Collective excitations in molten NaCl and NaI: A theoretical generalized collective modes study
Taras Bryk and Ihor Mryglod
Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii St., UA-79011 Lviv, Ukraine
Received 3 November 2004; revised manuscript received 4 January 2005; published 26 April 2005
A theoretical analysis of dispersion for two branches of propagating collective excitations in molten NaCl
and NaI is performed using an approach of generalized collective modes. Two molten salts with different mass
ratios were studied in order to clarify reported “fast sound” in molten NaCl F. Demmel, S. Hosokawa, M.
Lorenzen, and W.-C. Pilgrim, Phys. Rev. B 69, 012203 2004. Contributions of low- and high-frequency
branches to partial dynamical structure factors in molten salts are discussed.
DOI: 10.1103/PhysRevB.71.132202 PACS numbers: 61.20.Lc, 61.20.Ja
The interest to collective dynamics in many-component
liquids has been revived because of recent neutron-scattering
experiments in K-Cs Ref. 1 and Na-Sn Ref. 2 liquid al-
loys as well as inelastic x-ray-scattering experiments in vit-
reous silica
3
and a molten salt NaCl.
4
Thus far the theory of
collective processes in binary liquids has been far behind the
requirements of real and computer experiments. Analytical
expressions for dynamical structure factors of binary liquids
and molten salts are well known only in hydrodynamic
limit,
5,6
when the binary liquid is treated as continuum with-
out atomic structure. However, the real scattering experi-
ments and molecular-dynamics MD computer simulations
cover a window of wave numbers k, which is behind the
hydrodynamic region. That is why a generalized model of
collective dynamics in many-component liquids must be
used for analysis of experimental data. The generalized
model should take into account main dynamical processes
that contribute to the shape of dynamical structure factors
beyond the hydrodynamic region. One of the most promising
theoretical approaches is based on a concept of generalized
collective excitations GCM,
7,8
which treats the collective
dynamics beyond the hydrodynamic region as a variety of
microscopic processes between generalized hydrodynamic
excitations and so-called kinetic ones, which can exist only
beyond hydrodynamic window of wave numbers and fre-
quencies. As an example of kinetic propagating processes
one can mention heat waves
9
and optic phononlike excita-
tions in binary liquids,
10
whereas the most obvious kinetic
relaxing process not taken into account in hydrodynamics is
structural relaxation.
9
This paper was initiated by a recent report
4
on experimen-
tal study of propagating particle density fluctuations in mol-
ten NaCl. One of the conclusions was about a “fast sound”
found in this molten salt, which was interpreted as “the Na
+
subsystem moving independent on the anionic background at
high frequencies.” Following the conclusions of Ref. 4 it
seems that there does not exist a clear understanding of the
role played by light and heavy subsystems in binary ionic
melts, and the issue of spatial scales on which one can ob-
serve the dynamics of partial densities should be clarified.
The fast sound phenomenon was reported from analysis
of MD-derived partial dynamical structure factors in molten
metallic alloy Li
4
Pb,
11
for which the mass ratio of Pb and Li
atoms is about 30. The fast sound in Ref. 11 was implied by
the behavior of two almost linear dispersion laws with essen-
tially different slopes in the small-wave-number region, ob-
tained for two branches of collective excitations in the small-
wave-number region: the high-frequency branch was named
as a fast sound, whereas the low-frequency branch was sup-
posed to match hydrodynamic dispersion law. It is worth
noting that in Ref. 11 and following MD studies
12
of collec-
tive dynamics in molten Li
4
Pb, the dispersion laws of the
two branches was obtained either from the maxima positions
of current spectral functions C
k , , =Li,Pb, or Bril-
louin peak location on the shape of partial dynamical struc-
ture factors S
k , . It is necessary to mention that analysis
of the last neutron-scattering experiments
13
on Li
4
Pb implied
a nonacoustic origin of high-frequency excitations reflecting
“localized out-of-phase atomic motions.”
The goal of this study was to perform a theoretical GCM
analysis of dispersion of collective excitations in molten salts
NaCl and NaI. They essentially differ by a mass ratio of
heavy and light components R = m
h
/ m
l
: 1.54 for NaCl and
5.52 for NaI. We will show how the difference in mass ratio
is reflected in the behavior of high- and low-frequency
branches. Mode contributions to partial spectral functions in
the long-wavelength region will be discussed.
MD simulations for NaCl at 1260 K and NaI at 1080 K
were performed in the standard microcanonical ensemble on
a model systems of 1000 particles in a cubic box subject to
periodic boundary conditions. Potentials in the Tosi-Fumi
form for NaCl and NaI were taken from Ref. 14. The long-
range interaction was treated by the Ewald method, and the
short-range parts of two-body potentials were cut off at
12.66 Å for NaCl and at 14.39 Å for NaI. The smallest wave
numbers k
min
reached in the MD simulations were 0.19 Å
-1
for NaCl and 0.17 Å
-1
for NaI, respectively. The main aim of
the MD simulations was to obtain the time evolution of all
hydrodynamic and short-time extended dynamical variables,
forming the following eight-variable basis set A
8
k , t used
for our study of collective dynamics within the GCM ap-
proach:
PHYSICAL REVIEW B 71, 132202 2005
1098-0121/2005/7113/1322024/$23.00 ©2005 The American Physical Society 132202-1