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1973
Nuclear magnetic resonance in the amorphous transition metal Nuclear magnetic resonance in the amorphous transition metal VZr alloy
VZr alloy
Kwang Soo Han
College of William & Mary - Arts & Sciences
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Recommended Citation Recommended Citation
Han, Kwang Soo, "Nuclear magnetic resonance in the amorphous transition metal VZr alloy" (1973).
Dissertations, Theses, and Masters Projects. Paper 1539623666.
https://dx.doi.org/doi:10.21220/s2-0e1v-my15
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74-2303 HAN, Kwang Soo, 1931-
NUCLEAR. MAGNETIC RESONANCE IN THE AMORPHOUS TRANSITION METAL VZr ALLOT.
The College of William and Mary in Virginia, Ph.D., 1973
Physics, solid state
University Microfilms, A XEROX Com pany, Ann Arbor, Michigan
NUCLEAR MAGNETIC RESONANCE IN THE AMORPHOUS TRANSITION METAL VZr ALLOY
A T h e sis P r e s e n te d t o
The F a c u lty o f th e D epartm ent o f P h y s ic s The C o lle g e o f W illiam and Mary i n V ir g in i a
I n P a r t i a l F u l f i l l m e n t
Of th e R eq uirem ents f o r th e D egree o f D o c to r o f P h ilo s o p h y
by
Kwang Soo Han
A ugust 1973
APPROVAL SHEET
T h is t h e s i s i s s u b m itte d i n p a r t i a l f u f i l l m e n t o f th e re q u ire m e n ts f o r th e d e g re e o f
D o cto r o f Philosophy-
A pproved, A ugust 1973
H a rla n E. Schone
ron F . S o e s t
/ h ~ \ ( ^ A a ^ a -
R oy/L . Champion 7
W illia m J . K ossli
Melvyn BV S c h i a v e l l i Melvyn
D epartm ent o f C h em istry
NUCLEAR MAGNETIC RESONANCE IN THE AMORPHOUS TRANSITION METAL VZr ALLOY
T ab le o f C o n te n ts
Page A b s t r a c t ... i i i
I . I n t r o d u c t i o n ...
1
I I . Theory an d B ackground... U A. T r a n s it io n M e t a l ... 1*
B. K n ig h t S h i f t ... 6
C. A llo y s and L o c a l E f f e c t s ... 7
D. Q uadrupole E f f e c t s i n VZr A llo y ...
16
E . B e h a v io r o f S u p e rc o n d u c tin g T r a n s i t i o n T em p erature (Tfi) o f Amorphous and C r y s t a l l i n e M e ta l w ith r e s p e c t t o E l e c tr o n C o n c e n tr a tio n ... 18
I I I . E x p e rim e n ta l P ro c e d u re ... 23
A. P r e p a r a t io n o f S a m p l e s ... 23
B. T a r g e t and S u b s t r a t e ...25
C. S t r u c t u r e and C om p ositio n A n a ly s is o f VZr F ilm . . . . 25
D. NMR E q u ip m en t... 29
E . G e n e r a l...32
IV . R e s u lts and D i s c u s s i o n ... 37
A. K n ig h t S h i f t ... 37
B. L in e w id th ... ^5
C. Q uadrupole E f f e c t s ...5^
Page V. A c k n o w le d g e m e n ts ... 59 V I. R e f e r e n c e s ...60 V I I . L i s t o f T a b l e s ... 63 V I I I . L i s t o f F i g u r e s ... . . . 6 k
A b s t r a c t
The n u c l e a r m a g n e tic re s o n a n c e o f i n b o th th e amorphous a n d c r y s t a l l i n e p h a se o f VZr a l l o y f i l m h as b e e n i n v e s t i g a t e d i n an e f f o r t t o d e te rm in e th e p a r a m e te r s c o n t r o l l i n g th e e l e c t r o n i c s t r u c t u r e o f t h e amorphous p h a se r e l a t i v e t o t h e c r y s t a l l i n e p h a s e . Changes i n th e K n ig h t s h i f t , th e l i n e w id th , and th e i n t e n s i t y o f th e a b s o r p ti o n l i n e o f f o r b o th t h e am orphous p h a s e a n d t h e c r y s t a l l i n e p h a se h av e b e e n m easu red a t 77°K em ploy ing a s t a t i c m a g n e tic f i e l d r a n g in g from 8 t o
17
k i l o g a u s s .A l l o b s e rv e d ch an g e s i n K n ig h t s h i f t o f i n t h e amorphous p h a s e o f VZr a l l o y f i l m a r e s m a l l, and show a s l i g h t l i n e a r f i e l d depen dence as com pared w ith t h a t i n th e c o r re s p o n d in g c r y s t a l l i n e p h a s e . On th e o t h e r h a n d th e l i n e w id th o f V ^ i n t h e am orphous p h a s e i s c o n s id e r a b ly l a r g e r th a n t h a t i n th e c r y s t a l l i n e p h a s e , and h a s a s t r o n g l i n e a r f i e l d d ep en d e n ce. T h is b e h a v io r may b e a c c o u n te d f o r i n te rm s o f F r i e d e l o s c i l l a t i o n s o r t h e r i g i d b a n d m o del. The s i g n i f i c a n t d e c r e a s e i n t h e l i n e i n t e n s i t y o f t h e am orphous' p h a s e r e l a t i v e t o t h a t o f t h e c r y s t a l l i n e a p p e a rs t o b e c o n s i s t e n t w ith an a l l o r n o th in g w ip e o u t m o d el. I t i s c o n c lu d e d t h a t t h e q u a d ru p o le i n t e r a c t i o n o f V^1 w ith t h e l a r g e e l e c t r i c f i e l d g r a d i e n t , w hich i s
i i i
p ro d u c e d b y th e l a t t i c e d i s t o r t i o n an d r e d i s t r i b u t i o n o f t h e o c c u p ie d e l e c t r o n i c s t a t e s , i s p r o b a b ly a s s o c i a t e d w ith g a s i m p u r i t i e s tr a p p e d i n th e amorphous VZr f i l m .
I . INTRODUCTION
T h is t h e s i s d e s c r ib e s th e r e s u l t s o f an i n v e s t i g a t i o n o f th e n u c l e a r m a g n e tic re s o n a n c e (NMR) o f i n a t r a n s i t i o n m e ta l VZr a l l o y w hich was p r e p a r e d i n a h i g h l y d is o r d e r e d s t a t e b y th e RF
s p u t t e r i n g p r o c e s s . The p u rp o s e o f t h i s s tu d y i s t o a c h ie v e a b e t t e r u n d e r s ta n d in g o f th e changes i n n u c l e a r and e l e c t r o n i c p r o p e r t i e s o f th e t r a n s i t i o n m e ta l a l l o y i n t h e amorphous p h a se a s com pared w ith t h a t i n th e c r y s t a l l i n e o n e.
Vanadium was c h o s e n f o r th e s tu d y b e c a u s e i t h a s a l a r g e m a g n e tic moment (5*139 n u c l e a r m agneton) an d a s m a ll q u a d ru p o le moment, and i t form s a s o l i d s o l u t i o n i n th e amorphous p h a se w ith z irc o n iu m a t room te m p e r a tu r e i n th e RF s p u t t e r i n g p r o c e s s . V ^ h a s a n u c l e a r s p i n I = 7 /2 a n d a n a t u r a l abundance o f 9 9-75%• S in c e Zr^1 h a s a s m a ll m a g n e tic moment s o t h a t th e r e l a t i v e s e n s i t i v i t y o f Z r^ 1 m a g n e tic re s o n a n c e i s v e r y s m a l l , a Z r^1 NMR s tu d y was r u l e d o u t .
N u c le a r m a g n e tic r e s o n a n c e can p r o v id e in f o r m a tio n a b o u t th e e l e c t r o n i c s t r u c t u r e o f s o l i d s as a r e s u l t o f t h e e f f e c t on t h e n u c l e i o f v a r io u s i n t e r a c t i o n s w ith e l e c t r o n s . I n m e ta ls t h e m o st im p o r ta n t o f s u c h i n t e r a c t i o n s a r e t h e m a g n e tic h y p e r f in e i n t e r a c t i o n b etw ee n th e c o n d u c tio n e l e c t r o n s and t h e n u c l e i , a n d t h e n u c l e a r q u a d r ip o l e i n t e r a c t i o n b etw ee n n u c l e i w h ich p o s s e s s i n t r i n s i c
1
2
q u a d ru p o le moment and th e e l e c t r i c f i e l d g r a d i e n t g e n e r a te d b y th e p e r t u r b a t i o n o f th e e l e c t r o n i c c h a rg e d i s t r i b u t i o n . The m easurem ent o f K n ig h t s h i f t , th e NMB a b s o r p ti o n l i n e w i d t h , th e a b s o r p ti o n i n t e n s i t y , an d t h e i r v a r i a t i o n w ith Z r9 1 c o n c e n t r a t i o n o r th e a p p l ie d m a g n e tic f i e l d s h o u ld p r o v id e in f o r m a tio n a b o u t th e v a l i d i t y o f a r i g i d b a n d model'*', o r th e p re s e n c e o f th e lo n g ra n g e o s c i l l a t i o n i n th e co n - d u c tio n e l e c t r o n d e n s it y p r e v i o u s l y n o te d b y F r i e d e l e t a l i n th e 2 amorphous a n d c r y s t a l l i n e p h a s e s o f t r a n s i t i o n m e ta l a l l o y .
I n t h e f o llo w in g s e c t i o n o f t h i s p a p e r , th e th e o r y and b ac k g ro u n d o f t h i s p ro b le m w i l l b e c o n s id e r e d . The e x p e r im e n ta l te c h n iq u e , i n c l u d i n g a d is c u s s i o n o f t h e f a c t o r s w hich a f f e c t th e a c c u ra c y o f th e m easu rem en t, i s d e s c r ib e d i n S e c t io n I I I . S e c t io n IV p r e s e n t s th e e x p e r im e n ta l r e s u l t s and d i s c u s s i o n .
B e fo re p r o c e e d in g t o th e n e x t s e c t i o n , i t i s a p p r o p r i a t e to. g iv e some i d e a o f w h at i s m eant b y t h e te rm "am orphous m e ta l" . A v a r i e t y o f o t h e r te rm s h a v e b e e n u s e d i n p l a c e o f th e te rm am orphous, i n c lu d in g : la c k o f lo n g ra n g e o r d e r , t h e p r e s e n c e o f o n ly s h o r t ra n g e o r d e r , a c o m p le te ly random d i s t r i b u t i o n o f atom s w ith a s t a t i s t i c a l s p r e a d i n i n t e r a t o m i c s p a c in g a n d o r i e n t a t i o n , o r a c o l l e c t i o n o f s m a l l o r d e r e d u n i t s random ly o r i e n t e d w i t h r e s p e c t t o e a c h o t h e r . I n many t h e o r e t i c a l f o r m u la tio n s o f amorphous s t r u c t u r e s t h e in t e r a t o m i c s e p a r a t i o n a n d / o r t h e a to m ic p o t e n t i a l a r e t r e a t e d a s random v a r i a b l e s w i t h i n . c e r t a i n l i m i t s . H ow ever, f o r t h e p r e s e n t p u x p o s e , th e b e s t
d e f i n i t i o n o f am orphous i s t h a t due t o th e e x i s t i n g e x p e r im e n ta l l i m i t a t i o n s . T h is d e f i n i t i o n dep end s on t h e t e c h n i q u e , w h ich m ig h t
3
b e X -ra y o r e l e c t r o n d i f f r a c t i o n , o r e l e c t r o n m ic ro s c o p y . F i e l d io n m icro sc o p y h a s n o t y e t b e e n em p lo y ed , as f a r a s th e a u th o r i s a w a re , a lth o u g h i t w ou ld seem t o b e an e x c e l l e n t t o o l f o r u n d e r s ta n d in g th e am orphous s t r u c t u r e . D i f f r a c t i o n p a t t e r n s f o r amorphous m a t e r i a l s u s u a l l y e x h i b i t tw o t o f o u r b r o a d h a l o s an d g iv e in f o r m a tio n c o n c e r n in g th e a v e ra g e number o f n e a r e s t n e ig h b o rs a b o u t an atom, and t h e i r a v e ra g e s e p a r a t i o n .
Amorphous m a t e r i a l s a r e p r e p a r e d u n d e r c o n d itio n s t h a t s e e k t o k i n e t i c a l l y p r e v e n t t h e fo r m a tio n o f t h e th e rm o d y n a m ic a lly s t a b l e c r y s t a l l i n e s t r u c t u r e . A l l p r e p a r a t i o n te c h n iq u e s a c c o m p lish t h i s by r e s t r i c t i n g th e a b i l i t y o f th e atom t o d i f f u s e ; th e m ost common o f t h e s e b e i n g some fo rm o f r a p i d te m p e r a tu r e q u e n c h in g from a s t a t e o f h i g h e r e n tr o p y i . e . , a l i q u i d o r g as p h a s e . A n o th e r te c h n iq u e , w h ich
o f t e n o c c u rs i n a d v e r t e n t l y , i s t h e i n t r o d u c t i o n o f i m p u r i t i e s ,
e s p e c i a l l y g a s e s . Ifce p r e s e n c e o f th e o t h e r m e ta ls can a l s o s i g n i f i c a n t l y h i n d e r d i f f u s i o n and i s i n d i c a t e d b y a h ig h e r te m p e r a tu r e r e q u i r e d t o p ro d u c e th e am orphous t o c r y s t a l l i n e t r a n s f o r m a t i o n . I n t h i s s tu d y th e am orphous s t r u c t u r e s w ere p r e p a r e d b y s p u t t e r i n g vanadium and z irc o n iu m s im u lta n e o u s ly o n to a w a te r - c o o l e d s u b s t r a t e u n d e r an arg o n p la s m a .
I I . T heory and B ackground
A. T r a n s i t i o n M e ta l
T r a n s i t i o n m e ta ls a r e c h a r a c t e r i z e d by p a r t i a l l y f i l l e d d -b a n d s v h ic h a r e u s u a l l y q u i t e n arro w an d t h e r e f o r e have a h ig h
d e n s i t y o f s t a t e s a t th e Ferm i l e v e l . The d -b an d s u s u a l l y o v e r la p w ith a much w id e r s -b a n d and t h e d - e l e c t r o n s a r e more l o c a l i z e d th a n th e f r e e e l e c t r o n s . The s i m p l e s t m odel o f t r a n s i t i o n m e ta ls assum e t h a t th e s - an d d -b a n d s axe d i s t i n g u i s h a b l e a t th e Ferm i l e v e l . The v a r i a t i o n w ith e n e rg y o f th e d e n s i t y o f s t a t e s o f an s - b a n d i s much s lo w e r th a n t h a t o f a n arro w d -b a n d , and i t h a s b e e n common p r a c t i c e t o assum e t h a t t h e num ber o f e l e c t r o n s i n t h e s - b a n d i s i n t h e ra n g e o f 0 . 2 - 1 p e r atom .3
The c o n t r i b u t i o n o f t h e s - b a n d t o t h e t o t a l h y p e r f in e i n t e r a c t i o n can b e e s t i m a t e d by means o f t h e f r e e e l e c t r o n e n e rg y d e n s it y o f s t a t e s now. I n m o st c a s e s , h o w ev er, t h i s i s a d an g ero u s a p p r o x i
m a tio n b e c a u s e t h e c r y s t a l p o t e n t i a l may o v e r la p . S in c e t h e s - d m ix in g i s s i g n i f i c a n t , i t i s u s e f u l t o c h a r a c t e r i z e th e s t a t e a t t h e Ferm i l e v e l b y th e a v e ra g e f r a c t i o n a l s a n d 'd c h a r a c t e r . C o n s e q u e n tly , one may d e f i n e a f r a c t i o n a l s an d d d e n s i t y o f s t a t e s su ch t h a t
(1)
U
5
The r a t i o Ns(Ef ) / N ^ E ^ ) w i l l d ep en d , i n g e n e r a l , on th e d e t a i l s o f
• th e h a n d s t r u c t u r e . I f s p i n - o r h i t i n t e r a c t i o n s a r e n o t to o im p o r ta n t , th e n t h e t o t a l m a g n e tic s u s c e p t i b i l i t y o f a t r a n s i t i o n m e ta l can b e p a r t i t i o n e d i n t o s p i n and o r b i t a l c o n t r i b u t i o n s :
X ’ X , * -X, + X y , - t X L+ (2)
The f i r s t tw o te rm s i n E q. (2 ) a r e s and d s p in s u s c e p t i b i l i t i e s , r e s p e c t i v e l y , w hich can b e r e l a t e d b y ,
X = % X K = i < y < V ' N ( £ f i ) . o )
*}CVV i s a f i e l d in d u c e d o r b i t a l p a ra m a g n e tic s u s c e p t i b i l i t y w hich a r i s e s fro m th e o r b i t a l d e g e n e ra c y o f th e ato m ic d s t a t e s . O C yy i s
an alo g o u s t o t h e te m p e ra tu re in d e p e n d e n t Van Y leck s u s c e p t i b i l i t y i n th e m a g n e tic i n s u l a t o r s .
*ws I O '
kI U ***.>! (M
* * t f e ^ - E r «c
X u = - z CJe ^ N,(EF ^ /inV 3 ^ ) , (5 )
(L an d au d ia m a g n e tic s u s c e p t i b i l i t y ) , and
X w - - & - ? < * * > ( 6 )
due t o th e io n c o r e .
B ecause o f t h e h ig h d e n s i t y o f d s t a t e s a t th e Ferm i l e v e l , th e p a r a m a g n e tic c o n t r i b u t i o n s t o % i n t r a n s i t i o n m e ta ls a r e much l a r g e r th a n
T h is i s i n c o n t r a s t t o th e s i t u a t i o n i n s im p le m e ta ls w here
6
th e d ia m a g n e tic te rm u s u a ll y d o m in a te s . I n p r a c t i c e , th e i n d i v i d u a l c o n tr ib u tio n s t o X c a n n o t b e c a l c u l a t e d from f i r s t p r i n c i p l e s b e c a u se o f i n s u f f i c i e n t know ledge ab o u t th e c o n d u c tio n e l e c t r o n s t a t e s . One o f th e im p o r ta n t a p p l i c a t i o n s o f NMR i n th e t r a n s i t i o n m e ta ls in v o lv e s th e s e p a r a t i o n o f X i n t o i t s v a r io u s p a r t s on th e b a s i s o f th e m easured re so n a n c e s h i f t an d r e l a x a t i o n tim e .
B. K n ig h t S h i f t
When th e NMR fre q u e n c y i n a m e t a l l i c sam ple i s o b s e rv e d , i t i s fou n d t h a t t h i s fre q u e n c y d i f f e r s from t h a t d e t e c te d from th e same n u c l e a r s p e c ie s i n a d ia m a g n e tic compound, b o th m easurem ents h a v in g b een p e rfo rm e d i n th e same s t a t i c m a g n etic f i e l d . T h is d is p la c e m e n t
o f NMR fre q u e n c y i n m e ta ls i s c a l l e d th e K n ig h t s h i f t , a f t e r i t s
d is c o v e r e r , W. D. K n ig h t . k S in c e t h i s s h i f t i s g e n e r a lly an o r d e r o f
m agn itud e o r more g r e a t e r th a n c h e m ic a l s h i f t s , i t was r e a l i z e d t h a t such a s h i f t i s a s s o c i a t e d w ith th e c o n d u c tio n e l e c t r o n s o f th e m e ta l.
The Knigiht s h i f t h a s b e e n s u c c e s s f u l l y e x p la in e d i n te rm s o f th e h y p e r f in e i n t e r a c t i o n b etw een th e n u c le u s and th e n o n - lo c a liz e d c o n d u c tio n e l e c t r o n s . The im p o r ta n t c o n t r i b u ti o n s t o th e t o t a l K n ig h t s h i f t i n t h e t r a n s i t i o n m e ta l a re a s s o c i a t e d w ith th e t h r e e p a ra m a g n e tic c o n t r i b u t i o n s t o th e m a g n etic s u s c e p t i b i l i t y . The h y p e r f in e H a m ilto n ia n may b e w r i t t e n as
h (
7
)w here 0 o p e r a te s on th e o n e - e l e c tr o n s p in (S ) an d o r b i t a l a n g u la r momentum ( | ) c o o r d in a te s . U sing an obvio us n o t a t i o n ,
7
0 * e, + ed -»• §
w here a . C
_ i . LiVi)
(8)
" b ,
and ,»rfc
The K n ig h t s h i f t t h e r e f o r e becomes K = Kg + K j + K + h ig h e r te rm ,
«*' , L1Wl -1/ . _ M oi-b
= v ^ j . % * i - - x W 3 + h ig h e r o r d e r te rm ,
o r
= asXs + Od^A + <W K w , (9)
w here and a r e th e e f f e c t i v e s c o n t a c t an d d - s p in (c o re
p o l a r i z a t i o n ) h y p e r f in e f i e l d p e r e l e c t r o n r e s p e c t i v e l y , and j;s t h e o r b i t a l h y p e r f in e f i e l d p e r u n i t o r b i t a l a n g u la r momentum. S in c e
i s n e g a tiv e w h ile and a r e p o s i t i v e , th e t o t a l s h i f t i n t r a n s i t i o n m etals may b e o f e i t h e r s ig n . F o r i n s t a n c e , th e o r b i t a l te rm
5 6 T 8
d o m in ates i n V , VCr a l l e y , W , and Kb . A cco rd in g t o B u tte rw o rth and g
D ra in , ab o u t 2% o f t h e t o t a l p aram ag n etism o f p u re vanadium i s due t o US s p in p aram ag n etism . About 50% i s o r b i t a l p aram ag n etism and th e r e m ainder i s due t o 3d s p in p aram ag n etism . T h is i s n o t s u r p r i s i n g s in c e t h e s e m e ta ls h ave ro u g h ly h a l f - f i l l e d d -b a n d s , e n c o u ra g in g o r b i t a l
e f f e c t s , w hereas P t , Pd and Hh have a lm o st f i l l e d d -b an d s so t h a t d - c o re p o l a r i z a t i o n e f f e c t s w i l l d o m in ate.
C. A llo y s and L o c a l E f f e c t s
The i n t r o d u c t i o n o f a f o r e ig n atom i n a p u re m e ta l h a s two m ain e f f e c t s : ( l ) t h e NMR l i n e b r o a d e n s , (2 ) t h e r e i s u s u a ll y a s h i f t
8
i n th e re s o n a n c e fre q u e n c y f o r a g iv e n e x t e r n a l m a g n e tic f i e l d . The change i n K n ig h t s h i f t , A K , r e s u l t s from o s c i l l a t o r y v a r i a t i o n s i n th e c o n d u c tio n e l e c t r o n ch arg e d e n s ity a b o u t th e s o l u t e i o n s . T h a t i s t o s a y , any im p u r ity i n a m e ta l w i l l p ro d u ce a ch arg e d is tu r b a n c e . Atom ic s i z e and e l e c t r o n e g a t i v i t y e f f e c t s ca u se t h i s t o b e t r u e , t o a l i m i t e d e x t e n t ev en i n th e ca se when th e v a le n c e o f th e h o s t and t h a t o f th e s o l u t e a re i n d e n t i c a l . The c o n d u c tio n e l e c t r o n s a c t t o s c r e e n th e
P P
Pert~ unpert
Perturbation of Conduction Electron charge Density
I
F ig u re 1 . Schem atic I l l u s t r a t i o n o f co n d u ctio n e l e c t r o n charge s c r e e n in g induced in a m eta l h o s t by a s i n g l e Im purity a t r - 0 . The h a lf - p e r io d o f th e F r ie d e l o s c i l l a t i o n s , which i s p r o p o r tio n a l t o 1/Kp i s in d ic a t e d .
9
ch arg e d i f f e r e n c e a s s o c ia t e d w ith t h e im p u r ity . T here w i l l b e a b u i l d up o r d e c re a s e i n th e t o t a l c o n d u c tio n e l e c t r o n ch arg e i n th e v i c i n i t y o f t h e im p u r ity dep end ing on th e s ig n o f th e sum o f c h a rg e te r m s . The p e r t u r b a t i o n o f c o n d u c tio n e l e c t r o n ch arg e d e n s it y i s i l l u s t r a t e d in F ig u re 1 . T here i s a h ig h ly l o c a l "main p eak " w ith th e f a m i l i a r F r i e d e l o s c i l l a t i o n s t o th e o u t s i d e . These a r i s e from th e p r e s e n c e o f a con
d u c tio n e l e c t r o n Fermi s u r f a c e and have a p e r i o d w hich i s i n v e r s e l y p r o p o r t i o n a l t o 2 k _ , i . e . , th e e x tre m a l c a l i p e r o f th e Ferm i s u r f a c e
r
i n t h e d i r e c t i o n i n q u e s ti o n .
The l i n e b ro a d e n in g i s a consequence o f th e same ch arg e r e d i s t r i b u t i o n phenomenon. S in c e th e im p u r ity io n s axe random ly d i s t r i b u te d , s o lv e n t n u c l e i a t d i f f e r e n t d is ta n c e s from th e im p u r ity w i l l s u f f e r d i f f e r e n t s h i f t s i n t h e i r re s o n a n c e f r e q u e n c i e s . When summed o v e r a l l t h e s o lv e n t n u c l e i , t h i s p ro d u c e s l i n e b ro a d e n in g . T h is phenomenon i s s i m i l a r i n some r e s p e c t t o t h e b ro a d e n in g c a u s e d b y th e
a n i s o t r o p i c K n ig h t s h i f t . I t s h o u ld b e n o te d t h a t th e l i n e b ro a d e n in g due t o a l l o y i n g w i l l b e f i e l d d e p e n d e n t. A n o th er p o s s i b l e s o u rc e o f l i n e b ro a d e n in g i n t h i s s tu d y o f t h e VZr a l l o y i n b o th th e amorphous and c r y s t a l l i n e s t a t e w i l l b e th e a n i s o t r o p i c K n ig h t s h i f t b ro a d e n in g
V,
and seco n d o r d e r q u a d ru p o le b r o a d e n in g . W ith t h e e x p l i c i t assu m p tio n s t h a t o n ly inhom ogeneous K n ig h t s h i f t b ro a d e n in g i s p r e s e n t , B la n d in an d D a n ie l d e r iv e d th e r u l e t h a t t h e l i n e w id th s h o u ld in c r e a s e 2
p r o p o r t i o n a l l y t o th e s q u a re r o o t o f th e c o n c e n tr a ti o n i n t h e i n f i n i t e l y d i l u t e a l l e y . T h e r e f o r e , i t i s n o t e x p e c te d t h a t su ch a c o n c e n tr a ti o n
dependence w i l l b e o b se rv e d i n t h e h ig h ly d i s o r d e r e d VZr a l l o y s t u d i e d h e r e . In d e e d t h e d a t a on th e a l l o y s o f s i l v e r and c o p p e r a n a ly z e d b y B la n d in and D a n ie l show o n ly a f e e b l e agreem ent w ith t h i s s q u a re r o o t r u l e .
I
10
I n o r d e r t o a s s e s s th e adequacy o f th e B la n d in and D a n ie l th e o ry f o r th e VZr a l l q y i n v e s t i g a t e d h e r e , i t w i l l be u s e f u l t o d is c u s s t h e i r th e o ry and th e assu m p tio n s e n t e r i n g i n t o i t . They c o n s id e r o n ly th e ca se o f h e t e r o v a l e n t a l l o y s . E l e c t r i c a l n e u t r a l i t y r e q u i r e s a r e d i s t r i b u t i o n o f th e c o n d u c tio n e l e c t r o n s so a s t o p rod uce a s c r e e n in g o f th e p e r t u r b i n g p o t e n t i a l w hich i s s p h e r i c a l l y sym m etric and l i m i t e d i n ran g e t o th e atom ic s p h e re o f th e im p u rity i o n . E x p l i c i t l y assum ing a f r e e e l e c t r o n m odel and B loch f u n c t i o n s , th e y u s e s ta n d a r d s c a t t e r i n g t h e o r y i n o r d e r t o c a l c u l a t e an e x p r e s s io n f o r A fl Y ) t th e change i n th e e l e c t r i c a l ch a rg e d e n s it y in tr o d u c e d b y th e s h i e l d e d im p u r ity
p o t e n t i a l , i n te rm s o f p h a se s h i f t s i n th e f r e e e l e c t r o n w a v e f u n c tio n s . Assuming th e p r o p o r t i o n a l i t y o f th e K n ig h t s h i f t t o th e e l e c t r i c ch a rg e d e n s it y a t th e n u c le u s , th e y o b ta in th e s im p le e x p r e s s io n
c K )
K f*
w here K . i s th e change o f K nigh t s h i f t e x p e r ie n c e d by th e n u c le u s a t V
R . To r e p r e s e n t th e im p u r ity p o t e n t i a l th e y choose a s p h e r i c a l w e l l J
w ith th e same r a d iu s as t h e s o l u t e io n and a d e p th s u f f i c i e n t t o a t t r a c t th e e l e c t r o n i c ch arg e r e q u i r e d f o r th e s c r e e n i n g . They in v o k e th e
F r i e d e l sum r u l e c o n n e c tin g t h e p h a se s h i f t s w ith t h e im p u r ity ch a rg e and u se B l a t t ' s p h ase s h i f t , w hich accom odates any s i z e e f f e c t s by 9 means o f an e f f e c t i v e c h a r g e , t o c a l c u l a t e a s p e c tru m o f K n ig h t s h i f t s f o r s i l v e r i n a l l o y s o f AgCd, A gin an d AgSn. F i n a l l y t o o b ta in an e x p r e s s io n f o r th e a v e ra g e K n ig h t s h i f t o f th e s o lv e n t n u c l e i i n low c o n c e n tr a ti o n h e t e r o v a l e n t a l l o y s , th e y f u r t h e r assume a random su b
s t i t u t i o n a l a l l o y , t h a t e l e c t r o n s on th e Ferm i s u r f a c e underg o no
11
m u l tip l e s c a t t e r i n g from th e d is s o lv e d i m p u r i t i e s , and t h a t th e n e t e x c e s s e l e c t r o n d e n s ity i s due t o th e i s o l a t e d i m p u r i t i e s whence
^ * 0 1 ^ s;*? t,'- * f y s , ( 1 0 )
w here C i s th e c o n c e n t r a t i o n , ^ a re p h ase s h i f t s . The o(f and f t
a r e g iv e n by th e f o llo w in g c o m b in a tio n s o f s p h e r i c a l B e s s e l an d Neumann f u n c ti o n s :
<4 = I c ,
and
f t a - u n - o z .
The o n ly o t h e r a ssu m p tio n e n t e r i n g i n t o t h e i r p r e d i c t i o n f o r l i n e
b ro a d e n in g i s t h a t t h e c o n t r i b u t i o n due t o th e im p u r ity i s much g r e a t e r th a n th e l i n e w id th c h a r a c t e r i s t i c o f th e p u re s o l v e n t .
The fo llo w in g o b s e r v a tio n s a r e o f f e r e d c o n c e rn in g th e
a p p l i c a b i l i t y o f t h e th e o r y o f B la n d in a n d D a n ie l 2 o u t l i n e d above t p th e d a t a o b ta in e d i n th e s tu d y o f th e amorphous VZr a l l o y . I f we
c o n s id e r th e am orphous p h a s e t o b e l i q u i d - l i k e , th e n th e s m a ll d e c re a s e o f K n ig h t s h i f t o b se rv e d i n th e amorphous p h a se VZr a l l o y w ould seem t o im ply t h a t i t i s f r e e e l e c t r o n l i k e , s i m i l a r t o m ost m e ta ls .
7.1 man^ a rg u e d t h a t s m a ll change o b s e rv e d i n K n ig h t s h i f t f o r m ost m e ta ls i n d i c a t e s t h a t a f r e e e l e c t r o n p i c t u r e o f m e ta ls i s more n e a r l y c o r r e c t th a n was p r e v io u s l y re c o g n iz e d . F u th erm o re th e p h ase s h i f t d e s c r i p t i o n o f B la n d in and D a n ie l’ s th e o r y u se d b y Odle and F ly n n ‘S u s in g t h e new ly d e riv e d p h ase s h i f t s h av e b e e n p a r t i a l l y s u c c e s s f u l i n d e s c r ib in g K n ig h t s h i f t v e rs u s c o n c e n tr a ti o n b e h a v io r i n l i q u i d
12
a l l o y s . Thus i t m ight b e e x p e c te d t h a t t h e B la n d in -D a n ie l th e o ry w i l l be p e r t i n e n t f o r amorphous VZr a l l o y s , a s i t i s f o r s i l v e r o r c o p p e r
a l l e y s , t o w hich i t was o r i g i n a l l y a p p l ie d .
The a ssu m p tio n s i n t h e i r th e o r y o f a s p h e r i c a l Ferm i s u r f a c e ( p u r e ly s - c h a r a c t e r f o r th e e l e c t r o n i c wave f u n c tio n s ) and e f f e c t i v e mass i d e n t i c a l t o th e no rm al e l e c t r o n m ass, w ould how ever a p p e a r t o be s u s p e c t i n view o f th e b a n d s t r u c t u r e c a l c u l a t i o n s and F erm i s u r f a c e
.. 1 2 ,1 3 o f vanadium
The B la n d in -D a n ie l th e o r y in c lu d e s o n ly changes i n th e 2 e l e c t r o n d e n s i t y . No c o n s id e r a tio n i s g iv e n t o p o s s i b le chan ges i n th e m a g n e tic s u s c e p t i b i l i t y p ro d u c e d by a l l o y i n g . T h is i s c e r t a i n l y q u e s ti o n a b le , s in c e th e K n ig h t s h i f t i s known t o depend on th e
e l e c t r o n i c s u s c e p t i b i l i t y . A lthough changes i n s u s c e p t i b i l i t y c o u ld b e in c o r p o r a te d i n t o a r e f i n e d v e r s io n o f th e s c a t t e r i n g th e o r y th ro u g h
changes in d u c e d i n th e d e n s it y o f s t a t e s a t th e Ferm i s u r f a c e b y p h ase s h i f t s , su ch a r e f in e m e n t h a s n o t y e t b e e n a tte m p te d , p ro b a b ly b e c a u se co m parisons b etw een th e o r y and e x p e rim e n t h av e s o f a r b een o n ly s e m i- q u a n t i t a t i v e a t b e s t .
A c o n c e p tu a l scheme w hich i s f r e q u e n t ly em ployed i n
c o n s id e r i n g th e p r o p e r t i e s o f a l l o y s i s th e s o - c a l l e d r i g i d b a n d model^
d is c u s s e d i n th e e a r l i e r s e c t i o n . F o r a p u re m e ta l th e e l e c t r o n i c s t r u c t u r e may b e f a i r l y w e ll a c c o u n te d f o r on th e b a s i s o f t h e p r e s e n t t h e o r y . E m ploying s i n g l e p a r t i c l e B loch f u n c ti o n s , th e e n e rg y s t r u c t u r e o f th e p u re m e ta l i s a d e q u a te ly d e s c r ib e d i n te rm s o f B r i l l o u i n z o n e s,
I
13
e n e rg y g a p s , e n e rg y b a n d s , a Ferm i s u r f a c e , d e n s it y o f s t a t e s ^ - e t c . The s im p l e s t form o f t h e r i g i d b a n d model o f a l lo y s assum es t h a t th e
c o n s ta n t e n e rg y s u r f a c e s and d e n s it y o f s t a t e s c h a r a c t e r i s t i c o f th e s o lv e n t a re n o t m o d ifie d b y a l l o y i n g . The consequ ences o f ad d in g th e s o l u t e a r e ad d in g o r s u b t r a c t i n g e l e c t r o n s from th e b a n d , depen din g on th e r e l a t i v e v a le n c e o f th e s o l u t e . Thus th e Ferm i s u r f a c e w i l l be e i t h e r d i l a t e d o r c o n t r a c te d by ad d in g th e s o l u t e . F o r exam ple i f we c o n s id e r 3d t r a n s i t i o n m e ta l a l l o y o f Ti-V a n d V-Cr s y ste m , th e r e i s a g r a d u a l i n c r e a s e i n K w ith e l e c t r o n t o atom r a t i o , w ith a peak a t ab o u t 5 .6 e l e c t r o n to atom ( e / a ) . Between e / a = 5*6 t o 6 , t h e r e i s a g r a d u a l d e c re a s e i n K. These a r e shown i n F ig u re 2 .
The complex n a tu r e o f K n ig h t s h i f t som etim es c a u s e s th e c o r r e l a t i o n o f K n ig h t s h i f t , s u s c e p t i b i l i t y , and s p e c i f i c h e a t t o be o b s c u re d , and th e f a c t t h a t K does n o t fo llo w th e d e n s it y o f s t a t e s cu rv e i s n o t n e c e s s a r i l y an i n d i c a t i o n o f n o n - r i g i d b a n d b e h a v io r . To g iv e a f u r t h e r p i c t u r e o f th e sh ap e o f th e d e n s it y o f s t a t e s cu rv e f o r 3 d a n d Ud t r a n s i t i o n m e ta l a l l o y m e n tio n ed ab o v e, we show th e t o t a l s u s c e p t i b i l i t y and d e n s it y o f s t a t e s d a t a i n F ig u re 3 . B oth f o r th e 3d and Hd s e r i e s , th e r e i s a p o s s i b l e cusp a t e / a = 5 . Both s u s c e p t i b i l i t y c u rv e s have q u i t e s i m i l a r b e h a v i o r . From t h i s p i c t u r e we g e t a d i f f e r e n t im p re s s io n o f th e d e n s it y o f s t a t e s c u rv e th a n from th e cu rv e o b ta in e d from s p e c i f i c h e a t ( y ) d a t a a s shown i n F ig u re 3 . Thus t h e r e i s d is c re p a n c y b etw een t h e y curve on one h a n d , and th e % cu rv e on th e o t h e r . D epending on w h ich c u rv e s a r e u s e d , th e K n ig h t s h i f t d a ta may b e i n t e r p r e t e d i n a q u i t e d i f f e r e n t m anner. I n e i t h e r ca se t h e r e
VC r
0.6
VTi
0.4
| Q . 4 d a llo y s , R
Nib Mo
0.8
Z r N b
0.6
5.0 6.0
4.0
e/a
F ig u re
2
- V a r ia tio n o f K night s h i f t w ith e / a r a t i o f o r b . c . c . t r a n s i t i o n m e t a ls - o f th e 3d and 4d row s. The d atawere tak en from th e f o llo w in g s o u r c e s : T1.-V ( 1 8 ) , V-Cr ( 1 8 , 1 9 ) , Zr-Nb, Nb-Mo (1 5 )
15
F ig u re 3*
3 d alloy s el
1 200
1V
TiV
O
2 0 0 • 4d allow
(a)
i TiV VCr
7 ; 2.0
4d alloys
NbMo
2.0
5 .0
e /a ——»
V a r ia tio n o f (a ) s u s c e p t i b i l i t y and (b) d e n s it y o f s t a t e s a s measured by e l e c t r o n ic s p e c i f i c h e a t , w ith e / a r a t i o f o r b . c . c . t r a n s i t i o n m e ta ls o f 3d and 4d row s.
The d a ta were tak en from th e f o llo w in g so u rce s:
Ti-V ( 1 8 ) , V-Cr (1 8 , 1 9 ) , Zr-Nb ( 1 5 ) , Nb-Mo ( 1 4 ) .
16
i s no d i r e c t c o r r e l a t i o n b etw een K an d th e o th e r d a t a an d th e r e m ust be an i n t e r p l a y o f s e v e r a l te rm s as a f u n c tio n o f e / a . A number o f a tte m p ts h ave b e e n made u s in g y > X > K as w e l l as 3 ^ d a t a and th e K o rrin g a r e l a t i o n t o d e r iv e th e v a r io u s c o n t r i b u t i o n s t o K. F o r exam ple th e r e s u l t s o f F ig u re 2 and 3 hav e b e e n e x p la in e d (R e f. 6 , lU , 15) by a tw o-band m odel f o r th e P a u l i te rm as i n Eq. 9 , w ith
e s ti m a t e s o f th e Van V leck o r b i t a l e f f e c t s . A lth oug h th e s e do e x p la in th e r e s u l t s , th e d e s c r i p t i o n i s n o t u n iq u e . An a l t e r n a t i v e e x p la n a tio n i n te rm s o f v a ry in g s - d m ix tu re i n a s i n g l e b a n d h a s b e e n o f f e r e d
(R e f. 16, 17) t o e x p la in th e maximum i n K a t e / a ~ 5*6. I n th e r e g io n above e / a = 5 - 6 , b o th th e s p e c i f i c h e a t y and s u s c e p t i b i l i t y “X a re d e c r e a s in g . W ith in t h i s m o d el, th e d e c re a s e i n K a r i s e s from a P a u li c o n t r i b u t i o n w hich becomes l e s s n e g a t i v e , and i n f a c t , p o s i t i v e w ith i n c r e a s i n g e / a . Only 10 t o 15 p e r c e n t s - c h a r a c t e r i n th e d -b an d i s r e q u i r e d t o b a la n c e o r o v e rta k e th e n e g a tiv e d -c o re p o l a r i z a t i o n te rm s . Changes i n s - c h a r a c t e r o f o n ly a few p e r c e n t can p ro d u ce th e o b se rv e d v a r a t i o n i n K. I f th e h y b r i d i z a t i o n m odel i s p ro v en v a l i d , th e K nig ht s h i f t can p r o v id e a u s e f u l p ro b e o f t h e v a r i a t i o n o f th e d e n s it y o f s s t a t e s i n "d" b a n d s .
D. Q uad ru po le E f f e c t s i n VZr A llo y
I t was o b s e rv e d t h a t th e i m p u r i t i e s w ere n e c e s s a r y t o s t a b i l i z e an "am orphous" s t r u c t u r e i n th e s p u t t e r e d VZr a l l o y f i l m s . Thus oxygen an d o t h e r r e s i d u a l gas m o le c u le s tr a p p e d i n VZr a l l o y f i l m may p la y an im p o r ta n t r o l e i n th e i n t e n s i t y and w id th o f NMR li n e s i n th e amorphous VZr f i l m s . F o r in s t a n c e th e i n t e n s i t y o f NMR l i n e , w hich i s d e f in e d t o
17
"be th e p r o d u c t o f th e p eak t o peak h e i g h t and v i d t h , i s a b o u t f i v e
T h e re fo re i t i s w o rth w h ile d i s c u s s i n g q u a d ru p o le e f f e c t s due t o th e fo rm a tio n o f th e amorphous s t a t e .
th e i n t e n s i t y o f th e n u c l e a r re s o n a n c e s i g n a l i n m e t a l l i c co p p er
d e c re a s e s r a p i d l y when th e co p p e r i s c o ld w orked o r s m a ll q u a n t i t i e s o f th e o th e r e le m e n ts a r e a llo y e d w ith i t . These r e s u l t s r e q u i r e t h a t each s o l u t e atom p ro d u c e s a s u b s t a n t i a l f i e l d g r a d i e n t w hich a c t s on th e c o p p e r n u c le a r q u a d ru p o le moments o f as many as
85
n e ig h b o rin g n u c l e i . Kohn and Vosko 19 showed t h a t f i e l d g r a d i e n t s , o f a p p r o x im a te ly th e r e q u i r e d m a g n itu d e , a r i s e from th e r e d i s t r i b u t i o n o f th e c o n d u c tio n e l e c t r o n c h a rg e n e a r th e s o l u t e atom s. A t la r g e d is ta n c e s from a s o l u t e atom th e e l e c t r o n d e n s i t y b eh av e s as c o s (2 k Qr + <P ) / r , w here k Q i s th e Ferm i wave number and f i s a p h a se a n g le . Such an
o s c i l l a t o r y b e h a v io r i s a co nsequence o f a d is c o n tin u o u s drop a t th e Ferm i s u r f a c e o f n ( k ) , th e o c c u p a tio n p r o b a b i l i t y o f th e c o n d u c tio n b a n d s t a t e w ith wave v e c t o r k . A cco rd in g t o Kohn and V osko’ s
c a l c u l a t i o n , th e e l e c t r i c f i e l d g r a d i e n t q a t th e n ^ 1 s i t e i s g iv e n by
w here of i s an enhancem ent f a c t o r w hich m easure th e in c r e a s e o f q o v e r i t s v a lu e i n a p la n e wave th e o r y w ith o u t a n t i s h i e l d i n g . A and <f a re d e te rm in e d b y th e p h a s e s h i f t s i n th e f o llo w in g e x p r e s s io n s :
tim e s s m a l le r th a n th e i n t e n s i t y o f t h e NMR l i n e a f t e r a n n e a lin g t o 900°C.
i o
The e x p e rim e n ts o f Bloem bergen and Rowland have shown t h a t
Q - H * * Aco&<3-fcfc.-KfJ
* 3 r * ’
18
“ 4
t * W.
^ Sin lj|
Rowland 20 h a s u se d t h e i r q v a lu e f o r v a r io u s d i f f e r e n t s o l u t e s and o b ta in e d th e number o f a f f e c t e d co p p er n u c l e i n and th e c o rre s p o n d in g v a lu e o f qQ i n th e f o llo w in g c o n c e n tr a tio n dependence o f th e i n t e n s i t y .
I = i o ( i - c ) n ,
w here C i s t h e ato m ic c o n c e n tr a tio n o f s o l u t e and n i s th e number o f c o p p er n u c l e i a f f e c t e d . Thus Kohn and V o sk o 's th e o r y i s i n agreem ent w ith R ow land's r e s u l t .
21 51
R e c e n tly M eerw all and Rowland i n v e s t i g a t e d V q u a d ru p o le e f f e c t s i n vanadium t r a n s i t i o n m e ta l a l l o y s . T h e ir r e s u l t s show th e s e e f f e c t s t o be s e v e r a l tim e s s m a lle r f o r t r a n s i t i o n m e ta l ( s u b s t i t u t i o n a l ) s o l u t e s th a n f o r i n t e r s t i t i a l oxygen and n i t r o g e n i n vanadium . The s o l u t e dependence s u g g e s ts t h a t f i e l d g r a d ie n ts aro u n d s u b s t i t u t i o n a l atoms a r i s e m a in ly i n re s p o n s e t o l o c a l l a t t i c e d i s t o r t i o n r a t h e r th a n th e s h i e l d i n g o f th e e x c e s s c h arg e o f th e s o l u t e . They e s ti m a t e d t h a t th e a l l - o r - n o t h i n g w ip e o u t m odel 21, when a p p l i e d t o th e i n t e r s t i t i a l a l l o y s , y i e l d s w ip e o u t numbers n ^ = 126 +_ 7 f o r n i t r o g e n i n V an d n = 1 9 h +. 12 f o r oxygen i n V. T h is m odel assum es t h a t th e c o n t r i b u t i o n t o t h e MMR l i n e i s l o s t f o r n u c l e i i n s i d e a s p h e re c e n te r e d on th e d e f e c t . E . B e h a v io r o f S u p e rc o n d u c tin g T r a n s i t i o n T em p eratu re (Tq ) o f
Amorphous and C r y s t a l l i n e M e ta l w ith R e s p e c t t o E l e c tr o n C o n c e n tr a tio n I t i s w o rth w h ile h e r e t o m en tio n th e v a r i a t i o n o f T o f
c
amorphous and c x y s t a l l i n e m e ta ls w ith r e s p e c t t o e l e c t r o n c o n c e n tr a ti o n m easured b y C o llv e r and Hammond , b e c a u se i t may b e c o r r e l a t e d t o th e 22 v a r i a t i o n o f K n ig h t s h i f t o f th e amorphous t r a n s i t i o n b i e t a l a l l o y s
19
w ith r e s p e c t t o e l e c t r o n c o n c e n tr a ti o n . They showed t h a t Tfi o f th e amorphous f il m o f th e ltd and
5
d t r a n s i t i o n m e ta l a l lo y s in c r e a s e s as a f u n c tio n o f th e number o f e l e c t r o n s p e r atom i n a smooth n e a r l y l i n e a r f a s h io n t o a d e f i n i t e t r i a n g u l a r p eak n e a r th e m idd le o f th e d s e r i e s . The peak o c c u rs f o r th e ltd s e r i e s a t e /a ~6
.U i n c o n t r a s t t o th e c r y s t a l l i n e maximum a t 6 . J . The Tc d e c re a s e s a t n e a r l y th e same s lo p e ,fo llo w e d by a more r a p id d e c re a s e a t e / a - 7 . 0 . T h is i s shown i n F ig u re It.
The smooth b e h a v io r i n Tc a c r o s s two p h ase r e g io n s o f th e a l l o y sy ste m d e m o n stra te s t h a t e / a d e te rm in e s Tq i n th e "am orphous" s t a t e , in d e p e n - d e n t o f th e no rm al c r y s t a l s t r u c t u r e . A cco rd in g t o B. C. S . th e o ry 23, Tq i s r e l a t e d t o many n o rm al s t a t e p r o p e r t i e s in c lu d in g e l e c t r o n i c d e n s it y o f s t a t e s and phonon s p e c tru m as fo llo w s :
w here ui i s th e mean phonon fre q u e n c y , N(E„) i s th e d e n s it y o f s t a t e s
c r
a t th e Ferm i s u r f a c e , and V . . i s th e a v e ra g e a t t r a c t i v e i n t e r a c t i o n
CL vX
b etw een e l e c t r o n p a i r s . I n th e c i y s t a l l i n e s t a t e N(E„) e x h i b i t s a r
s t i l l u n e x p la in e d c o r r e l a t i o n w ith
1
/6
2^ (a n d t h e r e f o r e l / < <d > ) ,a n d i t i s b e l i e v e d t o b e th e f a c t o r c o n t r o l l i n g th e e l e c t r o n phonon i n t e r -2^
25
a c t i o n p a r a m e te r and Tq * . I n th e amorphous s t a t e th e N(Ep) i s
26
27assum ed t o b e sm oothed o u t v e rs u s e / a b y th e d i s o r d e r , * a llo w in g th e v a r i a t i p n w ith e / a o f th e amorphous Tc t o b e d e te rm in e d b y .th e i n t e r a c t i o n p a ra m e te r o r o t h e r ato m ic l i k e p a r a m e te r s . I n a h ig h ly d is o r d e r e d s t a t e a l l s t r u c t u r e i n N(Ep) i s sm eared o u t , r e d u c in g
Y Zr
Nb Mo (Tc) Ru3 4 5 6 7 *
' / ‘ — »
F ig u re
4 .
Su perconducting t r a n s i t i o n tem perature o f th e a s - d e p o s it e d vapor quenched 4d t r a n s i t i o n m e ta l f ilm s v e r su s th e number o f e le c tr o n s p er atom. The dashed l i n e i s fo r c r y s t a l l i n e s t a t e and th e s o l i d l i n e f o r th e amorphous s t a t e .T h is i s ta k en from r e fe r e n c e 2 2 .
21
N(E_) w here i t e x h i b i t s maxima ( n e a r Nb and Ta) and i n c r e a s i n g N(E_) r w here i t e x h i b i t s minima ( n e a r Mo and W).
28
C o llv e r a l s o i n d i c a t e d t h a to th e r "types o f sm earin g o r a l t e r a t i o n s a re p o s s i b l e w hich w ould s tr o n g l y a l t e r N(E ) . These in c lu d e a sm earin g due t o a v a r i a t i o n i n th e number
r
o f n e a r e s t n e ig h b o rs s and a l t e r a t i o n o f th e e f f e c t s o f s - d and d -d h y b r i d i z a t i o n due t o th e l o s s o f symmetry and change o f s h o r t ran g e o r d e r . The form o f s h o r t ra n g e o r d e r , i . e . , th e number o f n e a r e s t
n e ig h b o rs and t h e i r i n t e r a to m ic s p a c in g , w i l l in tr o d u c e a "b an d s t r u c t u r e "
a l l i t s own. T h is s h o r t ra n g e o r d e r w i l l te n d t o b e c lo s e p ack e d , i . e . , an h . c . p . o r f . c . c . s t r u c t u r e ( in c l u d in g V, Nb, Mo e t c . )22
Snow and Waber 29 made th e b a n d s t r u c t u r e c a l c u l a t i o n f o r 3d t r a n s i t i o n m e ta l s e r i e s assum ing t h a t th e y ta k e up f . c . c . s t r u c t u r e and o b ta in e d a N(E_) f o r f . c . c . w ith l e s s la r g e s c a l e v a r i a t i o n th a n
r
f o r th e b . c . c . s t r u c t u r e . F u rth erm o re th e e n t i r e b a n d sh ap e i . e . , N(E) v e rs u s E ta k e s on a b ro a d s i n g l e p eak b e h a v io r t o a f i r s t a p p ro x im a tio n , e s p e c i a l l y i f one f a v o r s th e s^d 11-^ o v e r sd n c o n f ig u r a tio n i n th e s o l i d .
2 n - 1
A cco rd in g t o Snow and Waber th e s d ~ i s t o b e p r e f e r r e d s in c e th e Ferm i l e v e l and e n e rg y s t a t e s l i e a t th e l a r g e r e n e rg y i n sd n c o n f ig u r a t i o n . T h is i s a r e f l e c t i o n o f th e e l e c t r o s t a t i c r e p u ls i o n betw een d e l e c t r o n s .
From t h e s e t h e o r e t i c a l c o n s i d e r a t i o n s , we w i l l s e e th e f o llo w in g p o i n t s p e r t i n e n t t o th e NMR s tu d y o f b o th th e amorphous and th e c r y s t a l l i n e VZr a l l o y : F i r s t l y , F r i e d e l o s c i l l a t i o n s a c c o u n t f o r th e li n e w id th an d t h e change o f K n ig ht s h i f t even th ou gh d e t a i l e d a p p l i c a t i o n o f th e o r y i s i n p o s s i b l e f o r th e s e c o n c e n tr a te d a l l o y s .
22
S eco ndly a b an d th e o ry c a n n o t be r u l e d o u t. Only a s m a ll p o r t i o n (~2%) o f s u s c e p t i b i l i t y X i s h ig h ly s e n s i t i v e t o b a n d changes and th e la c k o f a p p r e c ia b le changes i n K n ig h t s h i f t does n o t r u l e o u t changes such as C o llv e r d i s c u s s e s .
I I I . E x p e rim e n ta l P ro c e d u re
I n t h i s s e c t i o n d e t a i l s o f th e p r e p a r a t i o n o f th e amorphous t r a n s i t i o n m e ta l a l l o y VZr f i l m w i l l b e d is c u s s e d . T h is i s fo llo w e d by a b r i e f d is c u s s io n o f th e e x p e r im e n ta l a p p a r a tu s u s e d i n th e
d e t e c t i o n o f th e NMR s i g n a l s . A. P r e p a r a t io n o f Samples
The VZr f ilm s w ere p r e p a r e d b y th e RF s p u t t e r i n g p r o c e s s . S p u tt e r i n g i s a c o a tin g p r o c e s s w hich in v o lv e s th e t r a n s p o r t o f alm o st any m a t e r i a l from a s o u r c e , c a l l e d a t a r g e t , t o a s u b s t r a t e o f alm o st any m a t e r i a l . The e j e c t i o n o f th e s o u rc e m a t e r i a l i s a c c o m p lish e d by th e bombardm ent o f th e s u r f a c e o f th e t a r g e t w ith gas io n s a c c e l e r a t e d by h ig h v o l t a g e . P a r t i c l e s o f atom ic d im en sio n s from th e t a r g e t a re e j e c t e d a s a r e s u l t o f momentum t r a n s f e r b etw een i n c i d e n t io n s an d th e t a r g e t . The t a r g e t - e j e c t e d p a r t i c l e s t r a v e r s e th e vacuum cham ber and a r e s u b s e q u e n tly d e p o s ite d on a s u b s t r a t e a s a t h i n f i l m . The main f e a t u r e o f th e s p u t t e r i n g module u s e d i n t h i s r e s e a r c h i s shown i n F ig u re 5* The d e p o s i t i o n to o k p la c e i n th e s p u t t e r i n g cham ber w ith th e f o llo w in g c o n d itio n ^ : ( i ) RF fre q u e n c y 1 3 .5 6 MHz, ( i i ) RF pow er 100 w a t t s , ( i i i ) Argon gas p r e s s u r e 3 x 10 -•3 t o r r , and ( i v ) b ack g ro u n d p r e s s u r e i s 1 x 10- ^ t o r r .
23
2k
Matching
n e t w o r k
RF Generato
_ /*
Target .Removable shutter
Double Ended
’ 'Jar Assembly Substrate
y v c v
1
C l a m P
R F P o w e r
F ig u r e 5 . Schem atic diagram o f th e S p u tte r in g module
25
B. T a r g e t and S la b s tra te
To o b ta in VZr a l l o y f ilm s w ith v a r io u s c o n c e n tr a ti o n s , • f i v e in c h d ia m e te r d is c s o f p u re vanadium and zirc o n iu m w ere u s e d w ith th e f o llo w in g a rra n g e m e n ts : In o r d e r t o o b ta in a s u i t a b l e Zr
s p u t t e r i n g r a t e and u n ifo rm VZr f il m on a s u b s t r a t e , 6 l h o le s w ere d r i l l e d o n to a 5" d ia m e te r d is c o f th e vanadium t a r g e t . Then th e vanadium t a r g e t w ith 6 l h o le s was sandw iched w ith th e z irc o n iu m t a r g e t s o t h a t t h i s sand w ich ed t a r g e t was ex p o sed t o th e incom ing arg o n io n s as shown i n F ig u re 5• The amount o f z irc o n iu m c o n c e n tr a ti o n i n VZr a l l o y f i l m was d ep en d e n t on th e s i z e o f th e h o le s i n th e vanadium t a r g e t , b e c a u s e th e s i z e o f th e h o le s d e te rm in e d th e a r e a o f z irc o n iu m t a r g e t a c c e s s i b l e t o th e in co m in g arg o n i o n s . F o r exam ple,
S iz e o f h o le i n A pproxim ate
vanadium t a r g e t Zr c o n c e n tr a tio n
( i n d ia m e te r) i n VZr a l l o y f il m
0.202" 10Jg
0.282" 20%
0 .2 5 1 " 30%
0.U53" 1*0%
The f ilm s w ere d e p o s ite d on a 5" d ia m e te r c o p p er o r aluminum d is c (1 /1 6 " t h i c k ) . The s u b s t r a t e was th e n m ounted i n a s u b s t r a t e h o ld e r an d clam ped d i r e c t l y a g a i n s t th e w a te r - c o o le d co p p er p l a t e as shown i n F ig u re 5•
C. S t r u c t u r e and C o m p osition A n a ly s is o f VZr F ilm
The s t r u c t u r e o f th e s p u t t e r e d VZr f il m was d e te rm in e d b y
2 6
X -ray d i f f r a c t i o n . I n o r d e r t o e l i m i n a te X -ray d i f f r a c t i o n p a t t e r n s due t o co p p er o r aluminum s u b s t r a t e , X -ra y d i f f r a c t i o n o f th e s u b s t r a t e was ta k e n . U sing th e f o llo w in g fo rm u la 30 ( S c h e r r e r f o rm u la ),
t = 0.9X /B cos 0
2 2 2
w here t = g r a i n s i z e , X = w a v e le n g th o f X r a y u s e d , B = B„ - B0
M b
(Bm = th e m easured h a l f w id th o f X -ray i n t e n s i t y peak f o r th e sa m p le , Bg = th e m easured h a l f w id th o f th e s t a n d a r d ) , one can o b ta in th e
IT 2 28
ap p ro x im ate g r a i n s i z e o f VZr a l l e y f i l m . The amorphous VZr , VZr
k 6 U / 91
and VZr ’ f ilm s (w here th e s u p e r s c r i p t d e n o te s th e Z r c o n c e n tr a ti o n , i n ato m ic p e r c e n t) g iv e ab o u t 10 A° as u p p e r l i m i t f o r th e g r a i n s i z e . O ther f ilm s show th e c r y s t a l l i n e p h a s e , an d t h e i r g r a i n s i z e s a r e l a r g e r th a n a few th o u s a n d an g stro m s.
The co m p o sitio n o f b i n a r y a l l e y f ilm s i s d e te rm in e d b y b o th
31 32
R u th e rfo r d b a c k s c a t t e r i n g s p e c tro m e tr y and n e u tro n a c t i v a t i o n a n a l y s i s The R u th e r fo r d b a c k s c a t t e r i n g s p e c tr o m e tr y u s e s t h e f o llo w in g p r i n c i p l e . When a c o l lim a te d beam o f m o n o e n e rg e tic h e liu m io n s o r o f a n o th e r l i g h t e le m e n t im ping es on a t a r g e t , some o f th e h e liu m p a r t i c l e s a r e r e f l e c t e d by e l a s t i c c o l l i s i o n s w ith th e atom o f t a r g e t . The s c a t t e r e d p a r t i c l e
l o s e s e n e rg y i n amount r e l a t e d t o th e mass o f th e atom s t r u c k . F u th e r , th e number o f p a r t i c l e s so s c a t t e r e d i s a f u n c ti o n o f th e numiber o f atoms p r e s e n t . Hence b y m e asu rin g th e numiber o f th e em erg in g p a r t i c l e s , th e i d e n t i t y and number o f a to m sin th e f i l m can b e d eterm ined.. The r e l a t i o n s h i p b etw een th e numiber o f atoms N^/cm p r e s e n t i n a t a r g e t and th e number o f s c a t t e r e d p a r t i c l e n d e t e c te d w i l l b e g iv e n b y
£L
nA = ((MA - m) / (Mj + m ))2 Z2 NA ,
27
w here i s t h e mass o f ty p e A atom i n th e t a r g e t , m th e mass o f h e liu m atom and Z^ th e atom ic number o f ty p e A atom . S i m i l a r i l y f o r th e ty p e B atom ,
ng =(Mg - m/Mg + m) 2 Z^ Nfi.
Hence th e r e l a t i v e number o f ty p e A and B atom p r e s e n t i n a f i l m w i l l b e g iv e n by
"a = /mb - “ / mb + M lM. - m / M. +
B ‘ A A nB
The n^ / ng i s e v a lu a te d d i r e c t l y from th e o b s e rv e d e n e rg y sp e c tru m . The r e s u l t s o f th e s e m easurem ents a r e shown i n T ab le I .
T ab le I .
th e o r i g i n a l e s ti m a t e s R u th e r fo r d N eu tro n a c t i v a t i o n from th e a r e a o f h o le b a c k s c a t t e r i n g a n a l y s i s ,
s i z e . m ethod
V -Z r5 V-Zr6 * ^ V -Z r8 *5
V -Zr10 V -Zr8 *11 V -Zr2 0 *6
V -Zr20 V -Zr1 7 *2 V -Zr30
V -Zr30 V -Zr28 V -Z r1*9 *3
V -Zr5° V -Zr1*6 * ** V -Zr75 *8
The s u p e r s c r i p t d e n o te s t h e ato m ic p e r c e n t o f z irc o n iu m . The e x p e r im e n ta l e r r o r i n R u th e r f o r d b a c k s c a t t e r i n g m ethod w i l l b e l e s s th a n 0 .5 $ . N eu tro n a c t i v a t i o n a n a l y s i s f o r th e Z r 91 c o n c e n tr a ti o n i n VZr f i l m was p e rfo rm e d b y th e n u c l e a r e n g in e e r in g d e p a rtm e n t a t VPI and S t a t e U n i v e r s i t y . They c la im e d th e a c c u ra c y o f th e a n a l y s i s was low , b e c a u s e th e b ack g ro u n d a c t i v i t y o f th e c o p p e r s u b s t r a t e was h ig h .
H el m h o lt z C o il
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D. NMR Equipm ent
As NMR s p e c tr o m e te r, th e R obinson o s c i l l a t o r 32 was u se d f o r o b ta in in g th e d a t a . T his i s one o f t h e s ta n d a r d CW NMR d e t e c ti o n s y ste m s , and w i l l b e d is c u s s e d b elo w .
A b lo c k d iag ram o f th e NMR sy stem i s shown i n F ig u re 6 . R obinson o s c i l l a t o r c o n s i s t s e s s e n t i a l l y o f a v a r i a b l e R. F . fre q u e n c y o s c i l l a t o r o p e r a te d u n d e r such c o n d itio n s t h a t a d e c re a s e i n Q, o c c u r r in g as th e fre q u e n c y o r th e f i e l d i s sw ep t th ro u g h th e n u c le a r m a g n e tic re s o n a n c e , c a u se s a d e c re a s e o f th e l e v e l o f
o s c i l l a t i o n . The sam ple whose NMR i s t o be o b s e rv e d i s p la c e d d i r e c t l y i n s i d e an r f c o i l w hich i s a p a r t o f th e ta n k c i r c u i t o f th e o s c i l l a t o r . When th e sam ple a b s o rb s r f e n e rg y a t re s o n a n c e , t h i s r e p r e s e n t s a
d e c re a s e i n Q i n t h e ta n k c i r c u i t , and th e change i n t h e l e v e l o f o s c i l l a t i o n may b e o b se rv e d b y m e asu rin g th e r f v o lta g e a c r o s s t h i s sam ple b e a r i n g c o i l . The a d v a n ta g e s o f b o th R obinson and P o u n d - K n ig h t-W a tk in 's (PKW) m a rg in a l o s c i l l a t o r a r e as f o llo w s : ( l ) s in c e th e y re s p o n d t o changes i n r e s i s t a n c e o n ly , th e re s o n a n c e l i n e i s due e n t i r e l y t o % " , th e a b s o r p ti v e p a r t o f th e e f f e c t i v e s u s c e p t i b i l i t y ( e x c e p t w ith s i n g l e c r y s t a l s o r la r g e sam ple g r a i n s , w here eddy
c u r r e n t m ix in g o f and “TCi1 o c c u r s ) ; (2 ) th e y a re r e a d i l y a d a p t ib le t o p l a c i n g th e sam ple d i r e c t l y i n t o a v a r i a b l e te m p e ra tu re sy stem
— th e sam ple c o i l i s m e re ly s o ld e r e d t o a c o a x i a l c a b le by w hich i t i s su sp e n d e d i n s i d e th e dewar v e s s e l .
The R obinson o s c i l l a t o r c i r c u i t t h a t was u se d i n t h i s s tu d y was m o d ifie d b y P e t r i n o v i c OO and i s shown i n F ig u re 7 and. 8 .
• | |DMIV
30
M OO I
sA A /V ^
tc
Figure7*Robinson Oscillator and Limiter Circuit
» S t» N I
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31 MO
I
N/S/S/S/^
1
W r ctions foRobinSson CircueioFeigure
