FREQUENCY DISTRIBUTION AND DYNAMICAL STRUCTURE FACTOR OF A METALLIC GLASS

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FREQUENCY DISTRIBUTION AND DYNAMICAL STRUCTURE FACTOR OF A METALLIC GLASS

J.-B. Suck, H. Rudin, H.-J. Güntherodt, D. Tomanek, H. Beck, C. Morkel, W.

Gläser

To cite this version:

J.-B. Suck, H. Rudin, H.-J. Güntherodt, D. Tomanek, H. Beck, et al.. FREQUENCY DISTRIBU-

TION AND DYNAMICAL STRUCTURE FACTOR OF A METALLIC GLASS. Journal de Physique

Colloques, 1980, 41 (C8), pp.C8-175-C8-178. �10.1051/jphyscol:1980845�. �jpa-00220352�

JOURNAL DE PHYSIQUE

CoZZoque

C 8 ,

suppzdment n08, Tome

41,

aogt

1980,

page

C8-175

FREQUENCY D I S T R I B U T I O N AND DYNAMICAL STRUCTURE FACTOR OF A METALLIC GLASS

*L

^{X* **Y}

***

J.-B. Suck, H . RudinY, H.-J. ~ i i n t h e r o d t x ,

n.

^Tomanek

,

H . Beck

,

C. Norkel and 17. G l s s e r

I n s t i t u t Laue-Langevin,

156X, F-38042

GrenobZe Cedex, France.

X I n s t i t u t fiir Physik, Universitat,

CH-4056

Bale, Suisse,

* x I n s t i t u t de Physique, U n i v e r s i t l

CH-2000

NeuchBteZ, Suisse,

***Physik Department, T.U. Miinchen,

0-8046

Garching,

R.F.A.

Neutron i n e l a s t i c s c a t t e r i n g t e c h n i q u e s a r e a t h a t t h e 5 d e g r e e - s p e c t r u m was s u b t r a c t e d from. a l l w e l l e s t a b l i s h e d method f o r t h e i n v e s t i g a t i o n o f o t h e r s p e c t r a t o r e d u c e t h e i n f l u e n c e of t h e i n c o - t h e a t o m i c dynamics o f c r y s t a l s , b u t h a v e n o t o f t e n h e r e n t background from t h e H i n t h e s a ~ p l e . We b e e n a p p l i e d t o s t u d y t h e a t o m i c m o t i o n s i n amor- t h e r e f o r e h e s i t a t e t o g i v e S(Q,w) i n a b s o l u t e v a l u e s phous m e t a l s . We a r e r e p o r t i n g f i r s t r e s u l t s from [I/meV] a s i t was o r i g i n a l l y c a l c u l a t e d . As t h e t h e d e t e r m i n a t i o n o f t h e dynamic s t r u c t u r e f a c t o r s c a t t e r i n g from H m a i n l y c o n t r i b u t e s t o t h e i n e l a s - ( s c a t t e r i n g law) and t h e g e n e r a l i z e d f r e g u e n c y t i c s p e c t r u m f o r e n e r g i e s above 40 meV, t h e i n e l a s - d i s t r i b u t i o n of t h e m e t a l l i c g l a s s Ca

70 Mg30 and t i c s p e c t r u m of CaHg s h o u l d n o t b e s t r o n g l y a f f e c t e d t h e same s a n p l e a f t e r c r y s t a l l i z a t i o n . From t h e by t h i s s u b t r a c t i v e c o r r e c t i o n . More d e t a i l s a b o u t t h e o r e t i c a l p o i n t of v i e w , t h i s s y t e m i s p a r t i c u l a r - e x p e r i m e n t and d a t a t r e a t m e n t w i l l b e g i v e n e l s e - l y i n t e r e s t i n g , b e c a u s e t h e p a i r p o t e n t i a l o f t h e s e w h e r e [ 3 ] .

two m e t a l s can b e c a l c u l a t e d s o t h a t t h e experimen- t a l r e s u l t s c a n f i n a l l y b e i n t e r p r e t e d by model c a l - c a u l a t i o n s and P1.D s i n u l a t i o n o f t h i s s y s t e m . From t h e e x p e r i m e n t a l i s t p o i n t o f v i e w , t h i s s y s t e m t u r n e d o u t t o b e a v e r y d i f f i c u l t c h o i c e , a s t h e hydrogen, s t i l l l e f t i n even t h e p u r e s t Ca, p r o d u c e s a h i g h background of i n c o h e r e n t l y s c a t t e r e d neu- t r o n s . As a h e a t t r e a t m e n t t o r e d u c e t h e H con- t e n t [ I ] i s n o t p o s s i b l e w i t h a n amorphous m e t a l

( c r y s t a l l i z a t i o n ) we have t r i e d t o r e d u c e t h e s p o i l i n g e f f e c t o f H o n o u r r e s u l t s i n t h e d a t a t r e a t m e n t a f t e r t h e e x p e r i m e n t .

R e s u l t s and D i s c u s s i o n

F i g . 1 shows a c u t t h r o u g h t h e measured dy-nam- i c a l s t r u c t u r e f a c t o r S(Q,w) a t a momentum t r a n s f e r

O- 1

of Q = 2.04 A

,

i . e . j u s t b e f o r e t h e main peak o f t h e s t a t i c s t r u c t u r e f a c t o r S(Q) a t Q = 2.11

1 - I .

F o l l o w i n g s i m p l e arguments [ 4 ] we would e x p e c t a p r e f e r r e d e x c i t a t i o n o f t r a n s v e r s e modes a t t h i s Q v a l u e . I n f a c t , w e f i n d t h e s t r o n g e s t e x c i t a t i o n s f o r e n e r g i e s below 12 meV f o r t h e p o l y c r y s t a l and v e r y much more enhanced f o r t h e amorphous sample a t 6 and 273 K. The s h o u l d e r a t 16.3 meV i s m a i n l y due t o l o n g i t u d i n a l e x c i t a t i o n s a s c a n b e i n f e r r e d from Experiment and Data T r e a t r c e n t F i g . 2 where a s t r o n g e x c i t a t i o n i s s e e n a t t h i s

The e x p e r i m e n t was done a t t h e t h e r m a l n e u t r o n e n e r g y i n t h e s p e c t r u m of t h e p o l y c r y s t a l . F i g . 2 t-o-f s p e c t r o m e t e r IN4 a t t h e HFR o f t h e I L L i n shows a c u t t h r o u g h S(Q,w) a t Q = 4 . 3 8 A ^{O - 1}

,

i . e . Grenoble w i t h a n i n c i d e n t e n e r g y o f 60.6 meV. The between t h e second and t h i r d maximum o f S(Q), where m e t a l l i c g l a s s was measured a t 6 K and ( s h o r t l y ) a t one would e x p e c t p r e f e r r e d e x c i t a t i o n s o f l o n g i t u - 273 K, and t h e same sample a t 6 K a g a i n a f t e r c r y s - d i n a l phonons i n t h e p o l y c r y s t a l [ 4 ] . No s u c h s h a r p t a l l i z a t i o n i n a f u r n a c e a t 470 K . The d a t a were e x c i t a t i o n s o f l o n g i t u d i n a l phonons a r e s e e n i n t h e t r e a t e d a s d e s c r i b e d f o r CuZr [ 2 ] w i t h t h e e x c e p t i o n s p e c t r u m o f t h e amorphous sample. The i n t e n s i t y i n

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980845

JOURNAL DE PHYSIQUE

t h e r e g i o n below 12 meV i s reduced compared w i t h S(Q = 2 . 0 4 , ~ ) b u t i t i s s t i l l h i g h e r t h a n f o r t h e polycrys t a l l i n e sample.

F i g . 1 . D ~ n a m i c a l s t r u c t u r e f a c t o r of Ca 7oMg30 at Q = 2.04

.

x p o l y c r y s t a l 6 K,

.

g l a s s 6 K , - g l a s s 273 K ( s c a l e d down by a f a c t o r 2 ) . Two

l i n e s i n d i c a t e t h e f o o t of t h e e l a s t i c peak.

h

0

[ M ~ v ]

F i g . 2. Dynamical s t r u c t u r e f a c t o r of Ca70Kg30 a t

"-1

Q = 4 . 3 8 8

.

(See c a p t i o n - o f F i g . 1 ) .

From the sum of a l l t-o-f s p e c t r a a g e n e r a l i z e d frequency d i s t r i b u t i o n has been determined i n t h e same way a s d e s c r i b e d f o r Cu.Zr [21.

For t h e p o l y c r y s t a l we f i n d two peaks a t 16.4 and 30.3 meV which, f o l l o w i n g t h e d i s c u s s i o n of S(Q,w) may be a t t r i b u t e d t o mainly l o n g i t u d i n a l e x c i t a - t i o n s . The shoulder a t 10.9 meY Fepcesents t h e main p a r t of t h e t r a n s x e r s e modes, Two f u r t h e r . s h o u l d e r s a r e seen a t 1.8.4 and 22.3 meV which a r e a l s o seen i n t h e s c a t t e r i n g law. For a r e l i a b l e more d e t a i l e d

0 10 2 0 3 0 4 0

h w [MeV]

F i g . 3. Normalized frequency d i s t r i b u t i o n of CaT0Mgg0 x p o l y c r y s t a l 6 K , e g l a s s 6 K,

-

g l a s s 273 K.For e n e r g i e s below 5 meV, n o t a c c e s s i b l e due t o t h e f i n a l r e s o l u t i o n of t h e s p e c t r o m e t e r ( r e g i o n of e l a s t i c l i n e ) a Debye spectrum h a s been a r t i f i - c i a l l y i n s e r t e d .

d i s c u s s i o n of t h e s p e c t r a model c a l c u l a t i o n s o r MD s i m u l a t i o n s a r e n e c e s s a r y , b u t not having t h e s e , a l r e a d y t h e comparison w i t h t h e phonon d e n s i t y of s t a t e s of t h e pure m e t a l s can g i v e some f u r t h e r i n d i c a t i o n . The spectrum of Ca shows two p e a k s : a t 13 ( t r a n s v e r s a l ) and 18 ( l o n g i t u d i n a l ) meV [ I ] . It i s t h e r e f o r e very l i k e l y t h a t t h e peaks i n t h e poly- c r y s t a l l i n e spectrum a t 10.9 and 16.4 meV a r e main- l y caused by t r a n s v e r s e and l o n g i t u d i n a l movements of t h e Ca atoms, which should be predominantly s e e n i n our experiment (70 % w i t h 3.05 b ) . The spectrum of pure Mg shows van Hove s i n g u l a r i t i e s a t 16, 21.8, 23.5 and 27.2 meV [ 5 ]

.

We t h e r e f o r e t e n t a t i v e l y a t t r i b u t e t h e weaker s h o u l d e r s and peaks a t 18.4, 22.3 and 30.3 meV mainly t o t h e movement of Mg atoms (30 % w i t h 3.7b). The o r i g i n of t h e i n t e n s i t y above 30 meV i n t h e frequency s p e c t r a i s n o t c l e a r . It might be caused by t h e incomplete c o r r e c t i o n f o r

t h e hydrogen c o n t r i b u t i o n t o t h e spectrum.

Very s i m i l a r r e s u l t s a r e found f o r t h e f r e - quency s p e c t r a of t h e m e t a l l i c g l a s s w i t h only small d i f f e r e n c e s between t h e s p e c t r a a t 6 and 273 K.

Peaks and s h o u l d e r s a r e found a t a b o u t t h e same framework of l i n e a r s c r e e n i n g of (empty c o r e ) e n e r g i e s a s f o r t h e p o l y c r y s t a l , b u t t h e r e i s a

c o n s i d e r a b l e b r o a d e n i n g o f a l l t h e r e g i o n s o f t h e s p e c t r a .

0

a 8 1 6 2 4 3 2 40

h w [MeV]

F i g . 4 . Frequency d i s t r i b u t i o n o f C a 70M830 ( n o t n o r m a l i z e d f o r t h e g l a s s ) . See c a p t i o n of F i g . 3.

T h i s i s e v e n b e t t e r s e e n when t h e f r e q u e n c y s p e c t r a o f t h e m e t a l l i c g l a s s a r e p l o t t e d i n a way t h a t a l l t h r e e main maxima a t 16 meV c o i n c i d e . One s h o u l d t h e r e f o r e e x p e c t t h a t i n t e r a t o m i c p o t e n t i a l s g i v i n g a r e a s o n a b l e d e s c r i p t i o n o f t h e phonons i n t h e c r y s t a l l i n e a l l o y s h o u l d a l s o be a p p l i c a b l e t o t h e m e t a l l i c g l a s s , i f t h e d i s o r d e r i s t a k e n p r o p e r l y i n t o a c c o u n t .

We have a l s o performed a n a l y t i c c a l c u l a t i o n s o f t h e dynamical s t r u c t u r e f a c t o r o f a b i n a r y g l a s s y a l l o y o f s i m p l e m e t a l s o f t h e t y p e Mg70Zn30.

Such a d y n a m i c a l c o r r e l a t i o n f u n c t i o n c a n b e eva- l u a t e d i n a c o n t i n u e d f r a c t i o n r e p r e s e n t a t i o n [ 6 ] .

For a c l a s s i c a l s y s t e m t h e p e r t i n e n t r e l a t i o n s r e a d

S(Q) is t h e t o t a l s t a t i c s t r u c t u r e r a c t o r , and t h e Q-dependent 6; a s w e l l a s R ( z ) c a n b e e x p r e s s e d by

( e v e n ) f r e q u e n c y moments M _2n of S(Q,w) w i t h n > l [ 6 ] . Our c a l c u l a t i o n o f ( 1 ) i s proceeded a s f o l l o w s :

( i f e v a l u a t i o n o f t h e

air

p o t e n t i a l V ( R ) i n t h e

-

a 6

p s e u d o p o t e n t i a l s f o r t h e two i o n i c s p e c i e s . ( i i ) c a l c u l a t i o n o f Pi4(Q) u s i n g t h i s p o t e n t i a l and

-

t h e PY h a r d s p h e r e p a i r c o r r e l a t i o n f u n c t i o n . The p a r a m e t e r s i n ( i ) and ( i i ) a r e d e t e r m i n e d s u c h a s t o f i t t h e p o t e n t i a l s and g o f Heimendahl 173.

aB

( i i i ) c a l c u l a t i o n o f t h o s e terms o f M (Q) which

-

_- - 6 L -

<--

c o n t a i n g o n l y , a s t h e t e r m s c o n t a i n i n g t h e

aB

- s 7

unknown t r i p l e t c o r r . f u n c t i o n h -Can be shown

@BY

t o c a n c e l w i t h M,+(Q) i n ( 2 ) t o a good a p p r o x i m a t i o n ,

<. - -:

- -- i f haBy i s s u i t a b l y d e c o ~ ~ ~ e d [ a ] .

( i v ) t e r m i n a t i o n o f t h e c o n t i n u e d f r a c t i o n c h o o s i n g

-

a G a u s s i a n form f o r R (Q,z) [91. I t s p a r a m e t e r s a r e 2

d e t e r m i n e d such t h a t t h e f i n a l t e r m o f ( 2 ) y i e l d s t h e c o r r e c t moments t' Lo, El2, M and PI i n t h e c h o s e n

4 6

a p p r o x i m a t i o n .

The c o r r e s p o n d i n g S(Q,w) i s shown i n F i g . 5 f o r v a r i o u s Q v a l u e s . Two f e a t u r e s a r e o f i n t e r e s t :

F i g . 5 . C a l c u l a t e d d y n a m i c a l s t r u c t u r e f a c t o r f o r t h e m e t a I 1 i c g l a s s t f g 7 0 Z n ~ ~ .

C8-178 ^{JOURNAL DE PHYSlQUE}

t h e r e is a s t r o n g q u a s i e l a s t i c p e a k w i t h a s t r o n g maximum a t k = 2 . 4 6

2' ,

w h e r e S(Q) h a s i t s f i r s t

P

p e a k . U n l e s s t h e r e a r e v e r y i m p o r t a n t low e n e r g y e x c i t a t i o n s i n t h e s y s t e m , t h i s p e a k , r e p r e s e n t i n g s c a t t e r i n g f r o m t h e r i g i d i o n c o n f i g u r a t i o n

,

i s e x p e c t e d t o b e v e r y n a r r o w . I t s w i d t h i s c e r t a i n l y o v e r e s t i m a t e d by t h e c h o s e n t r u n c a t i o n o f ( 2 ) . E e s i d e s t h i s p e a k , t h e r e i s a n i m p o r t a n t Q-dependent

"-1

i n e l a s t i c t a i l . F o r Q

3

1 .13 A t h e r e i s e v e n a s e c o n d a r y maximum.

I n o r d e r t o c l a r i f y t h e n a t u r e of t h i s s t r u c - t u r e i n S(Q,w) wc a l s o c a l c u l a t e d t h e one-phonon p a r t D(Q,w) o f i t , which i s e s s e n t i a l l y t h e d i s - p l a c e m e n t c o r r e l a t i o n f u n c t i o n , u s i n g a c o n t i n u e d f r a c t i o n r e p r e s e n t a t i o n o f R ( Q , I I I ) = w D(Q,w). Our 2 H(Q,w) a g r e e s q u a l i t a t i v e l y w i t h t l e i m e n d a h l ' s c a l c u l a t i o n o f t h e same q u a n t i t y [ 7 ] . I t h a s a max- imum a t some f r e q u e n c y . ~ (Q) r e p r e s e n t i n g t h e

m

e n e r g y o f t h e most i m p o r t a n t l o n g i t u d i n a l e x c i t a - t i o n s f o r t h a t Q v a l u e w (Q) 2 i s a p p r o x i m a t e l y e q u a l

m

t o t h e 4-th moment o f D(Q,o,) , d i v i d e d by kHT :

- ₃ ^{+ +}

NI(U) = kBT

1

c a c 6 j d r ( l

-

c o s Q

.

^{r )}

aB

( c a i s t h e c o n c e n t r a t i o n o f c o n s t i t u e n t a ) . I t s Q- d e p e n d e n c e i s s i m i l a r t o t h a t o f t h e p h o n o n - r o t o n s p e c t r u m o f s u p e r f l u i d 4 ~ e . I t i s l i n e a r f o r s m a l l Q v a l u e s (sound w a v e s ) , h a s a maximum a t

@ I .

13

1 - I

and a minimum a t Q ?,

.

kP

S and D a r e t h e s u n s o f p a r t i a l f u n c t i o n s S a 6 and D We h a v e decomposed D , f o r s m a l l Q, i n t o

a 6 '

p a r t i a l c o n t r i b u t i o n s by d i a g o n a l i z i n g t h e m a t r i x

-

o f t h e 4-th moments, w h i c h c o r r e s p o n d s t o t h e M4aB

l o n g i t u d i n a l p a r t o f t h e d y n a m i c a l m a t r i x o f a b i n a - r y a l l o y . T h i s d e f i n e s a n " o p t i c " a n d a n " a c o u s t i c "

b r a n c h o f f r e q u e n c i e s . By i n t r o d u c i n g a w i d t h , w h i c h was somewhat s m a l l e r t h a n t h e o n e d i c t a t e d by o u r

F i g . 6 . One phonon p a r t D(q,w) f o r Q = 0 . 3 8 and

O - I Q = 0 . 7 6 A

.

t e r n i n a t i o n t e c h n i q u e , we w e r e a b l e t o d i s t i n g u i s h t h e c o n t r i b u t i o n s of t h e s e o p t i c and a c o u s t i c modes t o D(Q,w). They o c c u r a t t h e same p l a c e and w i t h a b o u t t h e same w e i g h t s a s i n H e i m e n d a h l ' s r e s u l t s , w h i c h s u g g e s t s t h a t t h e s t r u c t u r e i n t h e f r e q u e n c y d e p e n d e n c e o f h i s H(Q,w) i s duc t o p r e d o m i n a n t l y i n - p h a s e ( a c o u s t i c ) and o u t - o f - p h a s e ( o p t i c ) n e a r e s t n e i g h b o u r m o t i o n .

R e f e r e n c e s

[ I ] Gompf F . , Lau H . , ~ e i c h a r d t , W . , S a l g a d o J . ,

"i.leutron I n e l a s t i c S c a t t e r i n g " , IAEA : Wien ( 1 9 7 2 ) , 137.

121 Suck J . - B . , Rudin H., G u n t h e r o d t H.-J., Beck H . , D a u b e r t J . , G l z s e r W . , J. Phys.C. E , L 1 6 7 ( 1 9 8 0 ) . [ 3 ] Suck J . - R . , Rudin H . , G u n t h e r o d t H.-J., Beck M . ,

Morkel C . , G l a s e r W . , t o b e p u b l i s h e d . [ 4 ] E g e l s t a f f P.A., E R E N / R 1164 ( 1 9 5 3 ) .

151 Pynn R . , S q u i r e s C.L., P r o c . Roy. S o c .

e,

347 ( 1 9 7 2 ) .

[ 6 ] e . g . , C o p l e y J.R.D., Lovesey J.W., Rep. P r o g r . P h y s .

38,

461 ( 3 9 7 5 ) .

[ 7 ] v . Heimendahl L., J . P h y s . F z , 161 ( 1 9 7 9 ) . [ 8 ] B a l l e n t i n e L . E . , Adv. Chen. P h y s .

2,

²⁶³

( 1 9 7 5 ) .

[ 9 ] T u c k e r J.W., S o l . S t a t e Comn.

18,

4 3 ( 1 9 7 6 ) .