Local distortion of MnO6octahedron in La1-xSrxMnO3+δ(x = 0.1 – 0.9):
An EXAFS study
R. Bindu, S. K. Pandey, Ashwani Kumara, S. Khalidb, and A. V. Pimpale
UGC-DAE Consortium for Scientific Research, University Campus, Khandwa Road, Indore
452 017, India
aSchool of Physics, Devi Ahilya University, Khandwa Road, Indore 452 017, India
bNational Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York –
Room temperature Mn K-edge extended X-ray absorption fine structure (EXAFS)
studies were carried out on La1-xSrxMnO3+δ(x = 0.1 – 0.9) compounds. It is found from
the detailed EXAFS analysis that the local structure around Mn sites is different from the
global structure inferred from X-ray diffraction, especially for x ≤ 0.4, indicating
presence of local distortions in MnO6octahedra. For the rhombohedral compounds, x =
0.1 to 0.3 the distortion is maximum for x = 0.1 and two bond lengths are seen- short one
in basal plane and long one in apical plane. For compounds with x = 0.4 to 0.8 two short
bonds in basal plane and four long bonds- two in the basal plane and remaining two in the
apical plane are seen. For the compounds up to x = 0.3 compositions long bond length
decreases and short bond length increases with increase in x whereas for the compounds
0.4 ≤ x ≤ 0.8 both types of bond lengths decrease. Such behaviour of bond lengths is an
indication of the changed nature of distortion from Jahn-Teller type to breathing type at x
= 0.4 composition.
Transition metal oxides show interesting behaviour like metal insulator transition,
colossal magneto resistance (CMR), charge ordering (CO), orbital ordering (OO),
magnetic ordering etc. Currently, in this field, much research activity [1-5] is focused on
manganites belonging to the perovskite family as they show CMR effect. The compounds
under study La1-xSrxMnO3+δ also show above interesting properties for specific ranges of
x. Over composition range 0.175 ≤ x ≤ 0.5 transition from a paramagnetic insulator to a
ferromagnetic metal is seen as a function of temperature. The coexistence of
ferromagnetism and metallicity was explained earlier in terms of the double exchange
(DE) model, however more recently Millis et al.  have pointed out the inadequacy of
DE mechanism in explaining the observed properties and proposed a mechanism based
on polaron formation. The doping of Sr at La sites causes two-fold effects: (1) to vary the
number of electrons (band filling) and hence change the electronic configuration, and (2)
the size effect, which changes the inter-atomic distances and bond angles. Depending
upon the amount of chemical pressure introduced into the lattice, changes occur in the
local environment and later on extend throughout the lattice. These changes are reflected
in the Mn-O bond distances and Mn-O-Mn bond angles, which play crucial role in
governing the physical properties. Thus Mn K-edge X-ray Absorption Spectroscopy
(XAS) studies would help in understanding the above effects.
EXAFS region starts from about 50 eV above the edge and extends typically up to
about several hundred electron volts. In this region, the photoelectrons have high kinetic
energy (E-E0is large), and single scattering by the nearest neighbouring atoms normally
dominates. The fine structure observed in this region is mainly because of interference of
the ejected photoelectron represented by the outgoing wave and the back-scattered wave
from the neighbouring atoms [7-9].
Many workers [10-15] have studied local structure around Mn ions in manganites
with varying temperature and magnetic field with the aim of understanding magneto-
transport properties. Extensive EXAFS study has been carried out for La1-xCaxMnO3. In
the case of La1-xSrxMnO3, reports on local structure studies are available mainly for lower
doped samples up to x < 0.5. Louca et al.  studied neutron diffraction pair distribution
function (PDF) of La1-xSrxMnO3 (0 ≤ x ≤ 0.4) at T = 10 K and 300 K. In the
rhombohedral metallic phase they have observed distortion in MnO6 octahedra for
compounds up to x = 0.3 compositions and attributed it to formation of Jahn-Teller (JT)
polaron. Billinge et al. (for La1-xCaxMnO3; x = 0.12, 0.21 and 0.25 compounds)  also
observed distortion in the MnO6octahedra and attributed it to breathing type. Hibble et
al.  carried out PDF by pulsed neutron diffraction and have reported no such
distortion in La0.7Sr0.3MnO3below Tc≈ 370 K, i.e. in metallic phase. Mellergard et al.
 have reported absence of local distortion below Tcfor x = 0.2 sample using neutron
diffraction and inverse Monte Carlo analysis. They observed distortion above Tc
attributing its link with Mn4+ion, which is different from JT type associated with Mn3+
ion. They remark that the second Mn-O peak observed by Louca et al.  may be an
analysis artifact. Shibata et al.  have carried out EXAFS study on La1-xSrxMnO3(0 ≤
x ≤ 0.475) for two temperatures 10 K and 300 K, in the photoelectron wave vector range
3-15 Å-1. They have also observed distribution in Mn-O bonds in rhombohedral structure.
The difference in long and short bond lengths is small in comparison to that observed by
Louca et al. . Recently, Mannella et al.  have also carried out XAS and XPS
studies on these compounds for x = 0.3 and 0.4 compositions and shown the presence of
JT distortion. They have shown correlation between the disappearance of the splitting in
the O K-edge pre-edge region and the presence of JT distortion.
It seems that the presence or absence of distortion in the MnO6 octahedra in
rhombohedral metallic ferromagnetic phase where double exchange is expected to be the
dominant mechanism is still an open question. Moreover, for x ≥ 0.5 compositions
although the phase diagram reveals interesting behaviour  little EXAFS work is seen
in the literature. The present work on Mn K-edge EXAFS covering the composition range
0.1 to 0.9 would thus yield information about the nature of distortion produced in MnO6
octahedra in this system. We present here, the room temperature (T = 293 K) EXAFS
studies for the first coordination shell for all the compounds. The compounds show
structural transitions from perovskite to layered type and rhombohedral to orthorhombic
with Sr doping [22,23]. We have seen distortion in the MnO6 octahedra over the entire
composition range covering different structures. For compounds up to x = 0.3
compositions with rhombohedral structure there are four short Mn-O bonds in the basal
plane and two long in the apical plane. For 0.4 ≤ x ≤ 0.8 compositions two short Mn-O
bonds in the basal plane and four long Mn-O bonds, two of which in the basal plane and
remaining two in the apical plane are seen. Here the x = 0.4 compound is rhombohedral
and rest are orthorhombic. In the end layered compound there are three short and three
long Mn-O bonds. The nature of distortion is of JT type for x < 0.4 and of breathing type
for x ≥ 0.4.
2. Experiment and data analysis
The details of sample preparation and characterization are given in our earlier
publication . In short, powder samples of La1-xSrxMnO3+δ (x = 0.1- 0.9 in steps of
0.1) were prepared by solid-state reaction of La2O3, SrCoO3 and MnO3 with repeated
grinding and calcinations at 1000 °C. Final sintering for all the samples was done at 1400
°C for two days to have better crystalline quality. All the samples were characterized by
X-ray powder diffraction at room temperature and found to be single phase.The
Rietveld analysis of diffraction patterns revealed that the crystal structure is
rhombohedral for 0.1 ≤ x ≤ 0.4, orthorhombic for 0.5 ≤ x ≤ 0.8, and layered for x = 0.9
compositions. Iodometric redox titration was also carried out to estimate the oxygen
nonstoichiometric δ, which is given in Table 1. From the Table it is evident that while
the compounds x ≤ 0.4 are oxygen nonstoichiometric, the compounds 0.5 ≤ x ≤ 0.9 are
nearly stoichiometric within the experimental accuracy.
Room temperature Mn K-edge XAS experiments were done at beamline X-18 B
at the National Synchrotron Light Source, Brookhaven National Laboratory. The storage
ring was operated at 2.8 GeV, 300 mA. The beamline used a Si (111) channel cut
monochromator. The horizontal acceptance angle of the beam at the monochromator was
1 mrad. The vertical slit size used in this experiment was 1 mm, corresponding to an
energy resolution of 0.8 eV at the Mn K-edge. The average photon flux for this
bandwidth was 1010photons/sec. The monochromator was detuned by 35 % to reduce the
higher harmonics. The incident (I0) and the transmitted beam (It) were measured by
sealed ion chambers, with the combination of gases for appropriate absorption. Standard
Mn foil was placed between the detectors Itand Ireffor energy reference and to check the
stability of the beamline and optical system. The samples sieved through a 400 mesh
were spread uniformly on a cellophane tape and a four-fold of this tape was used to
minimize the pinhole and brick effects.
EXAFS fitting was carried out by using UWXAFS 3.0 software . The
threshold energy, E0, for all the spectra was taken as the first inflection point in the
absorption edge region. After the background subtraction, the absorption coefficient µ(E)
was converted to µ(k), where k = (2m(E-E0)/ħ2)1/2is the magnitude of wave vector of the
ejected photoelectron. The XAFS oscillation χ(k) is defined as, (µ-µ0)/µ0, where µ0is the
embedded atom absorption coefficient. The Fourier transform (FT) to the r-space was
taken in the k range 3-13 Å-1 by Fourier transforming k2χ(k) with Hanning window. First
shell fitting was done in the Fourier filtered k space in the range 0.76 to 1.93 Å for all the
compounds x ≤ 0.8. For x = 0.9 composition, the EXAFS fitting was carried out in the
range 0.89 to 1.93 Å. The upper limit of the filtering window was chosen by checking
the FT of the theoretical χ(k) calculated using FEFF6.01 , in which the peaks related
with the MnO6 octahedron were observed only below the upper limit indicated above.
The overall many body reduction factor S02was fixed to 0.82 for all the samples. The
back scattering amplitude and phase shifts were calculated using FEFF6.01 for LaMnO3
and the same were used for all the compounds. During the fitting N was kept fixed as per
the choice of model structure and only σ2was varied to reduce the number of correlated
parameters. Further, several different fits were performed in each case to verify the
robustness of the parameters. Both- simultaneous variation of different fitting parameters
as well as their independent variation was tried. A fit is considered to be good if the
goodness of fit parameter given by R-factor is less than 0.02 .Since for every
composition fitting was tried using different structure models, the model that resulted in
the least R-factor was considered to represent the local structure for that particular
We have used different model structures in order to get the information about the
local structure in these compounds. The average structure inferred from X-ray diffraction
for the compounds up to x = 0.4 compositions is rhombohedral . Therefore, one
expects that all the six Mn-O bonds of MnO6 octahedra should also be equal at local
level. Hence we tried 6 model consisting of only one shell with six equal Mn-O bond
lengths. Many workers [16,17,20] have reported the distorted MnO6 octahedra at local
level, which is similar to the distortion of MnO6 octahedra in LaMnO3. Structure of
LaMnO3is orthorhombic with four Mn-O bonds in the basal plane and two in the apical
plane. While in the apical plane the Mn-O bond length is 2.17 Å, in the basal plane these
are 1.91 Å and 1.97 Å . The long and short bond lengths differ by 0.26 Å. However,
the difference between the two short Mn-O bond lengths is just 0.06 Å. Moreover, it is
expected that the distortion of MnO6 octahedra would reduce with the doping of Sr.
Therefore, we also modeled local structure using 4+2 model consisting of two-shells with
four equal short bond lengths and two equal long bond lengths. This allows us to remain
within the limits of our experimental EXAFS resolution, ∆R = π/2 (kmax- kmin), for the k-
range used for fitting. According to our XRD results for compositions 0.5 ≤ x ≤ 0.8 the
structure is orthorhombic. In these compounds the bond lengths of two Mn-O bonds in
the basal plane are almost same as that of the two Mn-O bonds in the apical plane but the
bond lengths of the rest two bonds in the basal plane differ from them . Hence in
addition we used 2+4 model, which consists of two-shell fitting with two equal short
bond lengths and four equal long bond lengths. Similarly, based on the XRD results we
used 3+3 model consisting of two-shell fitting with three equal short bond lengths and
three equal long bond lengths for x = 0.9 composition.
In figure 1, we show the variation of absorption µt for different compositions in
the pre-edge, edge and XANES regions from about 25 eV below the edge to 50 eV above
it. Here the edge position is defined as usual as the inflection point on the main
absorption edge. It is seen to vary systematically with composition as shown in the inset
to this figure. There is roughly a linear increase in the edge position as the percentage of
divalent Sr ions replacing the trivalent La ions increases. Similar variation in the edge
position was observed in other manganite systems [20,27]. The pre-edge structure shows
two peaks marked by 1 and 2 in figure 1 and the first peak on the high energy side of the
absorption edge is marked as 3. These features are similar for all the samples. Simulation
studies have shown that these features are sensitive to the lattice distortion . If the
lattice distortion decreases, intensity of these features increase. We observed the
increased intensity of peaks 1, 2 and 3 with increase in x for compounds up to x = 0.8
compositions indicating that lattice distortion decrease with x. For the end compound it
decreases indicating that layered type structure is more distorted than the perovskite
structure. Details of pre-edge and XANES structure will be discussed elsewhere.
Figure 2 shows the k2weighted EXAFS spectra χ(k) for all the compounds. The
spectra are highly structured as expected from the powder crystal nature of the samples.
These spectra reveal systematic variations in peak shapes and intensities with x,
indicating changes in the local structure around Mn sites. These changes are even more
prominent when the structure changes from perovskite to layered type at x = 0.9, thus
hinting at different local environment for Mn sites in x = 0.9 composition. The FT of
these k2χ(k) spectra taken between 3 and 13 Å-1 is shown in figure 3. These spectra are
uncorrected for the central and back-scattered phase shifts. We observe a main peak,
marked 1 in the figure, which is ascribed to the first coordination shell of the central Mn
atom comprising of the O-atoms of the MnO6octahedron. Further peaks corresponding to
successive coordination shells are also seen. Peak 1′ close to the peak 1 for x = 0.9
composition can be identified with layered type structure. Our XRD work  reveals
that this compound is layered type with hexagonal phase possessing 6 layered with
stacking sequence of ABCACB type. In this compound Mn is surrounded by six oxygen
atoms at average distance of 1.9 Å and also by one Mn atom at a distance of about 2.5 Å.
Hence, peak 1′ arises from this neighbouring Mn atom. The intensity of the first peak for
x = 0.1 composition is lowest, indicating that its MnO6octahedron is most distorted. With
increase in the value of x the first peak becomes sharper indicating reduced distortion of
the octahedra with doping.
In figures 4, 5 and 6 representative fits for x = 0.2, 0.4 and 0.6 compositions are
shown. It is evident from these figures that 6 model does not describe the experimental
data at higher k values for any of the compositions. This would imply that all the Mn-O
bonds are not equal and MnO6 octahedron is distorted in these compounds. Between
different two shell-fits, 4+2 model gives the best fit for x = 0.1, 0.2, 0.3 compositions,
3+3 model for x = 0.9 composition and 2+4 model for rest of the compounds. Figure 5
shows the fits obtained using different models for x = 0.4 compound. It is clearly seen
from this figure that 2+4 model describes the experimental spectrum better in the whole
k-range used for the fitting in comparison to 4+2 model. One shell-fit gives undistorted
MnO6 octahedron with only one Mn-O bond distance with large Debye-Waller factors
whereas two shell-fit gives distorted octahedron with two Mn-O bond distances, with one
small and one large Debye-Waller factors for 0.1 ≤ x ≤ 0.3 compounds and with two
small Debye-Waller factors for rest of the compounds, Table 1. Shibata et al.  and
Subias et al.  who carried out EXAFS studies on La1-xSrxMnO3(0 ≤ x ≤ 0.475) and
La1-xCaxMnO3systems, respectively also observed similar behavior.
Figure 7 shows the Debye-Waller factors obtained from two shell-fits for all the
compounds. In this figure σ12and σ22are Debye-Waller factors corresponding to short
and long bonds, respectively. For 0.1 ≤ x ≤ 0.3 compositions σ12are small and σ22are
large, whereas for rest of the compounds opposite behavior is observed. While for x ≥
0.4 no appreciable change is observed in the values of σ12and σ22, for x ≤ 0.3 the σ12
decreases and σ22increases with x. At x = 0.3, the value of σ22is 0.0194 Å2. Such a
large value of Debye-Waller factor indicates that there may be a large distribution in long
bond lengths in the compound x = 0.3. This may result from the possibility that the
number of nearest neighbours (NN) with short bond lengths is smaller than 4 and that
with the long bond lengths is greater than 2 as a consequence of a combination of 4+2
and 2+4 model. We checked this possibility explicitly by varying the number of NN
with short and long bond lengths while keeping the total number of NN fixed at six. We
find that the fit improves considerably when the number of short and long bonds is 2.8
and 3.2, respectively with corresponding Debye-Waller factors as 0.0098 Å2and 0.0012
Å2. The values of bond lengths for the short and long bonds are found to be 1.907 Å and
1.946 Å. In the light of this result, we also checked if the quality of fit improves for x =
0.2 and 0.4 compounds if the number of NN with short or long bond lengths are varied
keeping the total number of NN fixed at six. We find that the best fits are obtained only
for structures of MnO6octahedron with 4 short, 2 long and 2 short, 4 long bond lengths
for x = 0.2 and 0.4 compounds, respectively. These results indicate that for some
composition between x = 0.2 and 0.3, a deviation from the 4+2 model starts and
completely changes to 2+4 model for 0.3 < x < 0.4. This would make the transition from
4+2 model (with 4 short and 2 long bonds) to 2+4 model (with 2 short and 4 long bonds)
a smooth one
Mn-O bond lengths obtained from EXAFS fitting using different models are summarized
in figure 8. As mentioned above up to x = 0.3 compositions 4+2 model gives the best fit.
In this model we have taken four short Mn-O bond distances in basal plane and rest two
long Mn-O bond distances in apical plane of the MnO6octahedron. With increase in x,
the bond length in the apical plane decreases and that in the basal plane increases. For 0.4
≤ x ≤ 0.8 compounds 2+4 model gives the best fit. In this model two short Mn-O bond
distances are in basal plane and out of four long Mn-O bond distances, two are in the
basal plane and the other two are in the apical plane. For these compounds both types of
bond distances decrease with increase in x and show almost linear behaviour. The two
lines connecting the points of small and large bond distances are almost parallel. In x =
0.9 composition 3+3 model gives the best fit to the data. In this model we have
considered three short Mn-O bond distances in the basal plane and out of three long Mn-
O bond distances, one is in basal plane and remaining two are in apical plane. However,
the short and long Mn-O bond lengths differ by ~ 0.03 Å and thus the single shell model
should also be adequate. The single shell model gives a fit with R-factor of 0.008, which
is somewhat larger than the R-factor of 0.002 for 3+3 model. This difference in R-factor
may be due to use of larger number of parameters used in fitting for the 3+3 model, as
they give extra freedom to adjust the parameters to get best fit. In the 3+3 model we have
two distances and two Debye-Waller factors as opposed to only one distance and one
Debye-Waller factor for single shell model. It may be seen that the Debye-Waller factor
and bond length for the single shell model are 4.65×10-3 Å2and 1.905 Å respectively,
which are in between the two Debye-Waller factors and two bond distances for the 3+3
model, Table 1. Thus the 3+3 model seems a better fit only from the R-factor point of
The X-ray diffraction studies have clearly shown that our compounds La1-
xSrxMnO3+δare rhombohedral (0.1 ≤ x ≤ 0.4), orthorhombic (0.5 ≤ x ≤ 0.8), and layered
type (x = 0.9) in structure . EXAFS studies reveal that all the compounds show
distortion in the MnO6 octahedron. On general grounds if one has double exchange
behaviour in these compounds such distortion should not appear in the rhombohedral
structures, although it may exist in the tetragonal and orthorhombic structures. Such
distortion in all structures including rhombohedral may be understood in terms of two
processes: (i) size effect, including the presence of oxygen non-stoichiometry and (ii)
electronic effect due to changed valency of the dopant ion. A combination of these can be
interpreted in terms of electron-phonon coupling and electron polarization causing in the
limit electron self trapping and polaronic effects [11,30].
The Mn-O bond distances are varying in three different fashions over the entire
composition. In the first region (0.1 ≤ x ≤ 0.3) the 4+2 model fits better, in the second
region ((0.4 ≤ x ≤ 0.8) 2+4 model and finally in the third region (x = 0.9) 3+3 model. We
now discuss these three regions.
Region-1: compounds up to x = 0.3 composition lie in this region. Here the Mn-O bond
distances in the apical plane decrease and those in the basal plane increase with
composition, figure 8. The difference in these two bond lengths for x = 0.1 composition
is largest, 0.19 Å and that for x = 0.3 composition is smallest, 0.08 Å, Table 1. The
observed XRD structure of the compounds up to x = 0.4 is rhombohedral having all six
Mn-O bond distances in MnO6octahedra equal . The distribution in the Mn-O bond
lengths thus indicates that the MnO6 octahedra are distorted in these compounds.
Presence of such a distortion at local level may be attributed to the formation of polaron
in consonance with earlier work on manganites [16,17,20,31]. Louca et al.  have
attributed this kind of distortion to the formation of Jahn-Teller (JT) polaron. The
theoretical studies reveal existence of distortion with volume of MnO6 octahedra
remaining the same to be consistent with JT polaron formation. Louca et al.have
modeled their experimental neutron diffraction data in such a way that the volume of the
MnO6 octahedron remains same but the number of short and long bonds vary as x
changes. In our case we have fixed the number of short bonds to 4 and that of long bonds
to 2 and varied the both type of bond lengths. We did not get the same volume for all the
three compounds. This deviation from volume preserving behavior may be due to the
contribution of ionic size effect in creating distortion in the octahedra.
Region-2: The compounds 0.4 ≤ x ≤ 0.8 lie in this region. Here the variation in the bond
distances shows different behaviour to that in the region-1. Both short and long bond
distances decrease with increase in x, indicating that the volume of the MnO6octahedron
decreases with x. Such a behavior cannot be identified with the formation of Jahn-Teller
polaron. This distortion at local level thus may be thought of as breathing type. Since the
structure for x = 0.4 is rhombohedral, the presence of long and short bond lengths for this
composition gives indication of polaron formation at local level. The structure of the
remaining compounds is orthorhombic, and it is expected to show distribution in Mn-O
bond distances. There is a clear difference in the average bond length estimated from
XRD  and the EXAFS results for the bond lengths, Table 1. The observed decrease of
bond length with increase in x may occur due to ionic size effect since replacing La3+by
Sr2+ion makes tolerance factor closer to unity.
From figure 8 it is seen that there is a qualitative change in the behaviour of Mn-O
bond length as x increases beyond 0.3. The XRD studies reveal a structural
transformation from rhombohedral to orthorhombic in the composition range 0.4 ≤ x ≤
0.5. Further, as mentioned in the results section, the transition from the 4+2 model starts
for some composition between 0.2 < x < 0.3 and completes for x between 0.3 and 0.4.
One may thus conclude that local changes in MnO6octahedra as a function of x start well
before global structure changes and this transformation is not an abrupt one but occurs
(3) Region-3: The last compound (i.e. x = 0.9) lies in this region. The average structure
of this compound is of layered type with hexagonal phase possessing 6 layers with
stacking sequence of ABCACB type . The EXAFS analysis for this composition
revealed that MnO6 octahedra in this compound have three short and three long Mn-O
bonds in agreement with the XRD results.
The room temperature EXAFS studies were carried out at Mn K-edge for the
complete series of La1-xSrxMnO3+δ, x = 0.1 to 0.9. Detailed analysis of EXAFS spectra
revealed that local structure of MnO6 octahedron can be described by two long Mn-O
bonds in the apical plane and four short bonds in the basal plane for compounds with x up
to 0.3. However, for 0.4 ≤ x ≤ 0.8 compositions it was found that there were two short
Mn-O bonds in basal plane and out of remaining four long bonds; two were in the basal
plane and other two in the apical plane. The observed distribution in the Mn-O bond
lengths shows that MnO6 octahedra are distorted for all the compounds and the local
structure is different from the average one, especially for x ≤ 0.4. The Debye Waller
factors also showed cross over behavior at x = 0.4. The change in the behaviour of long
and short Mn-O bond lengths at x = 0.4 is interpreted as the change in nature of
distortions from Jahn-Teller type to breathing type at x = 0.4.
RB and SKP thank UGC-DAE CSR for financial support. AK thanks CSIR, Government
of India for senior research associate position (pool scheme).
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Figure 1 Normalized pre-edge and XANES spectra at the Mn K-edge of
La1-xSrxMnO3+δ (0.1 ≤ x ≤ 0.9). Inset shows the chemical shift of these
compounds with doping with respect to x = 0.1 composition.
k2- weighted EXAFS spectra χ(k) of La1-xSrxMnO3+δ(0.1 ≤ x ≤ 0.9).
Figure 3 Fourier Transform of k2χ(k) for La1-xSrxMnO3+δ(0.1 ≤ x ≤ 0.9).
Figure 4Fitted patterns of La0.8Sr0.2MnO3+δ compound using 6 model having six
equal Mn-O bonds and 4+2 model having four short and two long Mn-O
Figure 5Fitted patterns of La0.6Sr0.4MnO3+δ compound using 6 model having six
equal Mn-O bonds, 4+2 model having four short and two long Mn-O
bonds and 2+4 model having two short and four long Mn-O bonds.
Figure 6 Fitted patterns of La0.4Sr0.6MnO3+δ compound using 6 model having six
equal Mn-O bonds and 2+4 model having two short and four long Mn-O
Figure 7 Debye-Waller factors σ12and σ22corresponding to short and long bonds,
respectively obtained from two-shell fitting for La1-xSrxMnO3+δ(0.1 ≤ x ≤
0.9). The values of Debye-Waller factors for 0.1 ≤ x ≤ 0.3, 0.4 ≤ x ≤ 0.8
and x = 0.9 correspond to 4+2 model, 2+4 model and 3+3 model,
respectively. For details please see the text.
Figure 8 Short bond length (R1) and long bond length (R2) obtained from two-shell
fitting for La1-xSrxMnO3+δ(0.1 ≤ x ≤ 0.9).