ANISOTROPIC HYPERFINE INTERACTIONS IN CUBIC METAL ALLOYS : MÖSSBAUER EFFECT MEASUREMENTS ON fcc Fe-Ni

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ANISOTROPIC HYPERFINE INTERACTIONS IN CUBIC METAL ALLOYS : MÖSSBAUER EFFECT

MEASUREMENTS ON fcc Fe-Ni

J. Hesse, J. Müller, B. Wiechmann

To cite this version:

J. Hesse, J. Müller, B. Wiechmann. ANISOTROPIC HYPERFINE INTERACTIONS IN CUBIC

METAL ALLOYS : MÖSSBAUER EFFECT MEASUREMENTS ON fcc Fe-Ni. Journal de Physique

Colloques, 1979, 40 (C2), pp.C2-161-C2-164. �10.1051/jphyscol:1979257�. �jpa-00218655�

ANISOTROPIC HYPERFINE INTERACTIONS IN CUBIC METAL ALLOYS : MOSSBAUER EFFECT MEASUREMENTS ON fee Fe~Ni

J. Hesse, J.B. Muller and B. Wiechmann

Inetitut A fur Physik, Technische Vnivevs-itat, Bvaunsahweig, Fed. Rep. Germany

Abstract.-Anisotropic dipolar and quadrupolar hyperfine interactions caused by first and second neighbor atoms are considered in a model description of Mossbauer spectra for fee and bee alloys.

Two examples are given. The temperature dependences for the quadrupole interaction in two diffe- rent Fe-Ni alloys are presented.

1. Introduction.- We consider Mossbauer spectra of polycrystalline y-Fe-Ni alloys. In the case of six well resolved lines the spectra show a remarkable special asymmetry. Numbering the lines from left to right, beginning with the largest value of negative velocity, the width G of corresponding lines are unequal IM : Gx > G6, G2 < G5 and G3 < C . This kind of asymmetry is found in the whole range of con- centrations of y-Fe-Ni alloys. It is also observed in the a-phase.

The observed behaviour of the line widths can- not be described by simply adding the magnetic con- tributions of first and successive neighbor atoms.

An attempt to explain the asymmetry by considering an isomer shift distribution which depends linearly on the number of neighbor atoms /2/, fails.

2. Description of model.- Following Window /l/, and Billard and Chamberod /3/ it is possible to explain the above spectra. It has to be realized that the siiriounding of an atom in a statistic alloy of cubic crystal structure is not necessarily cubic regarding the magnetic and electric interactions with its neighbor atoms /4/.

One has to distinguish between isotropic and anisotropic contributions /l,3,4,5/. Isotropic con- tributions are depending on the number of neighbor atoms of one kind only. Anisotropic contributions depend on the special configuration of the neighbor atoms. Their positons are described by an angle 0 between the direction from the Mossbauer atom to the neighbor atom and the direction of magnetization.

The anisotropic electric quadrupole and magnetic di- pole interactions are correlated with each other by the same dependence on 0, if small compared with the

mean isotropic magnetic hyperfine contribution.

There are two kinds of absorber configurations, where the angles 0 are definitely known and the ani-

sotropic contributions can be considered :

i) A polycristalline absorber with known easy direction of magnetization in the crystallites.

ii) A magnetically saturated single crystal absorber of known orientation with respect to an external magnetic field.

This work deals with polycrystalline samples, We use Fe as Mossbauer nucleus.

3. Mathematical formalism.- Considering both iso- tropic and anisotropic contributions of first and second neighbor atoms the description of the Moss- bauer spectrum f(v) reads :

The meanings of the symbols are :

p, m = numbers of the first or second neighbor atoms of one kind, respectively. U = underground counts, i denotes the Zeeman transitions, I. the probability of the ith transition. P(p) and P(m) are the bino- mial probabilities for p or m neighbor atoms in a statistical alloy. Q[§(p),p] and Q[s(m),mJ are gi- ven in table I and describe the probabilities for possible neighbor atom configurations with a struc- ture factor S(p) or S(m) /3,5/. v = relative velocity, JOURNAL

DE

Colloque C2, supplément au n° 3, Tome 40, mars 1979, page C2-161

Résumé.-Les interactions hyperfines anisotropes dipolaires et quadrupolaires dues aux atomes pre- miers et seconds voisins sont étudiés par un modèle de spectre Mossbauer d'alliages cfc et ccc. Deux exemples sont donnés. L'influence de la température sur l'interaction quadrupolaire est présentée par deux alliages Fe-Ni.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979257

C2- 162 JOURNAL DE PHYSIQUE

v. l,p,m,S(p) ,S(m) ⁼ Mzssbauer resonance velocities, From table I follows that for certain easy di- H = mean hyperfine field, hll, hIm = isotropic con- rections ED only first or only second neighbor atoms tributions to the hyperfine field, h

him

ZP'

sents the dipolar contributions and w

P' Wm are a 4. Experimental results.- As an example M6ssbauer measure for the quadrupole interactions. n = quantum spectra of two Fe-Ni alloys are shown in figure 1 .

number of the excited nuclear Zeeman level. Using equation (1) it is possible to fit the spectra

z-li 2

u . g

" s

09 9 m

cf R 0 cl li C P R

: 6 E i "

P P 3 0

a R rt cl

r m a (A

s-

O o-

R O F. O 0

2 E

m m

$ "

93 ,'

ID R t-t t-t P ' . F.

N O pl

"

R e

0 m 5 :

in excellent agreement to the theory. The parameters derived are given in the figure caption.

Fig. la. Spectrum of an fcc Fe-4lat.%Ni alloy and a fit to it using equation (1) and considering first neighbor contributions only. Temperature = 20.7 K.

ED =

Poo].

hip=-9.2

5. Temperature dependence of quadrupole interaction;

In the frame of the above model the strength of the quadrupole interaction w /3,5/ can be evaluated.

Measurements of the temperature dependence of w have been made for two different Fe-Ni alloys. The results are shown in figure 2. Both dependencies are stri- kingly different and demonstrate the behaviour of a normal alloy Fe-62 at.% Ni (alloy A) and of an invar alloy Fe-41 at.% Ni (alloy B).

Alloy A: Fe-62at% Ni

0 02 04 06 08 10 Eurie

M.!.

mms+l

Fig. 2 : The absolute value of the quadrupole in- teraction parameter w as a function of temperature for two fcc Fe-Ni alloys. Only first neighbor con- tributions are considered.

Fig. lb. Spectrum of an Fe-29.7at.ZNi alloy decompo- sed martensitically to a a(bcc) + ~(fcc) phase mix- ture. The fit relates only to the six line spectrum of the a-phase. Temperature=360 K. ED =

E O O ~ .

and second neighbor contributions are regarded. H =

331.3 kG, hlp=5.8 kG, hlm=7.9 kG, hZm=3.6 kG and O

w =-0.03 mm/s.

m

observed in metals and alloys can probably be des- cribed in the frame of the 'T law 161.

In the case of the invar alloy (alloy B) the parameter w is first nearly constant and than in- creases with rising temperature. For the explanation of the very different w course of the invar alloy two competing concepts can be regarded : One concept assumes the temperature dependence of the electric field gradient (EFG) to be caused by anharmonic lat- tice vibrations because in the invar concentration range anomalies in the temperature dependence of both thermal expansion /7/ and elastic constants /8/

are known.

The second concept follow an idea of Weiss /g/.

The iron atoms in the y-Fe-Ni alloys may exist in two electronically different states. Both states ha- ve different atomic volumes. In the case of the alloy A only the state with large volume is occupied. In the case of the alloy B the large volume belongs to the ground state and the one with small volume to the excited state. The transition from one state to the other should be of influence to the magnitude of the EFG and may be responsible for the observed be- haviour of w in figure 2b.

Acknowledgements.- We wish to thank Pr. Ch.Schwink for stimulations, interest and support. We are thank- ful to Pr. H.~riimer for his help and valuable com- ments. We acknowledge the financial support by the Deutsche ~orschungsgemeinschaft.

The parameter w of the alloy A decreases with increasing temperature. This behavior has been often

JOURNAL DE PHYSIQUE References

/ I / Window, B., J. Phys.

3

/ 2 / Drijver, J.W., Van der Woude, F., and Radelaar,

S., Phys. Rev. B E (1977) 985.

/3/ Billard, L . , and Chamberod, A., Solid State Commun.

fi

/ 4 / Cranshaw, T.E., J. Phys. (1972) 615.

/5/ Hesse, J . and Mcller, J.B. Solid State Commun.

22 (1977) 637.

-

/6/ Christiansen, J., Heubes, P., Keitel, R., Klinger, W., Loeffler, W., Sandner, W., and Witthiihn, W.

2. Physik B E (1976) 177.

/ 7 / Tanji, Y . , J. Phys. Soc. Japan

2

/8/ Hausch, G. and Warlimont, H., Acta Met.

2

(1973) 401.

/ 9 / Weiss, R.J., Proc. Phys. Soc.

82