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Magnetism and bonding in a D88 structure; Mössbauer and magnetic investigation of the system Mn5Si3-Fe5Si3
J. Phys. Chem. Solids
Pergamon
Press 1970. Vol. 3 I, pp. IS I I- 1524.
Printed in Great
Britain.
MAGNETISM AND BONDING IN A Dg8 STRUCTURE; MijSSBAUER AND MAGNETIC INVESTIGATION OF THE SYSTEM Mn,Si,-Fe,Si, K. S. V. I.. NARASIMHAN*. The University
W. M. REIFFt. H. STEINFINK*
of Texas
at Austin,
(Received
Austin, Texas
787
and R. I.. COLLINS
12,U.S.A.
9 June 1969)
Abstract -The
MGssbauer spectra and magnetic measurements of the phases Mn,. ,Fe,Si,. I G x 5 5, and Mn,S& were obtained from 4.2”K to above room temperature. The compounds crystallize with the hexagonal D8, structure (Mn,Si, type). space group MJmcm. The first iron atom substitutes into the 4(d) site. The second iron occupies mainly the 6(n) site while the third iron occupies both the 6(g) and 4(d) sites of the space group. The fourth iron substitutes in such a manner that 4(d) sites are completely occupied by iron and only one Mn is left in 6k). The phases Mn,FeSi, and Mn,Fe& show antiferromagnetic behavior similar to Mn,Si,; MnFe,Si, is ferromagnetic and displays a magnetization curve similar to Fe,%,. The data indicate that iron in the 4(d 1site can be described on the basis of a low spin 3d” configuration with covalent bonding between it and the surrounding six silicon atoms. Covalency is assigned on the basis of the internal field value H, = 130 kG. The 6(g) iron displays about 50 per cent covalent and SO per cent metallic character. A magnetic structure for MnFe,Si,, and Fe,%, is proposed in which canting of the sublattice magnetizations is considered.
I. INTRODUCTION THE
MAGNETIC
of Fe&, and Mn,Si, have been investigated by neutron diffraction techniques. Mijssbauer spectrosand by susceptibility measurements COPY. [l-6]. Both compounds crystallize with the D8, structure and Fe&, is ferromagnetic while Mn,Si,, is antiferromagnetic. The D8, type structure has the space group symmetry P6Jmcm (193) and contains two formula weights of composition M,Si,, (M = metal atom) in the unit cell. The metal ions are situated in two independent crystallographic sites designated 6(g) and 4;d) and the formula can be written as (M&M*) Si, to indicate the respective site occupants. The crystal structure of Mn,Si, was first determined by Amark et (11.[7] and more recently by Aronsson[8] and by Lander and Brown[9]. The environment of the metal ion in the 4(d) structures
*Materials Science Laboratories, Chemical Engineering. +Department of Chemistry. t.Department of Physics.
Department
of
site consists of six silicon atoms at the corners of a distorted octahedron. In Mn,Si,, the six distances from Mn in 4(d) to silicon vary from 2.413 to 2*419& The distances between adjacent 4(d) atoms, stacked parallel to the c axis in the form of a linear chain is 2.406& while the distances between chains exceeds 5 A. The Mn in the 6(a) sites form triangles around the c axis at z = 4 and z = :. and the two triangles are rotated by 60” with respect to each other. Miissbauer data obtained on carbon stabilized samples of Fe&[ I] were found to exhibit a hyperfine split pattern consisting of a set of sharp lines with an internal field H, = 137 kG, superposed on a more diffuse six line pattern for which the estimated internal field ranged from 180 to 240 kG. The field H, = I37 kG was assigned to iron in 4(d) sites and it was estimated that such iron has a AE = O-35 mmlsec. The principle component of the electric field gradient tensor was assumed axially symmetric and of positive sign. The iron exhibiting larger internal fields was presumed to correspond to the
1512
K. S. V. 1..NARASIMHAN
6(g)
sites of the
values
of
If,
D8,
for
the
structure.
The
two
were
sites
same
found by Shinjo and Nakamura[31. present spectra are better resolved
also
placed into an alumina crucible and melted in an induction furnance in an argon atmos-
The than
phere and the molten product cooled over a two hour period. The phase Fe,Si:, was
those in Ref. [3] and no spectra were presented in Ref. [ I J. Several
spin schemes
for
Fe&[
in
accord
I-3.
have been proposed
IO] which,
with
each
however,
other.
The
are not postulate
advanced to explain the spin of atoms in the 4(d) position of the D8, structure assumes that they are purely metallic, even though they are closely surrounded by distorted octahedral arrangement atoms
a slightly of silicon
and as a result considerable
bonding
should
exist.
er (II.
covalent
In order to investigate
prepared mixture
by
meter were obtained
tained
from
FeK
Mossbauer
Mn,_,Fe,Si,,.
powder
Straumanis
type
radiation.
in
a large range
constants shown in Table Magnetic susceptibility
systematically
for
have all
the
carried
and magnetic
Foner
Through
the
Mossbauer
of commeasure-
20
using
values
yielded
unfiltered the
of
lattice
I. measurements
out using the Faraday
magnetization a
as a function
paterns of 114.6 mm dia.
were
method and the
procedure and precision of measurements have been previously dcscribed[ I II. The
members of the series in order to obtain a reasonable picture of the change in electronic structure
a
camera.
I 5 s d 15, over
and in the case of Fe,Si,, of an external magnetic field.
and
A least squares refinement
measured
determined
position.
X-ray
exposed
of the series
The spectra and magnetic measurements been
for all preparations
spectra
of temperature in the presence
by
into a vycor for 36 hr and
the diagrams showed lines which were due only to the D8, structure with shifts in the ‘d’ spacings as expected for the solid soluwere obtions. Precise lattice parameters
phases Mn,_,Fe,Si,,, the
the stoichiometric
then quenching it by dropping it into water. X-ray diffraction patterns using a diffracto-
specimens
gated
melting
sealing the arc melted button tube and annealing it at 900°C
the spin arrangements in the 4(d) and 6(q) sites in greater detail we undertook a study of the 0 G x d 5. We investi-
arc
on a water cooled hearth followed
vibrating
measurements sample
type[ 121. This
producibility
better
detect changes in 5 X IO-“e.m.u. The
were done with
magnetometer instrument
of
the
has a re-
than
I per cent and can moment of magnetic instrument was cali-
ments, it has also been possible to follow the mode of substitution of iron for manganese in 4(d) and 6(g) lattice sites. This is not possible via X-ray methods as the scattering
brated with spectrosopically pure nickel. Mijssbauer spectra were obtained using a
power of iron and manganese are not sufficiently different. The mode of substitution is
constant acceleration drive operated in the time mode. Data were accumulated in a 400
significantly
channel analyzer. The source used was 75 mC of Co5’ diffused into copper foil and
behavior
related
from
to the change in magnetic
the antiferromagnetic
to the strongly ferromagnetic
Mn,Si,,
Fc,Si,,.
2. EXPERIMENTAL
Iron and manganese of 99.99 per cent nominal purity and silicon of 99.99 per cent purity were used to prepare the phases. Quantities of the powdered elements which yielded the desired stoichiometry were sealed into an evacuated vycor tube and heated for 36 hr at 800°C. The reacted material was then
used at room temperature. Calibrations were obtained using 0.00127 cm, 99.99 per cent iron foil. Samples consisted of finely ground powders suspended in a spray adhesive between filter paper discs. Samples ranged in thickness from 200 to 400 mg/in’. The spectra were fitted by least squares analysis assuming I-orentzian line shapes and using a modified National Bureau of Standards computer
program[l3].
The
reproducibility
for
MAGNETISM 'I‘ahle 1. Magnetic
AND
BONDING
and crystal purumeters of Mn,_,Fe,Si, Phuses. Numbers refer to stundard deviutions /.L,.,r(“)
Phase
Curie temp. T, or N&l
1513
IN A D&STRUCTURE
W&s
temp. 7‘” (“K)
(“K)
(Pardmagnetic) Per metal atom in Bohr magnetons
-9.
62
Mn,Si,,
temp. H,,
I
in parentheses
I .attice
/1 r:” ’
constants A
( FerroAagnetic) Per metal atom in Bohr magnetons
No
(‘0
6.901 6.873 (0.014) 6.864 (0.019) 6.862
4.812 (0.002) 4.782 (ow2) 4.7x0 (0.004) 4.779
(0405)
~0401)
6.770 (0.014) 6.7S7 (0.021)
4.728 (0.005) 4.717 to~oO2)
4.05
(0406) Mn, FeSi:,
99
10.4
4.3s
Mn,,l:c,Si,,
I62
12.4
3.34
IMn,ke,,Si,
I60
256.6
3.44
Mn Fe,%:,
325
346.0
3.52
kc&,
376
““Relative
0.89
error in pL,” (paramagnetic)
and p.,, (ferromagneticl
values of the isomer shifts, 6. and quadrupole splitting, AE, obtained from mathematical fitting of the data was &O*Ol mmlsec. For magnetically split spectra, error in determination of internal fields is estimated as 25 kG. The spectrum of Fe,Si,, in an externally applied field was obtained using a superconducting magnet such that the applied field, H,,. is parallel to the direction of gamma-ray propagation. Kefrigerants used to obtain low temperature spectra were dry ice-isopropanol slushes. liquid nitrogen and liquid helium. Mineral oil was used as a heat transfer medium for temperatures above room temperature. 3. MbSBAUER
I.11
MEASUREMENTS
(a) Mn,FeSi,, The phase Mn,FeSi:, shows the least complicated spectral behavior of the series Mn,_,Fe,Si,. At room temperature, Fig. I(a), a symmetric quadrupole doublet with relatively narrow lines, Table 2. is observed. The small L!Z for this system, Table 3 indicates a small but definite distortion of electronic symmetry. As the temperature is decreased magnetic splitting occurs, Fig. l(b) and I(c). and a single six line pattern
is I.6 and 0.5 per cent respectively.
results at 4.2”K. Although the peak heights of the spectrum at 4.2”K differ from the expected 3 :I!: 1 : I :2 :3 ratios, the areas of the six peaks do indicate an essentially random distribution of internal field directions in this sample. For a magnetically ordered, polycrystalline sample. the relative areas of the six absorptions are related to the angle 6, between the y-ray propagation direction and internal field directions by the equation [ 141: (COS’O) =
AI+A:,+A~+A,j-(A,+A,) $, Ai
where the Ai are the respective absorption areas. In the present case (cos’8) = 0.27. while for a perfectly random orientation of internal field directions (co&) = :%. The observation of a single six line pattern at 4.2”K and a ‘clean’ room temperature quadrupole doublet leads to the conclusion that essentially all of the first iron to be substituted into Mn,Si,, goes preferentially into a single crystallographic site. The low value of the internal field corresponding to spectrum I(c) suggests that the bonding to this iron is strongly covalent.
1514
K. S. V. L. NARASIMHAN
a
2 l
i:’ \‘.
3 1
y
b
.- : . -.
“. _z ‘ .
C
I 0
-6
6
Velocity Fig.
1. Miissbauer
mmlsec
spectrum of Mn,kSi-, (b) 78°K. Cc) 4.2”K.
at (a) 3OO’K.
et al.
For example, it has been well demonstrated for high spin Fe+“, that H, decreases with increasing covalency and that H, is, in fact, a more sensitive measure of covalency than the isomer shift [ 15, 161. This has been found with both tetrahedral and octahedral stereochemistries for a variety of ligands. Comparison with the values of H, found by Johnson et uf.[l], and Shinjo and Nakamura [3], and in this work, Table 4, for Fe&, indicates that the iron of Mn,FeSi,, is in a 4(d) site. i.e. within a slightly distorted octahedral array of silicon. The spectrum of Mn,FeSi,, at 4.2”K is indicative of combined quadrupole and magnetic hypetIme interactions [ 171. In Fig. I(c) the center of the inner four peaks is shifted to lower velocity such that the difference in splitting between lines I and 2 and lines 5 and 6 is 0.4 of the room temperature quadrupole splitting. The foregoing difference is a measure of the quadrupolc splitting [ 14, 171 for a magnetically split spectrum assuming an axially symmetric electric field gradient. In general, the value of AE for the case of combined magnetic and quadrupole interactions is dependent on the angle H. between the internal field If,. and the principle component V,,, of the electric field gradient tensor[ 14, 171. In the present case, assuming AE is temperature independent, a ratio of AE(4~2”K)/AE(300°K) = O-4 leads to a calculated angle 0 = 63”. l.andet ct 1r1.[4].
Trthle 2. Line Ir-idths ( I‘)‘;l’ Compound
-__
Mn,FeSi,
Mn,Fe$i:,
Mn,ke,,Si, Mnf-e,Si,,
Temp.(“K)
__._--_--.---300 195 7x 4.2 400 7x 3.0 300 195 470 420
‘J’All line widths
in mm/set
I’,
I‘,
1‘3
I‘.I
0.39 0.36 0.39 0.39 0.30 0.29 0.5 I 0.30 0.2x 0.32 0.32
0.44 0.42 0.57 0.56 0.36 0.75 0.71 0.32 0.29 0.33 0.34
0.41 0.41 0.36 0.57 0.74 0.27 0.25 0.29 0.29
0+x) 0.57 0.3x 0.32 0.47 0.35 0.34 0.36 0.35
~
relative
to iron foil for which
(I‘) observed
1‘ii
1‘5
0.50 0.49
0.49 0.5 I
0.81 0.69
0.70 0.6s
i: 0.27 mm/set.
MAGNETISM
AND
BONDING
IN
A D8,
STRUCTURE
I515
Table 3. Miissbauer data’“’ Temp. Compound
Isomer shift (8) 4(d)(l.3)*
t”K) 300 195 4.2 400 300 195 300 195 470 420 300
Mn,FeSi,,
Mn,Fe,Si,
Mn,l:e,Si, MnFe,Si,
0.21 0.28 0.25 0. 14 0.21 0.29 0.19 0.24 0.11 0.14 O-23
6(g)(2,4)*
Quadrupole 4(d)(l.3)*
0.38 040 044 0.43 0.45 0.33 0.37 0.36
060 0.59 0.24 0.56 0.48 0.5 1 0.54 0.47 0.50 0.50 0.51
splitting t&F) 6tg)t2,4)*
0.55 0.56 0.58 0.55 0.48 0.63 064 0.61
‘“‘All data in mmlsec relative to natural iron foil. ‘Identification of sites, enumerated on spectra.
Table 4. InternulJields’“’
Compound
Mn,l’eSi:, Mn,,le,Si,,
Mn,Fe:,Si, MnFe,Si,
Fe,Si,
Temp. (“K)
4(d)
78 4.2 78 4.2 3.0 7x 4.2 195 78 4.2
97 128 101 III 123 123 137 116 132 l3Y
187 228 177 209 226
300 78 4.2
91 123 132
168 228 243
6(x)
‘“‘All fields in kilo-Gauss relative IO iron foil for which the internal field at 300°K is taken as 330 2 3 kG [I?).
determined a value of 90” for this angle from a neutron diffraction study of the isomorphous Mn,Si, phase. In light of the assumptions made, 0 = 63” is a reasonable value for Mn,FeSi,. This value of 8, with a shift of the center of the inner four lines of Mn,FeSi, toward negative velocity, indicates V,, is negative at a 4(d) site. Johnson, et a/.[ l] assigned a positive value to V,, for 4(d) sites in Fe&, and this may have resulted from assuming 8 = 0” for 4(d) iron of Fe,!%,,. However this angle is difficult to determine
with any certainty from the complex spectrum of Fe&. Using a point charge model and interatomic angles and distances based on the parameters of the isomorphous Mn,Si, [g], a negative V,, is calculated for 4(d) sites. This can only be taken as qualitative theoretical support for the results of this investigation since covalency and 7r bonding effects are undoubtedly very large as indicated by the small value of H,l. (b) Mn,Fe,Si, Figures 2(a-d) show the Mossbauer behavior of Mn,Fe,Si:, over a wide range of temFrom the higher temperature perature. spectra, it is evident that more than one crystallographic type of iron is present in the system. On the basis of isomer shift and quadrupole splitting at several temperatures, Table 3, absorptions 1 and 3 of Figs. 2(a) and 2(b) are assigned to a quadrupole doublet resulting from 4(d) type iron as in Mn,FeSi,,. Peak 2 and the shoulder at positive velocity labeled 4 are assigned to another quadrupole doublet having a splitting of similar magnitude to the preceding 4(d) iron but a more positive isomer shift in all cases. In the following discussion this new doublet is attributed to iron in 6(g) lattice sites. The spectrum of Mn:,Fe,Si:, remains constant down to 78°K at which temperature magnetic
1516
K. S. V. 1.. NAKASIMHAN
CI a/.
in Fig. 2(d) for 3*O”K, i.e. only one type of iron appears to be significantly split by
f----+
magnetic
4 ,’
hyperfine
interaction
and the magni-
tude of II,,. Table 4. indicates this to be 4(d) iron. ‘I-he neutron diffraction study of Lander,
I:’
~1 ul. indicates that two of the 6(s) sites of are not magnetically ordered[41 Mn,Si:, although
crystallographically
are equivalent.
Hence.
for the absence inner
lines
all
6(g)
sites
a possible explanation
of noticeable
splitting
3 and 4 of Mn,,Fe,Si,,
of the
is that a
large fraction of the second iron preferentially the magnetically random 6(g)
occupies
sites. Such preferential occupation is difficult to explain along the usual lines of different crystal
field stabilization
involved.
energies of the sites
The exact electronic
configurations
for 4(d) and 6(,e) sites are not known and the 6(s) coordination environment is rather com-
-\.
f+--+C
plcx. On the other hand. the entropy of the system is expected to increase with filling of 6(v) as well as J(t/) sites. This suggests that 6(s)
sites are only
slightly
higher in energy
than 4(d) in Mn.,FeSi,, and Mn,Fe,Si,, phases. We next consider the relative occupation factors
for
factors
(recoil
temperature analysis.
different free
sites.
dependence
However.
.fhe
unknown
J
fractions) 1171 and their prevent
the analysis
an
exact
at high and
low temperature would be expected to differ significantly if the J‘values differ appreciably. A least squares fit to the spectrum of Mn,,FezSi,, at 400°K indicates peak 2 and shoulder 4 to correspond to 38 per cent of the total arca or therefore
Velocity Fig.
(mm/set)
2. Miissbauer spectrum of Mn,FqSi,, (b) 300°K. (cl 78°K. (d) 3WK.
at (a) 400°K.
splitting is noticeable. The general shape of this spectrum is reminiscent of that of Mn,FeSi,, at 78°K except for the two very intense peaks labeled 3 and 4. The spectrum at 4.2”K is essentially the same as that shown
From
0.76
iron
atoms
in 6(g)
a similar fit to the spectrum
sites.
of Mn,,Fe,-
Si,, at 3PK the intense absorptions 3 and 4 correspond to 42 per cent of the total absorption area. This includes the inner peaks of magnetically split 4(d) iron. If saturation effects are neglected. then the 6(x:) iron accounts for 3 I per cent of the total absorption area. i.e. 0.62 6(g) iron atoms. However. saturation is not negligible since peaks 3 and 4 of Mn,FeSi,, correspond to 25 per cent of the total area for spectrum l(c). Using this factor
MAGNETISM
AND
BONDING
to account for 4(d) intensity in peaks 3 and 4 of Fig. 2(d), 6(g) absorption corresponds to 25 per cent of the total absorption area, i.e. 0.50 6(g) iron atoms, This is a reasonable lower bound on the amount of 6(g) iron present. Possibly, all of the 6(g) absorption area of Mn:,Fe,Si:, at 3eO”K is not confined to the more intense central peaks as evidenced by the broadness (Table 2) of the peaks of spectrum 2(d) in Fig. 2. However, the approximate agreement of the percentage of total area corresponding to 6(g) iron for 4OWK and 3°K indicates that a significant fraction (between 3-a) of the second iron goes into 6(g) sites on formation of Mn,Fe,Si,.
IN A D8, 0
5
10 1
0
5
(d) MnFe,Si, A similar situation occurs in this phase except that the initial broadening effects of magnetic hyperhne splitting are evident even at room temperature. Comparison shows that the spectrum, Fig. 4(b), is very similar to that of Mn,Fe,,Si, at 300°K except that
(
%
:.
\/
”
b
‘.
”
:
(c) Mn,Fe&, The Mossbauer spectrum at 3OO”K, Fig. 3(a), shows the same general pattern of four lines as in Mn,,Fe,Si, although the increased 6(g) content leads to a better resolved spectrum. As for Mn:,Fe,Si,, lines I and 3 correspond to quadrupole split 4(d) iron while 2 and 4 represent similarly split 6(g) iron atoms. A least squares computer fit indicates that the spectra at 300°K and 195°K can be reconstructed from separate peaks as shown in Fig. 3(b) for the spectrum at 300°K where the area ratio (A, +A:,)/ (A., + AJ is 1 . I. This implies that occupation of 4(d) and 6(g) sites is nearly equal for Mn,Fe&. On decreasing the temperature, the system clearly shows two separate hyperfine patterns where the more diffuse pattern corresponding to a larger internal field is assigned to iron in 6(e) sites. It is reasonable to conclude that magnetically split 6(g) sites of Mn,Fe,Si, are now being occupied.
1517
STRUCTURE
10 i
.I 'p L 2"
-..
,.--\ \
Ai
C I.
5
.;
;
: :
:
1
_
‘,
.’
‘k;
Fig. 3. Miissbauer spectrum of Mn,l:e,Si:, at (a) 30O’K. (b) computer reconstructed spectrum at 300°K in terms of 4(d) and 6(x) absorptions, cc) 78°K. (d) 4.2”K. peaks I and 2 of the latter compound have coalesced into one broad intense peak in MnFe.,Si, at room temperature. Increasing the temperature to 420°K results in rapid fluctuation of internal magnetic fields causing line 4 in the spectrum of MnFe,Si, to narrow while the sloping baseline at positive velocity disappears. Similar behavior occurs for the
K. S. V.
1518
:
1
I NARASIMHAN
.. .’ .
H
Fig. 4. Mtissbauer spectrum of MnFe,Si,, at (al 470°K. (b) 300°K. (cl 195°K. (d) 78°K. (el4.2”K.
broad absorption at negative velocity, and at 47O”K, Fig. 4(a), a shoulder corresponding to peak I of 4(d) iron is evident. The best fit to the latter spectrum shows (A, +A3)/(A2 +A,)= 0.95, or nearly equal occupation of 4(d) and 6(g) sites as in Mn,Fe,Si,,.
et 01.
It is well known that for quadrupole split iron showing magnetic hyperfine splitting the I$, *s) + Ii, +$) transitions narrow more slowly than 1%.2-t) -+ 1’2.%3) transitions on going from a 6 line pattern to a quadrupole doublet1 181. The kets are the magnetic sublevels of the excited and ground nuclear energy states of 57Fe. With increasing temperature, the magnetic splitting can disappear and leave only a quadrupole doublet. Hence the behavior of MnFe,Si:, with increasing temperature is taken as tentatively indicating Vzp < 0 for 4(d) iron and k’,, > 0 for 6(g) iron. With decreasing temperature the phase MnFe,Si,, behaves in much the same way as Mn,Fe,Si,, except that magnetic interaction is now stronger and essentially complete hyperfine splitting occurs at higher temperatures. A comparison of the internal fields at different temperatures, Table 4, shows this trend of increasing ferromagnetic interaction with increasing number of iron atoms. (e) Fe&, The Mossbauer spectrum of Fe,Si, at 300°K has the same general appearance as that shown in Fig. 5(a) at 4.2”K. The internal fields corresponding to 4(d) and 6(g) iron of Mn,Fe.&, and MnFe,Si,, are calculated on the basis of two overlapping six line patterns as shown for Fe,Si,, at 4*2”K, where the lower pattern in Fig. 5(a) is that for 4(d) iron and the middle pattern for 6(g). It is evident that there is more uncertainty in the estimation of H,, for 6(g) iron than 4(d). This is in part attributable to the fact that the 6(g) sites are not all magnetically equivalent. For example. in Fe&,, fields corresponding to 6(g) iron range from about 190 to 240 kG. Johnson et al. [ I] made a similar observation for carbon stabilized Fe&,. Secondly, absorptions (dashed lines) attributable to Fe,,Si impurity are also present. This complicating feature was also found in the spectrum of Fe,%, by Shinjo and Nakamura[3]. who determined internal fields of 195 -t IO and 305 2 IO kG
MAGNETISM
AND
BONDING
1519
IN A D8, STRUCTURE
a
0
b 5 1
.: -6
Velocity
d
6
mmhec
Fig. 5. Miissbauer spectrum of Fe&, at (a) 4.2%. (b) 4.2”K. H; ,,,,,,,p,j= 26 kG.
for the two types of iron in Fe,Si and which agree with those found here. Hence, in Table 4 only the maximum value of H,, for 6(g) iron at each temperature is reported. In an effort to understand better the nature of magnetic ordering in Fe&, spectra were taken in external magnetic fields. A small field of the order of 1000 G had no effect on the spectrum at 4.2”K. A large field, 26 kG, caused a small decrease in the internal fields of both kinds of iron and although the signal to noise ratio is now lower, H,, for 4(d) iron is estimated as I22 5 IO kG while the maximum value for 6(g) is 227 -+ IO kG. The decrease in the respective internal fields is somewhat smaller than that expected if the system were a perfect ferromagnet with internal fields parallel. The system is magnetically saturated at this applied field and temperature, Fig. 7. and on this basis it is possible to make a crude calculation of the
H, ,,,,,,,,(, = 0,
angle between the internal fields from their observed decrease in an external field, assuming the resultant of the internal fields is collinear with the applied field. In the present case, this amounts to maximum angle of about 112”. Therefore it is assumed that the spins of the corresponding magnetic sublattices are canted at a maximum by approximately this angle. This result must be taken as approximate since the decreases in H, are small and difficult to estimate accurately from the spectrum. Furthermore, it is seen that the intensities of the spectral absorptions change in a complicated way which is not readily correlated with the observed decreases in internal fields. 4. MAGNETIC
MEASUREMENTS
The inverse magnetic susceptibilities of these compounds above their transition temperatures are shown as function of tem-
1520
K. S. V.
I_. NARASIMHAN
perature in Fig. 6. Mn,Si, exhibits typical antiferromagnetic behavior as expected and the Neel temperature, 62°K. agrees with previously reported values[4, 191. The variation in the susceptibility as iron is introduced into the structure reflects the decreasing antiferromagnetic influence and the conincrease of ferromagnetic spin comitant arrangements as the iron concentration increases. The transition temperatures also increase as the Fe&, end member is approached. The high temperature data for Fe,!+,, is not shown because this phase is unstable[20]. Table 1 summarizes the data from the magnetic measurements. In Fig. 7 are shown the magnetization curves for these materials. For Mn,_,Fe,Si,, x = I, 2, the curves reflect the antiferromagnetic behavior and for x = 4. 5 ferromagnetism is clearly evident. However, for x = 3 an intermediate state of magnetization can be inferred. IO’X35
CI (I/ 5. MAGNKTIC
STRUCTURE
The behavior of the susceptibility of the solid solution phases can be understood on the basis of the spin structures for the end members, Mn,Si,, and Fe,Si,,. The Mossbauer data show that the substitution of the first iron atom for manganese occurs in the 4(d) position. The susceptibility and magnetization curves for (Mn,)(MnFe)Si, indicate that the spin structure of this compound is only very slightly affected by the introduction of the iron atom and the effect is mainly manifested by an increase of the Niel and Weiss temperatures. The Mossbauer data for the phase Mn,,Fe,Si,, show that the second iron atom occupies mainly the h(g) position in the structure and an approximate formula indicating the probable distribution is (Mn,.,,Fe,,.,,)(Mn,,.,;,Fe, .,l,)Si,,. The magnetization for this phase, Fig. 7, is nearly unchanged from that of Mn,FeSi,, and the implication
Yn,_*F*yfi,
I
0
0
~3
200
3W
0
big.
6. ia)
I/x
400
100
500
200
600
MO
100
.oo
x=0
600
Xx)
600
Km
000
vs. 7‘ as a function of increasing Mn,Si,,-Fe,Si., system.
x=1
iron concentration
in the
MAGNETISM
AND
BONDING
IN A D8,
1521
STRUCTURE
b ?lO.,
20,
IO,,
.
0
loo
TEYPfRAWKC
Fig. 6(b).
200
300
400
so0
&
x(=3
(-1. I
I/x vs. 7‘ for hln,Fe,Si, and MnFe.,Si,. The magnetization latter compound is also shown.
must be drawn that the spin structure of this phase remains essentially unaltered except for a further increase in the Neel and Weiss temperatures. However, the susceptibility curve, Fig. 6(a). shows evidence of ferromagnetic interaction from the change in slope at about 350°K. This could be due to a predominant ferromagnetic interaction of the iron atoms in the 4(d) sublattice. The overall antiferromagnetic behavior becomes dominant at about 200°K. Mossbauer data obtained for Mn,Fe,,Si, can be interpreted on the basis that most of the third iron atom occupies a 6(g) position but with a definite increase of iron present in 4(d) sites. Thus a probable formulation is (Mn,.,Fe,.,)(Mn,,.,Fe,.,)Si,. The magnetic behavior exhibited by this phase indicates that its spin structure must be quite different from the previous compositions. The Mossbauer spectra are consistent with magnetically ordered 6(g) sites. The susceptibility and magnetization curves for this material definite-
vs. 7‘ for the
ly show the presence of ferromagnetic interactions with a sharp increase in the Weiss constant. The abrupt change in the transition temperature also supports this vrew of the spin structure. We attempted to obtain the ferromagnetic component of the magnetization, oO, from an extrapolation of the high field part of the (T vs. H curve on the assumption that the magnetization can be expressed as u = tr,,+xH where x is the antiferromagnetic susceptibility. The curve does not show a large degree of horizontal character at the fields available to us so that an extrapolation is expected to yield a low value of uo. A value of 09 pH per metal atom is obtained from the extrapolation of the high field portion of the curve. A moment of 0.26 p,] per metal atom is calculated on the basis of the following assumptions: (a) Iron contributes I cc,{per atom [I] and manganese contributes O-4 pB per atom [4] in the 4(d) site and the iron and manganese spins are oppositely aligned. The resultant moment for the 4(d) sublattice is 1.3 F~. (b)
1522
K. S. V.
0
2
4
Fig. 7. Magnetization
I_. NARASIMHAN
6
CI (11.
IO
vs. magnetic field intensity Mn,_,Fe,Si:,. 0 s x s 5.
The magnetic structure of the 6(x) sublattice retains the antiferromagnetic arrangement as in Mn,Si,[4]. Thus the total moment for (Mn,.,Fe,.,)(Mn,,.,Fe,.,)Si:, is I.3 ~~ or O-26 pII per metal atom. Since the material is not sufficiently saturated only a qualitative support for this spin scheme is to be expected. As indicated by the Mossbauer data. the introduction of the fourth iron atom to form the phase (MnFe,)(Fe,)Si, places two iron atoms into the 6(g) and two into the 4(d) positions and clearly ferromagnetic coupling among the atoms exist now in both sublattices. The behavior of the susceptibility and magnetization curves, Figs. 6. 7. is typical for a ferromagnetic compound. The magnetization curve for Fe&G,, is included for the sake of completeness. Powdered samples of MnFe,Si,, and Fe&:, were oriented in a magnetic field of about I4 kG and their X-ray diffraction patterns showed a strong enhancement of the 001 and a nearly complete disappearance of hkl lines indicating that the easy axis of magnetization is the c’axis. The difference in the permanent moments observed for Fe,Si,s and MnFe,Si,, Table 1, is significant. It can be explained on the basis that the ferromagnetic moment of one sublattice is canted with respect to the other and that the cant angle is a function of the
14
I6
for the system
composition. It was previously pointed out that the Mossbauer data are consistent with a maximum cant angle of about I 12” for atom for Fe,!&. The value 1. I I p,/metal the observed moment in ( MnFe2)( Fe,)Si,, can be accounted for on the basis that the atoms in the sublattices have parallel spin the sublattices are coupled alignments, parallel, and manganese occupies the magnetically random 6(g) positions. Using the values of 1 k,, for 4(d) iron and I.55 pH for 6(g) [ I ] iron the calculated moment is 143 F”/rnetal atom. It must be realized that such good agreement may be fortuitous but both the Mossbauer and magnetic data lend credence to this magnetic structure. The same magnetic structure for Fe&, i.e. random magnetic sites in 6(g), would again give rise to an expected moment of I.02 I,, as compared to the observed value of 0*9~,~. However. a cant angle of 120” between the sublattices will produce a resultant moment of 0.9~“. The required cant angle is close to the maximum value deduced from the Mossbauer spectrum of FesSi,, in an external held. Evidence for random spin in some of the 6(g) sites comes from the range of internal fields observed for 6(g) iron in Fe,Si, in the present investigation and also that of Johnson c’t al. [ 11. I.ander et al. [4] remarked that it
MAGNETISM
AND
BONDING
is difficult to understand why the 6(g) sites are divi’ded into two magnetically non equivalent groups one of which is random in Mn,Si,. This difficulty still exists in the case of MnFe,Si, and Fe&,. Perhaps the ‘randomness’ of the spin structure is due to a third sublattice for which the periodicity extends over many crystallographic unit cells. This could also account for the considerable range of hype&e field values which are observed. 6.
BONDING IN DS8 STRUCTURE
The bonding between an atom in the 4(d) site and surrounding silicon atoms is expected to be primarily covalent and the measured hyperfine field value confirms this expectation. Thus, it is reasonable to postulate that the low spin configuration is assumed by the metal atoms [2 I]. If Fe is considered to have contributed three of its electrons to the conduction band then the resultant low spin 3d” configuration would contain one unpaired electron and give rise to a moment of 1 pB in agreement with the reported value for that position by Johnson, et (I/.[ I]. It should be noted that the observed isomer shift, Table 3. for 4(d) iron is consistent with a low spin 38 configuration [23]. The discussion of the electronic configuration for the occupant of the 6(g) site is considerably more complicated because of the very complex near neighbor environment. The metal atom is bonded to five Si forming a trigonal bipyramid. The metal atom itself is outside this polyhedron. The covalent bonding to Si can be considered to impart a low spin, d”, configuration, i.e. I pH contribution to the observed moment. In addition there are ten other metal atoms nearby, six 6(g) atoms at distances varying from 2.82A to 2.87A and four 4(d) atoms at 2.95A. If one considers metallic type bonding to exist among these and assumes that the resultant contribution to the magnetic moment will be as in u iron, namely 2.2 pu, then an approximate 50-50 mixture of metallic and covalent bonding
IN A D8, STRUCTURE
1523
account for the observed moment of 1.55 pB for an atom in the 6(g) site. The explanations offered by Kanematsu [lo] and by Lecocq, erct1.[2] for the magnetic moment observed in Fe,!& rests on the assumption that the iron atom in the 4(d) site is purely metallic and that covalent bonding exists between iron in 6(g) and silicon. Kanematsu’s theory assigns 2 pB to the 4(d) site and 1 pB to the 6(g) site iron atom and he calculates a resultant moment per atom of 1.4 p,+ We believe that the assignment of the moments in the sublattices and the assumption of parallel coupling is not supported by our results. Similarly Lecocq CI al. assign a moment of 2.2~~ to the 4(d) Fe as in u iron and a moment of 0.606~~ to 6(g) Fe by analogy with nickel and obtain a calculated moment of I a243 pa/Fe atom for Fe&, still in rather poor agreement with the measured value.
could
Ackno~ledgemenrsResearch of the Materials Science group is sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force and the National Science Foundation. One of us, W.M.R., is pleased to thank the Chemistry Department of the University of Texas for the N.S.F.-U.S.D.P. Faculty Associate Award extended to him during the course of this research. The support of the Robert A. Welch Foundation is also gratefully acknowledged by R.L.C.
REFERENCES I. JOHNSON C. E., FORSYTH J. B., LANDER G. H. and BROWN P. J., J. nppl. Phgs. 39. 465 ( 1968). 2. LECOCQ Y.. LECOCQ P. and MICHEI. A., C.r. Acud. Sci. I’dcrris258.5655 ( 1964). 3. SHINJO T. and NAKAMURA Y., J. phys. Sec. Jopun 18,797 ( 1963). 4. LANDER G. H.. BROWN, P. J. and FORSYTH J. B., Proc. phju. SW. 91,332 ( 1967). 5. CON K. V., C.r. Acud. Sci. Paris 260, I 1I ( 1965). 6. UBEI.OCKER E. and l.ECOCQ P., C.r. Acud. Sci. Puris 262, 793 ( 1966). 7. AMARK K., BOREN B. and WESTGREN A.. Metalln~ir~. IS, 835 ( 1936). 8. ARQNSSON B.. Acrm chefn. sound. 14, 1414 ( 1960). 9. LANDER G. H. and BROWN P. J., P/Ii/. Meg. 16, 14ltl967). IO. KANEMATSU K., J. phy.~. Sot. Japcrn 17. 85 ( 1962).
1524
K. S. V. 1.. NARASIMHAN
11. NARASIMHAN K. S. V. I.., STEINI~INK H. and GANAPATHY E. V., J. oppl. Phys. 40. 51 (1969). 12. l:ONER S.. Rev. scienr. ln.strum. 30. 548 (1959). 13. RHODES E.. O’NEAI. W. and SPIJKERMAN J. J., NHS Tech. Nore 404. 108 t 1966). 14. GRANT R. W.. The Miisshouer Effect and Its Appliccttion in Chemisrry (Edited by (1. Seidel and R. Herher). Adwtrcrs in C‘hemisfry Series, No. 68, American Chemical Society. Washington, D. <‘. ( 1967). 15. EDWARDS P. R. and JOHNSON C. E.. J. chtm. Phys. 49. 2 I I t 1968). 16. RICKARDS R., JOHNSON C. E. and HII.1. H. A. O..J. c+c,m. f’hys. 48. 523 1 ( 1968). 17. WERTH El M <. H ., Mijsshouer E’cc.r: Princ+/c~s
18. 19.
20. 21.
22. 23.
CI ul.
and Appliwlicm. Academic Press. New York (1964). BI. UME. M., Plr.vs. Ret;. Leff. 14.96 (1965). I.ETUN S. M., GEI.‘D P. V. and SEREBRENNIKOV N. N.. RUSS. J. ofinorg. Chem. (Engl. transl.) 10,683 ( 1965). HANSEN M.. C‘onsti~rrtion of Binary Ailqs. p. 173. McGraw-Hill. New York (1958). ORGEL 1.. E.. An /ntroduc/& IO ‘frcr,l.sitiorr-M~rtrl Chemislr?: I.iprnd Field Theory. Wiley. New York t 1962). PRESTON R. S., HANNA S. S. and HEBERLXJ., P&s. Rec. 128.2207 (1962). REI t.F W. M.. BAKER W. A., Jr. and ERI<‘KSON N. E.,J. Am. c.hem. Sot.. 90. 4794 ( 1968).
Pergamon
Press 1970. Vol. 3 I, pp. IS I I- 1524.
Printed in Great
Britain.
MAGNETISM AND BONDING IN A Dg8 STRUCTURE; MijSSBAUER AND MAGNETIC INVESTIGATION OF THE SYSTEM Mn,Si,-Fe,Si, K. S. V. I.. NARASIMHAN*. The University
W. M. REIFFt. H. STEINFINK*
of Texas
at Austin,
(Received
Austin, Texas
787
and R. I.. COLLINS
12,U.S.A.
9 June 1969)
Abstract -The
MGssbauer spectra and magnetic measurements of the phases Mn,. ,Fe,Si,. I G x 5 5, and Mn,S& were obtained from 4.2”K to above room temperature. The compounds crystallize with the hexagonal D8, structure (Mn,Si, type). space group MJmcm. The first iron atom substitutes into the 4(d) site. The second iron occupies mainly the 6(n) site while the third iron occupies both the 6(g) and 4(d) sites of the space group. The fourth iron substitutes in such a manner that 4(d) sites are completely occupied by iron and only one Mn is left in 6k). The phases Mn,FeSi, and Mn,Fe& show antiferromagnetic behavior similar to Mn,Si,; MnFe,Si, is ferromagnetic and displays a magnetization curve similar to Fe,%,. The data indicate that iron in the 4(d 1site can be described on the basis of a low spin 3d” configuration with covalent bonding between it and the surrounding six silicon atoms. Covalency is assigned on the basis of the internal field value H, = 130 kG. The 6(g) iron displays about 50 per cent covalent and SO per cent metallic character. A magnetic structure for MnFe,Si,, and Fe,%, is proposed in which canting of the sublattice magnetizations is considered.
I. INTRODUCTION THE
MAGNETIC
of Fe&, and Mn,Si, have been investigated by neutron diffraction techniques. Mijssbauer spectrosand by susceptibility measurements COPY. [l-6]. Both compounds crystallize with the D8, structure and Fe&, is ferromagnetic while Mn,Si,, is antiferromagnetic. The D8, type structure has the space group symmetry P6Jmcm (193) and contains two formula weights of composition M,Si,, (M = metal atom) in the unit cell. The metal ions are situated in two independent crystallographic sites designated 6(g) and 4;d) and the formula can be written as (M&M*) Si, to indicate the respective site occupants. The crystal structure of Mn,Si, was first determined by Amark et (11.[7] and more recently by Aronsson[8] and by Lander and Brown[9]. The environment of the metal ion in the 4(d) structures
*Materials Science Laboratories, Chemical Engineering. +Department of Chemistry. t.Department of Physics.
Department
of
site consists of six silicon atoms at the corners of a distorted octahedron. In Mn,Si,, the six distances from Mn in 4(d) to silicon vary from 2.413 to 2*419& The distances between adjacent 4(d) atoms, stacked parallel to the c axis in the form of a linear chain is 2.406& while the distances between chains exceeds 5 A. The Mn in the 6(a) sites form triangles around the c axis at z = 4 and z = :. and the two triangles are rotated by 60” with respect to each other. Miissbauer data obtained on carbon stabilized samples of Fe&[ I] were found to exhibit a hyperfine split pattern consisting of a set of sharp lines with an internal field H, = 137 kG, superposed on a more diffuse six line pattern for which the estimated internal field ranged from 180 to 240 kG. The field H, = I37 kG was assigned to iron in 4(d) sites and it was estimated that such iron has a AE = O-35 mmlsec. The principle component of the electric field gradient tensor was assumed axially symmetric and of positive sign. The iron exhibiting larger internal fields was presumed to correspond to the
1512
K. S. V. 1..NARASIMHAN
6(g)
sites of the
values
of
If,
D8,
for
the
structure.
The
two
were
sites
same
found by Shinjo and Nakamura[31. present spectra are better resolved
also
placed into an alumina crucible and melted in an induction furnance in an argon atmos-
The than
phere and the molten product cooled over a two hour period. The phase Fe,Si:, was
those in Ref. [3] and no spectra were presented in Ref. [ I J. Several
spin schemes
for
Fe&[
in
accord
I-3.
have been proposed
IO] which,
with
each
however,
other.
The
are not postulate
advanced to explain the spin of atoms in the 4(d) position of the D8, structure assumes that they are purely metallic, even though they are closely surrounded by distorted octahedral arrangement atoms
a slightly of silicon
and as a result considerable
bonding
should
exist.
er (II.
covalent
In order to investigate
prepared mixture
by
meter were obtained
tained
from
FeK
Mossbauer
Mn,_,Fe,Si,,.
powder
Straumanis
type
radiation.
in
a large range
constants shown in Table Magnetic susceptibility
systematically
for
have all
the
carried
and magnetic
Foner
Through
the
Mossbauer
of commeasure-
20
using
values
yielded
unfiltered the
of
lattice
I. measurements
out using the Faraday
magnetization a
as a function
paterns of 114.6 mm dia.
were
method and the
procedure and precision of measurements have been previously dcscribed[ I II. The
members of the series in order to obtain a reasonable picture of the change in electronic structure
a
camera.
I 5 s d 15, over
and in the case of Fe,Si,, of an external magnetic field.
and
A least squares refinement
measured
determined
position.
X-ray
exposed
of the series
The spectra and magnetic measurements been
for all preparations
spectra
of temperature in the presence
by
into a vycor for 36 hr and
the diagrams showed lines which were due only to the D8, structure with shifts in the ‘d’ spacings as expected for the solid soluwere obtions. Precise lattice parameters
phases Mn,_,Fe,Si,,, the
the stoichiometric
then quenching it by dropping it into water. X-ray diffraction patterns using a diffracto-
specimens
gated
melting
sealing the arc melted button tube and annealing it at 900°C
the spin arrangements in the 4(d) and 6(q) sites in greater detail we undertook a study of the 0 G x d 5. We investi-
arc
on a water cooled hearth followed
vibrating
measurements sample
type[ 121. This
producibility
better
detect changes in 5 X IO-“e.m.u. The
were done with
magnetometer instrument
of
the
has a re-
than
I per cent and can moment of magnetic instrument was cali-
ments, it has also been possible to follow the mode of substitution of iron for manganese in 4(d) and 6(g) lattice sites. This is not possible via X-ray methods as the scattering
brated with spectrosopically pure nickel. Mijssbauer spectra were obtained using a
power of iron and manganese are not sufficiently different. The mode of substitution is
constant acceleration drive operated in the time mode. Data were accumulated in a 400
significantly
channel analyzer. The source used was 75 mC of Co5’ diffused into copper foil and
behavior
related
from
to the change in magnetic
the antiferromagnetic
to the strongly ferromagnetic
Mn,Si,,
Fc,Si,,.
2. EXPERIMENTAL
Iron and manganese of 99.99 per cent nominal purity and silicon of 99.99 per cent purity were used to prepare the phases. Quantities of the powdered elements which yielded the desired stoichiometry were sealed into an evacuated vycor tube and heated for 36 hr at 800°C. The reacted material was then
used at room temperature. Calibrations were obtained using 0.00127 cm, 99.99 per cent iron foil. Samples consisted of finely ground powders suspended in a spray adhesive between filter paper discs. Samples ranged in thickness from 200 to 400 mg/in’. The spectra were fitted by least squares analysis assuming I-orentzian line shapes and using a modified National Bureau of Standards computer
program[l3].
The
reproducibility
for
MAGNETISM 'I‘ahle 1. Magnetic
AND
BONDING
and crystal purumeters of Mn,_,Fe,Si, Phuses. Numbers refer to stundard deviutions /.L,.,r(“)
Phase
Curie temp. T, or N&l
1513
IN A D&STRUCTURE
W&s
temp. 7‘” (“K)
(“K)
(Pardmagnetic) Per metal atom in Bohr magnetons
-9.
62
Mn,Si,,
temp. H,,
I
in parentheses
I .attice
/1 r:” ’
constants A
( FerroAagnetic) Per metal atom in Bohr magnetons
No
(‘0
6.901 6.873 (0.014) 6.864 (0.019) 6.862
4.812 (0.002) 4.782 (ow2) 4.7x0 (0.004) 4.779
(0405)
~0401)
6.770 (0.014) 6.7S7 (0.021)
4.728 (0.005) 4.717 to~oO2)
4.05
(0406) Mn, FeSi:,
99
10.4
4.3s
Mn,,l:c,Si,,
I62
12.4
3.34
IMn,ke,,Si,
I60
256.6
3.44
Mn Fe,%:,
325
346.0
3.52
kc&,
376
““Relative
0.89
error in pL,” (paramagnetic)
and p.,, (ferromagneticl
values of the isomer shifts, 6. and quadrupole splitting, AE, obtained from mathematical fitting of the data was &O*Ol mmlsec. For magnetically split spectra, error in determination of internal fields is estimated as 25 kG. The spectrum of Fe,Si,, in an externally applied field was obtained using a superconducting magnet such that the applied field, H,,. is parallel to the direction of gamma-ray propagation. Kefrigerants used to obtain low temperature spectra were dry ice-isopropanol slushes. liquid nitrogen and liquid helium. Mineral oil was used as a heat transfer medium for temperatures above room temperature. 3. MbSBAUER
I.11
MEASUREMENTS
(a) Mn,FeSi,, The phase Mn,FeSi:, shows the least complicated spectral behavior of the series Mn,_,Fe,Si,. At room temperature, Fig. I(a), a symmetric quadrupole doublet with relatively narrow lines, Table 2. is observed. The small L!Z for this system, Table 3 indicates a small but definite distortion of electronic symmetry. As the temperature is decreased magnetic splitting occurs, Fig. l(b) and I(c). and a single six line pattern
is I.6 and 0.5 per cent respectively.
results at 4.2”K. Although the peak heights of the spectrum at 4.2”K differ from the expected 3 :I!: 1 : I :2 :3 ratios, the areas of the six peaks do indicate an essentially random distribution of internal field directions in this sample. For a magnetically ordered, polycrystalline sample. the relative areas of the six absorptions are related to the angle 6, between the y-ray propagation direction and internal field directions by the equation [ 141: (COS’O) =
AI+A:,+A~+A,j-(A,+A,) $, Ai
where the Ai are the respective absorption areas. In the present case (cos’8) = 0.27. while for a perfectly random orientation of internal field directions (co&) = :%. The observation of a single six line pattern at 4.2”K and a ‘clean’ room temperature quadrupole doublet leads to the conclusion that essentially all of the first iron to be substituted into Mn,Si,, goes preferentially into a single crystallographic site. The low value of the internal field corresponding to spectrum I(c) suggests that the bonding to this iron is strongly covalent.
1514
K. S. V. L. NARASIMHAN
a
2 l
i:’ \‘.
3 1
y
b
.- : . -.
“. _z ‘ .
C
I 0
-6
6
Velocity Fig.
1. Miissbauer
mmlsec
spectrum of Mn,kSi-, (b) 78°K. Cc) 4.2”K.
at (a) 3OO’K.
et al.
For example, it has been well demonstrated for high spin Fe+“, that H, decreases with increasing covalency and that H, is, in fact, a more sensitive measure of covalency than the isomer shift [ 15, 161. This has been found with both tetrahedral and octahedral stereochemistries for a variety of ligands. Comparison with the values of H, found by Johnson et uf.[l], and Shinjo and Nakamura [3], and in this work, Table 4, for Fe&, indicates that the iron of Mn,FeSi,, is in a 4(d) site. i.e. within a slightly distorted octahedral array of silicon. The spectrum of Mn,FeSi,, at 4.2”K is indicative of combined quadrupole and magnetic hypetIme interactions [ 171. In Fig. I(c) the center of the inner four peaks is shifted to lower velocity such that the difference in splitting between lines I and 2 and lines 5 and 6 is 0.4 of the room temperature quadrupole splitting. The foregoing difference is a measure of the quadrupolc splitting [ 14, 171 for a magnetically split spectrum assuming an axially symmetric electric field gradient. In general, the value of AE for the case of combined magnetic and quadrupole interactions is dependent on the angle H. between the internal field If,. and the principle component V,,, of the electric field gradient tensor[ 14, 171. In the present case, assuming AE is temperature independent, a ratio of AE(4~2”K)/AE(300°K) = O-4 leads to a calculated angle 0 = 63”. l.andet ct 1r1.[4].
Trthle 2. Line Ir-idths ( I‘)‘;l’ Compound
-__
Mn,FeSi,
Mn,Fe$i:,
Mn,ke,,Si, Mnf-e,Si,,
Temp.(“K)
__._--_--.---300 195 7x 4.2 400 7x 3.0 300 195 470 420
‘J’All line widths
in mm/set
I’,
I‘,
1‘3
I‘.I
0.39 0.36 0.39 0.39 0.30 0.29 0.5 I 0.30 0.2x 0.32 0.32
0.44 0.42 0.57 0.56 0.36 0.75 0.71 0.32 0.29 0.33 0.34
0.41 0.41 0.36 0.57 0.74 0.27 0.25 0.29 0.29
0+x) 0.57 0.3x 0.32 0.47 0.35 0.34 0.36 0.35
~
relative
to iron foil for which
(I‘) observed
1‘ii
1‘5
0.50 0.49
0.49 0.5 I
0.81 0.69
0.70 0.6s
i: 0.27 mm/set.
MAGNETISM
AND
BONDING
IN
A D8,
STRUCTURE
I515
Table 3. Miissbauer data’“’ Temp. Compound
Isomer shift (8) 4(d)(l.3)*
t”K) 300 195 4.2 400 300 195 300 195 470 420 300
Mn,FeSi,,
Mn,Fe,Si,
Mn,l:e,Si, MnFe,Si,
0.21 0.28 0.25 0. 14 0.21 0.29 0.19 0.24 0.11 0.14 O-23
6(g)(2,4)*
Quadrupole 4(d)(l.3)*
0.38 040 044 0.43 0.45 0.33 0.37 0.36
060 0.59 0.24 0.56 0.48 0.5 1 0.54 0.47 0.50 0.50 0.51
splitting t&F) 6tg)t2,4)*
0.55 0.56 0.58 0.55 0.48 0.63 064 0.61
‘“‘All data in mmlsec relative to natural iron foil. ‘Identification of sites, enumerated on spectra.
Table 4. InternulJields’“’
Compound
Mn,l’eSi:, Mn,,le,Si,,
Mn,Fe:,Si, MnFe,Si,
Fe,Si,
Temp. (“K)
4(d)
78 4.2 78 4.2 3.0 7x 4.2 195 78 4.2
97 128 101 III 123 123 137 116 132 l3Y
187 228 177 209 226
300 78 4.2
91 123 132
168 228 243
6(x)
‘“‘All fields in kilo-Gauss relative IO iron foil for which the internal field at 300°K is taken as 330 2 3 kG [I?).
determined a value of 90” for this angle from a neutron diffraction study of the isomorphous Mn,Si, phase. In light of the assumptions made, 0 = 63” is a reasonable value for Mn,FeSi,. This value of 8, with a shift of the center of the inner four lines of Mn,FeSi, toward negative velocity, indicates V,, is negative at a 4(d) site. Johnson, et a/.[ l] assigned a positive value to V,, for 4(d) sites in Fe&, and this may have resulted from assuming 8 = 0” for 4(d) iron of Fe,!%,,. However this angle is difficult to determine
with any certainty from the complex spectrum of Fe&. Using a point charge model and interatomic angles and distances based on the parameters of the isomorphous Mn,Si, [g], a negative V,, is calculated for 4(d) sites. This can only be taken as qualitative theoretical support for the results of this investigation since covalency and 7r bonding effects are undoubtedly very large as indicated by the small value of H,l. (b) Mn,Fe,Si, Figures 2(a-d) show the Mossbauer behavior of Mn,Fe,Si:, over a wide range of temFrom the higher temperature perature. spectra, it is evident that more than one crystallographic type of iron is present in the system. On the basis of isomer shift and quadrupole splitting at several temperatures, Table 3, absorptions 1 and 3 of Figs. 2(a) and 2(b) are assigned to a quadrupole doublet resulting from 4(d) type iron as in Mn,FeSi,,. Peak 2 and the shoulder at positive velocity labeled 4 are assigned to another quadrupole doublet having a splitting of similar magnitude to the preceding 4(d) iron but a more positive isomer shift in all cases. In the following discussion this new doublet is attributed to iron in 6(g) lattice sites. The spectrum of Mn:,Fe,Si:, remains constant down to 78°K at which temperature magnetic
1516
K. S. V. 1.. NAKASIMHAN
CI a/.
in Fig. 2(d) for 3*O”K, i.e. only one type of iron appears to be significantly split by
f----+
magnetic
4 ,’
hyperfine
interaction
and the magni-
tude of II,,. Table 4. indicates this to be 4(d) iron. ‘I-he neutron diffraction study of Lander,
I:’
~1 ul. indicates that two of the 6(s) sites of are not magnetically ordered[41 Mn,Si:, although
crystallographically
are equivalent.
Hence.
for the absence inner
lines
all
6(g)
sites
a possible explanation
of noticeable
splitting
3 and 4 of Mn,,Fe,Si,,
of the
is that a
large fraction of the second iron preferentially the magnetically random 6(g)
occupies
sites. Such preferential occupation is difficult to explain along the usual lines of different crystal
field stabilization
involved.
energies of the sites
The exact electronic
configurations
for 4(d) and 6(,e) sites are not known and the 6(s) coordination environment is rather com-
-\.
f+--+C
plcx. On the other hand. the entropy of the system is expected to increase with filling of 6(v) as well as J(t/) sites. This suggests that 6(s)
sites are only
slightly
higher in energy
than 4(d) in Mn.,FeSi,, and Mn,Fe,Si,, phases. We next consider the relative occupation factors
for
factors
(recoil
temperature analysis.
different free
sites.
dependence
However.
.fhe
unknown
J
fractions) 1171 and their prevent
the analysis
an
exact
at high and
low temperature would be expected to differ significantly if the J‘values differ appreciably. A least squares fit to the spectrum of Mn,,FezSi,, at 400°K indicates peak 2 and shoulder 4 to correspond to 38 per cent of the total arca or therefore
Velocity Fig.
(mm/set)
2. Miissbauer spectrum of Mn,FqSi,, (b) 300°K. (cl 78°K. (d) 3WK.
at (a) 400°K.
splitting is noticeable. The general shape of this spectrum is reminiscent of that of Mn,FeSi,, at 78°K except for the two very intense peaks labeled 3 and 4. The spectrum at 4.2”K is essentially the same as that shown
From
0.76
iron
atoms
in 6(g)
a similar fit to the spectrum
sites.
of Mn,,Fe,-
Si,, at 3PK the intense absorptions 3 and 4 correspond to 42 per cent of the total absorption area. This includes the inner peaks of magnetically split 4(d) iron. If saturation effects are neglected. then the 6(x:) iron accounts for 3 I per cent of the total absorption area. i.e. 0.62 6(g) iron atoms. However. saturation is not negligible since peaks 3 and 4 of Mn,FeSi,, correspond to 25 per cent of the total area for spectrum l(c). Using this factor
MAGNETISM
AND
BONDING
to account for 4(d) intensity in peaks 3 and 4 of Fig. 2(d), 6(g) absorption corresponds to 25 per cent of the total absorption area, i.e. 0.50 6(g) iron atoms, This is a reasonable lower bound on the amount of 6(g) iron present. Possibly, all of the 6(g) absorption area of Mn:,Fe,Si:, at 3eO”K is not confined to the more intense central peaks as evidenced by the broadness (Table 2) of the peaks of spectrum 2(d) in Fig. 2. However, the approximate agreement of the percentage of total area corresponding to 6(g) iron for 4OWK and 3°K indicates that a significant fraction (between 3-a) of the second iron goes into 6(g) sites on formation of Mn,Fe,Si,.
IN A D8, 0
5
10 1
0
5
(d) MnFe,Si, A similar situation occurs in this phase except that the initial broadening effects of magnetic hyperhne splitting are evident even at room temperature. Comparison shows that the spectrum, Fig. 4(b), is very similar to that of Mn,Fe,,Si, at 300°K except that
(
%
:.
\/
”
b
‘.
”
:
(c) Mn,Fe&, The Mossbauer spectrum at 3OO”K, Fig. 3(a), shows the same general pattern of four lines as in Mn,,Fe,Si, although the increased 6(g) content leads to a better resolved spectrum. As for Mn:,Fe,Si,, lines I and 3 correspond to quadrupole split 4(d) iron while 2 and 4 represent similarly split 6(g) iron atoms. A least squares computer fit indicates that the spectra at 300°K and 195°K can be reconstructed from separate peaks as shown in Fig. 3(b) for the spectrum at 300°K where the area ratio (A, +A:,)/ (A., + AJ is 1 . I. This implies that occupation of 4(d) and 6(g) sites is nearly equal for Mn,Fe&. On decreasing the temperature, the system clearly shows two separate hyperfine patterns where the more diffuse pattern corresponding to a larger internal field is assigned to iron in 6(e) sites. It is reasonable to conclude that magnetically split 6(g) sites of Mn,Fe,Si, are now being occupied.
1517
STRUCTURE
10 i
.I 'p L 2"
-..
,.--\ \
Ai
C I.
5
.;
;
: :
:
1
_
‘,
.’
‘k;
Fig. 3. Miissbauer spectrum of Mn,l:e,Si:, at (a) 30O’K. (b) computer reconstructed spectrum at 300°K in terms of 4(d) and 6(x) absorptions, cc) 78°K. (d) 4.2”K. peaks I and 2 of the latter compound have coalesced into one broad intense peak in MnFe.,Si, at room temperature. Increasing the temperature to 420°K results in rapid fluctuation of internal magnetic fields causing line 4 in the spectrum of MnFe,Si, to narrow while the sloping baseline at positive velocity disappears. Similar behavior occurs for the
K. S. V.
1518
:
1
I NARASIMHAN
.. .’ .
H
Fig. 4. Mtissbauer spectrum of MnFe,Si,, at (al 470°K. (b) 300°K. (cl 195°K. (d) 78°K. (el4.2”K.
broad absorption at negative velocity, and at 47O”K, Fig. 4(a), a shoulder corresponding to peak I of 4(d) iron is evident. The best fit to the latter spectrum shows (A, +A3)/(A2 +A,)= 0.95, or nearly equal occupation of 4(d) and 6(g) sites as in Mn,Fe,Si,,.
et 01.
It is well known that for quadrupole split iron showing magnetic hyperfine splitting the I$, *s) + Ii, +$) transitions narrow more slowly than 1%.2-t) -+ 1’2.%3) transitions on going from a 6 line pattern to a quadrupole doublet1 181. The kets are the magnetic sublevels of the excited and ground nuclear energy states of 57Fe. With increasing temperature, the magnetic splitting can disappear and leave only a quadrupole doublet. Hence the behavior of MnFe,Si:, with increasing temperature is taken as tentatively indicating Vzp < 0 for 4(d) iron and k’,, > 0 for 6(g) iron. With decreasing temperature the phase MnFe,Si,, behaves in much the same way as Mn,Fe,Si,, except that magnetic interaction is now stronger and essentially complete hyperfine splitting occurs at higher temperatures. A comparison of the internal fields at different temperatures, Table 4, shows this trend of increasing ferromagnetic interaction with increasing number of iron atoms. (e) Fe&, The Mossbauer spectrum of Fe,Si, at 300°K has the same general appearance as that shown in Fig. 5(a) at 4.2”K. The internal fields corresponding to 4(d) and 6(g) iron of Mn,Fe.&, and MnFe,Si,, are calculated on the basis of two overlapping six line patterns as shown for Fe,Si,, at 4*2”K, where the lower pattern in Fig. 5(a) is that for 4(d) iron and the middle pattern for 6(g). It is evident that there is more uncertainty in the estimation of H,, for 6(g) iron than 4(d). This is in part attributable to the fact that the 6(g) sites are not all magnetically equivalent. For example. in Fe&,, fields corresponding to 6(g) iron range from about 190 to 240 kG. Johnson et al. [ I] made a similar observation for carbon stabilized Fe&,. Secondly, absorptions (dashed lines) attributable to Fe,,Si impurity are also present. This complicating feature was also found in the spectrum of Fe,%, by Shinjo and Nakamura[3]. who determined internal fields of 195 -t IO and 305 2 IO kG
MAGNETISM
AND
BONDING
1519
IN A D8, STRUCTURE
a
0
b 5 1
.: -6
Velocity
d
6
mmhec
Fig. 5. Miissbauer spectrum of Fe&, at (a) 4.2%. (b) 4.2”K. H; ,,,,,,,p,j= 26 kG.
for the two types of iron in Fe,Si and which agree with those found here. Hence, in Table 4 only the maximum value of H,, for 6(g) iron at each temperature is reported. In an effort to understand better the nature of magnetic ordering in Fe&, spectra were taken in external magnetic fields. A small field of the order of 1000 G had no effect on the spectrum at 4.2”K. A large field, 26 kG, caused a small decrease in the internal fields of both kinds of iron and although the signal to noise ratio is now lower, H,, for 4(d) iron is estimated as I22 5 IO kG while the maximum value for 6(g) is 227 -+ IO kG. The decrease in the respective internal fields is somewhat smaller than that expected if the system were a perfect ferromagnet with internal fields parallel. The system is magnetically saturated at this applied field and temperature, Fig. 7. and on this basis it is possible to make a crude calculation of the
H, ,,,,,,,,(, = 0,
angle between the internal fields from their observed decrease in an external field, assuming the resultant of the internal fields is collinear with the applied field. In the present case, this amounts to maximum angle of about 112”. Therefore it is assumed that the spins of the corresponding magnetic sublattices are canted at a maximum by approximately this angle. This result must be taken as approximate since the decreases in H, are small and difficult to estimate accurately from the spectrum. Furthermore, it is seen that the intensities of the spectral absorptions change in a complicated way which is not readily correlated with the observed decreases in internal fields. 4. MAGNETIC
MEASUREMENTS
The inverse magnetic susceptibilities of these compounds above their transition temperatures are shown as function of tem-
1520
K. S. V.
I_. NARASIMHAN
perature in Fig. 6. Mn,Si, exhibits typical antiferromagnetic behavior as expected and the Neel temperature, 62°K. agrees with previously reported values[4, 191. The variation in the susceptibility as iron is introduced into the structure reflects the decreasing antiferromagnetic influence and the conincrease of ferromagnetic spin comitant arrangements as the iron concentration increases. The transition temperatures also increase as the Fe&, end member is approached. The high temperature data for Fe,!+,, is not shown because this phase is unstable[20]. Table 1 summarizes the data from the magnetic measurements. In Fig. 7 are shown the magnetization curves for these materials. For Mn,_,Fe,Si,, x = I, 2, the curves reflect the antiferromagnetic behavior and for x = 4. 5 ferromagnetism is clearly evident. However, for x = 3 an intermediate state of magnetization can be inferred. IO’X35
CI (I/ 5. MAGNKTIC
STRUCTURE
The behavior of the susceptibility of the solid solution phases can be understood on the basis of the spin structures for the end members, Mn,Si,, and Fe,Si,,. The Mossbauer data show that the substitution of the first iron atom for manganese occurs in the 4(d) position. The susceptibility and magnetization curves for (Mn,)(MnFe)Si, indicate that the spin structure of this compound is only very slightly affected by the introduction of the iron atom and the effect is mainly manifested by an increase of the Niel and Weiss temperatures. The Mossbauer data for the phase Mn,,Fe,Si,, show that the second iron atom occupies mainly the h(g) position in the structure and an approximate formula indicating the probable distribution is (Mn,.,,Fe,,.,,)(Mn,,.,;,Fe, .,l,)Si,,. The magnetization for this phase, Fig. 7, is nearly unchanged from that of Mn,FeSi,, and the implication
Yn,_*F*yfi,
I
0
0
~3
200
3W
0
big.
6. ia)
I/x
400
100
500
200
600
MO
100
.oo
x=0
600
Xx)
600
Km
000
vs. 7‘ as a function of increasing Mn,Si,,-Fe,Si., system.
x=1
iron concentration
in the
MAGNETISM
AND
BONDING
IN A D8,
1521
STRUCTURE
b ?lO.,
20,
IO,,
.
0
loo
TEYPfRAWKC
Fig. 6(b).
200
300
400
so0
&
x(=3
(-1. I
I/x vs. 7‘ for hln,Fe,Si, and MnFe.,Si,. The magnetization latter compound is also shown.
must be drawn that the spin structure of this phase remains essentially unaltered except for a further increase in the Neel and Weiss temperatures. However, the susceptibility curve, Fig. 6(a). shows evidence of ferromagnetic interaction from the change in slope at about 350°K. This could be due to a predominant ferromagnetic interaction of the iron atoms in the 4(d) sublattice. The overall antiferromagnetic behavior becomes dominant at about 200°K. Mossbauer data obtained for Mn,Fe,,Si, can be interpreted on the basis that most of the third iron atom occupies a 6(g) position but with a definite increase of iron present in 4(d) sites. Thus a probable formulation is (Mn,.,Fe,.,)(Mn,,.,Fe,.,)Si,. The magnetic behavior exhibited by this phase indicates that its spin structure must be quite different from the previous compositions. The Mossbauer spectra are consistent with magnetically ordered 6(g) sites. The susceptibility and magnetization curves for this material definite-
vs. 7‘ for the
ly show the presence of ferromagnetic interactions with a sharp increase in the Weiss constant. The abrupt change in the transition temperature also supports this vrew of the spin structure. We attempted to obtain the ferromagnetic component of the magnetization, oO, from an extrapolation of the high field part of the (T vs. H curve on the assumption that the magnetization can be expressed as u = tr,,+xH where x is the antiferromagnetic susceptibility. The curve does not show a large degree of horizontal character at the fields available to us so that an extrapolation is expected to yield a low value of uo. A value of 09 pH per metal atom is obtained from the extrapolation of the high field portion of the curve. A moment of 0.26 p,] per metal atom is calculated on the basis of the following assumptions: (a) Iron contributes I cc,{per atom [I] and manganese contributes O-4 pB per atom [4] in the 4(d) site and the iron and manganese spins are oppositely aligned. The resultant moment for the 4(d) sublattice is 1.3 F~. (b)
1522
K. S. V.
0
2
4
Fig. 7. Magnetization
I_. NARASIMHAN
6
CI (11.
IO
vs. magnetic field intensity Mn,_,Fe,Si:,. 0 s x s 5.
The magnetic structure of the 6(x) sublattice retains the antiferromagnetic arrangement as in Mn,Si,[4]. Thus the total moment for (Mn,.,Fe,.,)(Mn,,.,Fe,.,)Si:, is I.3 ~~ or O-26 pII per metal atom. Since the material is not sufficiently saturated only a qualitative support for this spin scheme is to be expected. As indicated by the Mossbauer data. the introduction of the fourth iron atom to form the phase (MnFe,)(Fe,)Si, places two iron atoms into the 6(g) and two into the 4(d) positions and clearly ferromagnetic coupling among the atoms exist now in both sublattices. The behavior of the susceptibility and magnetization curves, Figs. 6. 7. is typical for a ferromagnetic compound. The magnetization curve for Fe&G,, is included for the sake of completeness. Powdered samples of MnFe,Si,, and Fe&:, were oriented in a magnetic field of about I4 kG and their X-ray diffraction patterns showed a strong enhancement of the 001 and a nearly complete disappearance of hkl lines indicating that the easy axis of magnetization is the c’axis. The difference in the permanent moments observed for Fe,Si,s and MnFe,Si,, Table 1, is significant. It can be explained on the basis that the ferromagnetic moment of one sublattice is canted with respect to the other and that the cant angle is a function of the
14
I6
for the system
composition. It was previously pointed out that the Mossbauer data are consistent with a maximum cant angle of about I 12” for atom for Fe,!&. The value 1. I I p,/metal the observed moment in ( MnFe2)( Fe,)Si,, can be accounted for on the basis that the atoms in the sublattices have parallel spin the sublattices are coupled alignments, parallel, and manganese occupies the magnetically random 6(g) positions. Using the values of 1 k,, for 4(d) iron and I.55 pH for 6(g) [ I ] iron the calculated moment is 143 F”/rnetal atom. It must be realized that such good agreement may be fortuitous but both the Mossbauer and magnetic data lend credence to this magnetic structure. The same magnetic structure for Fe&, i.e. random magnetic sites in 6(g), would again give rise to an expected moment of I.02 I,, as compared to the observed value of 0*9~,~. However. a cant angle of 120” between the sublattices will produce a resultant moment of 0.9~“. The required cant angle is close to the maximum value deduced from the Mossbauer spectrum of FesSi,, in an external held. Evidence for random spin in some of the 6(g) sites comes from the range of internal fields observed for 6(g) iron in Fe,Si, in the present investigation and also that of Johnson c’t al. [ 11. I.ander et al. [4] remarked that it
MAGNETISM
AND
BONDING
is difficult to understand why the 6(g) sites are divi’ded into two magnetically non equivalent groups one of which is random in Mn,Si,. This difficulty still exists in the case of MnFe,Si, and Fe&,. Perhaps the ‘randomness’ of the spin structure is due to a third sublattice for which the periodicity extends over many crystallographic unit cells. This could also account for the considerable range of hype&e field values which are observed. 6.
BONDING IN DS8 STRUCTURE
The bonding between an atom in the 4(d) site and surrounding silicon atoms is expected to be primarily covalent and the measured hyperfine field value confirms this expectation. Thus, it is reasonable to postulate that the low spin configuration is assumed by the metal atoms [2 I]. If Fe is considered to have contributed three of its electrons to the conduction band then the resultant low spin 3d” configuration would contain one unpaired electron and give rise to a moment of 1 pB in agreement with the reported value for that position by Johnson, et (I/.[ I]. It should be noted that the observed isomer shift, Table 3. for 4(d) iron is consistent with a low spin 38 configuration [23]. The discussion of the electronic configuration for the occupant of the 6(g) site is considerably more complicated because of the very complex near neighbor environment. The metal atom is bonded to five Si forming a trigonal bipyramid. The metal atom itself is outside this polyhedron. The covalent bonding to Si can be considered to impart a low spin, d”, configuration, i.e. I pH contribution to the observed moment. In addition there are ten other metal atoms nearby, six 6(g) atoms at distances varying from 2.82A to 2.87A and four 4(d) atoms at 2.95A. If one considers metallic type bonding to exist among these and assumes that the resultant contribution to the magnetic moment will be as in u iron, namely 2.2 pu, then an approximate 50-50 mixture of metallic and covalent bonding
IN A D8, STRUCTURE
1523
account for the observed moment of 1.55 pB for an atom in the 6(g) site. The explanations offered by Kanematsu [lo] and by Lecocq, erct1.[2] for the magnetic moment observed in Fe,!& rests on the assumption that the iron atom in the 4(d) site is purely metallic and that covalent bonding exists between iron in 6(g) and silicon. Kanematsu’s theory assigns 2 pB to the 4(d) site and 1 pB to the 6(g) site iron atom and he calculates a resultant moment per atom of 1.4 p,+ We believe that the assignment of the moments in the sublattices and the assumption of parallel coupling is not supported by our results. Similarly Lecocq CI al. assign a moment of 2.2~~ to the 4(d) Fe as in u iron and a moment of 0.606~~ to 6(g) Fe by analogy with nickel and obtain a calculated moment of I a243 pa/Fe atom for Fe&, still in rather poor agreement with the measured value.
could
Ackno~ledgemenrsResearch of the Materials Science group is sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force and the National Science Foundation. One of us, W.M.R., is pleased to thank the Chemistry Department of the University of Texas for the N.S.F.-U.S.D.P. Faculty Associate Award extended to him during the course of this research. The support of the Robert A. Welch Foundation is also gratefully acknowledged by R.L.C.
REFERENCES I. JOHNSON C. E., FORSYTH J. B., LANDER G. H. and BROWN P. J., J. nppl. Phgs. 39. 465 ( 1968). 2. LECOCQ Y.. LECOCQ P. and MICHEI. A., C.r. Acud. Sci. I’dcrris258.5655 ( 1964). 3. SHINJO T. and NAKAMURA Y., J. phys. Sec. Jopun 18,797 ( 1963). 4. LANDER G. H.. BROWN, P. J. and FORSYTH J. B., Proc. phju. SW. 91,332 ( 1967). 5. CON K. V., C.r. Acud. Sci. Paris 260, I 1I ( 1965). 6. UBEI.OCKER E. and l.ECOCQ P., C.r. Acud. Sci. Puris 262, 793 ( 1966). 7. AMARK K., BOREN B. and WESTGREN A.. Metalln~ir~. IS, 835 ( 1936). 8. ARQNSSON B.. Acrm chefn. sound. 14, 1414 ( 1960). 9. LANDER G. H. and BROWN P. J., P/Ii/. Meg. 16, 14ltl967). IO. KANEMATSU K., J. phy.~. Sot. Japcrn 17. 85 ( 1962).
1524
K. S. V. 1.. NARASIMHAN
11. NARASIMHAN K. S. V. I.., STEINI~INK H. and GANAPATHY E. V., J. oppl. Phys. 40. 51 (1969). 12. l:ONER S.. Rev. scienr. ln.strum. 30. 548 (1959). 13. RHODES E.. O’NEAI. W. and SPIJKERMAN J. J., NHS Tech. Nore 404. 108 t 1966). 14. GRANT R. W.. The Miisshouer Effect and Its Appliccttion in Chemisrry (Edited by (1. Seidel and R. Herher). Adwtrcrs in C‘hemisfry Series, No. 68, American Chemical Society. Washington, D. <‘. ( 1967). 15. EDWARDS P. R. and JOHNSON C. E.. J. chtm. Phys. 49. 2 I I t 1968). 16. RICKARDS R., JOHNSON C. E. and HII.1. H. A. O..J. c+c,m. f’hys. 48. 523 1 ( 1968). 17. WERTH El M <. H ., Mijsshouer E’cc.r: Princ+/c~s
18. 19.
20. 21.
22. 23.
CI ul.
and Appliwlicm. Academic Press. New York (1964). BI. UME. M., Plr.vs. Ret;. Leff. 14.96 (1965). I.ETUN S. M., GEI.‘D P. V. and SEREBRENNIKOV N. N.. RUSS. J. ofinorg. Chem. (Engl. transl.) 10,683 ( 1965). HANSEN M.. C‘onsti~rrtion of Binary Ailqs. p. 173. McGraw-Hill. New York (1958). ORGEL 1.. E.. An /ntroduc/& IO ‘frcr,l.sitiorr-M~rtrl Chemislr?: I.iprnd Field Theory. Wiley. New York t 1962). PRESTON R. S., HANNA S. S. and HEBERLXJ., P&s. Rec. 128.2207 (1962). REI t.F W. M.. BAKER W. A., Jr. and ERI<‘KSON N. E.,J. Am. c.hem. Sot.. 90. 4794 ( 1968).