Spin crossover in (Mg,Fe)O: A Mössbauer effect study with an alternative interpretation of
X-ray emission spectroscopy data
I.Yu. Kantor, L.S. Dubrovinsky, C.A. McCammon
Online supplementary materials
Mössbauer spectroscopy data analysis.
decreases smoothly and continuously with increasing
pressure for both HS and LS components. The
systematic difference between high- and low-spin
components is about 0.15 mm/s. The quadrupole
splitting of the LS component was fixed to zero since its
value was too small to resolve, and the pressure
evolution of HS quadrupole splitting is discussed in
detail elsewhere2. Briefly, we believe that the slight
change in slope between 30 and 40 GPa is due to a
small structural rhombohedral distortion.
The sample studied has a large Mössbauer
thickness due to 57Fe isotopic enrichment, even at
high compression where the sample is thin. We
estimated the dimensionless effective thickness at 7090 GPa to be approximately 15, which is high
compared to commonly used thicknesses in
conventional Mössbauer spectroscopy. The thickness
of the source is also higher than in conventional
experiments due to the higher concentration of 57Co
in a point source, but thickness effects in the source
are much smaller compared to those in the absorber.
At a source age of six months, which is when the
measurements reported in this work were made, the
dimensionless effective thickness of the source is less
than 2.
The high thickness of the absorber results in
significant internal multiple absorption, which could
significantly distort the relative areas of the two
subspectral components in the mixed spin region.
Thickness corrections can be accounted for using a
full transmission integral calculation1. We used
NORMOS software (commercially available fitting
program written by R.A. Brand and distributed by
Wissenschaftliche Elektronik GmbH, Germany) to
perform simultaneous full transmission integral
calculations and non-linear least-squares spectrum
fitting. After correction for thickness effects the
linewidth (full width at half maximum) of the LS
component decreases from 0.81 mm/s to 0.40 mm/s,
which is only slightly greater than the linewidth
recorded for iron metal using the same source. The
relative areas are not significantly affected by
thickness effects, no more than 10-15%.
The fraction of LS Fe2+ calculated using the full
transmission intergral is not exact, because the
absorption area of a component in the Mössbauer
spectrum depends also on the recoil-free fraction f.
Since the f-factor is not expected to be equal for HS
and LS components, the resulting LS fraction should
be corrected using the fHS/fLS value. This ratio is not
expected to deviate significantly from unity, however,
particularly at high pressure in the case of
ferropericlase; hence we estimate that the resulting
values of S (Fig. 2) will be affected by less than 5%.
The pressure evolution of the centre shift and
quadrupole splitting of high- and low-spin Fe2+ in
ferropericlase is shown in Fig. S1. The centre shift
1.1
1.0
CS (mm/s)
0.9
0.8
0.7
a
0.6
0.5
0
20
40
60
80
100
120
80
100
120
Pressure (GPa)
1.4
1.2
QS (mm/s)
1.0
0.8
0.6
0.4
b
0.2
0.0
0
20
40
60
Pressure (GPa)
FIG. S1. Pressure evolution of the centre shift (a) and
quadrupole splitting (b) for the high- and low-spin (solid and
open circles, respectively) of Fe2+ in ferropericlase. CS values
are given relative to α-Fe at ambient conditions.
X-ray emission spectroscopy analysis.
The traditional “comparative” method of Fe-XES
data analysis at high pressure involves the following
steps3-8:
-1-
Kantor et al.
Spin crossover in (Mg,Fe)O…
online supplementary materials
peak area) will be therefore artificially reduced. Below
a certain value of ∆E further changes in spectral shape
would become lower than the noise level and a weak
peak will be “lost”. Moreover, below a particular value
of ∆E the weak peak visually disappears in the
spectrum, which can confuse the analysis. We
performed a synthetic test to demonstrate this
possibility. We simulated four artificial spectra,
consisting of two Lorentzian peaks with fixed
intensities and widths and with only the energy
difference changing between them. These spectra,
treated according to the abovementioned procedure, are
shown in Fig. S2a. The amplitude ratio of the two peaks
is 5/1, and the FWHM is 2 (arbitrary units). The
difference in the peak position is 3, 2.5, 2, and 1.5 units
for spectra a, b, c and d, respectively.
- All spectra are normalized to unity (relative to
the maximum value of main Kβ peak)
- The energy scale of all spectra is shifted so that
the maximum value of the Kβ peak occurs at the
same position (this compensates for the pressure
shift of emission energy)
- The XES spectrum collected at the final
pressure is subtracted from each of the other spectra
- The area of the Kβ' peak is measured in the
residual spectra and normalized to the value at the
starting pressure.
After this procedure a high-spin state fraction is
obtained as a function of pressure (varying from one
at the initial pressure to zero at the final pressure) and
is used as an indication of the spin crossover. This
algorithm was suggested and tested on Fe and FeS3,4
and was also used in the analysis of XES data from
ferropericlase6,8 and (Mg,Fe)SiO3 perovskite7 at high
pressures. This spectral analysis method is based on
spectra comparison and will be further referred to as
the comparative analysis method.
The comparative analysis method is applicable
only if three main conditions are satisfied:
(i): At ambient (initial) pressure the material is in
a purely high-spin state
(ii): At highest (final) pressure the material is in a
purely low-spin state
(iii): The energy separation between the Kβ' and
Kβ peaks remains constant with pressure.
The consequences of the first and second
conditions are obvious – if the initial and/or final
states are not purely high- and low-spin states, the
resulting high-spin fraction values will vary in a more
narrow range than one and zero. The ambient
pressure spin state can be easily confirmed by many
traditional methods, while the spin state at a given
final pressure is not usually known a priori. Indirect
proof that the spin transition is complete is the
observation that the resulting high-spin fraction does
not change further with increasing pressure (for
example the XES data do not change significantly
near ~7044 eV with increasing pressure).
Nevertheless, at least two scenarios in addition to the
completion of spin crossover could give such results:
(1) an intermediate spin state (with S = 1) could be
stable in a certain pressure range (hence the transition
is finished at only 50%); and (2) the energy
separation between the Kβ' and Kβ peaks becomes
small (see below).
The necessity of the third condition (∆E =
const) is not obvious and should be considered in
more detail. In the case of a weak peak shifting
towards a more intense one, the contribution of the
weak peak to the total intensity at the maximum point
increases. After the intensity normalization
procedure, the total subspectral area (and also the Kβ'
1.0
1.00
a (∆E = 3.0)
b (∆E = 2.5)
c (∆E = 2.0)
d (∆E = 1.5)
0.75
Intensity, arb. units
0.8
0.50
0.25
0.6
0.00
3.0
2.5
2.0
1.5
∆E
0.4
a
0.2
0.0
b
0
a-d
b-d
c-d
2
4
6
8
10
12
14
16
18
20
E, arb. units
FIG. S2. a) Simulated spectra consisting of two Lorentzian
peaks with fixed shape and intensity and varying relative
position. The inset shows the apparent decrease of satellite
peak intensity (obtained using the comparative analysis
method) as a function of energy separation ∆E.
b) Simulated difference spectra constructed from the curves
in Fig. S1a.
Spectrum d was subtracted from all the rest, and the
residual spectra are shown in Fig. S2b. The area of the
positive peak in the residual spectra decreases with
decreasing energy separation (Fig. S2a, inset), but the
actual area ratio of the two peaks remains constant. This
example shows that changes in the relative peak
position would affect the area of the weak peak
-2-
Kantor et al.
Spin crossover in (Mg,Fe)O…
online supplementary materials
calculated by the abovementioned procedure. Note
that visually the final spectrum (d) appears to consist
of one peak, although in reality it contains two. The
main evidence for such a scenario is the presence of a
second negative peak in the residual spectra, as seen
in Fig. S2b. If only the intensity of the weak peak
decreases, the negative peak would never appear in
the difference spectrum.
Is there any reason to expect the energy
separation ∆E between the Kβ' and Kβ emission
peaks to change with increasing pressure? The
answer is yes. ∆E is a product of the spin number S
and the value of the exchange integral J3, which has a
volume (pressure) dependence. ∆E should therefore
change upon compression even at a constant value of
S. Fig. S3 shows the experimental XES data for
(Mg0.75Fe0.25)O at ambient pressure and at 79 GPa
(data of Lin et al.8), as well as the difference between
these two spectra. It is clearly seen that the negative
peak is present in the residual spectrum (compare
with Fig. S2b), indicating that ∆E indeed decreases
with pressure, and that the Kβ' satellite peak is still
present in the spectrum at 79 GPa.
addition, the spin transitions in Fe and FeS are also
associated with structural changes, so spin crossover
occurs in a narrow pressure range, contrary to the case
in ferropericlase.
References
1
T.E. Cranshaw, J. Phys. E 7, 122 (1974).
2
I. Kantor, L. Dubrovinsky, C. McCammon et al., Phys.
Chem. Miner. in press (2006); DOI 10.1007/s00269-0050052-z
3
J.P. Rueff, M. Krisch, Y.Q. Cai, A. Kaprolat, M. Hanfland,
M. Lorenzen, C. Masciovecchio, R. Verbeni, and F. Sette,
Phys. Rev. B 60, 14510 (1999).
4
J.P. Rueff, C.C. Kao, V.V. Struzhkin, J. Badro, J. Shu, R.J.
Hemley, and H.K. Mao, Phys. Rev. Lett. 82, 3284 (1999).
5
J. Badro, V.V. Struzhkin, J. Shu, R.J. Hemley, H.K. Mao,
C.C. Kao, J.P. Rueff, G. Shen, Phys. Rev. Lett. 83, 4101
(1999).
6
J. Badro, G. Fiquet, F. Guyot, J.P. Rueff, V.V. Struzhkin, G.
Vanko, G. Monaco, Science 300, 789 (2003).
1.0
Intensity, arb. units
0.8
7
J. Badro, J.P. Rueff, G. Vanko, G. Monaco, G. Fiquet, F.
Guyot, Science 305, 383 (2004).
0.1 MPa
79 GPa
difference spectrum
8
J.F. Lin, V.V. Struzhkin, S.D. Jacobsen, M.Y. Hu, P. Chow,
J. Kung, H. Liu, H.K. Mao, R.J. Hemley, Nature 436, 377
(2005).
0.6
0.4
0.2
0.0
negative peak
positive peak
-0.2
7020
7030
7040
7050
7060
7070
Energy, eV
FIG. S3. Experimental XES data of (Mg0.75Fe0.25)O (Ref.
8) at ambient pressure and at 79 GPa, and their difference
spectrum. The presence of a negative peak in the residual
spectrum is clearly seen, indicating that the Kβ' satellite
peak is still present in the spectrum at 79 GPa, implying
the presence of some high-spin Fe2+.
These examples demonstrate that comparative
analysis of XES data for determination of spin state
can lead to incorrect results. The comparative
analysis method has only been verified for metallic
Fe and FeS3,4, where in both cases the spin transition
occurs at relatively low pressures (<15 GPa). The
effect of pressure on ∆E is therefore small. In
-3-