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Originally published 22 November 2012; corrected 7 December 2012

www.sciencemag.org/cgi/content/full/science.1229450/DC1

Supplementary Materials for

Phase Transformations and Metallization of Magnesium Oxide atHigh Pressure and Temperature

R. Stewart McWilliams,* Dylan K. Spaulding, Jon H. Eggert, Peter M. Celliers,Damien G. Hicks, Raymond F. Smith, Gilbert W. Collins, Raymond Jeanloz

*To whom correspondence should be addressed. E-mail: [email protected]

Published 22 November 2012 on Science ExpressDOI: 10.1126/science.1229450

This PDF file includes:

Materials and MethodsFigs. S1 to S6Tables S1 to S3

References

Correction: References were corrected.
mailto:[email protected]


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Materials and Methods

Materials and Targets

A laser target is shown in Figure 1A. Multi-layer targets for temperature and

reflectivity measurements consisted of a 50 m thick Al buffer with a 300 m thick

single crystal of MgO attached, stacked to produce a uniform-thickness sandwich ~ 1 mm

in diameter. The synthetic MgO, supplied by Marketech International, was oriented for

shock propagation in the crystallographic direction. The initial density and index

of refraction (at 532 nm) were taken to be 3.584 g/cm 3 and 1.743, respectively ( 38 ). A

broadband anti-reflection coating centered at 532 nm was deposited on the free-surface.

Samples were kept in dry or vacuum conditions as much as possible to prevent water

adsorption. The Al buffer was diamond-turned to mirror finish, and coated on the

ablation surface with ~10 m of CH polymer.

The P -V measurements were referenced to a quartz standard ( 35, 39 ), so used a 30

m thick c-cut quartz (

-SiO 2) crystal inserted between the MgO and the Al buffer ( 34 ),

taken to have an initial density and index of refraction (532 nm) of 2.65 g/cm 3 and 1.546,

respectively ( 40 ).

Parts were bonded using Norland-63 optical adhesive with a glue thickness of less

than ~5 m for Al-sample bonds and less than ~1 m for SiO 2-MgO bonds. Preheating

effects are negligible in these types of targets for the drive laser parameters used ( 41 ).

Drive Lasers

Experiments were conducted using the Omega (Laboratory for Laser Energetics,

University of Rochester) and Jupiter (Lawrence Livermore National Laboratory) laser

facilities ( 12, 13, 42 ). At the Omega Laser Facility, the laser drive consisted of six beams


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of the Omega laser, smoothed by SG8 phase plates to provide an 800-m diameter spot

of uniform irradiation on target to ensure planar loading. Laser energies of 850 J in a 1

ns pulse were used. At the Jupiter Laser Facility, the drive laser consisted of two beams

of the Janus laser; CPP phase plates provided uniform irradiation of a 600-m diameter

spot; laser energies up to 500 J in a 2 ns pulse were used.

One-dimensional loading is evidenced in our data by lateral uniformity in shock

features over ~ 500 m on the target (Figs 1B, 1C).

VISAR

A line-imaging laser interferometer, or line VISAR (Velocity InterferometerSystem for Any Reflector), measured the velocity and reflectivity of shock fronts in MgO

and quartz as functions of time and position in the target ( 42 ). A representative dataset is

shown in Fig. 1B. The shock velocity is

[ ] ++=0)1(2

)()()(n

t bt t U S

(Eq. S1)

where t is the time, (t ) is the observed fringe phase (a fraction of the fringe period, such

that a full period is unity), and b(t ) is the integer number of base fringe shifts. The right

term is referred to as the VPF (velocity-per-fringe) in which is the wavelength of the

VISAR probe laser (532 nm), is the optical delay time introduced by the etalon placed

in one leg of the interferometer, (1+ ) is a correction for optical dispersion in the etalon,

and n0 is the ambient index of refraction in the material where the reflecting shock is

propagating. For Fig. 1B, a VPF of 1.5673 km/s is used. Two independent VISAR

systems having different VPF were used in each shot to constrain b(t ) unambiguously.

Background fringes in the VISAR from immobile reflecting surfaces in the optical path


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(ghost fringes) were subtracted from our signal fringes with Fourier analysis ( 43 ), e.g.

between e 1 and e 6 in Fig. 1B.

Shock reflectivity, the coefficient of reflection between the shocked (opaque,

reflecting) and unshocked (transparent, ambient) states, was determined as

00

)()(

I t I

Rt R = (Eq. S2)

where I (t ) is the fringe intensity, corrected for probe beam power variation with time, and

I 0 is the initial fringe intensity due to reflection from a reference surface of known

reflectivity R0 (in this case, diamond-turned aluminum against an adhesive layer, with R0

~ 88%, which is observed early in the VISAR records). Fringe intensity was determined

from the fringe amplitude, measured via Fourier transform by filtering intensity

contributions from background (long wavelength) signals. At the Omega facility, the

probe power variation was measured in a reference image of the target obtained before

shocking it. While the intensity vs. time profile of the probe was constant, its timing

could shift slightly between images, so reference intensity was time-shifted when

normalizing the data; the accuracy of this shift was tested, for example, by ensuring

fringe intensity prior to shock breakout (i.e. before event e 1 in Fig. 1) was constant after

normalization. At the Jupiter facility, a portion of the probe beam was diverted before

reaching the sample and focused at the edge of the streak camera image to provide a

time-resolved intensity reference simultaneously with the experiment.

Hugoniot Compressibility Measurements

Our P -V - E -U S -U P Hugoniot measurements for MgO at P ~ 0.6 TPa (Figs 2D, S1,

S6, and Table S1) were accomplished in the manner of Ref. ( 34 ) using the quartz

Hugoniot ( 35, 39 ) and a thermodynamic description of the quartz reshock Hugoniot ( 34 ).


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This technique consists of driving a reflecting shock through a standard material (quartz)

into the sample material (MgO). Measurement of shock velocity in each material at the

moment the shock transits the standard-sample interface allows a determination of the

shock Hugoniot by impedance matching.

Temperature Measurements

A Streaked Optical Pyrometer (SOP) (44, 45 ) was used to measure thermal

emission from the shock front as a function of time and space, integrated over a 350 to

900 nm spectral window. A representative SOP dataset is shown in Figure 1C. In our

analysis, we apply a calibration based on the known shock temperatures in quartz ( 12 ).To do this, experiments on quartz alone were conducted in parallel to the MgO

experiments to correlate emission intensity with a standard temperature ( 14 ). In these

calibration experiments, as in the MgO experiments, U S (t ) and the spectral radiance L(t )

are simultaneously measured. Assuming grey-body behavior, L(t ) is given by Plancks

Law as

[ ] 1)( / exp12

)()( 52

=

t kT hchc

t t L

(Eq. S3)

where the emissivity (t ) is given by Kirchhoffs Law assuming an optically thick shock

front

)(1)( t Rt = (Eq. S4)

Comparison of quartz measurements with the standard ( 12 ) gives a relationship between

the observed SOP intensity I SOP (t ) and the temperature, defined as ( 44, 45 )

+=

)()(

1ln)(

0

t I At

t T T

SOP

(Eq. S5)


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where T 0 and A are fit parameters (Fig. S5) which are independent of material and

constant for all experiments provided the optical configuration of the pyrometer is

unchanged.

Calibration to a standard material ( 14 ), rather than a standard lamp of known

spectral radiance (44, 45 ), provides several advantages, including the ability to fit Eq. S5

to a range of temperatures (rather than to a single point) and to temperatures which are

characteristic of the experiment (as opposed to the low temperature of a lamp), as shown

in Fig. S5. Straightforward corrections to temperature are possible with future

improvements to the standard.Equation-of-State Modeling

A linear U S -U P model of compressibility on the Hugoniot provided a good

representation of the P -V - E -U S -U P data (Figs 2D and S1). This was defined by a

weighted linear fit, obtained by orthogonal distance regression, to appropriate MgO

Hugoniot data, giving U S = (6.743 0.070) + (1.316 0.017) U P . The y-intercept of this

fit agrees well with the bulk sound speed of MgO, 6.73 0.01 ( 32 ), showing the

reliability of the measurements and the fit. Data below U S = 9.3 km/s were excluded

because the shock exhibits two-wave structure in this regime ( 46 ) which can lead to

nonlinear U S -U P behavior. Also excluded was a datum obtained using the free-surface

release assumption U f = 2 U P which clearly deviates from other Hugoniot data ( 47 ). It is

noted that the data of Marsh ( 30 ) used in this fit appears to be identical to the earlier data

reported by van Thiel ( 48 ) but shifted, possibly from changes in a standard Hugoniot; it is

presumed the later dataset was accurate, and the earlier dataset was omitted. For our high

pressure data, the quartz Hugoniot of Ref. ( 35 ) was assumed (Table S1).


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Our multi-phase equation-of-state (EOS) for MgO is based on finite-strain and

Mie-Grneisen-Debye equations-of-state ( 16, 18 ). Basic thermodynamic differentials

(49 )

PdV TdS dE = (Eq. S6)

dT C dV V C T

PdE V V +

+= (Eq. S7)

dT V

C dV

V K

dP V T += (Eq. S8)

dT

T

C dV

V

C dS V V += (Eq. S9)

are used, where S is entropy, the Grneisen parameter, and K T the isothermal

compressibility. For shock states in a given pure phase and at thermodynamic

equilibrium, Hugoniot pressure P H can be defined as ( 16, 18 )

2 / ))( / (1))()( / ()(

)(0 H H

tr H S H H S H H V V V

E V E V V PV P

+=

(Eq. S10)

where the subscript H refers to conditions on the Hugoniot of the given phase, centered at

the initial P , T and V (P 0, T 0, V 0, respectively, where V 0 is the ambient volume of the

initial phase), the subscript S refers to conditions on the isentrope of the given phase

(centered at P 0, T 0, and V 0 HP , the ambient volume of the given phase), corresponds to

the given phase and is assumed to depend only on volume, and the energy of

transformation E tr is a difference in internal energy between the given phase and the

initial phase ( E tr 0 if the given phase is the initial phase). The Rankine-Hugoniot

relations ( 15, 49 ) give

[ ] 2 / 1000 ) /()( H H S V V PPV U = (Eq. S11)


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[ ] 2 / 100 ))(( H H P V V PPU = (Eq. S12)

2 / ))(( 00 H H H V V PP E += (Eq. S13)

The isentrope is defined by a third order Birch-Murnaghan equation ( 18 )

++= f K f f K f P S S S )4(23

1)21(3)( / 02 / 5

0 (Eq. S14)

where f = (1/2)[( V 0HP / V )2/3-1], and K 0S and K 0S

/ are the ambient bulk modulus and its first

pressure derivative, respectively, for isentropic conditions. From Eqs. S6-S9

= dV PV E S S )( (Eq. S15)

= dV V T

V T S

)( (Eq. S16)

and

+

+=)(

)(

)()( H H

tr H S

V E

E V E V H S H H C

dE V T V T (Eq. S17)

The Debye model is used to determine S and C V (16 )

)]1ln()()3 / 4[(6 3 x

gas e x D RS = (Eq. S18)

)]1 /(3)(4[6 3 =x

gasV e x x D RC (Eq. S19)

where

= x

zedz z

x x D

0

3

33 13

)( (Eq. S20)

and x = / T , where is the Debye temperature. This model gives C V 6 Rgas in the high-

temperature regime observed in our experiments, consistent with our specific heat results

(Fig. 2).


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It is assumed that / V = constant, and correspondingly that =V d d ln / ln

(16 ) in a given phase. We assume K T at given volume is temperature independent and

estimate it as ( 49 )

+

=

H

H V H

H H

H T V

T C PP

V P

V V V

K

22

)( 00 (Eq. S21)

(where C V corresponds to conditions on the Hugoniot) or, where the Hugoniot is

undefined (possible for high-pressure phases at large volume), as ( 50 )

1

2

2

1

+

+=T K V C

T K V K K

T V

S S T

(Eq. S22)

(where K S , T , and C V correspond to the isentrope, and the thermal expansivity

V K C T V / = ). Consistent with the assumption that K T (V ) is temperature independent,

these two estimates are virtually identical for MgO at V where both can be calculated.

To summarize, within a given phase , and K T are functions of V alone; C V

depends on V and T . Off-Hugoniot states in a given phase are determined using Eqs. S7-

S9. A phase is thus defined by 6 parameters: V 0HP (ambient volume, equal to V 0 for initial

phase), K 0S and K 0S / (ambient elastic constants), 0 and 0, (ambient thermodynamic

constants), and E tr (energy difference between phases).

Phase boundaries are located in P -T space where the Gibbs free energies of the

two relevant phases equalize; comparing the equations-of-state along the boundary yield

the entropies and volumes of transformation ( S tr and V tr , respectively). To model the

phase transformation regimes, the Hugoniot was assumed to fall on the phase boundary in

P -T space (i.e. the transformation was modeled as if it occurred at equilibrium ( 15 )), and

a linear U S -U P EOS was assumed for these regions. Model parameters (18 total) were


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adjusted to match the data, with emphasis on fitting regions of the Hugoniot

corresponding to pure phases, and on locating phase boundaries at the observed

conditions of transformation. Phase transition properties (Table I) were established by

examining a variety of models that fit the data. Two example models are shown in Fig.

S6 with associated parameters given in Table S3. The ranges given for phase transition

properties (Table I) include the possibility that our T -U S data in transformation regimes is

representative of thermodynamic equilibrium (e.g. best-fit model) and the possibility

that it does not represent thermodynamic equilibrium, either due to nonequilibrium

transformation effects such as superheating or due to time-resolution limitations (e.g.relaxed model).

Since transformation parameters and high-pressure phase equations-of-state are

determined relative to the B1 phase, it was important that the B1 phase model was as

accurate as possible (Table S3). We found it to be satisfactorily described by parameters

appropriate for B1 MgO determined near ambient conditions ( 19 ): density 0 = 3.584

g/cm 3, bulk modulus and its pressure derivative K 0S = 163.2 ( 0.7) GPa and K 0S = 4.13

( 0.02), and Grneisen parameter 0 = 1.52 (0.02). We take 0 for the B1 phase to be

760 K. For our complete multi-phase models, we used somewhat different K 0S and K 0S

(K 0S = 162, K 0S = 4.3) to enhance model agreement with the highest-pressure gas-gun

data ( 31, 33 ) (Figs S1, S6), presumed to also be in the B1-phase.

Details on Compilation of Table I

The results in Table I were compiled as follows. First, we characterized the

observed phase transformations using the equation-of-state modeling described above.

This established experimental ranges for the five quantities in Table I describing the


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phase transformations ( T , P , ( ) BT P / , S tr , and V tr ). The ranges of T and P

encompass the beginning and end of the transformations on the Hugoniot, and include

some model-dependant uncertainty; the ranges for the three other quantities represent

model-dependant uncertainties assessed by examining different parameters for the high

pressure phases. There are tradeoffs in selecting parameters for the high-pressure phases

that fit the measurements; for example, a large volume decrease at the first transition

must be accompanied by a relatively large volume increase at the second, to ensure good

agreement with compressibility data at higher pressure. The quantities S tr , T , and P are

found to be insensitive to the model parameters selected: that is, they are well constrained

by our data. The quantities V tr and ( ) BT P / are poorly constrained, as indicated by

the larger fractional uncertainty of these quantities in Table I; this is due in part to the

lack of compressibility data in the first high pressure phase, such that the volume of this

phase is poorly constrained.

Second, we examined the properties of theoretical phase transformations that

most closely matched our observed phase transformations, for comparison to our

measurements. The P , T and ( ) BT P / of the theoretical transformations were taken

from the regions of the theoretical phase boundaries that were closest to the observed

transitions. Since predicted V tr and S tr on calculated phase boundaries were not

available in the literature, we estimated these quantities using various assumptions. For

the first transition, two limiting assumptions were examined. In one, V tr / V was

presumed constant on the phase boundary (and defined by the zero-temperature value

predicted in first-principles calculations), which gives an approximate upper bound for

V tr and S tr at high temperature. In the other, S tr was presumed constant on the phase


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boundary and presumed to be infinitesimal (as it must be at low temperature), which sets

a lower bound of S tr ~ V tr ~ 0 at high temperature (since the Clapeyron slope, also

infinitesimal at low temperature, becomes finite at high temperature, requiring V tr

become small). For the second transition, we assume that volume of transformation on

melting is roughly constant at high pressure, regardless of local phase.

Specific Heat Calculation

The specific heat analysis used here has been described previously (Refs ( 12, 13 )

and references therein). From Eq. S7

( )( ) T V V T PV E C

H

H V ) / ( /

/ ++= (Eq. S23)

For the results in Fig. 2B, was taken from first-principles calculations for pure solid and

liquid MgO at relevant conditions ( 1.1) (3). In using a corresponding to a pure

phase in this calculation, the C V measured are accurate where the Hugoniot accesses a

pure-phase state; this is likely the case where the measurements approach the Dulong-

Petit limit. In regions of the Hugoniot corresponding to phase transformation, C V should

deviate from the Dulong-Petit limit (as observed), however here C V is not accurate

because in a mixed-phase regime can differ from that in a pure phase. Put another way,

the apparent specific heat in these regimes is a combination of specific heat and latent

heat.

Decay PredictionBelow 0.5-0.6 TPa, reflection from the shock front could not be measured (R

V V V V

PPPP

(Eq. S24)

where subscript 1 indicates conditions at the peak Hugoniot state in the low-pressure

phase, and subscript 2 indicates a state on the Hugoniot above this (i.e. within the

subsequent phase transition regime). Geometrically, this criterion can be evaluated by

examining the Hugoniot in P -V space (Fig. S6). Given the possible large increase in

density at the first transition, we considered whether this could lead to formation of a

two-wave structure. However, all EOS models tested are consistent with the occurrence

of only a single shock. For example, in an extreme model (with large volume decrease at

the first transition, Fig. S6), the left side of Eq. S24 is ~ 2; and it is larger for other

models.

Drude-Semiconductor Conductivity Model:

Shock front reflectivities beyond a few percent in insulating materials suggest the

presence of delocalized electrons and enhanced electronic conductivity ( 12-14, 43 ). The


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model used here to invert R, T , and V in shock-compressed MgO for electronic

conductivity is similar to that used in numerous prior studies (Refs ( 12, 43 ) and

references therein). For wide band-gap insulators, the quantitative results of this model

have been broadly supported by independent theory, e.g. for SiO 2 (12 ) and LiF ( 43 ).

Reflectivity is analyzed in terms of the Fresnel equation for normal incidence, R =

|(n-n0)/(n+n0)|2, where n = [ b+ 4 i ( )/ ]1/2 is the complex index of refraction, b is the

contribution of the bound electrons, is the frequency, and ( ) is the conductivity,

assumed to follow the Drude formulation ( ) = (2 nee2 / meff )(1- i )-1, where ne is the

carrier density,

is the carrier relaxation time, and meff is the carrier effective mass. It is

assumed that scattering occurs at the Ioffe-Regel limit ( 51 ), such that ev / = where ve is

the carrier velocity and 3 / 1)4 / 3(2 F A N N MV = is the interatomic distance, where M is

molar mass, N A is Avogadros number, and N F is the number of atoms in a formula unit.

Carrier activation is assumed to follow the behavior of an intrinsic semiconductor ( 52 ),

i.e. )]2 /([)2 / (2 2 / 12 / 32

kT E f kT mn geff e = , where dye y x f x ym

m )1 /( / 2][ 0

+=

is the Fermi-Dirac integral and E g is the activation gap energy. Carrier velocity is given

by )])2 /([ / )]2 /([)( / 2( 2 / 12 / 3 kT E f kT E f mkT v ggeff e = . This model has three

independent variables based on observation ( V , R and T ) and three unknown parameters

( b, E g and meff ) which in this study are fit to the measurements.

The unknown parameters were further parameterized for optimum fitting in the

presence of distinct phase transitions. We assume a volume-dependent energy gap ( E g)

between valence and conduction bands ( 12, 43 ), assumed to be sigmoidal in form as


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+=

T T g E E E exp0 (Eq. S25)

where the density = 1/ V , and E 0, E T , T , and are fit parameters. This allows for rapid

changes in the gap at phase transitions or for more continuous change across a broader

pressure range. In the latter limit, Eq. S25 is similar to the linear function of density

commonly used for materials that lack a sharp phase transition (e.g. refs ( 12, 43 ) and

references therein). In one present fit, the parameter E 0 was fixed at 8 eV, the ambient-

pressure gap of the B1 phase, and the predicted gap of the B2 phase ( 1); this choice was

made considering that the reflectivity at low pressure can be attributed solely to bound

electron effects (Figs S2 and S3) and therefore cannot meaningfully constrain the initial

gap. A second fit with an unconstrained initial gap gave broadly similar conclusions

regarding gap closure at the second transition (Fig. 2C and Fig. S4).

The quantity b was fit either as a constant, or such that the quantity b (equal

to the real index of refraction at low conductivity) was a linear function of density.

Constrained by the low-pressure end of the reflectivity data, where the reflectivity is

attributable to bound electron effects alone (Fig. S2), b gives an independent estimate for

the real index of refraction of MgO under pressure (Fig. S3). This model-based

measurement of the real index agrees reasonably well with extrapolation of shock data

from lower pressures ( 17 ).

Optical Depth of Shocked MgO

A small optical depth in shocked MgO is required in the present experiments for

accurate interpretation of the temperature data, such that emission originates from near

shock-front, and hence Hugoniot states, rather than from well behind the shock, where


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material undergoing rarefaction may lie off the Hugoniot or where target interfaces can

contribute anomalously to the emission. That is, we require that shocked MgO have an

optical thickness on the order of or less than the distance U S t where t is the time

resolution of the diagnostics (~100 ps), or ~1 m.

Several lines of evidence support a small optical depth in shocked MgO at the

conditions of our experiments:

1) The DC electronic conductivity is expected to be ~ 1000 S/m or larger in these

experiments, based on the Drude-semiconductor model results (Fig. S4), and also on

predicted carrier densities for warm solid MgO

(1). Estimating the optical penetration

depth d at a conducting surface (here, the shock front) as 8 / ~ cd (strong conductor)

and k cd 2 / = (arbitrary material) ( 53 ), where k is the imaginary part of the index and

can be estimated from our model, we estimate a maximum d of ~ 0.3 m and ~ 2 m,

respectively, in our experiments.

2) It is observed that above T ~ 8000 K and P ~ 0.3 TPa the data show good consistency

with prior measurements ( 36 ) and predictions ( 3, 36 ) of shock temperature, and as

discussed adhere closely to the Dulong-Petit limit. These observations would be highly

unlikely if the temperature data were in error. Below T ~ 8000 K, however, the apparent

temperature deviates from previously reported temperatures, suggestive of a large optical

skin depth at low T and P . This is not unexpected given that nearly-critical d are inferred

for the solid at conditions near the first transition. These observations evince the

accuracy of our temperature measurements except at low pressures ( P < 0.3 TPa) where

the data were discarded.


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3) We note that shocked MgO was opaque to VISAR in all experiments accessing the

present pressure range (including experiments with peak pressures at P < 0.3 TPa); this is

consistent with our conclusion of strongly absorbing conditions in solid MgO at high

temperature, though other sources of opacity (i.e. scattering) could contribute.

Data Quality and Measurement Uncertainties

Data collected at the Omega laser are considered to be of substantially higher

quality than those collected at the Jupiter laser (as discussed below), and T -U S - R data

from Omega have thus been used in our quantitative analyses here; lower-accuracy and

lower-precision measurements of T -U S - R from the Janus laser have been included todemonstrate that primary observations the existence of a temperature minimum on the

Hugoniot (Table S2), and the onset of shock reflectivity (Fig. S2) can be reproduced in

very different experimental configurations.

Error in the temperature (Fig. 2A error bars) is primarily systematic, such that

derivatives of temperature, e.g. ( ) H V T / , and quantities calculated from derivatives,

e.g. C V , are known more precisely. A comparison between Omega and Jupiter results for

the first transition temperature are presented in Table SII. Random error in temperature

is small, as is evident in the high reproducibility of measurements at a given facility (Figs

2A and 2B, and Table SII). Temperatures at the Omega laser are considered more

accurate due to improved diagnostic quality and improved accuracy in the relative timing

of VISAR and SOP datasets. Error in reflectivity at Omega (Fig. 2C and Fig. S2 error

bars) is also mostly systematic; the reproducibility of the measurements confirms that

random errors are small except at very high pressure. At Jupiter (Fig. S2 error bars)

reflectivity uncertainty is much larger and principally random in nature.


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Compressibility data were collected at the Jupiter laser. Uncertainty in these

results (Table S1) is considered random, consistent with the observed scatter in the

datapoints; additional systematic sources of error due to the choice of reference EOS

have been discussed (Figs S1 and S6), and are not included in Table S1.

All uncertainties reported here are equivalent to one standard deviation.


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Fig. S1:

Linear U S -U P fit to available shock data, as discussed in Supplementary Materials and

Methods, plotted with a theoretical U S -U P EOS ( 3) and two EOS models from this study

(see Fig. S6). Present measurements are shown using the standard quartz Hugoniots from

Ref. ( 39 ) (HEA) and Ref. ( 35 ) (KD); the latter was used in the linear fit.


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Fig. S2:

Shock reflectivity R vs. shock velocity U S . Grey and black curves are separate shots from

Omega; blue curve is a compilation of reflectivities from four Jupiter shots. At both

facilities, reflectivity became observable above U S =17.3 km/s, though the data from

Omega are more precise. The green curve shows the predicted reflectivity based on

extrapolation of the real index of refraction from shock data to P =0.023 TPa ( U S =7.8

km/s) ( 17 ), which agrees well with the lowest reflectivities observed here. This suggests,

independent of our Drude-semiconductor model analysis, that the reflectivity observed

below the second transition is principally due to bound electron contributions, and that

the rise beginning at ~18 km/s can be attributed to an increase in conductivity associated

with the second transformation.


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Fig. S3:

Real component of the index of refraction of MgO at low conductivity. Green and blue

solid lines are given by b in the present Drude-semiconductor model fits (for assumed

constant b or b varying linearly in density, respectively) with dashed portions

representing extrapolations beyond the reflectivity data. Solid black line is from Ref.

(17 ), with dashed line indicating extrapolation to high density.


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Fig. S4:

DC conductivities ( =0) and carrier densities inferred from the Drude-semiconductor

model, showing results for a constrained ( E 0=8 eV) and unconstrained ( E 0 fit) initial gap.

The predicted carrier density on a 10,000 K isotherm in solid (B2) MgO (1) is consistent

with our model results; this isotherm overlaps the Hugoniot at 0.49 TPa (here, predicted

carrier densities are ~10 19 cm -3 while observed carrier densities are 10 19 to 10 20 cm -3

depending on model assumptions).


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Fig. S5:

Pyrometer temperature-intensity relationship determined from measurements on a

decaying shock in quartz (red). The data is fit (dashed black line) to obtain T 0 and A in

Eq. S5. Note that the pyrometer is calibrated at temperatures corresponding to the phase

transitions in MgO.


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Fig. S6:

Mie-Grneisen-Debye, finite-strain EOS models for MgO; two example models are

presented with prior gas gun data ( 30-33, 36 ) and present measurements of T vs. U S (2

shots, colored as in Fig. 2), and P vs. V (2 shots). The best fit model required that

Hugoniot temperature data is precisely fit in mixed-phase regimes, whereas the relaxed

model examined the possibility of small density changes at transformation and deviations

from the data in mixed-phase regimes. Systematic uncertainty due to the reference EOS

of quartz (HEA ( 39 ), KD ( 35 )) is of the same order of magnitude as random error, and

was accounted for. Also shown is the Hugoniot model of Ref. ( 3) which overlaps our

model exactly in the B1 phase, and is similar to the relaxed model for the first phase

transformation.


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Table S1.Hugoniot compressibility measurements from two experiments. Quartz Hugoniot of Ref.(35 ) used.

Shot Laserfacility

MgO U S (km/s)

MgO U P (km/s)

MgO P (TPa)

MgO (g/cm 3)

Quartz U S (km/s)

MgO6 Jupiter 18.82 (0.49) 9.48 (0.42) 0.639 (0.030) 7.22 (0.40) 18.41 (0.46)MgO7 Jupiter 18.88 (0.49) 8.96 (0.40) 0.606 (0.028) 6.82 (0.34) 17.98 (0.45)


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Table S2.Temperature of the first transition as measured at the Jupiter and Omega laser facilities.The temperature minimum at the high-pressure end of the coexistence regime ( U S 16.5

km/s) was selected as a reference point.

Shot Laserfacility

Temperature minimum (K)(at P ~ 0.44 TPa)

MgO16 Jupiter 9540 (+850,-620)MgO17 Jupiter 9522 (+850,-620)MgO19 Jupiter 9068 (+850,-620)MgO29 Jupiter 9930 (+850,-620)MgO31 Jupiter 9881 (+850,-620)57513 Omega 8610 (+790, -752)57514 Omega 8432 (+790, -752)

Jupiter Average 9588 (+850,-620)Omega Average 8521 (+790, -752)


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Table S3.

Equation-of-state parameters for the two example models shown in Figs S1 and S6.

Best-fit model Relaxed model

B1 Phase

V 0 (cc/g) 0.2790

K 0S (GPa) 162

K 0S / (unitless) 4.3

0 (unitless) 1.5

0 (K) 760

E tr (J) 0

First High Pressure Phase

V 0HP / V 0-B1 0.862 0.927

K 0S / K 0S -B1 1.3 1.2

K 0S / / K 0S -B1 / 1.1 1.1

0 / 0-B1 1 1

0 / 0-B1 0.52 0.58

E tr / (V 0-B1 K 0S -B1) 0.3 0.175

Second High Pressure Phase

V 0HP / V 0-B1 0.92 0.972

K 0S / K 0S -B1 1.2 1.2

K 0S / / K 0S -B1 / 1.18 1

0 / 0-B1 1 1

0 / 0-B1 0.415 0.44

E tr / (V 0-B1 K 0S -B1) 0.25 0.225


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