PHYSICAL HE VIE% 8
VOLUME
X-ray spectroscopic
of
Physics,
NUMBEH
1
study of Mg-Mn ferritcs
B. D. Padaha*
Department
12,
and V. Krishnan
Indian Institute of Technology,
(Received 15 July 1974)
Bombay-40076,
India
X-ray extended fine structures (XEFS) of the K-absorption edges of manganese and iron in ferrites of
composition Mg, „Mn„Fe,04 (x = 0, 0.25, 0.50, 0.75, and 1.00) have been investigated. XEFS features
have been examined in the light of neutron-diffraction
data on the same ferrite samples. It is noted
that fine structures within an energy range of nearly 100 eV from the main edge are characteristic of
the cations present at the tetrahedral and octahedral sites in ferrites. Metal-oxygen distances are
determined
using x-ray fine-structure methods. The results of the present study lead us to believe that
x-ray fine-structure methods could be utilized to complement diffraction methods for the determination
of the bond lengths in samples containing atoms of nearly the same electronic structure.
I.
INTRODUCTION
IV. DISCUSSION
A. Gross characteristics of XEFS
X-ray spectroscopy provides an interesting
method for the determination of valence states of
eations in ferrites. ' X-ray fine-structure methods
have been used to estimate the bond lengths in
The results of our present investicompounds.
gation of the x-ray extended fine structures (XEFS)
associated with the K-absorption discontinuities of
manganese and iron in ferrites of composition
Mg, „Mn„Fe,O, (x =0, 0.25, 0. 50, 0.75 and 1.00)
are reported in this paper.
'3
II. EXPERIMENTAL
Ferrite samples were prepared using the standard ceramic techniques' and they were sintered
in air at 1250'C for 9 h and then annealed. The
complete formation of single-phase compounds
was checked by x-ray powder-diffraction method. '
XEFS were recorded on the x-ray films and the
measurements were made on the microphotometer
tracings with 100X magnification. The apparatus
and the experimental procedure were the same as
described elsewhere.
"
III. RESULTS
Mierophotometer tracings of the XEFS of K-absorption edges of manganese and iron in MnFe, O,
are shown in the same figure (Fig. 1), for the
purpose of comparison of their gross features.
The XEFS for manganese and iron in the other
ferrite samples are, however, shown separately
in Figs. 2 and 3, respectively.
Energies of XEFS
maxima and minima measured from the respective
main absorption-edge positions are given in Tables
I and II and the estimated bond lengths are listed in
the Tables III and IV.
Even a cursory look at the curves for MnFe, O,
Fig. 1 indicates that the gross features
of XEFS of the K-absorption edges of manganese
(curve 1) and iron (curve 2) a.re quite different.
within an energy range of nearly 100 eV from the
main absorption edges, the maxima and minima in
XEFS for manganese are of much lower amplitudes
and they appear closer to the K edge as compared
with those recorded for iron. Appearance gf a
broad and prominent peak designated as + in the
fine structure of iron (curve 2) is another distinguishing characteristic feature of the spectra
(Fig. 1). XEFS for manganese (Fig. 2) and for
iron (Fig. 3) in the other ferrite samples, respectively, resemble closely curves 1 and 2 of
Fig. 1. A perusal of the neutron-diffraction data
on cation distribution in these ferrites" reveals
the preference of Mn" and Fe" in MnFe, O, for
the tetrahedral (or A) and octahedral (or B) sites,
respectively. In other ferrite samples also there
is preponderance of Fe" at A sites and of Mn" at
B sites (except for x =0. 75). This implies that the
XEFS of curves 1 and 2 in Fig. 1 are the eharaeteristies of the absorbing ions present-at the A and
B sites, respectively. These features of the XEFS
are, however, diluted due to the presence of ions
other than the absorbing ion at the A and B sites.
The results of this study suggest that the XEFS
could be used to estimate the prevalence of the
absorbing ions at the A and B sites in spinel strucshown in
tures.
The observed dissimilarity in the XEFS of iron
in MnFe, O, (Fig. 1) and in other
ferrites (Figs. 2 and 3) is not a surprising result.
This observation is, in fact, consistent with an
earlier report on perovskite structures' and it
establishes the inability of long-range-order (LRO)
and manganese
PADALIAA AND V. KRISHNAN
K-e
CL
C)
ENERGY
50
150
100
ENERGY
FIG. 1. Microphotometer
-a so
cur 1) and iron
ganese (curve
soprtion edges of manganese
FIG.
G. 3,
3 Mxcrophotometer
e r tracin
racings of the XEFS for
z es o composition Mg 25 M llo 7)Fe204
1
n egO4.
O
(--4
t
"
(curve 2) M go VgMno 25Fe2O
The energy col re~
, ,
'
e -edgee position
of iron me
metal has been
oo
e energy scale.
no 5Fe204
K-ed
theories to account for the XEFS in anothe
no
un s.
is, however, interestining too note
FS are de p endent on the
e
samples.
f
e ers in ferrite
lattice paramete
B. Determination of bond
lengths
t 1963 have been
rior to
XEFS theories proposed prior
e y zKroff. ' Later, I evy' modified
Kozlenkov's theor y t o obtain a simple relation for
the estimation
I
0
100
50
of bond len
eng th s in compounds.
o too d etermine the
Ly tie'
e proposed another method
'
'
and this was suberatomic distances in metalss an
interatom
eratom
al .'o The
Th more
n y modified by Chivate et a
'
of
th
point-scatte
ering
eory
elegant
recent and
'
aayer et al. , which is capaablee of accounting for
has probably no significant effect on the
s.' In this work the
ddetermination of bond len
eng ths.
me o s of Lytle, Le vy, and Chivate et a/. have
metal-o
l-oxygen dsseen employed to estimate thee me
'
th ferrite samples. Thee d e ta, ils regardtances in the
'
for calculatining thee b ond lengths
r
in g thee procedures
cusse in our earlier reports.
'
nd aron ions exist both at th A
The manganese and
i the ferrite samples ' Each metal
and B sites in
"
er,
e,
1S0
ENERGY
tometer tracings of the XEFS for
FIG. 2. Micro p hotom
manganese in ferrites of compositon M go 75Mno 25Fe204
(curve 2), and Mg Mn
F
Mnno 75Fe204
(curve 1), Mg
.
nergy corresponding to the X-edge
e
i ~on o manganese metal has been taken ass th e zero
o the energy scale.
"
X-RAY SPECTROSCOPIC STUDY OF Mg-Mn FERRITES
12
TABLE I. Energy values (in eV) of XEFS of manganese K-absorption edge in ferrites measured from the
respective K-edge position. The estimated error in the
measurement of energy is +0.5 eV.
TABLE lI. Energy values (in eV) of XEFS of iron Kabsorption edge in ferrites ~ measured from the respective K-edge position. The estimated error in the measurement of energy is +0.5 eV.
Fine-
Fine-
structure
peaks
structure
peaks
x =1,0
8.0
A
x = 0.75
x =0.5
9.3
x =0.25
11.5
Q
A'
B
pt
B'
p
C
7
D
min
max
Inln
max
Inln
max
min
max
Inln
IIlax
IIlln
16.7
23.4
26.3
32.4
36.8
41.7
49.9
57.6
84.3
91.0
20.6
25.9
36.4
Pl
Mg&
32.2
35.0
64.2
73.4
43.4
47.4
51.5
56.5
81.4
82.4
86.6
85.2
91.9
124.4
129.0
134.9
139.5
90.7
95.3
97.0
105.9
109.7
7.7
18.4
21.3
41.9
39.0
B
B'
113.7
117.3
Of composition,
26.3
22.4
29.3
94.3
141.4
146.4
171.4
183.3
198.0
7.7
21.2
19.3
25.9
29.9
60.0
62.6
82.0
92.3
x=1.0 x=0.75 x=0.5 x=0.25
8.7
14.7
16.9
p
C
53.1
57.9
63.3
79.0
81.9
95.2
98.2
109.0
58.7
60.3
62.5
67.0
71.5
D
82.4
87.3
max
93.8
min
105.8
127.8
138.9
111.5
171.2
161.8
166.8
max
min
120.4
135.8
186.4
131.0
138.3
445
6.3
32.0
43.2
47.1
55.4
61.2
73.4
98.8
111,2
127.7
134.7
7.8
34.3
38.0
40.6
53.2
76.2
85.0
91.5
95.4
116.6
131.0
155.1
159.6
x=0
9.1
20. 7
23.1
38.6
45.9
50.3
54.2
59.5
63.9
86.0
99.8
114.6
123.6
142.5
147.0
152.0
160.6
127.0
139.7
143.1
154.3
172.3
181.4
198.0
143.0
143.7
170.5
„Mn„Fe204.
ion at the A and B sites is surrounded by four and
six oxygen atoms, respectively. The A-0 and
~" -=-'3 distances are calculated
using a value of the
oxygen parameter reported elsewhere. ' It may be
noted that the Mn-0 and Fe-0 bond lengths estimated from the XEFS methods correspond to the
average values of A-0 and B-0 distances listed
under crystallographic data in Tables III and IV.
A scrutiny of the data given in Tables III and IV
reveals that the bond lengths obtained from the
modified Lytle's method (Chivate et al.
are
close to the crystallographic data. The results
of our broad program of work on spinel structures
containing atoms of nearly the same electronic
structure lead us to believe that x-ray fine-structure methods could be used to complement diffraction methods for the determination of bond lengths.
However, it is important to note possible errors
inherent in the calculation. Kozlenkov, who attributed the XEFS to a variation in transition
probability, used a simple square-mell potential
to develop an expression for the absorption cross
section. This expression was subsequently simplified by Levy to calculate the distance r, of the
")
Of composition
Mg&
„Mn„Fe204.
center of the absorbing atom from its first coordination sphere of ligands using the known values
of prominent fine-structure maxima and minima.
The computed value of r, approximates the average
bond length.
An alternate method proposed by I ytle, which
bears certain similarity in its formalism to the
LRO theory developed by Hayasi (see Aziroff') estimates the radius r, of the spherical signer-Seitz
unit cell constructed around the absorbing atom assuming an infinite potential outside the sphere. r, is
determined from the slope of the (E, Q) curve
where E and Q represent, respectively, the energies of the fine-structure maxima and the zero
' Bessel functions which appear
roots of the order- —,
in the radial part of the solution of Schrodinger
equation. Since there is a limited number of values of Q for P-type symmetry, all the fine-structure maxima observed in our spectra could not be
utilized to obtain the required (E, Q) curve. This
constitutes a limitation of the method noted by
other investigators.
A modified form of Lytle's theory (Chivate
et at. assumes a finite potential outside the
VA'gner-Seitz sphere, rather than an infinite potential, but also suffers from the above limitation. A more recent theory given by Sayer et al.
assumes a muffin-tin potential for each atom and
considers the phase shift of the spherical wave
functions due to the scattering in the presence of
"
")
"
D. PADALIA AND V. KRISHNAN
TABLE III. Comparison of Mn-0 bond lengths in ferrites estimated using the x-ray finestructure methods vrith those obtained from the crystallographic data.
Mn-0 distances (in A)
x-ray fine-structure methods
Cystallographic
Chivate
Lytle
Levy
MnF e204
3.36
Mgp. 25Mnp. 75Fe204
2.65
Mgp 5Mnp
B-0"
A-0
1.99
1.96
1.95
2.09
)Fe204
3.18
Mgp 7)Mnp 25Fe204
6t Ql,
2.29
2. 11
2.50
2.09
data
Distance of oxygen from cations in A site.
"Distance of oxygen from cations in & site.
the absorbing atom. %'ith their calculation,
Sayer
et al. observe that as the effects of second and
additional neighbors are included, more and more
fine structure becomes evident. This result suggests that the secondary structures, w'hich remain
unaccounted for in the computation of bond lengths,
in the present work arise fram interaction of the
ejected electron with neighboring atoms other than
the first.
The methods of Lytle, Chivate et al„, and Levy
which consider only the effects of the first neighbors give approximate values of interatomic distances. It may be noted that the similarity in the
data of dilute solutions and solids indicates that
the nearest neighbors have the mast important
effect on the spectral features. "' Thus it appears that secand and other distant neighbors
probably have no significant effect on the determination of bond lengths. However, this point re-
"
quires further careful investigation.
It is difficult to state an accurate likely error in
the bond lengths calculated in the present work due
to the simplifying assumptions introduced in the
formalism and to experimental uncertainties in
the arrangement used. However, we estimate that
in the measurement of energies the error does not
exceed 0. 5 eV. It is noted that the difference between the bond lengths computed by the method of
Chivate et al. and those obtained from crystallographic data. is less than l(P/q. Accurate values of
bond lengths could be determined using the recent
method of Sayer et al. but it would require an accurate knowledge of phase shifts. An exact solution of this problem could be achieved with improved experimentation using, for example, syn-
chrotron radiation" as a source.
ACKNOW'LED GMENTS
(B.D. P. ) feels grateful to D:.
for arranging a visiting Senior Research Fellowship of the SRC, UK, to work at the
One of the authors
D.
J. Fabian
TABLE IV. Comparison of Fe-0 bond length in ferrites calculated using the x-ray finestructure methods vrith those obtained from the crystallographic data.
Fe-0 distance
x-ray fine-structure
Samples
Levy
2.25
MnFe204
5Fe)04
Mgp p5MnpggFe)04
MgFe204
' Distance
b
2.07
data
Crystallographic
A-0
a
Ob
2.05
1.99
2.04
1.95
1.88
p5F e204
Mgpg5Mnp
Mgp gMnp
Lytle
(in A)
methods
Chivate
et al.
2.56
2.25
of oxygen from cations in A site.
Distance of oxygen from cations ink site.
1.96
12
X-RAY SPECTROSCOPIC STUDY OF Mg-Mn FEHRITES
Metallurgy Department of the University of Strathc1yde, Glasgow, and the other author (V.K. ) wishes
to thank the Council of Scientific and Industrial Research, New Delhi for the award of a Senior Re-
search Fellowship. Thanks are also due to Professor A. B. Biswas, Professor C. M. Srivastava,
and Dr. M. J. Patni, for their cooperation and
*Present address: Department of Metallurgy, University of Strathclyde, Glasgow, United Kingdom.
K. RadB. D. Padalia, V. Krishnan, M. J. patni,
hakrishnan, and S. N. Gupta, J. Phys. Chem. Solids
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Phys. 58, 2084 (1973).
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9F. W. Lytle, Adv. X-Ray Anal. 9, 398 (1966).
~OP. Chivate, P. S. Damle, N. V. Joshi, and C. Mande,
J. Phys. C 1, 1171 (1968).
D. E. Sayers, F. W. Lytle, and E. A. Stern, Adv.
X-Ray Anal. 13, 248 (1970).
12
L. V. Azhroff and D. M. Pease, in X-Ray SpectxoscoPy,
edited by L. V. Azaroff (McGraw-Hill, New York,
1974), p. 284.
~3V. B. Singh and B. K. Agarwal, J. Phys. Chem. Solids
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¹
(unpublished).
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help in the present work.