CALCULATION OF HYPERFINE PARAMETERS IN SOME GARNETS

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CALCULATION OF HYPERFINE PARAMETERS IN SOME GARNETS

G. Amthauer, M. Grodzicki, S. Hafner, V. Marathe, A. Trautwein

To cite this version:

G. Amthauer, M. Grodzicki, S. Hafner, V. Marathe, A. Trautwein. CALCULATION OF HYPERFINE PARAMETERS IN SOME GARNETS. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-291-C1- 292. �10.1051/jphyscol:19801103�. �jpa-00219584�

JOURNAL DE PHYSIQUE Colloque C1, suppl6ment au n ^O 1, Tome 41, jarlvier 1980, page C1-291

CALCULATION OF HYPERFINE PARAMETERS I N SOME GARNETS

G. Amthauer, M. Grodzicki, S.S. Hafner, V.R. Marathe and + A.X. ~rautwein+

I n s t i t u t fur Mineralogie der Uniijersitiit Marburg, Lahnberge, 3550 Marburg, Germany (F.R.G.)

+

Angeuandte Physik, Universitiit des SaarZandes, 6600 Saarbdcken, Germany fF.R.G.1

In the past years, a large number of garnet hyperfine data obtained from Mass- bauer spectroscopy have been reported.

Here, we have calculated for the garnets Y3Fe5012 (YIG) and Ca3Fe2Si3012 (andra- dite) quadrupole splittings A = +QV,,

and electronic charge densities y(O) at the nucleus of ~ e in the tetrahedral as ~ + well as the octahedral position using se- miempirical iterative extended Hiickel the- ory (1).

The quadrupole splitting A was calcu- lated on the basis of two different models.

Each model should represent the valance contribution at the position of the ~ e ~ + nucleus exactly. In Model 1, the ligand contributions were considered by an effec- tive charge approximation according to Trautwein et a1. (2). The overlap contri- butions were neglected. The contributions of the ligands were computed from the point charge model. In Model 2, overlap and li- gand contributions were obtained from num- erical integration (3). Finally, the elec- tronic charge density, f(0). at the ~ e ~ ' nucleus was computed following Reschke et a1. (4).

I. !?e3+ at the P etrahedral Position

In Table 1 the computed values fordare listed. Comparison with the experimental data f o r A yields satisfactory agreement although only a small cluster of four neighbouring atoms was taken into account.

It is interesting to note that a small change in the geometry of the cluster pro- duces a significant change in 65. As a

test, the distance Fe-0 in YIG was in- creased from 1.8663

k

^{to 1,8720}

fo

This increase of 0.3 per cent yielded an in- crease of U from 0.924 mm/s to 0.853 mm/s, i.e. 7.7 per cent.

Table 1: Experimental and computed values for 3 of ~ e in Y3Fe5012. The ~ + experimental values are from reference (5).

Computed mental 1

mm/s

, ^'

Model 1 Model 2

'

-

Y Fe 0 i

3 5 1 2

,

^{-0.97 1 -0.708 -0.924} _{.._ ._}

.._/

11. ~ e at the Octahedral Position ~ + nwas calculated first using a cluster of only six neighbouring oxygen atoms.

However, the results were unsatisfactory:

.A = -1.064 mm/s for YIG and

A

= +0.192 mm/s for andradite compared to the exper- imental values of -0.47 mm/s and 0.56 mm/s, respectively. Thus, not even the sign of ,A seems to be generally established by the first coordination shell although the correct signs were found for YIG and andradite. In the following, a shell of 12 next nearest neighbouring atoms was included. This led to a significant im- provement (cf. Table 2).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19801103

JOURNAL DE PHYSIQUE

Table 2: Experimental and computed values (5) G.N. Belozerskii, V.N. Gitsovich, ford of pe3+ in Y3Fe501 and A.N. Murin, Yu,P. Khimich, and Yu.

M. Yakovlev: JETP Lett. 11, 106 Ca3Fe2Si5OI2. The experimental (1970) ; R.M. Housley anda.~. Grant:

values are from reference (5) Phys. Rev, 203 ( 1972) ; D.N. Beloze::::i,%. P. Khimich, and (6), respectively. and V.N. Gitsovich; Phys.Stat. Sol.

(b) 79, K125 (1977)

111. Atomic Charge Densities at the Iron Nucleus

Garnet

r

/

~~~~~~~0~~

Comparing the trends in the experi- mental isomer shift

d

with those of the calculated electron densities p(O), it was observed that only the expected ten- dency of increase of P(O) with decrea- sing

d

is reflected in the computations.

Unfortunately, the determination of a calibration factor seems not to be mean- ingful from these results.

In summary, it is concluded that clusters of up to 19 atoms seem to de- termine A for ~ e in garnets with an ~ + estimated error of 20 to 30 per cent, at least in end members of solid solutions.

In mixed crystals of the garnet type the situation may be more complicated.

Experimental mm/s

-0.47 -0.56

References

Computed mm/s Model 2 -0.449 +O. 523

(1) R. Rein, G, A. Clarke, F. E. Harris : Quantum aspects of heterocyclic com- pounds in chemistry and biochemistry, 11. Jerusalem, Israel Acad. of Scien- ces and Humanities, 1970.

(2) A. Trautwein, R. Zimmermann, F.E.

Harris: Theor. Chim. Acta

22,

89 (1975 )

(3) R. Reschke, A. Trautwein: Theor. Chim.

Acta

a,

^{85 (1978)}

(6) G,Amthauer, H. Annersten, and S,S.

Hafner: Z. Kristallogr.

143,

14 (1976)

( 4 ) R. Reschke, A. Trautwein, J. P,Desclaux:

J. Phys. Chem. Sol.%, 837 (1977)