FCC-HCP phase boundary in lead

Article abstract of DOI:10.1016/S0038-1098(02)00112-6

The temperature evolution of fcc-to-hcp transformation in lead metal was studied and pressure-temperature equation of state for fcc and hcp phases up to 800 K and 40 GPa was determined. Polycrystalline lead was studied in extremely heated, gasketed diamond anvil cell. In situ high-pressure-high-temperature data were obtained at the ID-30 beam line by angle dispersive X-ray diffraction techniques employing monochromatic X-radiation. An unexpected interaction of lead with sodium chloride surrounded the samples and significant reduction of the alloying temperature with gold was observed.

Full text of DOI:10.1016/S0038-1098(02)00112-6

PERGAMON
Solid State Communications 122 >2002) 125±127
www.elsevier.com/locate/ssc
FCC±HCP phase boundary in lead
a,
a
A. Kuznetsov , V. Dmitriev , L. Dubrovinsky , V. Prakapenka , H.-P. Weber
b
c
a,d
*
aGroup ªStructure of Materials under Extreme Conditionsº, European Synchrotron Radiation Facility,
Swiss±Norwegian Beam Lines at ESRF, P.O. Box 220, F-38043 Grenoble, France
bBayerisches Geoinstitut, Universitaet Bayreuth, D-95440 Bayreuth, Germany
cANL/CARS, University of Chicago, 9700 S. Cass Avenue, Argonne, IL 60439, USA
dInstitute of Crystallography, University of Lausanne, CH-1015 Lausanne, Switzerland
Received 8 February 2002; accepted 7 March 2002 by H. Eschrig
Abstract
The pressure±temperature phase diagram of Pb was mapped from synchrotron X-ray diffraction data measured to 40 GPa
and 800 K, in the region including the hexagonal-close-packed to face-centered cubic transformation; the corresponding
p±T±V equations of state were ®tted for both phases. An unexpected interaction of Pb with NaCl surrounded the samples
and signi®cant reduction of the alloying temperature with Au was observed. q 2002 Elsevier Science Ltd. All rights reserved.
PACS: 61.66.Bi; 62.50. 1 p; 64.90. 1 b
Keywords: A. Metals; C. Crystal structure and symmetry; D. Phase transitions; E. High pressure
Elemental lead, one of the oldest metal known to man
>mentioned in Exodus!), has many applications, some
derived from its low tensile strength >shockabsorbers in
foundations of high-rise buildings), others from its high
absorption of electromagnetic radiation >protective shield-
ing), its high resistance to corrosion >economical plumbing),
its easy alloyability >solder material)Ðto mention just a few
key attractive properties. In everyday life, its economically
most important use, however, comes from its favorable elec-
trical properties; lead-acid storage batteries, the demise of
which has been predicted for decades, are still being
continuously improved. In its compounded form, the uses
of lead are even more ubiquitous and therefore too numer-
ous to mention here.
from the face-centered cubic >FCC) form to the hexagonal-
close-packed >HCP) structure at 14 GPa [4] and then, at
about 120 GPa, to the body-centered cubic >bcc) phase
[5,6]. However, the phase boundaries, phase coexistence
regions and their evolution with an increase in temperature
were not studied. In the present letter, we communicate the
fcc-to-hcp transition region mapped to high temperature,
and the corresponding pressure±temperature equation of
state >EOS) of Pb metal.
In situ high-pressure±high-temperature data were
obtained at the ID-30 beam line of the European Synchro-
tron Radiation Facility >ESRF, Grenoble, France) by angle-
dispersive X-ray diffraction techniques employing
ꢀ
monochromatic ꢀl ˆ 0:3738 A† X-radiation. Small pieces
So lead is clearly, already in its elemental form, a material
of strategic importance, and it is therefore surprising that the
phase diagram of such an important element has been so
cursorily explored till now. Only the melting curve has
been mapped, ®rst up to 9 GPa and 1200 K using DTA
[1,2], and later on extended to 100 GPa and 4000 K [1,3]
with laser heating. Isothermal high-pressure X-ray diffrac-
tion experiments ®rst disclosed the transformation of Pb
of polycrystalline Pb >99.999% purity, Advent) were studied
in externally heated, gasketed diamond-anvill cell. The
existence of reliable data on pressure±temperature EOS
for NaCl [7] allowed us to use this material both as a
pressure-transmitting medium and the pressure calibrant at
high temperature. A K-type thermocouple placed close to
the high-pressure sample chamber was used to measure the
temperature of the sample. Diffraction measurements were
performed up to a maximum pressure of 40 GPa and to a
maximal temperature 800 K, these limits ensuring comple-
tion of the fcc-to-hcp transformation.
* Corresponding author. Tel.: 133-476882079; fax: 133-
476882694.
Fig. 1 shows the selected angle-resolved X-ray diffraction
E-mail address: akuznets@esrf.fr >A. Kuznetsov).
0038-1098/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.
PII: S0038-1098>02)00112-6

126
A. Kuznetsov et al. / Solid State Communications 122 >2002) 125±127
Fig. 2. P±T phase diagram of lead. Compression: 1, fcc phase; 2,
hcp; 3, two-phase mixture. Decompression: 4, fcc; 5, hcp.
Shadowed is the two-phase region.
between DG and the activation energy >barrier) GM of the
martensitic fcc-to-hcp transformation results in a kinetic
hysteresis of the transformation and the existence of a
large two-phase region [9].
Fig. 2 shows the results of diffraction experiments and
shows the phase diagram of the lead in the pressure range
covering the fcc-to-hcp transformation region. One can see
that the two-phase pressure range decreases with tempera-
ture increase, in full agreement with the kinetic interpreta-
tion of its nature. The progressive decrease of DV/V is
characteristic for this pressure-induced transition with
temperature increase >Table 1).
Fig. 1. Examples of high-pressure synchrotron radiation X-ray
powder diffraction patterns of Pb metal in different phases at
room temperature. p denote fcc NaCl peaks.
patterns of lead up to 21 GPa at ambient temperature, cover-
ing the transition region. Room-temperature results are in
good agreement with the previous reports of Refs. [5,6]. All
peaks could be indexed with the fcc, hcp structures of Pb and
the fcc NaCl structure. At room temperature, the onset of the
phase transition from the fcc phase to the hcp phase takes
place at a pressure of about 12.0 GPa, where at least two
diffraction peaks of the hcp Pb, 100 and 101, which do not
overlap with fcc peaks, are observed >Fig. 1). With increas-
ing pressure, the intensities of the hcp lines increase and the
fcc lines disappear. The fcc-to-hcp transition in Pb is very
sluggish, both the fcc and hcp phases coexist up to a pressure
of 20 GPa.
In order to obtain the p±T±V EOS for Pb, a series of
isothermal equations of the Birch±Murnaghan form [10]:
ꢀ
ꢁ
3
3
PꢀV; T† ˆ BꢀT†ꢀv7=3 2 v5=3† 1 1 ‰B0ꢀT† 2 4Šꢀv2=3 2 1†
2
4
ꢀ1†
with v ˆ V0ꢀT†=V; were ®tted to the experimental data. The
incorporation of the temperature effect proceeds by the
assumption of temperature dependence of the parameters
of Eq. >1). First, the thermal expansion at ambient pressure
should be taken into account:
ꢂ
ꢃ
ZT
The existence of a large two-phase region, observed also
in preceding experiments on Pb [8], is consistent with a
small volume reduction, DV/V, at the fcc-to-hcp transition
>Table 1) and thus a small free energy difference, DG,
between fcc and hcp phases. The considerable difference
V0ꢀT† ˆ V0ꢀT0†exp
aꢀT†dT
T0
ꢂ
ꢃ
ꢄ
ꢅ
ZT
ˆ V0ꢀT0†exp
a0 1 a1T 1 a2T2 dT
T0
ꢆ
ꢇ
1
1
ù V0ꢀT0† 1 1 a0t 1 a1t2 1 a2t3
;
ꢀ2†
2
3
Table 1
Volume reduction at the fcc-to-hcp phase transition at different
temperatures
where t ˆ ꢀT 2 T0† with T0 ˆ 296 K. Then a simplest poly-
nomial expansion in temperature can be applied to the bulk
modulus B and its pressure derivative B0:
21
21
Ê 3
T >K) P >GPa) Vfcc >A mol
Ê 3
)
Vhcp >A mol
)
DV/V >%)
BꢀT† ˆ B0 1 b1t 1 b2t2;
B0ꢀT† ˆ B00 1 b0t:
ꢀ3†
296
402
469
13.1
13.9
12.6
25.12
25.14
25.26
24.84
24.92
25.06
1.02
0.89
0.77
Thus, V0, B0, B00 ; a0, a1, a2, b1, b2, b 0 are the ®tted para-
meters. Table 2 summarizes the numerical results of the

A. Kuznetsov et al. / Solid State Communications 122 >2002) 125±127
127
Table 2
Parameters for the p±T±V EOS of lead
Parameter
fcc
hcp
21
Ê 3
V0 >A mol
)
30.307
29.908
B0 >GPa)
b1
b2
40.5
54.2
21:07 £ 1023
21:14 £ 1025
5.74
25:46 £ 1022
2:34 £ 1025
3.61
B0
0
b 0
a0
a1
a2
25:45 £ 1023
8:67 £ 1025
2:12 £ 1029
1:83 £ 10210
5:01 £ 1023
8:97 £ 1025
2:52 £ 1028
0.0
Fig. 4. Reaction of lead with NaCl. >a) X-ray powder diffraction of
Pb with NaCl as pressure-transmitting medium at p ˆ 10:9 GPa and
T ˆ 663 K. Dotted peaks correspond to fcc Pb and fcc NaCl. >b)
Simulated powder diffraction pattern of PbCl2.
®tting procedure. For both fcc and hcp phases the ®tted
equilibrium volume V0 is close to that found in earlier
experiments, bulkmodulus and the pressure derivative of
the bulkmodulus are also in reasonably good agreement at
300 K [6,11]. Fig. 3 shows the ®tted EOS curves plotted
with experimental data scaled to the room temperature by
Eqs. >2) and >3).
produced in the chemical reaction between the lead metal
and sodium chloride. We could not determine the precise
starting pressure of the reactionÐonly the pressure range
>between ambient and 10.0 GPa). The controlled annealing
of the Pb 1 NaCl mixture during 200 h at T ˆ 675 K, close
to the melting point, under ambient pressure did not affect
the initial components.
It is worthwhile to mention, in conclusion, some addi-
tional results concerning the interaction of the metal lead
with some materials. First, we had to discard gold as the
pressure calibrant because of its alloying with lead at
surprisingly low temperature. A discontinuity in the diffrac-
tion patterns evolution of Pb related to the alloying process
was observed, for example, at 460 K and 4.2 GPa. Another
interesting reaction was observed when we used the Pb 1
NaCl mixture, even under moderate pressure in the vicinity
of the melting curve. We succeeded in visualizing traces of
In summary, we have studied the temperature evolu-
tion of the fcc-to-hcp transformation in lead metal and
determined the p±T±V equations of state for the fcc and
hcp phases up to 800 K and 40 GPa. We believe our
results could be used for a pressure±temperature cali-
bration scale in future high pressure±high temperature
experiments.
Ê
PbCl2 >Fig. 4), with lattice parameters a ˆ 6:4575ꢀ6† A,
Ê
Ê
b ˆ 4:8139ꢀ6† A, c ˆ 9:9755ꢀ0† A; this compound was
References
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Fig. 3. Pressure±volume relations in Pb. Circles: fcc; squares: hcp.
The solid symbols represent the room temperature results; the open
symbols represent the reduced high-temperature data. The solid
curves are the ®ts of the Birch±Murnaghan EOS with the para-
meters listed in Table 1.
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