Short-range interaction in liquid rhodium probed by x-ray absorption spectroscopy

Article abstract of DOI:10.1088/0953-8984/11/6/001

Accurate XAFS spectra of solid and liquid rhodium at very high temperature have been recorded at the European Synchrotron Radiation Facility. Experiments have been analysed using advanced data analysis techniques and the results are compared with molecula

Full text of DOI:10.1088/0953-8984/11/6/001

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Short-range interaction in liquid rhodium probed by x-ray absorption spectroscopy
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1999 J. Phys.: Condens. Matter 11 L43
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J. Phys.: Condens. Matter 11 (1999) L43–L49. Printed in the UK
PII: S0953-8984(99)98696-4
LETTER TO THE EDITOR
Short-range interaction in liquid rhodium probed by x-ray
absorption spectroscopy
Andrea Di Cicco†, Giuliana Aquilanti†, Marco Minicucci†,
Adriano Filipponi‡ and Jaroslaw Rybicki§
† UdR INFM, Dipartimento di Matematica e Fisica, Universita` degli Studi di Camerino
Via Madonna delle Carceri, 62032 Camerino (MC), Italy
‡ UdR INFM, Dipartimento di Fisica, Universita` dell’ Aquila, 67010 Coppito, L’Aquila, Italy
§ Technical University of Gdansk, Naturowicza 11/12, 80-952 Gdansk, Poland
Received 23 October 1998
Abstract. Accurate XAFS spectra of solid and liquid rhodium at very high temperature have
been recorded at the European Synchrotron Radiation Facility. Experiments have been analysed
using advanced data analysis techniques and the results are compared with molecular dynamics
simulations performed using several different pair functionals as model potentials. High-
temperature data provided new insight on the details of the interaction potential allowing us to
test the validity of different functional forms. The short-range g(r) at about 2300 K of liquid Rh
and of the Rh–C alloy near the eutectic composition are measured for the first time and compared
with MD results.
The availability of high-brilliance third generation synchrotron radiation sources has opened
new opportunities for the study of condensed matter under extreme conditions at high pressure
and/or high temperature. The x-ray absorption spectroscopy (XAS) has been exploited up to
the 100 GPa high-pressure range [1]. Temperatures up to about 2000 K and pressures of about
2 kbar can be reached using sapphire cells in an autoclave system [2], a technique exploited
for the study of fluid Se up to the critical point [2, 3]. XAS measurements up to about 1500 K
and 50 kbar can be performed using a technique based on the use of the Paris–Edinburgh press
[4] and recent experiments on fluid I2 have been performed [5]. A containerless technique
based on electromagnetic levitation of molten and highly undercooled liquid specimens has
been also developed for high-temperature XAS experiments [6].
An alternative technique for high-temperature low-noise XAS experiments in high-
vacuum conditions is based on the measurement of sintered pellets of fine sample particles and
an inert matrix powder [7]. It has been exploited for the study of liquid and undercooled liquid
metals like Ge [8] and Sn [9] and was recently made available at the BM29 x-ray absorption
spectrometer of the European Synchrotron Radiation Facility (ESRF) [10].
Recent advances in the data analysis of the x-ray absorption fine structure (XAFS) [11]
have opened the way for the establishment of a reliable methodology for investigating highly
disordered systems. XAFS is particularly sensitive to the shape of the first peak of the pair
distribution function and can complement information on the medium- and long-range order
obtained, for instance, from diffraction techniques [8, 9, 12]. The possibility of testing the
short-range part of the interatomic potential by comparing XAS results to the model structure
provided by Monte Carlo (MC) or molecular dynamics (MD) computer simulations has been
emphasized [13].
0953-8984/99/060043+07$19.50 © 1999 IOP Publishing Ltd
L43

L44
Letter to the Editor
In this letter we report the results of a challenging experimental achievement such as
the first XAS measurement of liquid rhodium (melting point Tm ∼ 2236 K), which has
been performed at the third generation ESRF BM29 spectrometer. Due to the high Tm no
diffraction measurements have so far been reported for this system. The XAFS data of solid
and liquid Rh are analysed using calculations of the x-ray absorption cross-section in the
framework of the GNXAS method [11]. Results on high-temperature solid and liquid Rh are
compared with structural models obtained using MD simulations performed using different
pair functionals [14, 15] developed in recent years for transition metals.
The Rh K-edge XAS measurements were performed using a Si(311) double crystal
monochromator. The primary vertical slit were set to 0.5 mm achieving a typical resolution
of about 1.5 eV at 30 keV. XAS spectra were measured in transmission mode using ionization
chambers. High-temperature XAFS measurements were performed under high vacuum
condition ≈10−5 mbar using an improved version of the previously described oven [7, 10].
The sample temperature was measured using an optical pyrometer in the 1000–2500 K range
and various sets of thermocouples up to about 1800 K.
Samples suitable for high-temperature studies were produced by mixing ammonium
hexachlororhodate fine powder (99.999% purity) with different matrices such as high-purity
graphite, BN, ZrO2 and HfO2. The Rh salt was decomposed and reduced by an in situ heat
treatment into micrometric size metallic grains embedded in the matrix powder. Crucible
materials such as graphite 100 µm thick for the Rh/C sample, Mo 2.5 µm, Ta 2 µm, and W
5 µm for the other matrices, were used.
Good quality measurements of solid Rh in the 300–1900 K temperature range were
obtained in a wide wave-vector range (up to k ∼ 25 Å−1) using both Rh/C pellets and a
25 µm Rh foil heated directly through the electrodes. In the case of the Rh/C sample the
reversible diffusion of C in Rh is observed above 1600 K, in agreement with the known Rh–C
phase diagram [16], leading to the melting of a Rh–C alloy with the eutectic composition.
Attempts to measure pure liquid Rh using BN or ZrO2 matrices were not successful due to the
occurrence of chemical reactions. Successful measurements of pure liquid Rh just above the
melting point were instead possible using the HfO2 matrix and a W crucible. The difficulty of
collecting good quality spectra was enhanced by the high absorption of the crucible and of the
matrix, by the small sample size (about 1 mm2) and relatively short lifetime of the crucible at
very high temperature. For this reason the high photon flux provided by ESRF was essential
to obtain low-noise XAS spectra. Raw XAS data of liquid Rh and liquid Rh–C alloy around
the eutectic composition are shown in figure 1.
Realistic structural models for solid and liquid Rh were obtained by classical MD
calculations, performed using 864 atoms and experimental density values for temperatures
ranging from 100 to 3000 K. We used previously published pair functionals for which the
attractive part is computed using the second-moment approximation within the tight-binding
scheme. Two different functional forms containing a square-root (1/2Ros) [14] or a 2/3
dependence from the effective coordination were used. Two different 2/3 models has been
proposed in [15]. The first, hereafter referred as 2/3Gue-f1, has been derived using as
experimental constraints the cohesive energy, the bulk modulus and the elastic constant (C44),
while the second (2/3Gue-f2) has been calculated by introducing the vacancy formation energy
instead of C44.
First-neighbour average distances R and bond variances σ2 obtained from MD simulations
of solid Rh are compared with XAFS experimental results in figure 2 (data with error bars).
Note that XAFS (and MD) measure the interatomic distances including the contribution of
vibrations perpendicular to the bond direction (see [8] and references therein). Therefore, the
√
slight elongation of the average distance with respect to the cell parameter a = 2R measured

Letter to the Editor
L45
Figure 1. Raw x-ray absorption data of liquid Rh dispersed into HfO2 (upper curve) and graphite
(lower curve).
Figure 2. First-shell distance R and variance σ2 of solid Rh as a function of temperature
obtained from XAFS data analysis (data with error bars) compared with those determined from
MD simulations and with the mean equilibrium site-to-site distance measured by diffraction.
by diffraction [16], obtained increasing the temperature, is a normal effect. The first-neighbour
variance at high temperature is in quite good agreement with MD results using 1/2Ros and
2/3Gue-f1 models while is not compatible with that predicted using the 2/3Gue-f2 potential.

L46
Letter to the Editor
At moderate temperatures, 300–1000 K, the experimental bond variance lies in between the
1/2Ros and 2/3Gue-f2 curves. The inaccuracy of the 2/3 Gue-f2 potential in describing the
local structure of high-temperature Rh was also verified looking at the third cumulants of the
distribution (not shown) and melting point which was found to lie at much higher temperature
than the known experimental value.
Figure 3. Upper panels: g(r) of liquid Rh at about 2500 K obtained from MD simulations
decomposed into first-neighbour peaks and long-range tails. Lower panels: model γ (2)
signals calculated from corresponding g(r) functions (upper panels) compared with χ(k) XAFS
experimental data.
XAS data of liquid systems can be analysed starting from a model g(r) which satisfies
the correct long-range conditions [17]. Realistic model g(r) functions are provided by MD
simulations of liquid Rh at 2500 K using the above mentioned 1/2Ros and 2/3Gue-f1 pair
functionals (see figure 3, upper panels). The g(r) functions were decomposed into short-
range peaks and long-range tails (dashed curves in figure 3). XAS data analysis can provide a
refinement only of the short-range g(r) peak, parametrized using the mean distance, variance
and asymmetry parameters [17]. Model γ (2) two-body signals [11] related to the short-range
peaks and to the tail of the corresponding g(r) (upper panels) are compared with experimental
XAFS χ(k) data in the lower panels of figure 3. The main contribution γ((S2)) to the experimental
signal is clearly associated with the short-range peak. Both calculations are in qualitative
agreement with experimental data. However, the evident oscillation in the residual curve
(bottom in figure 3) indicates that a refinement of the short-range part of the g(r) is necessary.
(2)
(S)
(2)
(tail)
Best-fit γ and the (fixed) tail signal γ
are reported in figure 4, upper panel. The

Letter to the Editor
L47
Figure 4. Upper panel: best-fit calculated signals associated with the short range part (γ((S2))) and
the tail of the liquid Rh g(r) at 2240 K. The total best-fit curve is compared with χ(k) experimental
data. Lower panel: comparison between the g(r) reconstructed by XAFS (thick solid curve with
error bars) and those obtained by MD simulations (solid and dashed curves). A magnification of
the peak is drawn in the inset.
result of the fit, obtained by summing the individual contributions, is compared with liquid Rh
experimental data at 2240 K (solid curves, bottom). The agreement is excellent as shown by
the residual curve (dots). The reconstructed g(r) (thick solid) and its decomposition into the
best-fit short-range peak and tail functions (dot-dashed) are shown in figure 4, lower panel.
Error bars were evaluated for a 95% confidence level and accounting for correlations among
the relevant parameters. The best-fit g(r) is compared with the initial MD models (solid and
dashed curves). For liquid Rh the best-fit curve results are in better agreement with the 2/3
Gue-f1 model. A portion of the figure is magnified in the inset where the shift toward longer
distances (∼0.1 Å) of the first peak, with respect to both MD results, is evidenced. The foot
of the distribution remains approximately at the same distance and the rise of the g(r) is less
steep than that calculated by MD. This is an indication that a softer interatomic potential would
better reproduce the local structure of liquid Rh.
Using the present XAS high-temperature technique it was also possible to measure a Rh–
C alloy with a concentration close to the eutectic composition. In this case, very low-noise
measurements are possible due to the very low absorption of the matrix and crucible. The
Rh–C system melts at about 1967 K with a carbon atomic fraction of about 16% (eutectic
composition) [16] and the shape of XAS data is clearly different from that of pure liquid
Rh as shown in figure 1. The experimental XAFS χ(k) signal measured at about 2220 K

L48
Letter to the Editor
Figure 5. Upper panel: Comparison of experimental and calculated best-fit χ(k) XAFS signals
related to liquid Rh–C alloy at 2220 K. The agreement is very good, as shown by the residual
curve (bottom). Individual Rh–Rh and Rh–C contributions are reported (top). Left-lower panel:
reconstructed g(r) associated with Rh–Rh and Rh–C signals (data with error bars). The g(r) is
decomposed into its short- and long-range components (dot-dashed) and compared with the first
g(r) peak of pure liquid Rh reported in figure 4 (large dots). Right-lower panel: coordination
numbers N(r) associated with C (dashed) and Rh (dot-dashed) atoms as a function of distance
from a generic Rh atom. The total N(r) is also shown (solid).
is compared in figure 5 with the best-fit calculated curve obtained taking into account the
presence of C atoms at short distances (upper panel). Inclusion of a Rh–C γ (2) signal was
found to be necessary to explain the experimental data. Thus, the model signal included Rh–
Rh and Rh–C γ((S2)) short-range terms while long-range contributions were approximated using
the 1/2Ros Rh–Rh tail neglecting possible, although certainly very weak, Rh–C contributions.
(2)
(S)
The individual best-fit Rh–Rh and Rh–C γ terms are shown in the same frame of figure 5
(top). The best-fit was performed floating both the Rh–Rh and Rh–C mean distance, variance
and asymmetry parameters. The Rh–C coordination number was also floated. The agreement
between calculated and experimental XAFS is very good, as shown by the residual curve in
figure 5.
The final best-fit parameter values allowed us to reconstruct the g(r) centred on Rh atoms
shown in figure 5, left-lower panel. An evident peak due to C atoms at very short distances is
found, with mean distance R ∼ 2.06 Å, compatible with typical metal-C bond-lengths. The
final best-fit Rh–C coordination number N ∼ 1.9 (dashed, right-lower panel) is compatible
with a C dilution in the range 15–20%, near the eutectic composition. Presence of C atoms

Letter to the Editor
L49
at short distances causes a shift of the Rh–Rh first-neighbour peak toward longer distances
(∼ 0.1 Å). The peak is also slightly broadened compared with pure liquid Rh (dots). The
running Rh–C and Rh–Rh coordination numbers as functions of distance N(r) are reported
in the right-lower panel of figure 5. The total N(r) (solid) increases to typical close-packed
values reaching 12 atoms at about 3.3 Å.
Results reported in the present letter show that reliable very high-temperature XAS
measurements of liquid metals and alloys are feasible using third generation synchrotron
radiation sources and available experimental devices. Experimental XAS results for high-
temperature Rh have been compared with structural models obtained using MD simulations
allowing us to evaluate the accuracy of different proposed microscopic interaction potentials
in transition elements. The short-range part of the pair distribution function of liquid Rh at
2240 K was measured for the first time showing that the first peak is slightly broadened and
shifted toward longer distances compared with MD simulations. The short-range structure
of the Rh–C alloy at about 2220 K near the eutectic composition was also determined. An
evident peak in the g(r) associated with the presence of C atoms around 2 Å and a clear
elongation of the average Rh–Rh distance were found. These findings should stimulate further
experimental efforts to study local structure and interatomic interactions in liquid metals and
alloys in extreme conditions.
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