jim Sims.)
0 0 0 0
t o *
* s t c o * O D 0 0
* * * a a * *
s o * a 0 O o m 0 * o
* 0 0 *
t o * 0 0 0
* *
0 0 0 0 0 0 0
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