Near-equilibrium polymorphic phase transformations in Praseodymium under dynamic compression Page: 3 of 8
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Near-equilibrium polymorphic phase transformations in Praseodymium under
Marina Bastea* and D.B. Reisman
Lawrence Livermore National Laboratory, P.O. BOX 808, Livermore, CA 94550
We report the first experimental observation of sequential, multiple polymorphic phase transfor-
mations occuring in Praseodymium dynamically compressed using a ramp wave. The experiments
also display the signatures of reverse transformations occuring upon pressure release and reveal the
presence of small hysteresys loops. The results are in very good agreement with equilibrium hy-
drodynamic calculations performed using a thermodynamically consistent, multi-phase equation of
state for Praseodymium, suggesting a near-equilibrium transformation behavior.
PACS numbers: 64.70.Kb, 62.50.+p, 64.30.+t
The transition metals form an interesting class of
materials with complex phase diagrams strongly corre-
lated to the evolution of their electronic structure un-
der applied pressure. Following the enhancement in the
d-band occupancy, which at lower pressures results in
slight atomic re-arrangements in high symmetry struc-
tures with negligible density changes, several lanthanides
also undergo phase transformations to lower symmetry
structures marked by significant volume collapses and a
delocalization of the 4f electrons [1 3]. Praseodymium
(Pr) is a representative example for this type of behavior.
Comprehensive theoretical studies up to several Mbars
have created a rich basis for understanding both its ther-
modynamic and electronic properties at elevated pres-
sures . A wealth of static high pressure studies have
engaged a range of techniques to map the material behav-
ior under compression. While early experimental stud-
ies focused on static pressure conditions [5 9] or nearly-
instantaneous shock loading conditions , recent devel-
opments have enabled explorations on intermediate time-
scales [11 13].
We carried out comprehensive dynamic compression
experiments on high-purity (99.9 %) polycrystalline
Praseodymium. Disk shaped samples, 6 mm in diameter
and with thicknesses of 0.4 and 0.52 mm, were prepared,
metrologized and encapsulated between aluminum (Al)
panels and a transparent window, under controlled argon
(Ar) atmosphere in order to preclude oxydation. Four
identical panels, as shown in Fig. 1, were arranged symet-
rically around a central cathode to form the anode of the
Z-accelerator. The controlled discharge of a large capac-
itor bank generates a magnetically driven pressure wave
with an ~ 35GPa amplitude and a risetime of ~ 400ns,
followed by gradual release at the left boundary of the
panels, Fig. 1. The loading pressure was carefully de-
signed to avoid field penetration before the end of the
experiment, or the development of shocks in the sample,
and was monitored on each panel with a reference probe.
Variations of 2-3% were registered in the maximum pres-
*Electronic address: basteaiellni.gov
sure between panels and were ascribed to possible local
differences in the corresponding panel/cathode spacing.
We measured the velocity of the sample/window interface
during the experiment using interferometric techniques
(VISAR) . Four interferometer probes were pointed
at the center of each sample, with two or more different
sensitivities in order to eliminate fringe loss uncertainties.
Three types of windows were used in the experiments:
 single crystal lithium fluoride - LiF, poly-methil-
metacrillate - PMMA and z-cut sapphire - A1203. Their
optical properties in the pressure-temperature regime ac-
cessed in these experiments have been well studied and
are summarized in .
As a result of the rapidly applied pressure the samples
are compressed along a quasi- isentropic thermodynamic
path that intercepts several Pr phase boundaries during
both the compressive and subsequent release regimes -
see Fig. 2 and the discussion below. As noted in 
the dynamic impedance of the window plays an impor-
tant role in the evolution of the phase transformations
inside the sample. This effect is clearly illustrated by
the present experiments which, as mentioned above, have
been carried out with three types of windows: the "stiff"
sapphire window produces a significant pressure enhance-
ment at the interface, "soft" PMMA leads to a pressure
drop at the interface, while LiF single crystal, relatively
closely dynamically matched to Pr, provides a nearly in-
situ response. The general differences between the exper-
imental traces shown in Figs. 3 and 4 are rather obvious,
although they all display the characteristic changes in ve-
locity slope (acceleration) associated with the occurence
of phase transitions .
The detailed dynamic response of Pr under compres-
sion can be better understood by comparing the mea-
sured interface velocity v(t) to one-dimensional hydro-
dynamic simulations mimicking the experimental set-
up. We performed such calculations using a multi-phase
equation of state for Pr derived from a thermodynam-
ically consistent free energy model , Mie-Gruneisen
equations of state for the Al panels and windows ,
and the applied pressure history measured by the refer-
ence probes. At ambient conditions Pr assumes a dhcp
structure with initial density po 6.78g/cm3, while un-
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Bastea, M & Reisman, D. Near-equilibrium polymorphic phase transformations in Praseodymium under dynamic compression, article, February 12, 2007; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc887096/m1/3/: accessed February 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.