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On the structure of the quasicrystalline T phase in Al86Mn14 alloy
Scripta
METALLURGICA
ON THE
Vol. 20, pp. 4 0 1 - 4 0 5 , 1986 P r i n t e d in the U . S . A .
STRUCTURE
OF
THE
IN A186
P e r g a m o n P r e s s Ltd. All rights reserved
QUASICRYSTALLINE Mnl4
T PHASE
ALLOY
R.
+
On
leave
from
P~rez-Campos, J.G. P~rez-Rom~rez + A G6mez R. H e r r e r o and M. J o s ~ - Y o c a m 6 n I n s t i t u t o de F i s i c o , U . N . A . M . P. O. Box 2 0 - 3 6 4 , 0 1 0 0 0 M 6 x i c o , O.P. M~xico the ESFM, IPN, M ~ x i c o . (Received
I .-
December
9,
1985)
Introduction
Recent s t u d i e s of p h a s e f o r m a t i o n in r a p i d l y s o l i d i f i e d A I - M n a l l o y s hove shown the e x i s t e n c e of o p h a s e w i t h l o n g - r a n g e o r i e n t a t i o n o l o r d e r and i c o s o h e drol point g r o u p s y m m e t r y (m3S) (I). T h e s e new t y p e s of q u o s i p e r i o d i c structures ore a l r e a d y k n o w n as " q u a s i c r y s t o l s " (2). S t u d i e s of p h a s e f o r m a t i o n at s l o w e r s o l i d i f i c a t i o n rotes h o v e s h o w n that the i c o s a h e d r o l p h a s e is r e p l a c e d by the so-called T p h a s e (3). This p h a s e is a q u a s i c r y s t a l w i t h one-dimensional periodicity and planar quasiperiodicity in the o t h e r two d i m e n s i o n s (3) (4). The i c o s o h e d r o l and T p h a s e s ore c l o s e l y r e l a t e d in s t r u c t u r a l characteristics. For e x a m p l e , the d i f f r a c t i o n p a t t e r n s f r o m both s t r u c t u r e s h a v e s t r o n g s i m i l a r i ties (3). The i c o s o h e d r o l p h a s e of A I - 6 M n . has r e c e i v e d c o n s i d e r a b l e a t t e n t i o n in the literature, however, t h e r e ~ a v e 1 ~ e e n v e r y few i n v e s t i g a t i o n s on the structural c h a r a c t e r i s t i c s of the T p h a s e . In this c o m m u n i c a t i o n we r e p o r t on i n v e s t i g a t i o n on the s t r u c t u r e of the T p h a s e . This s t u d y was c a r r i e d out u s i n g different techniques such as: c o n v e n t i o n a l and high-resolution transmission electron microscopy, microdiffroction and i m a g e p r o c e s s i n g . The methods of sample p r e p a r a t i o n and c h a r a c t e r i z a t i o n by A u g e r s c a n n i n g m i c r o s c o p y and other m e t h o d s will be r e p o r t e d e l s e w h e r e . 2.-
Experimental
Results
The identification of the T p h a s e was c a r r i e d out using selected area diffraction p a t t e r n s (SAOP) f r o m the s u s p e c t e d a r e a s in the specimens. These p a t t e r n s w e r e o b t a i n e d for d i f f e r e n t o r i e n t a t i o n s . In o r d e r to a s s u r e that the entire groin hod long range o r i e n t o t i o n o l o r d e r and therefore that apparent quosiperiodicity was not p r o d u c e d by m u l t i p l e t w i n n i n g of o small c r y s t o l l i t e s , microdiffroction p a t t e r n s (with b e a m size ~ 20nm) w e r e o b t a i n e d from different r e g i o n s in the g i v e n g r o i n . T h e s e r e s u l t s ore i l l u s t r a t e d in Figs. 1o, b and c w h i c h show SADP w h i c h c o r r e s p o n d to the t e n - f o l d , t h r e e - f o l d and t w o - f o l d o r i e n tations. These p a t t e r n s s h o w o spot d i s t r i b u t i o n f o l l o w i n g the F i b o n o c c i seq u e n c e in two d i r e c t i o n s and o n o r m a l p e r i o d i c i t y in one d i r e c t i o n . It is i m p o r t a n t to n o t i c e the p r o n o u n c e d s t r e a k i n g in these diffraction patterns. Fig. 2o, b s h o w SADP and m i c r o d i f f r o c t i o n p a t t e r n s o b t a i n e d from the some area in the s p e c i m e n . As it is i l l u s t r a t e d in the figure) both d i f f r a c t i o n p a t t e r n s ore s i m i l a r . The some b e h a v i o r has been o b s e r v e d in microdiffroction patterns from o t h e r a r e a s . This shows that the f i v e - f o l d s i m m e t r y is not the r e s u l t of m u l t i p l e t w i n i n g of s e v e r a l c r y s t o l l i t e s . Most of the q u a s i c r y s t a l i n e a r e a s (T phase) f o u n d in our s p e c i m e n s show o characteristic s t r i o t e c o n t r a s t u n d e r b r i g h t or d a r k f i e l d i m a g i n g . This controst has been found to depend strongly on t h e t i l t i n g of the specimen. Thus, for example, Fig. 30 s h o w s on image B r i g h t F i e l d (BF) w i t h this pronounced c o n t r o s t ~ h o w e v e r , Fig. 3b s h o w s the some area in a n o t h e r o r i e n t a t i o n , in this
401 0 0 3 6 - 9 7 4 8 / 8 6 $ 3 . 0 0 + .00 C o p y r i g h t (c) 1986 P e r g a m o n P r e s s
Ltd.
402
QUASICRYSTALLINE
T PHASE
IN AI M n
Vol.
20, No.
3
case the above mentioned contrast has almost dissapeared. This contrast is similar to the one reported before for the icosahedral phase (5) and it has been associated with local strain fields in the phase. It should be n o t e d ~ h o w e v e r , that the observed contrast is more pronounced with respect to that found in conventional bright field images of strained crystals. A more detailed examination of this effect is necessary in ord~r to understand its origin. High resolution images [HREM) w e r e o b t a i n e d with an incident beam parallel to a two-fold zone axis. This orientation makes an angle o f 90 ° w i t h the fivefold axis. Most of the o r i g i n a l i m a g e s s h o w p o o r c o n t r a s t and we decided to c a r r y out an image p r o c e s s i n g a p p r o a c h on t h e s e m i c r o g r a p h s . Figs. 4a and b show an image and its c o r r e s p o n d i n g Fourier transform. The f i r s t i n t e r e s t i n g point to note from H R E M i m a g e s is the c o n t r a s t w h i c h c l e a r l y s u g g e s t s on arrangement of linear c h a i n s w h i c h a p p e a r to be p e r i o d i c a l l y twisted forming a kind of spiral s t r u c t u r e . The e x i s t e n c e of t h e s e t w i s t e d c h a i n s is a l s o supported from the SADP's (Fig. I) w h i c h c l e a r l y s h o w the p r e s e n c e of s h e e t s of i n t e n s i t y in r e c i p r o c a l space. This is o c o m m o n e f f e c t o b t a i n e d in the d i f f r a c t i o n of Xrays by chain m o l e c u l e s (6). This b e h a v i o r can a l s o be seen in the Fourier transform of the d i g i t i z e d i m a g e s h o w n in Fig. 40. This is a l s o s u p p o r t e d by the fact that in the p a t t e r n s the s p o t s ore not p e r f e c t l y o l l i g n e d a l o n g o row of i n t e n s i t y . The r e p e a t d i s t a n c e a l o n g the p e r i o d i c d i r e c t i o n was f o u n d to be 0 . 8 0 6 n m in a g r e e m e n t w i t h Ref. (4). The i m a g e s i n d i c a t e that the chains ore t w i s t e d over a l e n g t h of ~ 4 . 2 nm. Weak beam dark field images (WDF) w e r e o b t a i n e d for the T phase with the incident beam p a ' r a l l e l to a three-fold zone axis. The main reflection used for these i m a g e s was those in the corners of the 3-fold diffraction pattern shown in Fig. 5b. H o w e v e r , it is i m p o r t a n t to m e n t i o n that m o r e than one r e f l e c t i o n along o row was a l l o w e d to pass t h r o u g h the objective aperture. The same p r o c e s s i n g a p p r o a c h a b o v e m e n t i o n e d w a s a p p l i e d to t h e s e dark f i e l d m i c r o g r o p h s . Fig. 5 shows one of the r e c o n s t r u c t e d images. In this c a s e the f r i n g e s c o r r e s pond to the i n t e r f e r e n c e b e t w e e n s p o t s a l o n g o row. T h e r e f o r e , the b r i n g e s run p e r p e n d i c u l a r to the c h a i n d i r e c t i o n . T h e r e f o r e , this k i n d of image con p r o v i d e information a b o u t the F i b u n o c c i m o d u l a t i o n a l o n g the rows of i n t e n s i t y o b s e r v e d on t h e p a t t e r n s . The bringes hove a wavy a~pearance and many times ore shifted. Also extra lines produce a dislocation-like contrast (see arrow on t h e figure). These k i n d o f e f f e c t s might be d u e t o a t h i c k n e s s modulation or to a true defect structure along the chain boundaries.
3.-
Conclusions
The m o s t i m p o r t a n t r e s u l t w h i c h con be o b t a i n e d f r o m our i n v e s t i g a t i o n s is that the quasicrystalline T p h a s e of A I ^ . M n . . is m a d e of an arrangement of linear c h a i n s w h i c h ore p e r i o d i c a l l y t w i s t e d . 14 This s t a t e m e n t is b a s e d on the experimental e v i d e n c e of high r e s o l u t i o n and m i c r o d i f f r a c t i o n . This s t r u c t u r e was p r e v i o u s l y s u g g e s t e d by 8 e n d e r s k y (4) on the b a s i s of the p l a n a r intensity on the d i f f r a c t i o n p a t t e r n s . The high r e s o l u t i o n and dark f i e l d i m a g e s r e s u l t s in this work c o n f i r m the c h a i n one d i m e n s i o n a l s t r u c t u r e . 4.-
Acknowledgements
The a u t h o r s ore i n d e b t e d to Dr. L o r e n z o M o r t f n e z a n d J.L. A l b a r r 6 n his team for p r e p a r i n g the a l l o y s . We a l s o t h a n k to Mr. F. R u i z for o b t a i n i n g the high resolution p i c t u r e s and to Mr. Jos6 Reyes, A. S 6 n c h e z and R. Hern6ndez far technical assistance. We w o u l d like to thank for m a n y u s e f u l l c o m m e n t s on image p r o c e s s i n g to Dr. A. S e r r a n o of IAUNAM. This w o r k w a s s u p p o r t e d by the C O N A C Y T t h r o u g h g r a n t Ha. P U T / P Q / N A L / 2 6 5 1 .
Vol.
20,
No.
3
QUASICRYSTALLINE
T PHASE IN A1 Mn
403
1.
O. Shechtmon, I. Blech, D. G r a t i o s and J.W. Cahn Phys. Rev. L e t t . 53, 1951 ( 1 9 8 4 ) . D. L e v i n e and P. S t e i n h a r d t - Phys. Rev. Lett. 53, 2477 ( . 1 9 8 4 ) . k. Bendersky, R.J. Schaefer, F.S. Biancanello, W.J. Boettinger, M.J. Kaufman and D. S h e c h t m a n - S c r i p t a M e t . 19, 909 ( 1 9 8 5 ) . k. B e n d e r s k y - P h y s . R e v . L e t t . 55, 1461 ( 1 9 8 5 ) . K . F . K e l t o n and T.W. Wu - A p p l . Phys. Lett. 46, 1059 ( 1 9 8 5 ) . B.K. Vainshtein, Diffraction of X-rays by chain molecules, Elsevier P u b l i s h i n g Company Amsterdam-London-New York ( 1 9 6 6 ) .
References
2. 3. 4. 5. 6.
O
FIG.
1
S e l e c t e d area d i f f r a c t i o n the T p h a s e in A186 Mn]4 ten
fold,
fold axis.
b)
3-foIa
axis
p a t t e r n of s h o w i n g a) c)
two-
404
QUASICRYSTALLINE
T PHASE
IN AI Mn
Vol.
20, No. 3
m •
i
O
@ ®
Q
O
FIG. Comparison of diffraction Qreo, b) m i c r o d i f f r o c t i o n
p a t t e r n s f r o m t h e some a r e a o f on a r e a o f 20 nm i n s i z e .
FIG.
Bright tilting
2
field images of the o) i n i t i a l position,
o)
selected
3
T-phase showing change of contrast b) a f t e r o few degrees tilt.
with
Vol.
20, No.
3
QUASICRYSTALLINE
T PHASE
FIG.
a) High resolution processing, b) F o u r i e r
image of transform
the of
IN A1 Mn
405
4
T-phase obtained the image.
FIG.
after
image
5
Weak beam d a r k f i e l d of the T phase along fold axis. The i n s e t the conditions for the (processed image).
image a 3shows image
METALLURGICA
ON THE
Vol. 20, pp. 4 0 1 - 4 0 5 , 1986 P r i n t e d in the U . S . A .
STRUCTURE
OF
THE
IN A186
P e r g a m o n P r e s s Ltd. All rights reserved
QUASICRYSTALLINE Mnl4
T PHASE
ALLOY
R.
+
On
leave
from
P~rez-Campos, J.G. P~rez-Rom~rez + A G6mez R. H e r r e r o and M. J o s ~ - Y o c a m 6 n I n s t i t u t o de F i s i c o , U . N . A . M . P. O. Box 2 0 - 3 6 4 , 0 1 0 0 0 M 6 x i c o , O.P. M~xico the ESFM, IPN, M ~ x i c o . (Received
I .-
December
9,
1985)
Introduction
Recent s t u d i e s of p h a s e f o r m a t i o n in r a p i d l y s o l i d i f i e d A I - M n a l l o y s hove shown the e x i s t e n c e of o p h a s e w i t h l o n g - r a n g e o r i e n t a t i o n o l o r d e r and i c o s o h e drol point g r o u p s y m m e t r y (m3S) (I). T h e s e new t y p e s of q u o s i p e r i o d i c structures ore a l r e a d y k n o w n as " q u a s i c r y s t o l s " (2). S t u d i e s of p h a s e f o r m a t i o n at s l o w e r s o l i d i f i c a t i o n rotes h o v e s h o w n that the i c o s a h e d r o l p h a s e is r e p l a c e d by the so-called T p h a s e (3). This p h a s e is a q u a s i c r y s t a l w i t h one-dimensional periodicity and planar quasiperiodicity in the o t h e r two d i m e n s i o n s (3) (4). The i c o s o h e d r o l and T p h a s e s ore c l o s e l y r e l a t e d in s t r u c t u r a l characteristics. For e x a m p l e , the d i f f r a c t i o n p a t t e r n s f r o m both s t r u c t u r e s h a v e s t r o n g s i m i l a r i ties (3). The i c o s o h e d r o l p h a s e of A I - 6 M n . has r e c e i v e d c o n s i d e r a b l e a t t e n t i o n in the literature, however, t h e r e ~ a v e 1 ~ e e n v e r y few i n v e s t i g a t i o n s on the structural c h a r a c t e r i s t i c s of the T p h a s e . In this c o m m u n i c a t i o n we r e p o r t on i n v e s t i g a t i o n on the s t r u c t u r e of the T p h a s e . This s t u d y was c a r r i e d out u s i n g different techniques such as: c o n v e n t i o n a l and high-resolution transmission electron microscopy, microdiffroction and i m a g e p r o c e s s i n g . The methods of sample p r e p a r a t i o n and c h a r a c t e r i z a t i o n by A u g e r s c a n n i n g m i c r o s c o p y and other m e t h o d s will be r e p o r t e d e l s e w h e r e . 2.-
Experimental
Results
The identification of the T p h a s e was c a r r i e d out using selected area diffraction p a t t e r n s (SAOP) f r o m the s u s p e c t e d a r e a s in the specimens. These p a t t e r n s w e r e o b t a i n e d for d i f f e r e n t o r i e n t a t i o n s . In o r d e r to a s s u r e that the entire groin hod long range o r i e n t o t i o n o l o r d e r and therefore that apparent quosiperiodicity was not p r o d u c e d by m u l t i p l e t w i n n i n g of o small c r y s t o l l i t e s , microdiffroction p a t t e r n s (with b e a m size ~ 20nm) w e r e o b t a i n e d from different r e g i o n s in the g i v e n g r o i n . T h e s e r e s u l t s ore i l l u s t r a t e d in Figs. 1o, b and c w h i c h show SADP w h i c h c o r r e s p o n d to the t e n - f o l d , t h r e e - f o l d and t w o - f o l d o r i e n tations. These p a t t e r n s s h o w o spot d i s t r i b u t i o n f o l l o w i n g the F i b o n o c c i seq u e n c e in two d i r e c t i o n s and o n o r m a l p e r i o d i c i t y in one d i r e c t i o n . It is i m p o r t a n t to n o t i c e the p r o n o u n c e d s t r e a k i n g in these diffraction patterns. Fig. 2o, b s h o w SADP and m i c r o d i f f r o c t i o n p a t t e r n s o b t a i n e d from the some area in the s p e c i m e n . As it is i l l u s t r a t e d in the figure) both d i f f r a c t i o n p a t t e r n s ore s i m i l a r . The some b e h a v i o r has been o b s e r v e d in microdiffroction patterns from o t h e r a r e a s . This shows that the f i v e - f o l d s i m m e t r y is not the r e s u l t of m u l t i p l e t w i n i n g of s e v e r a l c r y s t o l l i t e s . Most of the q u a s i c r y s t a l i n e a r e a s (T phase) f o u n d in our s p e c i m e n s show o characteristic s t r i o t e c o n t r a s t u n d e r b r i g h t or d a r k f i e l d i m a g i n g . This controst has been found to depend strongly on t h e t i l t i n g of the specimen. Thus, for example, Fig. 30 s h o w s on image B r i g h t F i e l d (BF) w i t h this pronounced c o n t r o s t ~ h o w e v e r , Fig. 3b s h o w s the some area in a n o t h e r o r i e n t a t i o n , in this
401 0 0 3 6 - 9 7 4 8 / 8 6 $ 3 . 0 0 + .00 C o p y r i g h t (c) 1986 P e r g a m o n P r e s s
Ltd.
402
QUASICRYSTALLINE
T PHASE
IN AI M n
Vol.
20, No.
3
case the above mentioned contrast has almost dissapeared. This contrast is similar to the one reported before for the icosahedral phase (5) and it has been associated with local strain fields in the phase. It should be n o t e d ~ h o w e v e r , that the observed contrast is more pronounced with respect to that found in conventional bright field images of strained crystals. A more detailed examination of this effect is necessary in ord~r to understand its origin. High resolution images [HREM) w e r e o b t a i n e d with an incident beam parallel to a two-fold zone axis. This orientation makes an angle o f 90 ° w i t h the fivefold axis. Most of the o r i g i n a l i m a g e s s h o w p o o r c o n t r a s t and we decided to c a r r y out an image p r o c e s s i n g a p p r o a c h on t h e s e m i c r o g r a p h s . Figs. 4a and b show an image and its c o r r e s p o n d i n g Fourier transform. The f i r s t i n t e r e s t i n g point to note from H R E M i m a g e s is the c o n t r a s t w h i c h c l e a r l y s u g g e s t s on arrangement of linear c h a i n s w h i c h a p p e a r to be p e r i o d i c a l l y twisted forming a kind of spiral s t r u c t u r e . The e x i s t e n c e of t h e s e t w i s t e d c h a i n s is a l s o supported from the SADP's (Fig. I) w h i c h c l e a r l y s h o w the p r e s e n c e of s h e e t s of i n t e n s i t y in r e c i p r o c a l space. This is o c o m m o n e f f e c t o b t a i n e d in the d i f f r a c t i o n of Xrays by chain m o l e c u l e s (6). This b e h a v i o r can a l s o be seen in the Fourier transform of the d i g i t i z e d i m a g e s h o w n in Fig. 40. This is a l s o s u p p o r t e d by the fact that in the p a t t e r n s the s p o t s ore not p e r f e c t l y o l l i g n e d a l o n g o row of i n t e n s i t y . The r e p e a t d i s t a n c e a l o n g the p e r i o d i c d i r e c t i o n was f o u n d to be 0 . 8 0 6 n m in a g r e e m e n t w i t h Ref. (4). The i m a g e s i n d i c a t e that the chains ore t w i s t e d over a l e n g t h of ~ 4 . 2 nm. Weak beam dark field images (WDF) w e r e o b t a i n e d for the T phase with the incident beam p a ' r a l l e l to a three-fold zone axis. The main reflection used for these i m a g e s was those in the corners of the 3-fold diffraction pattern shown in Fig. 5b. H o w e v e r , it is i m p o r t a n t to m e n t i o n that m o r e than one r e f l e c t i o n along o row was a l l o w e d to pass t h r o u g h the objective aperture. The same p r o c e s s i n g a p p r o a c h a b o v e m e n t i o n e d w a s a p p l i e d to t h e s e dark f i e l d m i c r o g r o p h s . Fig. 5 shows one of the r e c o n s t r u c t e d images. In this c a s e the f r i n g e s c o r r e s pond to the i n t e r f e r e n c e b e t w e e n s p o t s a l o n g o row. T h e r e f o r e , the b r i n g e s run p e r p e n d i c u l a r to the c h a i n d i r e c t i o n . T h e r e f o r e , this k i n d of image con p r o v i d e information a b o u t the F i b u n o c c i m o d u l a t i o n a l o n g the rows of i n t e n s i t y o b s e r v e d on t h e p a t t e r n s . The bringes hove a wavy a~pearance and many times ore shifted. Also extra lines produce a dislocation-like contrast (see arrow on t h e figure). These k i n d o f e f f e c t s might be d u e t o a t h i c k n e s s modulation or to a true defect structure along the chain boundaries.
3.-
Conclusions
The m o s t i m p o r t a n t r e s u l t w h i c h con be o b t a i n e d f r o m our i n v e s t i g a t i o n s is that the quasicrystalline T p h a s e of A I ^ . M n . . is m a d e of an arrangement of linear c h a i n s w h i c h ore p e r i o d i c a l l y t w i s t e d . 14 This s t a t e m e n t is b a s e d on the experimental e v i d e n c e of high r e s o l u t i o n and m i c r o d i f f r a c t i o n . This s t r u c t u r e was p r e v i o u s l y s u g g e s t e d by 8 e n d e r s k y (4) on the b a s i s of the p l a n a r intensity on the d i f f r a c t i o n p a t t e r n s . The high r e s o l u t i o n and dark f i e l d i m a g e s r e s u l t s in this work c o n f i r m the c h a i n one d i m e n s i o n a l s t r u c t u r e . 4.-
Acknowledgements
The a u t h o r s ore i n d e b t e d to Dr. L o r e n z o M o r t f n e z a n d J.L. A l b a r r 6 n his team for p r e p a r i n g the a l l o y s . We a l s o t h a n k to Mr. F. R u i z for o b t a i n i n g the high resolution p i c t u r e s and to Mr. Jos6 Reyes, A. S 6 n c h e z and R. Hern6ndez far technical assistance. We w o u l d like to thank for m a n y u s e f u l l c o m m e n t s on image p r o c e s s i n g to Dr. A. S e r r a n o of IAUNAM. This w o r k w a s s u p p o r t e d by the C O N A C Y T t h r o u g h g r a n t Ha. P U T / P Q / N A L / 2 6 5 1 .
Vol.
20,
No.
3
QUASICRYSTALLINE
T PHASE IN A1 Mn
403
1.
O. Shechtmon, I. Blech, D. G r a t i o s and J.W. Cahn Phys. Rev. L e t t . 53, 1951 ( 1 9 8 4 ) . D. L e v i n e and P. S t e i n h a r d t - Phys. Rev. Lett. 53, 2477 ( . 1 9 8 4 ) . k. Bendersky, R.J. Schaefer, F.S. Biancanello, W.J. Boettinger, M.J. Kaufman and D. S h e c h t m a n - S c r i p t a M e t . 19, 909 ( 1 9 8 5 ) . k. B e n d e r s k y - P h y s . R e v . L e t t . 55, 1461 ( 1 9 8 5 ) . K . F . K e l t o n and T.W. Wu - A p p l . Phys. Lett. 46, 1059 ( 1 9 8 5 ) . B.K. Vainshtein, Diffraction of X-rays by chain molecules, Elsevier P u b l i s h i n g Company Amsterdam-London-New York ( 1 9 6 6 ) .
References
2. 3. 4. 5. 6.
O
FIG.
1
S e l e c t e d area d i f f r a c t i o n the T p h a s e in A186 Mn]4 ten
fold,
fold axis.
b)
3-foIa
axis
p a t t e r n of s h o w i n g a) c)
two-
404
QUASICRYSTALLINE
T PHASE
IN AI Mn
Vol.
20, No. 3
m •
i
O
@ ®
Q
O
FIG. Comparison of diffraction Qreo, b) m i c r o d i f f r o c t i o n
p a t t e r n s f r o m t h e some a r e a o f on a r e a o f 20 nm i n s i z e .
FIG.
Bright tilting
2
field images of the o) i n i t i a l position,
o)
selected
3
T-phase showing change of contrast b) a f t e r o few degrees tilt.
with
Vol.
20, No.
3
QUASICRYSTALLINE
T PHASE
FIG.
a) High resolution processing, b) F o u r i e r
image of transform
the of
IN A1 Mn
405
4
T-phase obtained the image.
FIG.
after
image
5
Weak beam d a r k f i e l d of the T phase along fold axis. The i n s e t the conditions for the (processed image).
image a 3shows image