High-pressure melt curve of shock-compressed tin measured using pyrometry and reflectance techniques

J. Appl. Phys. 

126

, 225103 (2019); 

https://doi.org/10.1063/1.5132318

126

, 225103

© 2019 Author(s).

High-pressure melt curve of shock-

compressed tin measured using pyrometry

and reflectance techniques

Cite as: J. Appl. Phys. 

126

, 225103 (2019); 

https://doi.org/10.1063/1.5132318

Submitted: 17 October 2019 . Accepted: 25 November 2019 . Published Online: 10 December 2019

B. M. La Lone

, P. D. Asimow

, O. V. Fat’yanov

, R. S. Hixson

, G. D. Stevens

, W. D. Turley

, and 

L. R.

Veeser

High-pressure melt curve of shock-compressed

tin measured using pyrometry and re

fl

ectance

techniques

Cite as: J. Appl. Phys.

126

, 225103 (2019);

doi: 10.1063/1.5132318

View Online

Export Citation

CrossMar

Submitted: 17 October 2019 · Accepted: 25 November 2019 ·

Published Online: 10 December 2019

B. M. La Lone,

P. D. Asimow,

O. V. Fat

’

yanov,

R. S. Hixson,

G. D. Stevens,

W. D. Turley,

and L. R. Veeser

1,3

AFFILIATIONS

Special Technologies Laboratory, Nevada National Security Site, Santa Barbara, California 93111, USA

Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, USA

New Mexico Operations, Nevada National Security Site, Los Alamos, New Mexico 87544, USA

Electronic mail:

lalonebm@nv.doe.gov

ABSTRACT

We have developed a new technique to measure the melt curve of a shocked metal sample and have used it to measure the high-pressure

solid-liquid phase boundary of tin from 10 to 30 GPa and 1000 to 1800 K. Tin was shock compressed by plate impact using a single-stage

powder gun, and we made accurate, time-resolved radiance, re

ectance, and velocimetry measurements at the interface of the tin sample

and a lithium

uoride window. From these measurements, we determined temperature and pressure at the interface vs time. We then

converted these data to temperature vs pressure curves and plotted them on the tin phase diagram. The tin sample was initially shocked

into the high-pressure solid

phase, and a subsequent release wave originating from the back of the impactor lowered the pressure at the

interface along a constant entropy path (release isentrope). When the release isentrope reaches the solid-liquid phase boundary, melt begins

and the isentrope follows the phase boundary to low pressure. The onset of melt is identi

ed by a signi

cant change in the slope of the

temperature-pressure release isentrope. Following the onset of melt, we obtain a continuous and highly accurate melt curve measurement.

The technique allows a measurement along the melt curve with a single radiance and re

ectance experiment. The measured temperature

data are compared to the published equation of state calculations. Our data agree well with some but not all of the published melt curve

calculations, demonstrating that this technique has su

ffi

cient accuracy to assess the validity of a given equation of state model.

(

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https://doi.org/10.1063/1.5132318

I. INTRODUCTION

The high-pressure phase diagram of materials is important in

many disciplines, including earth and planetary science, materials

science, astrophysics, armor penetration, and other military and

defense applications. Consequently, extensive research has focused

on measuring the temperature-pressure phase boundaries of

various substances using both diamond anvil cell (DAC) and shock

compression techniques. Melt conditions of shocked metals at high

pressure are notoriously di

ffi

cult to measure. Often, there is a sub-

stantial disagreement

—

sometimes thousands of degrees

—

between

theory, static measurements, and dynamic measurements on the

location of these boundaries.

Consequently, new and improved

metal melt curve measurement techniques and a better understand-

ing of the present methods are immediately needed. We have

begun using a new technique to measure the melt curve of tin, and

the method is applicable to other metals.

Static measurements of the solid-liquid phase boundary (the

melt curve) and solid-solid phase changes in tin were

rst made in

the early 1960s, typically using an anvil to pressurize a sample

exposed to resistive heating while a thermocouple measured the

temperature.

–

Melt was observed with techniques such as x-ray

raction or a change in resistance or temperature as a function of

pressure. More recently, extensive measurements have been made

using a DAC or other static compression mechanisms with x-ray

raction or other means of detecting melt.

–

In 2000, Mabire

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and Héreil

observed shock waves created by

yer plate impact

onto tin. Measured release wave velocity pro

les, which contain

sound speed information, had discontinuities that were used to

infer melting at various pressures. However, temperatures were not

measured. Using their data, they developed a three-phase equation

of state (EOS) and calculated the phase diagram up to 70 GPa and

3000 K. In a separate study,

they reported the pyrometric temper-

ature of shock-compressed tin measured at the interface between a

tin sample and lithium

uoride window. They measured a melt

temperature of 2110 ± 200 K at a pressure of 39 GPa, which agrees

well with their model. A similar work by Anderson

et al.

resulted

in a phase diagram up to 10 GPa with more emphasis on the solid-

solid transformation from the room-temperature

phase to the

high-pressure

phase. Anderson

’

s model was based on a

three-phase EOS model developed by Hayes

for bismuth. A

recent work in shock waves by Chauvin

et al.

used a thin carbon

layer of known emissivity between the tin and the window to

achieve a known emissivity and allow an accurate pyrometric tem-

perature measurement. However, the carbon causes complexities

that make it di

ffi

cult to identify the temperature at which the

release crosses the melt curve. In addition to the modeling by

Mabire and Héreil

and Anderson

et al

molecular dynamics

calculations were performed by Bernard and Maillet

and density

functional theory calculations by Mukherjee

et al.

Figure 1

shows

the experimental points for the static measurements, the Héreil

dynamic point, theoretically calculated curves for the solid-liquid

phase boundary in tin from various references, and the most recent

SESAME EOS calculation.

There is substantial scatter in the

experimental data and disagreement among the theories.

Our technique uses pyrometry and re

ectance to measure the

temperatures of shock-compressed tin across a large segment of the

melt curve at the interface between the tin sample and a transpar-

ent window. The window is necessary to maintain elevated pres-

sures at the surface of the sample after the arrival of the shock

wave. In two separate measurements, we used a two-channel

pyrometer to determine the spectral radiance of the sample surface

and an integrating sphere (IS) re

ectance technique to measure the

sample emissivity

(

). (For opaque materials including metals, the

emissivity

and re

ectance

are related by

−

from

Kirchho

’

s law of thermal radiation.) We generally perform these

measurements in separate experiments; however, in one experi-

ment, we performed both measurements simultaneously. From the

radiance and emissivity, we determine the temperature

(

) of the

tin-window interface. In all experiments, we measure the interface

velocity to obtain the pressure

(

). The temperature and pressure

measurements are combined to determine temperature vs pressure

(

) along the melt boundary.

We have previously described a similar pyrometer

and the

technique that were combined to determine the temperatures

of tin shocked by high explosives. In our prior work, the high-

explosive drive was not one-dimensional, which complicated the

analysis, and the pressures did not drop low enough to observe

melting. Here, we applied these diagnostics to better-characterized

loading conditions using tin targets impacted by

yer plates accel-

erated with a single-stage powder gun. Plate impact has two advan-

tages: it maintains one-dimensional uniaxial strain loading during

the experiment, and it enables more control over the pressure

history in the samples so that we can create the temperature and

pressure conditions necessary for melting to occur.

II. EXPERIMENTAL DETAIL

Figure 2

shows a schematic of the experimental apparatus. A

1.3 mm thick, 32 mm diameter copper impactor, backed by syntactic

foam (a low wave-impedance material), is launched to velocities

ranging from 1.7 to 2.3 km/s using the 40 mm diameter, single-stage

FIG. 1.

The melt curve of tin. Points are published static

temperature-vs-pressure measurements on the melt curve and the Mabire and

Héreil

dynamic measurement. Curves from published modeling and theoretical

calculations are from Mabire and Héreil

(solid black), Anderson

etal

(dotted

blue at low pressures), Bernard

etal

(gray medium dashes), Mukherjee

etal.

(red long dashes), and Xu

etal.

(green small dashes at low pressures).

The published Simon

fi

t to the Briggs DAC measurements

(light blue dotted-

dashed curve) and the SESAME 2169

data (dotted-dotted-dashed black) are

also shown. The pink shaded line shows our data, and the curve thickness

represents an upper limit of ±4% to the absolute uncertainty; see Sec.

III

Substantial scatter in the experimental data and disagreement among the

theories is evident.

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powder gun at Caltech

’

s Laboratory for Experimental Geophysics or

by the 40 mm diameter single-stage powder gun operated by the

Nevada National Security Site, Special Technologies Laboratory, in

Goleta, California. The target is a 3 mm thick, 40 mm diameter tin

sample

that is diamond turned on both sides to a specular

nish

and backed by either a 5 mm or 10 mm thick, 38 mm diameter [100]

oriented lithium

uoride (LiF) window. The LiF window is attached

to the tin with a thin (2

–

m) Loctite 326 glue layer; both the glue

and the window are transparent and nonemissive at shock pressures

below 70 GPa.

The emissivity or radiance diagnostic, or in one

case both, are mounted behind the window. The pyrometer has two

channels, with wavelengths centered around 1300 (300) and

1600 (170) nm (bandpass widths in parentheses), respectively.

Radiance in these short-wavelength infrared bands provides adequate

signal-to-noise ratio from the ampli

ed indium-gallium-arsenide

(InGaAs) detectors at blackbody temperatures of 825 K or higher.

We use a

ashlamp

–

illuminated IS

technique (depicted in

Fig. 2

)

to measure dynamic emissivity (re

ectance) of the tin-LiF interface

at detector wavelengths of 1300 (30) and 1550 (40) nm. Two wave-

lengths are su

ffi

cient for accurate temperature measurement

(as opposed to the many bands often used in shock wave experi-

ments) because the dynamic measurements of the sample emissivity

at nearly the same wavelengths are included. The velocity history of

the tin-LiF interface in each experiment is measured by photonic

Doppler velocimetry (PDV).

In one experiment (4R and 4E), the

thermal radiance was detected simultaneously with the emissivity

measurement, as depicted in

Fig. 2

, by placing a 400

mcore

ber-

optic radiance probe (in an extra penetration through the bottom of

the IS) 8 mm from the center of the sphere bottom. This is far

enough away from the porthole in the sphere that

ashlamp light

leaving the porthole to illuminate the tin cannot re

ect from the

surface and enter this

ber. Furthermore, this probe was encapsu-

lated in steel tubing, and the outside of the IS was painted black

where it was attached to the LiF for additional rejection of

ashlamp

light. The lamp light contamination in the radiance channels was

less than 15% of the thermal radiance signal and was easily sub-

tracted out because the lamp light levels change very little on the

time scale of the experiment.

When the copper plate impacts the tin sample, a shock wave

transits the tin layer and partially releases at the interface with the

lower-impedance LiF window. We chose impact velocities such that

the tin at the tin-LiF interface is initially compressed into the high-

pressure solid

(body-centered tetragonal) phase. A shock wave is

also launched backward into the copper

yer upon impact. When

the shock in the copper reaches the syntactic foam backing layer, it

FIG. 2.

Schematic diagram of the emissivity and radiance measurements. A

copper plate (Cu) mounted to the face of a powder gun projectile and backed

by syntactic foam (SF) impacts a tin (Sn) sample backed by a lithium

fl

uoride

(LiF) window and, for emissivity experiments, an integrating sphere (IS). The

tin-LiF interface velocity is measured using a photonic Doppler velocimetry

(PDV) probe. For pyrometry, thermal radiance from the tin is collected by a

400

m diameter

fi

ber (rad) and directed to an array of detectors. Each detector

has a bandpass

fi

lter and a high-speed photodetector. For emissivity, a xenon

fl

ashlamp (Xe) illuminates the inside of the IS. Flashlamp light from the walls of

the sphere is re

fl

ected from the tin-LiF interface, collected by the 1 mm diameter

collection

fi

ber (ref), and directed to the same or similar detectors. The emissiv-

ity is then determined from the re

fl

ectance. This

fi

gure depicts the one experi-

ment during which re

fl

ectance (4E) and radiance (4R) were measured

simultaneously by the radiance detectors; the radiance probe (rad) was placed

off-center and away from the porthole in the IS, as shown in the

fi

gure. This

radiance

fi

ber was encapsulated in steel tubing to minimize the amount of

unwanted xenon

fl

ashlamp light. In all other experiments, radiance (no IS, Xe,

or ref) or emissivity (no rad) were measured separately.

TABLE I.

Shock parameters for radiance and emissivity experiments. The interface pressure is determined immediately after the shock enters the LiF window. P

ressures and

temperatures upon initial melt are determined for each pair of re

fl

ectance and radiance measurements.

Experiment

number

Cu projectile

velocity (km/s)

Shock pressure

in tin (GPa)

Interface

velocity (km/s)

Initial pressure at

interface (GPa)

Pressure at initial

melt (GPa)

Temperature at

initial melt (K)

1.727

31.0

1.258

22.5

1.965

36.7

1.424

26.3

13.1

1173

2.108

40.3

1.516

28.7

18.9

1424

2.290

45.0

1.649

32.1

29.6

1821

1.829

33.4

1.319

24.2

1.961

36.6

1.413

26.3

1.973

36.8

1.427

26.5

2.290

45.0

1.649

32.1

4R and 4E were performed on the same experiment

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sends a ramped release wave back through the copper and into the

tin. This release wave reaches the tin-LiF interface about 300 ns

after the initial shock wave. The initial shock wave increases the

entropy of the tin, but it releases along an approximately constant

entropy path (release isentrope) and, if the initial shock tempera-

ture is close enough to the melt curve, the release isentrope inter-

sects it. At this intersection, the tin initially becomes a mixed phase

of solid and liquid at the melting temperature for that pressure.

While the pressure and temperature continue to drop, the release

isentrope follows a segment of the melt boundary to low pressures

as the liquid fraction of the phase mixture increases. With our

geometry, the release rate is low enough (about 75 GPa/

s) that it is

time resolved by our instruments.

Table I

gives the shock parame-

ters for four radiance (R) and four emissivity (E) experiments.

Shock pressures are calculated from the velocity measurements

using the stress vs particle velocity relationship for LiF,

and we

have assumed that the material strength is negligible in our experi-

ments so that the longitudinal stress and the pressure are equal for

both the tin sample and the LiF window. The interface pressure

values listed in

Table I

occur immediately prior to the arrival of the

release wave. The pressure and temperature values for the

rst melt

are determined from the change in slope of the

release curves

(see Sec.

III

III. RESULTS AND DISCUSSION

Shown in

Fig. 3

are the measured radiance and velocimetry

data from experiment 2R and re

ectance and velocimetry from

experiment 2E, both for an initial pressure of

∼

26.3 GPa at the

interface. When the shock reaches the tin-window interface, the tin

at the surface transforms almost immediately to the

phase, and

with this phase change, the tin

’

sre

ectance increases from 5% to

15%.

About 600 ns later, there is a subsequent drop in re

ectance

when the shock release reaches the tin melting point. These sudden

emissivity changes indicate that, at least for tin, the re

ectance

alone marks the onset of the phase change during shock release.

We suggest that other metals, too, often have re

ectance values that

er for di

erent phase states.

The ambient spectral re

ectance

of the tin-LiF interface is

measured before every experiment on a commercial IS instrument

by comparing the re

ectance to a calibrated standard. During anal-

ysis of the experiment, the measured detector voltage is normalized

to the signal just before shock breakout. The normalized signal,

, is equal to the relative re

ectance change,

. Multiplying

the normalized signal by

gives the dynamic re

ectance, which is

converted to dynamic emissivity through the relation

−

Combining the dynamic emissivity and radiance data into Planck

’

law, we determine the temperature vs time for each of the two wave-

lengths, verify that they agree, and combine the two curves statisti-

cally using the methods described in La Lone.

Uncertainties in the

measured interface temperatures for each experiment are estimated

to be ±4% or less.

The temperature determined from the radiance and re

ec-

tance measurements is plotted vs the shock pressure as derived

from the velocimetry.

Figure 4

shows the measured temperature-

pressure data along the release isentropes for all of our experiments.

The temperature curves as shown release from right to left.

Experiment 1R began at pressure and temperature values too low

to intersect the melt curve during the release, so the tin remained

in the solid phase. For experiments 2R and 3R, the release isen-

tropes do intersect the melt boundary. There the slope changes,

becoming sharply steeper, as the release isentrope becomes

con

ned to the melt boundary. The measured release isentropes for

the di

erent experiments, starting from di

erent temperature and

pressure conditions, overlap each other in this steeper section. The

overlap of two di

erent constant entropy paths in temperature-

pressure space is only possible at a phase boundary because the

erence in phase fractions can account for the entropy di

eren-

ces. Therefore, the observed overlap is further evidence of the melt

boundary location. Experiment 4R begins very near to, or perhaps

on, the melt boundary and stays on it for the majority of the

FIG. 3.

(a) Velocity and radiance signals for experiment 2R, and (b) velocity

and the ratio of dynamic to static re

fl

ectance for experiment 2E. The shock

arrives at the interface at time 0, and the experiment ends when the shock

reaches the back of the window, around 700 ns. The onset of melt occurs at

580 ns in the re

fl

ectance data and less obviously in the radiance. (c) The radi-

ance and re

fl

ectance measurements are combined to generate a temperature

vs time trace.

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release. Below about 16 GPa, the release isentrope for experiment

4R decreases in slope again and maintains slightly higher tempera-

tures than the other curves at the same pressures. We interpret this

segment as having reached complete melting so that the release

departs from the melt boundary and enters the liquid phase region.

t a Simon-Glatzel melt function to the portions of our

release paths believed to be on the melt curve. The function has

the form

melt

¼

triple

melt

triple

þ



(1)

where we used the triple-point

values

triple

= 562 K and

triple

= 3.02 GPa; we found best-

t values of

= 3.244 ± 0.013 GPa

and

= 1.885 ± 0.003. This curve de

nes the boundary between the

color-coded solid and liquid phase

elds in

Fig. 4

. As seen in

Fig. 1

, our melt curve data for tin are in agreement with the Mabire

and Héreil,

et al

and Bernard and Maillet

calculations, but

they are above the Mukherjee

et al

calculations and disagree

slightly with the new SESAME EOS calculations. These data show

that with this technique, we can determine a large, continuous

section of a melt curve with a single measurement of re

ectance

and radiance (or a pair of separate measurements). A further

advantage of our method, compared to other shock wave tech-

niques, is that we measure the melting temperature accurately, not

just the pressure at which melting occurs. Two limitations of our

technique are that the initial shock pressure must be on or below

melt on the Hugoniot (about 45 GPa for tin) and that we must know

approximately where in phase space to look for the phase boundary;

therefore, the experiments must be guided by prior modeling and

experimental e

orts. In principle, methods are available and could be

used to expand the accessible

range along the melting curve by

altering the initial conditions (temperature or pressure) or the loading

path (ramp compression, multiple shocks, etc.).

Temperatures we measure are not necessarily in thermal equi-

librium with the bulk, or sample interior, and are not perfectly on

the isentrope starting at the shock Hugoniot point because of the

potentially nonisentropic wave reverberations in the glue layer and

because of heat conduction between the interface and the bulk tin

and/or the glue.

We estimate that the measured interface tem-

peratures di

er by up to 50 K from the interior release isentrope

temperatures due to these interface e

ects.

Note that the <50 K

erence is only important for the release isentrope in the solid

phase and not important for the melt measurement. The interface

itself, where we observe the temperature and pressure, is partially

melted and, therefore, on the melt curve.

IV. SUMMARY

We have developed a method to measure the high-pressure

melt curve of a metal by combining re

ectance, pyrometry, and

velocimetry measurements to determine temperatures and pres-

sures during dynamic shock compression and release experiments.

In principle, such a measurement can be made with two experi-

ments, a measurement of the re

ectance at two or more wave-

lengths using an integrating sphere and a pyrometric measurement

of the shock radiance with the same or a similar set of detectors.

We executed several experiments at di

erent shock conditions to

help understand the reproducibility of the measurements.

By measuring the temperature vs pressure as the metal releases

isentropically from the shocked state, we have directly observed a

large segment of the tin melt boundary as indicated by a change in

slope of the release

(

). For tin, we have also found that the re

ec-

tivity alone is an indicator of the onset of melt because the re

ec-

tance changes abruptly at the point where the shock release

isentrope and melt curves intersect. We have obtained accurate

temperature data for tin across a signi

cant region of the phase

diagram, from 1000 to 1800 K from about 10 to 30 GPa, and we

compared our result to previous determinations of the melt curve

and the predictions of standard EOS models from the literature.

These techniques will enable similar temperature measurements in

the phase change regime for other metals. The glue layer limits

the peak stresses and, therefore, the present technique is only

FIG. 4.

Measured temperature vs pressure release isentropes (solid colored

lines). The experiment begins when the shock reaches the tin-LiF interface

(point A3 for measurement 3R). After a dwell time of about 300 ns at the shock

state, the rarefaction wave arrives and the tin-LiF interface releases isentropi-

cally (right to left). At point B3, the 3R release isentrope intersects the melt

curve, changing the slope of the release path. Subsequent release is along the

melt curve until the initial shock reaches the back of the LiF window, ending the

useful data at point C3. The error bar on the 4R curve and the width of the pink

curve in

Fig. 1

show a representative absolute temperature uncertainty of about

4%, which is typical for all measurements. (The point-to-point noise within an

experiment and the error on relative temperature differences between experi-

ments are much less than 4%). The boundary between the liquid region (yellow

shading, left) and the solid region (blue shading, right) is determined by a

Simon-Glatzel

fi

t to the segments of the experimental release paths believed to

be on the melt curve. The black dotted-dashed curve is a model calculation

from Mabire and Héreil,

which is also shown in

Fig. 1

and is in general agree-

ment with our results, although at the lowest pressures it is at the low limit of

our uncertainty band. The solid black line is the shock Hugoniot calculation from

Mabire and Héreil.

The shocked tin initially compresses onto the Hugoniot but

releases abruptly (see the dashed green curve for 3R) at the tin-LiF interface

due to the impedance mismatch between tin and the LiF window; therefore, the

measured paths begin at a lower stress than the Hugoniot.

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applicable to somewhat low melting point metals that melt when

shocked to below approximately 70 GPa (depending on shock

impedance) and released. We are exploring methods that omit the

glue layer such as mechanically pressing the window and sample

together or vapor depositing the sample onto the window.

Omitting the glue will enable melt boundary measurements with

our technique on high temperature and pressure melting metals.

In future experiments at higher stresses, we will explore more of

the melt curve of tin. Starting from higher shock stresses and tem-

peratures, we expect the release isentrope to eventually depart from

the melt curve and continue to unload into the liquid phase region.

These techniques will enable similar temperature measurements in

the phase change regime for other metals, and we anticipate measur-

ing the iron melt curve, where previous dynamic pyrometric mea-

surements have uncertainties of ±500 K

and ±900 K.

ACKNOWLEDGMENTS

We are grateful for the help of Michael Burns, Russel Oliver,

Ben Valencia, Mike Grover, Roy Abbott, Rick Allison, and

Matthew Staska in performing the experiments.

This manuscript has been authored by Mission Support and

Test Services, LLC, under Contract No. DE-NA0003624 with the

U.S. Department of Energy and supported by the Site-Directed

Research and Development Program, National Nuclear Security

Administration, NA-10 USDOE NA O

ffi

ce of Defense Programs

(NA-10). The United States Government retains and the publisher,

by accepting the article for publication, acknowledges that the

United States Government retains a non-exclusive, paid-up, irrevo-

cable, worldwide license to publish or reproduce the published

form of this manuscript, or allow others to do so, for United States

Government purposes. The U.S. Department of Energy will provide

public access to these results of federally sponsored research in

accordance with the DOE Public Access Plan (

http://energy.gov/

downloads/doe-public-access-plan

). The views expressed in the

article do not necessarily represent the views of the U.S.

Department of Energy or the United States Government. DOE/

NV/03624

–

0470.

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