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Temperature dependence of the ”Fe Mossbauer effect parameters for

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									J. Phys. F: Met. Phys. 14 (1984) 3083-3091. Printed in Great Britain




Temperature dependence of the ”Fe Mossbauer effect
parameters for amorphous Fel3MOTBzo

                 R A Dunlap and G Stroink
                 Department of Physics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 355


                 Received 25 April 1984, in final form 14 June 1984


                 Abstract. The magnetic properties of the amorphous ferromagnet Fe73M07Bzo         have been
                 studied from 4.2 K to room temperature using the Mossbauer effect. Fe hyperfine fields,
                 obtained from the Mossbauer measurements, show spin-wave-type behaviour and may be
                 described by the expression (ii(O)-ii(T))/ii(O)=BT”’+. . . up to temperatures of about
                 0.55Tc. For the low-temperature region the constant B is found to be 53 x        K-’”. The
                 hyperfine field distribution, P(H), was obtained from the Fe Mossbauer spectra and showed a
                 bimodal structure at 4.2 K. This two-peaked structure changed gradually to a single broad
                 peak with a low-field tail as the temperature increased. The relative intensity of the six
                 Mossbauer peaks given by 3: b : 1: 1:b: 3 yields a value of b- 2.2 at low temperatures. For
                 T b 180 K b changes to approximately 4.0, indicating that the magnetisation axis is in the
                 plane of the ribbons. The isomer shift of Fe7,Mo7Bz0 is constant at approximately
                 0.18 mm s - ’ relative to room-temperature a - F e for T < 100 K. At higher temperature the
                 isomer shift decreases linearly, as expected from the second-order Doppler shift. From
                 measurements of the isomer shift in Feao-,Mo,B20 alloys at 4.2 K we establish a correlation
                 between the isomer shift, 6 , and the Fe hyperfine field of the form 6=a+p(R-iio) with
                 /?=6.3 x lo-* mm s - ’ kOe-I.


1. Introduction

It is well known that the addition of group-VIB impurities to iron-metalloid amorphous
alloys causes rather drastic changes to the magnetic properties. These include (1) a large
decrease in the Curie temperature (see, e.g., Chien and Hasegawa 1978, Olivier et a1 1982),
(2) a large decrease in the average magnetic moment per transition-metal atom (e.g.,
Olivier et a1 1982, Dunlap and Stroink 1984a) and (3) a large decrease in the most
probable Fe hyperfine field (see, e.g., Chien and Chen 1979a, Sostarich et a1 1981). In
addition, some authors have reported that in many cases the inclusion of a group-VIB
impurity in amorphous Fe-based alloys results in a probability distribution for the
hyperfine field, P ( H ) , that is bimodal (see, e.g., Chien 1979, 1981, Whittle et a1 1982,
Dunlap 1984a, Rajaram et a1 1983). There has, however, been some controversy as to
whether the presence of a second peak in P ( H ) is real or merely an artefact of the fitting
procedure (see, e.g., Schaafsma 198 1, Keller 198 1).
     While many similarities seem to exist between alloys which contain Cr impurities and
those which contain MO impurities, it is not clear that the systems are entirely analogous.
For example, the ratio of the fields for the high-field and low-field peaks in P(H) for
Fe-Mo-B seems to be more or less independent of the impurity concentration (Dunlap
and Stroink 1984a). In similar alloys containing Cr, however, this does not seem to be the
case (Rajaram et a1 1983). While a detailed study of the temperature dependence of the

0305-4608/84/123083         + 09%02.25       @ 1984 The Institute of Physics                          3083
3084           R A Dunlap and G Stroink

Mossbauer effect parameters has been undertaken for an alloy containing Cr,
Fe32Ni36Cr14P12B6    (Chien 1979), the same is not the case for an alloy containing a
significant amount of MO.
    In this work we have performed 57FeMossbauer effect measurements as a function of
temperature on the amorphous ferromagnet Fe,, MO, Bzo. These are discussed in terms of
the Mossbauer effect parameters for other Fe-MO-B        alloys (Dunlap and Stroink
1984a, b).


2. Experimental methods

Fully amorphous ribbons of the composition Fe,, MO, B,, were prepared by rapid
quenching from the melt onto the surface of a single Cu roller (see, e.g., Dunlap 1982a, b).
The resulting ribbons were approximately 1 mm wide by 20pm thick. The amorphous
nature of the ribbons was confirmed by x-ray diffraction measurements (Cu Ka).
     A Mossbauer effect absorber was prepared from the as-quenched ribbons by laying
several pieces parallel to each other on a piece of tape. S7FeMossbauer effect spectra were
obtained with the absorber held at temperatures between 4.2 and 285 K using a
conventional constant-acceleration spectrometer and a room-temperature PdS7 source.CO
     Mossbauer effect spectra were analysed by expanding the hyperfine field distribution,
P(H), in a Fourier series and fitting to the Fourier coefficients as suggested by Window
(1971). The use of this procedure assumes the following. (1) The spectrum can be
described by a single value of the isomer shift, (2) there is no quadrupole splitting and (3) a
single, average value of the relative intensity of the second and fifth spectral lines, b, may
be used to describe the spectrum. While assumptions (1) and (2) may not, in general, be
strictly correct, Keller (198 1) has shown that Window's method can nonetheless be used to
describe P ( H ) accurately provided appropriate Mossbauer fitting parameters are used. The
parameters of importance are (1) the linewidth of the subspectra, r, (2) the number of
terms in the Fourier expansion, N , and (3) 6, given in terms of the intensity of the spectral
lines, in this work taken to be 3 :b: 1: 1:6 : 3.
     In this work we have taken r to be the intrinsic linewidth of "Fe, as suggested by
Keller ( 198 1)-0.12 mm s - ' (HWHM) for our source. Whittle et af (1 982) have pointed out
that small variations in the value of used for the fit do not affect the shape of the resulting
P ( H ) significantly.
     As suggested by Whittle et a1 (1982), we have taken the value of N to be that which
corresponds to the knee in the x2 against N curve. As we have reported previously (Dunlap
and Stroink 1984a), increasing N beyond this value does not alter the shape of P(H)
significantly but decreasing N may obscure some of the details of the shape of P(H). For
the fits reported in this work, typically 12 coefficients were found to be suitable to describe
P(H).
     The proper value of b was determined via a consideration of 2 for fits with different b.
While the value of b chosen for a particular fit does affect the shape of P(H), we have
observed that for the spectra reported here changing b by f0.4 or so from the value which
minimises x 2 does not alter the important features of the field distribution.


3. Results

',Fe Mossbauer effect spectra are shown for various temperatures in figure 1. The figure
Mossbauer parameters for amorphous Fe-MO-B                                             3085




              Velocity (mm s-’)                         H(k0el

                                                                              0
Figure I . Typical Mossbauer effect spectra and P ( H ) for F e 7 3 M ~ 7 B 2as a function of
temperature. Computer fits to the spectra are shown by the full curves.


                                                                       as
Table 1. Hyperfine field parameters obtained from P ( H ) for Fe73M07B20 a function of
temperature.

T(K)      R(k0e)     A H (kOe)

  4.2      233k5      l 8 8 + 10
 11.8      232        150
 20.0      231        150
 30.1      231        150
 45.0      229        150
 60.3      227        143
 80.7      223        146
115.0      217        162
151.1      210        153
180.7      203        155
228.5      183        171
256.9      161        174
285.4      124        174
3086          R A Dunlap and G Stroink




               Figure 2. Values of the parameter b, the relative intensity of the second and fifth Mossbauer
               lines, as a function of temperature.


also shows the resulting P(H) obtained by Window's Fourier expansion method. Table 1
gives values of the most probable hyperfine field, R, taken to be the peak in P(H), and A H ,
the full width at half maximum of the peak. Values of b which minimise x2 are shown as a
function of temperature in figure 2. The spectra all show a slight asymmetry. This is
common for "Fe Mossbauer effect spectra of amorphous alloys and probably results from
a distribution of isomer shifts in the sample (Chien 1978, Chien and Chen 1979b). Values
of the isomer shift relative to a-Fe at room temperature are shown as a function of
temperature in figure 3.




               Figure 3. The Mossbauer isomer shift as a function of temperature for Fe73M07Bzo.
                                                                                               Results
               are relative to a-Fe at room temperature.
                Mossbauer parametersf o r amorphous Fe-MO-B                             3087

4. Discussion

4 . 1 . Hyper-nejelds
The change of the most probable hyperfine field is given as a function of T3/* figure 4.
                                                                              in
Extrapolation of the measured hyperfine fields gives the Curie temperature, Tc Y 320 K.
The most probable hyperfine field at low temperatures in amorphous alloys is commonly
given in terms of the spin-wave model as (e.g., Chien 1978)
                (R(0)-R(T))/R(O)=BT312 . . .
                                    +,                                                    (1)
Figure 4 shows that the hyperfine field is described quite well by this model up to values of
(n(0)-  fi(T))/R(O) about 0.2, or approximately 0.55Tc. Thus the spin-wave expression
                    of
(1) is valid to much higher temperatures than in similar crystalline systems.
This is typical of the behaviour of Fe-based amorphous alloys (e.g., Chien 1978).
A fit to equation (1) for temperatures T < 180 K gives a value of the parameter
B = 53 x lo-, K-j12. This is shown in figure 5 in comparison with values of B for other
Fe-MO-B alloys reported by Chien and co-workers (Chien 1978, Chien and Hasegawa
1978). These results show an increase in B with MO concentration which is roughly linear.
Sostarich et a1 (1981) have reported anomalously high values for B for Fe-Mo-B alloys
with MO concentrations greater than about 3 at.%. This probably results from a lack of
sufficient data points at low temperatures.

4.2. Hyper-nejeld distribution
The hyperfine field distribution for Fe,, MO, B2,, at 4.2 K shown in figure 1 clearly shows
the presence of a low-field component. This low-field component, however, appears more
as a shoulder on the low-field side of the main peak. This field distribution is consistent
with that reported previously for this alloy by Dunlap and Stroink (1984a). Chien and
Chen (1979a) have also observed a similar P(H) at 4.2 K in Fe,,,5 MO,,, PI6B, Al, .




                                           TYK~Z)
                Figure 4. ( f i ( 0 ) -fi(T))/R(O) a function of T3’2for Fe,3Mo,B20.
                                                 as
3088           R A Dunlap and G Stroink




                   0   i
                       0        2
                                       Y
                                             4
                                           (at % MO)
                                                       6       8


               Figure 5. The parameter B from equation (1) as a function of x for Feso-,Mo,B20
               alloys. The data are taken from Chien (1978, 0),Chien and Hasegawa (1978, 0 ) and this
               work ( + ).


    The P ( H ) observed here supports the existence of a bimodal hyperfine field distribution
in this alloy, although the two peaks are not as distinct as those for many of the
Fe-metalloid glasses containing Cr, for example Fe32Ni36Cr14P12B6                  (Chien 1979),
Fe,, Ni34Cr loSnB20(Dunlap 1984a) and Fe38,5         Ni38.5 Mo2SiloB8 (Rajaram et a f 1983).
                                                          Cr3
It has been suggested recently that in these alloys containing Cr it is the presence of the Ni
along with the Cr that results in the markedly bimodal P(H) and that Fe-metalloid alloys
with Cr but without Ni show P ( H ) curves which are more similar to those in the
Fe-MO-metalloid alloys (Dunlap 1984a). Although it has been suggested (Chien 1979)
that the different peaks in P ( H ) correspond to inequivalent Fe sites in these alloys, it is not
clear how to correlate the shape of P ( H ) precisely to the distribution of microscopic Fe
environments (see, e.g., Dunlap 1984a, Dunlap and Stroink 1984a).
    The P ( H ) in figure 1 show that the low-field component becomes progressively less
distinct as the temperature increases and that for T 2 200 K the P(H) essentially show only
a single broadened peak with a low-field tail extending to H = O . This behaviour is in
                                                P
contrast to that observed in Fe32Ni36Cr14 I 2B6 (Chien 1979), where the bimodal nature
of P ( H ) exists essentially up to T, . Since the two peaks in P ( H ) are more clearly separated
in Fe32 Ni36Cr,, P I 2B6 than in Fe73M O 7 B20 at 4.2 K, it is not surprising that the two peaks
in the P ( H ) of Fe73MO, B20 become indistinguishable as the fields decrease with increasing
temperature. It is interesting to note from table 1 that, although fi changes considerably
between 4.2 and 285 K, the value of A H changes only a small amount. Although we
cannot define two distinct Fe sites at higher temperatures in Fe,3 MO, Bzo from the P(H),it
is obvious from the width of P ( H ) that there is still a much larger distribution of Fe
environments in this alloy than in FesoBZ0(e.g., Chien 1978).

4.3. Magnetisation axis
The value of the parameter b is given in terms of 0, the angle between the y-ray direction
and the direction of the magnetisation vector, as
               b = 4 sin2 e/( 1 + cos2 8).                                                        (2)
               Mossbauer parameters for amorphous Fe-Mo-B                                    3089




                             I      I      I            I   I   I
                      0            4                8           12
                                        x i a t % Ma)

               Figure 6 . The Mossbauer parameter b measured at 4.2 K for Feso-,Mo,B20 alloys (from
               Dunlap and Stroink 1984a).

The value of b ranges from zero (moments aligned parallel to the y-ray direction) to four
(moments aligned perpendicular to the y-ray direction). Since our fitting procedure fits to a
single value of b, this value reflects the average orientation of the moments.
    Figure 2 shows that the value of b is relatively constant at approximately 2.2 for
temperatures less than about 150 K. This is close to the value of b = 2.0 for the situation
where there is a random distribution of magnetisation axes. The parameter b has recently
been investigated in detail (Dunlap 1984b) for the amorphous alloy Fe,, B,, under various
conditions by rotating the sample relative to the y-ray direction. This study indicates that
the value of b z 2 observed at low temperatures in samples which are subject to stress from
being attached to tape indeed represents a random distribution of the magnetic moments.
Figure 6 shows that values of b close to 2.0 are also obtained at low temperature for Fe-B
containing up to a few per cent MO, and presumably this represents a similar arrangement
of magnetisation axes. Thus the values of b which minimise x2 at low temperatures in these
alloys are physically reasonable and provide some evidence that the value of b and the
shape of P ( H ) can be determined in a consistent manner. At higher temperatures the
reduction in anisotropy (Barton and Salamon 1982, Whittle and Stewart 1983, Campbell
et a1 1983) results in a magnetisation axis for Fe7,Mo,B2,, which is determined by the
demagnetising fields of the sample. This is seen in figure 2 where the value of b approaches
four. Figure 6 shows that this trend also occurs at low temperatures; this is because, as the
concentration of MO in the alloy increases, the domination of demagnetising effects as a
result of the reduction of anisotropy may be related to the softening of the magnetic
properties which results from the lowering of the magnetisation associated with either the
raising of the temperature (as in Fe,, MO, B,, , for example) or the increasing of the MO
content of the alloy (Dunlap and Stroink 1984a).

4.4. Isomer shifts
The isomer shift, 6, for Fe,, MO, as a function of temperature is shown in figure 3. We
                                   B2,
should point out that this is an average value of the isomer shift since there is, presumably,
a distribution of isomer shifts in the sample. The isomer shift remains constant at
approximately 0.18 mm s-' for temperatures less than about 100 K. For higher
3090           R A Dunlap and G Stroink

temperatures the isomer shift decreases approximately linearly with temperature. This is
expected on the basis of the second-order Doppler shift. The full line in figure 3 shows the
theoretical value of ad/aT=-7.3 x            mm s - l K-I. The data obtained here are in
reasonable agreement with the prediction.
      Isomer shifts obtained in this work for Fe-MO-B with 7 at.% MO may be compared
with isomer shifts of similar alloys. Figure 7 shows values of 6 for Feso-,Mo,B20
( O < x < 14) alloys at 4.2 K (Dunlap and Stroink 1984b). Values for small x are consistent
with those reported by Chien (1978) for Fe,, Bzo. The results in figure 7 show a roughly
linear decrease in 6 with increasing MO content. The most probable Fe hyperfine field in
these alloys has been reported to show a similar linear decrease with x (see, e.g., Dunlap
and Stroink 1984a). A correlation between H and 6 may be expressed in the form



as suggested by Chien and Chen (1979b). On the basis of the linear behaviour for
the isomer shifts shown in figure 7 and for the hyperfine fields as a function of x , it is
observed that terms to the order (A-H,) in equation (3) are sufficient to describe the
correlation between 6 and         in these alloys. From equation (3) we may write
p=a6/2H=(as/ax)(aA/ax>-'. A least-squares fit to 6(x) and fZ(x) yields a value of
p= +6.4 x         mm s-' kOe-'. It should be noted that the correlation observed here
between the hyperfine field and the isomer shift is a correlation between the most probable
hyperfine field and the mean isomer shift in a series of alloys of differing compositions. It is
not clear at present how this relates to the correlation between the hyperfine field
distribution and the isomer shift distribution in a single spectrum, as discussed by Chien
and Chen (1979b) and Eibschutz et a1 (1983). It is interesting, however, that the value ofp
obtained here is consistent with those reported by Chien and Chen (1979b) for spectra
which show asymmetries similar to those shown in figure 1. The positive value of /3 is
manifested by the fact that the Mossbauer lines on the right-hand (positive velocity) side of
the spectrum are less intense than those on the left-hand (negative velocity) side of the
spectrum. This seems to be the situation in other published spectra of Fe-based amorphous




                  o+,         ,       ,      ,        ,    ,       ,      ,j
                        0            4                 8          12
                                           x ( a t % Mol

               Figure 7. The Mossbauer isomer shift at 4.2 K for Feso-,Mo,Bzo alloys. Values are relative
               to a - F e at room temperature. Data are from Dunlap and Stroink (1984b).
               Mossbauer parametersfor amorphous Fe-MO-B                                   309 1

alloys with group-VIB impurities (see, e.g., Chien 1979, Rajaram et a1 1983, Chien and
Hasegawa 1978, Whittle et a1 1982). However, this is in contrast with the negative values
of p, and the corresponding opposite asymmetry of the spectra in CO-Fe amorphous
alloys (see Chien and Chen 1979b).


Acknowledgments

This work was supported by grants from the Natural Sciences and Engineering Research
Council of Canada and the Faculty of Graduate Studies, Dalhousie University.


References

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