DETERMINATION OF LONG RANGE ORDER IN Ni3Fe USING THE MOSSBAUER EFFECT TECHNIQUE

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DETERMINATION OF LONG RANGE ORDER IN Ni3Fe USING THE MOSSBAUER EFFECT

TECHNIQUE

J. Drijver, K. de Groot, F. van der Woude

To cite this version:

J. Drijver, K. de Groot, F. van der Woude. DETERMINATION OF LONG RANGE ORDER IN

Ni3Fe USING THE MOSSBAUER EFFECT TECHNIQUE. Journal de Physique Colloques, 1974, 35

(C6), pp.C6-465-C6-468. �10.1051/jphyscol:1974696�. �jpa-00215853�

JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 12, Tome 35, DCcembre 1974, page C6-465

DETERMINATION OF LONG RANGE ORDER IN Ni3Fe USING THE MOSSBAUER EFFECT TECHNIQUE

J. W. DRIJVER, K. DE GROOT and F. VAN DER WOUDE Solid State Physics Laboratory, Materials Science Center

University of Groningen, Groningen, The Netherlands

RbumB. - Nous avons determine le parambtre d'ordre a grande distance S par des spectres Mossbauer dans une serie des feuilles Ni3Fe avec un ordre 2 i grande distance ascendant. Notre analyse fait une part essentielle de la forme des raies extrsmes ensemble avec la supposition que le champ hyperfin H A un noyau de fer particulier est relit5 lineairement avec les nombres des atomes de fer dans la premikre et deuxikme couche voisine, n

et nz :

Comme la probabilitk pour l'occurrence d'une combinaison particulikre (nl, nz) depend de S, il reste a determiner quatre parambtres pour chaque spectre : S, H(0,6), AH1, AHz. Un ensemble consistant de ces parambtres Btait obtenu pour tous les spectres, avec S s'etendant entre 0,65 et 0,90, H(0,6) = 276,6 kOe, AH1 = + 11,l kOe/at Fe et AH2

+ ^2,7 kOe/at Fe.

Abstract. - We have determined the long range order parameter S from Mossbauer spectra in a series of Ni3Fe foils with increasing long range order. The shape of the outer lines plays an essential role in our analysis together with the assumption that the hypefine field H at a particular iron nucleus is linearly related to the numbers of iron atoms in the first and second neighbouring shell, n

and nz :

Because the probability for the occurrence of a particular combination (n

n2) depends on S, four parameters remain to be determined for each spectrum : S, H(0,6), AH1, AHz. A consistent set of these parameters was obtained for all spectra, with Sranging from 0.65 till 0.90, H(0,6)

276.6 kOe, AH1

+ ^{1 1 . 1} kOe/Fe at and AH2

+ 2.7 kOe/Fe at.

1. Introduction and experimental procedure. - I t is well known that the magnetic hyperfine fields at nickel and iron nuclei in Ni3Fe below the Curie temperature of 871 K always show a distribution around a mean value depending on the degree of order [I] [2]. Indi- rectly, e. g. from resistivity or magnetisation data [3], it is concluded that the alloy orders very slowly below about 770 K, so that the cause for this distribution has to be found in incomplete ordering, leading to different surroundings of the atoms. The long range order parameter S is usually determined from X-ray or neutron diffraction experiments. The intensity ratio of the superstructure and fundamental reflections is proportional to ( fA - f,). S2, where fA and f, are the atomic (X-ray) or nuclear (neutron diffraction) scat- tering factors for the two kinds of atoms. Unfortuna- tely are in both cases for nickel and iron these fac- tors nearly the same, leaving only a very low inten- sity for the superstructure lines. For X-ray diffraction only recently accurate measurements have been reported [4] [ 5 ] , for neutron diffraction this problem has been overcome by the use of special isotopes 161.

As part of our research program on the influence of atomic order on the magnetic properties of Ni3Fe - carried out with the Mossbauer effect technique -

we had to determine the degree of order in our alloys.

In this paper we describe how S can be derived from the above mentioned distribution of hyperfine fields, using the 57Fe Mossbauer transition. In a forthcoming paper the results for the kinetics of the ordering process will be discussed. In the case of Ni,Fe, which has the Cu3Au structure, the long range order para- meter is defined as 4/3(p - 114). Here p is the proba- bility for finding an Fe atom at a right site, that is a site that certainly should be occupied by Fe in the fully ordered lattice. When besides the long range order no further short range order is present, then from p the binomial distributions appropriate to the configura- tions around Fe atoms at the right and at the wrong sites will follow. It may be mentioned here that in the papers of Heilmann and Zinn [I] and of Burch et al. [2] the contribution of the atoms at the wrong sites is not taken into account. We measured at room temperature the absorption spectra of a series of

31

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974696

C6-466 J. W. DRIJVER, K. D E GROOT AND F. VAN DER WOUDE

Single line$ts. Annealing treatment (a + sign means the preceding time has to be added), isomer shift (IS, mean value of 4 outer lines), width of outer lines (T), hyperfine field (Hht) and calculated S

Foil nr.

-

1 2 3 4 5 6 7 8 9 10

Annealing treatment time (h) temp (OC)

- - as rolled

16 490

38.5 490

83.5 490

153 490

266 490

+ 118 429

214 429

+ 137 361

303 361

stoichiometric Ni3Fe foils which had obtained an for the most ordered foils and now we found for all increasing long range order by varying heat treatments spectra well defined minima in the x2 - S curves.

in vacuum (see Table I).

2. Results and discussion. - The effect of the anneal- The outer lines of these spectra were fitted to a set

ing procedure is shown in Table I as changes in the of Lorentzians with the following assumptions :

parameters of the Mossbauer spectra of which two 1) Ni and Fe atoms are distributed over the two are shown in figure I. We see that the isomer shift (IS) lattice sites in accordance with the proper binomial

distributions.

2) The effective hyperfine field is determined by the local environment of the Fe atoms and only the first and second neighbouring shell play a substantial role.

3) The field is linearly dependent on the number of Fe neighbours :

H = H(O,6) + nl AH, ^f (n, - 6 ) AH, Here H(O, 6 ) is the field in the fully ordered alloy with 0 Fe atoms in the first and 6 Fe atoms in the second shell, n , and n2 are the numbers of Fe atoms in the first and second shell, respectively.

4) The isomer shift is proportional to n,.

5) No dipolar or quadrupolar broadening is present.

First a least squares analysis was performed to all spectra from the ordered foils (nrs. 2-10 in Table I ) with ten chosen values for S ranging from 0.60 up to 1.00. This last analysis is essentially a single line fit giving mean values for isomer shift, linewidth and hyperfine field. For the most ordered foils (nrs. 7-10) a pronounced dip in the x2 - S curve was found for S between 0.88 and 0.91. The fits had here all nearly the same values for H(O,6), AH, and AH,. For the less ordered alloys each S in the region 0.60-0.80 gave a low x2 with varying values for the parameters of the fit. Since the completely disordered alloy could be fitted with S = 0 and nearly the same other para- meters as the most ordered ones, we concluded that certainly H(0, 6 ) would be the same for all the alloys.

So we performed a second analysis to all spectra keeping H(O,6) fixed at the mean value found earlier

Velocity Irnm/s) -

FIG. 1. - RT spectra of Ni3Fe foils nrs. 2 and 9. The drawn lines are computed fits using S

0.65 and S

0.91 respectively.

- calculated for a Ni3Fe source relative to a metal- lic iron absorber - stays close to the value of

- 0.02 mm/s found for Fe in nickel metal. The

width f of the outer lines does not reach the experi-

mental linewidth of 0.29 mmls. This means that in

the best ordered alloys still a spread of 1 5 kOe in

the hyperfine field is left. The mean field itself shifts

on ordering closer to 266 kOe, the value found for Fe

in nickel. When we consider the structure of Ni3Fe

these similarities are not surprising. Disregarding the

two kinds of atoms, Ni3Fe has the same fcc lattice

as metallic nickel ; upon ordering the Fe atoms move

to the corners and the Ni atoms to the faces of the

DETERMINATION OF LONG RANGE ORDER IN NisFe USING THE MOSSBAUER EFFECT TECHNIQUE C6-467

cubic unit cell. In this way an iron atom is surrounded by 12 nickel atoms, as in nickel metal, and in the next nearest neighbour shell by 6 iron atoms. In more distant shells (see Table 11) we find alternatingly only nickel or only iron atoms, while the difference in the successive shell radii decreases as the shell number increases. This is the basis for our assumption in the analysis of the spectra, that the local environment determines the hyperfine field and more distant shells give only a mean contribution not sensitive to ordering in the Ni,Fe superstructure.

Environment of an Fe atom in ordered Ni,Fe

Shell Occupation Rel. distance

- - -

1 12 Ni

2 6 Fe J'i

3 24 Ni 42

4 12 Fe J3

5 24 Ni 44

J5

In Table I11 are given the parameters of the mul- tiline fits with the lowest xZ. IS(0) is the isomer shift for an Fe with no Fe nearest neighbours, AIS is the increase in IS per Fe nearest neighbour, AH, is the increase in H per Fe atom in the first shell, AH, the same for the second shell, r is the linewidth of the individual components. H(0,6) was kept fixed at 276.6 kOe, the average value (error 0.2 kOe) found earlier for the four most ordered foils. Because we could only fit our spectra to discrete values of S , some results are small interpolations. This, however, caused no problem because the parameters for one spectrum changed smoothly with varying S . With this procedure

the estimated error in S is 0.02 for foils nrs. 2-5 and 0.01 for foils nrs. 6-10. The parameters in Tables I and I11 form a consistent set, a first condition to be fulfilled in such an analysis. Further the linewidths of the individual components are near the experimental minimum of 0.29 mm/s and finally the relative values of AH, and AH, confirm our assumption that the hyperfine field is determined only by the irnme- diate surrounding. The near constancy of AH, for S ranging from 0.90 (Fi,, the average number of Fe n. n. = 0.58) till 0.65 (ii, = 1.70) shows that H a n d n , are certainly linearly related to each other from n , = 0 till n , = 3. We like to add one comment to the results given for foil 1, because it was possible to get a lower value for x2 than stated in Table I11 with the same S = 0. We found x2 = 1.53 for

H(0, 6) ⁼ 246.8 kOe, AH, ⁼ + 12.8 kOe/Fe at, AH, ⁼ - 6.4 kOe/Fe at and I' = 0.26 mm/s. In our experience these parameters, especially the negative value of AH,, indicate that our choice of S = 0 for foil 1 has been too low and thus that some short range order remains in this foil.

The presence of dipolar or quadrupolar broadening was tested for several spectra by allowing two line- widths. One linewidth parameter was assumed for lines which obviously can not be broadened. This is the case when the Fe atom under consideration has a cubic symmetric environment (for instance in a fully ordered part of the lattice), or when the angle 8 between the direction of the hyperfine field ( [ I l l ] in ordered Ni,Fe) and the dipole axis or the main axis of the electric field gradient is such that cos2 8 = 113, resulting in zero lineshift. For instance, this is the case for an Fe atom at a Ni site in the otherwise ordered lattice. The second linewidth was given to the lines representing all the other iron positions. However, in all cases a slightly narrower instead of a broader line was found for the last category relative to the first. Therefore we

Multiline fits with corresponding S . Symbols are explained in the text.

The expectation value of x2 is 0.67, the number of counts is about 1.5 x lo6 per channel Foil nr. IS(0)

- ^(mmls) -

1 - 0.04

2 - 0.02

3 - 0.02

4 - 0.01

5 - 0.01

6 - 0.00

7 - 0.00

8 + 0.01

9 + 0.00

10 + 0.00

mean values for foils 2-10

AIS (mmls)

+ - 0.01

+ 0.01

+ 0.00

+ 0.00

$ 0.01

+ 0.01

+ 0.02

+ ^0.01

+ ^0.01

+ ^0.01

+ 0.008

(+ 0.002)

C6-468 J. W. DRIJVER, K. D E GROOT AND F. VAN DER WOUDE used further only one linewidth as listed in Table 111.

Concerning the quadrupole interaction no conside- rable broadening can be expected as concluded from our experience with iron doped Ni3Al [7]. For Fe at a Ni site in paramagnetic Ni3Al - which has the same structure and the same lattice parameter as Ni3Fe - the quadrupole splitting amounts 0.39 mm/s. Since this splitting is caused by 4 A1 nearest neighbours, we can estimate the splitting for I A1 neighbour to be of the order of 0.1 mm/s. This value can be regarded as an upper limit for the broadening in Ni3Fe for the following reasons. First when the efg is caused by ionic charges, the smaller electronegativity difference between Ni and Fe ensures a smaller charge difference between the two kinds of atoms. Second a size diffe- rence of surrounding atoms distorts the Fe wave functions asymmetrically and causes in this way an efg at the Fe nucleus. Then the quadrupole shifts caused by an Fe or an A1 neighbour will be about equal to each other, as the lattice parameters of Ni3Fe and

Ni3A1 are very nearly the same. Finally notice that for the configuration that could give a large shift - an Fe atom on a Ni site which has four Fe nearest neigh- bours - cos2 0 = 113, so the shift is zero.

In conclusion : We have shown that the line shape of Mossbauer spectra can successfully be used for determining the long range order in Ni3Fe. Only contributions of the first two neighbouring shells can be distinguished and the magnetic hyperfine field at a particular iron nucleus shows a linear relation with the numbers of iron atoms in these two shells. Further no evidence for dipolar or quadrupolar broadening has been found.

This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research on Matter -

FOM) and was made possible by financial support from the Nederlandse Organisatie voor Zuiver Weten- schappelijk Onderzoek (Netherlands Organization for the Advancement of Pure Research - ZWO).

References

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Lett. 22 (1969) 846. [6] GOMAN'KOV, V. I., PUZEY, I. M. and LOSHMANOV, A. A., [3] WAKELIN, R. J. and YATES, E. L., Proc. Phys. Soc. B 66

(1953) 221. Phys. Met. Metallogr. 22 (1966) 134.

[4] WILSON, W. L. and GOULD, R. W., J. Appl. Cryst. 5 (1972) [71 DRIJVER,

W. and

WOUDE, F.,

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125. L 206.