MÖSSBAUER SPECTROSCOPY AND COMPLEMENTARY TECHNIQUES : EXAFS AND µSR

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MÖSSBAUER SPECTROSCOPY AND

COMPLEMENTARY TECHNIQUES : EXAFS AND µSR

J. Chappert

To cite this version:

J. Chappert. MÖSSBAUER SPECTROSCOPY AND COMPLEMENTARY TECHNIQUES : EXAFS AND µSR. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-9-C1-16. �10.1051/jphyscol:1980102�.

�jpa-00219572�

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JOURNAL DE PHYSIQUE

Colloque

C l

, supplc5ment au n

^O

1 , Tome 41, janvier 1980, page

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!~SSBAUER SPECTROSCOPY AND COMPLEMENTARY ECHNIQUES : EXAFS AND PSR

J. Chappert

Centre drEtudes NucZe'aires de GrenobZe, D.R.F./Laboratoire d l I n t e r a c t i o n s Hyperfines, 85 X

-

38042 GrenobZe Cgdex, France.

ABSTRACT

An i n t r o d u c t i o n t o t h e p r i n c i p l e s o f t h e EXAFS and uSR techniques i s pre- sented f o l l o w e d by a review of v a r i o u s a p p l i c a t i o n s w i t h t h e h e l p o f t y p i c a l exam- p l e s t a k e n h m t h e r e c e n t l i t e r a t u r e . Comparison i s made w i t h r e s u l t s from o t h e r techniques, Massbauer spectroscopy i n p a r t i c u l a r .

Most o f t h e i n t e r n a t i o n a l conferences are one must "peel t h e onion", i . e . e l i m i n a t e t h e t o p i c s o r i e n t e d . Very few meetings a r e l i m i t e d p a r t s r e l e v a n t t o t h e technique. This i s more t o the a p p l i c a t i o n s o f a p a r t i c u l a r technique e a s i l y done i f one uses d i f f e r e n t approaches t o and when t h i s happens i t i s u s u a l l y o n l y d u r i n g describe o r t o apply these concepts.

t h e f i r s t years o f development. S t i l l meetings

F i n a l l y t h e danger o f such meetings may devoted t o t h e a p p l i c a t i o n s o f t h e MSssbauer e f f e c t

r e s i d e i n t h e l a c k o f challenge from s c i e n t i s t s Continue t o be organized twenty years o r so a f t e r

working i n o t h e r f i e l d s . One may q u e s t i o n t h e t h e b i r t h d a y o f t h i s spectroscopy. I t i s there-

system o f " i n t e r n a l " referees i n which t h e c r i t i - fore necessary t o be aware o f t h e p o t e n t i a l dangers

c a l e v a l u a t i o n o f t h e papers remains i n the same r e s u l t i n g e s s e n t i a l l y from t h e p o s s i b l e "confine-

s c i e n t i f i c community.

ment" o f MSssbauer s p e c t r o s c o p i s t s t o " t h e i r "

technique. For a l l these reasons, i t i s a s i n e qua non

Any s i n g l e technique, no m a t t e r how powerful, c o n d i t i o n f o r progress t h a t t h e MSssbauer spectros- gives o n l y a p a r t i a l view o f t h e s t r u c t u r e o r of

t h e p r o p e r t i e s o f m a t t e r . c o l l e c t i n g huge amounts Of data w i t h t h e h e l p o f o n l y one technique may then be s u b j e c t t o t h e law o f d i m i n i s h i n g r e t u r n s

or

even be mi'sleading w h i l e a s i n g l e a d d i t i o n a l piece of i n f o r m a t i o n provided by a complementary source may be p r i c e l e s s .

Also a s i n g l e technique deals o n l y w i t h a T i m i t e d number o f concepts. Moreover these concepts are o f t e n adapted t o t h i s technique. I n o r d e r t o r e a l l y understand t h e physics behind them,

c o p i s t s avoid g e t t i n g stuck i n a r u t and keep abreast o f any new idea. I t i s t h e r e f o r e the purpose o f t h i s t a l k t o b r i n g t o t h e i r a t t e n t i o n new techniques such as EXAFS (Extended X-ray Absorption F i n e S t r u c t u r e ) and uSR (muon Spin R o t a t i o n ) which are r a p i d l y developing and which may be complementary t o Missbauer spectroscopy.

The p r i n c i p l e s o f each technique

-

EXAFS i n t h e l e f t column, uSR i n t h e r i g h t one

-

w i l l be presen- ted, i l l u s t r a t e d w i t h t y p i c a l examples o f a p p l i c a - t i o n s taken

from the recent literature.

A

-

PRINCIPLES OF THE EXAFS AND pSR TECHNIQUES

EXAFS us R

X-rays are absorbed by m a t t e r according t o The p o s i t i v e muon

( v + )

i s a p a r t i c l e which,

the formula f o r t h e s o l i d s t a t e p h y s i c i s t , may be regarded as a

I = I exp(-ux)

0 l i g h t p r o t o n (mu = 0.11 m ) . B u t t h e p' i s n o t s t a - P

where I and I. are t h e i n c i d e n t and t r a n s m i t t e d b l e , decaying a f t e r a mean l i f e t i m e , .r = 2.2 micro- u

X-ray i n t e n s i t i e s r e s p e c t i v e l y ,

u

i s t h e 1 i near seconds, t o form a p o s i t r o n and two n e u t r i n o s :

+ + -

absorption c o e f f i c i e n t and x i s t h e absorber 1-1 + e + v + v

u e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980102

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C1-10 ^JOURNAL^DE^PHYSIQUE thickness. The a b s o r p t i o n spectrum as a f u n c t i o n

o f t h e i n c i d e n t photon energy i s c h a r a c t e r i z e d by several absorption edges which correspond t o sharp increases o f 11 when t h e X-ray energy matches e x a c t l y t h e energy necessary f o r e x t r a c t i n g an i h n e r e l e c t r o n from an atom.

When U' a r e stopped i n a t a r g e t , t h e p o s i t r o n count r a t e as a f u n c t i o n o f t h e t i m e t elapsed i s given by

N = No e x p ( - t h U )

T h i s i s represented i n f i g . 2a. If however a p e r t u r - b a t i o n acts upon t h e u+ ( e x t e r n a l magnetic f i e l d ,

Fig.

1

AbbatrpxXan npecXum

^LU

a ~ u n c t i a n o d i n - c i d e n t photon enehgy.

'

a / d i l a t e d a t o m ( n o EXAFS)

b/ atam w d h n e a h w t n e i g h b o w ( E X A F S

@ l g . e u 1

The absorption curve represented i n f i g . l a i3 t h a t o f a system where t h e e f f e c t of t h e neighbours can be neglected (monoatomic gas).

I n most cases however ( d i a t o m i c gas, l i q u i d , s o l i d ) the gradual decrease a t photon energies above the edge i s modulated by the Kronig o s c i 1 la t i o n s ClJ, r e c e n t l y renamed EXAFS [21 ( f i g . l b ) .

Fig.

2

T h e dependence od t h e p a o f i n count

ha-

t e e m i t t e d b y pooLtLve muom otopped i n a b o r n .

a / i n t h e aboence 06 petttwrbation b / i n

t h e p x u e n c e

04 a m a g n d c d i d d .

Vamped oobcieeatiom m e obomved [DR

opecthuml

magnetic t a r g e t )

,

osci 11 a t i o n s modulate t h e exponen- tl'al curve ( f i g . 2b). I n a d d i t i o n a damping o f these o s c i l l a t i o n s i s o f t e n observed. These f e a t u r e s c o n s t i t u t e t h e b a s i s f o r t h e new uSR spectroscopy developed i n t h e 'last few y e a r s Ill.

B

-

PHYSICAL ORIGIN OF THE SPECTRUM EXAFS

During t h e a b s o r p t i o n process, a photon w i t h energy hu disappears and a photoelectron of

ki'netic energy E i s e j e c t e d f r o m an atomic core s t a t e according t o t h e energy conservation law

E = hv

-

^EK

where EK i s $he i n i t i a l b i n d i n g energy o f t h e e l e c t r o n ( f i g . 3a). I f t h e absorbing atom i s i s o l a - ted, t h e f i n a l s t a t e i s an outgoing e l e c t r o n wave and decreases monotonically w i t h energy ( f i g . l a ) except f o r a f i n e s t r u c t u r e o f complicated atomic o r i g i n observed i n t h e f i r s t 50 eV above E,. If the absorbing atom i s surrounded w i t h nearest neighbours, t h e outgoing wave i n t e r f e r e s w i t h t h e

backscattered e l e c t r o n waves. When t h e amplitudes o f t h e two waves add a t t h e absorbing atom s i t e ,

a maximum o f t h e X-ray a b s o r p t i o n p r o b a b i l i t y i s observed ( f i g . 3h) w h i l e f o r a s m a l l e r X-ray energy, t h e p h o t o e l e c t r o n wavelength i s longer and t h e waves i n t e r f e r e d e s t r u c t i v e l y w i t h a r e s u l t i n g mi-

nimum i n t h e absorption.

Two important parameters have t o be c o n s i d e w d f o r e x p l a i n i n g t h e appearance o f o s c i l l a t i o n s . F i r s t th'e .u+ beams are h i g h l y p o l a r i z e d ( a 80 %)

,

ⁱ.e.

t h e i r spins Sp = 1/2 are p o i n t i n g i n t h e same d i r e c - t i o n , opposite t o t h e muon momentum. Second t h e emission o f t h e p o s i t r o n i s n o t i s o t r o p i c i n space b u t i s c o r r e l a t e d w i t h t h e s p i n d i r e c t i o n according t o the p r o b a b i l i t y f u n c t i o n W(e) = 1 + acose,where 8 i s t h e angle between Su and t h e p o s i t r o n d i r e c t i o n and a = 1/3 ( f i g . 4 ) . I n t h e presence o f an e x t e r - na1,magnetic f i e l d BeXt, t h e spins SU precess i n a plane perpendicular t o t h i s f i e l d w i t h a frequency w = y B where y i s t h e P

+

gyromagnetic r a t i o

P V U u

(13.55 MHz/kG) and BU i s t h e magnetic f i e l d seen by t h e ut. I t i s i m p o r t a n t t o r e a l i z e t h a t Bu i$

g e n e r a l l y d i f f e r e n t from Bext because t h e n u c l e i of t h e s o l i d c a r r y a magnetic moment and produce an a d d i t i o n a l magnetic f i e l d a t t h e P+ s i t e v i a the dip01 a r i n t e r a c t i o n . Since these moments a r e random- l y o r i e n t e d , t h e s i n g l e precession frequency w i s

u

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Therefore w h i l e X-ray d i f f r a c t i o n i n v o l v e s replaced by a spectrum o f very c l o s e l y spaced f r e - interference between X-rays, EXAFS may be v i z u a l i - quencies r e s u l t i n g i n t h e damping of t h e o s c i l l a t i o n s zed as e l e c t r o n d i P f r a c t i o n where t h e source o f because o f the d e p o l a r i z a t i o n o f t h e muon ensemble.

e l e c t r o n s i s w i t h i n t h e s t u d i e d m a t e r i a l .

excited 9'

lb

^{bound' a'} ^polarized

I Bma;l

I e+ detector "stop.

nea

magnetic field

F+g.

3

a/ S~henu&.Lc heptuentati.on 0 6 t h e & a ~ i -

son

occwLing when a bound demon A ^{Fig. 4} Simptidied PSR n &-up i n a ;Dram venn e excited .to a conCinuwn b M e . m a g n d c d i d d . The $etecXoh " n ~ iden- "

b/ Intetrdehence pattehn b m e e n t h e o u t - Z i d i e h an incqming 11

,

t h e detectoh "ntop"

going ( A ofid f i n e n ) and 6 c a w e d an oLLtgoing e

.

C

-

DATA ANALYSIS

EXAFS PSR

The EXAFS, ( k )

,

i s defined by x ( k )

=

) u ( k )

-

u 0 ( k ) l / u o ( k )

where k i s t h e p h o t o e l e c t r o n wave vector, u ( k ) i s the experimental a b s o r p t i o n c o e f f i c i e n t and po(k) i s i t s smooth m ~ n o t o n i c a l l y decreasing p a r t . A s i m p l i f i e d expression f o r ~ ( k ) i s 131 :

e x p ( - Z ~ ; k ~ ) s i n [ 2 k R ~ + ~ ~ ( k )

1

i = No. o f

I

d i s t i n c t distances

I

Ri

fi ( k ) = b a c k s c a t t e r i n g amp1 i tude

A i e l e c t r o n mean f r e e path P + = r o o t mean square f l u c t u a t i o n

The p o s i t r o n counting r a t e detected i n a given d i r e c t i o n as a f u n c t i o n o f t h e time t a f t e r stopping of t h e muons i n t h e substance i s given by [11 :

No = n o r m a l i s a t i o n constant r,,=p

+

l i f e t i m e

A = e f f e c t i v e decay asymmetry

P ( t ) = transverse r e 1 a x a t i o n f u n c t i o n d e s c r i b i n g t h e e v o l u t i o n o f t h e p o l a r i z a t i o n

w = Larmor precession frequency u

4 = phase constant determined by t h e p o s i t i o n of t h e p o s i t r o n d e t e c t o r

I f t h e muons d i f f u s e i n t h e s o l i d d u r i n g t h e i r l i f e t i m e , t h e damping f u n c t i o n P ( t ) i s w e l l appro- ximated by t h e ABRAGAM formula 121 :

Ri = distances between atoms

P ( t ) = exp[-02r:Cexp ( - t / - c C )

- ¹ +

t / r c I l Ci ( k ) = phase s h i f t depending on t h e k i n d o f where T~ i s a c o r r e l a t i o n t i m e p r o p o r t i o n a l t o t h e

n e i ghbours

muon residence time a t a g i v e n s i t e and u2 i s t h e We see t h a t t h e EXAFS s i g n a l i s p r o p o r t i o n a l second moment o f t h e w,, d i s t r i b u t i o n . TWO regimes of t p t h e number o f neighbours Ni a t Ri and i n v e r s e l y d i f f u s i o n can be d i s t i n g u i s h e d -:

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c1-12 JOURNAL DE PHYSIQUE

p r o p o r t i o n a l t o Ri 2

.

Each c o o r d i n a t i o n sphere con-

-

f a s t d i f f u s i o n : ⁰^'^~^: << 1 and P ( t ) ^%e x p ( - ~ ~ ~ ~ t ) t r i b u t e s a s i n e l i k e term of p e r i o d 2kRi

-

The Debye-

-

frozen muons : a 2 r $ 2, 1 and P ( t ) exp(-02t2/2).

K a l l e r type term, exp(-20!k2), i n c l u d i n g both t h e r -

b

I n t h e f i r s t case t h e damping i s L o r e n t z i a n ma1 and s t a t i c d i s o r d e r , i s responsible f o r t h e dam-

w h i l e i t i s Gaussian i n t h e second type o f regime.

p i n g o f t h e s i g n a l .

D -

APPLICATIONS EXAFS

1. Absorption edge and chemical changes

Nuclear energy l e v e l s are measurably a f f e c t e d by chemical changes i n .the valence e l e c t r o n d i s t r i - b u t i o n ; t h i s gives r i s e t o t h e w e l l known MFssbauer isomer s h i f t . I n n e r e l e c t r o n i c l e v e l s are s e n s i t i v e t o t h e chemical environment as w e l l , r e s u l t i n g i n a "chemical s h i f t " o f t h e absorption edge which r e f l e c t s t h e n e t charge o f an atom and which there- f o r e , l i k e the isomer s h i f t , can be used t o charac- t e r i z e t h e charge s t a t e of elements. As an example t h e absorption edge o f two Fe oxides i s shown i n . f i g . 5 L41. I t i s c l e a r t h a t t h e edge i s displaced towards h i g h energies when t h e charge s t a t e o f Fe increases. This has been a p p l i e d a t LURE (Orsay)

Fig. 5 S k i d t od t h e -&on K-edge t h e n h o l d doh

*wo &on oXide,b [4].

f o r t h e c h a r a c t e r i z a t i o n o f Fe i m p u r i t i e s i n glasses 151. CRAMER eJ

s.

[61 have observed a c o r r e l a t i o n between theMo K-edge p o s i t i o n and t h e c a l c u l a t e d c o o r d i n a t i o n charge o f a s e r i e s of Mo compounds. An approximately 1 i near r e l a t i o n s h i p has been

e s t a b l i s h e d which i s used t o determine t h e chemi- c a l s t a t e o f Mo i n t h e r e s t i n g nitrogenase. Such c o r r e l a t i o n s a r e a l s o w e l l known i n Mossbauer spectroscopy [71.

I t i s worth n o t i n g t h a t t h e EXAFS method i s

also

element s p e c i f i c . STERN

g a.

^[81f o r example have examined b o t h t h e L edges of t h e r a r e e a r t h and t h e K-edge o f t h e i r o n i n a s t r u c t u r a l study of amorphous RFe2 compounds.

1. Location o f t h e muon

The i n t e r p r e t a t i o n o f most o f t h e d a t a p r o v i - ded by the vf a c t i n g as a probe necessitates the knowledge o f i t s p r e f e r e n t i a l l o c a t i o n i n t h e matter. Moreover since a f r u i t f u l analogy between 1

1

' and proton i s made by people i n t e r e s t e d i n hydrogen d i f f u s i o n 131 i t i s a l s o o f g r e a t t e c h n o l o g i c a l i n t e r e s t t o know t h e f a t e o f t h e u

+

i n metals.

F i r s t o f a l l because o f i t s charge, t h e U+

is,expected t o remain between atoms a t i n t e r s t i t i a l S i t e s . Determination o f t h e t y p e o f i n t e r s t i t i a l s i t e i s p o s s i b l e i f one s t u d i e s t h e d e p o l a r i z a t i o n r a t e o f p+ stopped i n a s i n g l e c r y s t a l substance subjected t o an e x t e r n a l magnetic f i e l d . L e t us f o r example consider copper which has octahedral and t e t r a h e d r a l i n t e r s t i t i a l s i t e s . HARTMAW [41 has c a l c u l a t e d t h e d i p o l a r f i e l d s seen by t h e muon when BeXt i s a p p l i e d along [100], [110] o r 11111.

He found d i f f e r e n t values f o r the d e p o l a r i z a t i o n r a t e f o r t h e two types o f s i t e s . The experiments by CAMANI

9 2.

151 f i t q u i t e w e l l w i t h these c a l c u l a t i o n s i f one assumes an octahedral s i t e . L e t us note t h a t f o r such an i d e n t i f i c a t i o n Bext must be l a r g e enough i n o r d e r t o d e f i n e a quanti,- z a t i o n axis. T h i s i s because t h e pf d i s t o r t s t h e l a t t i c e and creates an e l e c t r i c f i e l d g r a d i e n t a t the nearby h o s t n u c l e i C41. Then t h e d i p o l a r f i e l d s a t t h e U+ s i t e must be c a l c u l a t e d by.assuming a Combined e l e c t r i c and magnetic i n t e r a c t i o n 163.

2. D i f f u s i o n o f t h e muon

The U+ i s g e n e r a l l y n o t s t a t i c b u t diffuses from s i t e t o s i t e v i a mechanisms which are i n many cases s i m i l a r t o those encountered i n hydrogen d i f f u s i o n [7]. However because t h e muon mass i s approximately one t e n t h t h a t o f t h e proton, quantum e f f e c t s are expected. This behaviour, t o g e t h e r w i t h t h i p o s s i b i l i t y o f d i f f u s i o n s t u d i e s a t low tempe- r a t u r e s and i n f i n u t i s i m a l concentrations, e x p l a i n s t h e surge o f i n t e r e s t from hydrogen s p e c i a l i s t s

towards uSR.

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Not only i s the position of the absorption edge of i n t e r e s t but a l s o i t s shape which may r e f l e c t the presence of several charge s t a t e s .

A

promising f i e l d of i n t e r e s t in t h a t respect i s the study of the anomalies observed in a number of rare earth compounds and which are interpreted i n terms of intermediate valency 191. Such a method was a1 ready proposed f i f t e e n years ago by VAINSHTEIN & 2. El01 who analyzed the L-absorption spectra of Sm in SmB6 and concluded the presence of two valence s t a t e s sm2' ^and sm3+, the r e l a t i v e content of Sm 2+

representing 35 + 5 I . B o t h charge s t a t e s a r e observed because the EXAFS measuring time i s very short (%lo-15s) while a motional l y narrowed s i n g l e l i n e corresponding t o an intermediate valence of 2.7 i s indicated

hy

the "longer" Miossbauer technique (lo-' sec) [ I l l . Using the same method but with the aid of high i n t e n s i t y X-ray synchrotron radiation, LAUNOIS g g. [12] have recently studied the LIiI-absorption edge i n a s e r i e s of compounds based on Ce,

Tm

and Tb. The accuracy of the valence determination i s about 1

^%,

indicating f o r example

2.65 + 0.03 f o r Yb i n YbInAu2

2, Structural information

EXAFS i s a very s e n s i t i v e tool f o r measuring the local environment of the absorbing atom. Eva-

luation of the distances Ri with an accuracy of

0

(1.01

A i s

obtained via the sinusoidal interference term while the amplitude of the signal has informa- tibn on the n.n. number

N i ,

the nature of the atoms involved and t h e local disorder.

I t must be realized t h a t the accuracy on d i s - tances R i i s inherently limited by the accuracy t o which the phase s h i f t s 6i(k) are known. Fortunately CITRIN a. [13] have introduced the very impor-

.

t a n t concept of chemical transferabi 1 i t y

:

phase s h i f t s are s u f f i c i e n t l y i n s e n s i t i v e t o chemical environment so as t o be transferable from one system t o the next. Therefore, in s t r u c t u r e studies, phase s h i f t s are determined f o r an atom p a i r of known d h t a n c e s and then used t o determine the interatomic diktances i n another compound containing the same stoms but i n a d i f f e r e n t chemical environment [131.

One major f i e l d of application i s biology since many of t h e large biological molecules have a unique heavy atom which governs t h e properties of the molecule and which may be used as a central absorbing atom i n EXAFS studies [14]. For example in rubredo- xin, it was deduced from conventional X-ray diffrac-

Two parameters, the temperature and the impu- r t t y concentration, may influence strongly the

'p

diffusion i n a metal. In a c l a s s i c a l picture the muons appear t o be frozen a t low temperature. Muons located a t d i f f e r e n t s i t e s feel d i f f e r e n t magnetic f i e l d s and t h e i r spins precess a t d i f f e r e n t frequen- c i e s . This gives r i s e t o a strong depolarization.

A t higher temperature,the muons sample a much larger

-

^fast

^-

C (D L a

-

₀

al 0

u

temperature

FLg.

6 CLannicd pi.icWre 06 .the !J+ diddunion i n a o f i & . A change 06 hcZghe d h 0 m aLow 20 dant di6dunion L e d 20

a

demesne

06

depoLa4ization ( m o ~ o d nmolcLing)

.

volume of s o l i d because of f a s t diffusion. Therefore they see only 3n average f i e l d and the depolariza- t i o n i s smaller ( f i g . 6). This i s the familiar motional narrowing e f f e c t well knownnot only i n

NMR

but a l s o i n Mtssbauer spectroscopy,which i s also a useful tool f o r diffusion studies

[8,91.

One knows t h a t two s i t u a t i o n s can occur depending on whether i t i s the Mossbauer nucleus which i s diffusing or not. In the f i r s t case a l i n e broadening i s observed (Au -

57

Fe [ 8 ] ) , while i n the second case motional narrowing takes place (G

H

[ l o ] ) resulting i n a narrower 1 inewidth.

The c l a s s i c a l picture described above f o r uSR does not hold a t very low temperature in ultra-pure metals where coherent tunnelling diffusion can take place

;

the muons are delocalized i n the form of a band s t a t e and depolarization i s very weak.

This i s the case i n pure aluminium 1111.

Impurities may also strongly a f f e c t diffusion since they a c t l i k e a t r a p f o r the muon. As a r e s u l t the depol a r i zation r a t e i s c h a r a c t e r i s t i c of the impurity, not of the

b u l k

material.

A

typical example i s provided by niobium [12,13]. The temperature dependence of the depolarization r a t e presents a complex shape due t o successive capture

snd

release of the

!J+

by the impurities.

3 .. Hyperfi ne magnetic f i e l d

In the above studies the physical information

was e s s e n t i a l l y provided by the damping of the

osci 1 la t i o n s , i .e. the depolarization r a t e re1 ated

(7)

C1-14 ^JOURNAL^DE^PHYSIQUE

ti'on measurements t h a t t h e i r o n atom was surrounded by f o u r s u l f u r atoms a t an average d i s t a n c e of

0

2.24 A b u t w i t h one d i s t a n c e anomalously s h o r t 2..05

i.

I n f a c t EXAFS r u l e s o u t t h i s s h o r t bond l e n g t h by p u t t i n g l i m i t a t i o n s on t h e d i s t r i b u t i o n s of pos- s i b l e Fe-S distances. The d a t a are o n l y compatible w i t h bonds p r e s e n t i n g a spread i n distances of

0

0.05 A 1151. T h i s r e s u l t i s extremely i m p o r t a n t s i n c e i t was argued t h a t t h e s h o r t bond was i n v o l v e d i n a mechanism by which t t i e p r o t e i n affected t h e e l e c t r o n t r a n s f e r f u n c t i o n o f t h e molecule.

Since b i o l o g i s t s are always concerned t h a t t h e c r y s t a l l i z e d o r f r o z e n samples may n o t be iden- t i c a l t o t h e b i o l o g i c a l l y a c t i v e form, EXAFS measurements on l i q u i d s are w e l l s u i t e d . For example EXAFS has been used t o determine t h e s t r u c t u r e of t h e Fe-containing core o f f e r r i t i n i n s o l u t i o n C161.

Considerable s t r u c t u r a l d i s t o r t i o n appears when the sample s o l u t i o n i s frozen. T h i s d i s t o r t i o n , which does n o t seem t o have .been noted p r e v i o u s l y , leads t o reconsider t h e i n t e r p r e t a t i o n o f t h e previous '

M'dssbauer and X-rays measurements performed on C r y s t a l l i z e d m a t e r i a l s .

The EXAFS technique i s a very u s e f u l t o o l f o r t h e study o f any p r o p e r t y r e l a t e d t o a change o f h t e r a t o m i c distances such as t h e c o n t r a c t i o n of bond l e n g t h induced by an e x t e r n a l pressure. INGALLS e t a l . [17] have r e c e n t l y demonstrated t h e a b i l i t y

--

of

t h e technique i n t h e study o f t h e c o m p r e s s i b i l i t y o f p y r i t e up t o 64 kbar. The Fe-S bond i s shown t o be considerably l e s s compressible than t h e u n i t - c e l l edge, r e f l e c t i n g s t r o n g c o v a l e n t character.

C o n t r a c t i o n o f nearest neighbour distances can a l s o be observed i n small p a r t i c l e s which a r e used as c a t a l y s t s . An EXAFS study by MORAWECK

g

a l .

[ l a ]

shows t h a t i n p l a t i n u m p a r t i c l e s having

-

0

a mean diameter o f 12 A,the P t - P t d i s t a n c e i s shor- t.ened by.0.12 w i t h r e s p e c t t o i t s value i p t h e h u l k metal. Such a c o n t r a c t i o n agrees q u a l i t a t i v e l y w i t h c a l c u l a t i o n s of GORDON f o r small n o n - c r y s t a l - l o g r a p h i c p a r t i c l e s 1191. The same c o n t r a c t i o n i s a l s o observed by APAI

&s.

1201 f o r Ni and Cu c l u s t e r s ( f i g . 8 ) . The changes i n n.n. separations e x h i b i t a c l o s e correspondence t o t h e changes i n K e d g e threshold. T h i s i s e x p l a i n e i by t h e i n c r e a - s i n g surface-to-volume r a t i o as t h e c l u s t e r s i z e decreases r e s u l t i n g i n

a

more free-atom-1 i ke confi

-

g u r a t i o n o f t h e metal atoms.

t o t h e d i s t r i b u t i o n o f f i e l d s A B ~ . But t h e value o f t h e f i e l d i t s e l f ( y w ) i s a l s o o f i n t e r e s t ,

11 1-1

e s p e c i a l l y i n magnetic m a t e r i a l s [141. The f i e l d seen by t h e muon is_,

-C -e -D

-

^-v

Bp = B e x t ⁺Bdem + B~ + B d i p ⁺B h f

f . f t t \

e x t e r n a l demagne- Lorentz dip01 a r hyperfine t i z i n g

Several remarks must be made :

i

.

The muon measures t h e f i e l d a t i n t e r s t i t i a l s i t e s w h i l e most o f t h e o t h e r spectroscopies (NMR, Massbauer) t e s t t h e s u b s t i t u t i o n a l s i t e s , ii. The experimental values o f B are very small

l '

( a few kG) compared w i t h most o f n u c l e a r hyper- f i n e f i e l d s .

iii .As a consequence, BL and Bdip (from e l e c t r o n i c moments) p l a y an i m p o r t a n t r o l e and t h e i r pre- c i s e e v a l u a t i o n i s e s s e n t i a l 1151.

i v . Bhf e x i s t s o n l y i n m e t a l l i c samples. I t o r i g i - nates from t h e p o l a r i z e d conduction e l e c t r o n s Since t h e muon does n o t possess an e l e c t r o n i c core. This p o l a r i z a t i o n i s due e i t h e r t o Bext (Knight s h i f t ) o r t o t h e l o c a l magnetization i n magnetic m a t e r i a l s

.

v. The s i g n o f B can be determined by comparing t h e phase constants

v o

o f several p o s i t r o n detectors placed around the sample.

Several s t u d i e s of magnetic s o l i d s have a l r e a - dy been performed. L e t us quote f o r example a-Fe2O3, w e l l known t o MSssbauer s p e c t r o s c o p i s t s . I n t h i s m a t e r i a l By = Bdip i n t h e absence o f Bext. T h i s

0 100 1000

temperature

Fig. 7 Tempehatwre dependence 0 6 hypm6ine b i d o h i n hematite.

a / 57Fe M6ni64baueh n p e a o n e o p y : t h e chan- ge

06

8 4 4

at

t h e Mohin

on

TU

O

batrdy v O i b l e because

B

<<

B

&P

e6d

(8)

9020 9420 9820

e n e r g y (eV

8 Coppm K-edge EXAFS npc&a doh a doil and

-

a hehies od couertages. kt umy

l o w

coue- hage Ahe EXAFS 6Lgna.t d i n a p p m (AoLa- Zed atom]

.

^Sm& nhow conthaotion od nemuZ-n&ghboum.

The mean f r e e p a t h o f t h e e1ect;on waves i n t h e s o l i d being o f t h e o r d e r o f 5-10 A, t h e p e r i o d i - c i t y o f t h e l a t t i c e does n o t p l a y an i m p o r t a n t r o l e and EXAFS can be used e q u a l l y w e l l f o r systems i n c r y s t a l l i n e o r n o n - c r y s t a l l i n e forms [4,221 .SAYERS a1

.

^{[ Z l ]}were t h e f i r s t t o demonstrate t h e p o s s i b i l i t y

-

Of t h e technique i n Ge02 glass. T h e i r r e s u l t s r u l e Out t h e proposed m i c r o c r y s t a l l i n e model and are i n agreement w i t h a random network model i n which t h e s t r u c t u r e i s b u i l t from Ge02 t e t r a h e d r a connected by oxygen w i t h d e v i a t i o n about bond angles d e s t r o y i n g t h e long-range p e r i o d i c i t y .

L i m i t a t i o n s o f t h e EXAFS technique f o r t h e study o f disordered m a t e r i a l s must however be considered because of incomplete t h e o r e t i c a l treatment of averaging t h e s p e c t r a and o f t h e l a c k o f low momentum t r a n s f e r i n f o r m a t i o n 1231.

a l l o w s a p r e c i s e study o f t h e Morin t r a n s i t i o n ( f i g . 7 )

[I61

since BU changes by a f a c t o r 2 a t t k e t r a n s i t i o n , 1 i ke t h e quadrupole i n t e r a c t i o n i n Mdssbauer spectroscopy. Another e x t e n s i v e l y s t u d i e d m a t e r i a l i s c o b a l t where b o t h Bdip and Bhf p l a y an i m p o r t a n t r o l e [17,181.

Since Bhf o r i g i n a t e s o n l y from t h e polarsized conduction e l e c t r o n s a t t h e i n t e r s t i t i a l s i t e , i t i s i n t e r e s t i n g t o compare Bhf i n ferromagnetic me- t a l s w i t h t h e l o c a l i n t e r s t i t i a l magnetization Mint, measured by p o l a r i z e d neutrons, o r w i t h t h e b u l k magnetization Ms. Several observations can be made

PI81

i. Bhf cannot be scaled by the b u l k magnetization.

ii. Bhf i s always n e g a t i v e i n agreement w i t h t h e negative Mint v z l ues

.

i ii

.

No p r o p o r t i o n a l i t y constant holds between Bhf and +int 8 : f o r example i n Fe t h e muon f e e l s a s t r o n g l y enhanced f i e l d . T h i s enhancement i's g e n e r a l l y a t t r i b u t e d t o screening o f t h e muon b y t h e conduction e l e c t r o n s .

i v . The temperature dependence o f Bhf does n o t f o l l o w t h a t o f t h e b u l k magnetization.

Some p o s s i b l e o r i g i n s f o r these d e v i a t i o n s have been proposed :. d i s t o r t i o n o f the l a t t i c e by t h e muon, f i n i t e s i z e of t h e muon l o c a t i o n , scree- n i n g by conduction e l e c t r o n s 1181, volume expansion e f f e c t 1191. No d e f i n i t e conclusion has however been drawn since i t i s l i k e l y t h a t a l l o f them c o n t r i b u t e more o r l e s s simultaneously. One can conclude however t h a t the pi i s n o t an "innocent"

probe. It i s t h e r e f o r e important t o understand t h e mechanism of t h e response o f t h e conduction e l e c - t r o n s t o t h e p e r t u r b a t i o n o f t h e p o s i t i v e muon.

COMPARISON OF THE TECHNIQUES

f

samp e o m

I

materiallli:itations (

( element s p e c i f i c : ( i m p u r i t y s e n s i t i v e : ( c h a r a c t e r i s t i c time : ( t y p i c a l sample s i z e :

f

need o f a b i g machine :

I

MOSSBAUER

s o l i d l i m i t e d number o f

n u c l e i

no 10'7-10-9 sec

100 mg

EXAFS

PC-

s o l i d , l i q u i d , gas : s o l i d , l i q u i d , gas ) ) almost any element : elements w i t h l a r g e ) : n u c l e a r o r e l e c t r o n i c ) : magnetic moments )

Yes no

1

no yes

1 0 - l 5 sec 10-6 sec

j

100 mg 10-30 g )

p r e f e r a b l y Yes

1

(9)

C1-16 JOURNAL DE PHYSIQUE E

-

CONCLUSION

I t may be wondered, i f EXAFS and pSR a r e i n - deed such u s e f u l t o o l s f o r t h e study of condensed matter, why have they n o t been developed l o n g ago.

As e a r l y as the 19301s, EXAFS had been observed and q u a l i t a t i v e l y e x p l a i n e d by KRONIG

.

^{I n 1957}

GARWIN, LEDERMAN and WEINRICH (Phys. Rev.

105

(1957) 1415) conceived t h e p r i n c i p l e s o f D R . But, because o f t h e o r e t i c a l and experimental d i f f i- c u l t i e s , i t i s o n l y i n t h e e a r l y 1970's t h a t b o t h techniques s t a r t e d t o develop r a p i d l y . U n t i l t h a t time EXAFS lacked q u a n t i t a t i v e understanding and i n t e n s e photon beams, l a t e r p r o v i d e d by synchro-

REFERENCES EXAFS

E l l K r ~ n i g , R. de L., Z. Phys. 70 (1931) 317.

121 Sayers, D.E., L y t l e , F.W. and Stern, E.A., l n Advances i n X-ray Analysis, ed. Henke, B.L., Newkirk, J.B. and M a l l e t t , G.R. (Plenum, N.Y.) 1970, v o l

.

^13.

131 Stern, E.A., Phys. Rev. B10 (1974) 3027.

141 Raoux, D., Petiau, J., BoEiot, P., Calas, G., Fontaine, A., Lagarde, P., L e v i t z , P., Loupias, G. and Sadoc, A.; Rev. Phys. Appl., t o be Published.

151 Bondot, P., Calas, G., L e v i t z , P., Loupias, G., and Petiau, J., Colloquium o f the French Physi- c a l Society, Toul ouse (1979)

.

161 Cremer, S.P., Eccles, T.K., K u t z l e r , F.W. and Hodgson, K.O., J. Am. Chem. Soc. 98 (1976) 1287 171 Herber, R., Adv. Chem. Ser. 68 (1%7) 8.

C81 Stern, E.A., R i n a l d i , S., CaTfen, E., Heald, S.

and Bunker, B., J . Magn. Magn. Mat.

1

(1978) 188.

191 Hewson, A.C., J . Magn. Magn. Mat.

12

(1979) 83.

[ I 0 1 Vainshtein, E.E., Blokhin, S.M. and Paderno, Yu.B., Sov. Phys. Sol. S t a t e 6 (1965) 2318.

C111 Cohen, R.L., Eibschutz, M. ana West, K., Phys.

Rev. L e t t . 24 (1970) 353.

El21 Launois, ~.,Raviso, M., Holland-Mari t z , R., P o t t , R., Sereni, J. and Wohlleben, D., I n t e r n . Conf. Magnetism, Munich (1979).

1131 C i t r i n , P.H., Eisenberger, P. and Kincaid, B.M., Phys. Rev. L e t t . 36 (1976) 1346.

C141 Eisenberger, P. a x Kincaid, B.M., Science

200

(1978) 1441.

C'151 Sayers, D.E., Stern, E.A. and H e r r i o t t , J.R., J. Chem. Phys. 64 (1976) 427.

1161

Heald, S.M., Stern, E.A., Bunker, B., H o l t , E.M. and H o l t , S.L., J. Am. Chem. Soc.

101

(1979) 67.

[ I 7 1 I n g a l l s , R., Garcia, G.A. and Stern, E.A., Phys. Rev. L e t t .

40

(1978) 334.

El81 Moraweck, B., Clugnet, G. and Renouprez, A.J., S u r f . Sci

.

8 1 (1979) L631.

C191 Gordon, M.B: Thesis, U n i v e r s i t@ de Grenoble (1978) ; Gordon, M. B.

,

Cyrot-Lackmann

,

^F

. ,

Desjonqueres, M.C., Surface S c i .

68

⁽¹⁹⁷⁷⁾

359.

1201 Apai

,

G.

,

Hami 1 ton, J. F.

,

~ t i i i r , J

.

^and

Thompson, A., Phys. Rev. L e t t .

43

(1979) 165.

1211 Sayers, D.E., Stern, E.A. and L y t l e , F.W., Phys. Rev. L e t t . 35 (1975) 584.

E221 Hayes, T.M., J. N c Cryst. S o l i d s 3 1 (1978) 57 [23] Eisenberger, P. and Brown, G.S., S T . S t a t e

Commun.

2

(1979) 481.

t r o n r a d i a t i o n , w h i l e h i g h energy p h y s i c i s t s were i n t e r e s t e d i n t h e muon i t s e l f , n o t i n

USR

and s o l i d s t a t e e f f e c t s considered as a nuisance.

These two techniques, using now e s s e n t i a l l y b i g machines such as dedicated storage r i n g s f o r EXAFS, synchrocyclotrons o r meson f a c t o r i e s f o r pSR, have c e r t a i n l y a b r i g h t f u t u r e i n t h e study o f condensed matter. L e t us hope t h a t Missbauer spectros- c o p i s t s w i l l s t r o n g l y c o n t r i b u t e t o t h e i r development

G.N. RAO i s g r a t e f u l l y acknowledged f o r a c r i t i c a l reading o f t h e manuscript.

REFERENCES uSR

[I] B r e ~ e r ,

J,H,

and Crowe, K.M.. Ann. Rev. Nucl.

P a r t . Sci'. 28 (1978) 239,

[21 Abragam,

he

P r i n c i p l e s o f Nuclear Magne- t i sm (Oxford, London) 1971.

C31 Seeger, A., i n Hydrogen i n Metals I, ed.

A l e f e l d , G. and VSlkl, J . (Springer, B e r l i n ) 1978.

E41 ~ a r t m a n n , O., Phys. Rev. L e t t .

2

(1977) 832.

C51 Camani, M., Gygax, F.N., Ruegg, W. ,Schenck, A,, a n d s c h i l l i n g , H., Phys. Rev. L e t t .

2

(1977)

Q 9 c U J O

.

161 Matthias, E., Schneider, W. and Stefen, R.M., Phys. Rev.

125

(1962) 261.

171 Kehr, K.W., i n Hydrogen i n Metals I, ed.

A l e f e l d , G. and V o l k l , J. (Springer, B e r l i n ) 1978.

C81 Mullen, J.G. and Knauer, R.C., i n MBssbauer E f f e c t Methodology, ed. Gruverman, I. J . (Plenum N.Y.) 1970, v o l . 5.

[91 Janot, Ch., J. de Phys. 37 (1976) 253.

C l O l Heidemann, A., Kaindl, G T Salomon, D., Wipf, H. and Wortmann, G., Phys. Rev. L e t t .

36

⁽¹⁹⁷⁶⁾

213.

El11 Hartmann, O., Karlsson, E., N o r l i n , L.O., R i c h t e r , 0. a n d N i i n i k o s k i , T.O., Phys. Rev.

L e t t . 4 1 (1978) 1055.

[ I 2 1 Borghiii'f, M., N i i n i k o s k i

,

^T.O., Souli@, J.C., Hartmann, O., Karlsson, E., N o r l i n , L .O., Pernestal, K., Kehr, K.W., R i c h t e r , D. and Walker, E;

,

phys. Rev. L e t t .

40

(1978) 1723 ; HYD. I n t e r . 6 (1978) 229.

El31 ~ j r n b a u m ,

H . X . ;

~ a n i a n i , M., F i o r y , A.T., Gygax, F.N., Kossler, W.J., Ruegg, W., Schenck, A.

and S c h i l l i n g , H., Phys. L e t t . 65A (1978) 435.

1141 Yamazaki

,

T., Physica 86-88B ( 1 3 7 ) 1053.

[ I 5 1 Kronmuller, H., H i l z i n g e r , H.R., Monachesi, P.

and Seeger, A., Appl. Phys.

18

(1979) 183.

C161 Graf, H., Hofmann, W., Kiindig, W., Meier, P.F., Patterson, B.D. and Rodriguez, A., Sol. S t a t e Comnun. 25 (1978) 1079.

1171 Graf, H.,Kindia. - . W . , Patterson, B.D., Reichart, W., Rogg"il let-,-P., ~ a m a n i

,

M., - ~ ~ ~ a x j F.N., - Schenck, A. and S c h i l l i n g , H., Phys. Rev. L e t t . 37 (1976) 24.

C181 m s h i d a , N., Nagamine, K., Hayano, R.S., Yamazaki

,

T., Fleming, D.G., Duncan, R.A., Brewer, J.H., Ahktar, A. and Hasnoka, H., J. Phys. Soc. Japan

44

(1978) 1131.

1191 Butz, T., Chappert, J., Dufresne, J.F., Hartmann, O., Karlsson, E., Lindgren, B., Longobardi

,