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FURTHER EXAMPLES OF A LIGAND FIELD
CALCULATION FOR THE SIXFOLD
COORDINATED COMPLEX Fe(H2O)2+6
H. Spiering, I. Dezsi, D. Nagy
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, suppl&ment au no 12, Tome 37, Ddcembre 1976, page C6-571
FURTHER EXAMPLES OF A LIGAND FIELD CALCULATION
FOR THE SIXFOLD COORDINATED COMPLEX
Fe(H20)2+
H. SPIERING
Physikalisches Institut der Universitat Erlangen-Niirnberg D 8520 Erlangen, Germany I. DEZSI, D. L. NAGY
Central Research Institute for Physics, H-1525 Budapest, Hungary
R&nm6.
-
Les ions paramagnetiques Fez+ dans Fe(BF4)2.
6 Hz0 dans Co(BF4)2.
6 Hz0 et dans Co(C104)~.
6 Hz0 ont etk observe ?i 4,2 K sous forme de poudre, par spectromdtrie Mossbauer, avec un champ magnetique longitudinal applique allant jusque 50 kG. Le champ de symetrie du ligand aux sites de fer est principalement de type D 3 d TOUS les spectres peuvent &ret r h bien interpretes dans le cadre de la thkorie du champ de ligand r6duit au sous-espace 5T2, des Btats de haut spin 5D, la symetrie rQlle dans le sous-groupe C2h de D 3 d . Pour surmonter le
grand nombre de paramMres concernes, la covalence, le couplage spin-orbite et les constantes hyperfines sont prises identiques pour tous les composks, ce qui est justifie par le fait que les liaisons du fer et par conskquent les mol~cules orbitales sont principalement dkterminees par le complexe Fe(HzO)i+. La distorsion identique de C2h dans ces composks, dans FeSiF6. 6 Hz0 et dans Fe(C104)~
.
6 Hz0 donne lieu ?i un abaissement de la symCtrie D 3d.Abstract. - Mossbauer spectra of powder samples of the paramagnetic Fez+ ion in Fe(BF4)z
.
6 Hz0 and diluted in Co(BF4)Z.
6 Hz0 and Co(C104)2.
6 Hz0 have been measured at 4.2 K i n longitudinal external magnetic fields up to 50 kG. The ligand field symmetry at the Fe-site is mainly D 3d. All spectra can be well reproduced within the ligand field theory restricted tothe 5T2,subspace of the 5D high spin state and the effective symmetry at the iron site being Czh,
the subgroup of D 3 d . TO overcome the large number of parameters involved the covalency, the
spin-orbit-coupling and the hyperfine constants are taken to be the same for all compounds due to the matter of fact that the binding to the iron ion and therefore the molecular orbitals are essen- tially determined by the Fe(~z0)62+cornplex. The similar Czh-distortions in these compounds and in FeSiFs
.
6 Hz0 and Fe(C104)~.
6HzO are a hint at the Fe(~?0)62+ complex itself giving rise to the lowering of the D 3 d symmetry rather than theenvironment in the crystal.1 . Introduction. - The high spin Fe2+ ion has been studied in many compounds to solve the problem of the appropriate ligand field. The usual methods, susceptibility and Mossbauer measurements, are not sufficient to determine uniquely the ligand field para- meters and hyperfine constants. To limit the number of independent parameters some are chosen with qualita- tive arguments, especially the covalency parameters and hyperfine constants. In our previous work [I] we used the following concept in the case of the F ~ ( H , o ) ~ + complex.
The hyperfine interaction of this complex is very similar for different crystals. The isomer shift Is and the bare quadrupole splitting
are almost the same indicating the same radial charge distribution of the Fez+ ion. This fact has been stated by Hazony [2] and is simply explained by the assump- tion that the F~(H,o):+ complex itself determines the
binding to the iron atom. The influence of the environ- ments is so small that it can be treated in terms of the first order in perturbation theory. The ligand field energies will be changed while the covalency parameter, the radial distribution of the d-electrons and the hyperfine constants are unchanged. The comparison of the energies involved supports this point of view. The binding energy of the F~(H,O);+ complex of about 4 x lo5 cm-' as known from the heat of hydration of the Fe2+ ion [3] is lo3 times larger than the change of the 5T2, energies of the Fe2+ ion in different com- pounds. This holds just for the compounds which are discussed in [I]. The ligand fields a t the iron site in FeSiF, . 6 H 2 0 and Fe(C104), . 6 H 2 0 could be para-
meterized with the same point symmetry and the ligand field energies differ only by about 250 cm-l.
To prove this concept further examples have to be evaluated. This work presents the Mossbauer measure- ments on the paramagnetic F~(H,O):' complex in Fe(BF4), .6 H 2 0 and diluted in Co(BF4), . 6 H,O
and Co(C104),.6 H 2 0 which are isostructural to
C6-572 H . SPIERING, I . DEZSI AND D. L. NAGY
Fe(C104), .6 H 2 0 [4] and show very similar phase transitions [5] to that observed in the latter [6].
2. Experimental.
-
The substances Co(BF4), . 6 H 2 0 and Co(ClO,), . 6 H 2 0 contain about 1 at%
57Fe (enriched in 5 7 ~ e to 85%).
Unfortunately about 10%
of the Fe(BF,), .6 H 2 0 compound has oxidized whichappears in the Mossbauer spectrum as a six line pattern. This part of the spectrum is almost indepen- dent of the applied magnetic field indicating an anti- ferromagnetic ordering of the Fe3 + fraction.
To avoid texture problems the thickness of the absorbers has been chosen relatively high (0.2
-
0.3 mg 57Fe/cm2). Additionally the substances have
been mixed with vaseline which hinders at low tem- peratures a rotation of the microcrystals in large applied magnetic fields [ 7 ] . The Mossbauer spectra have been measured in longitudinal magnetic fields of 10, 30 and 50 kG at 4.2 K with the equipment described in [8].
3. The ligand field and hyperfine parameters.
-
The ligand field Hamiltonian X is parameterized in 5T2g subspace of the Fez' high spin state
5D.
In C2, symmetry the eigenstates (with the notation in [ 9 ] )0 0 -
q = cos 8t2, - sin 8t&, q - = tZg
,
q + = sin 8tig+
cos 8tAand the corresponding eigenvalues
define two energy splittings 6 and a and one mixing angle 8. The parameters a and 8 vanish for an axial ligand field. There are four qualitatively different C2,- distortions corresponding to the two signs of a a n d o ( +
1
aI
and f 181).
The total Hamiltonian with the applied magnetic field H is given by
X
+
I L S+
,u,.(L+
2 S ) Hwhere the orbital momentum L is reduced by the covalency parameter a2 and 1 is the spin orbit coupling constant.
The effective magnetic field at the nucleus in the case of fast relaxation
requires two parameters HL = 2 pB
<
PL
>and the Fermi contact term H,., The constant
H,, = 2 ,uB
<
rsi3 > related to the spin dipole opera- tor O,, is assumed to be equal to HL. The dependence of the EFG tensor V = ( 1-
y,) V,,,+
(1-
R,) V,,, on the magnetic field H is neglected. The small lattice contribution ( 1-
y,) V,,, is assumed to be propor- tional to (1-
Re) V,,,, the EFG produced by the 3d-electrcns.The sign of V,, and the asymmetry parameter
v
= (VXX--
Vyy)/Vzz in the quadrupole splittingresult from the Hamiltonian X
+
ILS. In the 5T2g approximation with C2, symmetry therefore seven parameters, namely6, a, e , I , a2, HL, Hc
determine the Mossbauer spectra in external magnetic fields. Simulated Mdssbauer spectra of thin powder absorbers in an applied magnetic field of 50 kG are shown in figure 1. The axial ligand field with a singulet ground state (6 = 650 cm-l, a = 8 = 0 ) generates a
susceptibility tensor
x
whereX,
% ~ 1 1 at very low temperatures gives rise to the narrow absorption lines (Fig. la). The C2,-distortion(1
a1
= 50 cm-l,1
81
= 3.50) broadens and partly splits the lines. Theshape of the spectra significantly depends on the sign of the parameters a and 8 (Fig. lb, c, d, e) [ l o ] . The
remaining parameters are taken from [ I ] (see Table I).
,
- -4 -
Velocity (mrn/s)
FIG. 1. - Simulated Mossbauer spectra of thin powder samples in an applied field of 50 kG. a) The axial ligand field with a singulet ground state (tzg) shows narrow absorption lines. b), c),
d ) , e) The shapes of the spectra with a small Czh distortion signi- ficantly depend on the sign of the ligand field parameters a and 0.
4. Experimental results and interpretation.
-
Figure 2 shows as an example the powder Mossbauer spectra at 4.2 K in longitudinal magnetic fields up to
50
k G
of 57Fe diluted in Co(BF4), .6 H20. TheFURTHER EXAMPLES OF A LIGAND F E L D CALCULATION FOR Fe(H20);' C6-573
a) The isomer shifts (Is) and the quadrupole splittings (AEQ) are almost the same for the F~(H,O);+ complex in the five compounds.
b) 6 is the axial splitting o f the ZigandJield. The parameters of the C2,-distortion (angle 8 and the energy splitting a ) are small. There are two qualitatively diflerent combinations of the signs of a and 8 :
+
(- ] a1,
I
9I).
The spin-orbit-coupling 1, the covalency a2 and the hyper-ne constants HL, H, could be chosen identically for allJive examples.Compound 57Fe in 57Fe in
x 6 H 2 0 FeSiF6 Fe(C1O4), Fe(BF4), Co(C1O4), Co(BF,), error
-
-
-
-
-
-
-
Is in mm/s 1.41 1 1.398 1.413 1.408 1.410 f 0.010 a) AEQ (4.2 K ) 3.60 3.46 3.57 3.50 3.48+
0.010 in mm/s I I 1 -6 -b -2 0 2 L 6 Velocity (rnrnls)FIG. 2. - 57Fe Mossbauer spectra of the polycrystalline speci- men C O ( H ~ ~ ) ~ . @ F ~ ) ~ doped with 57Fe. They are measured at 4.2 K in longitudinal magnetic fields up to 50 kG. The solid
lines are calculated spectra (cf. text).
splitting AEQ are listed in Table Ia. The shape of these
spectra are quite similar to those obtained for ferrous
perchlorate hexahydrate described in [I]. The absorp- tion lines at positive velocities are broader and more asymmetric while the positions are nearly the same for all applied fields. The type of the 50 kG-spectrum ist that of figure le.
With our concept three parameters 6, a, 0 are left to fit the spectra. The spin orbit coupling 2, the covalency
parameter a2 and the hyperfine constants HL and Hc
are taken from [I]. The line positions are mainly determined by the axial splitting 6. With the shape of the spectra the signs of the C2,-parameter are also known from figure 1. Therefore a good fit (if possible) is easily obtained by a few simulated spectra. The spec- tra of 57Fe in Co(ClO,), .6 H 2 0 have poor statistics
compared with those of figure 2. Even in this case 6 is well confined by the line positions. The characteristic shape is not lost but the a- and 0-values have larger errors. For the Fe(BF,), .6 H 2 0 absorber the intensity of the antiferromagnetic fraction to be subtracted destroyed some features of the spectra so that the evaluation of the ligand field becomes more difficult. The results are collected in Table Ib including those
given in [I]. The five different compounds produce five different ligand fields at the Fe2+ ion site each depen- dent on seven parameters (5 x 7 = 35) but only
5 x 3
+
4 = 19 parameters are necessary to get a good fit for 15 magnetically perturbed sectra. This has to be expected if the hypothesis of our concept is true. Actually the fit shown in figure 2 has been qualified as good but there are some discrepancies in the intensities especially in the 50 kG spectrum. This was alsoobserved in the other compounds. In the case of ferrous perchlorate hexahydrate it was attributed to texture [I]. The correction for thickness is too small as proved by the Fourier procedure described by Ure and Flinn [l 11.
C6-574 H. SPIERING, I. DEZSI AND D, L. NAGY
the crystal structure. The space group of the M(BF,), . 6 H,O and M(C104),.6 H,O series is P2
,,,.
There are two molecules per unit cell. The two equi- valent metal sites are only inversion centers. Therefore we tried to get a better agreement with more ligand field parameters corresponding to a lower symmetry. With small deviations from C,,-symmetry a better fit could not be obtained.The deviations in the intensities could recently be explained by one of the authors [12]. On the compound Fe(ClO4),.6 H,O it could be demonstrated that the polarisation of the absorber in applied fields is respon- sible for an anomalous behaviour of the intensities of the absorption lines. The polarisation degree dependent on the velocity of the hyperfine split spectra has been calculated. For the very sharp line at positive velocities in the 50 kG spectrum it -is much higher than for the other absorption lines so that the absorption of an unpolarized y-beam by an absorber of finite thickness will be smaller for this line as compared with the other lines. This is observed in the 50 kG spectrum of figure 2. The situation to be discussed has now the following features :
i) The Mossbauer spectra of the F~(H,O):+ complex of mainly D,, symmetry in applied magnetic fields can be satisfactorily reproduced using ligand field theory.
ii) The covalency, the spin orbit coupling and hyperfine parameters have characteristic values for this complex.
iii) The distortions from D,, symmetry at low temperatures can be described with a ligand field of C,,-symmetry. Only two of the four different C,, distortions are realized in the five examples of Table lb.
To the authors knowledge there is no case where the simulations of the Mossbauer spectra of the para- magnetic Fez+ ion in applied magnetic fields have been so successful as for our compounds. The reasons may be the necessity for a highly developed program (including polarisation effect) and the number of the ligand field parameters involved. If the main distortion from cubic symmetry is a fourfold axis there are many possibilities to go down in symmetry. Generally the ligand field Hamiltonian within the T,, states has five independent parameters which indeed are very difficult to be uniquely determined. For the present examples a small C,,-distortion (two small parameters) of the axial ligand field (one parameter) has been sufficient to describe the spectra. The statement (iii) that only two of the four possible C,, distortions are realized in the five compounds (Table I) may be a hint at a mechanism for the F~(H,O);' complex to produce the distortion from axial symmetry itself rather than the environment of the complex.
Acknowledgements.
-
Financial support of the Bundesministerium fiir Forschung und Technologie is much appreciated. The authors are indebted to Dr. B. Molnar for the preparation of the compounds.References
[I] SPIERING, H., NAGY, D . L., ZIMMERMANN, R., J. Physique
Colloq. 35 (1974) C 6-231.
[2] HAZONY, Y., Mossbauer Effect Methodology (Ed. Gru- verman I. J.), Vol. 7, 1971.
[3] COTTON, F. A., WILKINSON, G., Advanced Inorganic Chemistry (John Wiley-New York) 1972 Chapter 21.9. [4] Moss, K. C., RUSSELL, D. R., SHARP, D. W. A., Acta
Cryst. 14 (1961) 330.
[5] ASCH, L., DEZSI, I., LOHNER, T. and MOLNAR, B., to be published in Chem. Phys. Lett.
[6] DEZSI, I. and KESZTHELYI, L., Solid State Cornmuv. 4
(1966) 511.
[7] NAGY, D . L., KULCSAR, K., RITTER, G., SPIERING, H., VOGEL, H., ZIMMERMANN, R., DEZSI, I., PARDAVI- HORVATH, M., J. Phys. Chem. 36 (1975) 759.
[8] KONIG, E., RITTER, G. and GOODWIN, H. A., Chem. Phys.
1 (1973) 17.
[9] BALLHAUSEN, C. J., Introduction to Ligand Field Theory
(McGraw Hill, New York) 1962, p. 68.
[lo] SPIERING, H., ZIMMERMANN, R., RITTER, G., Phys. Stat. Solids (b) 62 (1974) 123.
