NUCLEAR ELECTRIC FIELD GRADIENT OF THE IRON SITES IN FeS2 (PYRITE)

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NUCLEAR ELECTRIC FIELD GRADIENT OF THE IRON SITES IN FeS2 (PYRITE)

Yehan Liu

To cite this version:

Yehan Liu. NUCLEAR ELECTRIC FIELD GRADIENT OF THE IRON SITES IN FeS2 (PYRITE).

Journal de Physique Colloques, 1979, 40 (C2), pp.C2-400-C2-402. �10.1051/jphyscol:19792139�. �jpa-

00218511�

JOURNAL DE PHYSIQUE

Colloque C2, supplkment au no 3, Tome 40, mars 1979, page C2-400

Y.S. Liu

Department of Physics, University of Brasilia, 70.000 BrasiZia, DF, Brazil

RQsum6.- Les paramstres du t e n s e u r g r a d i e n t de champ d l e c t r i q u e o n t Q t 6 c a l c u l 6 s pour l e s q u a t r e s i t e s de f e r S q u i v a l e n t s

-

mais o r i e n t B s d i f f g r e m e n t - de chaque c e l l u l e BlCmentaire de l a p y r i - t e . On t r o u v e que l e s axes z pour l e s s i t e s ( 0 , 0 , 01, (112, 112, O), (112, 0, 112) e t (0, 1 1 2 , 112) s o n t respectivement dans l e s d i r e c t i o n s d + I? +

z, ^-

^{d +}

^{+ ?, 2}

⁺

^{F? -}

^{e t}

^{2 -}

^{$ + $; l e}

paramstre d 1 a s s y m 6 t r i e 17 e s t nu1 dans t o u s l e s c a s . S i l ' o n suppose que l a f r a c t i o n d ' e f f e t s a n s r e c u l e s t i s o t r o p e l e r a p p o r t des a i r e s a 3 / a l pour l e s p e c t r e ~ E s s b a u e r d'un absorbeur mo- n o c r i s t a l l i n s e r a independant de son o r i e n t a t i o n e t t o u j o u r s Qgal 1 l r u n i t Q .

Abstract.- The e l e c t r i c f i e l d g r a d i e n t t e n s o r parameters were c a l c u l a t e d f o r t h e f o u r e q u i v a l e n t , b u t d i f f e r e n t l y o r i e n t a t e d s i t e s of Fe i n each u n i t c e l l of p y r i t e . It i s found t h a t t h e EFG z- axes f o r t h e s i t e s a t (0, 0 , O), (112,

I/?,

01, (112, 0 , 112) and ( 0 , 112, 112) a r e r e s p e c t i v e l y i n t h e d i r e c t i o n s 3 +

If + 3, -2 +

+

f,

a + b

-

T f and 3

-

$ +

Zf,

t h e asymnetry parameter 17 being z e r o i n a l l c a s e s . I f t h e r e c o i l f r e e f r a c t i o n i s i s o t r o p i c , t h e n t h e a r e a r a t i o a s / a l , o f t h e Mijssbauer a b s o r p t i o n s p e c t r a f o r a s i n g l e c r y s t a l absorber w i l l be independent of i t s o r i e n t a t i o n and always e q u a l s t o u n i t y .

I n t r o d u c t i o n . - I r o n s u l f i d e with p y r i t e s t r u c t u r e i s a c u b i c c r y s t a l of c e l l c o n s t a n t a. = 5.4179

i,

Atoms a r e i n t h e p o s i t i o n s of T: (Pa 3) / I / , i e . F e atoms occupy t h e p o s i t i o n s a t (0, 0 , O), (112, 112, O), 112, 0 , 112) and ( 0 , 112, 112) and S atoms a t + ( u , u, u ) ,

+

( U + 112, 112

-

u, U ) ,

+

(8, u + 1 / 2 , -

112

-

u) and 2 (112

-

u, ii, u

+

1!2), with u =0.386.

The n e a r e s t neighbors of Fe a r e t h e s i x S a t d i s - t a n c e s Fe

-

S = 2.26

i,

forming a d i s t o r d e d octahe- d r a l . The quadrupole s p l i t t i n g and i t s temperature dependence, t h e i s o m e r i c s h i f t , a s w e l l a s t h e ma- g n e t i c p r o p e r t i e s of p y r i t e a l l i n d i c a t e 12-51 t h a t i t i s a ~ e " compound

,

with t h e Fe i n low s p i n s t a t e ( 3 d 6 ) . The a r e a r a t i o a3/,; of t h e ~ i j s s b a u e r a b s o r p t i o n peaks of a s i n g l e c r y s t a l of FeS2 p y r i t e h a s been s t u d i e d 161 w i t h y-rays r e s p e c t i v e l y along t h e c r y s t a l l o g r a p h i c axes a , b , and c . w i t h r e s u l t t h a t i s c o n s i s t e n t w i t h an EFG t e n s o r of which t h e p r i n c i p a l e z-axis i s along a

E,

^{1 , 1 1} d i r e c t i o n and t h a t 17 = 0, i n agreement w i t h a simple p o i n t charge model c a l c u l a t i o n . Recently a b s o r p t i o n spec- t r a of powder sample of p y r i t e i n t h e presence of e x t e r n a l mannetic f i e l d h a s been s t u d i e d 171 and i t

Ref. 6 t h a t t h e s i x n e a r e s t neighboring S a l s o can g i v e an EFG t e n s o r w i t h a s i m i l a r s t r u c t u r e t o what would be caused by t h e dumbbell. I n f a c t , f o r t h e Fe a t (0, 0 , O), t h e n e a r e s t neighbors a r e t h e s i x S a t

+

^(U

-

^{112, 112}

-

u, C ) ,

+

^(ti, u - 112, 1/2-11) and

+ (u,

u - 112, 112

-

^{u ) .} I f each s u l f u r atom h a s an e f f e c t i v e charge -qeff then t h e EFG w i t h r e s p e c t t o t h e t h r e e axes a , b , c i s

where ym i s t h e Sternheimer a n t i s h i e l d i n g f a c t o r ,

and 5

A = 6 a-3 ( U

-

1 / 2 ) 2 / (3u2

-

^{2u + 112)' (2)}

q e f f O

= 0.0383 q e f f

/ i3

f o r t h e c o n t r i b u t i o n from t h e n e a r e s t neighbors a l o n e . The c o n t r i b u t i o n from t h e dumbbell, i . e . S atoms a t ^f_ (u, u , u), would g i v e

A = 2qeff a o 3 (3u2)-3 (3)

=

-

0.042 q e f f

/ i3

whereas c o n t r i b u t i o n from a l l i o n s , w i t h e f f e c t i v e

- charge of S b e i n g -qeff and of Fe being 2 q e f f , i s

i s concluded t h a t e2qQ i s n e g a t i v e and t h a t Fe

posses no magnetic moment, w h i l e AE = 0.65 mm/s. A = 0.024 q e f f / g 3 ( 4 )

Q

The E l e c t r i c F i e l d Gradient.- It i s ' g e n e r a l l y Only t h e dumbbell g i v e s c o r r e c t s i g n of e Z q q . I f thought t h a t t h e quadrupole s p l i t t i n g i s a conse- t h i s i s t h e o n l y c o n t r i b u t i o n , t h e n t h e e f f e c t i v e quence of t h e d i s t o r t i o n from o c t a h e d r a l symmetry charge of t h e S atom should be -1.5e f o r y m + l l , i n caused by t h e two s u l f u r atoms a l o n g t h e

c,

^{1 , IJ} o r d e r t o g i v e AEQ

-

^{0.65 m/s.} This would seem r e a - d i r e c t i o n ( i e t h e dumbbell) However, a s shown i n sonable i f t h e c o v a l e n t bonding of FeSz a r e t h e pa

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19792139

between Fe and t h e S atoms a t t h e s i t e s

+

(u, u , u ) . One can t h e n i n t e r p r e t t h a t t h e averaged d i s t a n c e of t h e e l e c t r o n i c charge i s a t a d i s t a n c e

1

Reff = (1.5)-3 R

from t h e Fe atom, w i t h R = 3.62 b e i n g t h e d i s t a n - ce Fe-S.

Taking i n t o account of t h e symmetry of t h e c r y s t a l s t r u c t u r e , o r by d i r e c t c a l c u l a t i o n , one can e a s i l y v e r i f y t h a t f o r t h e s i t e s a t (0, 0, 0) (1/2, 0, 1/2), 0 , 1/2) and (0, J / 2 , 1/2) t h e EFG t e n s o r s a r e r e s p e c t i v e l y , a p a r t from t h e f a c t o r

I f one a d o p t s t h e convention t h a t

>

I V I

^>

I v 1 ,

t h e n one o b t a i n s ,

Ivzzl yy Z Z '

and

n

⁼ (Vxx

-

vyy)'vzz (6)

= 0

The z-axis a r e i n t h e d i r e c t i o n s

p ,

^{1 ,}

,

E l . 1 ,

11 , P,

1 ,

-11

^and

E,

- 1 ,

17

r e s p e c t i - v e l y , t h e x-axis and t h e y-axis a r e indetermined.

I n t h e n e x t s e c t i o n we s h a l l a n a l y s e t h e consequence of t h e s e d i f f e r e n c e s i n t h e o r i e n t a t i o n of EFG p r i n c i p l e a x i s t o t h e experimental a r e a r a - t i o .

The Area r a t i o . - Since t h e asymetry parameter i s z e r o , t h e n i f t h e r e c o i l f r e e f r a c t i o n i s i s o t r o p i c t h e a r e a r a t i o of a q u a d r i p o l e s p l i t t i n g doublet i s given by / 8 /

5 -

C O S ~ ~ . a 3 i 3

-

⁼

a1

C

I + cos2ei (7)

1

where 8 . i s t h e a n g l e between t h e i n c i d e n t

-

14.4 kev y-rays :nd t h e EFG z-axis of t h e i t h - s i t e . It i s r e l a t e d t o t h e experimental angle O and @ through cos 8 . = s i n O cos @ (z^;.P)

+

s i n O c o s Q (z^ _i'

b^)

+ cos 0 (Ei.S) (8)

where ( Z . .

P) ,

(zi

.s)

and (2;. C) a r e t h e c o s i n e s of t h e a n g l e s between t h e EFG z-axis and t h e c r y s t a l -

+ +

l o g r a p h i c a x e s 3, b , and c , a s shown i n F i g u r e 1.

The e x p l i c i t e x p r e s s i o n s f o r c o s 2 8. a r e given i n Table I.

When t h e i n c i d e n t y-ray i s a l o n g a c r y s t a l - l o g r a p h i c a x i s , O = 0 and @ = 0, we have cos 8. = 1 and hence

2

= 1 .

a 1

F i g . 1 : Schematics of t h e a b s o r p t i o n p r o c e s s of t h e 14.4 kev y-rays by 5 7 ~ e , r e l a t i v e t o t h e c r y s t a l axes ( a , b , c) and t o t h e EFG p r i n c i p l e axes

A h

(xi, yi,

P.)

of t h e i t h s i t e .

I n r e f e r e n c e (6) t h e EFG was c a l c u l a t e d f o r t h e F e - s i t e a t ( 0 , 0 , 0 ) . The a r e a r a t i o f o r y-rays

-P -P 3

along a , b , o r c axes were c o r r e c t l y p r e d i c t e d t o b e equal t o u n i t y w h i l e experimental o b s e r v a t i o n was found t o be approximatelyequal t o 1, 0.9, 0.9.

More c a r e f u l experiments a r e b e i n g c a r r i e d o u t /9/

and t h e p r e l i m i n a r y r e s u l t s show t h a t they a r e a l l c o n s i s t e n t w i t h u n i t y . However, by t a k i n g i n t o ac- count o f t h e d i f f e r e n t o r i e n t a t i o n of t h e EFG axes f o r t h e f o u r e q u i v a l e n t Fe s i t e s , we can a l s o con- clude t h a t f o r a r b i t r a r y p r a y d i r e c t i o n , t h e a r e a r a t i o must always b e u n i t y , a s long a s t h e r e c o i l f r e e f r a c t i o n i s i s o t r o p i c . The r e a s o n f o r t h i s i s t h a t , when summed o v e r t h e f o u r F e - s i t e s , t h e terms i n v o l v i n g t h e azimuthal a n g l e j u s t cancel o u t each o t h e r and we have

I

which, when s u b s t i t u t e d i n t o e q u a t i o n (7) g i v e s a 3 / a l = I .

Acknowledgement.- The a u t h o r would l i k e t o thank D r V.K. Garg f o r some h e l p f u l d i s c u s s i o n s .

JOURNAL DE PHYSIQUE

Table I

D i r e c t i o n of

:

Fe s i t e s

i

^{EFG 3-axis I c o s 2}

ei

I 1

1 I

(000) [ I , I, I]

:

p + s i n z

a

s i n Z a + s i n z

a

( c o ~ @ + s i n @ ) J

I

:

3

I

I I

1 1

(T

^{0 )}

! ^El,

^{1, I]}

^{: I}

P - s i n z 0 s i n 2 @

+

s i n 2

0

(-cosm + s i n @ )

:

³

I

1 1

1 1 '

(T o ;

1 1 , 1 , I

j f

c + s i n 2

o

s i n 2 @

-

s i n

' e

( cos@ + s i n @ ) ]

I

I 1

1 I

1 1 1

( 0

?) ;

1 1 ,-I, 1

7 : 7

P - s i n 2

O

s i n 2 @ + s i n 2

0

(cosa

-

^sin@)]

1 I

1 I

Expression f o r cos2 8. (8. b e i n g t h e a n g l e between t h e y-ray d i r e c t i o n and t h e EFG z - a x i s ) i: t e h s of experimental a n g l e s

O

and @

.

References

/

1

/

Strong,H., "Mineralogical Tables" (A Radenise Verlag, Leipzig, 1957).

/ 2 / Neel, L., and Benoit, R., C.R. Acad. S c i . 237 (1953) 444.

/ 3 / Miyahara, S., and T e r a n i s h i , T., J . Appl. Phys. 39 1968) 896.

/ 4 / K e r l e r , W., Neuwirth, W., Fluck, E . , Kuhn, P. and Zimermann, B., Z. Phys. 173 (1963) 321.

/ 5 / K e r l e r , W., Newwirth, W., and Fluck, E . , Z. Phys. 175 (1963) 200.

/ 6 / Garg, V.K., Liu, Y.S. and P u r i , S.P., J . Appl. Phys. 45 (1974) 70.

/ 7 / Montano, P.A. and Seehra, M.S., S o l i d S t a t e communication 20, (1976) 897.

/8/ Zory, P., Phys. Rev. 140, (1965) A 1401.

1 9 1 Garg, V.K., P r i v a t e communication.