AN AB-INITIO CALCULATION FOR PRESSURE SHIFTS OF OPTICAL ABSORPTION BANDS IN Fe2+ - BEARING GARNETS

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AN AB-INITIO CALCULATION FOR PRESSURE SHIFTS OF OPTICAL ABSORPTION BANDS IN

Fe2+ - BEARING GARNETS

Shen Guo-Yin, Zhao Min-Guang

To cite this version:

Shen Guo-Yin, Zhao Min-Guang. AN AB-INITIO CALCULATION FOR PRESSURE SHIFTS OF

OPTICAL ABSORPTION BANDS IN Fe2+ - BEARING GARNETS. Journal de Physique Colloques,

1984, 45 (C8), pp.C8-93-C8-96. �10.1051/jphyscol:1984818�. �jpa-00224316�

J O U R N A L DE PHYSIQUE

Colloque C8, suppl6rnent au n O l I , Tome 45, novernbre 1984 page C8-93

AN AB-INITIO CALCULATION FOR PRESSURE SHIFTS OF OPTICAL ABSORPTION BANDS IN

~ e * + -

BEARING GARNETS

Shen Guo-yin and Zhao Min-guang

. h s l i t u t e o f S o l i d S t a t e P h y s i c s , Sichuan Teachers U n i v e r s i t y , Chengdu C 10066, China

Rdsum6 Nous avons r 6 a l i s i . un c a l c u l " a b - i n i t i o " pour c o r r 6 l e r l e s bandes d ' a b s o r p t i o n o p t i q u e du Fe2+ dans l e s g r e n a t s , avec l e u r s s t r u c t u r e s

c r i s t a l l i n e s 2 l ' a i d e de l a thGorie SCF des o r b i t a l e s d proposge par Zhao e t a l . Connaissant l e s paramstres c r i s t a l l i n s , on peut c a l c u l e r l e s niveaux d 1 6 n e r g i e de 1>e2+ dans l e c r i s t a l . On montre que l e changement de s t r u c t u r e c r i s t a l l i n e e s t prGpondGrant dans l e deplacement des bandes sous l ' a c t i o n dc l a p r e s s i o n . Dans l e s g r e n a t s , l e f e r e s t en sym6tric dod6ca6drale D2, de n a t u r e fortement ionique cornme l e confirment l e s mesures d ' e f f c t Mossbauer.

A b s t r a c t An a b - i n i t i o c a l c u l a t i o n has been made t o i n v e s t i g a t e t h e r e l a t i o n between t h e o p t i c a l a b s o r p t i o n bands of Fe(11) i n g a r n e t and its c r y s t a l s t r u c t u r e , adopted t h e

self-consistent- field(^^^)

d - o r b i t a l t h e o r y proposed by Zhao e t a l . The energy l e v e l s of Fe(11) i n c r y s t a l can be g o t a s l o n g as we know t h e c r y s t a l l i n e parameters. It is shown t h a t t h e change of c r y s t a l s t r u c t u r e plays t h e main r o l e i n t h e s h i f t s of c r y s t a l bands and t h a t Fe(11) at dodechedral Dz s i t e i n g a r n e t i s of h i g h l y i o n i c n a t u r e which is i n accord w i t h t h e isomer s h i f t s and quadrupole s p l i t t i n g s of Fe(11) i n g a r n e t .

One a r e a of s o l i d s t a t e physics where h i g h p r e s s u r e s t u d i e s have been important is t h a t of d-d t r a n s i t i o n s of metal i o n s i n c r y s t a l s . Usually, p r e s s u r e s h i f t s of o p t i - c a l a b s o r p t i o n bands provide a u s e f u l method f o r d i s t i n g u i s h i n g and i d e n t i f y i n g s p e c i f i c t r a n s i t i o n s by comparison w i t h t h e o r e t i c a l l y p r e d i c t e d s h i f t s . A d i f f i c u l t y i n p r e d i c t i n g high p r e s s u r e e f f e c t s , however, a r i s e s from t h e l a c k of t h e s a t i s f a c - t o r y t h e o r y which r e l a t e s t h e d-d t r a n s i t i o n s of i o n s i n c r y s t a l s t o t h e parameters of c r y s t a l l i n e l a t t i c e s i n c e t h e p r e s s u r e e f f e c t s a r e u s u a l l y a d i r e c t consequence of i t s c r y s t a l s t r u c t u r e . R e c e n t l y , an a b - i n i t i o c a l c u l a t i o n h a s been made f o r t h e s p e c t r a of F ~ ( I I ) , ~ ( I I ) , C ~ ( I I I ) , CO(II), and ~ ~ ( 1 1 ) i n c r y s t a l s /1-5/ on t h e basis of approximation self-consistent-field(~cF') d - o r b i t a l t h e o r y which a l l o w s u s t o e s t a b l i s h a r e l a t i o n between d-d t r a n s i t i o n s and i t s c r y s t a l l i n e parameters.

Therefore it is p o s s i b l e now t o i n v e s t i g a t e more f u l l y t h e p r e s s u r e s h i f t s with t h e c r y s t a l l i n e parameters under v a r i o u s p r e s s u r e .

Here t h e a t t e n t i o n i s focussed on t h e ~ e ( 1 1 ) i n s i l i c a t e g a r n e t s which a r e g e n e r a l l y assumed t o be important mantle s i l i c a t e minerals. The u s e s o f t h e s u p e r p o s i t i o n model and point-charge i o n i c bonding model t o a n a l y z e t h e spectrum of Fe(1.T) i n pyrope m r n e t have been d e s c r i b e d / 6 / , adopted Zhao and Duls d - o r b i t a l f o r F e ( I 1 ) . I n t h i s communication, we extend our e a r l i e r work and a r e concerned w i t h t h e o r e t i - c a l l y p r e d i c t e d p r e s s u r e s h i f t s of o p t i c a l a b s o r p t i o n bands i n ~ e ( 1 1 ) - g a r n e t s . I

-

THEORETICAL MALYSIS

Garnet c r y s t a l l i n e s i n t h e space group Ia3d. The ~ e ( 1 1 ) i o n s occupy t h e p o s i t i o n 240 w i t h dodechedral D2 point symmetry. I t i s g e n e r a l l y a c c e p t e d t h a t Fe(11) is respon- s i b l e f o r a &oup of t h r e e s t r o n g n e a r - i n f r a r e d bands due t o spin-allowed t r a n s i - t i o n s and f o r a number of weak s h a r p bands i n t h e v i s i b l e due t o spin-forbidden

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984818

C8-94 JOURNAL DE PHYSIQUE

t r a n s i t i o n s . A q u a n t i t a t i v e assignment f o r t h e bands i n t h e n e a r - i n f r a r e d and v i s i - b l e r e g i o n of Fe(11)-bearing g a r n e t h a s been r e c e n t l y reached /6/ having c o n s i d e r e d t h e a c t u a l s y m e t r y D2 of t h e i o n s s u r r o u n d i n g t h e ~ e ( 1 1 ) . The r e s u l t s show that t h e low symmetry c o n t r i b u t i o n , which p l a y s an important r o l e i n t h e complexity o f t h e s p e c t r a , is l a r g e and should n o t be n e g l e c t e d . So, t o p r e d i c t t h e p r e s s u r e s h i f t s of t h e bands, we should c o n s i d e r t h e a c t u a l

D p

c r y s t a l f i e l d r a t h e r t h a n t h e c u b i c f i e l d only. It should a l s o be emphasized t h a t p r e d i c t i n g t h e p r e s s u r e s h i f t s r e q i r e s e x a c t assignment of t h e a b s o r p t i o n hands and t h a t , on t h e o t h e r hand, t h e t h e o r e t i c a l l y p r e d i c t e d s h i f t s would be expected a s a u s e f u l method f o r i d e n t i f y i n g t h e s p e c i f i c t r a n s i t i o n s by comparison w i t h t h e experimental f i n d i n g s .

The c r y s t a l f i e l d t h e o r y i s commenly assumed t o provide a r e a s o n a b l e d e s c r i p t i o n o f metal i o n s i n c r y s t a l s which a r e i o n i c . S e v e r a l r e s u l t s , however, have a l r e a d y shown t h a t Fe(11) a t g a r n e t Dz s i t e i s of h i g h l y i o n i c n a t u r e /7/ and t h a t t h e pre- dominantly c o n t r i b u t i o n t o t h e c r y s t a l f i e l d i n t h i s system a p p e a r s t o a r i s e from i o n s i n t h e f i r s t c o o r d i n a t i o n s p h e r e

/a/.

Therefore t h e s u p e r p o s i t i o n model and point-charge i o n i c bonding model a r e a p p r o p r i a t e t o c a l c u l a t e t h e energy l e v e l s of Fe(11) i n g a r n e t . Now a c c o r d i n g t o t h e r e s u l t s of /6/, a p u r e l y t h e o r e t i c a l approach t o p r e s s u r e s h i f t s a r e performed.

Under t h e point-charge i o n i c bonding model, F ~ ( I I ) , with 3d 6 c o n f i g u r a t i o n , i s sub- jected t o t h e D2 c r y s t a l f i e l d p o t e n t i a l

where

a, p , 3, 8,

E can be c a l c u l a t e d from t h e parameters of l a t t i c e ; ZhQ 16) (

&it Ti

) denotes r e a l s p h e r i c a l harmonic f u n c t i o n s ; r i , &, 9; a r e c o o r d i n a t e s of d-electron on Fe(11); e t h e proton charge; q t h e e q u i v a l e n t charge of t h e l i g a n d Ox-.

Using t h e proper b a s i s f u n c t i o n s of DZ symmetry, we o b t a i n t h e Hamiltonian m a t r i x elements of t h e t r i p l e t s t a t e s 3~~ ( 9 x

9

m a t r i x ) , 'R,, 3 ~ 2 , 3 ~ 3 (12 X 12 m a t r i c e s ) and of t h e q u i n t e t s t a t e s I A f ( 2 x 2 m a t r i x ) , 5 R ~

,

5BI, 5Bj ( 1 X 1 m a t r i c e s ) . The m a t r i x elements a r e e x p r e s s i o n s of t h e Racah parameters B, C , t h e T r e e s c o r r e c t i o n

Q, and t h e c r y s t a l f i e l d parameters which a r e t h e f u n c t i o n s of e x p e c t a t i o n v a l u e s

< r 2 > , <r4> and c r y s t a l l i n e parameters. Because Zhao and Du's d - o r b i t a l f o r Fe(11) /I/ h a s been employed, t h e e x p e c t a t i o n v a l u e s of r 2 , r 4 and Racah parameters B , C-?

can be t h e o r e t i c a l l y obtained: < r 2 ) = 2.2949 ( a . u . ) , <r4) = 14 (a.u.), B = 947 cm

,

C = 3375 cm-'. Thus t h e r e l a t i o n between d-d t r a n s i t i o n s of Fe(11) i n g a r n e t and i t s c r y s t a l l i n e parameters can be e s t a b l i s h e d by s o l v i n g s e v e r a l determinants.

A s f o r t h e s u p e r p o s i t i o n model, t h e e q u a t i o n f o r t h e c r y s t a l f i e l d parameters at g a r n e t DL s i t e i s of t h e form

where K:(A), K:(B) can be c a l c u l a t e d from t h e a n g u l a r c o o r d i n a t e ; A,(R) a r e i n t r i n -

-

s i c parameters which can be g o t by employing d - o r b i t a l f o r ~ e ( 1 1 ) /1/; t n a r e power l a w exponents. U i t h t h e power l a w exponents /6/ t2 = 3, t 4 = 7 , t h e geometric para- meters

a, 6 ,

^t),

6

and

E

a r e o f t h e form

S i m i l a r l y , t h e energy l e v e l s of Fe(11) i n g a r n e t can be o b t a i n e d a s l o n g as we know t h e c r y s t a l l i n e parameters.

S i n c e Fe(11) i n g a r n e t is o f h i g h l y i o n i o n a t u r e /6,7/, it is expected t h a t t h e change of t h e c r y s t a l s t r u c t u r e p l a y s an important r o l e i n t h e s h i f t s of c r y s t a l bands. The u n i t - c e l l volume

- (A3

⁾ and p r e s s u r e (kbar) have t h e r e l a t i o n

/ 9 / :

V ^{m o p e}

_--

-

= 1503.5

-

1.13P

+

0.004~'

.

Under t h e assumption t h a t t h e r e a r e no i n t e r n a l d i s t o r - t i o n of t h e c r y s t a l s t r u c t u r e a p a r t from t h e uniform compression, we g e t , f i n a l l y , t h e t h e o r e t i c a l l y p r e d i c t e d p r e s s u r e s h i f t s without i n t r o d u c i n g any new parameters.

The Fig. i n n e x t page shows t h e p r e d i c t i o n i n comparison w i t h t h e experimental d a t a /10,11/.

I1

-

DISCUSSION

The n e a r - i n f r a r e d bands of ~ e ( 1 1 ) i n c r y s t a l s a r e s t r o n g spin-allowed t r a n s i t i o n s t h a t a r i s e from t h e same energy l e v e l SD and that, consequently, a r e independent of Raoah parameters B, C. So t h e pressure s h i f t s of f e r r o u s bands i n t h e near-infrared a r e a measure of c r y s t a l f i e l d . The p r e d i c t e d s l o p e i s c l o s e agreement w i t h Balchan and Drickamer's /11/ and o n l y a l i t t l e g r e a t e r t h a n t h a t r e p o r t e d i n

/lo/,

a s shown i n Fig.(a). So it can be s a i d t h a t t h e r e l a t i o n we o b t a i n e d between c r y s t a l f i e l d parameters f o r g a r n e t Dz symmetry and its c r y s t a l l i n e parameters i s a reasonable one which is fundamental t o t h e o r e t i c a l e x p l a n a t i o n of o t h e r bands i n t h e v i s i b l e . The v i s i b l e bands a r e spin-forbidden t r a n s i t i o n s that a r e t h e f u n c t i o n s of c r y s t a l f i e l d parameters, Racah parameters and T r e e s c o r r e c t i o n . A s shown i n ~ i ~ . ( b , c , d ) , t h e agreement of p r e d i c t e d s h i f t s with experiments shows t h a t t h e Racah parameters change v e r y l i t t l e w i t h p r e s s u r e , which i s i n accordence w i t h t h e f a c t t h a t ~ e ( I 1 ) i n many s i l i c a t e m i n e r a l s i s h i g h l y i o n i c /6,12,13/. This i m p l i e s t h a t t h e i o n i c model f o r ~ e ( 1 1 ) d bond i n g a r n e t s t i l l h o l d s at t h e pressure up t o 50 kbar.

G e n e r a l l y , it is expected t h a t t h e a b s o r p t i o n bands would s h i f t t o higher energy w i t h i n c r e a s i n g c r y s t a l f i e l d parameters /14/. But t h e p r e d i c t e d s h i f t s of t h e band at 17600 cm-' is t o lower energy, which i s q u a n t i t a t i v e l y agreement with t h e experi- ment, w i t h i n c r e a s i n g p r e s s u r e , i.e., w i t h i n c r e a s i n g c r y s t a l f i e l d parameters. This i n d i c a t e s t h a t t h e r e l a t i o n between t h e d-d t r a n s i t i o n s and t h e r a m e t e r s of low

P"

symmetry c r y s t a l f i e l d i s complicated r a t h e r t h a n simple D q e R-.

A s shown i n F i g . ( a , b , c , d ) , t h e b l u e - s h i f t of t h e band 7800 cm-l, t h e r e d - s h i f t of t h e band 17600 cm-' and t h e n e a r l y - z e r o - s h i f t s of t h e bands 19100, 19800, 21600 cm"

have been w e l l i n t e r p r e t e d . This i m p l i e s t h a t :

1 ) t h e d e f i n i t e assignment i n our e a r l i e r work o f t h e spectrum of Fe(11) i n g a r n e t i s reasonable,

2 ) t h e change o f c r y s t a l s t r u c t u r e plays t h e main r o l e i n t h e s h i f t s of c r y s t a l bands and, e s p e c i a l l y , t h e main c o n t r i b u t i o n t o t h e s h i f t s of spin-forbidden t r a n s i t i o n s i s s t i l l t h e change of c r y s t a l s t r u c t u r e r a t h e r than t h e dec- r e a s e of Racah parameters which i s g e n e r a l l y regarded at p r e s e n t .

and 3 ) Fe(11) at dodechedral D2 s i t e i s s t i l l of h i e h l y i o n i c n a t u r e a t t h e pres- s u r e u p t o 50 kbar.

JOURNAL DE PHYSIQUE

PRESSURE (kbar ) PRESSURE ( k b a r )

5N-

-. ^{m -} -

Fig.

-

T h e o r e t i c a l predicted s h i f t s comparison with t h e experimental f i n d i n g s . The r e s u l t s obtained from two models a r e n e a r l y t h e same. Line-1 corresponds t o t h e t h e o r e t i c a l predicted s h i f t s , l i n e - 2 t o t h e experimental f i n d i n g s from /lo/, l i n e - 3 t o t h e r e s u l t s from /11/.

I PRESSURE (kbar)

vo

^{= 7800 cm- 1}

,'

^{10 2 0 30 40 50}

./' ./'

References

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2. M.C. Zhao, G.R. Bai and H.C. J i n , J. Phys. C I S o l i d S t a t e Physics

15,

5959 (1982) 3. M.G. Zhao at a l . , Phys. Rev.

3,

1516 (1983)

4. M.G. Zhao and Y.F. Zhang, IEEE TRANSACTIONS ON MAGNETICS MAG-12, 1972 (1983)

5.

W.L. Yu and M.G. Zhao, J. Phys. C: S o l i d S t a t e Physics l8, L525 (1984) 6. G.Y. Shen and M.G. Zhao, Phys. Rev.

s,

( i n p r e s s )

7. G. Amthauer, H. Annerstea, and S.S. Hafner, Z. K r i s t a l l o g r .

141,

14 (1976) 8. F.E. Huggins, Am. Mineral. 60, 316 (1975)

9. R.M. Hazen and L.W. Finger, Am. Mineral.

a,

297 (1978)

10. T.J. Shankland, A.C. Duba, and A. Woronow, J. Geophys. Res.

'&

3273 (1974) I t . A.S. Balchan and H.G. Drickamer, J. Appl. Phys.

2

1446 (1959j

12. R.M. Abu-Eid and R.G. Wlms, Am. Mineral.

fi,

391 (1976) 13. M.L. Du, p r i v a t e communication

14. H.G. Drickamer, i n SOLID STATE PHYSICS e d i t e d by F. S e i t z and D. Turnbull v01.17 1 (1965)

- E

³⁰⁰

^-

²

1 P

"

1 -300

2

-

= 17600 om-'

-@O-

0 60