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: jackson@gps.caltech.edu2 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 Mossbauer 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 velocitieswere 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 ingood agreement with sound velocities obtained using Brillouin spectroscopy and ultrasonic methods for similar compositions. Animportant advantage of NRIXS is access to additional thermodynamic information, such as the average force constant, mean-squaredisplacement, obtained from the PDOS. We discuss the contribution of the vibrational spectra to these quantities. In addition to thePDOS, the electronic environment of the iron sites in (Mg0.87

57Fe0.13)SiO3 orthoenstatite was determined using 57Fe SMS andconventional Mossbauer spectroscopy. Evaluation of the Mossbauer spectra reveals two distinct iron sites, which are well distin-guished by their hyperfine fields. The minority and majority sites are consistent with high-spin Fe2þ in the M1 and M2 sites,respectively.

1. Introduction

One of the best resolved properties throughout Earth’sinterior are seismologically determined sound velocities,which probe the in-situ state of crustal, mantle, and corematerial with high spatial resolution. Accurate determina-tion of the sound velocities of deep Earth materials istherefore essential for mapping chemical and thermalproperties of Earth’s interior to seismic observations(e.g., Bass & Anderson, 1984; Wagner et al., 2008).Experimental methods to determine the compressionaland shear sound velocities of materials include: ultrasonicinterferometry (US), impulsively stimulated light scatter-ing (ISLS), Brillouin inelastic light scattering (BS), inelas-tic neutron scattering (INS), momentum-resolved inelasticX-ray scattering (IXS), and nuclear resonant inelasticX-ray scattering (NRIXS). All of the above-mentionedmethods can be applied to single-crystal or polycrystallinespecimens. Selective vibrational quantities are obtained foreach method. For example, US, BS, and ISLS provideaccess to the low-energy (long-wavelength) vibrationalstates: the sound velocities. The neutron-weighted densityof states (DOS) obtained by INS requires larger samples,which in turn strongly limits the highest pressure thatcan be obtained. IXS provides experimental access tospecific phonon branches under extreme pressures (e.g.,

Antonangeli et al., 2004) and has been successfullycombined with theoretical phonon calculations (e.g.,Ghose et al., 2006). However, in the case of IXS, onemust measure over all momentum-space to determine theDOS, which often requires months of data collection.Under extreme conditions (e.g., confined systems, mag-netic fields, high-pressures, high-temperatures), the DOSobtained from NRIXS is much more accessible than othermethods and provides access to thermodynamic quantities.The importance in determining accurate thermodynamicquantities from measured vibrational spectra is imperativefor accurate modeling of Earth’s interior (e.g., Kieffer,1982). Further comparisons and descriptions of thesemethods can be found in Angel et al. (2009) and referencestherein. NRIXS requires a sample bearing a nuclearresonant isotope and has been applied to single-crystalsor powdered samples as small as 10 mm laterally (and 1 mmthick).

NRIXS is a high-resolution X-ray spectroscopic methodthat provides direct access to the partial phonon density ofstates (PDOS) of the nuclear resonant isotope, 57Fe in thiscase. That is, all lattice vibrations involving 57Fe-nucleicontribute to the measured PDOS and one may obtainaveraged thermodynamic quantities related to the 57Fe-participating nuclei, including: vibrational specific heatper atom at constant volume (cV), vibrational entropy per

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eschweizerbartxxx ingenta

atom (Svib), Lamb-Mossbauer factor (fLM), mean forceconstant (D), vibrational kinetic energy (EK), and vibra-tional kinetic energy at 0 K (EZ) (Sturhahn, 2004). Fromthe kinetic energy of the 57Fe-nuclei, one can calculatethe b-factor, which relates the equilibrium iron isotopefractionation between two substances (e.g., Polyakovet al., 2007). With known density, the Debye sound velo-city is obtained from the low-energy portion of the PDOS.If the bulk modulus of the material is known, the compres-sional and shear wave velocities and shear modulus can becomputed. NRIXS studies related to geophysical applica-tions have primarily been conducted on high symmetryand/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 lowsymmetry phases (Mao et al., 2006; Gao et al., 2008). InSection 3.2, we discuss the relevance of symmetry to thePDOS. In this contribution, we present NRIXS measure-ments for three powdered synthetic samples of orthorhom-bic-structured (Mg,57Fe)SiO3 orthoenstatite containingrepresentative upper mantle iron concentrations of: 20,13, and 7 mol % FeSiO3. We show that the sound velocitiesof orthoenstatite determined from NRIXS are in goodagreement with previous ultrasonic (Kumazawa, 1969;Frisillo & Barsch, 1972; Webb & Jackson, 1993; Fleschet al., 1998; Kung et al., 2004) and Brillouin scatteringstudies (Weidner et al., 1978; Bass & Weidner, 1984;Duffy & Vaughan, 1988; Jackson et al., 1999, 2007) onsimilar compositions.

Most of the minerals and polymorphs expected inEarth’s interior incorporate low concentrations of ferrous(Fe2þ) and/or ferric (Fe3þ) iron. The valence state of ironin phase assemblages has been shown to affect the pre-sence of metallic iron (Lauterbach et al., 2000; Frostet al., 2004; Auzende et al., 2008) and to a lesser extent,absorption properties (which in turn may affect radiativethermal conduction) (Goncharov et al., 2006; Goncharovet al., 2008; Keppler et al., 2008). The spin state ofoctahedrally-coordinated Fe2þ in minerals has beenshown to affect the sound velocities and density ofcandidate deep Earth phases at high pressures at roomtemperature (Lin et al., 2006a; Fei et al., 2007; Crowhurstet al., 2008). Mossbauer spectroscopy is an excellentprobe of the fine structure of iron and lends insight intothe 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 ofiron in the orthoenstatite structure have been examined inthe past under ambient and non-ambient temperaturesusing conventional Mossbauer spectroscopy (Shenoyet al., 1969; Virgo & Hafner, 1969; Skogby et al., 1992;Fei et al., 1994; Dyar et al., 2007). We have used bothconventional and synchrotron Mossbauer spectroscopy(SMS) to determine the room pressure hyperfine para-meters of (Mg0.87

57Fe0.13)SiO3 orthoenstatite. A compar-ison of the results obtained from SMS reveals excellentagreement with hyperfine parameters obtained fromconventional Mossbauer spectroscopy.

2. Sample description

Three powdered samples of (Mg,57Fe)SiO3 orthoensta-tite containing 20, 13, and 7 mol % FeSiO3 were preparedfor the NRS measurements. The 57Fe-enriched polycrys-talline samples were synthesized from oxides in a piston-cylinder apparatus at the Geophysical Laboratory ofthe Carnegie Institution of Washington. The startingmaterial consisted of 95 % enriched 57Fe2O3, SiO2, andMgO. The 57Fe2O3 was reduced to FeO in a gas-mixingfurnace. SiO2 and MgO were furnace-fired in an effortto dehydrate the starting materials. Synthesis conditionsin the piston cylinder were 1.5 GPa and 1000 �C for aduration of 48 h. Verification of the structure (spacegroup: Pbca) and chemistry of the samples were obtainedvia powder X-ray diffraction (XRD) and electron micro-probe analysis (EMPA), respectively. (Mg,57Fe)SiO3

was identified as the only phase present at the resolutionof the above-mentioned techniques (XRD: 5 vol % andEMPA: 5 mm).

3. Nuclear resonant inelastic X-ray scattering(NRIXS)

3.1. NRIXS experiments

The NRIXS experiments were performed at sector 3 ID-B of the Advanced Photon Source (APS) at ArgonneNational Laboratory under ambient conditions. Theenergy bandwidth of the incident X-rays determinesthe resolution of the phonon spectra of the samples.The X-rays were prepared with bandwidths of 1 meVusing a multiple-crystal Bragg reflection monochroma-tor (Toellner, 2000). We used a Kirkpatrick-Baez mirrorsystem to obtain a focal spot size of 6 � 6 mm2 at thefull width at half maximum (Zhao et al., 2004). The X-ray flux in this spot was 8 � 108 ph/s, and the resultingspectral flux density was 2 � 1016 ph/s/eV/mm2

(Sturhahn, 2004). The storage ring was operated inlow-emittance top-up mode with 24 bunches that wereseparated by 153 ns. The �2 mm thick samples weremounted in air on holders for the NRIXS measure-ments. For each spectrum, the monochromator wastuned from �80 meV to þ100 meV (in 0.25 meVstep size with 5 s collection time per energy point)around the nuclear resonance energy of 57Fe, 14.4125keV. The radiation emitted from the samples wasobserved with two avalanche photodiode detectors.One detector was placed close to the sample (�2 mmaway) to collect the incoherent inelastic scatteredphotons, and the other detector was placed downstream(100 cm) in the forward scattering direction, in orderto obtain the resolution function independently(Fig. 1). High counting rates were achieved due tothe thickness and enrichment of the samples. Therefore,one spectrum per composition was collected. The rawNRIXS spectra are shown in Fig. 2.

2 J.M. Jackson, E.A. Hamecher, W. Sturhahn Fast Track Article

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3.2. Determination of the PDOS and sound velocities

The NRIXS method directly provides the Fourier-transformed self-intermediate scattering function,Sðk;EÞ ¼ 1

2��h

ReikrðtÞe�ikrð0Þ� �

eiEt=�hdt, where �h is Plank’sconstant, k is the wave vector of the X-rays incident on thesample, and r(t) is the displacement operator of the reso-nant nucleus (Sturhahn, 2004). The quasi-harmonic modelof lattice vibrations is then used to extract the partial (dueto 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 ofS(k, E) on the direction of the incident X-rays is implicitlycontained in S(k, E) and is expressed via the directionaldependence of the phonon DOS. The description of theanisotropy of the PDOS is given by a symmetric second-rank tensor (e.g., Sturhahn & Kohn, 1999), whereas theelastic anisotropy requires a symmetric fourth-rank tensor.For a sample characterized with symmetry lower thancubic, direct inversion of the measured NRIXS spectrum

provides a reliable value of the averaged PDOS, if theLamb-Mossbauer factor remains high (see Sturhahn &Jackson, 2007, for a detailed discussion). In the case oforthoenstatite, the Lamb-Mossbauer factor remains highfor all three compositions, �0.7 (see Section 3.3).

As explained in previous reports, the energy of anacoustic mode a (Ea) with a small wave number q (longwavelength) that propagates in the direction q is given byEa ¼ �hqvaðqÞ, where va is the sound velocity of mode a.The number of phonon states (Na) in momentum spaceis then dNa ¼ V

Rk2adkad�q, where ka ¼ Ea=ð�hvÞ, V is a

normalization volume, and the integration is performedover all directions q, symbolized by ‘‘d�q’’. The linearphonon dispersion leads to a Debye-like phonon DOS:

DðEÞ ¼ m

2�2�h3�

1

v3DE2; (1)

with1

v3D¼ 1

3

X

a

Z1

v3aðqÞd�q

4�; (2)

where vD is the Debye sound velocity, r is the density ofthe material, and m is the mass of the nuclear resonantisotope, 57Fe in this case. This relationship is exact forsufficiently small energies (long phonon wavelengths).

The quantitative description of the low-energy region ofthe phonon DOS provides the Debye sound velocity, vD.However, the derivation of the Debye sound velocity relieson a linear dispersion that will only be accurate within alimited energy range. Obtaining high-resolution data atlow energies is crucial for studies like the present case,where iron is the heavy element in a relatively light matrixof Mg, Si, and O, thereby providing only a small window ofaccessible low-energy phonon-energies to evaluate thesound velocities. A systematic evaluation of the errorsresulting in the selective energy interval (E1, E2) of thelow-energy portion of the PDOS is therefore necessary inthe present case, where E1 and E2 represent the low- and

Fig. 2. Raw NRIXS energy spectra, S(E), of (Mg,57Fe)SiO3 orthoen-statites. The elastic peak has not been removed. Data for En87 andEn93 are shifted vertically. The errors in S(E) for En87 and En93 aresimilar to those of En80, but are not plotted for clarity.

energy (meV)

PDO

S, g

(E) (

1/eV

)

Fig. 3. Partial phonon density of states (PDOS), g(E), of iron in(Mg,57Fe)SiO3 orthoenstatites. The PDOS for En87 and En93 areshifted vertically by 100 eV�1 and 200 eV�1, respectively.

SR source monochromatorsample

DNRIXS

RF

D

SMS

Fig. 1. Typical experimental set-up for NRIXS experiments at thirdgeneration synchrotron sources. For high-pressure experiments,focusing mirrors are placed after the monochromator and a diamondanvil cell contains the sample. The ‘‘SMS’’ detector is placed in theforward scattering direction and hence, measures the resolutionfunction (RF) of the NRIXS spectrum independently (modifiedfrom Sturhahn & Jackson, 2007).

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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 theelastic contribution was less than 10 % over the selectedenergy range, therefore ensuring that the influence ofelastic scattering is small compared to the total scattering.Using these selective energy intervals and an improvedempirical relation for the dispersion of the acoustic pho-nons at low-energy (Sturhahn & Jackson, 2007), the Debyesound velocity has been determined from the PDOS ofeach composition. We show a representative fit procedurein Fig. 4 for En80.

For an isotropic solid, the relationship of the Debye soundvelocity to the compressional, vP, and shear, vS, velocities isdetermined from equations (1) and (2) (Sturhahn & Jackson,2007):

3

v3D

� �

¼ 1

v3P

� �

þ 2

v3S

� �

: (3)

One can see from the above relationship that the Debyesound velocity is heavily weighted towards the shearsound velocity. With known density (r) and adiabaticbulk modulus (KS), the isotropic vP and vS and shearmodulus (m) follow the additional relationships:

KS

�¼ v2� ¼ v2P �

4

3v2S; (4)

�

�¼ v2S: (5)

Combining equations (3) and (4), one obtains the approx-imate general solutions for vS and vP (within 0.1 % error,see Sturhahn & Jackson, 2007):

vs ¼ 0:952vD � 0:041v (6)

and

vP ¼ 0:908vþ 0:297vD þ ð0:243v2D=vÞ: (7)

The density of our samples was determined from theirmeasured volumes and chemistry and corrected for theirnatural iron-enrichment. The KS values for this study weredetermined from a linear regression of the Brillouinscattering 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 deter-mined sound velocities and elasticity of (Mg,Fe)SiO3

orthoenstatites from NRIXS (Table 1) along with resultsfrom previous ultrasonic and Brilloun scattering measure-ments. In the cases where the full elastic tensor was avail-able, the vD values were determined from the Christoffelequation and equation (2). If only the isotropic valuesof vS and vP were given, equation (3) was used to deter-mine vD. We find good agreement with the results fromNRIXS 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) onsimilar compositions. Within the experimental uncertain-ties of our NRIXS data, all three iron-bearing composi-tions exhibit the same Debye sound velocity. Reports fromultrasonic measurements on similar compositions also

density (g/cm³)

velo

city

(km

/s)

vS

vD

vP

Fig. 5. Debye (vD, circles), compressional (vP, diamonds), and shear(vS, squares) velocities from this experiment (open symbols) alongwith previous measurements of the enstatite-ferrosilite solid solutionseries (filled symbols). The dashed lines represent a linear regressionof the enstatite and ferrosilite end-members from Brillouin scatter-ing. 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 correc-tion (,1 %) to account for natural iron-enrichment was appliedto our data. In the cases where the full elastic tensor was available,the vD values were determined from the Christoffel equation andequations (1) and (2).

energy (meV)

Deb

ye v

eloc

ity (m

/s)

vD = 5.08 km/s at E = 0 meV

Fig. 4. Debye velocity (vD) determination for En80 using animproved method for extracting the sound velocity (see text). Thefit was performed on the data (open circles) starting from 2.8 meV(E1) and ending at 10.8 meV (E2) (solid line), then extrapolated toE ¼ 0 to determine vD (dashed line). This fit produced a w2 of 0.33.

4 J.M. Jackson, E.A. Hamecher, W. Sturhahn Fast Track Article

eschweizerbartxxx ingenta

appear independent of iron content for some elastic para-meters (Kumazawa, 1969; Frisillo & Barsch, 1972; Webb& Jackson, 1993; Kung et al., 2004). In Fig. 6, we alsoinclude the bulk modulus obtained on a suite of synthetic(Mg,Fe)SiO3 samples determined from single-crystalX-ray diffraction measurements (Hugh-Jones & Angel,1994, 1997), using the isothermal to adiabatic bulk mod-ulus conversion of K0S ¼ K0T ð1þ ��TÞ at 300 K, wherea ¼ 3.2 � 10�5 K�1 and g ¼ 1.009 (Angel & Jackson,2002). Natural orthopyroxenes (OPX) are known to con-tain minor amounts of Al and Ca, in addition to iron. Thesubstitution of small amounts of Ca into the M2 octahedralsite 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 tetrahedraland octahedral sites or simply the substitution of Al into thetetrahedral site of OPX appears to stiffen the bulk modulusof OPX, in comparison to the Mg end-member (Chai et al.,1997). The vD values calculated from the measured elastictensors of the (Al,Fe)- (Chai et al., 1997) and Ca-bearing(Perrillat et al., 2007) orthopyroxenes are 5.37 and5.31 km/s, respectively, compared to a vD values of

5.40 km/s for MgSiO3 (Jackson et al., 2007) and5.20 km/s for (Mg0.8Fe0.2)SiO3 (Frisillo & Barsch, 1972)orthoenstatites.

3.3. Thermodynamic parameters extractedfrom the PDOS

The PDOS provides access to several thermodynamicquantities of the material (Sturhahn, 2004). For theorthoenstatite samples measured, we determined thefollowing from the PDOS: cV, vibrational specific heatper atom at constant volume (kB/atom); Svib, the vibrationalentropy per atom (kB/atom); fLM, the average Lamb-Mossbauer factor; D (N/m), the mean force constant; EK,the vibrational kinetic energy; EZ, the vibrational kineticenergy at 0 K of the 57Fe nucleus (Table 2; Fig. 7). Theseare thermodynamic parameters of the 57Fe-participatingvibrations. It is interesting to note that although the soundvelocities of orthoenstatite do not show an obvious trendwithin the low iron-concentration region of the solid-solu-tion, quantities derived from the whole spectrum (thePDOS) do show trends. The shape of the PDOS indeedchanges as a function of iron content (Fig. 3). This can beunderstood quantitatively by analyzing the contributions ofthe vibrational spectrum to the individual thermodynamicquantities. The energy dependence of the PDOS, g(E),of the contribution to the mean force constant (D) isproportional to g(E)*E2 (Fig. 8). The higher energy regions(E . 10 meV) of the spectra differ significantly as afunction of iron content. These differences rusult in adecrease of the mean force constant as iron concentrationincreases (Fig. 7d). Therefore, as the bonds related to theiron atoms weaken, the remaining structural componentsmust stiffen in order to maintain roughly constant values ofthe isotropically averaged elastic properties (Fig. 5 and 6).

In Fig. 9 we plot the energy dependence of the vibra-tional contributions to the vibrational specific heat peratom at constant volume (cV) for En80:

cV ¼ 3kB

ðE2 2kBT sin h

E

2kBT

� �� ��2gðEÞdE: (8)

Table 1. Debye sound velocities and other elastic parameters oforthoenstatites determined from the low-energy region of the PDOS.

Density(g/cc)

vD

(km/s)vS

(km/s)vP

(km/s)K0S*(GPa)

m(GPa)

En93 3.26(1) 5.12(20) 4.62(2) 7.83(20) 107.2 70(6)En87 3.31(1) 5.11(5) 4.62(5) 7.79(10) 106.8 71(2)En80 3.36(1) 5.08(7) 4.59(7) 7.23(11) 106.4 71(2)

Notes: (*) fixed values obtained from a linear regression of pre-vious Brillouin scattering results for MgSiO3 and FeSiO3 orthopyr-oxene as a function of density. A density correction (,1 %) toaccount for natural iron-enrichment was applied to our data. Valuesin parentheses represent the error in the last significant digit(s).

density (g/cm³)

elas

tic m

odul

i (G

Pa)

KS

µ

Fig. 6. Adiabatic bulk and shear elastic moduli determined from thisexperiment (diamonds) along with previous results (squares) for theorthoenstatite-orthoferrosilite solid solution series. Note that KS wasfixed in our study (see text). Symbols and reference numbers havethe same meaning as in Fig. 5. Additionally, 11 ¼ (Mg,Fe)SiO3

orthoenstatite (Hugh-Jones & Angel, 1997); 12 ¼ MgSiO3 orthoen-statite (Hugh-Jones & Angel, 1994).

Table 2. The 57Fe weighted thermodynamic parameters of orthoen-statites determined from the PDOS.

cV

(kB/atom)

Svib

(kB/atom) fLM

D(N/m)

EZ

(meV/atom)

EK

(meV/atom)

En93 2.74(2) 3.61(2) 0.723(3) 195(5) 6.38(8) 14.7(1)En87 2.75(1) 3.60(1) 0.730(2) 170(3) 6.15(6) 14.01(7)En80 2.77(2) 3.71(2) 0.709(3) 165(5) 6.11(8) 15.1(1)

Notes: cV - specific heat per atom at constant volume; Svib - thevibrational entropy per atom; fLM – the average Lamb-Mossbauerfactor; D – the mean force constant; EZ, EK – vibrational kineticenergy of the nucleus at 0 K and room-temperature, respectively.

Fast Track Article Nuclear resonant spectroscopy of (Mg,Fe)SiO3 orthoenstatites 5

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One can see that all energies are essentially weightedequally at 300 K, which results in minimal effects fromcV to the shapes of the PDOS. The differences willdecrease even further at higher temperatures. This effect

is the same for En87 and En93. The relationship betweenthe PDOS, g(E), and the Lamb-Mossbauer factor (fLM)(Chumakov & Sturhahn, 1999) is as follows:

� ln fLM ¼ ER

ð1þ e��E

1� e��E

� �gðEÞE

dE ¼ k2 x2� �

; (9)

where k is the incident wave vector and ,x2. is themean-square-displacement of the 57Fe atoms. For vibra-tional entropy, the relationship is as follows (Sturhahn,2004):

Svib ¼ 3kB

ð�E

2

e�E þ 1

e�E � 1

� �

� ln e�E2 � e�

�E2

h i�

gðEÞdE

(10)

c V (k B/a

tom

)

(a)2.80

2.78

2.76

2.74

2.72

2.70

S vib (

k B/ato

m)

(b)3.74

3.70

3.66

3.62

3.58

f LM

(c)0.735

0.730

0.725

0.720

0.715

0.710

0.705

0.700

Mea

n Fo

rce

Cons

tant

, D (N

/m)

3.24 3.26 3.28 3.30 3.32 3.34 3.36 3.38density (g/cm3)

(d)200

190

180

170

160

Fig. 7. Selected thermodynamic parameters extracted from the PDOSof 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 Lamb-Mossbauer factor, and (d) the mean force constant, D (N/m).

Fig. 8. The energy dependence of the vibrational contributions to themean force constant (D). The higher energy regions (E > 15 meV) ofthe spectra differ significantly as a function of iron content.

energy (meV)

g(E)

*Q Q = E2[2kBTsinh(E/2kBT)]-2

Fig. 9. The energy dependence of the vibrational contributions to thevibrational specific heat at constant volume (cV), where Q is the factorrelating g(E) to cV is Q, kB is the Boltzman factor, and T ¼ 300 K forEn80 (open circles); g(E) for En80 is plotted for comparison (solidblack line).

6 J.M. Jackson, E.A. Hamecher, W. Sturhahn Fast Track Article

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4. Mossbauer spectroscopy

Nuclear forward scattering of synchrotron X-radiation is aMossbauer spectroscopic method. 57Fe Mossbauer spec-troscopy provides access to the hyperfine structure of theiron component in a solid material containing the 57Feresonant isotope (see Dyar et al., 2006 for a recent reviewon the application to Earth and planetary materials). Thehyperfine interaction describes the splitting of nuclearenergy levels as a result of the hyperfine coupling to atomicor molecular energy levels. The quantities observed whichare most relevant to the current study are isomer shift (IS)and quadrupole splitting (QS). The IS is proportional to thes-electron density at the nucleus, and hence is indirectlyinfluenced (via shielding effects) by the d-electron popula-tion in the valence shell. The IS thus provides informationon the valence (i.e, oxidation) state. A QS is observed whenan inhomogeneous electric field (i.e., a gradient) at theMossbauer nucleus is present. In general, two factors cancontribute to the electric field gradient, an electron distri-bution in the valence shell and/or a nearby, lattice environ-ment with non-cubic symmetry. Thus, QS data yieldinformation on local structure and, in a complementarymanner to the isomer shift, the oxidation state. Asexplained in previous reports, a single doublet (quadrupolesplitting and isomer shift) in conventional Mossbauer spec-troscopy (MBS) produces a characteristic oscillation in theSMS time spectrum with a periodicity equal to 2h/QS,where h is Planck’s constant (Zhang et al., 1999). Detailsof the comparison between these two methods have beendiscussed elsewhere (Alp et al., 1995). The presence ofadditional sites leads to coherent superposition with respec-tive weights, isomer shift(s), and line broadening, all ofwhich are directly determined by analysis of the SMS timespectrum. IS are only observable in a relative sense: in thecase of MBS, the IS is usually reported relative to theemission line of the source. In the case of SMS, IS valuesare obtained by placing a reference absorber with knowncomposition and thickness, usually stainless steel, in theX-ray beam-path with the sample. If there is more thanone iron site observed in the spectrum, one may obtain anIS of the one site relative to the other site. These quantities(IS and QS) have successfully been used to identify thevalence and spin states of iron at various temperatures atroom-pressures (Gutlich & Goodwin, 2004; Dyar et al.,2006; McCammon, 2006) and in some well-defined systemsat high-pressures (Sarkisyan et al., 2002; Lin et al., 2006b).

4.1. Synchrotron Mossbauer spectroscopy (SMS)measurements

The SMS experiments were performed at beamline 3-ID-Bat the APS under ambient conditions. The X-rays wereprepared exactly the same as that described for theNRIXS measurements in Section 3 of this paper. Onlyone detector is needed for SMS, which is placed 100 cmfrom the X-ray focused spot (Fig. 1). Saturation of nuclearresonant absorption scales with the effective thickness.

Values of more than one per resonance line have a signifi-cant influence on the time spectra and exact thicknessvalues are necessary to extract accurate hyperfine para-meters (Burnham et al., 1971; Sturhahn, 2000). Due to thevery large effective thickness and irregularities in shape ofthe 57Fe enriched En87 sample used for NRIXS, a smallportion of the En87 sample was pressed into a �20 mmthick pellet and mounted in the X-ray focus spot.Additional constraints on the hyperfine parameters of thesample were provided by placing a 57Fe-enriched stainlesssteel foil with a physical thickness of 0.5 mm in the X-raybeam path (Alp et al., 1995). Therefore, spectra werecollected with and without stainless foil with collectiontimes of 30 min per spectrum (Fig. 10). Accounting fordetector-related effects, we were able to observe nuclearresonant scattering in a time window of 20 to 125 nsfollowing excitation.

4.2. Evaluation of the Mossbauer spectra

The measured SMS spectra were evaluated using theCONUSS software (Sturhahn, 2000). Spectra withoutstainless steel foil were evaluated first, to constrain thequadrupole splittings and weights of the sites. With thisinformation, the isomer shifts of all sites were determinedusing the spectra containing the stainless steel foil refer-ence. We report all isomer shift values relative to a-iron atambient conditions, which is typical for results reportedfrom conventional Mossbauer spectroscopy. The isomershift of stainless steel relative to a-iron is �0.09 mm/s(Hawthorne, 1988). Figure 10 displays the time spectratogether with the best-fit hyperfine parameters.

We observed two sites in the SMS time spectrumof (Mg0.87Fe0.13)SiO3 orthoenstatite, which are welldistinguished by their hyperfine fields. One site, represent-ing 93 % of the total iron, is characterized by a QS of2.22 � 0.01 mm/s and an IS of 1.15 � 0.01 mm/s. These

0 20 40 60 80 100 120 140time (ns)

100

1000

10000

coun

ts

En87En87 with SS

299 K, 1 atm.

En87M1 M2

Wt.(%) 7 93(4)QS (mm/s) 2.46(5) 2.22(1)IS (mm/s) 1.19(1) 1.15(1)

Fig. 10. Synchrotron Mossbauer spectra of En87 with (closedspheres) and without (open spheres) the reference stainless steelabsorber (SS). The lines through the data represent the best-fithyperfine parameters (Table 3). The normalized w2 values for thefits are 2.4 and 4.7, respectively.

Fast Track Article Nuclear resonant spectroscopy of (Mg,Fe)SiO3 orthoenstatites 7

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QS and IS values are consistent with previous reports onthe behavior of high-spin Fe2þ in the more distorted M2polyhedron site of the Pbca orthopyroxene structure(Shenoy et al., 1969; Virgo & Hafner, 1969; Skogbyet al., 1992; Fei et al., 1994; Angel et al., 1998; Dyaret al., 2007). The remaining 7 % of the iron is characterizedby 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. Incorporationof 3 % Fe3þ, an amount close to the detection limit, did notchange our w2 values. We observed no line-broadening. Inthe method of SMS, the source has no influence on the timespectrum and any line-broadening observed can be attributedto the sample. In conventional Mossbauer spectroscopy(MBS), line-broadening in the spectra can be a result of thesource and the sample.

A small portion of the En87 sample used in the NRIXSmeasurements was mounted in a small aperture confined bylead for conventional Mossbauer spectroscopy measure-ments using a new Co(Rh) source (Fig. 11). The MBS

spectrum was fit using CONUSS. The best-fit hyperfineparameters are listed in Table 3 and agree very well withthe parameters obtained from our SMS measurements.

5. Concluding remarks

We have shown that the sound velocities of a suite oforthoenstatite samples measured by NRIXS are in goodagreement with sound velocities obtained using ultrasonicand Brillouin scattering methods. More importantly, thelattice vibrations pertaining to the 57Fe-nuclei have beenmeasured. The quantities derived from NRIXS measure-ments of the PDOS for orthoenstatites offer uniqueinsights into the behavior of iron in materials. The natureof the PDOS obtained from NRIXS involving only 57Feparticipating vibrations suggests that these measurementsshould be complemented with the total phonon density ofstates to obtain representative thermodynamic behavior ofthe entire sample. We have also demonstrated that hyper-fine parameters of En87 determined using SMS agree verywell with those determined using MBS.

Acknowledgments: We thank Y. Fei (CarnegieInstitution of Washington) for synthesizing the orthoen-statite samples, E.E. Alp (ANL) for performing theconventional Mossbauer measurements, J. Zhao (ANL)for technical assistance at sector 3, D. Zhang (Caltech)for discussions, and two anonymous reviewers for theircomments and suggestions. Support for this work wasprovided by the National Science Foundation (NSF)EAR #0711542 (JMJ). Use of the Advanced PhotonSource was supported by the US DOE, Office ofScience, and BES (DE-AC02-06CH11357). This researchwas partially supported by COMPRES under NSFCooperative Agreement EAR 06–49658.

-10 -5 0 5 10velocity (mm/s)

370000

380000

390000

400000

410000

420000

coun

ts

En87M1 M2

Wt.(%) 8 92(2)QS (mm/s) 2.55(2) 2.17(1)IS (mm/s) 1.19(1) 1.16(1)

300 K1 atm.

Fig. 11. Conventional Mossbauer spectrum of En87 collected with anew Co(Rh) source (open symbols). The lines through data repre-sent the best-fit hyperfine parameters (Table 3).

Table 3. The best-fit hyperfine parameters of En87 obtained from fits to the SMS time spectra and a comparison with literature values forsimilar pyroxenes at ambient pressure.

M1 M2

Phase Method T (K) Wt (%) QS (mm/s) IS (mm/s) Wt (%) QS (mm/s) IS (mm/s)

(Mg0.87Fe0.13)SiO3a OEN SMS 299 7 2.46(5) 1.19(1) 93(4) 2.22(1) 1.15(1)

(Mg0.87Fe0.13)SiO3a OEN MBS 300 8 2.55(2) 1.19(1) 92(2) 2.17(1) 1.16(1)

(Mg0.975Fe0.025)SiO3b OEN MBS 293 13.9 2.55 1.17 86.1 2.12 1.14

(Mg0.90Fe0.10)SiO3b OEN MBS 293 15.9 2.45 1.16 84.1 2.09 1.14

(Mg0.90Fe0.10)SiO3c OEN MBS 77 nr 3.06 1.28 nr 2.15 1.27

(Mg1.857Fe0.134)2(Si1.996Al0.004)2O6d OEN MBS 77 18.9 nr nr 81.1 nr nr

CaFeSi2O6e CPX SMS 300 100 2.25 nr na na na

(Mg0.892Fe0.108)SiO3f CPX MBS 81 nr 3.14(2) 1.290(5) nr 2.17(2) 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 Mossbauer spectroscopy, MBS – conventional Mossbauer spectroscopy, nr – not reported, na – notapplicable. Parameters with error values were varied in the fits. The weights are normalized to 100 %. Uncertainties are given in parenthesis atthe 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).

8 J.M. Jackson, E.A. Hamecher, W. Sturhahn Fast Track Article

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Received 27 November 2008

Modified version received 16 January 2009

Accepted 11 March 2009

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