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High resolution neutron diffraction study on Fe81B19 metallic glass
~
Solid State Communications, Printed in Great Britain.
HIGH
RESOLUTION
Vol.44,No.8,
NEUTRON
DIFFRACTION E.
Central
Research
Institute
S.N. I.V.
Atomic
(Received
Svab,
for
Ishmaev,
Kurchatov
pp.1151-I155,
STUDY N.
Physics, Hungary
I.P.
ON F e 8 1 B 1 9
H-1525
METALLIC
Budapest,
A.A.
Institute
1982
0038-1098/82/441151-05503.00/0 Pergamon Press Ltd.
GLASS
Kroo
Sadikov,
Energy
1 August
1982.
by A.
114,
P.0.B.
49,
Chernyshov 123182
Moscow,
USSR
Zawadowski)
The s t r u c t u r e f a c t o r of F e ~ B metallic glass was mea• ~l 1 Q - . . sured by the conventlonal and tlme-of-~llght neutron d i f f r a c t i o n m e t h o d s in the 0 . 4 < Q < 2 4 ~- ± m o m e n t u m t r a n s fer r a n g e , y i e l d i n g h i g h r e s o l u t i o n ( ~ 0 . 2 6 ~) in r - s p a c e . The p a i r d i s t r i b u t i o n f u n c t i o n o b t a i n e d by F o u rier transformation is r e s o l v e d i n t o s u b p e a k s . The distances and distribution w i d t h s of t h e F e - B a n d F e - F e first neighbours, the p a r t i a l c o o r d i n a t i o n numbers and t h e s h o r t r a n g e o r d e r p a r a m e t e r are given. The r e s u l t s clearly indicate preferential chemical bonding between i r o n a n d b o r o n atoms.
i.
w a s not p o s s i b l e in p r e v i o u s w o r k s . Furthermore the f i r s t n e i g h b o u r d i s tances, coordination numbers and the s h o r t r a n g e o r d e r p a r a m e t e r are g i v e n .
Introduction
Recently several experiments have been performed in o r d e r to o b t a i n detailed information about the short range o r d e r in m e t a l l i c g l a s s e s a n d to c l a r i f y the r o l e of c h e m i c a l i n t e r a c t i o n s , rev i e w s are g i v e n , for e x a m p l e in r e f s . l , 2 The m a i n t a s k of s c a t t e r i n g e x p e r i m e n t s is to d e t e r m i n e t h e p a r t i a l a t o m i c c o r r e l a t i o n f u n c t i o n s p r o v i d i n g the m o s t direct s t r u c t u r a l information. On t h e F e - B amorphous system several recent investig a t i o n s are known, p e r f o r m e d r e c e n t l y ; combined X-ray and neutron diffraction on n a t u r a l 3 a n d u s i n g 57Fe i s o t o p e subs t i t u t e d s a m p l e s 4, ~ i m e - o f - f l i g h t (TOF) n e u t r o n d i f f r a c t i o n I, e n e r g y d i s p e r s i v e X-ray diffraction (EDXD) ° a n d e x t e n d e d X-ray absorption fine s t r u c t u r e (EXAFS measurements. The s t r u c t u r a l parameters o b t a i n e d in the v a r i o u s w o r k s are r a t h e r different (see T a b l e 2). The high Q-range measurements, w h e r e the p a r t i a l s t r u c t u r a l p a r a m e t e r s can be o b t a i n e d f r o m a s i n g l e m e a s u r e m e n t , h a v e t h e a d v a n t a g e in c o n t r a s t to the c o m b i n e d d i f f r a c t i o n methods, that some p r o b l e m s l i k e n o r m a l i z a t i o n of three independent measurements and unaccuracies originating f r o m the s e p a r a tion procedure into p a r t i a l s t r u c t u r e f a c t o r s are a v o i d e d . In t h i s p a p e r the r e s u l t s of h i g h Q - r a n g e T O F n e u t r o n diffraction experiment are d e s c r i b e d on F e s I B I 9 m e t a l l i c g l a s s m e a s u r e d w i t h m o r e t h a n one o r d e r b e t t e r s t a t i s t i c s t h a n r e p o r t e d by us e a r l i e r 5 as preliminary data. From t h e p r e s e n t d a t a the fluctuation of the F e - B a n d F e - F e f i r s t n e i g h b o u r d i s t a n c e s can be o b tained with satisfactory accuracy which
2.
Experimental
The same s a m p l e and t h e same n e u tron diffraction equipments as u s e d previously 5 were used here therefore o n l y the m o s t i m p o r t a n t p a r a m e t e r s of the e x p e r i m e n t a l conditions are g i v e n . The Fe81BIo metallic glass sample e n r i c h e d in ~ I I B i s o t o p e (99.2 %) was p r e p a r e d by r a p i d q u e n c h i n g from the m e l t . The ~ 3 m m w i d e a n d ~ 2 0 ~ t h i c k r i b b o n s of 16 g t o t a l w e i g h t w e r e w o u n d on a v a n a d i u m tube. T w o t y p e s of n e u t r o n d i f f r a c t i o n measurements w e r e c o m b i n e d to o b t a i n the S(Q) s t r u c t u r e f a c t o r . In t h e r e l atively low scattering vector range Q = O . 4 - 1 0 ~ - i the m e a s u r e m e n t was perf o r m e d on a d o u b l e axis n e u t r o n d i f fractometer at t h e W W R S - M r e a c t o r in Budapest. The magnetic scattering was separated by using 1.8 T magnetic field. In t h e h i g h Q = 5 - 4 8 ~ - i s c a t t e r i n g v e c t o r r a n g e t h e s c a t t e r i n g was m e a s u r e d b y m e a n s of a T O F n e u t r o n d i f f r a c t o m e t e r i n s t a l l e d at the e l e c t r o n L I N A C p u l s e d n e u t r o n s o u r c e in M o s c o w K u r c h a t o v Inst i t u t e . A l t h o u g h the s c a t t e r e d s p e c t r u m w a s m e a s u r e d up to Q = 4 8 ~ - l t h e d a t a of the s t r u c t u r e ~ a c t o r , S(Q) w e r e u s e d only up to 2h ~ - ~ in the F o u r i e r t r a n s f o r mation process since the small osci~at i o n in S(Q) for h i g h e r s c a t t e r i n g v e c tors are b u r i e d in t h e b a c k g r o u n d . This is due to the s t a t i s t i c a l e r r o r of S(Q) b e i n g a b o u t 1.2 % at Q = 2 0 ~ - l
1151
1152
DIFFRACTION STUDY ON Fe81BI9 METALLIC GLASS 3.
Results
and
The reduced distribution function can be w r i t t e n as the w e i g h t e d sum of the p a r t i a l a t o m i c d i s t r i b u t i o n funct i o n s , w h i c h can be g i v e n in our c a s e as
Discussion
The S(Q) s t r u c t u r e f a c t o r , as seen in F i g . l d i s p l a y s s m a l l b u t w e l l d e f i n e d oscillations up to Q = 2 4 ~-i. The G(r) r e d u c e d a t o m i c d i s t r i b u t i o n f u n c t i o n was d e d u c e d f r o m S(Q) b y F o u r i e r transformation u s i n g the u s u a l e q u a t i o n Qmax 2 G(r)=-~-# Q(S(Q)-l) sin Qr dr. (1)
G(r)=0.758 GFeFe(r)+0.225
Table
,
O IO<¢
I¢/)
H a l f w i d t h v a l u e s A(~) of t h e split f i r s t p e a k l i n G(r) for v a r i o u s Q m a x (~-±) t r u n c a t i o n s in F o u r i e r t r a n s f o r m a t i o n
~max
AFT
16,4 19.2 23.2
0.232 0.198 0.164
meas
0.32 0.30 0.27
AFeBreal 0.22 0.22 0.21
meas
AFeFereal
0.47 0.46 0.44
0.41 0.41 0.41
1
FeB1 B19
," "'i -. , ../""}- . /".,.: ..... .:"..<..'..."...1]
2,5
0.%
M. I,M t,p. tO
I
..
-3,5
1.o41' ",
GFeB(r)+0.017 GBB(r).(2)
S i n c e the B - B c o n t r i b u t i o n is less t h a n 2 % it can be n e g l e c t e d a n d the r e s o l v e d s u b p e a k s of the f i r s t c o o r d i n a t i o n shell of F i g . 2 can be r e l a t e d to t h e F e - B f i r s t n e i g h b o u r d i s t a n c e at r_ _ = 2 . 1 6 + 0 03 • ~ e ~ -" . a n d to the F e - F e f l r s t n e l g h b o u r d i s t a n c e at r F _ = 2 . 5 5 + 0 . 0 2 ~. F r o m the a n a l y s i s of efe -. t h e s e s u b p e a k s an i m p o r t a n t p a r a m e t e r can be e v a l u a t e d viz. t h e w i d t h of the a t o m i c distance distribution ( f u l l w i d t h at h a l f height), characterizing the f l u c t u a t i o n of the f i r s t n e i g h b o u r distance. These widths are c o l l e c t e d in T a b l e i for s e v e r a l u p p e r l i m i t s of t r u n c a t i o n in the F o u r i e r t r a n s formation.
The finite integration r a n g e l e a d s to a limited resolution in r - s p a c e (Ar=2H/Qmax). In our e x p e r i m e n t the measured momentum t r a n s f e r r a n g e w a s e x t e n d e d to h i g h e r v a l ues t h a n t h a t in t h e u s u a l c o n v e n t i o n a l measurements, thereby resulting in h i g h e r resolut~n in t h e d i s t r i b u t i o n function. In o r d e r to d e m o n s t r a t e the e f f e c t of increased resolution on t h e o b s e r v a b l e fine s t r u c t u r e of G ( r ) , a set of d i s t r i b u t i o n functions was calculated with increasing u p p e r l i m i t s of t r u n c a t i o n in S(Q). S o m e of t h e s e f u n c t i o n s are s h o w n in Fig. 2. The v a l u e of t h e a p p r o p r i a t e Qmax was c h o s e n in e a c h case at p o s i t i o n s w h e r e S(Qmax)=O in o r d e r to m i n i m i z e t r u n c a t i o n oscillations at s m a l l a t o m i c d i s t a n c e s . F r o m Fig. 2 it is o b v i o u s t h a t w i t h increasing truncation the f i r s t p e a k of G(r) s p l i t s a n d t h e s e c o n d p e a k s h o w s a well pronounced fine ~ t r u c t u r e .
v
Vol. 44, No. 8
.... "''"" ""'/,," "<'',', "-....i-'":', ", I
1.5
1 0.5~ 10 ,
i
,
i
SCATTERING Fig.
i
Structure
I
, |
i
VECTOR, factor
for
,
15 I
,
210
i
Q[ ~_1] Fe81BI9
metallic
glass
,
/
Vol. 44, No. 8
DIFFRACTION -6
Fe-Fe
s -4 -3
1153
STUDY ON Fe8IBI9 METALLIC GLASS
FeB1 B19
3 [i"]
Qmax
Fe-Fe
[ Fe-B
FeET |
-2
,
23.2
:'.
"
[
L?'<
F ,..,.
J
/ Fe-Fe
'!
1
...°,,
• ..-'..
"
l:. . . .
.
"
.,"
,
" " ....
ff o Z
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-"
!
"'""'""u....
..'"'"'"..., ". ..... ." .
...--"... "
I.''.
"'
:-o'.....,
0
a
3
'
135
L
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/'1
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'/ tl
~'
.'
t
t
.
"',
"
'".
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:
.-"
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1
2
3
4
5
6
7
8
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I
I
I
i
o
ATOMIC
Fig.
2
DISTANCE,
r[A]
Reduced distribution function for v a r i o u s truncations in Fourier transformation
The broadening of t h e r e a l a t o m i c d i s tance distribution c a u s e d by t h e F o u r i e r transformation in a f i n i t e i n t e g r a t i o n r a n g e c a n be o b t a i n e d ~ as A F T = 3 . 8 / Q m a x . T h e r e a l w i d t h of F e - B a n d F e - F e f i r s t neighbour distance distribution was calculated using a Gaussian approximation i.e. t h e ( A r e a l ) 2 = ( A m e a s ) 2 - ( A F T ) 2 ex- ' pression. The main characteristics of t h e obtained results is, t h a t t h e F e - B d i s tribution is s i g n i f i c a n t l y smaller than t h a t of t h e F e - F e d i s t r i b u t i o n , being ~ A~r e a~l = 0 . 2 2 + 0 . 0 3 ~ and A~e~l=0.41+O.02 ~en . -~e -respectlvely. This resu~ proves that e
r o l e of c h e m i c a l interactions c a n n o t be neglected in t h e s t r u c t u r e model calculations. The importance of t h e f i r s t neighhour distribution width, characteri z i n g t h e s h o r t r a n g e o r d e r in m e t a l l i c glasses was recently emphazisedg. There the fluctuation of t h e F e - B d i s t a n c e was determined indirectly using the measured high-pressure dependence of M o s s b a u e r parameters resulting in A~ ~ = 0 . 2 0 ~. T h i s . , v e r y g o o d a g r~eee~m e n t r e s u l t is in w l.t h our data. The Z ~ partial first neighbour . °aD coordlnatlon numbers were calculated as
||54
DIFFRACTION STUDY ON Fe81B]9 METALLIC GLASS
Zab
=
c b Nab Wab
,
(3)
w h e r e a a n d b are s t a n d i n g for Fe a n d B atoms, respectively, Ca,C b is t h e c o n c e n t r a t i o n , W a b is t h e w e i g h t i n g factor and N a b is t h e a r e a of t h e c o r r e s p o n d i n g subp e a k s in the r a d i a l d i s t r i b u t i o n function, RDF(r)=4Hr2Po+rG(r). F o r the i n v e s t i g a t e d Fe81BI o sample the average atomic density ~i0 is p = 0 . 0 9 2 0 a t o m ~-3. S h o r t range order coefficients were recently i n t r o d u c e d by C a r g i l l II to d e s c r i b e t h e chemical short range order (deviation from random distribution) of t w o c o m p o n e n t amorphous alloys with very different concentrations, t h a t is, C a > > C b. T h e y are d e f i n e d as
o
qab
qab
max
' where
qab
qab
Zab Cb Za Zb
-i
and
max qab =
Cb Ca
Zb Za
(4)
Here Za=Zaa+Zab and Zb=Zbb+Zba are t h e nearest neighbours of a a n d b a t o m s , r e s pectively, a n d : C a Z a + e b Z b is the a v e r a g e n u m b e r of t h e f i r s t n e i g h b o u r s . In t h e case of c o m p l e t e chemical disord e r q a b = 0 w h e r e a s for c o m p l e t e c h e m i c a l o r d e r , i.e. w i t h p r e f e r e n c e for a-b n e a r e s t n e i g h b o u r p a i r S , n a b t a k e s its m a x i m u m v a l u e a n d the n o r m a l i z e d coeff i c i e n t b e c o m e s u n i t y . T h i s f o r m a l i s m is very convenient for c o m p a r i n g t h e c h e m i c a l o r d e r i n g of s y s t e m s w i t h d i f f e r e n t concentrations. The o b t a i n e d d a t a of t h e f i r s t neighbour distances, the p a r t i a l f i r s t neighbour coordination numbers and the normalized short range order parameter for F e - B a m o r p h o u s a l l o y s as m e a s u r e d by v a r i o u s m e t h o d s are c o l l e c t e d in T a b l e 2. The a g r e e m e n t b e t w e e n the g i v e n p a r a m e t e r s in the last t h [ e ~ w o r k s , i.e. the p r e s e n t one a n d refs. " , ~ is good. The slight difference b e t w e e n the short range order parameters calculated from h the p a r t i a l c o o r d i n a t i o n n u m b e r s in r e f . Table
2
D a t a for f i r s t n e i g h b o u r dist a n c e s r ~ (~), p a r t i a l c o o r d i • aD natlon numbers Z b and normal. a zzed short range order parameo t e r qab for F e - B m e t a l l i c glasses measured by various methods
rFeFe rFeB Fe
B 2.56 83~17
Fe80~20
2.55 2.55
Fe75B25 2.57 80~20 re81~19 2.55
2.27
o ZFeFe ZFeB ZBFe ~ab 10.7
2.25 2.14
. .
2.14 2.16
12,4 10.6
2.6 . .
. .
6.9 . .
2.16 8.64 1.9 8.3
-
refs.
3 7 6
1 4 0.8 present
Vol. 44, No. 8
a n d t h e p r e s e n t w o r k can be e x p l a i n e d by the l i m i t e d a c c u r a c y of Zab data. T h e r e s u l t of b o t h w o r k s , as seen in T a b l e 2, o s h o w s t h a t q a b is n e a r to u n i t y , m e a n i n g a h i g h d e g r e e of c h e m i c a l o r d e r i.e. a preference for u n l i k e a t o m i c n e i g h b o u r s in t h i s m e t a l - m e t a l l o i d amorphous alloy. It s h o u l d be m e n t i o n e d that this short range order parameter is v e r y s e n s i t i v e to t h e c o o r d i n a t i o n n u m b e r v a l u e s . This can be s e e n f r o m its n o n p h y s i c a l l y high v a l u e of n ° ~ = 9 . 7 2 as can be c a l c u l a t e d ao . f r o m the p a r t l a l c o o r d i n a t i o n n u m b e r s , as g i v e n in ref. 3 A further consequence of the h i g h e r r-space resolution is t h e a p p e a r a n c e of fine s t r u c t u r e in the second n e i g h b o u r peak of G(r). The two m a i n s u b p e a k s at 4.25 ~ a n d 4 . 9 ~ w h i c h are g e n e r a l l y o b ser ~ d for a m o r p h o u s a l l o y s b e c o m e m o r e pronounced a n d t h e N are s l i g h t l y s h i f t e d to 4.15 ~ and 5.0 ~, r e s p e c t i v e l y . At the same t i m e n e w s m a l l s u b p e a k s m a y be o b s e r v e d at 4.6 ~ and at 3.6 ~ . T h e o r i g i n of t h e s e s u b p e a k s can be u n d e r s t o o d by c o m p a r i n g G(r) w i t h r e s u l t s o b t a i n e d r e c e n t l y by the h i g h r e s o l u t i o n E D X D m e t h o d ~ on F e 7 5 B 2 5 . On t h e b a s i s of a qualitative comparlson t h e two m a i n s u b p e a k s can be a t t r i b u t e d to t h e s e c o n d n e i g h b o u r F e - F e p a i r s , w h e r e a s the s m a l l s u b p e a k s can be a t t r i b u t e d to s e c o n d n e i g h b o u r F e - B p a i r s . The a g r e e m e n t bet w e e n the p r e s e n t c o n c l u s i o n s and the data given forhthe second neighbour dist a n c e s in r e f . - - w h i c h were obtained using different experimental methods s u p p o r t the a c t u a l e x i s t e n c e of the fine s t r u c t u r e in t h e s e c o n d c o o r d i n a t i o n s h e l l for the Fe-B m e t a l l i c glass. 4.
Conclusions
Due to t h e h i g h r e s o l u t i o n in r - s p a c e originating from this wide Q-range measu r e m e n t , the f i r s t p e a k in G(r) w a s r e s o l v e d into F e - B a n d F e - F e f i r s t n e i g h bour distributions a n d fine s t r u c t u r e was o b s e r v e d in the s e c o n d c o o r d i n a t i o n shell. Parameters characterizing the short r a n g e o r d e r in t h i s a m o r p h o u s system were o b t a i n e d : the f i r s t n e i g h b o u r F e - B a n d Fe-Fe distances, coordination numbers and short r a n g e o r d e r p a r a m e t e r showing preferential coordination b e t w e e n u n l i k e atomic neighbours. Furthermore the w i d t h of the r e s o l v e d f i r s t n e i g h b o u r p e a k s in C(r) w a s o b t a i n e d w i t h s a t i s f y i n g accur a c y and it was o b s e r v e d t h a t t h e f l u c t u a t i o n of t h e F e - B d i s t a n c e is s i g n i f i c a n t l y s m a l l e r t h a n t h a t of the F e - F e pairs. This clearly demonstrates a strong chemical interaction between iron and b o r o n atoms. Acknowledgement - we are g r a t e f u l to A. L o v a s for p r e p a r i n g the sample, to F. F o r g a c s for s o f t w a r e w o r k s a n d to Drs T. K e m e n y a n d I. V i n c z e for h e l p f u l a n d stimulating discussions.
Vol. 44, No. 8
DIFFRACTION STUDY ON Fe81B19 METALLIC GLASS
1155
References
1. U. Gonser, " A p p l i c a t i o n of Nuclear T e c h n i q u e s to the Study of A m o r p h o u s Metals" Atomic Energy Review, Supplement ~, (1981) 2. Y. Waseda, P r o g r e s s in M a t e r i a l s Science 26, 1 (1981) 3. T. Fujiwara, H.S. Chen and Y. Waseda, J. Phys. F: Metal Phys. ll, 1327 (1981) 4. E. Nold, P. Lamparter, H. Olbrich, G. R a i n e r - H a r b a c h , S. Steeb, Z. Naturforsch. ~6, 1032 (1981) 5. E. Svab, S.N. Ishmaev, F. Forgacs, I.P. Sadikov, A.A. Chernyshov, Proc. of Int. Conf. on A m o r p h o u s Systems Inv e s t i g a t e d by Nuclear Methods, Balat o n f u r e d (1981) Vol. II. p. 833 (to
6.
7.
8. 9. i0. ll.
be p u b l i s h e d in Nucl. Instr• and Methods, 1982) S. Aur, T. Egami, I. Vincze, Proc. Conf. Rapidly Q u e n c h e d Metals IV., Sendal (1981) Vol• l, p. 351 M. De Crescenzi, A. Balzarotti, F. Comin, L. Incoccia, S. Mobilio, N. Motta, Solid State Comm. 37, 921 (1981) C•N•J. Wagner, H. R u p p e r s b e r g , see ref • 1 , p . 123 M.M. A b d - E l m e g u i d , H. Micklitz, I. Vincze, Phys. Rev. B, 25, i (1982) F. Hajdu, Phys. Stat. Sol. (a) 60, 365 (1980) G.S. Cargill III., F. Spaepen, J. of Non-Cryst. Solids 43, 91 (1981)
Solid State Communications, Printed in Great Britain.
HIGH
RESOLUTION
Vol.44,No.8,
NEUTRON
DIFFRACTION E.
Central
Research
Institute
S.N. I.V.
Atomic
(Received
Svab,
for
Ishmaev,
Kurchatov
pp.1151-I155,
STUDY N.
Physics, Hungary
I.P.
ON F e 8 1 B 1 9
H-1525
METALLIC
Budapest,
A.A.
Institute
1982
0038-1098/82/441151-05503.00/0 Pergamon Press Ltd.
GLASS
Kroo
Sadikov,
Energy
1 August
1982.
by A.
114,
P.0.B.
49,
Chernyshov 123182
Moscow,
USSR
Zawadowski)
The s t r u c t u r e f a c t o r of F e ~ B metallic glass was mea• ~l 1 Q - . . sured by the conventlonal and tlme-of-~llght neutron d i f f r a c t i o n m e t h o d s in the 0 . 4 < Q < 2 4 ~- ± m o m e n t u m t r a n s fer r a n g e , y i e l d i n g h i g h r e s o l u t i o n ( ~ 0 . 2 6 ~) in r - s p a c e . The p a i r d i s t r i b u t i o n f u n c t i o n o b t a i n e d by F o u rier transformation is r e s o l v e d i n t o s u b p e a k s . The distances and distribution w i d t h s of t h e F e - B a n d F e - F e first neighbours, the p a r t i a l c o o r d i n a t i o n numbers and t h e s h o r t r a n g e o r d e r p a r a m e t e r are given. The r e s u l t s clearly indicate preferential chemical bonding between i r o n a n d b o r o n atoms.
i.
w a s not p o s s i b l e in p r e v i o u s w o r k s . Furthermore the f i r s t n e i g h b o u r d i s tances, coordination numbers and the s h o r t r a n g e o r d e r p a r a m e t e r are g i v e n .
Introduction
Recently several experiments have been performed in o r d e r to o b t a i n detailed information about the short range o r d e r in m e t a l l i c g l a s s e s a n d to c l a r i f y the r o l e of c h e m i c a l i n t e r a c t i o n s , rev i e w s are g i v e n , for e x a m p l e in r e f s . l , 2 The m a i n t a s k of s c a t t e r i n g e x p e r i m e n t s is to d e t e r m i n e t h e p a r t i a l a t o m i c c o r r e l a t i o n f u n c t i o n s p r o v i d i n g the m o s t direct s t r u c t u r a l information. On t h e F e - B amorphous system several recent investig a t i o n s are known, p e r f o r m e d r e c e n t l y ; combined X-ray and neutron diffraction on n a t u r a l 3 a n d u s i n g 57Fe i s o t o p e subs t i t u t e d s a m p l e s 4, ~ i m e - o f - f l i g h t (TOF) n e u t r o n d i f f r a c t i o n I, e n e r g y d i s p e r s i v e X-ray diffraction (EDXD) ° a n d e x t e n d e d X-ray absorption fine s t r u c t u r e (EXAFS measurements. The s t r u c t u r a l parameters o b t a i n e d in the v a r i o u s w o r k s are r a t h e r different (see T a b l e 2). The high Q-range measurements, w h e r e the p a r t i a l s t r u c t u r a l p a r a m e t e r s can be o b t a i n e d f r o m a s i n g l e m e a s u r e m e n t , h a v e t h e a d v a n t a g e in c o n t r a s t to the c o m b i n e d d i f f r a c t i o n methods, that some p r o b l e m s l i k e n o r m a l i z a t i o n of three independent measurements and unaccuracies originating f r o m the s e p a r a tion procedure into p a r t i a l s t r u c t u r e f a c t o r s are a v o i d e d . In t h i s p a p e r the r e s u l t s of h i g h Q - r a n g e T O F n e u t r o n diffraction experiment are d e s c r i b e d on F e s I B I 9 m e t a l l i c g l a s s m e a s u r e d w i t h m o r e t h a n one o r d e r b e t t e r s t a t i s t i c s t h a n r e p o r t e d by us e a r l i e r 5 as preliminary data. From t h e p r e s e n t d a t a the fluctuation of the F e - B a n d F e - F e f i r s t n e i g h b o u r d i s t a n c e s can be o b tained with satisfactory accuracy which
2.
Experimental
The same s a m p l e and t h e same n e u tron diffraction equipments as u s e d previously 5 were used here therefore o n l y the m o s t i m p o r t a n t p a r a m e t e r s of the e x p e r i m e n t a l conditions are g i v e n . The Fe81BIo metallic glass sample e n r i c h e d in ~ I I B i s o t o p e (99.2 %) was p r e p a r e d by r a p i d q u e n c h i n g from the m e l t . The ~ 3 m m w i d e a n d ~ 2 0 ~ t h i c k r i b b o n s of 16 g t o t a l w e i g h t w e r e w o u n d on a v a n a d i u m tube. T w o t y p e s of n e u t r o n d i f f r a c t i o n measurements w e r e c o m b i n e d to o b t a i n the S(Q) s t r u c t u r e f a c t o r . In t h e r e l atively low scattering vector range Q = O . 4 - 1 0 ~ - i the m e a s u r e m e n t was perf o r m e d on a d o u b l e axis n e u t r o n d i f fractometer at t h e W W R S - M r e a c t o r in Budapest. The magnetic scattering was separated by using 1.8 T magnetic field. In t h e h i g h Q = 5 - 4 8 ~ - i s c a t t e r i n g v e c t o r r a n g e t h e s c a t t e r i n g was m e a s u r e d b y m e a n s of a T O F n e u t r o n d i f f r a c t o m e t e r i n s t a l l e d at the e l e c t r o n L I N A C p u l s e d n e u t r o n s o u r c e in M o s c o w K u r c h a t o v Inst i t u t e . A l t h o u g h the s c a t t e r e d s p e c t r u m w a s m e a s u r e d up to Q = 4 8 ~ - l t h e d a t a of the s t r u c t u r e ~ a c t o r , S(Q) w e r e u s e d only up to 2h ~ - ~ in the F o u r i e r t r a n s f o r mation process since the small osci~at i o n in S(Q) for h i g h e r s c a t t e r i n g v e c tors are b u r i e d in t h e b a c k g r o u n d . This is due to the s t a t i s t i c a l e r r o r of S(Q) b e i n g a b o u t 1.2 % at Q = 2 0 ~ - l
1151
1152
DIFFRACTION STUDY ON Fe81BI9 METALLIC GLASS 3.
Results
and
The reduced distribution function can be w r i t t e n as the w e i g h t e d sum of the p a r t i a l a t o m i c d i s t r i b u t i o n funct i o n s , w h i c h can be g i v e n in our c a s e as
Discussion
The S(Q) s t r u c t u r e f a c t o r , as seen in F i g . l d i s p l a y s s m a l l b u t w e l l d e f i n e d oscillations up to Q = 2 4 ~-i. The G(r) r e d u c e d a t o m i c d i s t r i b u t i o n f u n c t i o n was d e d u c e d f r o m S(Q) b y F o u r i e r transformation u s i n g the u s u a l e q u a t i o n Qmax 2 G(r)=-~-# Q(S(Q)-l) sin Qr dr. (1)
G(r)=0.758 GFeFe(r)+0.225
Table
,
O IO<¢
I¢/)
H a l f w i d t h v a l u e s A(~) of t h e split f i r s t p e a k l i n G(r) for v a r i o u s Q m a x (~-±) t r u n c a t i o n s in F o u r i e r t r a n s f o r m a t i o n
~max
AFT
16,4 19.2 23.2
0.232 0.198 0.164
meas
0.32 0.30 0.27
AFeBreal 0.22 0.22 0.21
meas
AFeFereal
0.47 0.46 0.44
0.41 0.41 0.41
1
FeB1 B19
," "'i -. , ../""}- . /".,.: ..... .:"..<..'..."...1]
2,5
0.%
M. I,M t,p. tO
I
..
-3,5
1.o41' ",
GFeB(r)+0.017 GBB(r).(2)
S i n c e the B - B c o n t r i b u t i o n is less t h a n 2 % it can be n e g l e c t e d a n d the r e s o l v e d s u b p e a k s of the f i r s t c o o r d i n a t i o n shell of F i g . 2 can be r e l a t e d to t h e F e - B f i r s t n e i g h b o u r d i s t a n c e at r_ _ = 2 . 1 6 + 0 03 • ~ e ~ -" . a n d to the F e - F e f l r s t n e l g h b o u r d i s t a n c e at r F _ = 2 . 5 5 + 0 . 0 2 ~. F r o m the a n a l y s i s of efe -. t h e s e s u b p e a k s an i m p o r t a n t p a r a m e t e r can be e v a l u a t e d viz. t h e w i d t h of the a t o m i c distance distribution ( f u l l w i d t h at h a l f height), characterizing the f l u c t u a t i o n of the f i r s t n e i g h b o u r distance. These widths are c o l l e c t e d in T a b l e i for s e v e r a l u p p e r l i m i t s of t r u n c a t i o n in the F o u r i e r t r a n s formation.
The finite integration r a n g e l e a d s to a limited resolution in r - s p a c e (Ar=2H/Qmax). In our e x p e r i m e n t the measured momentum t r a n s f e r r a n g e w a s e x t e n d e d to h i g h e r v a l ues t h a n t h a t in t h e u s u a l c o n v e n t i o n a l measurements, thereby resulting in h i g h e r resolut~n in t h e d i s t r i b u t i o n function. In o r d e r to d e m o n s t r a t e the e f f e c t of increased resolution on t h e o b s e r v a b l e fine s t r u c t u r e of G ( r ) , a set of d i s t r i b u t i o n functions was calculated with increasing u p p e r l i m i t s of t r u n c a t i o n in S(Q). S o m e of t h e s e f u n c t i o n s are s h o w n in Fig. 2. The v a l u e of t h e a p p r o p r i a t e Qmax was c h o s e n in e a c h case at p o s i t i o n s w h e r e S(Qmax)=O in o r d e r to m i n i m i z e t r u n c a t i o n oscillations at s m a l l a t o m i c d i s t a n c e s . F r o m Fig. 2 it is o b v i o u s t h a t w i t h increasing truncation the f i r s t p e a k of G(r) s p l i t s a n d t h e s e c o n d p e a k s h o w s a well pronounced fine ~ t r u c t u r e .
v
Vol. 44, No. 8
.... "''"" ""'/,," "<'',', "-....i-'":', ", I
1.5
1 0.5~ 10 ,
i
,
i
SCATTERING Fig.
i
Structure
I
, |
i
VECTOR, factor
for
,
15 I
,
210
i
Q[ ~_1] Fe81BI9
metallic
glass
,
/
Vol. 44, No. 8
DIFFRACTION -6
Fe-Fe
s -4 -3
1153
STUDY ON Fe8IBI9 METALLIC GLASS
FeB1 B19
3 [i"]
Qmax
Fe-Fe
[ Fe-B
FeET |
-2
,
23.2
:'.
"
[
L?'<
F ,..,.
J
/ Fe-Fe
'!
1
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• ..-'..
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l:. . . .
.
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.,"
,
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ff o Z
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-"
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t
t
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2
3
4
5
6
7
8
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I
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i
o
ATOMIC
Fig.
2
DISTANCE,
r[A]
Reduced distribution function for v a r i o u s truncations in Fourier transformation
The broadening of t h e r e a l a t o m i c d i s tance distribution c a u s e d by t h e F o u r i e r transformation in a f i n i t e i n t e g r a t i o n r a n g e c a n be o b t a i n e d ~ as A F T = 3 . 8 / Q m a x . T h e r e a l w i d t h of F e - B a n d F e - F e f i r s t neighbour distance distribution was calculated using a Gaussian approximation i.e. t h e ( A r e a l ) 2 = ( A m e a s ) 2 - ( A F T ) 2 ex- ' pression. The main characteristics of t h e obtained results is, t h a t t h e F e - B d i s tribution is s i g n i f i c a n t l y smaller than t h a t of t h e F e - F e d i s t r i b u t i o n , being ~ A~r e a~l = 0 . 2 2 + 0 . 0 3 ~ and A~e~l=0.41+O.02 ~en . -~e -respectlvely. This resu~ proves that e
r o l e of c h e m i c a l interactions c a n n o t be neglected in t h e s t r u c t u r e model calculations. The importance of t h e f i r s t neighhour distribution width, characteri z i n g t h e s h o r t r a n g e o r d e r in m e t a l l i c glasses was recently emphazisedg. There the fluctuation of t h e F e - B d i s t a n c e was determined indirectly using the measured high-pressure dependence of M o s s b a u e r parameters resulting in A~ ~ = 0 . 2 0 ~. T h i s . , v e r y g o o d a g r~eee~m e n t r e s u l t is in w l.t h our data. The Z ~ partial first neighbour . °aD coordlnatlon numbers were calculated as
||54
DIFFRACTION STUDY ON Fe81B]9 METALLIC GLASS
Zab
=
c b Nab Wab
,
(3)
w h e r e a a n d b are s t a n d i n g for Fe a n d B atoms, respectively, Ca,C b is t h e c o n c e n t r a t i o n , W a b is t h e w e i g h t i n g factor and N a b is t h e a r e a of t h e c o r r e s p o n d i n g subp e a k s in the r a d i a l d i s t r i b u t i o n function, RDF(r)=4Hr2Po+rG(r). F o r the i n v e s t i g a t e d Fe81BI o sample the average atomic density ~i0 is p = 0 . 0 9 2 0 a t o m ~-3. S h o r t range order coefficients were recently i n t r o d u c e d by C a r g i l l II to d e s c r i b e t h e chemical short range order (deviation from random distribution) of t w o c o m p o n e n t amorphous alloys with very different concentrations, t h a t is, C a > > C b. T h e y are d e f i n e d as
o
qab
qab
max
' where
qab
qab
Zab
-i
and
max qab =
Cb Ca
Zb Za
(4)
Here Za=Zaa+Zab and Zb=Zbb+Zba are t h e nearest neighbours of a a n d b a t o m s , r e s pectively, a n d
2
D a t a for f i r s t n e i g h b o u r dist a n c e s r ~ (~), p a r t i a l c o o r d i • aD natlon numbers Z b and normal. a zzed short range order parameo t e r qab for F e - B m e t a l l i c glasses measured by various methods
rFeFe rFeB Fe
B 2.56 83~17
Fe80~20
2.55 2.55
Fe75B25 2.57 80~20 re81~19 2.55
2.27
o ZFeFe ZFeB ZBFe ~ab 10.7
2.25 2.14
. .
2.14 2.16
12,4 10.6
2.6 . .
. .
6.9 . .
2.16 8.64 1.9 8.3
-
refs.
3 7 6
1 4 0.8 present
Vol. 44, No. 8
a n d t h e p r e s e n t w o r k can be e x p l a i n e d by the l i m i t e d a c c u r a c y of Zab data. T h e r e s u l t of b o t h w o r k s , as seen in T a b l e 2, o s h o w s t h a t q a b is n e a r to u n i t y , m e a n i n g a h i g h d e g r e e of c h e m i c a l o r d e r i.e. a preference for u n l i k e a t o m i c n e i g h b o u r s in t h i s m e t a l - m e t a l l o i d amorphous alloy. It s h o u l d be m e n t i o n e d that this short range order parameter is v e r y s e n s i t i v e to t h e c o o r d i n a t i o n n u m b e r v a l u e s . This can be s e e n f r o m its n o n p h y s i c a l l y high v a l u e of n ° ~ = 9 . 7 2 as can be c a l c u l a t e d ao . f r o m the p a r t l a l c o o r d i n a t i o n n u m b e r s , as g i v e n in ref. 3 A further consequence of the h i g h e r r-space resolution is t h e a p p e a r a n c e of fine s t r u c t u r e in the second n e i g h b o u r peak of G(r). The two m a i n s u b p e a k s at 4.25 ~ a n d 4 . 9 ~ w h i c h are g e n e r a l l y o b ser ~ d for a m o r p h o u s a l l o y s b e c o m e m o r e pronounced a n d t h e N are s l i g h t l y s h i f t e d to 4.15 ~ and 5.0 ~, r e s p e c t i v e l y . At the same t i m e n e w s m a l l s u b p e a k s m a y be o b s e r v e d at 4.6 ~ and at 3.6 ~ . T h e o r i g i n of t h e s e s u b p e a k s can be u n d e r s t o o d by c o m p a r i n g G(r) w i t h r e s u l t s o b t a i n e d r e c e n t l y by the h i g h r e s o l u t i o n E D X D m e t h o d ~ on F e 7 5 B 2 5 . On t h e b a s i s of a qualitative comparlson t h e two m a i n s u b p e a k s can be a t t r i b u t e d to t h e s e c o n d n e i g h b o u r F e - F e p a i r s , w h e r e a s the s m a l l s u b p e a k s can be a t t r i b u t e d to s e c o n d n e i g h b o u r F e - B p a i r s . The a g r e e m e n t bet w e e n the p r e s e n t c o n c l u s i o n s and the data given forhthe second neighbour dist a n c e s in r e f . - - w h i c h were obtained using different experimental methods s u p p o r t the a c t u a l e x i s t e n c e of the fine s t r u c t u r e in t h e s e c o n d c o o r d i n a t i o n s h e l l for the Fe-B m e t a l l i c glass. 4.
Conclusions
Due to t h e h i g h r e s o l u t i o n in r - s p a c e originating from this wide Q-range measu r e m e n t , the f i r s t p e a k in G(r) w a s r e s o l v e d into F e - B a n d F e - F e f i r s t n e i g h bour distributions a n d fine s t r u c t u r e was o b s e r v e d in the s e c o n d c o o r d i n a t i o n shell. Parameters characterizing the short r a n g e o r d e r in t h i s a m o r p h o u s system were o b t a i n e d : the f i r s t n e i g h b o u r F e - B a n d Fe-Fe distances, coordination numbers and short r a n g e o r d e r p a r a m e t e r showing preferential coordination b e t w e e n u n l i k e atomic neighbours. Furthermore the w i d t h of the r e s o l v e d f i r s t n e i g h b o u r p e a k s in C(r) w a s o b t a i n e d w i t h s a t i s f y i n g accur a c y and it was o b s e r v e d t h a t t h e f l u c t u a t i o n of t h e F e - B d i s t a n c e is s i g n i f i c a n t l y s m a l l e r t h a n t h a t of the F e - F e pairs. This clearly demonstrates a strong chemical interaction between iron and b o r o n atoms. Acknowledgement - we are g r a t e f u l to A. L o v a s for p r e p a r i n g the sample, to F. F o r g a c s for s o f t w a r e w o r k s a n d to Drs T. K e m e n y a n d I. V i n c z e for h e l p f u l a n d stimulating discussions.
Vol. 44, No. 8
DIFFRACTION STUDY ON Fe81B19 METALLIC GLASS
1155
References
1. U. Gonser, " A p p l i c a t i o n of Nuclear T e c h n i q u e s to the Study of A m o r p h o u s Metals" Atomic Energy Review, Supplement ~, (1981) 2. Y. Waseda, P r o g r e s s in M a t e r i a l s Science 26, 1 (1981) 3. T. Fujiwara, H.S. Chen and Y. Waseda, J. Phys. F: Metal Phys. ll, 1327 (1981) 4. E. Nold, P. Lamparter, H. Olbrich, G. R a i n e r - H a r b a c h , S. Steeb, Z. Naturforsch. ~6, 1032 (1981) 5. E. Svab, S.N. Ishmaev, F. Forgacs, I.P. Sadikov, A.A. Chernyshov, Proc. of Int. Conf. on A m o r p h o u s Systems Inv e s t i g a t e d by Nuclear Methods, Balat o n f u r e d (1981) Vol. II. p. 833 (to
6.
7.
8. 9. i0. ll.
be p u b l i s h e d in Nucl. Instr• and Methods, 1982) S. Aur, T. Egami, I. Vincze, Proc. Conf. Rapidly Q u e n c h e d Metals IV., Sendal (1981) Vol• l, p. 351 M. De Crescenzi, A. Balzarotti, F. Comin, L. Incoccia, S. Mobilio, N. Motta, Solid State Comm. 37, 921 (1981) C•N•J. Wagner, H. R u p p e r s b e r g , see ref • 1 , p . 123 M.M. A b d - E l m e g u i d , H. Micklitz, I. Vincze, Phys. Rev. B, 25, i (1982) F. Hajdu, Phys. Stat. Sol. (a) 60, 365 (1980) G.S. Cargill III., F. Spaepen, J. of Non-Cryst. Solids 43, 91 (1981)