THE PROBLEM OF TEXTURE IN MOSSBAUER SPECTROSCOPY

In Mtissbauer spectroscopy it is desirable to work with single crystals or with polycrystalline material of random orientation. The actual, most occuring, case of preferred orientation (texture) and its influence on the relative line intensities of hyperfine split Mrssbauer spectra is analysed. Texture information which can be obtained from such an analysis is demonstrated with variously prepared barium ferrite (BaFe 12019) samples.


INTRODUCTION
Concerning the relative line intensities the interpretation of hyperfine split Mrssbauer spectra on polycrystalline samples is complicated because of the existence of three different effects influencing the intensity ratios: effective thickness of the absorber, lattice vibrational anisotropy (Goldanskii-Karyagin effect) and preferred orientation of the crystallites (texture). While the effective thickness of the absorber in most cases can be kept small it is very difficult to produce a random orientation distribution in powder samples. Thus, an interpretation of the line intensities, in general, has to take into account the lattice vibrational anisotropy and the effect of preferentially oriented crystallites.
In a recent study the two competing effects have been analysed; and it was pointed out that the effect of the lattice vibrational anisotropy is often overestimated. A computer program, which calculates Mtissbauer spectra for simultaneous magnetic dipole and electric quadrupole interaction of a polycrystalline sample with any distribution of the crystallites, allows one to estimate the nonrandom orientation effect. Thus the relative magnitude of the two contributions (Goldanskii-Karyagin effect vs. texture) influencing the relative line intensities in M/Sssbauer spectroscopy can be determined. In the meantime, one will also obtain useful information about the orientation distribution function of the electric field gradient and the internal magnetic field.
We have recently determined the spin orientation in Fe3C by correlating X-ray textures with relative Mtissbauer line intensities2. Now we have reversed the problem. That is, from the relative Mrssbauer line intensities and the known orientation relation of spin and quadrupole parameters in regard to the crystal axes we wish to obtain information about the texture of the specimens.

DEFINITION OF CORRELATIONS
The line positions of a M/Sssbauer spectrum are given by the transition energies between the excited and the ground states of the Mrssbauer nucleus, and the line intensities are proportional to the transition probabilities P which depend on the orientations of the magnetic field at the nucleus H--(0) and of the axes of the electric field gradient (EFG) tensor ((Vk)i, k x, y, z) with respect to the propagation direction kr of the y-rays. Figure 1 defines the angles 0, , 0 and 99, which specify the orientation of H(0) and the y-beam with respect to the EFG axes V, V, and V.
The probability of a transition between the excited state [i > and the ground state [j > may be given by P(O, ok, O, tp, i, j). So the intensity I of the transition in a polycrystalline sample with an orientation distribution of the crystallites described by a distribution function F(& 0o, tp, qgo) will be given by the expression I(0, ok, 0o, qo, i, j) I dO [.' do P(O, dp, O, (p, i, j) F(9, ,90, tO, 990) sin0 (1) The angles ,90 and q9 o define the preferred orientation of the EFG axes with respect to the propaga-tion direction of the y-rays (see Figure 2). The distribution function F(0, '9o, go, goo) df represents the probability to find a crystallite with Vz-axis within the solid angle element df. The probability to find a crystallite with any orientation of the Vzaxis must be unity. So the distribution function has to be normalized by the condition" dO " dgo F(O, 00, go, go0) 1.
(2) FIGURE 1 The angles 0, and 9, 07 defining the orientations of the internal field H(0) and the propagation direction k of the 7,-beam, respectively.

THE PROGRAM
The program is an extension of the work by W.
Kiindiga, which generates theoretically M6ssbauer spectra for powder and single crystal samples con- The angles 9o, 070 defining the center of the orientation distribution of the Vzz-axis. e is the charge of the proton, Q, the electric quadrupole moment of the nucleus, g, the nuclear gfactor of the excited state and #, the nuclear magneton.
The various distribution functions F are calculated in a subprogram; thus the number of distribution functions can easily be completed. In general, it will be difficult to perform the physically correct normalization condition (2). The area of the functions used in this work (Lorentzian and Gaussian functions) is proportional to the width and the depth ofthe lines, so we normalized our distribution functions dividing by the width of the distribution. The numerical integration with respect to the angles and go is carried out in steps of ten degrees. In order to cheek the program we calculated a M/ssbauer spectrum for a randomly oriented powder sample (distribution function equal to unity). We obtained the normalized intensity values 0.2475, 0.1699, 0.0825, 0.0825, 0.1699 and 0.2475 whereas a calculation with Kiindig's original powder program z leads to the intensities 0.2500, 0.1667, 0.0833, 0.0833, 0.1667 and 0.2500. Using steps of five degrees for the numerical integration (requiring fourfold computer time) we obtained the values: 0.24937, 0.16751, 0.08312, 0.08312, 0.16750 and 0.24936.

APPLICATIONS
In the interpretation of the relative line intensities of an experimentally obtained Mfssbauer spectrum the influence of the absorber thickness can be estimated#'s. However, it is difficult to differentiate between the two contributions: preferred orientation of the crystallites and lattice vibrational anisotropy.
The influence of preferred orientation on the intensity ratios for the special cases of pure electric quadrupole interaction (assuming axial symmetry of the EFG tensor (r/--0)) and of pure magnetic dipole interaction has been calculated 1. This program generates M6ssbauer spectra resulting from transitions between Fe z 7 nuclear levels for a general combination of magnetic dipole and electric quadrupole interaction and for any orientation distribution of the EFG axes. Assuming different functions for the orientation distribution of the EFG axes used for the calculation of Mfssbauer spectra, the program is useful (i) to estimate the effect of preferred orientation, (ii) to obtain informarion about the distribution function of the EFG axes, and (iii) to evaluate the distribution of the internal magnetic field directions (by knowing the angles 0 and used as input parameters).
Furthermore, this program might have some significant technological applications in regard to the orientation distribution of the internal magnetic fields. For example, the important permanent magnets consisting of Me-ferrite, MeFe12019' (Me Ba, Sr, Pb) are made by orienting very fine powder in a magnetic field under pressure (we used a similar procedure preparing sample 2, see below). The width of the H(0) orientation distribution may be used as a parameter, which contains information about the magnetic properties of the product.

Samples Preparation
Measurements with three different barium ferrite (BaFe120 9) absorbers have been carried out. In order to evaluate the three spectra this program has been applied. The samples have been prepared as follows: Sample 1 9 mg of very fine barium ferrite powder have been embedded in Araldit; the density of the absorber was 0.15 mg Fe s 7/cm yielding for the effective thickness TA n fao 2.4, where n is the number of Fe s 7 atoms per unit area, f is the absolute Debye-Waller factor, and ao represents the resonance cross section. Sample 2 In order to prepare a preferentially oriented powder sample we mixed 9 mg of very fine barium ferrite powder with Araldit (density 0.15 mg Fe 7/cm2) and put the mixture in a magnetic field ofabout 1 k0e. The direction ofthe field was parallel to the plane of the sample. Due to the high uniaxial crystal energy of the hexagonal crystal lattice the c-axes of the particles are forced to align themselves preferentially in the direction of the external magnetic field. Sample 3 An industrial permanent magnet (DE 1, Siemens) was ground to a thickness of about 0.01 cm (density of about 0.2 mg Fe7/cm2). The preferred orientation was perpendicular to the plane of the sample.
Measurements on the three samples were made at room temperature with a single line source (Co 7 in a Cu matrix) moved with constant acceleration.
A proportional counter detected the transmitted v-rays which were stored in 512 channels of a multichannel analyzer.

Results and Discussion
The barium ferrite spectrum consists of a superposition of five different subspectra corresponding to the five different iron sublattices6-11. We have been able to fit the obtained M6ssbauer spectra by resolving four spectra. In the case when the propagation direction of the v-rays was parallel to the the z-axis of the electric field gradient tensor, V=, the orientation distribution found for the EFG axes is the distribution of the internal magnetic field directions.
For the computer fits we used different intensity ratios of the inner lines 3 or 4 (Am +_ transitions) to the lines 2 or 5 (Am 0 transitions). The best fitted M/Sssbauer spectra were obtained using the intensity ratios summarized in the left column of Table I.
In order to synthesize the measured M6ssbauer spectra, we assumed, in the thin absorber approximation, Lorentzian and Gaussian shapes of the orientation distribution functions. We used as input parameters the known values 0 0 , qb 0 , r/= 0 and the interaction ratio R 0.14 (quadrupole splitting AEQ-0.41 mm/sec and internal field H(0)= 415 k0e for the considered spectrum 12 k. Sample 1 and sample 3 can be expected to be randomly oriented with respect to the azimuthal angle go. In this case the distribution function depends only on the angle ,9. Sample 2, however, does not have an orientation with rotational symmetry relative to the v-beam. So we have to use a distribution function depending on both ,9 and go. It was realized by the multiplication of a ,9 dependent Lorentzian (Gaussian) function with a go dependent Lorentzian (Gaussian) function. Using the known values for 0, tk, r/and R, and the distribution functions determined by the parameters shown in Table I, we calculated M6ssbauer spectra showing the experimentally obtained intensity ratios. For the three selected cases, the theoretically generated M/Sssbauer spectra of the 12 k sublattice are shown in Figure 4. The Lorentzian distribution functions are plotted in Figure 5.
The intensity ratio of a randomly oriented powder sample has the value of 0.5 (1" 2). The experimentally found value of 0.59 for sample indicates a small deviation from randomness. The c-axes of the crystallites, and also the internal fields, are slightly preferentially oriented parallel to the v-ray propagation direction. Quantitatively the data can be explained by assuming an orientation distribution described by a Lorentzian (Gaussian) function with the center at ,90 0 and a width of 100 (106).
Concerning sample 2 we used distribution functions which are the product of a 9-dependent and a go-dependent Lorentzian (Gaussian) function. The understood by the fact, that the original crystallites had the form of platelets with c-axes (H(0) orientation) perpendicular to the plane 13. This special shape of the BaFel 2 O19 crystallites may also be the reason for the observed deviation from randomness of sample 1. For the spectrum of sample 3 we obtain a Lorentzian (Gaussian) distribution with the center at 0 o 0 and width of 11 (54). The industrial permanent magnet (sample 3) shows a very strong texture, a feature which is important for the technological application of barium ferrite.
In this work we used two special distribution functions, and we made comparisons with experimental intensity ratios for each of the two functions.
Other functions could be used likewise. However, for many practical cases the Lorentzian or Gaussian functions are reasonable approximations to the physical reality. It is clear that the described method cannot determine the distribution function in a definite manner, but it yields some information regarding direction and the magnitude of the texture. Also, there might be some biological application of this method, where, instead of the orientation distribution of the crystallites, the distribution of the principal axes of the EFG is of interest. A Fortran listing of the computer program is available on request.

ACKNOWLEDGMENT
The financial contributions by the "Deutsche Forschungsgemeineinschaft" and "IRSID" are appreciated.