# Laser-driven shock compression and equation of state of Fe2O3 up to 700 GPa

Alexis Amouretti  Institut de Minéralogie de Physique des Matériaux et de
Cosmochimie, CNRS, Sorbonne Université, MNHN, Paris, FRANCE  Graduate School
of Engineering, Osaka University, Suita, Osaka, JAPAN  Marion Harmand
Institut de Minéralogie de Physique des Matériaux et de Cosmochimie, CNRS,
Sorbonne Université, MNHN, Paris, FRANCE  PIMM, Arts et Metiers Institute of
Technology, CNRS, Cnam, HESAM University, 75013 Paris, FRANCE  Bruno
Albertazzi  LULI, École Polytechnique, CNRS, CEA, UPMC, Palaiseau, FRANCE
Antoine Boury  Institut de Minéralogie de Physique des Matériaux et de
Cosmochimie, CNRS, Sorbonne Université, MNHN, Paris, FRANCE  Alessandra
Benuzzi-Mounaix  LULI, École Polytechnique, CNRS, CEA, UPMC, Palaiseau, FRANCE
D. Alex Chin  Laboratory for Laser Energetics, University of Rochester,
Rochester, UNITED STATES  François Guyot  Institut de Minéralogie de Physique
des Matériaux et de Cosmochimie, CNRS, Sorbonne Université, MNHN, Paris,
FRANCE  Michel Koenig  LULI, École Polytechnique, CNRS, CEA, UPMC, Palaiseau,
FRANCE  Tommaso Vinci  LULI, École Polytechnique, CNRS, CEA, UPMC, Palaiseau,
FRANCE  Guillaume Fiquet  Institut de Minéralogie de Physique des Matériaux et
de Cosmochimie, CNRS, Sorbonne Université, MNHN, Paris, FRANCE

###### Abstract

We report here the first equation of state measurements of Fe2O3 obtained with
laser-driven shock compression. The data are in excellent agreement with
previous dynamic and static compression measurements at low pressure, and
extend the known Hugoniot up to 700 GPa. We observe a large volume drop of
$\sim$10% at 86 GPa, which could be associated, according to static
compression observations, with the iron spin transition. Our measurements also
suggest a change of the Hugoniot curve between 150 and 250 GPa. Above 250 GPa
and within our error bars, we do not observe significant modifications up to
the maximum pressure of 700 GPa reached in our experiment.

##  I Introduction

Super-Earths are rocky exo-planets, with a mass 1 to 10 times that of the
Earth. The increasing number of discoveries of such planetory bodies implies
to extend the studies of the rocks composing them to much more important
pressures than for the Earth [1]. As a first approximation, the mantle of a
Super-Earth is supposed to be similar to the Earth mantle, and essentially
composed of Mg-rich silicates and oxides [2]. The presence of iron oxides,
even in small quantities, plays a fundamental role in the formation of
minerals in the Earth’s mantle. It is thus necessary to define the fundamental
physical properties, starting with the equation of state (EOS) and phase
transition boundaries, of iron oxides at very high pressure. Among iron
oxides, wüstite FeO and hematite Fe2O3 are the two end-members of the ferrous
and ferric states of iron. Unlike FeO, studied in static and dynamic
compression at very high pressure [3, 4], data on Fe2O3 are still limited to a
rather small pressure range.

Several static compression studies agreed that Fe2O3 goes through a series of
phase transitions at 50 GPa, including a Mott transition and a spin transition
[5, 6, 7, 8]. In particular, the pressure-induced spin transition of iron is
well known and it can significantly affect the physical and chemical
properties of the mantle minerals [9]. Most recent studies have measured the
isothermal compression of Fe2O3 up to 105 GPa [10] using diamond anvil cells
(DAC) and has been validated with a theoretical approach using density
functional theory and dynamical mean-field theory (DFT + DMFT) up to 100 GPa
[5]. First, the rhomboedric $\alpha$-Fe2O3 phase is stable up to $\sim$ 40
GPa. Between 40 GPa and 47 GPa and at elevated temperature ($\sim$1000 K), the
$\iota$-Fe2O3 phase (Rh2O3-II type structure) can be synthetized after a
temperature quench [11]. Above 54 GPa, at ambient temperature, the
$\zeta$-Fe2O3 phase (distorted perovskite) is observed up to 67 GPa, and a
metastable phase, $\theta$-Fe2O3 (a structure with orthorhombic symmetry), is
observed up to 110 GPa. Between 57 GPa and 110 GPa, but at high temperatures
($\sim$2000 K) or after a temperature quench, the phase $\eta$-Fe2O3 (a post-
perovskite) is stable. In the pressure regime above 200 GPa, theoretical
studies using DFT method at zero-temperature, predict solid - solid phase
transitions at 233 GPa [12] and at 330 GPa [13]. We notice that no high-
pressure melting phase transition of Fe2O3 has so far been reported, either
experimentally nor by simulation. From a (exo-)planetology point of view, the
potential presence of liquid metal oxides, which would be related to the
presence of a deep conductive liquid layer in the mantle of Super-Earths which
could directly contribute to the dynamo process in exoplanets [14].

In this framework, laser compression techniques are highly relevant as they
enable reaching very high pressures, of the order of a few TPa [15]. In
particular, pressures achieved using laser compression are so high that they
allow constraining EOS despite large error bars. Furthermore, understanding
the dynamic phase diagram of iron oxides at large strain rates typical of
hypervelocity impact conditions [16], such as meteorite impacts during
accretion processes, is key to constraining composition and oxygen budget of
the planet [17]. In the case of Fe2O3, very few dynamic compression
experiments have been performed, mostly due to the complexity of target design
and stoichiometry control when using natural samples. Up to now, a dynamic
compression dataset has been measured up to 140 GPa along the Hugoniot using
high-explosive method by McQueen et al. [18] (used in [19, 20] and compiled in
[21]). In 1980, Kondo et al. measured the electrical resistivity of Fe2O3
using a double-stage light-gas gun on large natural crystals [22] and reported
a transition to a low-resistivity metal-like state at 44-52 GPa pressures.

The very limited data on Fe2O3 at extreme pressure calls for additional
Hugoniot measurements under laser shock compression (1) to extend the low-
pressure data to several hundreds of GPa, (2) to obtain an EOS, possibly
confirming the SESAME table, and (3) to highlight additional phase transitions
by detecting anomalies in the Hugoniot curve. We present here the results of a
laser shock compression experiment on Fe2O3 over a large range of pressures,
from 20 GPa to 700 GPa. We show the EOS along the Hugoniot obtained from the
velocity measurements and discuss the potential presence of phase transitions
in this range along with previous studies.

##  II Method

Experiments were conducted at the LULI 2000 high-energy laser facility. We
used two laser beams at 527 nm, with either 2 ns or 5 ns square pulses and a
single-pulse energy of up to 500 J. The 800 $\mu$m diameter focal spot was
generated using phase plate smoothing, with a resulting maximum intensity of
1x1014 W.cm-2 on target when combining two laser pulses branches. Optical
diagnostics such as Velocity Interferometer System for Any Reflector (VISAR)
[23] and reflectivity measurement (which will be named Reflectivity) were used
to obtain shock and particle velocities along the Hugoniot. Different types of
targets were designed to perform these measurements in all the desired
pressure conditions.

The target designs are shown in figure 1. They consist of a CH plastic
parylen-N ablator, flashed with 500 nm Ti, and a 50 $\mu$m Al foil to avoid
preheating due to x-rays produced at the ablation front. Target design
($\alpha$) corresponds to a Fe2O3 layer on half of the Al surface making a
”step” target. Target design ($\beta$) corresponds to a Fe2O3 step on 30
$\mu$m quartz fixed to an Al layer with $\sim$ 2 $\mu$m thick UV glue. Fe2O3
layers are polycrystalline samples obtained by Physical Vapor Deposition (PVD)
and have been characterized by x-ray diffraction and energy-dispersive x-ray
spectroscopy (EDS). From this analysis, we verified that our starting sample
had the following characteristics: an homogeneous stoichiometry equal to the
one of Fe2O3, and a crystallographic phase corresponding to $\alpha$-Fe2O3.
Moreover, transmission electron microscopy (TEM) and scanning electron
microscope (SEM) measurements show no particular porosity of the deposit, and
the initial density was measure to be: $4.98\pm 0.12$ g/cm3, close to natural
sample, 4.9-5.3 g/cm3, and the standard value of 5.008 g/cm3 used by
McQueen[18]. Samples also have a several hundred-nm-diameter columnar grains
which are oriented along the direction of the shock propagation. Due to target
masking manufacturing, the deposited thickness was not constant near the step.
To correct for this effect, we measured the exact profile thickness of the
Fe2O3 using an interferometry profilometer (3D Optical Surface Metrology
System Leica DCM8). The relative error of each measurement was around 1% of
the thickness.

On all targets, the shock velocity Us was determined from the transit time of
the shock in the Fe2O3 step. The transit time was obtained by measuring the
difference of the breakout time of the material before the Fe2O3 step
(aluminum or quartz) and the breakout time of the Fe2O3 step. Breakout times
were determined from reflectivity changes or velocity changes in the data. For
($\alpha$) targets, the breakout time is measured by the change in velocity of
the free surface of aluminum and Fe2O3, at different positions (considering 0
the position of the step; from 50 $\mu$m to 100 $\mu$m and from -50 $\mu$m to
-100 $\mu$m). Note that the shock breakout is deduced from the time
corresponding to the mid-height of the speed jump. On each shot, we have many
data (shock breakout times and free surface velocity), from which we extracted
a mean value and the standard deviation is included in the error bar. In
general, the reflectivity diagnostic was more accurate for breakout time
measurements than the VISAR diagnostic, where the reflectivity was convoluted
with interfringe intensity variations and timing modified due to the etalon
delay. For ($\beta$) targets, the breakout time is measured by the change in
reflectivity, since fringe contrast is lost at such high pressure (no free
surface measurements and no windows) and no particle velocity change could be
extracted. The change in reflectivity and therefore the shock breakout time
can be defined for each vertical pixel line. By comparing the transit time in
Fe2O3 along the sample to the step profile itself, a shock velocity can be
determined for each position of the step. Finally, the shock velocity is
averaged over the Fe2O3 region on interest, i.e. over the 50 $\mu$m to 100
$\mu$m.

Figure 1: Target designs used to mesure $U_{s}$ and $U_{p}$ from 20 GPa to 700
GPa. Each target has the same ablator, which consists of a layer of parylen-N
of 10 um, a layer of Al of 50 um to avoid x-rays from CH plasma heating the
sample. Fe2O3 has a step in order to measure the shock transit time. Two
different targets, $\alpha$) and $\beta$), were designed to be able to perform
$U_{p}$ measurements in all the desired pressure conditions. An example of
VISAR 2 signal is shown in the figure below each target design. On the VISAR
measurements, we can clearly distinguish the breakout time profil representing
the Fe2O3 step. The titanium flash coating is there to avoid damage to the
target due to a possible pre-pulse present in the laser pulse. Target design
$\alpha$) was used for low pressure where the weak shock approximation is
valid $U_{p}\approx U_{fs}/2$. For design $\beta$), quartz was used as
reference material for relative measurement of $U_{p}$ by impedance matching
technic, for pressures above 250 GPa, for which the shock front in quartz is
reflective[24].

Particle velocities were measured differently for each target. Targets
($\alpha$) were designed to measure the Hugoniot in a pressure regime low
enough to be in the “weak shock” limit. In this case, the free surface
velocity of Fe2O3 is approximately the double of the fluid velocity [25]. For
iron, this approximation has been experimentally verified and yields a
precision within 3 % up to 200-300 GPa. This result is coherent with the
definition of a weak shock, for which the energy deposited by the shock is not
sufficient to melt or vaporize it. In our case, we used this target design and
approximation up to 100-200 GPa, for which we are confident that we are
investigating the solid phase of Fe2O3. The particle velocity for targets
($\beta$) was obtained using impedance matching technique with quartz as a
reference (we used 7362 SESAME EOS for the quartz, equivalent to table 7360
for our pressure range).

Shock velocity in quartz and free surface velocity of Fe2O3 were measured
using two different line-imaging VISAR systems operating at 1.05 $\mu$m (VISAR
1) and 0.53 $\mu$m (VISAR 2). We used a time-resolved reflectivity measurement
at 0.53 $\mu$m to measure changes in reflectivity, and, with the VISARs, to
measure the shock transit times of the samples. The VISAR etalon velocity per
fringe (VPF) associated with VISAR 1 and VISAR 2 were 12.81 and 4.96
km/s/fringe, respectively. However, the VISAR 1 etalon was 3.43 km/s/fringe
for low-pressure measurements. Fringe positions in the data analysis were
resolved to within 5% of the respective VPF. Examples of VISAR 2 data are
shown in Fig. 1. Depending on the 10 ns or 5 ns temporal windows,
uncertainties on the breakout time were respectively 23 ps and 12 ps for the
VISAR 1 and the Reflectivity streak camera, and 12 ps and 8 ps for the VISAR 2
streak camera.

##  III Results

Figure 2: Hugoniot of Fe2O3 in the ($U_{p}$,$U_{s}$) plane. Our shock data are
represented by empty black diamond-shaped symbols. Green full circles are
measurements from [18]. The blue dashed line represents the sesame table of
hematite (7440). The cyan solid line is a linear fit ($U_{s}=sU_{p}+c_{0}$) of
our data from $U_{p}=4.5$ km/s to 9 km/s. The green solid lines are a linear
fit of [18] data. The inset focuses on the data for a particle velocity
between 0 and 3.5 km/s, illustrates the transition from the low pressure phase
to the high pressure phase. Experimental uncertainties are plotted in black
for each points. Uncertainty in $U_{s}$ of the gas gun experiment data are
assumed to be constant at 0.082 km/s[26].

Figure 2 shows the shock velocity $U_{s}$ versus the particle velocity $U_{p}$
of Fe2O3 determined along the principal Hugoniot. The points obtained cover
the range in particle velocity from 0.6 km/s to 9 km/s. The inset corresponds
to our data for particle velocities between 0 and 3.5 km/s and highlights the
phase transition along the Hugoniot. Experimental uncertainties are shown in
black for each point.

In our experimental data, we observe a linear behavior for particle velocity
from 2 km/s to 3.6 km/s as well as from 4.5 to 9 km/s. Points between 0.6 and
2 km/s deviate from the general linear trend and appear to have a linear
behavior with a slope coefficient near zero, forming a plateau up to $\sim$2
km/s. For velocities above 4.5 km/s, where no previous data exist, a linear
fit of the form $U_{s}=sU_{p}+c_{0}$, where $s$ an c0 are respectively the
slope and the value at the origin, resulted in :

$U_{s}(km/s)=1.31(7)U_{p}+3.9(4)$ (1)

The linear fit takes into account the data uncertainty by using a weighted-
linear-regression model. A similar linear fit was also applied to the regions
from 0.6 km/s to 2 km/s, from 2 km/s to 3.6 km/s and from 2 to 9 km/s, and the
results are reported in the table 1, although they are not represented on
figure 2. Data in those two velocity regions show very good agreement with
high explosive measurements obtain by [18], plotted in green in figure 2. The
Hugoniot from SESAME table 7440 is plotted together with a dashed blue line.
In the 4.5 to 9 km/s region, the data are also in good agreement with the
extrapolation to high pressure of [18] data (green line) and data from sesame
table of hematite (7440).

Generally, a change of slope in the Us-Up relation associated with an
important volume change is often related to a phase transition. This change of
the linear trend is often referred to as a plateau in the Hugoniot curve [25].
In our low velocity data set, shown as empty diamonds symbols in figure 2, we
observe a change of the linear trend at $\sim$2 km/s. This suggests that we
may have a phase transition. When considering previous datasets from Mc Queen
and Marsh (green dots in figure 2) [18], the related slope change is even
clearer. We can identify 3 regions of interest : a first region, labelled A,
up to the first breaking point at 0.87 km/s ; then a plateau up to 2.28 km/s,
labelled B, and a third region, labelled C, at higher pressure, above 2.28
km/s. Breaking point values were inferred from the crossing point of the
linear fits from Mc Queen’s data with the plateau. Region A and C is
interpreted here as two different phases, phase A and C, and the plateau in
between is interpreted as a mixed phase region. As explained by Mc Queen and
Marsh [27], this plateau can not be strictly related to an Hugoniot
measurement due to experimental possible bias from measuring the 1st shock
wave arrival time only in the case of double-wave splitting from phase
transitions. As a consequence, the phase C onset, measured at 2.28 km/s, can
be overestimated and the phase C could be produced at lower velocities. At
very high pressure, in the region D corresponding to data between 4.5 and 9
km/s, the linear shape and the good precision that we have on the coefficient
of the slope suggests that we do not detect any phase transition with a large
volume change in this region. However, we observe a general shift characterize
by the c0 coefficient value of equation (1) lower with a deviation of 10%
compared to c0 of previous data [18] in the second phase region, who might
suggest a phase transition between 3.5 km/s and 4.5 km/s.

Figure 3: Hugoniot measurement of iron oxides in the ($\mathbf{\rho}$, P)
plane. Same colors as figure 2 are used for our experimental points, those of
[18] and the SESAME EOS 7440. The black solid lines in the inset are plotted
from the EOS measured using static compression [10]. Three 3rd order Birch-
Murnaghan fits were performed to describe the Hugoniot in the range of 0-34
GPa; 85-140 GPa and 250-700 GPa, corresponding to region A, C, and D
respectively. They are plotted as dotted green lines on the figure.

Figure 3 shows pressure (P) versus density ($\rho$) of Fe2O3 along the
principal Hugoniot. Pressures and densities are determined respectively from
the Hugoniot-Rankine relation $P=\rho_{0}U_{s}U_{p}$, and
$\rho=\rho_{0}U_{s}/(U_{s}-U_{p})$, with $\rho_{0}=5.008~{}g/cm^{3}$ the
standard density of Fe2O3 at ambient conditions. The data of Mc Queen and
Marsh [18] are also shown on figure 3. The isothermal equation of state, at
300 K, by Bykova et al. [10] is also represented, with an ambient density of
5.008 $g/cm^{3}$, in order to compare directly with the shock data. The
different domains of stability of phases from region A, C, and D are
respectively represented by the blue, white, and brown regions.

The low-pressure phase identified above in [18] data corresponds to the
pressure range of region A, from 0 GPa to $34.0\pm 0.4$ GPa, with the pressure
uncertainty obtained from the uncertainty on $U_{s}$ given by Van Thiel et al.
[26]. And the high-pressure phase, corresponding to region C, is detected at
$85.0\pm 0.9$ GPa. Measurements show that densities up to 11 g/cm3 and
pressure up to 700 GPa are reached for the highest intensity shot. A 3rd order
Birch-Murnahan fit[28] was used to describe the Hugoniot in the ranges of 0-34
GPa, 85-140 GPa and 250-700 GPa, corresponding respectively to the region A,
region C, and region D. The best fit parameters for phase A are
$K_{0}=207~{}\pm~{}27$ GPa with $K_{0}^{\prime}=3.3~{}\pm~{}2.3$, and
$\rho_{0}$ = 5.008 g/cm3. The bulk modulus is in very good agreement with
published literature data for hematite namely 219 GPa [10], 206 GPa [29], 203
GPa [19], and 187 GPa and 192 GPa [5, 30]. All parameters are reported in
table 2.

For the Birch-Murnaghan fit of region C, we used a fixed zero pressure density
of 5.80 g/cm3 as in [20], similar to the one obtained with ab initio
calculations [5]. Results are given in table 2. The bulk modulus best fit
parameter is $K_{0}=238\pm 5$ GPa, which is in good agreement with the ab
initio calculation result [5] $K_{0}=225$ GPa for the post-perovskite high
pressure phase starting at 76 GPa. For region D, the initial density was
included as a fit parameter, and the best fit parameter is
$K_{85~{}GPa}=471\pm 21$ GPa. In comparison, fits to static experiments data
[10] (on the 67-100 GPa range) resulted in a bulk modulus of
$K_{67~{}GPa}=418\pm 11$ GPa. The discrepancy at high pressure may come from
non-isothermal effects due to the high temperature achieved during the shock.
It is observed that the density of the high-pressure phase is significantly
higher than that predicted by the low-pressure phase equation of state. At 85
GPa, the two Birch-Murnaghan equation of state fits give a relative density
(or volume) drop $(\rho_{C}-\rho_{A})/\rho_{A}=11.3\%$.

##  IV Discussion

In the following section we discuss the interpretation of phases in region A,
C and D by comparing with static phase diagram of Fe2O3 and with a simple
model for melting.

First of all, we can assume the phase in region A is the $\alpha$-Fe2O3
corundum structure from the ambient sample characterization (see Method
section). As suggested by Mc Queen and Marsh [18], this structure is expected
to be stable up to 34 GPa as also reported by Anderson et al. [20]. At this
pressure, the plateau in the Hugoniot curve suggests that a phase transition
occurs. X-ray structural measurements should be performed to confirm and
identify the nature of this phase transition. Recent static compression
measurements [11, 9] can help suggest possible phase transitions. While the
first phase transition occurs at 54 GPa along the ambient isotherm [10], LH-
DAC (Laser-Heated Diamond Anvil Cell) report the $\alpha$-Fe2O3 to
$\iota$-Fe2O3 (Rh2O3(II)-type structure) phase transition at higher
temperatures. At 34 GPa, the $\alpha$-Fe2O3 to $\iota$-Fe2O3 phase boundary
temperature is at 600 K [11] which is in rather good agreement with the SESAME
table that estimates temperatures of 435 K at the same pressure. However, the
volume drop of this phase transition is only 3% in LH-DAC studies [31, 10].
This is not in agreement with our dataset, that shows a volume drop of 11.3%
between phase in region A and region C at 85 GPa. Consequently, phase in
region C would not be consistent with the $\iota$-Fe2O3 phase. The
$\alpha$-Fe2O3 \- $\iota$-Fe2O3 transition might appear at 34 GPa but should
be followed by other phase transitions to explain the large volume drop
observed in the shock data. Alternatively, the volume drop associated with the
spin transition is of the same order [8, 10]. Our shock data are in good
agreement with the isotherm plot between 80 and 110 GPa (black line on the
inset of figure 3), from Bykova et al. [10] who also report a spin transition.
When using the EOS from the supplementary material of Bykova et al. [10], the
exact volume drop between the $\alpha$-Fe2O3 (here labelled phase A) and the
85 GPa high-pressure phase ($\eta$-Fe2O3 or $\theta$-Fe2O3) is estimated to be
12.1%. Moreover, Kondo et al. [22] have observed a discontinuity of the
electrical resistivity along the Hugoniot between 44 and 52 GPa, suggesting
metallization of hematite under shock. Kondo et al. mention the possibility of
hematite undergoing a spin transition along with a Mott-insulator to metal
transition. This suggests that the volume drop could be attributed to the spin
transition. Assuming this volume drop is also accompanied by a structural
change seen in static compression experiments, and without considering kinetic
effects, the cristalline structure of phase in region C could be either
$\eta$-Fe2O3, $\theta$-Fe2O3 or a mixture of the two [10]. However, as the
relaxation time for those transitions is not known, only in situ diagnostics
such as diffraction could determine if one or none of those two phases is
observed under shock.

The plateau observed in region B might be interpreted as the effect of the
spin transition. The spin transition at room temperature occurs over a very
narrow pressure range around 50 GPa; however, the shock data indicate a
softening of the spin transition ranging from 34 GPa to 85 GPa, which could be
related to the temperature of the shock. Wentzcovitch et al. [48] have shown,
using an elastic model (and in the case of the ferropericlase
Mg0.8125Fe0.1875O), that the higher the temperature, the greater the
softening. From SESAME table EOS7440, the temperature of the shock in Fe2O3 at
our pressures is estimated to be $\sim$400 K. The pressure range of the
plateau in the shock data of [18] and our data seem to agree with the
softening effect observed in the calculation of [48], especially with the data
of this paper corresponding to a temperature of $\sim$1000 K, were softening
goes from 30 GPa to 70 GPa.

In the very high-pressure range, one could expect an additional phase
transitions : a solid-liquid transition or a solid-solid transition at 233 GPa
or at 330 GPa as suggested by 300 K ab initio calculations [12, 13]. In the
($P,\rho$) plot figure 3, however the large experimental uncertainty makes it
difficult to observe any Hugoniot discontinuities that could be associated
with such phases transitions. In our data, the typical relative uncertainty on
the density is 7%. In comparison, calculations estimate the volume drop for
melting at 200-300 GPa to be 2% for iron[33]. The melting of iron occurs at a
particle velocity of $\sim$3 km/s (SESAME 2140 and [34]). If we assume the
same order of magnitude for Fe2O3, the Hugoniot curve would cross the melting
curve of Fe2O3 before 4.5 km/s, and in this case phase in region D could
correspond to the liquid state. Moreover, an estimation of the melting point
under shock for Fe2O3 can be made by comparing the sesame 7440 equation of
state plotted in the ($\rho$, T) plane with the melting curve given by the
Lindemann model[35, 36] :

$T_{m}=T_{m}^{0}\biggr{(}\frac{\rho_{0}}{\rho}\biggl{)}^{2/3}\exp\biggr{(}2\gamma_{0}\biggr{(}1-\frac{\rho_{0}}{\rho}\biggl{)}\biggl{)}$
(2)

with $T_{m}^{0}=1865K$ and $\gamma_{0}=2.09$[19], respectively the melting
temperature and the Gruneïsen parameter of Fe2O3 at ambient pressure. The
result of this comparison indicates a melting point at $\rho=8.84~{}g/cm^{3}$,
and $T=6600~{}K$. This value supports the hypothesis that phase in region D is
most probably liquid Fe2O3. In this case, equation (1) would be a measure of
the liquid Fe2O3 equation of state.

If the shift of the Hugoniot observed at very high pressure (region D in
figure 2) with respect to extrapolation of lower pressure data is confirmed by
future more precise equation of state measurements, it could be interpreted in
several ways. One possible explanation could be, that Fe2O3 Hugoniot crosses
between 150 GPa and 250 GPa a melting curve having a negative $dT_{m}/dP$
slope similarly as in diamond [37]. Another plausible explanation could
involve a polyamorphic phase transition associated to changes in coordination
number which can result in observable changes in the Hugoniot, as observed for
Mg2SiO4 [39]. Finally, dissociation reactions of Fe2O3, such as to Fe25O32 and
Fe5O7 might be considered [10, 40, 41].

Table 1: Comparison of $s$ and $c_{0}$ coefficients obtained from the linear fit on each different linear region of the $U_{s}-U_{p}$ Fe2O3 Hugoniot. Fits realized on McQueen et al. data are labelled by [18], and fit on laser shock data are labelled by LULI. For regions A, B, and C, we encourage using more precise coefficients resulting from fit on [18] data.  | Data |  Up range (km/s) | s | c0 (km/s)
---|---|---|---|---
Region A | [18] |  0 $\rightarrow$ 0.88 | 1.37$\pm$0.05 | 6.25$\pm$0.03
Region B | [18] |  0.88 $\rightarrow$ 2.28 | 0.03$\pm$0.02 | 7.44$\pm$0.03
| LULI |  0.6 $\rightarrow$ 2 | 0.1$\pm$0.4 | 7.1$\pm$0.5
Region C | [18] |  2.28 $\rightarrow$ 3.2 | 1.37$\pm$0.04 | 4.4$\pm$0.1
| LULI |  2 $\rightarrow$ 3.6 | 1.1$\pm$0.5 | 5.0$\pm$1.5
Region D | LULI |  4.5 $\rightarrow$ 9 | 1.31$\pm$0.07 | 3.9$\pm$0.4
Region C+D | LULI |  2.28 $\rightarrow$ 9 | 1.24$\pm$0.05 | 4.4$\pm$0.3
Table 2: Summary of parameters obtained with a Birch-Murnaghan fit on Fe2O3
Hugoniot for this study, static compression study, and ab initio calculation.
These parameters correspond to the low-pressure region A, high-pressure region
C and very high pressure region D. To compare the coefficients for the high-
pressure phase in region C, two different fits were done, one with an initial
state at ambient pressure and one at starting pressure of the high-pressure
phase.

|  K0 (GPa) |  K’0 |  $\rho_{0}$(g/cm3)
---|---|---|---
Region A |  |  |
LULI + [18] |  207$\pm$27 |  3.3$\pm$2.3 |  5.008
Static [10] |  219$\pm$7 |  3.5$\pm$0.4 |  5.27
Static [29] |  206$\pm$5 |  4.3$\pm$0.3 |
Ab. inito |  187[5]-192[30] |  4.1(fixed) |  4.94
Region C |  |  |
LULI + [18] |  238$\pm$5 |  4(fixed) |  5.80(fixed)
Ab. inito |  DPv:259[5] |  4.1 |  5.80
|  PPv:225[5] |  4.1 |  5.84
Region D |  |  |
LULI |  367$\pm$18 |  4(fixed) |  6.50

DPv : Distored-perovskite, PPv : Post-perovskite

| KHP | K’HP | $\rho_{HP}$
---|---|---|---
LULI + [18] (85 GPa) | 471$\pm$21 | 4.0 (fixed) | 7.20
Static [10] (67 GPa) | 418$\pm$11 | 4.0 (fixed) | 6.95

## Conclusion

In conclusion, we have measured the equation of state of Fe2O3 with laser
shock compression and VISAR diagnostics up to 700 GPa. We observed a phase
change at low pressure that is attributed to the previously observed spin
transition. Our results are in good agreement with previous gas gun
measurements and consistent with the SESAME table of Fe2O3. Our data extend
the EOS gas gun measurements on Fe2O3 up to pressures of 700 GPa and show that
there is no significant volume change between 250 and 700 GPa. However,
between 150 and 250 GPa a slight shift of the Hugoniot could suggest a phase
transition with a small volume change, such as a liquid to liquid transition.

###### Acknowledgements.

This experiment has been realized on the LULI2000 platform, we thank all the
support team and the LULI staff for their great contribution to this work.
This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation program (ERC
PLANETDIVE grant agreement No 670787).

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