Lin et al., mw Nature ms Page 1 2/6/16
Supplementary Figures:
SFig. 1 Representative X-ray emission spectra of Fe-K in magnesiowüstite
[(Mg0.40,Fe0.60)O] at high pressures. Insert, integrated and normalized intensity of the
satellite peak of iron in magnesiowüstite-(Mg0.40,Fe0.60)O as a function of pressure. The
magnetic transition occurs at approximately 84 to 102 GPa. The electronic transition
pressure is rather broad in comparison with (Mg0.83,Fe0.17)O results.
SFig. 2 Relative volume of (Mg0.40,Fe0.60)O as a function of pressure at 300 K. The
sample remains in the NaCl-type structure at all pressures9. Insert, normalized stress (F)
versus normalized strain (f) plot. The K0T and K0T’ of the high-spin state are 167.4
(+4.9) GPa and 3.15 (+0.15), respectively. A deviation of the relative volume from the
weighted least squares fit to the high-spin state (red curve) is observed at above 95 GPa,
indicating a volume decrease of 1.6 % due to the spin transition. Our systematic studies
on the spin transition of iron in a series of compositions show that addition of MgO in
FeO stabilizes the low-spin state.
Lin et al., mw Nature ms Page 2 2/6/16
Estimation of effects of volume and entropy change at the spin transition:
Parameters: density of FeO (FeO) at 75 GPa is calculated as FeO=7.3 g/cm3
(K0T=160.7 GPa, K0T‘=3.28, 0=5.7 g/cm3).
1 mole of FeO : 72 g.
1 cm3 of FeO contains 7.3/72=0.1 mole at 75 GPa.
1 mole has 6.02*10 23 formula units of FeO.
There are N=0.6*1023 FeO formula units in 1 cm3.
5% change in 1 cm3 at 75 GPa is equivalent to PV=(75*109)*(10-6*5*10-2) =3750
Joule.
Energy change per one FeO formula unit is PV/N= (3.75*103)/(0.6*1023)=6.25*10-20
Joule
To estimate the temperature effect on the Clapeyron slope of the electronic spin
transition of iron in magnesiowüstite in the Earth’s interior, we follow the
thermodynamic consideration developed by D. M. Sherman [S1,S2] together with our
current experimental data. We consider the change in the electronic internal energy
change (U), entropy change (TS), and volume change (PV) [S1,S2] in order to
determine the Clapeyron slope. Since (Mgx,Fe1-x)O at different compositions (x) has
comparable K0T and K0T’ [S3], this estimate is valid for ferropericlase as well. Our Xray diffraction studies give 1.6% volume change at around 90 GPa in (Mg0.4,Fe0.6)O,
which in turn is 2.7 % change in volume for one FeO formula unit. This gives us the
volume contribution to the enthalpy change per one FeO formula unit 0.39 eV if 5%
volume change is assumed (1 eV is 1.6*10-19 Joule). For the 2.7% volume change at 75
GPa that gives 0.21 eV/formula unit in energy change. The entropy contribution to the
Lin et al., mw Nature ms Page 3 2/6/16
enthalpy change (TS) at 2000 K is -ln(15)kT=-0.47 eV [S1]. At the spin transition, the
free energy change (G) is the sum of the electronic internal energy change (U),
entropy change (TS), and volume change (PV) between the high-spin and low-spin
configurations at 2000 K [S1,S4], which is:
G=Ghs-Gls=U-TS+PV=U-Usp-T(Shs-Sls)+P(Vhs-Vls)= U-Usp-0.47+0.21= U-Usp0.26 eV
(1)
where, in Sherman’s notation [S1], the crystal field stabilization energy (U) is equal to
20Dq=22000 cm-1 =2.7 eV at Fe-O distance R(Fe-O)=2.16 Å (10Dq is the crystal field
splitting), and the spin-pairing energy (Usp) (per two electron pairs) would be interelectronic exchange and repulsion energy. Usp=2(5B+8C)=~4.1 eV (B and C are the
Racah parameters) [S1]. Since spin-pairing energy depends on the intratomic overlap of
the electronic wavefunctions, we neglect the volume dependence of the spin-pairing
energy as compared to the crystal field splitting energy, which is determined by
interatomic interactions. We also assume that volume collapse close to 60-90 GPa is not
strongly temperature-dependent. With this assumptions, we obtain that at high
temperature (T) the transition will be shifted to high pressures by P=U(P+P,T)ln(15)kT=U(P,0), and approximately:
P=ln(15)kT/(U/P)T=2000 – [U(P,T)- U(P,0)]
(2)
Using U~R5 and equation of state of the high-spin state (Mg0.83,Fe0.17)O (K0T=160.8
GPa, K0T’=3.28) from this study, we obtain U =4.1 eV at 63 GPa (which is fairly good
estimate of the high-spin to low-spin transition with this simple model), and P~23 GPa
for T=2000K due to the entropy term. Thus, the high-spin to low-spin transition in
ferropericlase would occur 23 GPa higher at 2000 K, neglecting thermal expansion
effect on U (term in the brackets of Eq. 2). The thermal expansion () is estimated to
Lin et al., mw Nature ms Page 4 2/6/16
be (0)=13x10-6 K-1 at P=0 for [FeO6]10- polyhedron [S5]. Assuming (P)=(0)*KT(0)/
KT(P) (KT is the isothermal bulk modulus) we estimate that the transition pressure is
shifted by ~13 GPa to higher pressure at T=2000 K. Both entropy and thermal
expansion shift the transition by 36 GPa, which gives the Clapeyron slope of the highspin to low-spin transition of 56 K/GPa. We note that the calculated Clapeyron slope for
pure FeO is approximately 70 K/GPa [S1]; the difference in the Clapeyron slope
between our study and Sherman (1988) [S1] is mainly attributed to the estimated
volume change across the transition. It is believed that the composition of
magnesiowüstite in the lower mantle contains approximately 20% FeO. Considering the
compositional and temperature effects on the Clapeyron slope, the high-spin to low-spin
transition of iron in magnesiowüstite is likely to occur at ~120 GPa and 2500 K (at the
top of the D” zone).
References:
[S1] Sherman, D. M. High-spin to low-spin transition of iron(II) oxides at high
pressures: possible effects on the physics and chemistry of the lower mantle, in
Structural and Magnetic phase transitions in minerals, (eds. S. Ghose, J.M.D. Coey,
and E. Salje), pp. 113-118, Springer-Verlag, New York, 1988.
[S2] Sherman, D. M. The high-pressure electronic structure of magnesiowüstite
(Mg,Fe)O: applications to the physics and chemistry of the lower mantle. J. Geophys.
Res. 96, B9, 14299-14312 (1991).
[S3] Jacobsen, S. D. et al. Structure and elasticity of single-crystal (Mg,Fe)O and a new
method of generating shear waves for gigahertz ultrasonic interferometry. J. Geophys.
Res. 107, B2, 10.1029/2001JB000490 (2002).
Lin et al., mw Nature ms Page 5 2/6/16
[S4] Burns, R. G. Mineralogical Applications of Crystal-Field Theory, 2nd Edition,
Cambridge University Press, Cambridge (UK), 1997.
[S5] Hazen, R. M., & Finger, L. W. Comparative crystal chemistry, Wiley, New York,
(1982).