Nanometer range correlations between molecular orientations in liquids of molecules
with perfect tetrahedral shape: CCl 4 , SiCl 4 , GeCl 4 , and SnCl 4
Sz. Pothoczki, L. Temleitner, P. Jóvári, S. Kohara, and L. Pusztai
Citation: The Journal of Chemical Physics 130, 064503 (2009); doi: 10.1063/1.3073051
View online: http://dx.doi.org/10.1063/1.3073051
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THE JOURNAL OF CHEMICAL PHYSICS 130, 064503 共2009兲
Nanometer range correlations between molecular orientations in liquids
of molecules with perfect tetrahedral shape: CCl4, SiCl4, GeCl4,
and SnCl4
Sz. Pothoczki,1 L. Temleitner,1 P. Jóvári,1 S. Kohara,2 and L. Pusztai1,a兲
1
Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, Budapest,
P.O. Box 49, H-1525, Hungary
2
Japan Synchrotron Radiation Research Institute (SPring-8/JASRI), 1-1-1 Kouto, Sayo-cho, Sayo-gun,
Hyogo 679-5198, Japan
共Received 30 October 2008; accepted 29 December 2008; published online 11 February 2009兲
Neutron and x-ray weighted total scattering structure factors of liquid carbon, silicon, germanium,
and tin tetrachlorides, CCl4, SiCl4, GeCl4, and SnCl4, have been interpreted by means of reverse
Monte Carlo modeling. For each material the two sets of diffraction data were modeled
simultaneously, thus providing sets of particle coordinates that were consistent with two
experimental structure factors within errors. From these particle configurations, partial radial
distribution functions, as well as correlation functions characterizing mutual orientations of
molecules as a function of distance between molecular centers were calculated. Via comparison with
reference systems, obtained by hard sphere Monte Carlo simulations, we demonstrate that
orientational correlations characterizing these liquids are much longer ranged than expected,
particularly in carbon tetrachloride. © 2009 American Institute of Physics.
关DOI: 10.1063/1.3073051兴
I. INTRODUCTION
The structure of liquid tetrachlorides 共XCl4兲, and particularly, of liquid CCl4, has been considered by a multitude of
papers over the past 3 decades. These are the simplest systems of molecules with genuine three-dimensional molecular
structure and therefore, they have been studied extensively
by neutron 关for CCl4,1 VCl4,2 GeCl4,3 SiCl4,4 SnCl4,4 and
TiCl4 共Ref. 4兲兴 and x-ray 关for CCl4,5,6 SiCl4,6 GeCl4,6 and
SnCl4 共Ref. 6兲兴 diffraction, computer simulation7,8 and integral equation theories.9 In spite of the great efforts of the 70s
and 80s, the only palpable results from this period are some
models consisting of only two molecules 共see, e.g., Refs. 1
and 10兲. Among these, the best known is the so-called Apollo
model of CCl4,1 which is a scheme in which neighboring
molecules form pairs with “corner-to-face” contacts, that is,
a chlorine atom—a “corner”—of a molecule is threefold coordinated by three chlorine atoms—forming a “face”—of the
other molecule.
The Apollo idea is so attractive that it is worthwhile to
investigate whether in these tetrachlorides, with increasing
X-Cl bond length, there is any indication of its 共enhanced兲
occurrence. Increasing the X-Cl bond length enlarges the
“hollow” formed by the three Cl atoms on a face of an XCl4
molecule, so that a corner 共i.e., a Cl atom兲 of a neighbor
molecule may be able to “dock” into the hollow more easily
than in CCl4. Earlier reverse Monte Carlo11 共RMC兲 studies
indicated that the dominance of Apollo-type clusters can be
ruled out12,13 for CCl4, SiCl4, GeCl4, SnCl4, VCl4, and TiCl4.
Without going into details, we just note that this result could
have been derived earlier, provided that proper models 共cona兲
Electronic mail: [email protected].
0021-9606/2009/130共6兲/064503/7/$25.00
taining not only two molecules兲 had been fitted to the experimental total structure factors. On the other hand, very recent
RMC studies of liquid SnI4,14 whose molecules are also of
the shape of a perfect tetrahedron, found a significant 共although still not dominant兲 fraction of Apollo pairs in that
liquid.
Once the easiest to understand, very specific, mutual orientation of neighboring molecules must be excluded, questions about orientational correlations open up again: What
are the most frequent conformations of two molecules? Are
they different from random 共i.e., from what is expected if
only the density and the molecular structure would influence
orientations兲? Do they vary with the size of the central atom
共i.e., with the increasing X-Cl bond length兲? These are the
main issues that could not be clarified in our previous study13
and that have been investigated in detail in the present work.
In addition, further new elements have been introduced during the present research: 共a兲 neutron and x-ray diffraction
data have been interpreted simultaneously, for which we
have carried out our own 共synchrotron兲 x-ray measurements
on carbon tetrachloride and tin tetrachloride 共see Sec. II兲; 共b兲
a detailed comparison with hard sphere reference systems
共similar to that described in Ref. 12兲 has been carried out
here, in order to clearly separate steric effects 共for details, see
Sec. III兲; 共c兲 a novel, assumption-free tool for characterizing
orientational correlations15 has been applied systematically
for each material, which has made unbiased comparison possible between different liquids, as well as between “real” and
reference systems.
For understanding liquid structures, the interpretation of
diffraction data is probably at least as important as collecting
data. Throughout this study, microscopic 共atomic兲 level mod-
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eling of experimental results, via the RMC technique, has
been extensively made use of for interpretation purposes.
Particle configurations obtained by RMC have been analyzed
in detail. Partial radial distribution functions 共prdfs兲 have
been determined and compared to those calculated from hard
sphere reference systems, similarly to Refs. 12 and 14. For
describing orientational correlations between neighboring
molecules, a method developed recently by Rey15 has been
utilized.
This paper is organized as follows: Sec. II describes
shortly the experimental procedures while Sec. III deals with
structural modeling aspects. Section IV provides the main
findings and finally, in Sec. V, concluding remarks are given.
II. EXPERIMENTAL DETAILS
Chemicals were obtained from Aldrich Chemical and
were all of higher purity than 99%. Neutron diffraction measurements were carried out earlier for all liquids,13 using the
PSD powder diffractometer installed at the Budapest Research Reactor.16
X-ray diffraction data for CCl4 have been taken at the
SPring-8 synchrotron radiation facility 共Japan兲, using the
single detector diffractometer setup of the BL04B2 共highenergy x-ray diffraction兲 beamline.17 X-ray diffracted intensities from liquid SnCl4 were recorded in Hasylab at DESY
共Germany兲, using the BW5 hard x-ray diffraction
instrument.18 Standard correction procedures have been carried out in both cases, as described, for instance, in Ref. 19.
For SiCl4 and GeCl4, total scattering structure factors 共tssfs兲
were taken from literature.6
III. REVERSE MONTE CARLO MODELING:
COMPUTATIONAL DETAILS
The RMC modeling method has been described in detail
elsewhere 共e.g., Refs. 11 and 20–22兲, so only a brief summary of relevant details is given here.
Total scattering structure factors applied as input data
contain both intra- and intermolecular scatterings, so the molecular form factor has not been subtracted. We have used the
flexible molecule approach, where molecules are considered
to be collections of atoms, which are held together by geometric constraints. A convenient choice for these constraints
is the “fixed neighbors constraints”21,22 共fncs兲 method, in
which a neighbor list is set up for the initial configuration
and each individual atom is given specific bonding constraints to its individual neighbors.
Starting configurations were randomly oriented collections of molecules, with the appropriate densities and molecular geometry, in cubic boxes. After the initial placement
of particles, long hard sphere 共HS兲 Monte Carlo simulations
were run, in order to ensure that RMC calculations would be
started from randomly oriented molecules with no overlap
between them. These systems were later used as reference
system, too; in this way differences between features resulting from HS system and RMC simulations signature the influence of diffraction data.
In the present study, four 共sets of兲 calculations have been
performed for XCl4 共X = C , Si, Ge, Sn兲 liquids: HS Monte
TABLE I. Basic characteristics of the materials and models considered.
CCl4
Atomic density 共Å 兲
Box length 共Å兲
fnc 共X-Cl兲 共Å兲
fnc 共Cl-Cl兲 共Å兲
rc 共X-X兲 共Å兲
rc 共X-Cl兲 共Å兲
rc 共Cl–Cl兲 共Å兲
−3
SiCl4
GeCl4
SnCl4
0.0319
0.0263
0.0264
0.02575
26.958 546 28.750 237 28.713 890 28.953 489
1.71–1.83 1.96–2.08 2.05–2.17 2.22–2.34
2.77–3.01
3.16–3.4
3.33–3.57 3.60–3.84
3.3
4.0
4.0
4.0
1.69
2.7
2.7
2.7
2.7
2.7
2.7
2.7
Carlo reference runs 共denoted throughout the rest of the paper as “HS”兲, modeling the neutron data only 共“N”兲, modeling the x-ray data only 共“X”兲 and modeling both neutron and
x-ray diffraction data simultaneously 共“NX”兲. In each calculation, 1000 molecules 共5000 atoms兲 were put in a cubic box.
Atomic densities, box lengths, fnc limits, and intermolecular
cutoff distances are given by Table I. The largest displacement in each direction was 0.1 Å. All calculations were continued for several million accepted moves, where the ratio of
accepted/rejected moves varied between 1:3 and 1:10; thus,
typically several thousand accepted moves per atom could be
completed.
Orientational correlation functions have been calculated
according to the method suggested by Rey.15 In brief, given a
pair of tetrahedral molecules, we constructed two parallel
planes to contain the centers of these molecules. Molecular
pairs are classified by the number of chlorine atoms, belonging to one and the other of the two molecules, between these
planes; that is, six simple orientational groups 共“Rey
groups”兲 arise. These groups, one by one, represent the
corner-to-corner 共1:1兲, corner-to-edge 共1:2兲, edge-to-edge
共2:2兲, corner-to-face 共1:3兲 共this is the so-called Apollo orientation兲, edge-to-face 共2:3兲, and face-to-face 共3:3兲 orientations. The normalized populations of these groups, as a function of distance, can provide a very detailed picture of the
orientational correlations found in systems of tetrahedral
molecules. As a general rule of thumb, the sharper the features 共maxima/minima兲 of these distance dependent functions are the better defined is the structure. Also, similarly to
the cases of tssf and prdfs, larger deviations from the reference system indicate higher information content 共and thus,
greater importance of the presence兲 of the experimental data.
We would also like to point out here that in our earlier
papers,12,13 there were only two kinds of orientations distinguished, the Apollo and the “non-Apollo” types, which were
then called 共perhaps somewhat misleadingly兲 corner-to-face
and corner-to-corner, respectively. Here, as it may also be
derived from the above classification, the old corner-tocorner 共i.e., non-Apollo兲 orientations are further sectioned;
from this point on, we use the new nomenclature only, as
suggested in Ref. 15.
IV. RESULTS AND DISCUSSION
Experimental, RMC and hard sphere Monte Carlo
共HSMC兲 total structure factors for XCl4 liquids are shown in
Fig. 1. The agreement between experimental data and RMC
structures is nearly perfect for each calculation. The “neutron
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Nanometer range order in molecular liquids
(a)
(b)
FIG. 1. Total structure factors for XCl4 liquids: 共a兲 CCl4; 共b兲 SiCl4; 共c兲 GeCl4; 共d兲 SnCl4. Symbols: experimental data; dotted lines: RMC; solid lines: HSMC
reference systems.
weighted” total structure factor of the HS system and the
“x-ray weighted” total structure factor of the HS system
show good agreement with the RMC models 共and with experiments兲 above about 6 Å−1. This agreement reflects the
widely accepted view that the high Q region of the structure
factor is dominated by the molecular structure and, in turn,
the molecular structure is meaningfully defined by the aforementioned fnc constructions. On the other hand, differences
between RMC and HSMC models are apparent at lower Q
values. It may be noticed that these deviations are the best
visible in the case of CCl4, forasmuch not only the position
of the second peak shifts, as it does for the other XCl4 liquids, but also, the second and third peaks of the RMC model/
experiment merge in the HSMC model. This suggests that
the intermolecular behavior of CCl4 differs from other XCl4
liquids. It would be an instructive test of classical pairwise
interaction models whether they are able to capture such a
difference, at least qualitatively.
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FIG. 2. 共X-X兲 partial radial distribution functions for XCl4 liquids: 共a兲 CCl4;
共b兲 SiCl4; 共c兲 GeCl4; 共d兲 SnCl4, resulting from hard sphere 共solid line兲,
neutron-only 共dashed line兲, x-ray-only 共dotted line兲, and neutron + x-ray
共dash-dotted line兲 calculations.
It is interesting to notice that the characteristics of the
second maximum in case of the two 共neutron and x-ray兲
experimental structure factors are becoming more dissimilar
with increasing size of the central atom. The intensity of this
peak of the x-ray diffraction results decreases so much that
for SnCl4 it transforms into a small shoulder on the low-Q
side of the third maximum. The fact that the weighting factors of the partial pair correlations are changing as the size
共i.e., the number of electrons兲 of the central atom can account only partly for this variation.
prdfs calculated directly from particle coordinates are
shown in Figs. 2–4. Surprisingly, prdfs corresponding to X,
N, and NX models hardly show any differences. This similarity supports the conjecture formulated in Ref. 13 that for
XCl4 共or more generally, XY4兲 liquids if RMC modeling is
performed with only one single experimental data set 共from
either neutron or x-ray diffraction兲 then the loss of information 共at least at the two-particle level兲 is negligible. In other
words, for liquids containing perfect tetrahedral molecules
one diffraction measurement is sufficient for describing the
microscopic structure in detail, provided that proper modeling techniques are applied for interpreting the data. If possible, the diffraction data to be chosen should be dominated
by ligand-ligand partial correlations, which condition is practically always fulfilled due to the fact that the number of
ligands is four times higher than that of the centers. It must
be stressed that, in general, such an approach is not applicable and more data 共in the form of combining neutron and
x-ray diffraction, possibly with isotopic substitution in the
J. Chem. Phys. 130, 064503 共2009兲
FIG. 3. X-Cl partial radial distribution functions for XCl4 liquids: 共a兲 CCl4;
共b兲 SiCl4; 共c兲 GeCl4; 共d兲 SnCl4, resulting from hard sphere 共solid line兲,
neutron-only 共dashed line兲, x-ray-only 共dotted line兲 and neutron + x-ray
共dash-dotted line兲 calculations.
former case, and/or widening the experimental Q-range兲 certainly mean better defined structure. It is exactly because of
this general rule that the case of molecular liquids containing
tetrahedral XY4 molecules should be mentioned as an exception to the rule—as it could be proven by the present work.
The X-X prdfs are estimated surprisingly well by the HS
models for each material, particularly for the “intermediate”
SiCl4 and GeCl4 liquids where deviations are hardly detectable. For CCl4, the magnitude of the first maximum is visibly, whereas the position of the peak is very slightly, underestimated by the HS reference system. For SnCl4 the HS
reference noticeably overestimates the distance between molecular centers. It seems, therefore, that intermolecular forces
draw SnCl4 molecules closer to each other than it would
follow from simple geometric considerations. It is interesting
that the X-X prdfs oscillate beyond the fourth coordination
sphere, especially in the case of CCl4, and that this behavior
is also followed by the HS reference system; as such, this
must also be taken as the consequence of pure geometric
effects. 共Note that such observations, like similar ones in the
forthcoming discussion, could not be made in our earlier
work,13 for the lack of suitable reference systems.兲
On the other hand, significant deviations can be observed between the HS and NX 共HS and X, HS, and N兲
systems concerning the X-Cl and Cl–Cl prdfs. The intramolecular and the intermolecular regions are perfectly separated
in case of the X-Cl prdfs for every XCl4 liquid. The intramolecular parts are indistinguishable for the HS reference and
the NX共/N/X兲 models, which confirm the choice of fnc limits
共see Sec. II and Table I兲. The deviations appear solely in the
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J. Chem. Phys. 130, 064503 共2009兲
FIG. 4. Cl–Cl partial radial distribution functions for XCl4 liquids: 共a兲 CCl4;
共b兲 SiCl4; 共c兲 GeCl4; 共d兲 SnCl4, resulting from hard sphere 共solid line兲,
neutron-only 共dashed line兲, x-ray-only 共dotted line兲 and neutron + x-ray
共dash-dotted line兲 calculations.
intermolecular parts and concern only molecules that are in
the immediate neighborhood: the double peak of the X-Cl
prdfs appearing invariably between 3 and 9 Å for each liquid
originates to chlorine atoms of the same molecule. As a
qualitative measure, the more distinct the two peaks are the
better defined the average orientation of the molecular neighbor is. Accordingly, the strongest orientational correlations
can be expected for carbon tetrachloride whereas the weakest
ones will characterize liquid germanium tetrachloride. This
latter liquid seems to resemble the most to the corresponding
HS reference system. It is also worth noting that small oscillations extend to about 15 Å, especially for CCl4; these oscillations are synchronized with the ones of the X-X prdfs
and show that center-center correlations bring about ligandligand ordering, as well. Finally, we would like to draw the
attention to the fact that the X-Cl prdfs of the different liquids are qualitatively similar to each other, as well as to the
corresponding reference systems: variations in terms of peak
positions can be ascribed purely to size differences.
As it was pointed out earlier,12 the most visible differences between HS reference and NX共/N/X兲 model共s兲 can be
found in case of the Cl–Cl prdf. HS reference systems cannot
even hint even the presence 共not to mention shape and amplitude兲 of the first intermolecular maximum and therefore,
HS predictions concerning higher maxima positions also fail.
This difference cannot be explained by anything else but by
the preferential ordering of neighboring molecules which ordering, in turn, induces longer ranged Cl–Cl pair correlations. It is instructive to notice that intermolecular Cl–Cl pair
FIG. 5. Orientational correlation functions for liquid CCl4 and SiCl4 as
calculated after Ref. 15. Left panels: HSMC reference system; right panels:
RMC. Solid line with crosses: 1:1; solid line with open circles: 1:2; solid
line with solid squares: 2:3.
correlations look remarkably similar for all liquids considered here. What is changing is the intramolecular Cl–Cl distance and as a consequence, while intra- and first intermolecular distances are nearly entirely distinct for carbon
tetrachloride, they nearly entirely overlap in tin tetrachloride.
Orientational correlation functions have been obtained
via the aforementioned way;15 the functions are shown in
Figs. 5–8. Such qualification 共and quantification兲 could not
be performed in our earlier work,13 for the lack of suitable
tools of analyses.15 Differences between HSMC reference
systems and RMC models are apparent for XCl4 liquids studied here: it may be stated in general that for each liquid 共and
especially in the case of CCl4兲 the RMC model exhibits
sharper and longer range oscillations. These oscillations are
the most visible in the cases of 1:2 共corner-to-edge兲 and 2:3
共edge-to-face兲 orientations, which functions, moreover, alternate for each liquid. This alternating nature seems to be an
inherent feature of XCl4 liquids that is present 共although to a
much smaller extent兲 in the HSMC reference systems, as
well as in the molecular dynamics simulation of carbon tetrachloride by Rey.15 The sharpness and range of oscillations
seem to vary with the size of the central atom, i.e., with the
X-Cl bond length: it is carbon tetrachloride where the amplitude of oscillations is the largest whereas 1:2 and 2:3 curves
for tin tetrachloride are the most smeared out. A separate
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FIG. 6. Orientational correlation functions for liquid CCl4 and SiCl4 as
calculated after Ref. 15. Left panels: HSMC reference system; right panels:
RMC. Solid line with open circles: 2:2; solid line: 1:3; solid line with
crosses: 3:3. Note that the y-axis scale is different in panels 共c兲 and 共d兲.
study, aiming at the full understanding of this feature via
visualization of the RMC particle configurations, is being
designed.
The most preferable orientation is the 2:2 共edge-to-edge兲
one. As it can be derived from the asymptotic value and from
the behavior of the corresponding reference functions, this is
the type of mutual arrangement that is most likely to occur if
molecules of tetrahedral shape are placed randomly at the
given density. Differences between HS reference and real
共RMC兲 systems are visible but they remain far below the
level experienced for 1:2 and 2:3 orientations. It is interesting to note that in terms of the 2:2 orientations, it is GeCl4
共and SiCl4兲 that exhibit共s兲 the longest ranged oscillations.
The 共relative and absolute兲 occurrences of 1:1, 1:3,
and—apart from the shortest center-center distances—3:3
orientations are much less than those of the ones discussed
above. On the other hand, as far as their occurrences in relation to the corresponding asymptotic values are concerned,
a few interesting remarks can be made. First of all, the ratio
of 3:3 pairs at the shortest 共in other words, “‘contact”兲 X-X
共i.e., center-center兲 distances becomes very high in CCl4,
SiCl4, and GeCl4; SnCl4 appears to be different in this sense.
This may be related to the fact that SnCl4 molecules are a
little closer to each other than it would follow from simple
geometric considerations 共see above discussion of X-X
prdfs兲. Second, the weight of these “rare” orientations is significantly higher up to about 10 Å than it would follow from
FIG. 7. Orientational correlation functions for liquid GeCl4 and SnCl4 as
calculated after Ref. 15. Left panels: HSMC reference system; right panels:
RMC. Solid line with crosses: 1:1; solid line with open circles: 1:2; solid
line with solid squares: 2:3.
either the HS reference or from the asymptotic values. This
indicates considerable ordering that is brought about by 共and
therefore, reflected in兲 the experimental data. Finally, concerning the 1:3 共Apollo兲 orientations, their ratio only touches
10% and only for a very narrow distance range in each liquid
considered here; that is, in accordance with our previous
studies,12,13 the dominant nature of Apollo pairs is must be
excluded on the basis of the “Rey-group” analysis, too. We
note, however, that in another XY4 liquid, SnI4, the ratio of
Apollo pairs does reach 20%,14 which fact shows that this
easiest-to-understand orientation also may play a significant
role—in other materials.
V. CONCLUSIONS
Concerning details of the microscopic structure of
XCl4共X = C , Si, Ge, Sn兲 molecular liquids, the following
statements can be made:
共a兲
共b兲
共c兲
Intermolecular Cl–Cl pair correlations look remarkably
similar for all liquids considered here.
The strongest orientational correlations were found for
carbon tetrachloride whereas the weakest ones will
characterize liquid germanium tetrachloride.
The most preferable orientation is the 2:2 共edge-toedge兲 one; this is the type of mutual arrangement that is
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共ii兲
共iii兲
Comparison with hard sphere reference systems
shows, on the other hand, that it is impossible to understand even the most basic structural properties on
the sole basis of excluded volume effects: the role of
diffraction data proved to be essential for each liquid
investigated here.
Perhaps the most unexpected structural finding is the
presence of 共for a simple molecular liquid, unexpectedly兲 long, nanometer range orientational correlations,
particularly in carbon tetrachloride. Based on the fact
that these correlations appear already in the simplest
of molecular liquids it is believed that in more sophisticated systems even greater surprises would show up.
ACKNOWLEDGMENTS
Sz.P., L.P., L.T., and P.J. are grateful for the financial
help of the Hungarian Basic Research Fund 共OTKA兲, under
Grant Nos. T048580 and IN64279.
P. A. Egelstaff, D. I. Page, and J. G. Powles, Mol. Phys. 20, 881 共1971兲.
I. P. Gibson and J. C. Dore, Mol. Phys. 37, 1281 共1979兲.
3
J. H. Clarke, J. C. Dore, I. P. Gibson, J. R. Granada, and G. W. Stanton,
Faraday Discuss. Chem. Soc. 66, 277 共1978兲.
4
J. B. van Tricht, J. Chem. Phys. 66, 85 共1977兲.
5
A. H. Narten, M. H. Danford, and H. A. Levy, J. Chem. Phys. 46, 4875
共1967兲.
6
K. M. Jöllenbeck and J. U. Weidner, Ber. Bunsenges. Phys. Chem. 91, 11
共1987兲; 91, 17 共1987兲.
7
I. R. McDonald, D. G. Bounds, and M. L. Klein, Mol. Phys. 45, 521
共1982兲.
8
J. C. Soetens, J. G. Jansen, and C. Millot, Mol. Phys. 96, 1003 共1999兲.
9
L. J. Lowden and D. Chandler, J. Chem. Phys. 61, 5228 共1974兲.
10
M. Misawa, J. Chem. Phys. 91, 5648 共1989兲.
11
R. L. McGreevy and L. Pusztai, Mol. Simul. 1, 359 共1988兲.
12
L. Pusztai and R. L. McGreevy, Mol. Phys. 90, 533 共1997兲.
13
P. Jóvári, Gy. Mészáros, L. Pusztai, and E. Sváb, J. Chem. Phys. 114,
8082 共2001兲.
14
L. Pusztai, Sz. Pothoczki, and S. Kohara, J. Chem. Phys. 129, 064509
共2008兲.
15
R. Rey, J. Chem. Phys. 126, 164506 共2007兲.
16
E. Sváb, Gy. Mészáros, and F. Deák, Mater. Sci. Forum 228–231, 247
共1996兲.
17
M. Isshiki, Y. Ohishi, S. Goto, K. Takeshita, and T. Ishikawa, Nucl.
Instrum. Methods Phys. Res. A 467–468, 663 共2001兲; S. Kohara, M.
Itou, K. Suzuya, Y. Inamura, Y. Sakurai, Y. Ohishi, and M. Takata, J.
Phys.: Condens. Matter 19, 506101 共2007兲.
18
R. Bouchard, D. Hupfeld, T. Lippmann, J. Neuefeind, H.-B. Neuamann,
H. F. Poulsen, U. Rütt, T. Schmidt, J. M. Schneider, J. Süssenbach, and
M. von Zimmermann, J. Synchrotron Radiat. 5, 90 共1998兲; see also at
http://www-hasylab.desy.de/facility/experimental_stations/BW5/
BW5.htm.
19
S. Kohara, K. Suzuya, Y. Kashihara, N. Matsumoto, N. Umesaki, and I.
Sakai, Nucl. Instrum. Methods Phys. Res. A 467–468, 1030 共2001兲.
20
R. L. McGreevy, J. Phys.: Condens. Matter 13, R877 共2001兲.
21
G. Evrard and L. Pusztai, J. Phys.: Condens. Matter 17, S1 共2005兲.
22
O. Gereben, P. Jóvári, L. Temleitner, and L. Pusztai, J. Optoelectron. Adv.
Mater. 9, 3021 共2007兲.
1
2
FIG. 8. Orientational correlation functions for liquid GeCl4 and SnCl4 as
calculated after Ref. 15. Left panels: HSMC reference system; right panels:
RMC. Solid line with open circles: 2:2; solid line: 1:3; solid line with
crosses: 3:3. Note that the y-axis scale is different in panels 共c兲 and 共d兲.
共d兲
most likely to occur if molecules of tetrahedral shape
are placed randomly at the given density.
The alternating nature of 1:2 and 2:3 correlation functions seems to be an inherent feature of XCl4 liquids
that is present 共although to a much smaller extent兲 in
the HSMC reference systems, as well as in the molecular dynamics simulation of carbon tetrachloride.
In addition, a few more general findings have become
apparent:
共i兲
It is now explicitly shown that for these 共but only for
these!兲 liquids, containing molecules with perfect tetrahedral symmetry, one single diffraction measurement 共either neutron or x ray兲 is sufficient for detailed
structural analyses: not even for SnCl4, where the
contrast between neutron and x-ray diffraction is
large, the second set of experimental data provided
any significant improvement.
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