TEXTURE EFFECTS IN 3/2-1/2 MÖSSBAUER SPECTRA

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TEXTURE EFFECTS IN 3/2-1/2 MÖSSBAUER

SPECTRA

T. Ericsson, R. Wäppling

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 12, Tome 37, Dtcembre 1976, page C6-719

TEXTURE EFFECTS IN

3/2-1/2

MOSSBAUER SPECTRA

T. ERICSSON and R. WAPPLING

Institute of Physics, Uppsala University, Box 530, S-751 21 Uppsala, Sweden

R6sum6. - Une methode d76viter les effets de texture dans les spectres Mijssbauer en conservant les proprikths autosupportantes et la bonne conductivite thermale des absorbants est introduite. La mkthode doit 6tre d'une importance particulikre dans la mineralogie et pour 1'8tude des effets Goldanskii-Karyagin sur les specimens polycristallins.

Abstract.

-

A way of avoiding texture effects in Mossbauer spectra while retaining self-supporting, good thermal conductivity absorbers is introduced. The method should be of particular importance in mineralogy and in the study of Goldanskii-Karyagin effects on polycrystalline samples.

1. Introduction.

-

In the preparation of powder Mossbauer absorbers one usually encounters a uni- directional reduction in size, usually be compression. If the powder used is non-spherical oneoft en obtains a preferred orientation giving rise to the so called texture effects. These manifest themselves as a difference in line intensities compared to what is obtained in a random absorber and they often complicate the analysis of the spectra, in particular in the case of

4-3

nuclear transitions. There have been several methods proposed to overcome the texture effects or to correct them [I, 2, 31. The most popular method to overcome the texture effects is to mix the powdered absorber material with some inert powder such as sugar, active charcoal or, in our case, boron nitride. In order to obtain a self-supporting absorber with good thermal conductivity the boron nitride powder- absorber powder mixture is pressed to discs. In this way suitable absorbers for high and low temperature studies are obtained. Compressed absorbers do, however, in some cases show texture effects [4]. The purpose of the present paper is to present a way to overcome the texture effects even for a compressed absorber of the type described above. The discussion is limited to

3-+

dipole transitions, since for other cases one has several absorption lines usually making an interpretation possible.

2. Theoretical background.

-

With a single line source and an absorber with a sufficiently large electric quadrupole interaction, the Mossbauer spectrum consists of two lines. In the random absorber case the two lines have the same intensity while for an absorber with a preferred orientation they usually have different intensities. If we assign index 1 to the line resulting from transitions between magnetic

sublevels

+ +

and

+

and index 2 to the

+ +-

f

3

line we can write the relative intensities [5]

P1(8, q ) = 4[(3

+

y 2)/3]1/2

+

(3 cos2 8

-

1

+

y sin2 0 cos 2 q ) P2(d, q ) = 4[(3

+

q2)/3]"2

-

(3 cos2 0

-

1

+

y sin2 B cos 2 q ) (1) where d and 9 are the usual polar and azimuthal angles of the gamma ray direction referred to the electric field gradient [EFG] principal axes system and q is the asymmetry parameter of the EFG.

For a random absorber one has to integrate over all 8 and q values, the second term in P1 and P, then vanishes giving lines of equal intensities. For an absorber with a preferred orientation on the other hand some values of 0 and 9 will occur relatively more often. The extreme case is of course a single crystal where one has only one value for 0 and 9

for each different position and gamma radiation direction. The largest intensity difference is found for 8 = 0 and y = 0 giving PI = 6 and P, = 2.

3. Absorber preparation.

-

In order to know which angular distribution one has in an actual absorber, the way of making the absorber has to be discussed. When a sample is crushed the grains formed reflect the crystallographic anisotropy. As a result one obtains in many cases needles or flakes instead of the expected spherical grains. If the anisotropic powder is spread on adhesive tape the grains will orient with their largest dimension in the plane-of the tape for- ming an absorber with a marked texture. Even if the powder is mixed with a solution of some plastic and a suitable solvent and the solvent is allowed to evaporate, the absorber will still not be a random one since during the sedimentation the grains will

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partly turn so that their largest dimension is parallel to the plane of the absorber.

Essentially the same happens when a non-hydrosta- tic pressure is applied to a mixture of absorber material and an inert powder. This problem has been discussed recently by Nagy [lo].

4. Needles. - In the case of needle shaped grains or microcrystals it is natural to define the orientation of a grain by the orientation of its axis. Let us introduce a coordinate system according to figure 1. If

FIG. 1.

-

Schematic model and coordination system.

the sample is compressed along the z-axis it is natural to assume that the grains simply rotate. This means that

p

stays constant, and in the most pronounced case the final value of a, a,, is related to the initial value ai by

r cos a, = cos af (2) Eq. (2) results from a uniform compression with the ratio between final and initial thickness equal to r, and it is assumed that the ratio between the projec- tions of a needle (or flake) on the z-axis before and after the compression is also equal to r. Nagy et al.

in their paper [lo] assume a dependence of the form

We can now introduce a density function D(a, P) describing the orientation of the grains. We assume that in the initial state, i. e. before the compression, all orientations have the same probability and with the normalization condition

J

o.

J

0 D(a, B) sin a do dB = 1 (4)

we obtain

In figure 2 the rotation of the grains is further exemplified and one sees that the grains which in the initial state had orientations described by the surface A, will in the final state be found directed through A,. The corresponding solid angles are

SZ, = sin a, da, dPi

SZf = sin a, da, dp,

.

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FIG. 2.

-

Orientation model. The crystallites in Ai are assumed to be in Af after compression. The z-axis is the compression

axis.

A pure rotation does not affect the angle j3 which implies

dPi = (7)

and from differentiation of eq. (2)

r sin ai da, = sin a, dcl, (8) which gives

Finally, since the number of microcrystals with orientations within the two solid angles is the same, we obtain combining eqs. (9) and (5)

In this idealized model we also find the restriction arc cos r

<

a,

<

900

.

(1 1) 5. Flakes.

-

The orientation of a flake is usually described by the direction of its normal. Instead of eqs. (2) and (8) we obtain

r sin a, = sin a, (12) r cos a, da, = cos a, da,

.

₍₁₃₎ Combining these two equations with eqs. (5), (6), (7) we arrive at the density function for flakes

1 cos a,

Df@, P) = - (14)

2 n r J r Z

-

s i n z % '

Analogous to eq. (11) the possible values for a, are given by

0

<

a,

<

arc sin r

.

(15)

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TEXTURE EFFECTS IN 312-112 MOSSBAUER SPECTRA C6-721

thus for each a value there is a uniform distribution in

8.

Since the EFG principal axes system is directly related to the crystallographic axes system and the latter is related to the shape of the microcrystals it is reasonable to assume that also the EFG has a conical distribution. It is now possible, from a purely geo- metrical consideration, to relate the angle 8 to the angles 6, 8, o defined in figure 3. The result is

cos 8 = cos E cos 6

+

sin E sin S cos o

.

₍₁₆₎ For p all values are assumed to occur with the same probability. It now remains to correlate the angles,

E and o with a and

8.

axis

Vjz

t h e press

FIG. 3.

-

Definitions of the angles 6, e, 8, o. The press axis coincides with the normal of the absorber plane.

7. Intensities.

-

In the majority of cases one finds that the main component, Vm* of the EFG for

needles is parallel to the needle axis. In that case we have

Furthermore, since we assume that we have a random

cp orientation for each 8-value, the last terms in eq. (1) disappear and we obtain

P1(6, r, @ =

J

f

Jzi2 D(E, CO) [4(1

+

1'/3)11'

+

arc cos r

+

3 cos2 8

-

11

sin E d o ds

or, in the most pronounced case discussed earlier

+

3

C2'

[*I2 (ms B cos

s

+

sin e sin

s

cos x

x sin E d o ds

I

leading to

In the same way we arrive at

In order to obtain the corresponding expressions for flakes we note that the most common situation is that V,, is parallel t o the normal of the flake. Thus

eq. (17) is valid and combined with eqs. (I), (14), (15) and (16) we obtain after performing the integrations

The intensities calculated (eqs. (18)-(21)) are only relative intensities, i. e. it is only the ratio P1 to P2 that is important, giving rize to the asymmetries observed. We can draw three concIusions from eqs. (18)-(21) :

1) The asymmetry increases when r decreases i. e. when the sample is compressed.

2) The asymmetry decreases when q increases. 3) The spectrum is symmetric, irrespective of the values of r and q, for cos 6 = 1/

J3

i. e. 6 = 54.70.

The most important point is, obviously, that if one allows the gamma radiation to pass through the absorber at an angle of 54.70 to the normal the intensities are equal. This applies when the EFGs have conical distributions and random cp orientations, whatever the density function actually is, and allows for a simple way of avoiding texture effects [6].

In figure 4 two Mossbauer spectra of a fine grain clay mineral are shown. The one recorded in the usual geometry shows asymmetric lines whereas the one recorded at 54.70 does not.

The validity of the magic angle concept does, of course, depend on the validity of the assumptions made. Let us, therefore, discuss these assumptions in some detail. The assumption that the EFG have conical distributions should be fulfilled when the material is randomized from the beginning and the absorber is made by a uni-axial compression.

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macroscopic intensity tensor is diagonal in the coordinate system introduced in figure 1.

Thus, with a carefully made absorber no texture

FIG. 4.

-

Mossbauer spectra of a chlorite powder absorber recorded with the y-radiation parallel to the normal of the

absorber plane (top) and at 5 4 . 7 O to the normal (bottom).

effects should be seen in a spectrum recorded at 54.70 to the axis of compression.

Concerning the magnitude of the texture effects, in an absorber manufactured as described above, it is important to remember that our model represents an extreme case. It is difficult to imagine a situation where more pronounced texture effects than according to this model will appear and in general they are much smaller. Especially for small compressions, the absorber contains much air and turbular pro- cesses will occur giving rise to random orientation effects. We have measured, in normal transmission geometry, line intensities as a function of compression for chlorite of the type mentioned earlier. The results are given in figure 5 together with the theoretical curves, according to Nagy et al. [lo] and here pre- sented model. In the latter, for r = 0, five degrees deviation from 54.70 will result in

-

6

%

asymmetry in the line intensities for needles but

--

12

%

for flakes.

8. Goldanskii-Karyagin effect. - Until now we have assumed that the lattice vibrations are isotropic. If this is not the case the absorption probability is different in different crystallographic directions. Eq. (1) should then be multiplied with a factor describing the angular variation of the absorbtion probability. After integration over the possible directions one obtains an asymmetrical spectrum, the Goldanskii- Karyagin effect [ l l , 121, even in the absence of texture. In many cases the occurrence of unequal line intensities have been attributed to the Goldanskii-Karyagin effect, although texture is the real cause of the asymmetry. The actual reason is to be found in the relative changes of line intensities for the two effects. Even in a case where the lattice vibration anisotropy is very large, the effect on the intensity is small. In a recent study [13] it was deduced from single crystal measurements that the recoilfree fractions in KAu(CN), varied with a factor of three for gamma- rays parallel and perpendicular to the c-axis. The effect on the powder absorber spectrum, however, was an asymmetry of only 5

%.

A similar insensitivity in the case of 57Fe has been pointed out by Pfannes and Gonser [3]. The texture effects, on the other hand, can be very large as is exemplified in figure 4. A misalignment of only a few degrees may give an asymmetry that will obscure the Goldanskii-Karyagin effect completely.

FIG. 5.

-

Theoretical curves for in this work presented model (full lines) and for the model proposed by Nagy et al. in ref. [lo]

(dashed lines and only for q = 0). The y-ray is parallel to the normal of the absorber plane. The upper curves are for flakes, the lower ones for needles. The crosses denote experimental results on a chlorite absorber. The compression is defined

a s l - r .

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TEXTURE EFFECTS IN 312-112 MOSSBAUER SPECTRA C6-723

References

[I] HOGG, C. S. and MEADS, R. E., Min. Mag. 37 (1970) 606. [9] NAGY, D. L., private communication.

[2] NAGY, D. L., K U L C ~ , K., SPIERING, H. and ZIMMERMAN, 1101 NAGY, D. L., DEZSI, I. and K U L C S ~ , K., Proc. Znt., Conf.

R., J. Physique Colloq. 35 (1974) C6-385. Miissbauer Spectroscopy, Vol. 1, Cracow Poland [3] PFANNES, H.-D. and GONSER, U., Appl. Phys. 1 (1973) 93. (1975) 25.

141 HOGARTH, D. D., BROWN, F. F. and -CHARD, A. M., [111 GOLDANSKII, V. I., GORODINSKII, G. M., ~ A G I N , S. V.,

Can. Min. 10 (1970) 710. KORYTKO, L. A., KRIZHANSKII, L. M., MAKAROV, E. F.,

[5] ZORY, P., Phys. Rev. 140 (1965) A 1401. SUZDALEV, I. P. and KHRAPOV, V. V., Proc. Acad.

Sci. USSR, Phys. Chem. Sect. 147 (1963) 766. [61 ERICSSON, T. and WAPPLING, R., Int. Conf. Mossbauer _f12]_KARyAGIN, _S._V.,

PYOC. Acad. Sci. USSR, Phys. ,-hem.

Spectroscopy, Corfu Greece (1976). _Sect.₁₄₈_{(1964) 110.}