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A twelve-fold quasicrystalline phase in BiMn alloys
Scripta METALLURGICA et MATERIALIA
Vol. 25, pp. 325-330, 1991 Printed in the U.S.A.
Pergamon Press plc All rights reserved
A TWELVE-FOLD @UASICRYSTALLINE PHASE IN Bi-Mn ALLOYS ~. Reyes-Gasga,
R. Hernandez
and M. Jom@-YacamJn
I n s t i t u t o de F ~ s i c a , U n i v e r s i d a d N a t i o n a l Aut6noma de M~xico, A p a r t a d o P o s t a l 20-364. D e l e g a c i 6 n A l v a r o Obreg6n 01000 M~xico, D. F. MEXICO
(Received October 9, 1990) (Revised November 16, 1990) Introduction The d i s c o v e r y o~ t h e i c o s a h e d r a l q u a s i c r y s t a l l i n e phase by Shechtman et a l . (1> was t h e b e g i n n i n g o~ an intensive and s y s t e m a t i c activity on modeling c h a r a c t e r i z a t i o n and a s e a r c h o~ new m a t e r i a l s exhibiting quasicrystallinity. Phases w i t h ~ive-fold(1), eight-~old(2)~ ten-fold(3) and twelve-Gold(4.5) r o t a t i o n axes have been r e p o r t e d . C o m p a r a t i v e l y speaking~ the o c t a g o n a l and dodecagonal phases have r e c e i v e d l e s s a t t e n t i o n , p r o b a b l y because o~ t h e scarce e x p e r i m e n t a l d a t a them. Ishimasa e t a l . (4) ~ound t h e dodecagonal phase i n small p a r t i c l e s in Ni-70.6 at.%Cr alloy. The t w e l v e - G o l d q u a s i c r y s t a l l i n e phase c o e x i s t s w i t h r e g i o n s oG m u l t i p l e t w i n n e d ~ - p h a s e domains as w e l l as two other c r y s t a l l i n e phases. Chert e t a l . (5) r e p o r t e d t h e t w e l v e - E o l d phase i n rapidly this phase is s o l i d i f i e d VsNi z and VieNi,oSi a l l o y s . These a u t h o r s f o u n d t h a t q u a s i p e r i o d i c i n two dimensions and p e r i o d i c i n t h e p e r p e n d i c u l a r a x i s as i n t h e case o f t h e decagonal phase. T h e i r phase has t h e same q u a s i l a t t i c e r e p o r t e d by Ishimasa e t a l . (4) and i t s e l e c t r o n d i G G r a c t i o n p a t t e r n i s t h e same as t h e ones calculated theoretically (6). I n t h e p r e s e n t paper a t w e l v e - G o l d q u a s i c r y s t a l l i n e phase i n t h i n ~ i l m s o~ t h e Bi-Mn a l l o y i s r e p o r t e d . T h i s phase has a q u a s i l a t t i c e which, i n some regions, i s v e r y s i m i l a r t o t h e one r e p o r t e d by Ishimasa e t a l . ( 4 ) . The Bi-Mn t h i n Gilms were produced by s u c c e s s i v e e v a p o r a t i o n s as r e p o r t e d by Yoshida and Yamada(7-8>. (.0 B e f o r e e v a p o r a t i o n•, t h e s u b s t r a t e was h e a t e d a t 27.) C f o r one hour Gor c l e a n i n g . AGter c o o l i n g t o room t e m p e r a t u r e ~ t h e e v a p o r a t i o n took p l a c e on s u b s t r a t e s c o v e r e d p r e v i o u s l y w i t h a c a r b o n ~ i l m . Composited Gilms o~ Bi and Mn l a y e r s were p r e p a r e d by s u c c e s s i v e vacuum e v a p o r a t i o n o f a Bi with a t h i c k n e s s o~ 3Ohm, ~ o l l o w e d by a Mn ~ i l m , w i t h 20nm. E v a p o r a t i o n s were made on b o t h NaC1 and g l a s s s u b s t r a t e s i n a 10 -a Pa vacuum. A ~ t e r w a r d s t h e Gilm t e m p e r a t u r e was r a i s e d t o 270°C, s l i g h t l y below t h e m e l t i n g t e m p e r a t u r e o f Bi~ d u r i n g different periods. The e l e c t r o n d i ÷ f r a c t i o n t i l t i n g e x p e r i m e n t s and c h e m i c a l a n a l y s i s were o b t a i n e d using a J E O L IOOCX a n a l y t i c a l electron microscope equipped w i t h a -+60° g o n i o m e t e r and an EDX X - r a y a n a l y z e r . The high resolution o b s e r v a t i o n s were c a r r i e d o u t i n a JEOL 4000-EX h i g h r e s o l u t i o n m i c r o s c o p e . Images were computer p r o c e s s e d t o enhance t h e i r c o n t r a s t u s i n g an I n n o v i o n system on l i n e w i t h a 1178 VAX computer. The X - r a y chemical a n a l y s i s of the ~ilms o b t a i n e d showed a c o m p o s i t i o n i n t h e r a n g e oG 70 t o 80 at.%Mn. However i n t h e a r e a s which produce the d i f f r a c t ion pattern shown in figure I the composition corresponds a p p r o x i m a t e l y t o BiMnm. A c c o r d i n g w i t h Yoshida and Yamada(7), c r y s t a l s w i t h t h i s c h e m i c a l c o m p o s i t i o n have space group R~m and 12Bi and 36 Mn atoms a r e situated i n i t s u n i t c e l l . A ~ t e r h e a t i n g t h e ~ i l m a t 270oC ~or i 0 0 hours, the selected area d i ~ r a c t i o n p a t t e r n shown i n ~ i g u r e 1 i s o b s e r v e d i n many a r e a s . At ~irst g l a n c e , i t seems t o have a t w e l v e - G o l d symmetry, but w i t h c l o s e r e x a m i n a t i o n we
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can observe some ~eatures which reduce the overall symmetry from 12mm to 6mm. T h e s p o t s m a r k e d by a r r o w s in f i g u r e 1 s h o w a h e x a g o n a l a r r a y g i v i n g a s a r e s u l t t h r e e m a i n s p o t s rows w h o s e c o r r e s p o n d i n g interplanar distances in reciprocal u n i t s h a v e b e e n t a b u l a t e d in t a b l e I. The real distances are labeled by c a p i t a l l e t t e r s in t h e r a t i o b e t w e e n s u c c e s s i v e distances. These ratios can be compared with the ones calculated from the theoretical diffraction pattern of the dodecagonal quasilattice(6). The diffraction pattern shown in fig. I~ is different from the one presented by C h e n et al. (5)~ a n d a l s o (see t a b l e I) f r o m t h e o n e c a l c u l a t e d for t h e d o d e c a g o n a l quasilattice in r e f e r e n c e 6. When dark f i e l d i m a g e s w e r e o b t a i n e d by u s e w i t h a n y s p o t s o f t h e d i f f r a c t i o n pattern of ~ i g u r e i, i n c l u d i n g t h e o n e s w h i c h f o r m t h e h e x a g o n a l a r r a y , a n u m b e r of small g r a i n s a r e o b s e r v e d in fig. 2. T h e s e g r a i n s h a v e a m e a n s i z e o f 40nm. When the film is tilted ~rom this diffraction pattern towards a perpendicular orientation, it is o b s e r v e d t h a t t h e f i l m p l a n e c o r r e s p o n d s to t h e " d o d e c a g o n a l " p l a n e o f t h e s e grains. T h i s m e a n s t h a t an e p i t a x i a l growth has occurred and any axis zone perpendicular to this dodecagonal plane cannot be observed experimentally. It w a s a l s o not p o s s i b l e t o o b t a i n a d i f f r a c t i o n pattern from an i n d i v i d u a l grain. T h e m a i n r e a s o n w a s t h a t t h e v e r y s m a l l e l e c t r o n beam size (~ 1Ohm) required produced substantial radiation damage, which alters the diffraction pattern.
F i g u r e i . S e l e c t e d area electron diff r a c t i o n p a t t e r n from the Bi-Mn t h i n f i l m e v a p o r a t e d on g l a s s and heated a t 270°C d u r i n g 100 hours.
I
~LT~ ~' /
F i g u r e 2. thin film
(a) b r i g h t f i e l d and (b) d a r k f i e l d image from t h e a r e a o f t h e Bi-Mn which p r o d u c e s t h e d i f f r a c t i o n p a t t e r n shown i n 2.
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T h e e x i s t e n c e oF t h e d o d e c a g o n a l quasicrystalline p h a s e in the grains of the Bi-Mn thin films are made plausible using High Resolution Electron Microscopy. T h e i m a g e s (Gig. 3) s h o w s e v e r a l t w e l v e - d o t m o t i f s w h i c h c a n be r e l a t e d w i t h t h e ones reported in.some theoretical models (6, 9-11). In certain areas these m o t i f s f o l l o w a p a t t e r n w h i c h is v e r y s i m i l a r t o t h a t o b s e r v e d by Ishimasa et al. (4) (Gig. 3a); in o t h e r s a r e a s t h e p a t t e r n s h o w s defects (fig. 3b). This means that the arrangements of the bright-dots m o t i f s in s o m e areas (-Fig. 3a) a r e not p e r i o d i c , but i n s t e a d a r r a n g e d on a p a t t e r n s i m i l a r t o t h e o n e observed in f i g u r e 2 o f r e f e r e n c e 6; o t h e r a r e a s s h o w a pattern where some of these m o t i f s a r e isolated. S o m e m o t i f s t o u c h e a c h o t h e r a n d s o m e a r e i n t e r l o c k e d (Gig. 3b) s i m i l a r t o the p a t t e r n s h o w n in f i g u r e 1 of r e f e r e n c e 6. An experiment to rule out the possibility of twinning was performed by F F T processing the HREM photographs to obtain the Fourier transforms of s e v e r a l a r e a s of t h e sample in such a way that they were r o t a t e d by 30 ° t o e a c h o t h e r . In t h e c a s e o f t w i n n i n g t h e F F T s h o u l d vary considerably after each rotation. The result of such a n a l y s i s is s h o w n in f i g u r e 4 in w h i c h t h e F F T of a n u m b e r o G r e g i o n s is shown. As c a n be s e e n the d o d e c a g o n a l F F T p a t t e r n is c o n s e r v e d along all directions. This therefore rules out the possibility of multiple twinning. We can then c o n c l u d e t h a t in t h e B i - M n s y s t e m t h e r e a r e g r a i n s in t h e s i z e range oG ~50nm with a true dodecagonal symmetry.
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F i g u r e 3. H i g h r e s o l u t i o n images from the area which produces "the diffraction p a t t e r n s h o w n in 2. (a) t h e r e a r e s e v e r a l twelve-fold motifs which Follow a p a t t e r n v e r y s i m i l a r t o t h a t o n e o b s e r v e d by I s h i m a s a et al. (4). (b) different area showing are several d e f e c t s in t h e p a t t e r n . These images were computer processed'to enhance its contrast. In t h e b o t t o m of t h e s e F i g u r e (as a2 a n d b2) schematic representations oF t h e t w e l v e - d o t motifs are shown.
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F i g u r e 4. HREM image oE a B i - M n Gilm and its c o r r e s p o n d i n g FFT p a t t e r n s o b t a i n e d in different areas o~ the image.
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It s h o u l d be noted t h a t Y o s h i d a et al. (8) n o t e d the existence o~ arrays o~ t w e l v e s p o t s in the HREM. H o w e v e r t h e y d i d not recognize the presence o~ a dodecagonal quasilattice. T h e y i n t e r p r e t e d t h e e G ~ e c t as d u e to a short-range a t o m i c order. As in t h e c a s e s r e p o r t e d by I s h i m a s a et al. (4) a n d Chert et al. (5)~ we E o u n d a d d i t i o n a l p h a s e s c o e x i s t i n g w i t h t h e d o d e c a g o n a l phase. As was p o i n t e d out by Y o s h i d a a n d Y a m a d a ( 7 - 8 ) ~ s e v e r a l c r y s t a l l i n e p h a s e s a r e ~ o u n d in t h e B i - M n t h i n ~ilms~ m o s t o~ t h e m w i t h l o n g - p e r i o d c r y s t a l lattices. We have ~ o u n d at least t h r e e c r y s t a l l i n e p h a s e s c o e x i s t i n g w i t h t h e dodecagonal phase. All o~ t h e m have t e t r a g o n a l u n i t c e l l s and two are long-period structures m o d u l a t e d (~ig. 5). O n e o ~ t h e s e p h a s e s has l a t t i c e p a r a m e t e r s o F a = 0 . 2 7 n m and c = 0 . 9 1 n m (~ig. 5a-b). T h e s e c o n d p h a s e is c l o s e l y r e l a t e d t o t h e t e t r a g o n a l one~ but s h o w i n g s u p e r s t r u c t u r e r e f l e c t i o n s (fig. 5c-d). T h i s phase corresponds to t h a t r e p o r t e d by Y o s h i d a a n d Y a m a d a ( 7 ) . T h e t h i r d o n e has u n i t cell parameters a=0.27 and c=l.82nm a n d its s t r u c t u r e is o E t h e l o n g - p e r i o d m o d u l a t e d structure t y p e (~ig.5e-~:}.
F i g u r e 5. (a,c, a n d e) t h r e e c r y s t a l l i n e p h a s e s w h i c h were ~ound w i t h t h e d o d e c a g o n a l p h a s e . In (b~d a n d ~) t h e d i f f r a c t i o n o b t a i n e d t h e s a m p l e u-, a l o n g t h e d i r e c t i o n i n d i c a t e d by t h e a r r o w in (a).
coexisting by t i ! t i n 0
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We c o n c l u d e t h a t a t w e l v e - f o l d s y m m e t r i c phase occurs in Bi-Mn alloys. This phase i s n o t due t o m u l t i p l e t w i n n i n g as shown by t h e H i g h Resolution Electron M i c r o s c o p y and t h e FFT e x p e r i m e n t . T h i s p h a s e , h o w e v e r , occurs only in small g r a i n s and can be c o n s i d e r e d as a n a n o - p h a s e . We n e v e r f o u n d d o d e c a g o n a l g r a i n s l a r g e r t h a n a b o u t 5Ohm. The d e c a g o n a l phase i s a l w a y s s u r r o u n d e d by different crystalline phases.
Acknowledgements We w o u l d like t o thank Mr. S. T e h u a c a n e r o , Mr. L u i s R e n d b n , Mrs. C. Zorrilla~ Mr. A. S i n c h e z a n d Mrs. R o s a Ma. Lima for technical support. We thank the f i n a n c i a l s u p p o r t Grom t h e N a t i o n a l C o u n c i l f o r S c i e n c e a n d T e c h n o l o g y (CONACYT) for t h i s w o r k (REG. A 1 2 8 C C 0 5 9 0 0 2 7 3 (FI-7) a n d P 2 2 8 C C O X 8 9 1 5 9 4 ) .
References 1. D. S h e c h t m a n , I. B l e c h , D. G r a t i a s a n d J.W. Cahn, Phys. Rev. Lett. 53~ 195 (1984). 2. N. Wang, H. C h e n a n d K.H. Kuo, Phys. R e v . Lett. 59, I 0 1 0 (1987). 3. L. B e n d e r s k y , Phys. Rev. Lett. 55, 1461 (1985). 4. T. I s h i m a s a , H. U. N i s s e n a n d Y. F u k a n o , Phys. Rev. Lett. 55, 511 (1985). 5. H. Chen~ D. X. Li a n d K.H. Kuo, Phys. Rev. Lett. 60, 1645 (19881. b. N. N i i z e k i a n d H. M i t a n i , J. Phys. A: M a t h . Gen. 20, L 4 0 5 (1987). 7. K. Y o s h i d a a n d T. Y a m a d a , Appl. S u r f . Sci. 3 3 - 3 4 ~ 5 1 6 (1988). 8. K. Y o s h i d a , T. Y a m a d a a n d Y. T a n i g u c h i , A c t a C r y s t . B45, 40, (1989). 9. J.Q. Y o u a n d T.B. Hu, P h i l . Mag. Lett. 57, 195 (19881. 10. P . S t a m p f l i , Helv. Phys. A c t a 5 9 , 1 2 6 0 (1986). Ii. F. G ~ h l e r a n d J. R h y n e r , J. Phys. A: M a t h . Sen. 19, 2 6 7 (19867. Figure 1
From
Theoretical
values(b)
L I N E 1
a - ( . 5 2 5 n m ) ~ A/B = 2 . 7 b - ( . 1 9 3 n m ) - I B / C = 1.36 c-(.142nm) -i d-(.131nm}
(.138nm) -i B / C (.081nm) -i
L I N E 2
e - ( . 2 7 b n m ) - i E/F = 1 . 7 4 ~ - ( . 1 5 8 n m ) - i F/G = 1 . 1 5 g-(.137nml -i
(.276nm) (.097nm) - i (.072nm) - i
L I N E 3
h-(.525nm) i-(.226nm) j-(.193nm) k-(.142nm)
=
1.70
ElF = 2 . 8 4 F/G = 1.34
~ H/I = 2 . 3 2 -i I/J = 1.17 -i J / K = 1.35 ~
T a b l e i. D i s t a n c e s f r o m t h e c e n t e r t o t h e e l e c t r o n d i f f r a c t i o n s p o t s l a b e l e d by small letters the a l o n g t h r e e p r i n c i p a l l i n e s s h o w n in F i g u r e i. These small l e t t e r s r e p r e s e n t ~ t h e r e f o r e , d i s t a n c e s in r e c i p r o c a l s p a c e . T h e real distances are labeled by their corresponding capital letters. The ratios between s u c c e s s i v e d i s t a n c e s have been compared w i t h the ones calculated From the theoretical diffraction p a t t e r n p r e s e n t e d i n r e ~ e r e n c e b.
Vol. 25, pp. 325-330, 1991 Printed in the U.S.A.
Pergamon Press plc All rights reserved
A TWELVE-FOLD @UASICRYSTALLINE PHASE IN Bi-Mn ALLOYS ~. Reyes-Gasga,
R. Hernandez
and M. Jom@-YacamJn
I n s t i t u t o de F ~ s i c a , U n i v e r s i d a d N a t i o n a l Aut6noma de M~xico, A p a r t a d o P o s t a l 20-364. D e l e g a c i 6 n A l v a r o Obreg6n 01000 M~xico, D. F. MEXICO
(Received October 9, 1990) (Revised November 16, 1990) Introduction The d i s c o v e r y o~ t h e i c o s a h e d r a l q u a s i c r y s t a l l i n e phase by Shechtman et a l . (1> was t h e b e g i n n i n g o~ an intensive and s y s t e m a t i c activity on modeling c h a r a c t e r i z a t i o n and a s e a r c h o~ new m a t e r i a l s exhibiting quasicrystallinity. Phases w i t h ~ive-fold(1), eight-~old(2)~ ten-fold(3) and twelve-Gold(4.5) r o t a t i o n axes have been r e p o r t e d . C o m p a r a t i v e l y speaking~ the o c t a g o n a l and dodecagonal phases have r e c e i v e d l e s s a t t e n t i o n , p r o b a b l y because o~ t h e scarce e x p e r i m e n t a l d a t a them. Ishimasa e t a l . (4) ~ound t h e dodecagonal phase i n small p a r t i c l e s in Ni-70.6 at.%Cr alloy. The t w e l v e - G o l d q u a s i c r y s t a l l i n e phase c o e x i s t s w i t h r e g i o n s oG m u l t i p l e t w i n n e d ~ - p h a s e domains as w e l l as two other c r y s t a l l i n e phases. Chert e t a l . (5) r e p o r t e d t h e t w e l v e - E o l d phase i n rapidly this phase is s o l i d i f i e d VsNi z and VieNi,oSi a l l o y s . These a u t h o r s f o u n d t h a t q u a s i p e r i o d i c i n two dimensions and p e r i o d i c i n t h e p e r p e n d i c u l a r a x i s as i n t h e case o f t h e decagonal phase. T h e i r phase has t h e same q u a s i l a t t i c e r e p o r t e d by Ishimasa e t a l . (4) and i t s e l e c t r o n d i G G r a c t i o n p a t t e r n i s t h e same as t h e ones calculated theoretically (6). I n t h e p r e s e n t paper a t w e l v e - G o l d q u a s i c r y s t a l l i n e phase i n t h i n ~ i l m s o~ t h e Bi-Mn a l l o y i s r e p o r t e d . T h i s phase has a q u a s i l a t t i c e which, i n some regions, i s v e r y s i m i l a r t o t h e one r e p o r t e d by Ishimasa e t a l . ( 4 ) . The Bi-Mn t h i n Gilms were produced by s u c c e s s i v e e v a p o r a t i o n s as r e p o r t e d by Yoshida and Yamada(7-8>. (.0 B e f o r e e v a p o r a t i o n•, t h e s u b s t r a t e was h e a t e d a t 27.) C f o r one hour Gor c l e a n i n g . AGter c o o l i n g t o room t e m p e r a t u r e ~ t h e e v a p o r a t i o n took p l a c e on s u b s t r a t e s c o v e r e d p r e v i o u s l y w i t h a c a r b o n ~ i l m . Composited Gilms o~ Bi and Mn l a y e r s were p r e p a r e d by s u c c e s s i v e vacuum e v a p o r a t i o n o f a Bi with a t h i c k n e s s o~ 3Ohm, ~ o l l o w e d by a Mn ~ i l m , w i t h 20nm. E v a p o r a t i o n s were made on b o t h NaC1 and g l a s s s u b s t r a t e s i n a 10 -a Pa vacuum. A ~ t e r w a r d s t h e Gilm t e m p e r a t u r e was r a i s e d t o 270°C, s l i g h t l y below t h e m e l t i n g t e m p e r a t u r e o f Bi~ d u r i n g different periods. The e l e c t r o n d i ÷ f r a c t i o n t i l t i n g e x p e r i m e n t s and c h e m i c a l a n a l y s i s were o b t a i n e d using a J E O L IOOCX a n a l y t i c a l electron microscope equipped w i t h a -+60° g o n i o m e t e r and an EDX X - r a y a n a l y z e r . The high resolution o b s e r v a t i o n s were c a r r i e d o u t i n a JEOL 4000-EX h i g h r e s o l u t i o n m i c r o s c o p e . Images were computer p r o c e s s e d t o enhance t h e i r c o n t r a s t u s i n g an I n n o v i o n system on l i n e w i t h a 1178 VAX computer. The X - r a y chemical a n a l y s i s of the ~ilms o b t a i n e d showed a c o m p o s i t i o n i n t h e r a n g e oG 70 t o 80 at.%Mn. However i n t h e a r e a s which produce the d i f f r a c t ion pattern shown in figure I the composition corresponds a p p r o x i m a t e l y t o BiMnm. A c c o r d i n g w i t h Yoshida and Yamada(7), c r y s t a l s w i t h t h i s c h e m i c a l c o m p o s i t i o n have space group R~m and 12Bi and 36 Mn atoms a r e situated i n i t s u n i t c e l l . A ~ t e r h e a t i n g t h e ~ i l m a t 270oC ~or i 0 0 hours, the selected area d i ~ r a c t i o n p a t t e r n shown i n ~ i g u r e 1 i s o b s e r v e d i n many a r e a s . At ~irst g l a n c e , i t seems t o have a t w e l v e - G o l d symmetry, but w i t h c l o s e r e x a m i n a t i o n we
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can observe some ~eatures which reduce the overall symmetry from 12mm to 6mm. T h e s p o t s m a r k e d by a r r o w s in f i g u r e 1 s h o w a h e x a g o n a l a r r a y g i v i n g a s a r e s u l t t h r e e m a i n s p o t s rows w h o s e c o r r e s p o n d i n g interplanar distances in reciprocal u n i t s h a v e b e e n t a b u l a t e d in t a b l e I. The real distances are labeled by c a p i t a l l e t t e r s in t h e r a t i o b e t w e e n s u c c e s s i v e distances. These ratios can be compared with the ones calculated from the theoretical diffraction pattern of the dodecagonal quasilattice(6). The diffraction pattern shown in fig. I~ is different from the one presented by C h e n et al. (5)~ a n d a l s o (see t a b l e I) f r o m t h e o n e c a l c u l a t e d for t h e d o d e c a g o n a l quasilattice in r e f e r e n c e 6. When dark f i e l d i m a g e s w e r e o b t a i n e d by u s e w i t h a n y s p o t s o f t h e d i f f r a c t i o n pattern of ~ i g u r e i, i n c l u d i n g t h e o n e s w h i c h f o r m t h e h e x a g o n a l a r r a y , a n u m b e r of small g r a i n s a r e o b s e r v e d in fig. 2. T h e s e g r a i n s h a v e a m e a n s i z e o f 40nm. When the film is tilted ~rom this diffraction pattern towards a perpendicular orientation, it is o b s e r v e d t h a t t h e f i l m p l a n e c o r r e s p o n d s to t h e " d o d e c a g o n a l " p l a n e o f t h e s e grains. T h i s m e a n s t h a t an e p i t a x i a l growth has occurred and any axis zone perpendicular to this dodecagonal plane cannot be observed experimentally. It w a s a l s o not p o s s i b l e t o o b t a i n a d i f f r a c t i o n pattern from an i n d i v i d u a l grain. T h e m a i n r e a s o n w a s t h a t t h e v e r y s m a l l e l e c t r o n beam size (~ 1Ohm) required produced substantial radiation damage, which alters the diffraction pattern.
F i g u r e i . S e l e c t e d area electron diff r a c t i o n p a t t e r n from the Bi-Mn t h i n f i l m e v a p o r a t e d on g l a s s and heated a t 270°C d u r i n g 100 hours.
I
~LT~ ~' /
F i g u r e 2. thin film
(a) b r i g h t f i e l d and (b) d a r k f i e l d image from t h e a r e a o f t h e Bi-Mn which p r o d u c e s t h e d i f f r a c t i o n p a t t e r n shown i n 2.
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T h e e x i s t e n c e oF t h e d o d e c a g o n a l quasicrystalline p h a s e in the grains of the Bi-Mn thin films are made plausible using High Resolution Electron Microscopy. T h e i m a g e s (Gig. 3) s h o w s e v e r a l t w e l v e - d o t m o t i f s w h i c h c a n be r e l a t e d w i t h t h e ones reported in.some theoretical models (6, 9-11). In certain areas these m o t i f s f o l l o w a p a t t e r n w h i c h is v e r y s i m i l a r t o t h a t o b s e r v e d by Ishimasa et al. (4) (Gig. 3a); in o t h e r s a r e a s t h e p a t t e r n s h o w s defects (fig. 3b). This means that the arrangements of the bright-dots m o t i f s in s o m e areas (-Fig. 3a) a r e not p e r i o d i c , but i n s t e a d a r r a n g e d on a p a t t e r n s i m i l a r t o t h e o n e observed in f i g u r e 2 o f r e f e r e n c e 6; o t h e r a r e a s s h o w a pattern where some of these m o t i f s a r e isolated. S o m e m o t i f s t o u c h e a c h o t h e r a n d s o m e a r e i n t e r l o c k e d (Gig. 3b) s i m i l a r t o the p a t t e r n s h o w n in f i g u r e 1 of r e f e r e n c e 6. An experiment to rule out the possibility of twinning was performed by F F T processing the HREM photographs to obtain the Fourier transforms of s e v e r a l a r e a s of t h e sample in such a way that they were r o t a t e d by 30 ° t o e a c h o t h e r . In t h e c a s e o f t w i n n i n g t h e F F T s h o u l d vary considerably after each rotation. The result of such a n a l y s i s is s h o w n in f i g u r e 4 in w h i c h t h e F F T of a n u m b e r o G r e g i o n s is shown. As c a n be s e e n the d o d e c a g o n a l F F T p a t t e r n is c o n s e r v e d along all directions. This therefore rules out the possibility of multiple twinning. We can then c o n c l u d e t h a t in t h e B i - M n s y s t e m t h e r e a r e g r a i n s in t h e s i z e range oG ~50nm with a true dodecagonal symmetry.
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F i g u r e 3. H i g h r e s o l u t i o n images from the area which produces "the diffraction p a t t e r n s h o w n in 2. (a) t h e r e a r e s e v e r a l twelve-fold motifs which Follow a p a t t e r n v e r y s i m i l a r t o t h a t o n e o b s e r v e d by I s h i m a s a et al. (4). (b) different area showing are several d e f e c t s in t h e p a t t e r n . These images were computer processed'to enhance its contrast. In t h e b o t t o m of t h e s e F i g u r e (as a2 a n d b2) schematic representations oF t h e t w e l v e - d o t motifs are shown.
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F i g u r e 4. HREM image oE a B i - M n Gilm and its c o r r e s p o n d i n g FFT p a t t e r n s o b t a i n e d in different areas o~ the image.
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It s h o u l d be noted t h a t Y o s h i d a et al. (8) n o t e d the existence o~ arrays o~ t w e l v e s p o t s in the HREM. H o w e v e r t h e y d i d not recognize the presence o~ a dodecagonal quasilattice. T h e y i n t e r p r e t e d t h e e G ~ e c t as d u e to a short-range a t o m i c order. As in t h e c a s e s r e p o r t e d by I s h i m a s a et al. (4) a n d Chert et al. (5)~ we E o u n d a d d i t i o n a l p h a s e s c o e x i s t i n g w i t h t h e d o d e c a g o n a l phase. As was p o i n t e d out by Y o s h i d a a n d Y a m a d a ( 7 - 8 ) ~ s e v e r a l c r y s t a l l i n e p h a s e s a r e ~ o u n d in t h e B i - M n t h i n ~ilms~ m o s t o~ t h e m w i t h l o n g - p e r i o d c r y s t a l lattices. We have ~ o u n d at least t h r e e c r y s t a l l i n e p h a s e s c o e x i s t i n g w i t h t h e dodecagonal phase. All o~ t h e m have t e t r a g o n a l u n i t c e l l s and two are long-period structures m o d u l a t e d (~ig. 5). O n e o ~ t h e s e p h a s e s has l a t t i c e p a r a m e t e r s o F a = 0 . 2 7 n m and c = 0 . 9 1 n m (~ig. 5a-b). T h e s e c o n d p h a s e is c l o s e l y r e l a t e d t o t h e t e t r a g o n a l one~ but s h o w i n g s u p e r s t r u c t u r e r e f l e c t i o n s (fig. 5c-d). T h i s phase corresponds to t h a t r e p o r t e d by Y o s h i d a a n d Y a m a d a ( 7 ) . T h e t h i r d o n e has u n i t cell parameters a=0.27 and c=l.82nm a n d its s t r u c t u r e is o E t h e l o n g - p e r i o d m o d u l a t e d structure t y p e (~ig.5e-~:}.
F i g u r e 5. (a,c, a n d e) t h r e e c r y s t a l l i n e p h a s e s w h i c h were ~ound w i t h t h e d o d e c a g o n a l p h a s e . In (b~d a n d ~) t h e d i f f r a c t i o n o b t a i n e d t h e s a m p l e u-, a l o n g t h e d i r e c t i o n i n d i c a t e d by t h e a r r o w in (a).
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We c o n c l u d e t h a t a t w e l v e - f o l d s y m m e t r i c phase occurs in Bi-Mn alloys. This phase i s n o t due t o m u l t i p l e t w i n n i n g as shown by t h e H i g h Resolution Electron M i c r o s c o p y and t h e FFT e x p e r i m e n t . T h i s p h a s e , h o w e v e r , occurs only in small g r a i n s and can be c o n s i d e r e d as a n a n o - p h a s e . We n e v e r f o u n d d o d e c a g o n a l g r a i n s l a r g e r t h a n a b o u t 5Ohm. The d e c a g o n a l phase i s a l w a y s s u r r o u n d e d by different crystalline phases.
Acknowledgements We w o u l d like t o thank Mr. S. T e h u a c a n e r o , Mr. L u i s R e n d b n , Mrs. C. Zorrilla~ Mr. A. S i n c h e z a n d Mrs. R o s a Ma. Lima for technical support. We thank the f i n a n c i a l s u p p o r t Grom t h e N a t i o n a l C o u n c i l f o r S c i e n c e a n d T e c h n o l o g y (CONACYT) for t h i s w o r k (REG. A 1 2 8 C C 0 5 9 0 0 2 7 3 (FI-7) a n d P 2 2 8 C C O X 8 9 1 5 9 4 ) .
References 1. D. S h e c h t m a n , I. B l e c h , D. G r a t i a s a n d J.W. Cahn, Phys. Rev. Lett. 53~ 195 (1984). 2. N. Wang, H. C h e n a n d K.H. Kuo, Phys. R e v . Lett. 59, I 0 1 0 (1987). 3. L. B e n d e r s k y , Phys. Rev. Lett. 55, 1461 (1985). 4. T. I s h i m a s a , H. U. N i s s e n a n d Y. F u k a n o , Phys. Rev. Lett. 55, 511 (1985). 5. H. Chen~ D. X. Li a n d K.H. Kuo, Phys. Rev. Lett. 60, 1645 (19881. b. N. N i i z e k i a n d H. M i t a n i , J. Phys. A: M a t h . Gen. 20, L 4 0 5 (1987). 7. K. Y o s h i d a a n d T. Y a m a d a , Appl. S u r f . Sci. 3 3 - 3 4 ~ 5 1 6 (1988). 8. K. Y o s h i d a , T. Y a m a d a a n d Y. T a n i g u c h i , A c t a C r y s t . B45, 40, (1989). 9. J.Q. Y o u a n d T.B. Hu, P h i l . Mag. Lett. 57, 195 (19881. 10. P . S t a m p f l i , Helv. Phys. A c t a 5 9 , 1 2 6 0 (1986). Ii. F. G ~ h l e r a n d J. R h y n e r , J. Phys. A: M a t h . Sen. 19, 2 6 7 (19867. Figure 1
From
Theoretical
values(b)
L I N E 1
a - ( . 5 2 5 n m ) ~ A/B = 2 . 7 b - ( . 1 9 3 n m ) - I B / C = 1.36 c-(.142nm) -i d-(.131nm}
(.138nm) -i B / C (.081nm) -i
L I N E 2
e - ( . 2 7 b n m ) - i E/F = 1 . 7 4 ~ - ( . 1 5 8 n m ) - i F/G = 1 . 1 5 g-(.137nml -i
(.276nm) (.097nm) - i (.072nm) - i
L I N E 3
h-(.525nm) i-(.226nm) j-(.193nm) k-(.142nm)
=
1.70
ElF = 2 . 8 4 F/G = 1.34
~ H/I = 2 . 3 2 -i I/J = 1.17 -i J / K = 1.35 ~
T a b l e i. D i s t a n c e s f r o m t h e c e n t e r t o t h e e l e c t r o n d i f f r a c t i o n s p o t s l a b e l e d by small letters the a l o n g t h r e e p r i n c i p a l l i n e s s h o w n in F i g u r e i. These small l e t t e r s r e p r e s e n t ~ t h e r e f o r e , d i s t a n c e s in r e c i p r o c a l s p a c e . T h e real distances are labeled by their corresponding capital letters. The ratios between s u c c e s s i v e d i s t a n c e s have been compared w i t h the ones calculated From the theoretical diffraction p a t t e r n p r e s e n t e d i n r e ~ e r e n c e b.