Eur. J. Mineral
Fast Track DOI: 10.1127/0935-1221/2009/0021-1932
Fast Track Article
HP-HT mineral physics:
implication for geosciences
Nuclear resonant X-ray spectroscopy of (Mg,Fe)SiO3 orthoenstatites
JENNIFER M. JACKSON1,*, EMILY A. HAMECHER1 and WOLFGANG STURHAHN1,2
1
Division of Geological and Planetary Sciences, Seismological Laboratory, California Institute of Technology,
1200 E. California Blvd, Pasadena, CA 91125, USA
*Corresponding author, e-mail: [email protected]
2
Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, USA
Abstract: We present nuclear resonant inelastic X-ray scattering (NRIXS) and synchrotron Mössbauer spectroscopy (SMS)
measurements, both nuclear resonant X-ray spectroscopic methods, on synthetic samples of orthoenstatite-structured
(Mg,57Fe)SiO3, a representative component in Earth’s upper mantle. All measurements were performed at ambient conditions.
NRIXS spectra were measured for three samples of orthoenstatite containing 20, 13, and 7 mol% FeSiO3. The Debye sound velocities
were determined from the low-energy region of the partial phonon density of states (PDOS). With known density and bulk modulus,
the shear modulus, compressional and shear wave velocities have been computed. The sound velocities obtained from NRIXS are in
good agreement with sound velocities obtained using Brillouin spectroscopy and ultrasonic methods for similar compositions. An
important advantage of NRIXS is access to additional thermodynamic information, such as the average force constant, mean-square
displacement, obtained from the PDOS. We discuss the contribution of the vibrational spectra to these quantities. In addition to the
PDOS, the electronic environment of the iron sites in (Mg0.8757Fe0.13)SiO3 orthoenstatite was determined using 57Fe SMS and
conventional Mössbauer spectroscopy. Evaluation of the Mössbauer spectra reveals two distinct iron sites, which are well distinguished by their hyperfine fields. The minority and majority sites are consistent with high-spin Fe2þ in the M1 and M2 sites,
respectively.
eschweizerbartxxx ingenta
1. Introduction
One of the best resolved properties throughout Earth’s
interior are seismologically determined sound velocities,
which probe the in-situ state of crustal, mantle, and core
material with high spatial resolution. Accurate determination of the sound velocities of deep Earth materials is
therefore essential for mapping chemical and thermal
properties of Earth’s interior to seismic observations
(e.g., Bass & Anderson, 1984; Wagner et al., 2008).
Experimental methods to determine the compressional
and shear sound velocities of materials include: ultrasonic
interferometry (US), impulsively stimulated light scattering (ISLS), Brillouin inelastic light scattering (BS), inelastic neutron scattering (INS), momentum-resolved inelastic
X-ray scattering (IXS), and nuclear resonant inelastic
X-ray scattering (NRIXS). All of the above-mentioned
methods can be applied to single-crystal or polycrystalline
specimens. Selective vibrational quantities are obtained for
each method. For example, US, BS, and ISLS provide
access to the low-energy (long-wavelength) vibrational
states: the sound velocities. The neutron-weighted density
of states (DOS) obtained by INS requires larger samples,
which in turn strongly limits the highest pressure that
can be obtained. IXS provides experimental access to
specific phonon branches under extreme pressures (e.g.,
Antonangeli et al., 2004) and has been successfully
combined with theoretical phonon calculations (e.g.,
Ghose et al., 2006). However, in the case of IXS, one
must measure over all momentum-space to determine the
DOS, which often requires months of data collection.
Under extreme conditions (e.g., confined systems, magnetic fields, high-pressures, high-temperatures), the DOS
obtained from NRIXS is much more accessible than other
methods and provides access to thermodynamic quantities.
The importance in determining accurate thermodynamic
quantities from measured vibrational spectra is imperative
for accurate modeling of Earth’s interior (e.g., Kieffer,
1982). Further comparisons and descriptions of these
methods can be found in Angel et al. (2009) and references
therein. NRIXS requires a sample bearing a nuclear
resonant isotope and has been applied to single-crystals
or powdered samples as small as 10 mm laterally (and 1 mm
thick).
NRIXS is a high-resolution X-ray spectroscopic method
that provides direct access to the partial phonon density of
states (PDOS) of the nuclear resonant isotope, 57Fe in this
case. That is, all lattice vibrations involving 57Fe-nuclei
contribute to the measured PDOS and one may obtain
averaged thermodynamic quantities related to the 57Feparticipating nuclei, including: vibrational specific heat
per atom at constant volume (cV), vibrational entropy per
0935-1221/09/0021-1932 $ 4.50
DOI: 10.1127/0935-1221/2009/0021-1932
# 2009 E. Schweizerbart’sche Verlagsbuchhandlung, D-70176 Stuttgart
2
J.M. Jackson, E.A. Hamecher, W. Sturhahn
atom (Svib), Lamb-Mössbauer factor (fLM), mean force
constant (D), vibrational kinetic energy (EK), and vibrational kinetic energy at 0 K (EZ) (Sturhahn, 2004). From
the kinetic energy of the 57Fe-nuclei, one can calculate
the b-factor, which relates the equilibrium iron isotope
fractionation between two substances (e.g., Polyakov
et al., 2007). With known density, the Debye sound velocity is obtained from the low-energy portion of the PDOS.
If the bulk modulus of the material is known, the compressional and shear wave velocities and shear modulus can be
computed. NRIXS studies related to geophysical applications have primarily been conducted on high symmetry
and/or iron-rich materials (Giefers et al., 2000; Mao et al.,
2001; Struzhkin et al., 2001; Hu et al., 2003; Mao et al.,
2004; Lin et al., 2005; Lin et al., 2006a; Gao et al., 2008),
but far fewer measurements have been conducted on low
symmetry phases (Mao et al., 2006; Gao et al., 2008). In
Section 3.2, we discuss the relevance of symmetry to the
PDOS. In this contribution, we present NRIXS measurements for three powdered synthetic samples of orthorhombic-structured (Mg,57Fe)SiO3 orthoenstatite containing
representative upper mantle iron concentrations of: 20,
13, and 7 mol % FeSiO3. We show that the sound velocities
of orthoenstatite determined from NRIXS are in good
agreement with previous ultrasonic (Kumazawa, 1969;
Frisillo & Barsch, 1972; Webb & Jackson, 1993; Flesch
et al., 1998; Kung et al., 2004) and Brillouin scattering
studies (Weidner et al., 1978; Bass & Weidner, 1984;
Duffy & Vaughan, 1988; Jackson et al., 1999, 2007) on
similar compositions.
Most of the minerals and polymorphs expected in
Earth’s interior incorporate low concentrations of ferrous
(Fe2þ) and/or ferric (Fe3þ) iron. The valence state of iron
in phase assemblages has been shown to affect the presence of metallic iron (Lauterbach et al., 2000; Frost
et al., 2004; Auzende et al., 2008) and to a lesser extent,
absorption properties (which in turn may affect radiative
thermal conduction) (Goncharov et al., 2006; Goncharov
et al., 2008; Keppler et al., 2008). The spin state of
octahedrally-coordinated Fe2þ in minerals has been
shown to affect the sound velocities and density of
candidate deep Earth phases at high pressures at room
temperature (Lin et al., 2006a; Fei et al., 2007; Crowhurst
et al., 2008). Mössbauer spectroscopy is an excellent
probe of the fine structure of iron and lends insight into
the above-mentioned phenomena (e.g., Burns, 1993;
Speziale et al., 2005; Dyar et al., 2006; Lin et al.,
2006). The hyperfine parameters and site occupancy of
iron in the orthoenstatite structure have been examined in
the past under ambient and non-ambient temperatures
using conventional Mössbauer spectroscopy (Shenoy
et al., 1969; Virgo & Hafner, 1969; Skogby et al., 1992;
Fei et al., 1994; Dyar et al., 2007). We have used both
conventional and synchrotron Mössbauer spectroscopy
(SMS) to determine the room pressure hyperfine parameters of (Mg0.8757Fe0.13)SiO3 orthoenstatite. A comparison of the results obtained from SMS reveals excellent
agreement with hyperfine parameters obtained from
conventional Mössbauer spectroscopy.
Fast Track Article
2. Sample description
Three powdered samples of (Mg,57Fe)SiO3 orthoenstatite containing 20, 13, and 7 mol % FeSiO3 were prepared
for the NRS measurements. The 57Fe-enriched polycrystalline samples were synthesized from oxides in a pistoncylinder apparatus at the Geophysical Laboratory of
the Carnegie Institution of Washington. The starting
material consisted of 95 % enriched 57Fe2O3, SiO2, and
MgO. The 57Fe2O3 was reduced to FeO in a gas-mixing
furnace. SiO2 and MgO were furnace-fired in an effort
to dehydrate the starting materials. Synthesis conditions
in the piston cylinder were 1.5 GPa and 1000 C for a
duration of 48 h. Verification of the structure (space
group: Pbca) and chemistry of the samples were obtained
via powder X-ray diffraction (XRD) and electron microprobe analysis (EMPA), respectively. (Mg,57Fe)SiO3
was identified as the only phase present at the resolution
of the above-mentioned techniques (XRD: 5 vol % and
EMPA: 5 mm).
3. Nuclear resonant inelastic X-ray scattering
(NRIXS)
3.1. NRIXS experiments
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The NRIXS experiments were performed at sector 3 IDB of the Advanced Photon Source (APS) at Argonne
National Laboratory under ambient conditions. The
energy bandwidth of the incident X-rays determines
the resolution of the phonon spectra of the samples.
The X-rays were prepared with bandwidths of 1 meV
using a multiple-crystal Bragg reflection monochromator (Toellner, 2000). We used a Kirkpatrick-Baez mirror
system to obtain a focal spot size of 6 6 mm2 at the
full width at half maximum (Zhao et al., 2004). The Xray flux in this spot was 8 108 ph/s, and the resulting
spectral flux density was 2 1016 ph/s/eV/mm2
(Sturhahn, 2004). The storage ring was operated in
low-emittance top-up mode with 24 bunches that were
separated by 153 ns. The 2 mm thick samples were
mounted in air on holders for the NRIXS measurements. For each spectrum, the monochromator was
tuned from 80 meV to þ100 meV (in 0.25 meV
step size with 5 s collection time per energy point)
around the nuclear resonance energy of 57Fe, 14.4125
keV. The radiation emitted from the samples was
observed with two avalanche photodiode detectors.
One detector was placed close to the sample (2 mm
away) to collect the incoherent inelastic scattered
photons, and the other detector was placed downstream
(100 cm) in the forward scattering direction, in order
to obtain the resolution function independently
(Fig. 1). High counting rates were achieved due to
the thickness and enrichment of the samples. Therefore,
one spectrum per composition was collected. The raw
NRIXS spectra are shown in Fig. 2.
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SR source
Nuclear resonant spectroscopy of (Mg,Fe)SiO3 orthoenstatites
3
RF
monochromator
sample
NRIXS
D
SMS
Fig. 1. Typical experimental set-up for NRIXS experiments at third
generation synchrotron sources. For high-pressure experiments,
focusing mirrors are placed after the monochromator and a diamond
anvil cell contains the sample. The ‘‘SMS’’ detector is placed in the
forward scattering direction and hence, measures the resolution
function (RF) of the NRIXS spectrum independently (modified
from Sturhahn & Jackson, 2007).
PDOS, g(E) (1/eV )
D
energy (meV)
Fig. 3. Partial phonon density of states (PDOS), g(E), of iron in
(Mg,57Fe)SiO3 orthoenstatites. The PDOS for En87 and En93 are
shifted vertically by 100 eV1 and 200 eV1, respectively.
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Fig. 2. Raw NRIXS energy spectra, S(E), of (Mg,57Fe)SiO3 orthoenstatites. The elastic peak has not been removed. Data for En87 and
En93 are shifted vertically. The errors in S(E) for En87 and En93 are
similar to those of En80, but are not plotted for clarity.
3.2. Determination of the PDOS and sound velocities
The NRIXS method directly provides the Fouriertransformed R self-intermediate
ikrðtÞ ikrð0Þ iEt=h scattering function,
1
e
e
e
dt, where h is Plank’s
Sðk; EÞ ¼ 2
h
constant, k is the wave vector of the X-rays incident on the
sample, and r(t) is the displacement operator of the resonant nucleus (Sturhahn, 2004). The quasi-harmonic model
of lattice vibrations is then used to extract the partial (due
to information about motions of the resonant nuclei only)
and projected (due to a potential angular dependence on k)
phonon DOS from S(k, E) (Sturhahn et al., 1998; Sturhahn,
2000) for each composition (Fig. 3). The dependence of
S(k, E) on the direction of the incident X-rays is implicitly
contained in S(k, E) and is expressed via the directional
dependence of the phonon DOS. The description of the
anisotropy of the PDOS is given by a symmetric secondrank tensor (e.g., Sturhahn & Kohn, 1999), whereas the
elastic anisotropy requires a symmetric fourth-rank tensor.
For a sample characterized with symmetry lower than
cubic, direct inversion of the measured NRIXS spectrum
provides a reliable value of the averaged PDOS, if the
Lamb-Mössbauer factor remains high (see Sturhahn &
Jackson, 2007, for a detailed discussion). In the case of
orthoenstatite, the Lamb-Mössbauer factor remains high
for all three compositions, 0.7 (see Section 3.3).
As explained in previous reports, the energy of an
acoustic mode a (Ea) with a small wave number q (long
wavelength) that propagates in the direction q is given by
Ea ¼ hqva ðqÞ, where va is the sound velocity of mode a.
The number of phonon
states (Na) in momentum space
R
is then dNa ¼ V ka2 dka d
q , where ka ¼ Ea =ðhvÞ, V is a
normalization volume, and the integration is performed
over all directions q, symbolized by ‘‘d
q’’. The linear
phonon dispersion leads to a Debye-like phonon DOS:
DðEÞ ¼
m
1
22 h3 v3D
1
1X
with 3 ¼
vD 3 a
Z
E2 ;
1 d
q
;
4
v3a ðqÞ
(1)
(2)
where vD is the Debye sound velocity, r is the density of
the material, and m is the mass of the nuclear resonant
isotope, 57Fe in this case. This relationship is exact for
sufficiently small energies (long phonon wavelengths).
The quantitative description of the low-energy region of
the phonon DOS provides the Debye sound velocity, vD.
However, the derivation of the Debye sound velocity relies
on a linear dispersion that will only be accurate within a
limited energy range. Obtaining high-resolution data at
low energies is crucial for studies like the present case,
where iron is the heavy element in a relatively light matrix
of Mg, Si, and O, thereby providing only a small window of
accessible low-energy phonon-energies to evaluate the
sound velocities. A systematic evaluation of the errors
resulting in the selective energy interval (E1, E2) of the
low-energy portion of the PDOS is therefore necessary in
the present case, where E1 and E2 represent the low- and
4
J.M. Jackson, E.A. Hamecher, W. Sturhahn
Fast Track Article
vs ¼ 0:952vD 0:041v
(6)
Debye velocity (m/s)
and
vP ¼ 0:908v þ 0:297vD þ ð0:243v2D =vÞ:
energy (meV)
Fig. 4. Debye velocity (vD) determination for En80 using an
improved method for extracting the sound velocity (see text). The
fit was performed on the data (open circles) starting from 2.8 meV
(E1) and ending at 10.8 meV (E2) (solid line), then extrapolated to
E ¼ 0 to determine vD (dashed line). This fit produced a w2 of 0.33.
high-energy cut-offs in the PDOS. The energy interval
(E1, E2) for each PDOS is as follows: En80 (2.8 meV,
10.8 meV), En87: (3.8 meV, 12.8 meV), and En93
(6.8 meV, 12 meV). The ranges were selected so that the
elastic contribution was less than 10 % over the selected
energy range, therefore ensuring that the influence of
elastic scattering is small compared to the total scattering.
Using these selective energy intervals and an improved
empirical relation for the dispersion of the acoustic phonons at low-energy (Sturhahn & Jackson, 2007), the Debye
sound velocity has been determined from the PDOS of
each composition. We show a representative fit procedure
in Fig. 4 for En80.
For an isotropic solid, the relationship of the Debye sound
velocity to the compressional, vP, and shear, vS, velocities is
determined from equations (1) and (2) (Sturhahn & Jackson,
2007):
eschweizerbartxxx ingenta
3
1
2
¼ 3 þ 3 :
3
vD
vP
vS
(3)
The density of our samples was determined from their
measured volumes and chemistry and corrected for their
natural iron-enrichment. The KS values for this study were
determined from a linear regression of the Brillouin
scattering results for the Mg- (Weidner et al., 1978;
Jackson et al., 1999, 2007) and Fe- (Bass & Weidner,
1984) end-members. In Fig. 5 and 6, we plot our determined sound velocities and elasticity of (Mg,Fe)SiO3
orthoenstatites from NRIXS (Table 1) along with results
from previous ultrasonic and Brilloun scattering measurements. In the cases where the full elastic tensor was available, the vD values were determined from the Christoffel
equation and equation (2). If only the isotropic values
of vS and vP were given, equation (3) was used to determine vD. We find good agreement with the results from
NRIXS in comparison with Brillouin (Weidner et al.,
1978; Bass & Weidner, 1984; Duffy & Vaughan, 1988;
Jackson et al., 1999; 2007) and ultrasonic measurements
(Kumazawa, 1969; Frisillo & Barsch, 1972; Webb &
Jackson, 1993; Flesch et al., 1998; Kung et al., 2004) on
similar compositions. Within the experimental uncertainties of our NRIXS data, all three iron-bearing compositions exhibit the same Debye sound velocity. Reports from
ultrasonic measurements on similar compositions also
vP
velocity (km/s)
vD = 5.08 km/s at E = 0 meV
(7)
vD
vS
One can see from the above relationship that the Debye
sound velocity is heavily weighted towards the shear
sound velocity. With known density (r) and adiabatic
bulk modulus (KS), the isotropic vP and vS and shear
modulus (m) follow the additional relationships:
KS
4
¼ v2 ¼ v2P v2S ;
3
(4)
¼ v2S :
(5)
Combining equations (3) and (4), one obtains the approximate general solutions for vS and vP (within 0.1 % error,
see Sturhahn & Jackson, 2007):
density (g/cm³)
Fig. 5. Debye (vD, circles), compressional (vP, diamonds), and shear
(vS, squares) velocities from this experiment (open symbols) along
with previous measurements of the enstatite-ferrosilite solid solution
series (filled symbols). The dashed lines represent a linear regression
of the enstatite and ferrosilite end-members from Brillouin scattering. Sources of data: 1 ¼ Weidner et al. (1978); 2 ¼ Flesch et al.
(1998); 3 ¼ Jackson et al. (1999); 4 ¼ Kung et al. (2004);
5 ¼ Jackson et al. (2007); 6 ¼ Duffy & Vaughan (1988);
7 ¼ Kumazawa (1969); 8 ¼ Frisillo & Barsch (1972); 9 ¼ Webb
& Jackson (1993); 10 ¼ Bass & Weidner (1984). A density correction (,1 %) to account for natural iron-enrichment was applied
to our data. In the cases where the full elastic tensor was available,
the vD values were determined from the Christoffel equation and
equations (1) and (2).
elastic moduli (GPa)
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Nuclear resonant spectroscopy of (Mg,Fe)SiO3 orthoenstatites
5
5.40 km/s for MgSiO3 (Jackson et al., 2007) and
5.20 km/s for (Mg0.8Fe0.2)SiO3 (Frisillo & Barsch, 1972)
orthoenstatites.
KS
3.3. Thermodynamic parameters extracted
from the PDOS
µ
density (g/cm³)
Fig. 6. Adiabatic bulk and shear elastic moduli determined from this
experiment (diamonds) along with previous results (squares) for the
orthoenstatite-orthoferrosilite solid solution series. Note that KS was
fixed in our study (see text). Symbols and reference numbers have
the same meaning as in Fig. 5. Additionally, 11 ¼ (Mg,Fe)SiO3
orthoenstatite (Hugh-Jones & Angel, 1997); 12 ¼ MgSiO3 orthoenstatite (Hugh-Jones & Angel, 1994).
Table 1. Debye sound velocities and other elastic parameters of
orthoenstatites determined from the low-energy region of the PDOS.
Density
(g/cc)
vD
(km/s)
vS
(km/s)
vP
(km/s)
En93 3.26(1) 5.12(20) 4.62(2) 7.83(20)
En87 3.31(1) 5.11(5) 4.62(5) 7.79(10)
En80 3.36(1) 5.08(7) 4.59(7) 7.23(11)
K0S*
(GPa)
m
(GPa)
107.2
106.8
106.4
70(6)
71(2)
71(2)
eschweizerbartxxx ingenta
Notes: (*) fixed values obtained from a linear regression of previous Brillouin scattering results for MgSiO3 and FeSiO3 orthopyroxene as a function of density. A density correction (,1 %) to
account for natural iron-enrichment was applied to our data. Values
in parentheses represent the error in the last significant digit(s).
appear independent of iron content for some elastic parameters (Kumazawa, 1969; Frisillo & Barsch, 1972; Webb
& Jackson, 1993; Kung et al., 2004). In Fig. 6, we also
include the bulk modulus obtained on a suite of synthetic
(Mg,Fe)SiO3 samples determined from single-crystal
X-ray diffraction measurements (Hugh-Jones & Angel,
1994, 1997), using the isothermal to adiabatic bulk modulus conversion of K0S ¼ K0T ð1 þ T Þ at 300 K, where
a ¼ 3.2 105 K1 and g ¼ 1.009 (Angel & Jackson,
2002). Natural orthopyroxenes (OPX) are known to contain minor amounts of Al and Ca, in addition to iron. The
substitution of small amounts of Ca into the M2 octahedral
site in OPX does not significantly affect its elasticity
(Nestola et al., 2006; Perrillat et al., 2007). However,
either the coupled substitution of Al into the tetrahedral
and octahedral sites or simply the substitution of Al into the
tetrahedral site of OPX appears to stiffen the bulk modulus
of OPX, in comparison to the Mg end-member (Chai et al.,
1997). The vD values calculated from the measured elastic
tensors of the (Al,Fe)- (Chai et al., 1997) and Ca-bearing
(Perrillat et al., 2007) orthopyroxenes are 5.37 and
5.31 km/s, respectively, compared to a vD values of
The PDOS provides access to several thermodynamic
quantities of the material (Sturhahn, 2004). For the
orthoenstatite samples measured, we determined the
following from the PDOS: cV, vibrational specific heat
per atom at constant volume (kB/atom); Svib, the vibrational
entropy per atom (kB/atom); fLM, the average LambMössbauer factor; D (N/m), the mean force constant; EK,
the vibrational kinetic energy; EZ, the vibrational kinetic
energy at 0 K of the 57Fe nucleus (Table 2; Fig. 7). These
are thermodynamic parameters of the 57Fe-participating
vibrations. It is interesting to note that although the sound
velocities of orthoenstatite do not show an obvious trend
within the low iron-concentration region of the solid-solution, quantities derived from the whole spectrum (the
PDOS) do show trends. The shape of the PDOS indeed
changes as a function of iron content (Fig. 3). This can be
understood quantitatively by analyzing the contributions of
the vibrational spectrum to the individual thermodynamic
quantities. The energy dependence of the PDOS, g(E),
of the contribution to the mean force constant (D) is
proportional to g(E)*E2 (Fig. 8). The higher energy regions
(E . 10 meV) of the spectra differ significantly as a
function of iron content. These differences rusult in a
decrease of the mean force constant as iron concentration
increases (Fig. 7d). Therefore, as the bonds related to the
iron atoms weaken, the remaining structural components
must stiffen in order to maintain roughly constant values of
the isotropically averaged elastic properties (Fig. 5 and 6).
In Fig. 9 we plot the energy dependence of the vibrational contributions to the vibrational specific heat per
atom at constant volume (cV) for En80:
cV ¼ 3kB
ð
2
E
E 2kB T sin h
gðEÞdE:
2kB T
2
(8)
Table 2. The 57Fe weighted thermodynamic parameters of orthoenstatites determined from the PDOS.
cV
(kB/
atom)
En93
En87
En80
Svib
(kB/
atom)
fLM
2.74(2) 3.61(2) 0.723(3)
2.75(1) 3.60(1) 0.730(2)
2.77(2) 3.71(2) 0.709(3)
D
(N/m)
EZ
(meV/
atom)
EK
(meV/
atom)
195(5)
170(3)
165(5)
6.38(8)
6.15(6)
6.11(8)
14.7(1)
14.01(7)
15.1(1)
Notes: cV - specific heat per atom at constant volume; Svib - the
vibrational entropy per atom; fLM – the average Lamb-Mössbauer
factor; D – the mean force constant; EZ, EK – vibrational kinetic
energy of the nucleus at 0 K and room-temperature, respectively.
6
J.M. Jackson, E.A. Hamecher, W. Sturhahn
Fast Track Article
cV (kB/atom)
2.80
2.78
(a)
2.76
2.74
2.72
2.70
3.74
Svib (kB/atom)
(b)
3.70
Fig. 8. The energy dependence of the vibrational contributions to the
mean force constant (D). The higher energy regions (E > 15 meV) of
the spectra differ significantly as a function of iron content.
3.66
3.62
3.58
0.735
g(E)*Q
(c)
0.730
0.725
Q = E2[2kBTsinh(E/2kBT)]-2
fLM
eschweizerbartxxx ingenta
0.720
0.715
0.710
0.705
energy (meV)
Mean Force Constant, D (N/m)
0.700
200
Fig. 9. The energy dependence of the vibrational contributions to the
vibrational specific heat at constant volume (cV), where Q is the factor
relating g(E) to cV is Q, kB is the Boltzman factor, and T ¼ 300 K for
En80 (open circles); g(E) for En80 is plotted for comparison (solid
black line).
(d)
190
180
is the same for En87 and En93. The relationship between
the PDOS, g(E), and the Lamb-Mössbauer factor (fLM)
(Chumakov & Sturhahn, 1999) is as follows:
170
160
3.24
3.26
3.28
3.30 3.32 3.34 3.36
density (g/cm3)
3.38
Fig. 7. Selected thermodynamic parameters extracted from the PDOS
of the orthoenstatites measured with NRIXS in this study: (a) cV:
vibrational specific heat per atom at constant volume (kB/atom), (b)
Svib: the vibrational entropy per atom (kB/atom), (c) fLM: the LambMössbauer factor, and (d) the mean force constant, D (N/m).
One can see that all energies are essentially weighted
equally at 300 K, which results in minimal effects from
cV to the shapes of the PDOS. The differences will
decrease even further at higher temperatures. This effect
ln fLM
ð
1 þ eE gðEÞ
dE ¼ k 2 x2 ;
¼ ER
E
E
1e
(9)
where k is the incident wave vector and ,x2. is the
mean-square-displacement of the 57Fe atoms. For vibrational entropy, the relationship is as follows (Sturhahn,
2004):
Svib ¼ 3kB
ð E
h E
i
E
E e þ 1
2 e 2
ln
e
gðEÞdE
2 eE 1
(10)
Nuclear resonant spectroscopy of (Mg,Fe)SiO3 orthoenstatites
4. Mössbauer spectroscopy
Nuclear forward scattering of synchrotron X-radiation is a
Mössbauer spectroscopic method. 57Fe Mössbauer spectroscopy provides access to the hyperfine structure of the
iron component in a solid material containing the 57Fe
resonant isotope (see Dyar et al., 2006 for a recent review
on the application to Earth and planetary materials). The
hyperfine interaction describes the splitting of nuclear
energy levels as a result of the hyperfine coupling to atomic
or molecular energy levels. The quantities observed which
are most relevant to the current study are isomer shift (IS)
and quadrupole splitting (QS). The IS is proportional to the
s-electron density at the nucleus, and hence is indirectly
influenced (via shielding effects) by the d-electron population in the valence shell. The IS thus provides information
on the valence (i.e, oxidation) state. A QS is observed when
an inhomogeneous electric field (i.e., a gradient) at the
Mössbauer nucleus is present. In general, two factors can
contribute to the electric field gradient, an electron distribution in the valence shell and/or a nearby, lattice environment with non-cubic symmetry. Thus, QS data yield
information on local structure and, in a complementary
manner to the isomer shift, the oxidation state. As
explained in previous reports, a single doublet (quadrupole
splitting and isomer shift) in conventional Mössbauer spectroscopy (MBS) produces a characteristic oscillation in the
SMS time spectrum with a periodicity equal to 2h/QS,
where h is Planck’s constant (Zhang et al., 1999). Details
of the comparison between these two methods have been
discussed elsewhere (Alp et al., 1995). The presence of
additional sites leads to coherent superposition with respective weights, isomer shift(s), and line broadening, all of
which are directly determined by analysis of the SMS time
spectrum. IS are only observable in a relative sense: in the
case of MBS, the IS is usually reported relative to the
emission line of the source. In the case of SMS, IS values
are obtained by placing a reference absorber with known
composition and thickness, usually stainless steel, in the
X-ray beam-path with the sample. If there is more than
one iron site observed in the spectrum, one may obtain an
IS of the one site relative to the other site. These quantities
(IS and QS) have successfully been used to identify the
valence and spin states of iron at various temperatures at
room-pressures (Gütlich & Goodwin, 2004; Dyar et al.,
2006; McCammon, 2006) and in some well-defined systems
at high-pressures (Sarkisyan et al., 2002; Lin et al., 2006b).
eschweizerbartxxx ingenta
4.1. Synchrotron Mössbauer spectroscopy (SMS)
measurements
The SMS experiments were performed at beamline 3-ID-B
at the APS under ambient conditions. The X-rays were
prepared exactly the same as that described for the
NRIXS measurements in Section 3 of this paper. Only
one detector is needed for SMS, which is placed 100 cm
from the X-ray focused spot (Fig. 1). Saturation of nuclear
resonant absorption scales with the effective thickness.
7
Values of more than one per resonance line have a significant influence on the time spectra and exact thickness
values are necessary to extract accurate hyperfine parameters (Burnham et al., 1971; Sturhahn, 2000). Due to the
very large effective thickness and irregularities in shape of
the 57Fe enriched En87 sample used for NRIXS, a small
portion of the En87 sample was pressed into a 20 mm
thick pellet and mounted in the X-ray focus spot.
Additional constraints on the hyperfine parameters of the
sample were provided by placing a 57Fe-enriched stainless
steel foil with a physical thickness of 0.5 mm in the X-ray
beam path (Alp et al., 1995). Therefore, spectra were
collected with and without stainless foil with collection
times of 30 min per spectrum (Fig. 10). Accounting for
detector-related effects, we were able to observe nuclear
resonant scattering in a time window of 20 to 125 ns
following excitation.
4.2. Evaluation of the Mössbauer spectra
The measured SMS spectra were evaluated using the
CONUSS software (Sturhahn, 2000). Spectra without
stainless steel foil were evaluated first, to constrain the
quadrupole splittings and weights of the sites. With this
information, the isomer shifts of all sites were determined
using the spectra containing the stainless steel foil reference. We report all isomer shift values relative to a-iron at
ambient conditions, which is typical for results reported
from conventional Mössbauer spectroscopy. The isomer
shift of stainless steel relative to a-iron is 0.09 mm/s
(Hawthorne, 1988). Figure 10 displays the time spectra
together with the best-fit hyperfine parameters.
We observed two sites in the SMS time spectrum
of (Mg0.87Fe0.13)SiO3 orthoenstatite, which are well
distinguished by their hyperfine fields. One site, representing 93 % of the total iron, is characterized by a QS of
2.22 0.01 mm/s and an IS of 1.15 0.01 mm/s. These
En87
10000
Wt.(%)
QS (mm/s)
IS (mm/s)
M1
7
2.46(5)
1.19(1)
M2
93(4)
2.22(1)
1.15(1)
299 K, 1 atm.
counts
Fast Track Article
1000
En87
En87 with SS
100
0
20
40
60
80
100
120
140
time (ns)
Fig. 10. Synchrotron Mössbauer spectra of En87 with (closed
spheres) and without (open spheres) the reference stainless steel
absorber (SS). The lines through the data represent the best-fit
hyperfine parameters (Table 3). The normalized w2 values for the
fits are 2.4 and 4.7, respectively.
8
J.M. Jackson, E.A. Hamecher, W. Sturhahn
QS and IS values are consistent with previous reports on
the behavior of high-spin Fe2þ in the more distorted M2
polyhedron site of the Pbca orthopyroxene structure
(Shenoy et al., 1969; Virgo & Hafner, 1969; Skogby
et al., 1992; Fei et al., 1994; Angel et al., 1998; Dyar
et al., 2007). The remaining 7 % of the iron is characterized
by a QS ¼ 2.46 0.05 and an IS ¼ 1.19 0.01 mm/s,
consistent with high-spin Fe2þ in the M1 site. Incorporation
of 3 % Fe3þ, an amount close to the detection limit, did not
change our w2 values. We observed no line-broadening. In
the method of SMS, the source has no influence on the time
spectrum and any line-broadening observed can be attributed
to the sample. In conventional Mössbauer spectroscopy
(MBS), line-broadening in the spectra can be a result of the
source and the sample.
A small portion of the En87 sample used in the NRIXS
measurements was mounted in a small aperture confined by
lead for conventional Mössbauer spectroscopy measurements using a new Co(Rh) source (Fig. 11). The MBS
420000
counts
410000
400000
Fast Track Article
spectrum was fit using CONUSS. The best-fit hyperfine
parameters are listed in Table 3 and agree very well with
the parameters obtained from our SMS measurements.
5. Concluding remarks
We have shown that the sound velocities of a suite of
orthoenstatite samples measured by NRIXS are in good
agreement with sound velocities obtained using ultrasonic
and Brillouin scattering methods. More importantly, the
lattice vibrations pertaining to the 57Fe-nuclei have been
measured. The quantities derived from NRIXS measurements of the PDOS for orthoenstatites offer unique
insights into the behavior of iron in materials. The nature
of the PDOS obtained from NRIXS involving only 57Fe
participating vibrations suggests that these measurements
should be complemented with the total phonon density of
states to obtain representative thermodynamic behavior of
the entire sample. We have also demonstrated that hyperfine parameters of En87 determined using SMS agree very
well with those determined using MBS.
En87
Wt.(%)
QS (mm/s)
IS (mm/s)
M1
8
2.55(2)
1.19(1)
M2
92(2)
2.17(1)
1.16(1)
eschweizerbartxxx ingenta
390000
380000
300 K
1 atm.
370000
-10
-5
0
5
10
velocity (mm/s)
Fig. 11. Conventional Mössbauer spectrum of En87 collected with a
new Co(Rh) source (open symbols). The lines through data represent the best-fit hyperfine parameters (Table 3).
Acknowledgments: We thank Y. Fei (Carnegie
Institution of Washington) for synthesizing the orthoenstatite samples, E.E. Alp (ANL) for performing the
conventional Mössbauer measurements, J. Zhao (ANL)
for technical assistance at sector 3, D. Zhang (Caltech)
for discussions, and two anonymous reviewers for their
comments and suggestions. Support for this work was
provided by the National Science Foundation (NSF)
EAR #0711542 (JMJ). Use of the Advanced Photon
Source was supported by the US DOE, Office of
Science, and BES (DE-AC02-06CH11357). This research
was partially supported by COMPRES under NSF
Cooperative Agreement EAR 06–49658.
Table 3. The best-fit hyperfine parameters of En87 obtained from fits to the SMS time spectra and a comparison with literature values for
similar pyroxenes at ambient pressure.
M1
(Mg0.87Fe0.13)SiO3a
(Mg0.87Fe0.13)SiO3a
(Mg0.975Fe0.025)SiO3b
(Mg0.90Fe0.10)SiO3b
(Mg0.90Fe0.10)SiO3c
(Mg1.857Fe0.134)2(Si1.996Al0.004)2O6d
CaFeSi2O6 e
(Mg0.892Fe0.108)SiO3f
Phase
Method
OEN
OEN
OEN
OEN
OEN
OEN
CPX
CPX
SMS
MBS
MBS
MBS
MBS
MBS
SMS
MBS
M2
T (K) Wt (%) QS (mm/s) IS (mm/s) Wt (%) QS (mm/s) IS (mm/s)
299
300
293
293
77
77
300
81
7
8
13.9
15.9
nr
18.9
100
nr
2.46(5)
2.55(2)
2.55
2.45
3.06
nr
2.25
3.14(2)
1.19(1)
1.19(1)
1.17
1.16
1.28
nr
nr
1.290(5)
93(4)
92(2)
86.1
84.1
nr
81.1
na
nr
2.22(1)
2.17(1)
2.12
2.09
2.15
nr
na
2.17(2)
1.15(1)
1.16(1)
1.14
1.14
1.27
nr
na
1.269(5)
Notes: Wt – weight fraction of the site, QS – quadrupole splitting, IS – isomer shift (relative to a-iron), OEN – orthoenstatite, CPX –
clinopyroxene, SMS – synchrotron Mössbauer spectroscopy, MBS – conventional Mössbauer spectroscopy, nr – not reported, na – not
applicable. Parameters with error values were varied in the fits. The weights are normalized to 100 %. Uncertainties are given in parenthesis at
the 90 % confidence level for the last reported significant digit. The normalized w2 values for the SMS fits are 2.4 without the stainless steel
(SS) reference absorber and 4.7 with SS. References: a – En87 (this study), b – Dyar et al. (2007), c – Fei et al. (1994), d – Skogby et al.
(1992), e – Zhang et al. (1999), f – Angel et al. (1998).
Fast Track Article
Nuclear resonant spectroscopy of (Mg,Fe)SiO3 orthoenstatites
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Received 27 November 2008
Modified version received 16 January 2009
Accepted 11 March 2009