MÖSSBAUER ELECTRIC FIELD AND MEAN SQUARE DISPLACEMENT IN NATURALLY OCCURING FeS2 (PYRITE) SINGLE CRYSTALS

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MÖSSBAUER ELECTRIC FIELD AND MEAN SQUARE DISPLACEMENT IN NATURALLY OCCURING FeS2 (PYRITE) SINGLE CRYSTALS

R. Garg, V. Gupta, V. Garg

To cite this version:

R. Garg, V. Gupta, V. Garg. MÖSSBAUER ELECTRIC FIELD AND MEAN SQUARE DISPLACE-

MENT IN NATURALLY OCCURING FeS2 (PYRITE) SINGLE CRYSTALS. Journal de Physique

Colloques, 1980, 41 (C1), pp.C1-355-C1-356. �10.1051/jphyscol:19801133�. �jpa-00219617�

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JOURNAL DE PHYSIQUE Colloque

Cl ,

supplkment au

n

^O

^1,

Tome

41,

janvier 1980, page

C1-355

M~~SSBAUER

ELECTRIC FIELD GRADIENT AM)

MEN

SQUARE DISPLACEMENT IN NATURALLY OCCURING

FeS2

(PYRITE) SINGLE CRYSTALS

R. Garg, Vishwamitter, V.P. Gupta and V.K. Garg

Departamento de Fisica e Quirnica, Unioersidade Federal do Espirito Santo, 29.000 Victoria, E.S., Brazi 2.

Pyrite, cubic mineral of FeS2, has four molecules per unit cell [I]. The Fe ions are coordinated to six S ions which are located at the centers o f slightly dis- torted (4.43') octahedron with a = 5.4179k F e atoms are located at (0,0,0),(0,1/2,1/2)

(1/2,0,1/2) and (1/2,1/2,0) positions, and S atoms are located at +(U,U,U), (U+1/2,1/2 -u,c), (e,u+1/2,1/2-U) and (1/2-~,:,1/2+~) with U = 0.386, forming four equivalent but differently oriented sites. M8ssbauer spectra of pyrite, fig. 1, were recorded in the standard transmission geometry.

d I

20 1 5 1.0 0.5 0 0 5 10 1.5

- V E V E L O C I T Y IN mm/Src + v L

Fig. 1. Typical M8ssbauer spectra of pyrite (a) powder, and single crystals (b) 111

plane,(c)llO plane and (d)100 plane.

M8ssbauer parameters at room temperature are tabulated below.

absorber a3/al thickness

r

to. 0 2 -+0.01 co. 0 2

mm mm

powder 1.01 0.165 0.377

111 plane 1.00 0.06 0.298 110 plane 1.00 0.07 0.328 100 plane 1.02 0.05 0.318

6/Fe = 0.325 10.005 mm/sec.

Q.S. = 0.62 '0.01 mm/sec.

Theory and analysis- Considering the first neighbours, with point charge model, the EFG tensor of pyrite is of the form [21,

(~'-~/e)

considering the crystal symmetry, the EFG tensor for F e sites are (1-ym) times,

-A 0 -A -A A -A -A A -A 0 but l ~ z z l ] ~ y y l ~ I v x x ~ , thus

Vzz = 2A (1-y,), and Vxx = Vyy = -A(l-yw) and rl = ( Vxx-Vyy

)/

^{V z z}⁼0, which agrees with value obtained by magnetic perturba-

tion [3] .Thus Z axis for different sites of Fe are 11,1,1],\-1,1,1),)1,1,-1) and

11,-1,lI directions which make an angle of

-

¹

cos 1/d3 with crystal axes. X and Y axes remain indetermined.

I n thin absorber limit, the peak area ratio of a3(f3/2+t1/2) and a '(P1/2++-112)

1 after Zory [4] is

here p 3 and pl are the relative angular dependent absorption probability for the

(f3/2+?1/2) and (+1/2+f1/2) transitions.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19801133

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c1-356 JOURNAL DE PHYSIQUE

f' is the Lamb

-

M8ssbauer fraction of the absorbing nuclei. The angle (8i,t$i) define the incident y-ray beam with respect to EFG axes (Xi,Yi,Zi), fig. 2.

&

b

C ?I

Fig. 2 Schematics of the absorption of 14.4 5 7

kev gamma rays by F e

.

Employing explicit expressions for p3 and pl and expressing (ei,t$;) in terms of known experimental angles, and relating a site i to the crystal axes (a,b,c),then

a x (zit1 (ei,ai) (4(3+ri2)

-

[ ~ C O S ~ O ~ - I

I

-l+q ~ i n ~ 8 ~ c o s 2 Q ~ ] } ) - ~ , here cosei = sin0 cos@(~i.a)+sin0sin@(~i.b)+cos0(2i.c), here (Fi.a) etc. are the cosines of angles bet- ween EFG axis and the crystal axes.

on simplifying a3xai1 = 3 ( ~ + c o s ~ ~ ~ ) x ( ~ - ~ cos28i)-1, giving if

ei

= cos-ll,,/3,

The recoilfree fraction fi = exp.-k2<r2>, if <x2> <y2> and <z2> are the three compo- nents of the diagonalised MSD tensor, then

in any direction

E,

<r2> is

cos26

,

where 6 and E are polar and azi- muthal angles of

E.

If a,@ and y are the Euler's angles specifying the orientation of the MSD principal axes with respect to crystal axes, then MSD along these axes are

(sinasiny -cosacosf3cosy) +<z2>(cos2asinZf3) 2

cos2f3

Since, in each site of Fe, the EFG axis is the symmetry axis

b

The three possible solutions of these eqs.

1.<x2> # <y2> # < z 2 > can not solve further.

2.<x2> = <y2> = < z 2 > , i s an obvious solution 3.<x2> = <y2> # < z 2 > but is the more

general solution than so1.2; a n d w i l l give a = (2n+l)n/4, 0 = cos-11//3 and y is indetermined. Therefore, for each site of F e EFG and MSD axes can be considered to coincide with each other.

Now, putting <x2> = Cy2> # <z2> in f i, fi = exp.-k2 [ < ~ ~ > s i n ~ e ~ + < z ~ > c o s ~ 8 ~ ] and the peak areas are

where V = <z2>

-

<x2>

A + - = sin20sin2@ ? sin20(cos@ + sin@ )

B? ⁼sin20sin2@ ? sin20(cos@

-

^cos@⁾

the upper and the lower signs of 2 in a; represent a3 and al respectively.

If in area ratios v is zero or the

recoiless fraction is isotropic, then, this ratio will always be unity for any values

of 0 and a . The peak area ratio of 1 for

the pyrite single crystals M8ssbauer spectra, and the known EFG imply that the recoilless fraction is isotropic, i.e. the MSD tensor is isotropic. But, i n the case of powder sample of pyrite the peak area ratio is unity because the angular dependent parts cancel out and the lattice vibrational anisotropy is zero.

Further s t u d i e s , ( M O calculatios ) are being planned.

Acknowledgements

-

Financial support from Conselho Nacional de Desenvolvimento

~ i e n t l f i c o e Tecnolzgico (CNPq), Brasil is thankfully acknowledged.

1. Brostigen, G., Kjekshus, A., Acta Chemica Scandinavica. 2 3 (1969) 2186. )I.

2. Garg, V. K., Liu, Y. S., Puri, S.P., J. Appl. Phys. 45 (1974) 70.

3. Montano, P. A., Seehra, M. S., Solid State Commun. 20 (1976) 897.

4. Zory, P., Phys, Rev. 140 (1965) A1401.