Zhu Mao
1
, Jung-Fu Lin
1
, Jin Liu
1
, Vitali B. Prakapenka
2
1 Department of Geological Sciences, Jackson School of Geosciences, The University of
Texas at Austin, Austin TX 78712, USA
2
Consortium for Advanced Radiation Sources, University of Chicago, Chicago, IL 60637,
USA
1

Polycrystalline ferropericlase [(Mg
0.75
Fe
0.25
)O] was synthesized by sintering stoichiometric mixtures of MgO and metallic Fe powder at approximately 1450 K for 8 hours under a controlled CO
2
-CO atmosphere near the Fe-FeO buffer [ Lin et al ., 2006].
Electron microprobe analyses showed that the sample was chemically homogeneous and contained 25% Fe, whereas X-ray diffraction spectra showed that the sample was in a rocksalt structure (B1) with a cell parameter of 4.2421 (±0.0002) Å. Potential impurities in the sample, such as magnetite (Fe
3
O
4
), were not detected in X-ray and electron microprobe analyses. Conventional and synchrotron Mössbauer spectroscopic measurements showed that Fe in the sample was predominantly Fe 2+ and that Fe 3+ content was below the detection limit of the techniques (2-3%) [ Jacobsen et al ., 2002;
Lin et al ., 2006].
Previous studies showed that MgO and magnesium-rich HS (Mg,Fe)O (thus named ferropericlase) exhibit similar thermal EoS parameters, albeit a large unit cell volume for
(Mg,Fe)O with the addition of the larger Fe 2+ cation [e.g., Jacobsen et al ., 20002; van
Westrenen et al., 2005; Speziale et al ., 2007; Tange et al ., 2009]. Here we have first compared our pressure-volume ( P-V ) curves with the thermal EoS of MgO as the starting reference at corresponding pressure-temperature ( P-T ) conditions to determine the width of the transition and the occurrence of the HS and LS states systematically. In the
2

comparison, the volume deviation between our data and MgO showed up as a constant volume offset of 1.3 Å 3 in the HS state, and a continuous decreased offset by approximately 1.5 Å
3
across the transition. The volume of the LS state is 0.2 Å
3
smaller than that of MgO. These allowed us to proceed with further thermal EoS data analyses with confidence, including derivation for the isothermal bulk modulus at ambient pressure ( K
T0
), the pressure derivative of the bulk modulus ( K
0
’
), the unit cell volume for the LS state at ambient conditions ( V
0LS
), the temperature derivative of the bulk modulus at constant pressure ((∂
K
/∂
T )
P
), and the thermal expansion coefficient (
α
0
). Here, the thermal EoS of ferropericlase and related thermoelastic parameters are obtained following the method by Duffy and Anderson [1989].
To construct the isosymmetric spin transition diagram of ferropericlase, we derived the temperature (T) dependence of the LS fraction, n
LS
, using the equation [ Tsuchiya et al .,
2006; Wentzcovich et al ., 2009]: n
LS

1

1 exp(

G ( P , T ) * / T )
, (1)
Here, Δ G ( P,T )* is the difference of the Gibbs free energy between the LS and HS state, defined as:

G ( P , T )*
 b
0
( T )
 b
1
( T ) P n
, (2)
3

P n
is the normalized pressure, determined by the ending pressure of the HS state ( P
HS
) and the onset pressure of the LS state ( P
LS
):
P n

P
P
LS


P
HS
P
HS
, (3) b
0
and b
1
are two temperature-dependent constants. With the high P-T experimental results, we determined n
LS
at a given P-T condition (Figure 2). Parameters b
0
and b
1
are derived from the non-linear least square fit of n
LS
as a function of P-T:
b
0
(K)=-156+3.6
T -4.45×10
-4
T
2
, (4)
b
1
(K/GPa)=-2909-1.2
T -2.6×10
-2
T
2
, (5)
Using the obtained thermal EoS, we modeled the thermal expansion coefficient, isothermal bulk modulus, and bulk sound velocity of ferropericlase along the lowermantle geotherm [ Brown and Shankland, 1981 ]. Using equations (15) with determined n
LS
, the unit cell volume of ferropericlase across the spin transition can be computed by
[ Wentzcovich et al ., 2009]:
V

( 1
 n
LS
) V
HS
 n
LS
V
LS
, (6)
4

where V
HS and V
LS
are unit cell volume of the HS and LS states at a given pressuretemperature, respectively. The isothermal bulk modulus is described by [ Wentzcovich et al ., 2009]:
V
K
T
 n
LS
V
LS
K
LS

( 1
 n
LS
)
V
HS
K
HS

( V
LS

V
HS
)(
 n
LS
P
)
T
, (7) where K
HS
and K
LS
are the isothermal bulk modulus of the HS and LS state at a given P-T condition, respectively.
Thermal expansion coefficient is defined by:
 
1

V
V

T
, (8)
Together with equation (6), we have:
 
1
V
{

[( 1
 n
LS

T
) V
HS
]


( n
LS
V

T
LS
)
}
,
(9)
With known α and K
T
, the bulk sound velocity, V
Φ
, is calculated using:
V


( 1
 
T

) K
T
, (10) where γ is the Grüneisen parameter. An anomaly in the Grüneisen parameter across the transition has been found to accompany by the anomaly in the thermal expansion coefficient. However, since this value remains unknown across the spin transition, we have simply used the value for MgO given in the literature for the calculation [ Fei et al .,
1992; Tange et al ., 2009]
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Figure S1. Representative X-ray diffraction patterns of ferropericlase [(Mg
0.75
Fe
0.25
)O] in a laser-heated DAC at high pressures and temperatures.
Figure S2. Fraction of the LS state in ferropericlase along the mantle geotherm. The transition from the HS to LS state along the mantle geotherm shown in our modeling starts at a deeper depth than what have been reported in previous experimental and theoretical studies [ Tsuchiya et al., 2006; Lin et al., 2007] , whereas the width of the spin crossover is narrower.
Figure S3. Thermal elastic parameters of ferropericlase [(Mg
0.75
Fe
0.25
)O] at constant temperatures derived from our experimental results.
Table S1. Pressure-volume data of ferropericlase
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0.6
Fe
0.4
)O, Phys. Chem. Miner., 18, 416-422.
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0.6
Fe
0.4
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Wentzcovitch, R. M., J. F. Justo, Z. Wu, C. R. S. da Silva, D. A. Yuen, and D. Kohlstedt
(2009), Anomalous compressibility of ferropericlase throughout the iron spin cross-over,
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