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CONDUCTION ELECTRON SPIN RESONANCE OF LITHIUM AMMONIA SOLUTIONS IN THE RANGE
OF THE METAL TO NON METAL TRANSITION
P. Damay, J. Lelieur, P. Devolder
To cite this version:
P. Damay, J. Lelieur, P. Devolder. CONDUCTION ELECTRON SPIN RESONANCE OF LITHIUM AMMONIA SOLUTIONS IN THE RANGE OF THE METAL TO NON METAL TRANSITION.
Journal de Physique Colloques, 1980, 41 (C8), pp.C8-24-C8-27. �10.1051/jphyscol:1980806�. �jpa-
00220190�
JOURNAL DE PHYSIQUE CoZZoque C8, suppZ6ment au n08, Tome 41, ao6t 1980, page C8-24
CONDUCTICM ELECTRON S P I N RESONANCE O F L I T H I U M AMMONIA S O L U T I O N S I N T H E RANGE OF T H E M E T A L TO NON M E T A L T R A N S I T I O N
P . Damay
,
J . P . L e l i e u r and P . D e v o l d e r (t)Laboratoire dlEtudes des Surfaces e t I n t e r f a c e s , E. H E I
,
13, rue de TouZ, 59046 LiZZe, France ( i l U n i v e r s i t 6 des Sciences e t Techniques de LiZZe, U E R de Chimie, 59650 VXZeneuve dlAscq, FranceINTRODUCTION
It i s well e s t a b l i s h e d t h a t s o l u t i o n s o f a l k a l i m e t a l s i n l i q u i d ammonia d i s p l a y a c o n t i n u - o u s t r a n s i t i o n , when t h e m e t a l c o n c e n t r a t i o n is i n c r e a s e d , f r o m a n e l e c t r o l y t i c t o a m e t a l l i c s t a t e T h i s non-metal t o m e t a l t r a n s i t i o n i s w e l l d i s - p l a y e d by e x p e r i m e n t a l q u a n t i t i e s l i k e t h e e l e c - t r i c a l c o n d u c t i v i t y . T h e o r e t i c a l d e s c r i p t i o n o f t h e t r a n s i t i o n has been a m a t t e r o f controversy d u r i n g t h e p a s t years, and i s s t i l l a s u b j e c t o f i n t e r e s t . 8 9 9 y 11' A microscopic d e s c r i p - t i o n o f t h i s t r a n s i t i o n r e q u i r e s knowledge of e x p e r i m e n t a l p r o p e r t i e s w i t h a s t r o n g l o c a l cha- r a c t e r . E l e c t r o n s p i n r e s o n a n c e h a s been o b s e r v e d f o r a l o n g time i n t h e s o l u t i o n s of a l k a l i m e t a l s i n l i q u i d ammonia 2. The l i n e w i d t h o f t h e E S R s i g n a l f o r t h e d i l u t e s o l u t i o n s (when t h e mole r a t i o ammonia/metal is l a r g e r t h a n a b o u t 200, i.e.
when t h e m e t a l c o n c e n t r a t i o n is s m a l l e r t h a n a b o u t 0.5 Mole p e r Cent o f M e t a l (M P M) is o f t h e o r d e r o f 3 0 m G and i s o n e t h e n a r r o w e s t known E S R l i n e s . For v e r y c o n c e n t r a t e d s o l u t i o n s (mole r a t i o s m a l l e r t h a n a p p r o x i m a t e l y 10, i . e . m e t a l concen- t r a t i o n l a r g e r t h a n a b o u t 9 MPM), t h i s l i n e i s a few Gauss wide, d e p e n d i n g upon t h e a l k a l i m e t a l i n t h e s o l u t i o n . F o r t h e s e v e r y c o n c e n t r a t e d s o l u - t l o n s , t h e e l e c t r i c a l c o n d u c t i v i t y is l a r g e r t h a n a b o u t l o 3 d 1 cm-I, and t h e r e f o r e f o r t h e X-band f r e q u e n c y r a n g e of a t y p i c a l E S R e x p e r i m e n t t h e s k i n d e p t h is s m a l l e r t h a n t h e d i a m e t e r o f t h e s a m p l e . C o n s e q u e n t l y t h e e l e c t r o n s d i f f u s e i n t o o r o u t of t h e s k i n d e p t h . I n t h e s e c o n d i t i o n s t y p i c a l o f m e t a l s , a d i s t o r t i o n of t h e E S R s i g n a l is ob- served 3' 4' 5 , 6 .
I n t h e p r e s e n t p a p e r , we r e p o r t a d e t a i l e d e x p e r i m e n t a l s t u d y o f E S R i n l i t h i u m ammonia s o l u t i o n s i n t h e c o n c e n t r a t i o n r a n g e o f t h e non- m e t a l t o m e t a l t r a n s i t i o n . I n t h i s c o n c e n t r a t i o n r a n g e t h e l i n e w i d t h o f t h e E S R s i g n a l i n c r e a s e s r a p i d l y w i t h t h e l i t h i u m c o n c e n t r a t i o n , and t h e
e l e c t r i c a l c o n d u c t i v i t y i n c r e a s e s r a p i d l y t o o . T h e r e f o r e t h e l i n e s h a p e i s s t r o n g l y c o n c e n t r a t i o n d e p e n d e n t . The v a r i a t i o n s o f t h e l i n e s h a p e h a v e been a n a l y z e d v e r s u s t h e l i t h i u m c o n c e n t r a t i o n between 0 and -80°C. The r e l a x a t i o n time T2 and t h e d i f f u s i o n t i m e TD have been o b t a i n e d . The g
-
s h i f t h a s a l s o been measured a s a f u n c t i o n o f l i t h i u m c o n c e n t r a t i o n and t e m p e r a t u r e . P a r a m e t e r s r e l a t e d t o t h e E S R l i n e s h a p e i n p r e s e n c e of s k i n e f f e c t , e x p e r i m e n t a l p r o c e d u r e and r e s u l t s a r e s u c c e s s i v e l y p r e s e n t e d .
I n l i t h i u m ammonia s o l u t i o n s , t h e e l e c t r i c a l c o n d u c t i v i t y i n c r e a s e s q u i t e r a p i d l y w i t h t h e li- t h i u m c o n c e n t r a t i o n , and a l s o w i t h t h e t e m p e r a t u r e . C o n s e q u e n t l y t h e s k i n d e p t h v a r i e s and t h e E S R s i g n a l l i n e s h a p e is c o n c e n t r a t i o n and t e m p e r a t u r e d e p e n d e n t . The p a r a m e t e r s which c h a r a c t e r i z e t h e l i n e s h a p e a r e h e r e b y g i v e n . A l s o t h e f i r s t and t h e s e c o n d d e r i v a t i v e s o f t h e s p i n r e s o n a n c e a b s o r p t i o n s i g n a l h a v e been r e c o r d e d and a n a l y z e d . The t h e o r y o f E S R i n m e t a l s was f i r s t g i v e n by Dyson 3 , and d e t a i l e d by F e h e r and K i p 4. A n o t h e r f o r m u l a t i o n of t h e t h e o r y was g i v e n by Kaplan and d e Gennes 6
.
The u s e f u l n e s s o f t h e s e c o n d d e r i v a t i v e was d e t a i - l e d by G l a u n s i n g e r and S i e n k o
'.
It a p p e a r s f r o m t h e t h e o r y t h a t t h e b a s i c p a r a m e t e r which d e t e r - m i n e s t h e l i n e s h a p e is t h e r a t i o R -(T,/T~)YL
where TD i s t h e d i f f u s i o n time o f a n e l e c t r o n t h r o u g h t h e s k i n d e p t h , a n d T2 is t h e s p i n r e l a - x a t i o n time. A l l t h e usual parameters o f t h e f i r s t d e r i v a t i v e ( i . e . t h e asymmetry parameter A(')/ ~ ( l ) , l i n e w i d t h a t h a l f maximum
AH(^)
peak t o peak l i n e - w i d t h AH;:), d i s p l a c e i e n ts ~ ( ' )
o f t h e resonance w i t h t h e apparent resonance p o s i t i o n , a r e d e f i n e d( 1 )
,
i n r e f . 7. The q u a n t i t i e s A(')/B('), yTt AHpp YT~AH(') have been expressed i n t h e l i t e r a t u r e v e r - sus R
.
Therefore t h e measurement o f A/B gives t h eArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980806
v a l u e of R f o r a g i v e n sample and yT2 can t h e n be The two modulation f r e q u e n c i e s f o r d e t e r m i n i n g t h e deduced. AS t h e e l e c t r o n gyromagnetic r a t i o y f i r s t and second d e r i v a t i v e of t h e s i g n a l were v a l u e of R f o r a given sample and yT2 c a n t h e n be r e s p e c t i v e l y 100 k Hz and 1 kHz
.
Usual r e s p o n s e deduced. As t h e e l e c t r o n gyromagnetic r a t i o y t i m e s were 8 o r 4 m i l l i s e c o n d s .can be determined q u i t e a c c u r a t e l y with t h e f r e e The r e l a t i v e u n c e r t a i n t y f o r t h e d e t e r m i n a t i o n e l e c t r o n g v a l u e , T2 c a n t h e n be o b t a i n e d , and a l s o of AH(1) f o r t h e f i r s t d e r i v a t i v e i s l e s s t h a n
T ~ ' one p e r c e n t . The a b s o l u t e
error
f o r t h e tempera-The same procedure has been used f o r t h e second t u r e c o e f f i c i e n t & d T i s
+
2 x xad1]
p e rd e r i v a t i v e . The parameters
are
l a b e l l e d w i t h d e g r e e . A f t e r p r e p a r a t i o n , t h e samples were s t o r e dindex ('). i n l i q u i d n i t r o g e n . Before t h e e x p e r i m e n t s t h e
r a t e measurements of A ( 2 ) / ~ ( 2 ) , and t h e n T2 and TD samples were homogenized a t room t e m p e r a t u r e . c a n be e x t r a c t e d by t h e measurement of e i t h e r Measurements
were
t a k e n e v e r y f i v e d e g r e e s , from( 2 )
AH(^)
o r d~~~.
room t e m p e r a t u r e down t o -60° C. For most o f t h e8 s
T h e r e f o r e , t h e b a s i c p h y s i c a l q u a n t i t i e s T2, samples, t h e f u l l r u n s have been c a r r i e d o u t a t TD, and a l s o t h e g s h i f t , c a n be o b t a i n e d from l e a s t a n o t h e r
time.
R e s u l t s were found p e r f e c t l y e i t h e r t h e f i r s t o r t h e second d e r i v a t i v e of t h e r e p r o d u c i b l e .s p i n r e s o n a n c e a b s o r p t i o n s i g n a l . However t h e RESULTS d e t e r m i n a t i o n of t h e s e q u a n t i t i e s from both d e r i -
The v a r i a t i o n of t h e l i n e w i d t h AH(') i s v a t i v e s a s s u r e s t h e coherence o f e x p e r i m e n t a l r e -
r e p o r t e d on F i g . 1 v e r s u s t h e l i t h i u m c o n c e n t r a t i o n . s u l t s and c a n c o n f i r m o r i n f i r m t h e Dysonian cha-
r a c t e r of t h e l i n e s h a p e .
AH(^)
is a l s o more well r3of9PTetl e x p e r i m e n t a l l y t h a n PP A H ( ' ' due t o t h ePP
'
f a c t t h a t t h e second d e r i v a t i v e i s more compact t h a n t h e f i r s t .
EXPERIMENTAL
Samples o f l i t h i u m i n l i q u i d ammonia have been p r e p a r e d i n q u a r t z o r pyrex c y l i n d r i c a l t u b i n g o f 4 mm o u t e r d i a m e t e r and 2 mm i n n e r d i a m e t e r . Samples
05
-
were a b o u t 8 cm h i g h , and t h e s o l u t i o n i n s i d e was
about 3 cm high. The l i t h i u m was c u t under argon
I /
i n a g l o v e bag, and w e i g h e d under vacuum o r argon
I /
atmosphere. The amount of ammonia condensed on t h e
I
l i t h i u m was determined by t h e v o l u m e t r i c determina- t 2 3 4 concentratton 5 r u p ~ 1
.
. llt i o n o f ammonia g a s t h e r e f o r e t h e c o n c e n t r a t i o n s o f
t h e samples were known v e r y a c c u r a t e l y . It must be fig. 1 : Peak to Peak linewidth n H ( l ) of the noted t h a t i n t h i s s t u d y a r e l a t i v e l y narrow con- f i r s t d e r i v a t i v e (Gauss) v e r s u s t h e l i t h i u m concen- c e n k r a t i o n r a n g e
is
sampled, which r e q u i r e s an t r a t i o n (Mole P e r Cent of l i t h i u m )a t
-3!j0C.a c c u r a t e knowledge of t h e l i t h i u m c o n c e n t r a t i o n . For a few samples, t h e c o n c e n t r a t i o n was n o t known a p r i o r i , and was t h e n determined by t h e v a l u e o f
AH'^),
on t h e c u r v e AH") v e r s u s t h e l i t h i u m c o n c e n t r a t i o n . The e x p e r i m e n t s have been performed on a V a r i a n S p e c t r o m e t e r E 109. The f i e l d sweep was c o n t r o l e d v i a t h e Varian F i e l d l o c k U n i t which l o c k s t h e f i e l d on t h e r e s o n a n c e of a sample of dpph. I n t h i s way a c c u r a t e d e t e r m i n a t i o n o f g value can be o b t a i n e d . The t e m p e r a t u r e is s t a b i l i z e d bymeansof a f l o w of n i t r o g e n c o o l e d i n l i q u i d n i t r o g e n u s i n g t h e v a r i a n t e m p e r a t u r e c o n t r o l u n i t .
P o i n t s on t h i s c u r v e a r e r e l a t e d t o samples of known c o n c e n t r a t i o n . T h i s c u r v e was used t o d e t e r m i n e t h e c o n c e n t r a t i o n o f some samples f o r which t h e c o n c e n t r a t i o n was p r e v i o u s l y unknown.
T h i s c u r v e shows t h a t t h e l i n e w i d t h i n c r e a s e s r a p i d l y d u r i n g t h e non m e t a l t o metal t r a n s i t i o n , The l i n e w i d t h s h o u l d s t i l l i n c r e a s e f o r more con- c e n t r a t e d s o l u t i o n s , b u t with a s m a l l e r s l o p e . T h i s c u r v e r e l a t i v e t o t h e Linewidth c o n t a i n s of c o u r s e t h e i n f o r m a t i o n r e l a t i v e t o t h e s p i n
-
s p i nr e l a x a t i o n t i m e T2, whtch is c o n t i n u o u s l y d e c r e a - s i n g when t h e m e t a l c o n c e n t r a t i o n i n c r e a s e s .
C8-26 JOURNAL DE PHYSIQUE
b e e q u a l t o one. F o r t h e most d i l u t e s a m p l e w e h a v e
1 2 4 6 8 10
concentration [ M P M ]
s t u d i e d , t h e c o n c e n t r a t i o n o f which was c l o s e t o 1 M P M t h e asymmetry i s a l r e a d y i m p o r t a n t , and i s i n c r e a s i n g w i t h t h e l i t h i u m c o n c e n t r a t i o n up t o a b o u t 3 M P M and t h e n d e c r e a s e s and becomes a c o n s t a n t c l o s e t o 2 . 5 5 f o r c o n c e n t r a t i o n s l a r g e r t h a n a b o u t 6 M P M. The v a l u e o f t h e asymmetry r a t i o o f 2.55 i s t h e v a l u e p r e d i c t e d by Dyson t h e o r y f o r v e r y l a r g e v a l u e s o f R -
-t- F i . e . when t h e d i f - f u s i o n time TD t h r o u g h t h e s k i n d e p t h i s much l a r - , g e r t h a n t h e s p i n r e l a x a t i o n time. Note t h a t t h e maximum of t h e c u r v e o f A/B v e r s u s t h e l i t h i u m c o n c e n t r a t i o n i m p l i e s a minimum i n t h e c u r v e of R v e r s u s t h e l i t h i u m c o n c e n t r a t i o n . T h i s w i l l be t h e F i g . 2 : T e m p e r a t u r e c o e f f i c i e n t d A H ( ' ) i d T
c a u s e of a minimum i n t h e v a r i a t i o n s o f T v e r s u s (m G p e r d e g r e e ) v e r s u s t h e l i t h i u m c o n c e n t r a t i o n t h e l i t h i u m c o n c e n t r a t i o n . On f i g . 3 , a n e x p e r i - D
a t -35OC. m e n t a l p o i n t a t a b o u t 3 . 5 M P M is a p p a r e n t l y o u t o f
The t e m p e r a t u r e c o e f f i c i e n t o f t h e l i n e w i d t h d
AH(')/^^
is p l o t t e d on F i g . 2 v e r s u s t h e l i t h i m c o n c e n t r a t i o n . T h i s t e m p e r a t u r e c o e f f i c i e n t is a l - most c o n s t a n t f o r c o n c e n t r a t i o n s between 4 and 1 0 MPM. For c o n c e n t r a t i o n s between 1 and 4 M P M t h e v a r i a t i o n s o f t h i s t e m p e r a t u r e c o e f f i c i e n t a r e r a p i d . However e x p e r i m e n t a l r e s u l t s a r e a c c u r a t e and t h e p l o t s o f A H ( ' ) v e r s u s T f o r t h e c o r r e s p o n d i n g sam- p l e s g i v e well d e f i n e d l i n e a r v a r i a t i o n s . Note t h a t t h i s t e m p e r a t u r e c o e f f i c i e n t c a n be d i r e c t l y r e l a t e d t o t h e t e m p e r a t u r e c o e f f i c i e n t o f t h e s p i n-
s p i n r e l a x a t i o n time T2.t h e c u r v e . T h e r e was no r e a s o n f o r u s t o d r o p t h i s v a l u e , b e c a u s e t h e c o r r e s p o n d i n g e x p e r i m e n t i s s e e m i n g l y p e r f e c t l y p r e c i s e . T h e r e f o r e o t h e r sam- p l e s of c o n c e n t r a t i o n c l o s e t o 3 . 5 M P M s h o u l d b e made t o c o n f i r m t h e v a r i a t i o n s of A/B i n t h i s r e g i o n .
A s was e x p l a i n e d p r e v i o u s l y , f r o m t h e v a l u e s of A/B t h e v a l u e s of R c a n b e o b t a i n e d from F i g . 4 of r e f e r e n c e 7 f o r t h e f i r s t d e r i v a t i v e and from F i g . 7 of t h e same r e f e r e n c e f o r t h e s e c o n d d e r i v a t i v e . With t h e v a l u e s o f R and AH, T2 i s o b t a i n e d f r o m t h e v a l u e s of yT2 AH p l o t t e d v e r s u s R on F i g . 5 and 8 o f r e f e r e n c e 7. From t h e v a l u e s of R and T2, TD is t h e n d i r e c t l y o b t a i n e d .
F i g . 3 : Asymmetry r a t i o (AIB) o f t h e f i r s t d e r i - v a t i v e v e r s u s t h e l i t h i u m c o n c e n t r a t i o n a t -35OC.
The asymmetry r a t i o ,416 o f t h e f i r s t d e r i - F i g . : TD and T2 v e r s u s t h e l i t h i u m c o n c e n t r a - v a t i v e o f t h e E S R a b s o r p t i o n l i n e is p l o t t e d on t i o n a t -35OC.
F i g . 3 v e r s u s t h e l i t h i u m c o n c e n t r a t i o n . For e x t r e - mely d i l u t e s o l u t i o n s t h e asymmetry r a t i o s h o u l d
The v a l u e s o f TD and T2 a r e p l o t t e d on f u s i o n c o n s t a n t and t h i s c o u l d p o s s i b l y be i n c o r - F i g . 4 v e r s u s t h e l i t h i u m c o n c e n t r a t i o n . T d e c r e a s e s 2
s m o o t h l y when t h e l i t h i u m c o n c e n t r a t i o n i n c r e a s e s , w h i l e TD h a s a d e e p minimum a t a b o u t 3 M P M.
F i g . 5 : g v a l u e s v e r s u s t h e l i t h i u m c o n c e n t r a t i o n a t -35OC.
The g v a l u e s o b t a i n e d a s i n d i c a t e d i n t h e e x p e r i m e n t a l s e c t i o n a r e r e p o r t e d i n F i g . 5 v e r s u s t h e l i t h i u m c o n c e n t r a t i o n . T h e r e is a w e l l d e f i n e d i n c r e a s e o f g when t h e l i t h i u m c o n c e n t r a t i o n i n - c r e a s e s . F o r t h e most c o n c e n t r a t e d s a m p l e ( a b o u t 1 0 M P M) t h e g v a l u e is s t i l l l o w e r t h a n t h e f r e e e l e c t r o n g v a l u e o r t h a n t h e g v a l u e o f p u r e li- t h i u m m e t a l . T h m e i s m o v a l u e of g i n t h e l i t e r a t u r e f o r v e r y d i l u t e l i t h i u m ammonia s o l u t i o n s .
DISCUSSION
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CONCLUSIONOur r e s u l t s h a v e been a n a l y z e d w i t h i n t h e framework of t h e Dyson t h e o r y
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F o r c o n c e n t r a t i o n s between 6 and 1 0 M P M , l i t h i u m ammonia s o l u t i o n s a r e i n t h e l i m i t i n g c a s e o f R l a r g e , i. e. a d i f f u - s i o n time TD l a r g e compared t o T2. F o r s o l u t i o n s o f c o n c e n t r a t i o n l o w e r t h a n 1 M P M , t h e asymmetry r a t i o g o e s below 2 . 5 t o w a r d u n i t y , which is n o t p r e d i c t e d by t h e Dyson t h e o r y , v a l i d when t h e s i z e o f t h e s a m p l e i s l a r g e compared t o t h e s k i n d e p t h . It must a l s o b e n o t e d t h a t when t h e asymmetry r a t i o A/B i s s m a l l e r t h a n a b o u t 3 , it i s n o t v e r y a c c u r a t e t o r e a d R o n F i g . 4 a n d 7 o f r e f e r e n c e 7. T h e r e f o r e a more a c c u r a t e n u m e r i c a l t a b u l a t i o n o f R v e r s u s A/B s h o u l d be made t o o b t a i n a p r e c i s e v a l u e of R i n t h i s r e g i o n . Such c a l c u l a t i o n s a r e r e q u i r e d t o a s c e r t a i n w i t h o u t a m b i g u i t y t h e Dysonian c h a r a c t e r of t h e l i n e s h a p e below 1 0 M P M. T h i s is i m p o r t a n t b e c a u s e t h e Dyson t h e o r y is b a s e d on a s i n g l e d i f -rect i n t h e non-metal t o m e t a l t r a n s i t i o n when t h e d e l o c a l i z a t i o n of e l e c t r o n s happens. I t must be n o t e d t h a t t h e i m p o r t a n t v a r i a t i o n s of A!B o c c u r below 6 bl P P. I n t h e same c o n c e n t r a t i o n r a n g e , l a r g e v a r i a t i o n s a r e d i s p l a y e d by t h e t e m p e r a t u r e c o e f f i c i e n t o f AID. Near 2 M P M , t h e t e m p e r a t u r e c o e f f i c i e n t of t h e l i n e w i d t h shows a r a t h e r d e e p minimum which i s reminiscent of the extremum of the temperature coefficient of the electric51 conductivity.
These E S R e x p e r i m e n t s p r o v i d e d e t a i l e d m i c r o s c o p i c i n f o r m a t i o n a b o u t t h e non-metal t o m e t a l t r a n s i t i o n i n lithium-ammonia s o l u t i o n s
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L a r g e and u n e x p e c t e d v a r i a t i o n s o f s e v e r a l quan- tities (A/B, i.e. R, d A H ( ' ) / ~ T ) o b l i g e u s t o c o m p l e t e t h e set of o u r e x p e r i m e n t s t o c o n f i r m and d e t a i l t h e o b s e r v e d v a r i a t i o n s b e f o r e d i s c u s s i n g t h e p h y s i c a l p a r a m e t e r s which a r e deduced f r o m t h e s e e x p e r i m e n t s .
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