EVALUATION OF COMPLEX MöSSBAUER SPECTRA IN AMORPHOUS AND CRYSTALLINE FERROMAGNETS
I. Vincze
Central Research Institute for Physics, Budapest (Received 1 October 1977 by A. Zawadowski)
A general method is worked out for an important simplifIcation of the complex Mossbauer spectra often obtained in ferromagnets. The evaluation of the hyperfme field distribution and the effects of isomer and quadrupole shift distributions will be discussed. Application will be shown for an amorphous Fe80 B20 (METGLAS 2605) and for a crystalline disordered (Fe0.65Co0. 35)B alloy.
IN DISORDERED SYSTEMS the strength of the hyper. correct only in the case of rather smooth and broad fine interactions changes from site to site due to the distributions but quite inaccurate if sharp peaks occur in the fluctuating environments. According to this in disorder- the distribution (i.e. discrete values of the hyperfine ed ferromagnets an unresolved Mössbauer spectrum field). A further serious problem arises from the ill- consisting of many overlapping lines is often found. In defined background: the resulting negative p(1i) values principle we can describe such systems by the distribu- cause a distortion of the determined p(H) (i.e. the real tion of the hyperfine fields, isomer shifts and quadrupole magnitude of p(ll) is unknown).
splittings. However, the evaluation of these distributions In real cases, generally, none of the assumptions from the measured spectra is a very difficult task which made under (a) and (b) are satisfied. For example, the is not solved yet. uncertainties in the intensity ratios of the single com- Usually in the calculation of the hyperfine field ponents due to texture in the sample affects strongly distribution p(ll) the basic assumptions are the following: the evaluation of Hesse and Rübartsch [5]. Also, no
(a) the effects of both the quadrupole and isomer attempt has been made according to our knowledge to shift distributions are negligible, separate the isomer shift and quadrupole splitting
(b) the intensity ratios and linewidths of the single distributions from the hyperfine field distribution.
components of the distribution are known. In the following we propose a general method for Even if these conditions are satisfied the evaluation of simplifying the complex Mossbauer spectra obtained in
ferromagnetic systems, then a modified version of p(H) is generally carried out in two fundamentally
method (i) which allows the determination of the hyper- different manner:
fme field distribution. The effects of the isomer and (i) by assuming a known shape for p(H) (e.g. simple quadrupole shift distributions will be discussed also.
Gaussian [1] ,modified Lorentzian [2] or split Room temperature measurements will be presented on Gaussian [3] distribution) where the parameters of an amorphous Fe80B20 (METGLAS 2605) and a crystal- these presupposed functions are determined by a least line (Fe0.65Co0.35)B alloy (this sample was measured
square procedure, or earlier in [6]).
(ii) by series expansion of p(H) using trigonometric It is well-known that in the case of a -~~Ml functions (Window [4]) or step-functions (Hesse and transition (Fe57 case) there are six lines in the Mossbauer Rubartsch [5]) as a basis. spectrum, the relative intensities of which are given as
The basic short-coming of the first method is rather ‘1.6 :12.5 :13.4 =~(l + cos2O) : 3 sin2 0 : ~(1+ cos20), clear: there are neither experimental nor theoretical where 0 is the angle between the direction of the y-rays arguments for the chosen form of p(R) and it is possible and the magnetic moments in the sample (see the insert to obtain a symmetric p(H) form even if the real distri. of Fig. 1). By using a small permanent magnet
(~
few bution is asymmetric. Thus the methods of Window [4] hundred gauss) the samples can be polarized almost of Hesse and Rubartsch [5] seems superior to these completely in the plane of the sample then we can turn methods since they do not require the assumption of any this plane with respect to the y-direction. This results in special p(H) shape. However, according to the detailed a significant change in the intensities of the second and investigations of Hesse and Rübartsch [5] they are fifth lines. Figures 1(a, b) show for an amorphous689
/ ...~
•.~....--...• . b)
- . : ~. C)
sample ~mognet •..•
:
~ dsource ________ •.
:
~
-L
-~ vetocity(mm/sec)Fig. 1. Room temperature Mössbauer spectra of amorphous Fe80B20(METGLAS 2605) alloy at 0 90°(a) and 0 30°(b). The insert shows the geometry of the measurements. The linear combinations of these spectra give the
1—3—4—6 lines (c) and the 2—5 lines (d) of the spectrum respectively.
a
b
- C
..‘... .. ..~•
d
-3 -2 —1 0 1 2 3
ve[c~ty[rnm/sec]
Fig. 2. Room temperature Mössbauer spectra of crystalline disordered (Feo65Co0.35)B alloy at 0 90°(a) and 0 30°(b). The linear combinations of these spectra give the 1—3-4—6 lines (c) and the 2—5 lines (d) of the spectrum respectively.
Fe~B20(METGLAS2605) the measured spectra for two ~
r~i~
different angles (0 90°and 30°,respectively). From I L a.
the linear combinations [7] of the two spectra we
obtain two sub-spectra which separately contain the — — — — 1-6
first, third fourth, sixth lines [Fig. 1(c)] and the ~1 2-5
second, fifth lines [Fig. 1(d)] respectively. 0.010 In principle other sets of lines may be separated for
other nuclear transitions, e.g. for Ni6’
(~
-~ ~ transition)a 4 and an 8 line-set could be separated from the 12-line 0.005 r ~I spectrum.
In this way we get rid of the problems connected
with overlapping lines, thickness and texture effects. r
Moreover, there is a very strong internal check from the 0 00 300 H~kOe~
two sub-spectra for the evaluation of the spectra since
the determined p(tf) distributions should be the same. p/HI rkOel-l None of the other earlier used evaluations had the 0.015
possibility of such control. b
A more complicated case is shown in Fig. 2 which - 2-5
shows the similarly decomposed sub-spectra for a crystal- noio -, ~ 12
line (Feo.65Coo.35 )B compound. r z .20
In the following we restrict ourselves mainly to the -
case of the amorphous Fe80B20 alloy. The inspection of the sub-spectra in Fig. 1 shows that the linewidths of the 0005
second and fifth lines are rather different [0.80(2) and 0.94(2) mm sec’, respectively],while those of the
first and sixth lines are about the same within the — r
0 100 300 H
expenmental error [1.55(4) and 1.52(4) mm sec
respectively].Since the distribution of the isomer shifts -l
(~)
affects the shape of the line-pairs in the same manner,~
iiI
Hf[kOeJthis difference in the shape of the lines is due to quad-
rupole interactions. As it is well-known, the ~.E quad- c.,
rupole interaction shifts the 1—6 lines by ~L~Eand the — 25 1=20
2—3—4—5— lines by — ~L~E(if i~.Eis much less than the ODlO aS ~
hyperfine interaction). Thus the observed asymmetry in r 1, AS 0
the shapes of the 1—6 and 2—5 line-pairs clearly contra-
clicts the very often used assumption [1—3,8] that the 0.005 1 quadrupole interaction in amorphous ferromagnets is
averaged out for each iron site due to its directional dependence and thus results only in a homogeneous
broadening rather than in a line shift. 0 100 300 H[kC~]
Also there is no sign of any zero hyperfine field
component (this can be best seen from the 2—5 sub- Fig. 3. Hyperfine field distributions for amorphous spectra), the existence of which is often deduced [1,9] Fe80B20 determined: (a) from the 2—5 lines (continuous from the fitted p(I-f) distribution in other amorphous line) and from the 1—6 lines (broken line), respectively.
alloys and used to explain the observed resistance Here z=20; (b) from the 2—5 lines for z 20 (continu- minima from 2—5 lines for zous line) and for z==12 (broken line), respectively; (c)20 with (broken line) and with-
To determine the hyperfine field distnbution p(H) out (continuous line) the use of the p(S) shift-function we use a modified version of the method (i) —namely defined in the text.
p(ll) is approximated by the superposition of binomial distributions. For the case of a single binomial distri-
bution this means that the relative amplitudes of the where the x parameter of the binomial distribution is elementary components are given by determined from a least-square fitting to the spectra, z
/ \ is an arbitrary positive number (the maximum number
Pbin(k) = xe(l _xy~e (k =0.1 z), of fields picked out of the distribution is z+ 1). The
1mm- 64 p(fI) distributions for z= 20 (continuous line) and for
pJS~
[si~J t
z= 12 (broken line) determined from the 2—5 lines.So far it was assumed that the effects of the isomer
15 --- - —6 and quadrupole shift distributions are negligible. How-
— 2~ ever, as we have seen, they have a rather strong
I influence on the line shapes. In the following the
10 - possible asymmetry of the lines in the sub-spectra is
I taken into account by an arbitrary p(5) shift-function, for which
5. I
S(k)=S0+kt~S,
— p(S) pbjn(k)//.~S between S(k— 1) and5(k),
0 0.1 0 -0.1 —0.2 S~~]
where z~S= 6 +~E for the 1—6 lines, and ~ = 6—
Fig. 4. The p(S) shift-functions for amorphous f~Efor the 2—5 lines (and 3—4 lines), respectively Fe80B20 (z =20) determined from the 2—5 lines (con- (here 6 is the isomer shift). So the ~S are fitted to the tinuous line) and from the 1—6 lines (broken line),
respectively, spectra. This approach corresponds to an assumption of
a linear relation betweenHand S where the coefficients of the linear relation are determined from the least- hyperfine field values belonging to the distribution are square fit of the spectra. Only the width of p(S) is
given by characteristic of the shift distribution since the func-
H(k) = H0 + k~H tional form ofp(S) is rather arbitrary.
The measured spectra are well discnbed by the whereH0 and~H are determined from the least-square curves calculated with the help of the shift-function fitting of the spectra. The value of p(R) between [there is a 20—30% decrease in the value of
x2
asH(k— 1) andH(k) is obviously given by pbjfl(k)/L~H. compared to the case =0 (fixed)]. Figure 3(c) The f”p(ff) dH= 1 condition is automatically satisfied shows that the assumption of p(S) does not influence in our case: i.e. with this method we can compare p(If) the p(H) distribution;h~rethe broken line is re- distributions determined from different spectra. calculated p(H) for z= 20. Figure 4 shows the p(S)
Figure 3(a) shows the p(Ii) distributions for shift-functions calculated for the 1—6 and 2—5 lines, amorphous Fe80B20 determined in this manner from the respectively. The earlier mentioned asymmetry is 2—5 lines (continuous line) and from the 1—6 lines clearly reflected in the values of p(S).
(broken line), respectively. The two p(11) distributions Of course, for the description of the spectra we may are the same within the experimental error. Here z=20 use a superposition of several binomial distributions.
was used, generally the form of p(ll) is not influenced In this case the connection between theHandSvalues above a critical z value (z~~ 6). Figure 3(b) shows the will be less defined and more complicated. However,
p/H/LkOe]1 p
0.015 60 — — — 1—6
0.010
~JT’11~
40 ~ —2—50~05 r1~
[1
20I r’ - IS~~
100 200 HLkOeJ 0.1 0 —0.1
sf~]
a b
Fig. 5. Hyperfme field distributions (a) and p(S) shift-functions (b) for the crystalline disordered (Feo.6sCoo.~)B alloy determined from the 2—5 lines (continuous line) and from the 1—6 lines (brokenline),respectively.
already the fit of two binomial distributions does not and quadrupole shifts. This agrees well with the results improve the description of the spectra
(x2
remains the obtained [6] from the concentration dependence of same within the error ofx2).
these parameters and suggests a rather localizedThe similarly evaluated distributions for the behaviour.
crystalline disordered (Fe0.65Co035)B alloy are shown in Fig. 5. These differ from those found for the
amorphous Fe~B20alloy in the very sharp p(S) func- Acknowledgement— It is a pleasure to thank tions, which correspond to discrete values of the isomer Dr. D.L. Nagy for valuable discussions.
REFERENCES
1. SHARON T.E. & TSUEI C.C., Solid State Commun. 9, 1923 (1971).
2. SHARON T.E. & TSUEI C.C.,Phys. Rev. B5, 1047 (1972).
3. LOGAN J. & SUN E.,J. Non-cryst. Solids 20,285 (1976).
4. WINDOW B.,J. Phys. E: Sc Instrum. 4,401(1971).
5. HESSE J. & RUBARTSCH A.,J. Phys. E: Sci.Instrum. 7, 526 (1974).
6. TAKACS L., CADEVILLE M.C. & VINCZE I., J. Phys. F.- Metal Phys. 5, 800 (1975).
7. I am grateful to TAKACS L. for this computer program.
8. MARCI-L&L G., MANGIN P., PIECUCH M. & JANOT C.,J. de Phys. 37, C6-763 (1976).
9. TSUEI C.C. & LITLIENTHAL H.,Phys. Rev. B13, 4899 (1976).
