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Decrease of Mössbauer recoil-free fraction in small tungsten particles
Volume 25A, number 4
DECREASE
PHYSICS LETTERS
28 August 1967
OF M~SSBAUER RECOIL-FREE SMALL TUNGSTEN PARTICLES
FRACTION
IN
S. ROTH and E. M. HORL Osterreichische Studiengesellsckafl f l i t Atomenergie l.situt M#tallurgie, Reaktorzentrum Seibersdorf. Austria Received 4 July 1967 The Debye Waller factor of tungsten microcrystals has been investigated by the MtSssbauer technique and found to decrease with particle size. The results a r e discussed in terms of the Debye model a s ~vll as in terms of a modified Debye model. The f r e q u e n c y s p e c t r u m of the l a t t i c e v i b r a t i o n s of e x t r e m e l y s m a l l c r y s t a l s i s e x p e c t e d to d i f f e r f r o m the s p e c t r u m of the hulk m a t e r i a l . T h i s d i f f e r e n c e can be due to the f i n i t e s i z e of the c r y s t a l s , which p r o h i b i t s p r o p a g a t i o n of p h o nons with wave lengths l o n g e r than t w i c e the d i a m e t e r of the c r y s t a l s , and to the change of the l a t t i c e f o r c e s a t the s u r f a c e . T h e s e e f f e c t s can c a u s e d i f f e r e n c e s of the Debye W a l l e r f a c t o r and hence of the D e b y e t e m p e r a t u r e . M a c R a e and G e r m e r [1] have m e a s u r e d a d e c r e a s e of the Debye t e m p e r a t u r e of n i c k e l s i n g l e c r y s t a l s by e l e c t r o n d i f f r a c t i o n . M a r s h a l l and W i l e n z i c k [2] have i n v e s t i g a t e d the M ~ s s b a u e r effect in s m a l l gold c r y s t a l s and have found the Debye W a l l e r f a c t o r to i n c r e a s e . S c h r o e e r [3] h a s m e n t i o n e d an e x p e r i m e n t of G o l d a n s k i i on tin, which h a s y i e l d e d a d e c r e a s e of the D e b y e f a c t o r . In t h i s p a p e r M S s s b a u e r e x p e r i m e n t s on tungsten m i c r o c r y s t a l s a r e r e p o r t e d . A d e c r e a s e of the f a c t o r with p a r t i c l e s i z e was o b s e r v e d . The a v e r a g e d i a m e t e r of the t u n g s t e n m i c r o c r y s t a l s u s e d in the e x p e r i m e n t was 30 A. T h i s value was determined from electron microg r a p h s and a l s o f r o m the b r o a d e n i n g of the X - r a y r e f l e c t i o n s . The c r y s t a l s w e r e grown by p y r o l y s i s of tungsten h e x a c a r b e n y l at about 4 0 0 ° C u s i n g a r g o n a s c a r r i e r g a s . The tungsten p a r t i c l e s w e r e s e p a r a t e d f r o m the c a r r i e r in an e l e c t r o s t a t i c f i e l d . No oxydation of the c r y s t a l s could be d e t e c t e d a f t e r e x p o s i n g t h e m to the a i r ( X - r a y check). F o i l s w e r e p r e p a r e d by slow s e d i m e n t a t i o n of s u s p e n s i o n s in o r g a n i c s o l u tions. Neutron irradiated tantalum foils were used as g a m m a ray sources. The _g~ll.ma spectrum contained the 46.5 keV line of 183W. The MOssbauer effect of this level has been measured by
completely free surface atoms :
e L =107°K \
\
.< .,_6(
measured value for /
\
30 ,~ partial
..1¢
rigidly fixed surface atoms: e L =29.3"K
0 20 >, J~ (b ¢3
i0o T25
e. [..]'~
~0
Fig. 1. Dependence of the Debye Waller factor on the characteristic temperatures 8 L and BH in the modified Debye model. s e v e r a l a u t h o r s [4,5]. The n a t u r a l width of t h i s l i n e i s l a r g e enough to n e g l e c t e x t e r n a l b r o a d e n ing. The f - f a c t o r a m o u n t s to a p p r o x i m a t e l y 60% a t liquid n i t r o g e n t e m p e r a t u r e . The e x p e r i m e n t a l s e t - u p was of the type c o m m o n l y u s e d in a b s o r p t i o n e x p e r i m e n t s . An electromagnetic transducer served as a constant a c c e l e r a t i o n d r i v e . S o u r c e and a b s o r b e r w e r e c o o l e d with liquid n i t r o g e n . The g a m m a r a y s w e r e r e c o r d e d with a p r o p o r t i o n a l c o u n t e r and a n a l y z e d with a m u l t i c h a n n e l a n a l y z e r o p e r a t i n g in the t i m e mode. B e c a u s e of the v e r y c o m p l i c a t e d g a m m a - r a y s p e c t r u m of the s o u r c e the b a c k g r o u n d w a s v e r y l a r g e . S p e c i a l c a r e had t h e r e f o r e to be t a k e n to k e e p the b a c k g r o u n d c o n t r i b u t i o n constant. V e l o c i t y s p e c t r a w e r e r e c o r d e d with a b s o r .299
Volume 25A. n u m b e r 4
P HYSI CS L E T T E R S
b e r s of m i c r o c r y s t a l s a s well as a b s o r b e r s of l a r g e t u n g s t e n c r y s t a l s (1 m i c r o n d i a m e t e r ) . T h e s e s p e c t r a were evaluated by a l e a s t s q u a r e method to get the effect s t r e n g t h e = ( N ~ - N o ) / N c ¢ , where N~ is the n u m b e r of counts in a channel c o r r e s p o n d i n g to a v e r y l a r g e r e l a t i v e velocity of the s o u r c e and N O the n u m b e r of counts for zero velocity. • was plotted a g a i n s t the s u r f a c e density of the a b s o r b e r s . T h e s e plots were again fitted by a l e a s t s q u a r e method to gain the M 0 s s b a u e r r e c o i l - f r e e f r a c t i o n f a c c o r d i n g to the f o r m u l a s published by v a r i o u s a u t h o r s [6,7]. A value of f l = 0.57 was obtained for the m i c r o c r y s t a l s , o f f 2 = 0.61 for the 1 m i c r o n powder. The absolute v a l u e s of these q u a n t i t i e s a r e not v e r y a c c u r a t e ( i 20%), s i n c e they a r e the r e s u l t of a n o r m a l i z a t i o n to the calculated value of the s t a n d a r d a b s o r b e r (tantalum foil), for which s e v e r a l p h y s i c a l quantities were not e x a c t ly known n o r p r e c i s e l y m e a s u r e d . The r a t i o fl/f2, however, is exact to ±3%. The r e l a t i v e reduction of the r e c o i l - f r e e f r a c t i o n i s 7%. If one a s s u m e s a Debye t e m p e r a t u r e of 320°K [8] for the bulk m a t e r i a l , the value f 2 would c o r r e s ponded to a Debye t e m p e r a t u r e of 280°K on the b a s i s of the conventional Debye model. The lattice s p e c t r u m of v e r y s m a l l c r y s t a l s i s b e t t e r a p p r o x i m a t e d by a modified Debye m o del [2] than by the c u s t o m a r y one. This modified model is c h a r a c t e r i z e d by a low frequency cutoff in addition to the high frequency cutoff. This low f r e q u e n c y cutoff o r i g i n a t e s from fact, that in a c l a s s i c a l c r y s t a l s t a n d i n g waves m u s t see b o u n d a r i e s s e p a r a t e d at l e a s t one half of the w a v e length. This cutoff f r e q u e n c y and its c o r r e s p o n d ing c h a r a c t e r i s t i c t e m p e r a t u r e 0 L can be c a l c u lated f r o m the c r y s t a l d i m e n s i o n . If the Debye W a l l e r factor i s m e a s u r e d , the high f r e q u e n c y cutoff and i t s c o r r e s p o n d i n g c h a r a c t e r i s t i c t e m p e r a t u r e OH can be d e t e r m i n e d . OH can be d i f f e r ent f r o m the conventional Debye t e m p e r a t u r e 0D, b e c a u s e the different binding of the a t o m s at the s u r f a c e . S c h r o e e r [3] has pointed out, that the difference between 0 D and OH could be the r e s u l t of a change of the lattice c o n s t a n t a c c o r d i n g to the f o r m u l a OH/0 D = (1 -~ • AV/Vo), w h e r e ~ is
300
28 A u g u s t 1967
the G r ~ l e i s e n constant and Vo the volume of the e l e m e n t a r y cell. AV is equal to Vo of bulk m a t e r i a l m i n u s Vo of the m i c r o c r y s t a l s . The value of 0 L depends to some extent on the s u r f a c e conditions of the m i c r o c r y s t a l s . Rigidly fixed s u r f a c e s a t o m s (wave nods) y i e l d a 0 L = = 29.3°K for our 30A t u n g s t e n c r y s t a l s . If the s u r f a c e a t o m s a r e completely f r e e to move a value 0 L = 107°K r e s u l t s . In a r e a l c r y s t a l the s u r f a c e a t o m s will be n e i t h e r fixed n o r c o m p l e t e ly free and the lattice waves will propagate somewhat into the embedding m a t e r i a l . Fig. 1 shows the dependence of the Debye W a l l e r factor on the upper c h a r a c t e r i s t i c t e m p e r a t u r e OH for the two c a l c u l a t e d values of 0 L. A OH value for the 30/~ p a r t i c l e s m u s t t h e r e f o r e exist in the r a n g e from 225°K to 290°K. This value is probably c l o s e r to 225°K than to 290°K since M a r s h a l l and W i l e n zick [2] have shown that the s u r f a c e a t o m s can move quite f r e e l y if an o r g a n i c embedding m a t e r ial i s used. OH i s t h e r e f o r e c e r t a i n l y lower than the Debye t e m p e r a t u r e of the bulk m a t e r i a l (320°K). T h i s fact might indicate a c o n s i d e r a b l e weaker binding force for the s u r f a c e a t o m s than for the a t o m s within the c r y s t a l . The a u t h o r s acknowledge helpful d i s c u s s i o n s with Univ. P r o f . Dr. E. Schmid and Dr. P. Koss and the kind a s s i s t a n c e of M r . M. Drosg in p r e p a r i n g the e x p e r i m e n t a l setup.
References 1. A . U . M c R a e and L . H . G e r m e r , P h y s . Rev. L e t t e r s 8 (1962) 489. 2. S . W . M a r s h a l l and R. M. Wilenziek, P h y s . R e v . L e t t e r s 16 (1966) 219. 3. D . S c h r o e e r , P h y s . L e t t e r s 21 (1966) 123. 4. S . V . M a l e e v , Soviet P h y s i c s J E T P 12 (1961) 617.
5. M.Drogs, Acta Phys. Austriaca, to be published. 6. S.S.Hanna and P.S.Preston, Phys. Rev. 139A (1965) 722. 7. S.Margulies and J.R.Ehrmann, Nucl. Instr. and Methods 12 (1961) 131. 8. J.S.Kaspar and K. Lonsdale, eds. International tables of X-ray crystallography, Vol. HI, (The Knoch Press, BirmIngham, 1959).
DECREASE
PHYSICS LETTERS
28 August 1967
OF M~SSBAUER RECOIL-FREE SMALL TUNGSTEN PARTICLES
FRACTION
IN
S. ROTH and E. M. HORL Osterreichische Studiengesellsckafl f l i t Atomenergie l.situt M#tallurgie, Reaktorzentrum Seibersdorf. Austria Received 4 July 1967 The Debye Waller factor of tungsten microcrystals has been investigated by the MtSssbauer technique and found to decrease with particle size. The results a r e discussed in terms of the Debye model a s ~vll as in terms of a modified Debye model. The f r e q u e n c y s p e c t r u m of the l a t t i c e v i b r a t i o n s of e x t r e m e l y s m a l l c r y s t a l s i s e x p e c t e d to d i f f e r f r o m the s p e c t r u m of the hulk m a t e r i a l . T h i s d i f f e r e n c e can be due to the f i n i t e s i z e of the c r y s t a l s , which p r o h i b i t s p r o p a g a t i o n of p h o nons with wave lengths l o n g e r than t w i c e the d i a m e t e r of the c r y s t a l s , and to the change of the l a t t i c e f o r c e s a t the s u r f a c e . T h e s e e f f e c t s can c a u s e d i f f e r e n c e s of the Debye W a l l e r f a c t o r and hence of the D e b y e t e m p e r a t u r e . M a c R a e and G e r m e r [1] have m e a s u r e d a d e c r e a s e of the Debye t e m p e r a t u r e of n i c k e l s i n g l e c r y s t a l s by e l e c t r o n d i f f r a c t i o n . M a r s h a l l and W i l e n z i c k [2] have i n v e s t i g a t e d the M ~ s s b a u e r effect in s m a l l gold c r y s t a l s and have found the Debye W a l l e r f a c t o r to i n c r e a s e . S c h r o e e r [3] h a s m e n t i o n e d an e x p e r i m e n t of G o l d a n s k i i on tin, which h a s y i e l d e d a d e c r e a s e of the D e b y e f a c t o r . In t h i s p a p e r M S s s b a u e r e x p e r i m e n t s on tungsten m i c r o c r y s t a l s a r e r e p o r t e d . A d e c r e a s e of the f a c t o r with p a r t i c l e s i z e was o b s e r v e d . The a v e r a g e d i a m e t e r of the t u n g s t e n m i c r o c r y s t a l s u s e d in the e x p e r i m e n t was 30 A. T h i s value was determined from electron microg r a p h s and a l s o f r o m the b r o a d e n i n g of the X - r a y r e f l e c t i o n s . The c r y s t a l s w e r e grown by p y r o l y s i s of tungsten h e x a c a r b e n y l at about 4 0 0 ° C u s i n g a r g o n a s c a r r i e r g a s . The tungsten p a r t i c l e s w e r e s e p a r a t e d f r o m the c a r r i e r in an e l e c t r o s t a t i c f i e l d . No oxydation of the c r y s t a l s could be d e t e c t e d a f t e r e x p o s i n g t h e m to the a i r ( X - r a y check). F o i l s w e r e p r e p a r e d by slow s e d i m e n t a t i o n of s u s p e n s i o n s in o r g a n i c s o l u tions. Neutron irradiated tantalum foils were used as g a m m a ray sources. The _g~ll.ma spectrum contained the 46.5 keV line of 183W. The MOssbauer effect of this level has been measured by
completely free surface atoms :
e L =107°K \
\
.< .,_6(
measured value for /
\
30 ,~ partial
..1¢
rigidly fixed surface atoms: e L =29.3"K
0 20 >, J~ (b ¢3
i0o T25
e. [..]'~
~0
Fig. 1. Dependence of the Debye Waller factor on the characteristic temperatures 8 L and BH in the modified Debye model. s e v e r a l a u t h o r s [4,5]. The n a t u r a l width of t h i s l i n e i s l a r g e enough to n e g l e c t e x t e r n a l b r o a d e n ing. The f - f a c t o r a m o u n t s to a p p r o x i m a t e l y 60% a t liquid n i t r o g e n t e m p e r a t u r e . The e x p e r i m e n t a l s e t - u p was of the type c o m m o n l y u s e d in a b s o r p t i o n e x p e r i m e n t s . An electromagnetic transducer served as a constant a c c e l e r a t i o n d r i v e . S o u r c e and a b s o r b e r w e r e c o o l e d with liquid n i t r o g e n . The g a m m a r a y s w e r e r e c o r d e d with a p r o p o r t i o n a l c o u n t e r and a n a l y z e d with a m u l t i c h a n n e l a n a l y z e r o p e r a t i n g in the t i m e mode. B e c a u s e of the v e r y c o m p l i c a t e d g a m m a - r a y s p e c t r u m of the s o u r c e the b a c k g r o u n d w a s v e r y l a r g e . S p e c i a l c a r e had t h e r e f o r e to be t a k e n to k e e p the b a c k g r o u n d c o n t r i b u t i o n constant. V e l o c i t y s p e c t r a w e r e r e c o r d e d with a b s o r .299
Volume 25A. n u m b e r 4
P HYSI CS L E T T E R S
b e r s of m i c r o c r y s t a l s a s well as a b s o r b e r s of l a r g e t u n g s t e n c r y s t a l s (1 m i c r o n d i a m e t e r ) . T h e s e s p e c t r a were evaluated by a l e a s t s q u a r e method to get the effect s t r e n g t h e = ( N ~ - N o ) / N c ¢ , where N~ is the n u m b e r of counts in a channel c o r r e s p o n d i n g to a v e r y l a r g e r e l a t i v e velocity of the s o u r c e and N O the n u m b e r of counts for zero velocity. • was plotted a g a i n s t the s u r f a c e density of the a b s o r b e r s . T h e s e plots were again fitted by a l e a s t s q u a r e method to gain the M 0 s s b a u e r r e c o i l - f r e e f r a c t i o n f a c c o r d i n g to the f o r m u l a s published by v a r i o u s a u t h o r s [6,7]. A value of f l = 0.57 was obtained for the m i c r o c r y s t a l s , o f f 2 = 0.61 for the 1 m i c r o n powder. The absolute v a l u e s of these q u a n t i t i e s a r e not v e r y a c c u r a t e ( i 20%), s i n c e they a r e the r e s u l t of a n o r m a l i z a t i o n to the calculated value of the s t a n d a r d a b s o r b e r (tantalum foil), for which s e v e r a l p h y s i c a l quantities were not e x a c t ly known n o r p r e c i s e l y m e a s u r e d . The r a t i o fl/f2, however, is exact to ±3%. The r e l a t i v e reduction of the r e c o i l - f r e e f r a c t i o n i s 7%. If one a s s u m e s a Debye t e m p e r a t u r e of 320°K [8] for the bulk m a t e r i a l , the value f 2 would c o r r e s ponded to a Debye t e m p e r a t u r e of 280°K on the b a s i s of the conventional Debye model. The lattice s p e c t r u m of v e r y s m a l l c r y s t a l s i s b e t t e r a p p r o x i m a t e d by a modified Debye m o del [2] than by the c u s t o m a r y one. This modified model is c h a r a c t e r i z e d by a low frequency cutoff in addition to the high frequency cutoff. This low f r e q u e n c y cutoff o r i g i n a t e s from fact, that in a c l a s s i c a l c r y s t a l s t a n d i n g waves m u s t see b o u n d a r i e s s e p a r a t e d at l e a s t one half of the w a v e length. This cutoff f r e q u e n c y and its c o r r e s p o n d ing c h a r a c t e r i s t i c t e m p e r a t u r e 0 L can be c a l c u lated f r o m the c r y s t a l d i m e n s i o n . If the Debye W a l l e r factor i s m e a s u r e d , the high f r e q u e n c y cutoff and i t s c o r r e s p o n d i n g c h a r a c t e r i s t i c t e m p e r a t u r e OH can be d e t e r m i n e d . OH can be d i f f e r ent f r o m the conventional Debye t e m p e r a t u r e 0D, b e c a u s e the different binding of the a t o m s at the s u r f a c e . S c h r o e e r [3] has pointed out, that the difference between 0 D and OH could be the r e s u l t of a change of the lattice c o n s t a n t a c c o r d i n g to the f o r m u l a OH/0 D = (1 -~ • AV/Vo), w h e r e ~ is
300
28 A u g u s t 1967
the G r ~ l e i s e n constant and Vo the volume of the e l e m e n t a r y cell. AV is equal to Vo of bulk m a t e r i a l m i n u s Vo of the m i c r o c r y s t a l s . The value of 0 L depends to some extent on the s u r f a c e conditions of the m i c r o c r y s t a l s . Rigidly fixed s u r f a c e s a t o m s (wave nods) y i e l d a 0 L = = 29.3°K for our 30A t u n g s t e n c r y s t a l s . If the s u r f a c e a t o m s a r e completely f r e e to move a value 0 L = 107°K r e s u l t s . In a r e a l c r y s t a l the s u r f a c e a t o m s will be n e i t h e r fixed n o r c o m p l e t e ly free and the lattice waves will propagate somewhat into the embedding m a t e r i a l . Fig. 1 shows the dependence of the Debye W a l l e r factor on the upper c h a r a c t e r i s t i c t e m p e r a t u r e OH for the two c a l c u l a t e d values of 0 L. A OH value for the 30/~ p a r t i c l e s m u s t t h e r e f o r e exist in the r a n g e from 225°K to 290°K. This value is probably c l o s e r to 225°K than to 290°K since M a r s h a l l and W i l e n zick [2] have shown that the s u r f a c e a t o m s can move quite f r e e l y if an o r g a n i c embedding m a t e r ial i s used. OH i s t h e r e f o r e c e r t a i n l y lower than the Debye t e m p e r a t u r e of the bulk m a t e r i a l (320°K). T h i s fact might indicate a c o n s i d e r a b l e weaker binding force for the s u r f a c e a t o m s than for the a t o m s within the c r y s t a l . The a u t h o r s acknowledge helpful d i s c u s s i o n s with Univ. P r o f . Dr. E. Schmid and Dr. P. Koss and the kind a s s i s t a n c e of M r . M. Drosg in p r e p a r i n g the e x p e r i m e n t a l setup.
References 1. A . U . M c R a e and L . H . G e r m e r , P h y s . Rev. L e t t e r s 8 (1962) 489. 2. S . W . M a r s h a l l and R. M. Wilenziek, P h y s . R e v . L e t t e r s 16 (1966) 219. 3. D . S c h r o e e r , P h y s . L e t t e r s 21 (1966) 123. 4. S . V . M a l e e v , Soviet P h y s i c s J E T P 12 (1961) 617.
5. M.Drogs, Acta Phys. Austriaca, to be published. 6. S.S.Hanna and P.S.Preston, Phys. Rev. 139A (1965) 722. 7. S.Margulies and J.R.Ehrmann, Nucl. Instr. and Methods 12 (1961) 131. 8. J.S.Kaspar and K. Lonsdale, eds. International tables of X-ray crystallography, Vol. HI, (The Knoch Press, BirmIngham, 1959).