HAL Id: jpa-00214632
https://hal.archives-ouvertes.fr/jpa-00214632
Submitted on 1 Jan 1971
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
ON THE MECHANISM OF 3 d-TRANSITIONS IN K-ABSORPTION SPECTRA OF
TRANSITION-METAL COMPOUNDS
O. Brümmer, G. Dräger, W. Starke
To cite this version:
O. Brümmer, G. Dräger, W. Starke. ON THE MECHANISM OF 3 d-TRANSITIONS IN K- ABSORPTION SPECTRA OF TRANSITION-METAL COMPOUNDS. Journal de Physique Col- loques, 1971, 32 (C4), pp.C4-169-C4-171. �10.1051/jphyscol:1971431�. �jpa-00214632�
JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 10, Tome 32, Octobre 1971, page C4-169
ON THE MEXHANISM
OF 3 d-TRANSITIONS IN K-ABSORPTION SPECTRA OF TRANSITION-METAL COMPOUNDS
0. BRUMMER, G. DRAGER and W. STARKE Sektion Physik der Martin-Luther-Universitat Halle-Wittenberg
R6sum6. - On a BtudiC les transitions 1s-3d dans le spectre d'absorption K du fer dans des monocristaux de FezO3. Au moyen de rayonnement X polarise rectilignement et des rhgles de selection correspondante on vkrifie le caract6re dipolaire des transitions. On verit3e le caracthre dipolaire des transitions. On explique le mecanisme de melange des orbitales 3d et 4p par le champ crystallin.
Abstract. - 1s-3d transitions in K-absorption spectra of Fe in Fez03 single crystals have been investigated. By means of linearly polarized X-radiation and corresponding selection rules the dipole character of transitions is verified. Mixing mechanism of 3d- and 4p-orbitals via crystalline fields is explained.
In many K-absorption spectra of 3d-transition metals and their compounds small absorption peaks or humps exist at the low energy side of the main absorp- tion edge. This so called initial absorption is caused by transitions of K-electrons to 3d-levels. Taking into account the selection rules for dipole transitions there must be some admixture of p-symmetry to the 3d- states for initial absorption can take place.
In metals a strong hybridisation of wave functions and delocalization of atomic states exists. The mixing of functions of different symmetries and the resulting transition probabilities into original 3d-states are determined by the translation symmetry of crystal lattice [I]. But also in ionic and covalent crystals one finds initial absorption in spite of strong localization of atomic states. Therefore the question arises :
What kind of mechanism does p-d-mixing for the realization of dipole transitions cause or is the initial absorption produced by quadrupole transitions ?
In this paper we will first report experiments to distinguish between dipole and quadrupole transitions.
Then some mechanisms for mixing p-and d-states of atoms in ionic and covalent crystals will be explained.
The experimental determination of the character of transitions causing the initial absorption bases on measurements of absorption spectra of single crystals using linearly polarized radiation as well as by making use of corresponding selection rules.
We have investigated the initial absorption of two single crystal foils of a-Fe203 or hematite. This compound has a rhombohedra1 structure which may
be described by means of hexagonal coordinates. If the two axes a, and a, lie in the paper plane as in figure 1, the threefold axis a, stands perpendicular to
FIG. 1. - Coordinate systems for crystallographic orientation of single crystal absorbers.
this plane. In a second cartesian coordinate system the x-axis shall be parallel to a, or [loo]-direction and the z-axis parallel to the threefold axis a,. Then the y-axis extends along the [120]-direction.
Corresponding to these coordinate systems one absorber foil was cut from a natural hematite single crystal parallel to the xy-plane, the other one parallel to the xz-plane. Each foil was ground by a special method [2] to a thickness of 20 pm.
K-absorption spectra, especially the range of main absorption edge and initial absorption, were recorded
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971431
using a Johann type spectrograph. The principal experimental set up [2,3] is seen in figure 2. Conti- nuous X-radiation from a linear focus is reflected and monochromatized by the bent spectrometer
spectromete_r crystal
FIG. 2. - Principle experimental set up.
crystal. The (1330)-~lane of the quartz crystal reflects the radiation in the wavelength range of the iron-&
edge at glancing angles near 450. Therefore monochro- matized and focussed radiation is linearly polarized with the polarization vector perpendicular to the plane of focussing circle. By rotating and tilting of the single crystal absorbers several orientations relative to the polarization vector P and X-ray beam direction may be realized. The spectra are recorded on film and measured by a photometer point by point.
Figure 3 shows transmitted X-ray intensity against photon energy for some spectra in the range of the main absorption edge and initial absorption of Fe
ENERGY
-
FIG. 3. - K-absorption edge and initial absorption of Fe in Fez03 single crystals for several directions of polarisation vector
relative to the crystal axes.
in Fe,O,. If the polarization vector P goes from x-or [loo]-direction to z-or [001]-direction initial absorp- tion decreases. In the first case (a = 00, P 11 x-direc- tion) on the film a white line is seen, in the second case (a = 900, P 11 z-direction) only a small edge of blackening. These spectra were recorded at the foil cut parallel to the xz-plane with X-ray beam parallel to the y-direction. The foil parallel to the xy- plane was investigated with the X-ray beam parallel to
the z-direction and P parallel to the x- and y-direction, respectively. In both cases the white line was seen on the film. In general, for the polarization vector parallel to the x-or y-direction the white line, for P z-direc- tion the small edge of blackening appears. These results are independent of the X-ray beam direction relative to the absorber.
In the case of dipole transitions the strength of initial absorption is determined by the absolute of the matrix element
D,, = j y I $2) for P 11 y-direction and
D, = ($1 1 z 1 $2) for P 11 z-direction.
$, and $, are the wave functions of the initial and final states.
On the other hand, if quadrupole transitions are present, the amounts of the matrix elements
are the determining expressions for absorption strengths.
Here y is the coordinate of the direction of polarisa- tion vector and z the coordinate of the X-ray beam direction and vice versa.
The spectra which were recorded with inverted directions of y and z for the polarization vector and X-ray beam direction are different. From this expe- rimental result follows :
1. At least the difference of absorption strength between the two spectra must result from dipole transitions, because the amount of matrix elements for quadrupole transitions remains constant.
2. There is a mechanism for mixing 3d-states with p-symmetry for dipole transitions being able to take place between 1s-and 3d-states.
In case of ionic and covalent crystals this mechanism consists of mixing 3d- and 4p-orbitals via the crys- talline field prevailing at the place of absorbing atoms.
Probably only this mixing causes initial absorption in ionic and covalent crystals, because in spectra of water soluted ions [4] without the effect of the crystal- line field but with the possibility of quadrupole tran- sitions taking place, there is no symptom of initial absorption.
As perturbation theory predicts, the amount of orbital mixing is proportional to the matrix element
($3d I V I $4p), where V is the potential of the crys- talline field. Only if the potential V is an odd function, this matrix element does not vanish, because the d- and p-functions are of different parity. This means that mixing is present only for absorbing atoms with point symmetry of lattice sites without centre of symmetry.
In Fe203 the iron atoms occupy lattice sites with point symmetry C,. This point group has no centre of
ON THE MECHANISM OF 3 D-TRANSITIONS I N K-ABSORPTION (24-171 symmetry and mixing of 3d- and 4p-orbitals is
possible. The orientation dependence of initial absorp- tion may be explained by different admixtures of 4pz-and 4p,,z-orbitals to the 3d-functions. In this way different transition probabilities and absorption strengths result, if dipole transitions take place for polarisation vectors parallel to z- and x- or y-direction, respectively. The spectra for P parallel to x- and y-direction are the same, because in dipole transitions threefold symmetry axes can not be distinguished from continuous rotation axes.
Sometimes initial absorption is observed in the K-spectra of ionic and covalent crystals, even if absor-
bing atoms occupy lattice sites having centre of sym- metry. In this case one can suppose, that the centre of symmetry is uneffective, for instance by vibronic interac- tions. Destruction of the centre of symmetry and the resulting mixing of orbitals by asymmetrical vibrations could be proved by measuring the temperature depen- dence of initial absorption. A second possibility of orbital mixing is caused by lattice defects, first of all by vacancies. Expecially in oxides of 3d-transition metals such vacancies can exist in result of non-stoi- chiometric composition of metal and oxygen. Their influence on initial absorption will be investigated in future experiments.
References
[I] buum (Yu. P.), Fiz. metal. metalloved, 1961, 11, 10. [3] B R ~ ~ M M E R (0.) and DRXGER (G.), Phys. stat. sol., 1966 121 BR~MMER (0.) and DRXGER (G.), (t Riiltfgempektren
.
14, K 175.und chemisehe Bindung )I, Symposium Leipzig [4] BEEMAN (W. W.) and BEARDEN (J. A.), Phys. Rev., 1942,
1965, p. 35. 61,455.
