Shock Waves (2002) 11: 385–392

An investigation of shock induced temperature rise

and melting of bismuth using high-speed optical pyrometry

D. Partouche-Sebban

1

, D. B. Holtkamp

2

, J.L. P´elissier

1

, J. Taboury

3

, A. Rouyer

1

1

Commissariat `a l’Energie Atomique, BP12, 91680 Bruy`eres Le Chˆatel, France

2

Los Alamos National Laboratory, Los Alamos, NM 87545, USA

3

Institut d’Optique Th´eorique et Appliqu´ee, BP 147, 91403 Orsay, France

Received 10 June 2001 / Accepted 31 October 2001

Abstract. Temperature is a basic parameter in physics, but in the case of shock-compressed metals its

measurement remains difficult and controversial. Improvements in accuracy of a high-speed optical pyrom-

eter enabled us to study interestingfeatures of bismuth: temperatures of shock-loaded samples measured

through a lithium-fluoride anvil and (indirectly) part of the fusion curve. An improved method of analyzing

optical pyrometry data is also discussed.

Key words: Temperature, Bismuth, Emissivity, Pyrometry, Shock, Melting

1 Introduction

Temperature is almost absent in most hydrodynamics

problems: for instance, it does not explicitly appear in the

well-known Rankine-Hugoniot equations (see Zeldovich

andRaizer 1967) which govern shock-wave propagation

inside matter. In particular, temperature measurements of

shock-loaded metals remain rather rare up to now, as ob-

taining temperature in such experiments raises several is-

sues (cf. for example Nellis andYoo 1990; Tan andAhrens

1990; McQueen andIsaak 1990 andtheir references).

The short duration (1 µs or less) of phenomena under

study generally limits the diagnostic approach to optical

methods exclusively. For example in the present work, ex-

periments were performedwith an eight-channel optical

pyrometer (spanning the 0.4 to 4 µm wavelength range).

The light is guided by optical fibers from the shock-heated

surface to the detectors. For opaque media like metals, the

surface observedby a pyrometer remains at the Hugoniot

temperature for at most a few ps (Zeldovich and Raizer

1967, p. 771). This duration is much shorter than the time

resolution of our pyrometer (a few ns). Consequently, with

the present state of the art, one can only measure the tem-

perature of a metal either directly from its free surface or,

in order to inhibit the full pressure unloading of the sam-

ple, through a transparent anvil.

In the case of bismuth, the free-surface temperature

was studied a few years ago over a wide range of dynamic

Correspondence to: D. Partouche-Sebban

(e-mail: [e-mail])

excitation pressures (Mondot 1993). Then preliminary ex-

periments (Blanco 1997; Blanco et al. 1999) have been

performed with lithium-fluoride windows, but the corre-

sponding results were not completely satisfying for two

reasons:

– the observedsignals didnot always exhibit a reason-

able time dependence (a flat “plateau” as long as no

release wave reaches the bismuth-LiF interface) as ex-

pected, andas obtainedon free-surface experiments

(Mondot 1993)

– the induced temperatures were substantially higher,

particularly at low shock pressures when comparedto

those predicted by a subsequent calculation (Wetta

andP´elissier 2001). On the contrary, for free-surface

temperatures theoretical andexperimental results

were in goodagreement andwere corroboratedby the

experimental investigation of two other phenomena:

matter ejection andvariation of surface reflectivity

(Elias et al. 1988; Mondot 1993).
So we have undertaken the present work in order to

clarify the situation. A first experiment, carriedout with

the experimental configuration described by Blanco (1997)

andBlanco et al. (1999), enabledus to identify proba-

ble sources of optical contamination andto improve the

design (see Sect. 3). Then, with the modified set-up, we

have studied the solid-liquid coexistence region of bismuth

(Sect. 4). The experiment is described below (Sect. 2), but

more information can be foundin previous works (Nellis

andYoo 1990; Bass et al. 1990; Blanco 1997; Blanco et al.

1999).

386

D. Partouche-Sebban et al.: An investigation of shock induced temperature rise and melting of bismuth

Projectile

Before impact

After impact

(p

H

,T

H

)

(p

0

,T

0

)

Shockwave

Vp

Target

Transmitter

(p

0

,T

0

)

Anvil

D

1

Fig. 1. The beginning of the experiment: (p

0

, T

0

) and (p

H

, T

H

)

are respectively the initial and Hugoniot states; and D

1

repre-

sents the shock wave velocity in the target

After shock reflection

on the sample-LiF interface

The experiment in the

(pressure,temperature) diagram

p

T

T

H

p

H

p

0

T

i

Isentropic

release

p

i

Hugoniot

curve

T

fs

(p

H

,T

H

)

(p

i

,T

i

)

D

2

D

3

Emitted

light

T

0

Fig. 2. The end of the experiment: (p

i

,T

i

) is the interface state

and T

fs

is the free-surface temperature; D

2

and D

3

represent

shock-wave or release-wave velocities

2 Description of experiment

2.1 Principle

The experiment geometry is illustratedin Fig. 1. After

impact of copper flyer, the induced shock wave trav-

els through the copper transmitter plate, andis succes-

sively transmittedto the bismuth sample plate andto

the lithium-fluoride window. As soon as the shock reaches

the bismuth-window interface, thermal radiation is emit-

tedanddetectedby the pyrometer (see Fig. 2).

Lithium fluoride (LiF) is often chosen as window for

two reasons:

– the temperature of LiF does not rise significantly un-

der shock loading (Tan and Ahrens 1990); therefore,

the corresponding optical radiance remains negligible

comparedto the sample radiance

– LiF remains transparent in the visible spectrum up to

160 GPa shock pressure (Wise andChhabildas 1986).
The metal target andLiF anvil are optically polished

andgluedtogether to minimize interface effects (Urtiew

andGrover 1974). The glue layer (Loctite

r

358) is less

than 10 µm thick. The glue remains transparent over the

Blackbody + chopper

Experimental target assembly

Optical fiber bundle

Lenses &

filters

Detectors

Amplifiers

Data acquisition system

Vp

InSb

Ge

PMT

HgCdTe

Fig. 3. Schematic diagram of the eight channel optical pyrom-

eter

investigatedpressure range andits emission can be ne-

glected, as verified experimentally (H´ereil andMabire

2000). Another solution, which we did not employ in the

present work, is to add on the window a vapour-deposited

film of the studied metal, the thickness of which is typi-

cally 10 µm (Nellis andYoo 1990; Bass et al. 1990).

In our experiments, we used a 60 mm diameter powder-

gun to launch the projectile. The velocity was measured

with Doppler Laser Interferometry (DLI) over a range be-

tween a few hundreds m · s

−1

and1500 m · s

−1

.

2.2 Pyrometer

A schematic of the pyrometer is shown in Fig. 3. The py-

rometer has eight channels spanning a range of wavelength

from 0.4 to 4 µm. All eight channels are coupledback to

the experiment by means of an optical fiber bundle (six

200 µm diameter fluoride glass IR fibers and two 550 µm

diameter visible fibers). The light from these fibers is fo-

cusedonto each IR detector element with ZnSe lenses and

restrictedto the selectedwavelength by optical passband

filters. The photomultiplier channels do not need lenses

because of their photocathode size.

Four of the detectors (HgCdTe and InSb) are liquid-

nitrogen cooled, while the remaining channels (Ge and

photomultiplier tubes) are operatedat room tempera-

ture. InSb, HgCdTe and Ge detector signals are amplified

through custom-built preamplifiers (100 MHz frequency

bandwidth for InSb and HgCdTe channels and 1 GHz for

Ge channel). PM tubes do not needamplifiers andtheir

frequency bandwidth is about 1 GHz.

Recording of the pyrometry data is performed with

standard digital oscilloscopes. We use three gain ranges

(sometimes four) for each detector to avoid digitization

noise andto assure that they were always on scale even for

large amplitudes (especially for the photomultiplier chan-

nels). The recording system (cables and oscilloscopes) has

been time-calibratedwith a pulse generator: synchrone

pulses were generatedin the eight input cables. When

D. Partouche-Sebban et al.: An investigation of shock induced temperature rise and melting of bismuth

387

the characteristics of detectors and amplifiers (rise times

andtransit times) are taken into account, this calibration

shows that cross timing between the different pyrometer

channels is about 2 ns.

Before the experiment, the first step is to calibrate the

pyrometer with a blackbody source to obtain the relation

between measuredvoltage andradiance for each channel

of the pyrometer. Blackbody radiance is calculated from

the selectedtemperature, the source emissivity (0.99) and

the wavelength dependence of each channel of the pyrom-

eter. At this stage, the blackbody is mechanically chopped

at 10 kHz to be compatible with the amplifier bandwidths.

Portable calibratedpyrometers are usedto verify that the

blackbody source is at the specifiedtemperature anduni-

form over the area of interest.

After the experiment, detector voltages and uncertain-

ties are processed, using the previous calibration, to pro-

duce the experimental radiances with their respective ac-

curacies.

2.3 Pyrometry data analysis

Planck’s law gives the spectral radiance of an ideal black-

body radiator and is used to calculate the temperature.

This expression (Eq. 1) is a function of wavelength (λ)

andtemperature (T ) (C

1

and C

2

are respectively the first

andsecondradiation constants):

L

0

(λ, T ) =

C

1

· λ

−5

exp

C

2

λ·T

− 1

(1)

For each experiment, we measure the N experimental

radiances (L

i

(λ, T ), i = 1 to N) corresponding to each

pyrometer wavelength range. The N relations between the

temperature T , the emissivities ε

i

andthe experimental

radiances L

i

(λ, T ) come from integration of Planck’s law

over the passbandof each channel (Eq. 2):

L

i

(λ, T ) =

∆λ

i

ε

i

· L

0

(λ, T ) · dλ (for i = 1toN)

(2)

Thus, we have N measurements with N + 1 unknowns

(N emissivities plus temperature) andmore information

is required. Many methods have been tried to solve this

problem, for example by adding an equation that con-

strains the relative variation of emissivity versus wave-

length. In particular, the greybody approximation is of-

ten used, i.e. emissivity is assumed to be almost the same

for two or more different channels. However, since a grey-

body calculation is very sensitive to the real wavelength

dependence of the emissivity (even for small dependence),

it frequently results in erroneous temperature values. Fur-

thermore, in case of optical contamination from other ra-

diance sources, which can easily appear in shock experi-

ments, such a calculation becomes largely inappropriate.

We have developeda robust method(Blanco 1997;

Blanco et al. 1999 andPartouche-Sebban et al. 2001) fol-

lowing the suggestion of Herv´e (Herv´e et al. 1990). Our

methodassumes two reasonable hypotheses: (a) that the

radiances of all channels of the pyrometer are described

by a single temperature (andassociateduncertainty), al-

though the emissivity of each channel may be different (as

it depends on wavelength); and (b) that the emissivity of

each channel is constrainedby an upper boundandlower

boundthat is derivedfrom physical information about the

material. The constraints on the emissivities provide ad-

ditional 2N constraints that make it possible to obtain a

single experimental temperature in a physically reason-

able way with associateduncertainties that have physical

significance.

The upper boundon the emissivity is usually assumed

to be 1 (i.e. a blackbody). For shocked surfaces, the lower

boundis taken to be the static emissivity (i.e. the initial

value of emissivity at p

0

and T

0

) of the material in the

same wavelength range as this pyrometer channel. The

static emissivity, ε

S

, is a goodlower boundbecause emis-

sivity increases with degradation of the surface state, often

with material phase transitions (andin particular melting,

see Lange andSchenck 1968) andgenerally with increas-

ing temperature (depending on material and wavelength;

see Touloukian andDeWitt 1970). Part or all of these

phenomena appear in shock heating experiments.

The driving force in the analysis, as a consequence

of Eqs. (1) and(2), is the fact that the temperature is

most strongly constrainedby the shortest wavelength (i.e.

“bluest”) pyrometer channels that have detectable levels

of radiance signal. For the “bluer” channels, the tempera-

ture can be determined quite accurately even when there

are large uncertainties in the radiance (or large uncertain-

ties in the emissivity). Correspondingly, it is very difficult

to obtain accurate temperatures at longer wavelengths

without precise knowledge of the emissivity.

The temperature calculation includes :

– only channels that have detectable energy from the

surface to be studied.

– radiance and its uncertainty for each channel (radiance

uncertainty depends on the measurement noise level

andthe calibration uncertainty).

– constraints on the emissivity for each channel, using

the static emissivity as the lower boundandthe emis-

sivity of a perfect blackbody (ε = 1) as the upper

bound.
This calculation assumes that there is a single tem-

perature (plus associateduncertainty) that produces the

observedradiances in all pyrometer channels. The inter-

section of allowed temperature bands from the different

channels provides the range of possible temperatures. The

most precise temperature measurements using this tech-

nique are obtainedwhen emissivity is strongly wavelength

dependent. Usually, in case of metals, the minimum over-

all temperature allowedby the measuredradiances is con-

strainedby the minimum temperature limit of the bluest

channel (with ε = 1). Andthe maximum allowedtemper-

ature is usually that maximum allowedby the minimum

emissivity constraint of one of the bluer channels.

Once a temperature band has been determined, one

can deduce values for the dynamic emissivity as a func-

388

D. Partouche-Sebban et al.: An investigation of shock induced temperature rise and melting of bismuth

Transmitter

Target metal

8 timing pins

DLI probe

(flyer plate velocity)

(2)
(3)
(3)

Transparent

anvil

Pyrometer

fiber bundle

Wall

Flyer

plate

Vp

Fig. 4. Schematic diagram of initial experimental apparatus

tion of wavelength for each pyrometer channel. These val-

ues are not single values for each wavelength. They are

bands of allowed emissivities that can produce the band

of allowedtemperature andthe experimental radiances

(with included radiance errors) for each channel.

In case of bismuth, the static emissivity of the polished

target (deduced from reflectivity measurements, through

an integrating sphere, at room temperature) is typically

higher than 0.3 in the 300–1800 nm wavelength range and

higher than 0.2 in the 1800–3500 nm range. So we decided

to choose 0.1 as a conservative lower boundof the dynamic

emissivity in all data processing in the present paper.

3 Reduction of optical contamination

(first and second experiments)

According to calculations (Wetta and P´elissier 2001),

when the incident shock pressure is between 14 and

28 GPa, bismuth releasing against a LiF window enters its

solid-liquid coexistence region and the interface tempera-

ture becomes less sensitive to shock intensity. For this rea-

son a first experiment was performednear p

H

= 24 GPa,

where the interface temperature T

i

was expectedto be

about 1500 K.

The experimental apparatus for the first experiment

is shown schematically in Fig. 4, andis similar to the one

usedpreviously (Blanco 1997; Blanco et al. 1999). Be-

sides the DLI measurement of the flyer velocity, ferroelec-

tric pins are usedfor triggering andtiming. The copper

flyer was either 3 or 5 mm thick andthe copper trans-

mitter was either 2 or 3 mm thick. The bismuth sample

andthe LiF anvil thicknesses were always 3 and10 mm

respectively. The diameters of copper projectile, copper

transmitter, bismuth target and lithium fluoride window

are respectively 58 mm, 66 mm, 66 mm and40 mm.

Experiment #1 provided data with significant prob-

lems (see Fig. 5): first, the shape of the detector traces

were qualitatively different for each wavelength channel

andfew of them exhibitedconstant radiances over the

constant pressure interval (∼ 1 µs). Secondly, the radi-

ances of the visible channels (PM tubes) were very high,

implying very high temperatures (T ∼ 2400 K). Finally,

andperhaps most tellingly, the apparent shock breakout

times among the various channels differed as a function

of wavelength. In particular, the visible channels begin to

grow in amplitude almost 200 ns before the redder wave-

length channels.

All these observations ledus to conclude that these

measurements were likely contaminatedby a bright opti-

cal background(mainly in the visible andnear infrared)

that arose from sources external to the LiF-bismuth sam-

ple interface. As a result, we added different features to

the secondexperiment to reduce the coupling of exter-

nal light into the optical pyrometer system (see Fig. 6).

The first modification was to apply a suspension of black

graphite to the exterior surface of the LiF anvil to prevent

light external to the target surface from entering the py-

rometer fiber bundle. Blackening was also applied to most

of the inner metal surfaces of the assembly surrounding

the LiF anvil. A clear region, tailoredto the physical di-

ameter of the fiber bundle, was left open for pyrometry

on the outer surface of the LiF anvil. The secondmodifi-

cation was motivatedby experience with jetting near the

corners of shock-loaded metal joints: black modeling clay

was put on the corners andplastic tubes were put around

some of the ferroelectric pins to help to attenuate jet light

contribution.

Experiment #2 provided more satisfying data than the

first. Note that the radiances are essentially flat for about

1.5 µs (see Fig. 7). The bluest channel (550 nm in wave-

length) is barely visible above baseline, as comparedto

being several volts in the first experiment. Perhaps most

importantly, the bluer wavelength channels show basically

exactly the same shape versus time as the redder wave-

length channels. The shock-breakout times among the

channels are the same within 10-20 ns, which is consistent

with the relative delays in the recording triggers among

the oscilloscopes, with delays in the detector amplifiers,

etc.

The experimental temperature appears to rise some-

what during the shock propagation in the anvil. Fur-

ther experiments exploring this question are plannedand

will be reportedin due course. A straightforwardcalcu-

lation shows that release waves coming back from the

sabot-flyer interface reach bismuth-window interface be-

yond4.6 µs, inducing in the metal a slight progressive

temperature decrease which is visible in Fig. 7. At the end

of the experiment, near 5.2 µs the shock wave breaks out

of the transparent anvil anda high level of light is pro-

duced. We calculated the interface temperature from the

data collectedbetween 3.7 and3.9 µs, i.e. just after the

time when the shock reaches the bismuth external sur-

face. The corresponding temperature is T = 1646 ± 157 K

to be rounded off to T = 1650 ± 160 K (projectile ve-

locity V

p

= 1430 ± 61 m · s

−1

). Table 1 gives further

details about pyrometry data analysis. Experiment #2

yields a much lower temperature than experiment #1

(T ∼ 2400 K, V

p

∼ 1400 m · s

−1

) which reproduces the re-

sults of previous works rather well (Blanco 1997; Blanco

et al. 1999). These earlier results were almost certainly

D. Partouche-Sebban et al.: An investigation of shock induced temperature rise and melting of bismuth

389

0

500

1000

1500

2000

2500

3000

3.0

3.5

4.0

4.5

5.0

Time (

µ

s)

V

o

lt

age (

m

V

)

0.69-0.73 µm
(/2)

0.31-0.63 µm
(*1.33)

1.08-2.12 µm
(*2)

2.05-2.60 µm
(*2.66)

1.08-1.55 µm
(*3)

1.19-1.71 µm
(*2.33)

2.07-3.03 µm

3.04-3.98 µm

Fig. 5. Experiment #1 pyrometry

data

Transmitter

Target metal

Modeling clay

Adhesive colloïdal

graphite

Plastic tubes

Flyer

plate

Vp

Fig. 6. Modifications to previous setup for experiment #2

contaminated by optical backgrounds, likely produced by

shock-generatedmetal jets.

Once the modifications discussed above were carried

out, we were in a better position to study certain inter-

esting features in the bismuth phase-diagram.

4 Investigation of bismuth melting-curve

by means of shock waves

According to a recent theoretical work (P´elissier and

Wetta 2001), under shock loading body-centered cubic

(bcc) bismuth begins to melt near 17 GPa andis com-

pletely meltedabove about 28 GPa. Furthermore, when

shockedbetween 14 GPa and28 GPa andthen released

against a lithium-fluoride window (which leads to an in-

terface pressure p

i

between 10 and18 GPa), bismuth re-

mains in the solid-liquidcoexistence region andits temper-

ature (i.e. the interface temperature T

i

) follows the melt-

ing curve (Wetta andP´elissier 2001). We have performed

eight experiments in this pressure range with the improved

device, in order to deduce part of the bismuth fusion curve

from temperature measurements on shock-loaded samples.

A similar behaviour has been observedwith magnesium

for 35 GPa < p

i

< 50 GPa (Urtiew andGrover 1977), and

Table 1. Pyrometry data analysis for experiment #2; λ is the

mean channel-wavelength, ∆λ is the optical filter bandwidth

(at 50% of the maximal transmittance), L and ∆L are respec-

tively the experimental radiance and its uncertainty; T

min

and

T

max

were calculated with ε = 1 and 0.1 respectively, the inter-

section of allowed temperature bands for the different channels

giving the highest (1803 K) and the lowest (1489 K) of the pos-

sible temperatures; finally ε

min

and ε

max

are, for each chan-

nel, the calculated minimal and maximal emissivities which

are compatible with the experimental radiance, its uncertainty

and these two limit temperatures. λ = 3.51

µ

m channel was

not used as we believe that its calibration was erroneous

λ(

µ

m) ∆λ(

µ

m) L (W · m

−2

· sr

−1

) ∆L (W · m

−2

· sr

−1

)

0.55

0.04

4.3

±2.0

0.705 0.04

26.4

±6.6

1.2

0.09

764

±34.3

1.315 0.47

4904.7

±1073.4

1.5

0.09

1123.1

±38.8

1.6

1.04

11698.1

±1640.7

2.55

0.96

6858.9

±451.8

λ(

µ

m) T

min

(K) T

max

(K)

ε

min

ε

max

0.55

1489

1838

0.13 1

0.705 1443

1803

0.1 0.64

1.2

1381

1906

0.14 0.53

1.315 1332

2009

0.19 0.43

1.5

1338

1996

0.17 0.48

1.6

1286

2032

0.18 0.39

2.55

1110

2043

0.15 0.26

the qualitative results of this early work have been later

corroboratedby calculation (P´elissier 1986). In the same

way, Ahrens et al. (1990) and Bass et al. (1990) concluded,

in case of experiments on iron andon stainless steel re-

spectively, that they couldinfer the melting curves of these

materials (typically between 120 and230 GPa) from their

390

D. Partouche-Sebban et al.: An investigation of shock induced temperature rise and melting of bismuth

0

20

40

60

80

100

120

3.0

3.5

4.0

4.5

5.0

5.5

Time (

µ

s)

V

o

lt

age (

m

V

)

3.04 - 3.98 µm
(/1.6)

2.07-3.03 µm
(/4)

1.08-2.12 µm
(/2)

1.08-1.55 µm
(/2)

0.69-0.73 µm
(/1.7)

1.46-1.55 µm
(/1.7)

1.15-1.25 µm

0.53-0.57 µm

Fig. 7. Experiment #2 pyrometry

data

Pressure

mass velocity

p

H

p

i

Vp/2

Vp

Cu shock-locus

Bi shock-locus

LiF shock-locus

Cu release isentrope

Bi release isentrope

Fig. 8. The experiment in the (mass velocity, pressure) dia-

gram

temperature measurements through lithium fluoride and

sapphire windows.

4.1 Experimental results

Our results are given in Table 2. Shock andinterface

pressures in bismuth were obtainedin the (mass veloc-

ity, pressure) diagram, as illustrated in Fig. 8. Indeed,

because of symmetrical copper-copper impact, mass ve-

locity in shockedcopper is half of the flyer velocity V

p

.

For Cu, Bi andLiF, experimental shock Hugoniot data

(Marsh 1980) were usedandthe release isentropes of cop-

per andbismuth were assumedto be the mirror images

of corresponding shock-loci. This well-known approxima-

tion (Zeldovich and Raizer 1967, p. 729) is appropriate for

copper in the investigatedpressure range. The hypothesis

seems more questionable for bismuth, which experiences a

10% volume reduction when shocked at low pressure and

also phase transitions during release (Wetta and P´elissier

2001). We have checked, by a theoretical calculation of

Bi Hugoniot curve andrelease isentropes, that the mir-

ror reflection approximation remainedreasonable in the

present case. It comes from the fact that, in our exper-

iments, LiF rather large shock-impedance prevented the

Table 2. Experimental results. Apart from bismuth interface

temperature T

i

, we have only measured the flyer velocity V

p

,

from which we have deduced (cf. text) the shock and interface

pressures (respectively p

H

and p

i

) in bismuth. Accordingto

theoretical calculations, the correspondingcompression factor

ρ

i

/ρ

0

(ρ

i

and ρ

0

beingrespectively the interface and initial

densities) varies between 1.3 and 1.34

Exp.

V

p

(m · s

−1

)

p

H

(GPa)

p

i

(GPa)

T

i

(K)

#2

1430 ± 61

24.7 ± 1.8

17.5 ± 1.1

1650 ± 160

#3

1347 ± 26

22.7 ± 0.9

16.4 ± 0.5

1470 ± 190

#4

1391 ± 21

23.2 ± 0.6

16.8 ± 0.4

1690 ± 240

#5

1329 ± 53

22.0 ± 1.5

16.0 ± 1.0

1520 ± 230

#6

972 ± 27

14.1 ± 0.8

11.1 ± 0.6

880 ± 170

#7

867 ± 30

12.4 ± 0.7

9.9 ± 0.5

800 ± 120

#8

1209 ± 36

19.5 ± 0.9

14.5 ± 0.6

1270 ± 160

#9

1167 ± 50

18.4 ± 1.2

13.8 ± 0.8

1250 ± 160

interface pressure from decreasing drastically (cf. Fig. 8);

consequently, releasing bismuth stayedin closed-packed

form (bcc or liquid) and never underwent a reverse tran-

sition to a low-density phase like Bi I.

The first two high-pressure points (experiments 2 and

3) were obtainedassuming that bismuth emissivity was

between 0.1 and1 for the two visible channels (cf. dis-

cussion in Sect. 2). Using this methodwe have shown that

the emissivity was less than 0.6 for infraredchannels. Con-

sequently for other experiments, specifically when the ob-

servedsignals are too low in the visible spectrum, we have

only usedinfraredradiances andconstrainedthe dynamic

emissivity between 0.1 and0.6.

4.2 Discussion of the results

As discussedpreviously (Wetta andP´elissier 2001), the

fact that the sample is gluedto the LiF window has two

consequences that we have not yet dealt with:

– even if glue is a goodthermal insulator (especially

regarding a ∼ 1 µs duration experiment), a small

D. Partouche-Sebban et al.: An investigation of shock induced temperature rise and melting of bismuth

391

Fig. 9. Shock, interface and free-surface temperatures of

bismuth versus incident shock pressure. Theory (Wetta and

P´elissier 2001): dashed line (shock), full line (LiF window) and

dotted line (free surface). Experimental: squares, triangles (LiF

window, respectively Blanco 1997 and present work) and cir-

cles (free surface, Mondot 1993)

cooling effect takes place in the metallic sample at

the bismuth-LiF interface; this effect wouldbe much

stronger with a vapor-deposited film (Ahrens et al.

1990; Bass et al. 1990; Tan andAhrens 1990)

– a series of shocks andre-shocks occurs across the glue

layer before pressure andmass velocity come in equi-

librium on both sides of this interface; so that, since a

certain amount of irreversibility is added in this pro-

cess, the interface temperature T

i

is somewhat higher

than expected.

Fortunately, in the case of bismuth, as long as excita-

tion pressure does not exceed 35 GPa, both corrections

remain limited (about 50 or 100 K) and, according to our

estimates, typically cancel each other. Moreover, as long

as bismuth remains in the solid-liquid coexistence region,

small heating or cooling effects are inhibitedby the melt-

ing curve. Their only consequence is a variation of the

solid-liquid proportion.

Figure 9 shows that the results obtainedin the present

work are in much better agreement with theoretical pre-

diction than the previous ones. The accord becomes com-

parable to that for free-surface experiments, which is more

satisfactory. Of the previous results, only the one near

p

H

= 43 GPa seems in agreement with calculation since

the interface cooling is close to 100 K at this pressure

(which is not taken into account in the theoretical curve).

Even if bismuth andlithium fluoride are not perfectly

shock-impedance matched, for a given shock-pressure one

can note that the temperature decrease T

H

–T

i

along the

rarefaction isentrope remains rather limited.

The previous observation is confirmedby the examina-

tion of Fig. 10, where the theoretical isentrope correspond-

ing to p

H

= 43 GPa appears. This is typically the highest

shock-pressure reachedin previous experiments (Blanco

Fig. 10. Temperature of shocked bismuth against a lithium-

fluoride window in the (pressure, temperature) diagram. Locus

of interface temperature versus interface pressure for LiF anvil:

experiment (squares: Blanco 1997 and triangles: present work)

and theory (thin full line: Wetta and P´elissier 2001). The the-

oretical Hugoniot and melting curves are also recalled (respec-

tively dashed and dotted lines), and the release isentrope for

p

H

=43 GPa appears as a thick full line

1997). According to calculations, the interface temper-

ature versus interface pressure curve (for LiF window)

merges with the melting curve in the 10–18 GPa pres-

sure range, andconsequently one can expect to observe

well-markedinflections near 10 and18 GPa. The exper-

imental point set seems to indicate the fusion-line shape

but with less drastic slope-changes than predicted theoret-

ically. Similarly the plateau which characterizes the free-

surface temperature versus shock-pressure curve seemed

somewhat smoothedas shown by Fig. 9 experimental data.

A possibility (see Fig. 10) is that solid-liquid coexistence

region couldbe somewhat narrower than calculated, as in-

dicated by the two points near 10 GPa. In fact, the point

p

i

= 9.9 GPa appears to be somewhat below the melt-

ing curve, as fusion was reachedtypically at 780 K for

p = 6.5 GPa (Klement et al. 1963).

We plan to perform several more experiments on bis-

muth with lithium fluoride and sapphire windows. Since

the shock impedance of sapphire is higher than that of

bismuth, we couldobtain an interface temperature some-

what greater than shock temperature andstudy the melt-

ing curve between about 17 and28 GPa. Anda subsequent

comparison to diamond-anvil cell results in the 10–28 GPa

range wouldbe of great interest.

5 Conclusion

We have reportedthe results from a series of experi-

ments, giving the surface temperature of bismuth initially

shockedandthen partially releasedagainst a transpar-

ent lithium-fluoride anvil. During this work, previous ex-

perimental technique was refined, especially with regard

392

D. Partouche-Sebban et al.: An investigation of shock induced temperature rise and melting of bismuth

to reducing optical background. The improved device al-

lowedus to investigate dynamically a part of the melting

curve (as expectedfrom previous calculations), andseems

to provide a sound basis for future experiments.

Acknowledgements. The authors wish to thank J.P. Aubry for

his careful and professional contributions to the experiments.

We also would like to thank C. Rion, S. Verdelet and P. Os-

trowski for their help in settingup the experiment and record-

ingthe data. Finally, the authors are indebted to the referee

for interestingremarks.

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