American Mineralogist, Volume 85, pages 943–952, 2000
Temperature dependence of the hyperfine parameters of synthetic
P21/c Mg-Fe clinopyroxenes along the MgSiO3-FeSiO3 join
S.G. EECKHOUT,1,* E. DE GRAVE,1,† C.A. MCCAMMON,2 AND R. VOCHTEN3
1
Department of Subatomic and Radiation Physics, University of Gent, Belgium
2
Bayerisches Geoinstitut, University of Bayreuth, Germany
3
Department of Chemistry, University of Antwerp, Belgium
ABSTRACT
Transmission 57Fe Mössbauer measurements were acquired in the temperature range 11–745 K
from a suite of nine synthetic Ca-free P21/c Mg-Fe clinopyroxenes (cpx) along the MgSiO3-FeSiO3
join. The paramagnetic Mössbauer spectra (MS) consist of one doublet produced by Fe2+ ions at an
almost regular octahedral M1 site and a second doublet at a more distorted octahedral M2 site. The
temperature dependencies of the Fe2+ center shifts were fit to equations derived from the Debye
model for the lattice vibrations, allowing the determination of the characteristic Mössbauer temperatures for the two Fe sites. The temperature variations of the M1 and M2 quadrupole splitting
∆EQ(T) are consistent with the higher distortions of the M2 octahedra. Applied-field MS revealed
that the principal component of the electric field gradient, Vzz, is positive, implying a tetragonal
compression of both octahedral sites. The crystal-field model was used to analyze ∆EQ(T) and to
calculate the energy gaps ∆1 and ∆2 of the first excited electronic states within the 5D orbital term,
both at M1 and M2. The various physical quantities derived from the MS are discussed in terms of
the Fe/(Fe + Mg) ratio.
INTRODUCTION
Ca-poor Mg-Fe pyroxenes are important components of the
Earth’s crust and upper mantle. They exhibit both orthorhombic and monoclinic symmetries depending on the external conditions of pressure and temperature (e.g., Woodland and Angel
1997). The crystal structure of all pyroxenes can be described
in terms of alternating tetrahedral and octahedral layers that lie
parallel to the (100) plane. Within the tetrahedral layer, each
SiO4 tetrahedron shares two corners with adjacent tetrahedra
to form infinite chains parallel to the c axis. The octahedral
layer contains two sixfold-coordinated sites for Fe2+ and Mg2+,
denoted as M1 and M2.
The high-pressure C2/c polymorph relevant for the upper
mantle is non-quenchable (Angel et al. 1992; Hugh-Jones et
al. 1994). Thus in-situ Mössbauer measurements at high pressure are needed, as reported by McCammon and Tennant (1996)
on FeSiO3. Their spectra were collected at room temperature
(RT), whereas variable-temperature Mössbauer spectroscopy
(MS) provides important information on lattice temperatures,
electronic structures and distortions of the iron sites. Variabletemperature MS studies are only mentioned in literature for
orthopyroxenes (e.g., Lin et al. 1993; Regnard et al. 1987; Sinha
et al. 1993; Van Alboom et al. 1993, 1994). For a better understanding of the other polymorphs in the MgSiO3-FeSiO3 system, it is useful to extend this variable-T work to the
*Research Assistant, Fund for Scientific Research, Flanders,
Belgium. E-mail: [email protected]
†Research Director, Fund for Scientific Research, Flanders,
Belgium.
0003-004X/00/0708–943$05.00
943
low-pressure P21/c structures. The object of this study is to
extend the results of Angel et al. (1998) on Ca-free P21/c
clinopyroxenes to more temperatures and to extend the results
of Eeckhout et al. (2000) to more compositions.
EXPERIMENTAL METHODS
Clinopyroxenes of nine different compositions between the
end-members MgSiO3 (XFe = 0.00) and FeSiO3 (XFe = 1.00) were
synthesized in a multi-anvil press operating at 10 GPa and 1200
o
C. The duration of the multi-anvil experiments was 10 hours
in the 1000 ton uniaxial split-sphere press (Hymag 1000,
samples H819, H750, H1089, and H1090) and 12 hours in the
1200 ton press (Sumitomo UHP 1200, samples U1853, S2102,
U1850, U1847, and U1848). For the samples XFe = 0.092(3),
0.193(5), and 0.469(23) a 70% 57Fe-enriched synthesized
fayalite was used, whereas for the other compositions the 57Fe
enrichment was 20%. More details about the synthesis procedure and conditions are provided by Eeckhout et al. (2000).
Our samples were synthesized under conditions in which
the C2/c pyroxene polymorph is stable, but reverts to the P21/c
structure upon quenching. The formation of single-phase P21/c
clinopyroxene was confirmed by powder X-ray diffraction
(XRD) using a Siemens D5000 diffractometer. Chemical analyses were performed by electron microprobe. The results of the
syntheses are summarized in Table 1.
Mössbauer spectra (MS) were collected in transmission
geometry. A 57Co(Rh) source was driven by a constant-acceleration, triangular waveform. For absorber preparation the
MgxFe1–xSiO3 powders were diluted with boron nitride and the
mixture was sealed in a boron nitride capsule. The absorber
temperature was varied between 11 K and 745 K. MS with 512
944
EECKHOUT ET AL.: MÖSSBAUER OF Mg-Fe CLINOPYROXENES
channels were obtained after numerical folding in order to improve statistics. Baseline counts of the unfolded MS were typically ~106. The spectrometer was periodically calibrated using
a spectrum of an Fe foil recorded at RT at a velocity range of
±4 mm/s. All center-shift values quoted are relative to this standard. Care was taken to ensure that all experimental conditions
remained unaltered throughout each temperature scan for all
compositions. Additional MS were collected with the sample
in an external magnetic field of 60 kOe.
SPECTRAL ANALYSES AND RESULTS
All MS collected in zero external magnetic field consist of
two quadrupole doublets attributed to Fe2+ in the M1 and M2
sites (Fig. 1). By analogy with orthopyroxenes, the inner doublet with smallest center shift δ and quadrupole splitting ∆EQ
is attributed to Fe2+ at the M2 sites (Virgo and Hafner 1970).
Visual inspection reveals a slightly asymmetric peak depth
for the low- and high-velocity components of the doublets, even
for exclusively ferrous samples. Possible causes of the asymmetry include texture effects and next-nearest-neighbor interactions.
To check whether texture effects might be responsible for
this asymmetry (Nagy 1978), RT spectra were additionally collected for all samples with the respective absorber planes held
at the magic angle (~54°) with respect to the incident γ-ray
beam. Comparison with the conventional MS (i.e., normal incidence) showed no evidence for such effects.
Asymmetric peak depths were attributed to next-nearestneighbor interactions by Seifert (1983) for aluminous
orthopyroxene and by Woodland et al. (1997) and Angel et al.
(1998) for Ca-free P21/c clinopyroxene. As a test, we applied
the fitting model of Woodland et al. (1997) and Angel et al.
(1998), who used Voigt singlets with equal component areas
and unequal line widths, to our spectra from the sample with
composition Mg0.22Fe0.78SiO3. We analyzed the temperature
variation of the resulting Fe2+ center shifts using the Debye
model for the lattice vibrations (see next section), but obtained
unrealistically low values for the M1 and M2 Mössbauer temperature. The failure of the model might be due to the low spectral resolution at higher temperatures, because Woodland et al.
(1997) and Angel et al. (1998) reported hyperfine parameters
only for spectra collected at 81 K. To obtain consistent results
at all temperatures, our spectra were fit to Lorentzian doublets.
Although this results in slightly higher residuals, the values of
the derived center shifts and quadrupole splittings do not vary
within experimental error from values obtained from asymmetric fits at low temperature.
Due to the small spectral contribution of Fe2+(M1) for the
clinopyroxenes with low Fe-content, XFe = 0.092(3), 0.193(5),
and 0.318(5), the line width (Γ) of the M1 and M2 doublets
were constrained to be equal in order to obtain consistent results. All other MS collected at T < 300 K were analyzed without such constraints. As a result of the strong overlap of the
doublets at higher temperatures, the MS collected in the range
325–745 K were fitted with constrained area ratios for these
doublets. The values were fixed to those obtained from the respective MS at 40 K for the iron-rich compositions, and at 11
K for the iron-poor compositions. At these lower temperatures
the resolution of the doublets is significantly higher.
A small amount of Fe3+ (2–4%) was detected in samples
with compositions XFe = 0.781(6), 0.874(5), and 1.00, but its
subordinate effect can be ignored. The weak, ferric doublet was
fitted by fixing the center shift (δ) and by constraining the line
width to be equal to the value of the M2 doublet.
Hyperfine parameters based on the above fitting constraints
are listed in Table 2. The smaller center shift corresponding to
the M2 site reflects the more covalent character of the Fe-O
bond on M2. As previously observed by Woodland et al. (1997),
Fe is enriched at the M2 sites as shown by the relative areas
(RA) of the two doublets. For Mg-Fe clinopyroxenes with high
Mg contents, the M1 doublet appears as a weak shoulder of the
intense M2 doublet. Consequently, the errors on the corresponding hyperfine parameters are higher. Along the MgSiO3-FeSiO3
join, the RA of the M1 doublet gradually increases with increasing Fe content. For FeSiO3 the RA values of the two doublets are found to be close to 0.5.
The synthetic Mg-Fe clinopyroxenes used in this study are
all 57Fe-enriched and the effective Mössbauer thicknesses are
relatively high. We therefore corrected the observed line widths
for both M1 and M2 doublets for thickness effects. These corrections provide qualitative information about the homogeneity of the samples, provided that instrumental vibrations or
saturation effects are absent. Because instrumental broadening
is equivalent for all samples, different next-nearest-neighbor
TABLE 1. Microprobe analyses of the Mg-Fe P21/c clinopyroxene samples and the partitioning of Fe 2+ among the M1 and M2 octahedral
sites
Sample
XFe
% M1
XFe,M1
XFe,M2
Sample*
H819
0.092(3)
0.259(10)
0.048(15)
0.136(15)
0.108(24)
U1853
0.193(5)
0.280(10)
0.108(15)
0.278(15)
–
S2102
0.318(5)
0.300(10)
0.191(15)
0.443(15)
0.296(31)
U1850
0.469(23)
0.358(10)
0.336(35)
0.602(35)
0.387(16)
U1847
0.613(4)
0.383(10)
0.469(15)
0.756(15)
0.597(20)
H750
0.781(6)
0.446(10)
0.697(15)
0.897(15)
0.800(20)
H1089
0.874(5)
0.462(10)
0.808(15)
0.975(15)
–
H1090
0.913(5)
0.483(10)
0.882(15)
0.944(15)
0.899(10)
U1848
1.000
0.490(10)
0.980(10)
1.020(10)
1.000
Notes: The percentage of Fe at M1 has been determined from Mössbauer spectra collected at 40 K.
* The partition coefficients of comparable compositions determined by Woodland et al. (1997).
XFe,M1 *
0.066(15)
–
0.173(19)
0.238(13)
0.420(18)
0.690(24)
–
0.847(20)
0.982(20)
XFe,M2 *
0.150(34)
–
0.419(44)
0.536(23)
0.774(29)
0.910(28)
–
0.951(21)
1.018(20)
EECKHOUT ET AL.: MÖSSBAUER OF Mg-Fe CLINOPYROXENES
945
FIGURE 1. Mössbauer spectra at selected temperatures of Mg0.81Fe0.19SiO3 (A) and FeSiO3 (B, see next page). At low T, the outer doublet is due
to Fe2+ at M1 and the inner doublet to Fe2+ at M2. A small amount of ferric iron is also detected in FeSiO3. + = data; solid lines = fits and components.
946
FIGURE 1—continued.
EECKHOUT ET AL.: MÖSSBAUER OF Mg-Fe CLINOPYROXENES
EECKHOUT ET AL.: MÖSSBAUER OF Mg-Fe CLINOPYROXENES
947
TABLE 2. Hyperfine parameters of Ca-free P21/c clinopyroxenes along the MgSiO3-FeSiO3 join at 40 and 275 K
XFe
0.092(3)
0.193(5)
0.318(5)
0.469(23)
0.613(4)
0.781(6)
0.874(5)
0.913(5)
1.000
δ (mm/s)
M1
1.293(5)
1.298(5)
1.303(5)
1.305(5)
1.302(5)
1.304(5)
1.288(5)
1.295(5)
1.309(5)
M2
1.273(5)
1.280(5)
1.280(5)
1.276(5)
1.272(5)
1.259(5)
1.253(5)
1.253(5)
1.271(5)
∆EQ (mm/s)
M1
M2
3.078(10)
2.174(10)
3.087(10)
2.159(10)
3.080(10)
2.150(10)
3.086(10)
2.114(10)
3.108(10)
2.092(10)
3.109(10)
2.047(10)
3.149(10)
2.042(10)
3.172(10)
2.048(10)
3.167(10)
2.028(10)
Γ (mm/s)
M1
0.269(10)
0.264(10)
0.267(10)
0.269(10)
0.264(10)
0.257(10)
0.251(10)
0.254(10)
0.259(10)
RA
M2
0.252(10)
0.253(10)
0.251(10)
0.247(10)
0.248(10)
0.252(10)
0.267(10)
0.256(10)
0.249(10)
M1
0.259(10)
0.280(10)
0.300(10)
0.358(10)
0.383(10)
0.446(10)
0.462(10)
0.483(10)
0.490(10)
M2
0.741(10)
0.720(10)
0.700(10)
0.642(10)
0.617(10)
0.554(10)
0.538(10)
0.517(10)
0.510(10)
T = 275 K
0.092(3)
1.172(5)
1.158(5)
2.625(10)
2.119(10)
0.287(10)
0.245(10)
0.193(5)
1.174(5)
1.159(5)
2.637(10)
2.105(10)
0.282(10)
0.253(10)
0.318(5)
1.189(5)
1.161(5)
2.650(10)
2.088(10)
0.290(10)
0.243(10)
0.469(23)
1.185(5)
1.157(5)
2.676(10)
2.057(10)
0.297(10)
0.259(10)
0.613(4)
1.187(5)
1.156(5)
2.653(10)
2.048(10)
0.292(10)
0.268(10)
0.781(6)
1.182(5)
1.137(5)
2.654(10)
1.993(10)
0.296(10)
0.252(10)
0.874(5)
1.179(5)
1.132(5)
2.684(10)
1.981(10)
0.277(10)
0.281(10)
0.913(5)
1.175(5)
1.128(5)
2.686(10)
1.994(10)
0.277(10)
0.251(10)
1.000
1.197(5)
1.147(5)
2.682(10)
1.971(10)
0.287(10)
0.250(10)
Notes: Center shift δ (mm/s, relative to α-Fe), quadrupole splitting ∆EQ (mm/s), corrected absorber thickness Γ (mm/s)
octahedral sites M1 and M2.
environments might cause variations of Γ across the MgSiO3FeSiO3 join on the M1 and/or M2 octahedral sites. The fitting
procedure with symmetric Lorentzian-shaped doublets, however, averages out these differences due to next-nearest-neighbor interactions.
Thickness corrections were performed using the following
formula for the observed line width (O’Connor 1963):
Γ = (Γs + Γa) (1.00 + 0.135 tA)
with Γs the source line width and Γa the absorber line width for
the effective absorber thickness tA → 0. This effective thickness is defined as:
tA = waa(nada)σ0f
in which w is the relative absorption area (being 0.5 for symmetric doublets), aa the 57Fe-enrichment (~0.022 for natural Fe),
nada the number of iron species per square centimeter for the
involved site, σ0 the maximum resonant cross section (2.57 ×
10–18 cm2), and f the Mössbauer fraction.
The M1 and M2 Mössbauer fractions f at any given temperature are evaluated from the experimental temperature dependence of the center shifts using the Debye approximation
for the lattice-vibrational spectrum to quantify the second-order Doppler shift (see next section for more details). Results
from the thickness correction show that the corrected line widths
are relatively constant for all compositions, confirming the
homogeneity of the samples (Table 2).
DISCUSSION
Temperature dependence of the center shifts
The temperature variation of the center shift is commonly
interpreted based on
0.300(20)
0.600(20)
0.289(20)
0.711(20)
0.315(20)
0.685(20)
0.329(20)
0.671(20)
0.367(20)
0.633(20)
0.436(20)
0.564(20)
0.450(20)
0.550(20)
0.499(20)
0.501(20)
0.483(20)
0.517(20)
and relative area RA at both
δ(T ) = δ I + δSOD (T )
(1)
or
δ(T) = δΙ –
9 k BT  T 


2 Mc  Θ M 
3 Θ M /T
∫
0
x 3dx
ex − 1
(2)
with δΙ the intrinsic isomer shift, considered to be constant and
δSOD the second-order Doppler shift. The latter quantity originates from the non-zero mean square velocity of the nuclei,
and hence is related to the lattice vibrations of the probe nuclei. Using the Debye approximation for the lattice-vibrational
spectrum the so-called characteristic Mössbauer temperature
ΘM and the intrinsic isomer shift δI are evaluated. The tightness of binding is qualitatively measured by ΘM, which is especially useful for comparative studies of related structures. Once
ΘM is known, the recoil-free fraction f at any temperature can
be evaluated from the following formula (Pound and Rebka
1960):
 3 E
R
f (T ) = exp −
 2 kBΘ M
2 Θ /T

 T  M xdx  
1+ 4 
 ∫ x 
 Θ M  0 e − 1 

(3)
with ER the recoil energy (= 3.13425 × 10–22 J for the 14.4 keV
transition of 57Fe). The Debye integrals in Expressions 2 and 3
can be calculated using the series-expansion method as described by Heberle (1971).
Precise experimental δ data spanning a broad temperature
interval are required in order to extract reliable quantitative
information from observed δ(Τ) curves (De Grave and Van
Alboom 1991). In the case of Ca-free clinopyroxene, the reliability of the obtained results deteriorates as resolution decreases. In initial attempts to calculate the characteristic
Mössbauer temperatures, all MS (~26 in total for each compo-
948
EECKHOUT ET AL.: MÖSSBAUER OF Mg-Fe CLINOPYROXENES
sition) collected between 11–750 K (Mg-rich samples) or 40–
750 K (Fe-rich samples) were used, assuming the intrinsic isomer shift δ I to be independent of temperature. The calculated
temperature variations of the isomer shifts did not agree with
experimental values, however, particularly above 300 K. At
these temperatures the M1 and M2 doublets are poorly resolved,
resulting in a lack of required precision for their δ values.
De Grave and Van Alboom (1991) used a linear correlation
δI(T) = δI(0) + a 10–5 T
(4)
with a the linear correlation coefficient, to explain the hightemperature mismatch between their observed and computed
δ(T) curves for the Fe2+(M1) site in a natural hedenbergite. The
M1 doublet for this mineral is sharply defined and hence its
center shift at any given temperature is determined to very high
precision. The weak temperature dependence of δΙ is proposed
to be due to the thermal radial expansion of the t2g and eg wave
functions (Perkins and Hazony 1972). By including the correlation Equation 4 in the model calculations, we obtained closer
agreement between experimental and calculated data, particularly at higher temperatures. The physical meaning of the linearity, however, remains unclear.
To obtain ΘM (and f) values for the present spectra, Equation 4 was used with no constraints imposed on the coefficient
a. This procedure led to unrealistically large variations of a
along the MgSiO3-FeSiO3 join. Therefore we fixed the slope a
at the value found for hedenbergite, i.e., –7.0 mm/(s · K) (Van
Alboom 1994). For Mg0.22Fe0.78SiO3, ΘM values obtained with
this assumption were similar to results obtained if no temperature variation for δI was considered. For the Mg- and Fe-rich
compositions, however, the calculations resulted in either unrealistically small or unrealistically large ΘM values, whereas
across the MgSiO3-FeSiO3 join a wide scatter of ΘM values
was obtained.
Only the data up to 300 K were used to calculate the characteristic Mössbauer temperatures of M1 and M2. At these temperatures, the approximation of the Debye model with δ I
considered to be constant, is adequate. As an example, both
experimental and calculated curves for XFe = 0.193 and 1.000
are shown in Figure 2. For the Fe-rich compositions, departure
of the experimental curve from the calculated one at higher
temperatures is observed. This might be due to the significant
overlap of M1 and M2 ferrous doublets at higher temperatures,
which causes higher errors in hyperfine parameters. The characteristic Mössbauer temperatures ΘM at M1 remain constant
along the MgSiO3-FeSiO3 join, whereas a slight decrease in
ΘM at M2 is observed at higher Fe content (Table 3). These
results suggest a similar bonding strength at M1 and a slightly
decreasing bonding strength at M2 with increasing Fe concentration.
Although the Debye model is unrealistic for most solids, it
is useful as a relative measure of bonding properties across a
solid solution. We find that the recoil-free fractions for Fe2+ at
M1 and M2 sites are equal within the error and do not show
any marked variation across the MgSiO3-FeSiO3 join (Table
3). This implies that chemical bonding at both octahedral sites
is similar and that there is little influence of the Fe2+-for-Mg 2+
FIGURE 2. Experimental and calculated temperature variations of
the Fe2+ center shifts δ at M1 and M2 (a) for Mg0.81Fe0.19SiO3 and (b)
FeSiO3.
substitution on the Mössbauer fraction. The obtained ΘM values are similar to values obtained from aluminium-containing
orthopyroxenes reported by De Grave and Van Alboom (1991).
No data are currently available for Ca-free clinopyroxenes.
Woodland et al. (1997) attempted to estimate f for Ca-free C2/
c clinopyroxenes based on two data points (293 K and 81 K),
but no values are mentioned. However, it is the authors’ experience that extracting reliable values of f generally requires
many precise data points.
The Mössbauer fraction f is an important factor in calculating site occupancies from the relative areas of the subspectra
because significant differences between f will affect these areas. Our results show that recoil-free fractions determined at a
specific temperature are equal within the experimental error
for M1 and M2 sites, and do not vary with Mg-Fe composition. No correction for different f values is therefore required.
To obtain site occupancies, the Fe distribution obtained from
MS at 40 K is multiplied by the Fe content of the sample as
determined by microprobe analyses. The results (Table 1) agree
with values determined by Woodland et al. (1997) from MS at
81 K. The reported errors in site occupancies (Table 1) take
into account errors from both MS and microprobe analyses.
Another factor influencing the site distribution of Fe2+ between M1 and M2 sites is the presence of other Fe-bearing
phases with absorption lines that overlap those of clinopyroxenes,
e.g., olivine and orthopyroxene. We do not expect this factor to
EECKHOUT ET AL.: MÖSSBAUER OF Mg-Fe CLINOPYROXENES
949
TABLE 3. Characteristic Mössbauer temperature ΘM (K), intrinsic isomer shift δI (mm/s) and recoil-free fractions f at 40K and 275K (f40
and f275) of M1 and M2 for Ca-free P21/c clinopyroxenes along the MgSiO3-FeSiO3 join
XFs
0.092
0.193
0.318
0.469
0.613
0.781
0.874
0.913
1.000
ΘM(K)
350(35)
345(35)
375(35)
335(35)
375(35)
340(35)
390(35)
340(35)
355(35)
δI(mm/s)
1.395(5)
1.394(5)
1.409(5)
1.397(5)
1.405(5)
1.397(5)
1.391(5)
1.390(5)
1.411(5)
M1
f40
0.901
0.898
0.908
0.895
0.907
0.896
0.911
0.897
0.901
f275
0.730
0.720
0.759
0.708
0.755
0.710
0.772
0.716
0.733
influence our reported site distributions, because X-ray diffraction and microprobe analyses did not detect the presence of
such impurity phases.
Temperature variation of the quadrupole splittings
All compositions display similar experimental temperature
variations of the quadrupole splitting, ∆EQ(T), for the M1 and
M2 sites as the samples in Figure 3. At M1, ∆EQ of Fe2+ is
strongly temperature dependent. For Mg0.81Fe0.19SiO3 it decreases from 3.087 to 1.366 mm/s between 40 and 705 K and
for FeSiO3 from 3.167 to 1.461 mm/s. In contrast, the temperature variation of ∆EQ at M2 is considerably weaker, viz., 2.159–
1.639 mm/s for Mg0.81Fe0.19SiO3 and 2.028–1.370 mm/s for
FeSiO3, both between 40 and 705 K. This different degree of
temperature variation results in a stronger overlap of the M1
and M2 doublets above 300 K and hence in greater errors in
hyperfine parameters, particularly for the weaker M1 component.
The quadrupole splitting ∆EQ at any temperature is given
by
∆EQ =
(eQ) Vzz 
2
η2 
 1+ 

3
ΘM(K)
400(25)
340(25)
365(25)
335(25)
400(25)
325(25)
340(25)
315(25)
310(25)
δI(mm/s)
1.380(5)
1.373(5)
1.380(5)
1.370(5)
1.386(5)
1.348(5)
1.343(5)
1.340(5)
1.357(5)
M2
f40
0.914
0.897
0.905
0.896
0.919
0.892
0.896
0.887
0.885
f275
0.782
0.715
0.747
0.710
0.780
0.695
0.712
0.676
0.667
δ, Vzz (including sign) and η, three field-reduction parameters
can be derived from the experimental line shape. These field
reductions arise from spin-polarization effects, and are in general different along the principal axes of the EFG tensor (Varret
1976). Because their values are of no importance in the scope
of this contribution, no further attention will be devoted to this
effect.
The solid lines in Figure 4 represent the obtained line shapes
of the M1 and M2 subspectra and their superposition. The agreement is adequate considering the complexity of the absorption
effect. We conclude that the Fe2+ species at both sites experience a positive Vzz, implying that the principal distortion term
1/2
(5)
where eQ is the nuclear quadrupole moment, Vzz the principal
component of the electric field gradient (EFG) and η=Vxx–
Vyy/Vzz the asymmetry parameter, being zero for axial symmetry.
The quadrupole splitting ∆EQ of high-spin ferrous iron is
mainly due to its non-spherical 3d6 electron shell. Distortion
from octahedral site symmetry removes the threefold degeneracy of the lower t2g and the twofold degeneracy of the upper
eg orbitals of the 3d6 (5D) electrons. The values of the lowtemperature M1 and M2 quadrupole splittings, i.e., those exceeding 2 mm/s, indicate that for both sites Fe2+ is a singlet
electronic ground state (Ingalls 1964). Further information on
this ground state, and hence on the nature of the non-axial site
distortions was obtained from the MS accumulated with the
absorbers subjected to an external magnetic field of 60 kOe.
All compositions gave similar typical applied-field MS
(AFMS) as that shown in Figure 4. These spectra cannot be
interpreted in terms of a Lorentzian approximation. Instead,
the complete hyperfine-interaction Hamiltonians of ground and
14.4 keV states must be considered, from which by diagonalization the energies of the nuclear levels and transition probabilities are calculated. In addition to the hyperfine quantities
FIGURE 3. Temperature variations of the quadrupole splitting ∆EQ
of Fe2+ at M1 and M2 in (a) Mg0.81Fe0.19SiO3 and (b) FeSiO3. The solid
lines represent the theoretical curves calculated from the static crystalfield model.
950
EECKHOUT ET AL.: MÖSSBAUER OF Mg-Fe CLINOPYROXENES
F IGURE 4. External-field (60 kOe) Mössbauer spectrum of
Mg 0.81Fe0.19SiO3 clinopyroxene at 180 K. Solid lines represent the
calculated subspectra and their superposition. Dots = data.
represents a tetragonal compression. As for the magnitudes of
η, no sound conclusions can be assessed, except that they are
likely non-zero at both sites, indicating a further distortion from
axial symmetry.
Within the crystal-field approach, the non-axial site deformation results in two excited electronic states separated by
energies ∆1 and ∆2 from the singlet ground state of the lowlying t2g orbital. The thermal population of these states explains
the temperature dependence of the valence component of the
quadrupole splitting, ∆EQ,val , and can be expressed in terms of a
reduction function F(T;∆1, ∆2), allowing the temperature dependence of ∆EQ to be written as (Ingalls 1964)
∆EQ(T) = ∆EQ,val(0) F(T; ∆1, ∆2) + ∆EQ,lat ,
(6)
∆EQ,val(0) is the zero-Kelvin valence contribution and ∆EQ,lat is
the lattice contribution due to the surrounding ionic charges,
commonly acting in the opposite sense to ∆EQ,val. The magnitude of the lattice contribution, ∆EQ,lat, is usually smaller
than∆EQ,val and may be approximated as (Ingalls 1964)
∆EQ,lat = –(7/3)(∆1+∆2)/e2<r2>
cpx compounds, at least down to ~25 K (Ingalls 1964). In general, the spin-orbit interaction lifts the fivefold spin degeneracy
of each orbital state and mixes the orbital wave functions, which
decreases the value of the reduction function F and hence the
quadrupole splitting ∆EQ (Gonser 1975).
The ∆1 values at M1 are not significantly affected by the
Mg-Fe composition, whereas the ∆1 values at M2 show a small
decrease with increasing iron content (Table 4). Hence, the principal tetragonal distortion of the octahedral M1 symmetry is
not affected by the Mg-Fe composition, whereas for M2 it is
smallest at the FeSiO3 end member. Further, the energy gap for
the first excited state at M2 is approximately twice the value
for M1, a direct proof of the stronger distortion of the M2 site.
The energies of the second excited states at M2 are relatively
high. Consequently, the thermal population of these states is
low at the temperatures used in this study and the energy gap
∆2(M2) is only poorly defined.
Lin et al. (1993) determined similar values for ∆1 in synthetic orthopyroxenes from measured ∆EQ(T), viz., 480 cm–1 at
the M1 site and 817 cm–1 at the M2 site and Van Alboom et al.
(1994) in two natural orthopyroxenes, viz., 480(50) cm–1 for
M1 and 950(50) cm–1 for M2. These values for ∆1 are significantly larger than those mentioned in earlier reports by Goldman
and Rossman (1977), ∆1(M2) = 354 cm–1, and by Steffen et al.
(1988), ∆1(M2) = 150 cm–1. The latter authors calculated ∆1 at
M2 from electronic absorption spectra at wavelengths in the
visible and near-infrared regions, which hold direct information on the positions of the higher energy levels. On the contrary, ∆EQ(T)-curves obtained from MS provide valuable
quantitative information about the low-energy part of the 5D
level scheme and hence about the symmetry deformation. This
means that MS recorded within a broad T range and electronic
absorption spectra provide supplementary information for the
full interpretation of the crystal-field.
Variation of hyperfine parameters with Mg-Fe composition
In general, the characteristic Mössbauer temperature ΘM of
M1 and M2 remains constant along the MgSiO3-FeSiO3 join
(see Table 3) and ΘM of M1 is somewhat larger than ΘM of M2,
especially at the FeSiO3 end member. This reflects the some-
(7)
where <r2> is the expectation value of the square of the radius
of the 3d orbital.
Neglecting spin-orbit coupling (see below), the reduction
function F(T; ∆1, ∆2) can be expressed as a series of Boltzmann
functions, allowing the energy gaps ∆1 and ∆2 to be determined
from the experimental ∆EQ(T) curve by a common fitting procedure.
The solid lines in Figure 3 represent the fitted ∆EQ(T) curves
based on the crystal-field approximation. The adjusted ∆1 and
∆2 values for the various compositions are listed in Table 4.
Below 80 K, ∆EQ at both octahedral sites levels off because the
reduction function approaches unity when the ground state is
orbitally non-degenerate. This leveling-off also implies that the
effect of the spin-orbit interaction is indeed negligible in these
TABLE 4. Values of the energy gaps ∆1 and ∆2 (in cm–1) at the octahedral M1 and M2 sites in the Ca-free P2 1/c
clinopyroxenes
M1
M2
XFe
∆1
∆2
∆1
∆2
0.092
385
1050
1365
1380
0.193
450
880
930
1910
0.318
430
1130
930
1650
0.469
435
805
940
1960
0.613
440
840
895
2985
0.781
435
835
895
2585
0.874
430
1060
840
1270
0.913
405
995
1010
–
1.000
420
950
835
1335
Notes: Calculated using the static crystal-field model. Estimated errors
are 50 cm–1, except for ∆ 2(M2) which is poorly defined.
EECKHOUT ET AL.: MÖSSBAUER OF Mg-Fe CLINOPYROXENES
what higher bond strengths and slightly smaller volumes at the
M1 site, confirmed by the M-O bond lengths as determined by
X-ray diffraction (Angel et al. 1998). The obtained ΘM values
at M1 and M2 fall within the range 300–400 K reported by De
Grave and Van Alboom (1991) for Fe2+ in silicates. The intrinsic isomer δI of M1 is slightly larger compared to δI of M2
(Table 3). At the M1 site, a small increase of δI is observed
with increasing Fe content whereas δI at M2 decreases along
the MgSiO3-FeSiO3 join (Fig. 5). The value of δI depends on
the s-electron density at the nucleus, which can be affected by
the nature of ligand bonding through shielding of 4s electrons
by 3d electrons. The uniform expansion of the M1 octahedron
by substitution of Mg2+ by the larger Fe2+ ion (Angel et al. 1998)
results in a decrease of electron density at the Fe nucleus and
hence in an increase of the intrinsic isomer shift. The larger
distortion of the M2 octahedron with increasing Fe content
causes the valence electron density to increase and δI to decrease. The latter effect is more prominent than the former one.
Angel et al. (1998) observed similar trends in the center shift
of Ca-free P21/c clinopyroxenes, where they neglected the second-order Doppler shift and considered the measured center
shift to be equal to the intrinsic isomer shift.
The quadrupole splitting ∆EQ measured at 40 K for M1 increases from Mg0.91Fe0.09SiO3 to FeSiO3 whereas the opposite
trend is observed at M2 (Fig. 6). Substitution of Mg2+ ions by
larger Fe2+ ions increases the average (M1,M2)-O distances only
slightly by a few hundredths of Å (Yang and Ghose 1994). The
geometry of the M1 site is invariant with compositional changes,
whereas that of the M2 site is determined by the rotations of
the tetrahedral chains (e.g., Cameron and Papike 1980; Christy
and Angel 1995). As mentioned above, ∆EQ has a valence and
a lattice contribution, the latter acting in the opposite sense. In
general, the valence term dominates, but at the more distorted
M2 site the influence of the lattice term is more important than
at the more regular M1 site. This explains the observed trends
as shown in Figure 6. Domeneghetti and Steffen (1992) reported similar observations on orthopyroxenes and Angel et al.
(1998) on monoclinic P21/c pyroxenes.
ACKNOWLEDGMENTS
Multi-anvil experiments were performed at the Bayerisches Geoinstitut under
the EC “Human Capital and Mobility—Access to Large Scale Facilities” program (contract no. ERBCHGECT940053 to D.C. Rubie) and under the EU
“TMR—Large Scale Facilities” program (contract no. ERBFMGECT980111 to
D.C. Rubie). The authors thank De Parseval for performing the EDX analyses
at the “Service Microsonde Electronique de l'Université Paul Sabatier de
Toulouse”. Financial support for the Mössbauer study was obtained from the
Fund for Scientific Research—Flanders, grant no. 3G.0007.97.
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MANUSCRIPT ACCEPTED FEBRUARY 17, 2000
PAPER HANDLED BY BRIAN PHILLIPS