Structure of the equiatomic liquid alloys K-Sb, K-Bi, and Rb-Bi over a wide temperature range

Article abstract of DOI:10.1063/1.481328

We report on neutron diffraction measurements on the equiatomic liquid alloys K-Sb, K-Bi, and Rb-Bi up to temperatures of T = 1800K. The prepeaks in the resulting total structure factors S(Q) are indicative of intermediate range ordering. The shift of the prepeak positions towards smaller momentum transfer Q with increasing temperature suggests increasing distances between the structural polyanionic units. From reverse Monte Carlo (RMC) simulations the prepeak is assigned essentially to correlations between the polyvalent metal atoms (Sb or Bi), remaining even up to the highest temperatures measured. The simulations lead to models exhibiting Sb (or Bi) atoms clustered in short chains and dumbbells rather than in higher coordinated clusters or networklike structures.

Full text of DOI:10.1063/1.481328

Structure of the equiatomic liquid alloys K–Sb, K–Bi, and Rb–Bi over a wide
temperature range
K. Hochgesand and R. Winter
Citation: The Journal of Chemical Physics 112, 7551 (2000); doi: 10.1063/1.481328
View online: http://dx.doi.org/10.1063/1.481328
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 112, NUMBER 17
1 MAY 2000
Structure of the equiatomic liquid alloys K–Sb, K–Bi, and Rb–Bi
over a wide temperature range
K. Hochgesand and R. Winter
Department of Chemistry, Physical Chemistry I, University of Dortmund, D-44227 Dortmund, Germany
͑Received 5 November 1999; accepted 10 February 2000͒
We report on neutron diffraction measurements on the equiatomic liquid alloys K–Sb, K–Bi, and
Rb–Bi up to temperatures of Tϭ1800 K. The prepeaks in the resulting total structure factors S(Q)
are indicative of intermediate range ordering. The shift of the prepeak positions towards smaller
momentum transfer Q with increasing temperature suggests increasing distances between the
structural polyanionic units. From reverse Monte Carlo ͑RMC͒ simulations the prepeak is assigned
essentially to correlations between the polyvalent metal atoms ͑Sb or Bi͒, remaining even up to the
highest temperatures measured. The simulations lead to models exhibiting Sb ͑or Bi͒ atoms
clustered in short chains and dumbbells rather than in higher coordinated clusters or networklike
structures. © 2000 American Institute of Physics. ͓S0021-9606͑00͒51717-6͔
I. INTRODUCTION
but no changes in the physical properties appear at the MBi2
composition of the liquid phase. Instead, the resistivity peaks
at about 40 at. % Bi ͑pronounced for Rb and Cs, weak for K
and not visible for Li and Na͒, a composition where no con-
gruently melting solid compound seems to exist.6,7 More-
over, measurements of the Darken stability function of liquid
K–Bi8 and Rb–Bi9 indicate a compound at the equiatomic
composition, which is inconsistent with the results from re-
sistivity measurements.10
Due to these uncertainties we considered it worth while
to perform neutron scattering experiments on the liquid al-
loys K–Bi and Rb–Bi to learn what structural features make
up the peculiarities of the liquid. A further aim was to inves-
tigate structural changes of liquid K–Sb, K–Bi, and Rb–Bi
over a large temperature range to explore the stability of
polyanionic structural features in these systems.
Alloys of alkali metals M with group 13, 14, and 15
polyvalent metals PM are known to form compounds at dif-
ferent stoichiometric compositions in their solid state. Due to
the large difference in electronegativity, an electron is trans-
ferred from the alkali metal to the polyvalent metal resulting
in saltlike bonding and structure. On the one hand, if the
composition is such that the number of electrons transferred
is insufficient to complete the octet shell of the electronega-
tive element, a saturated chemical bond can be formed only
if valence electrons are shared among the electronegative
atoms. This results in the formation of polyanionic clusters
stabilized by strong covalent bonds which are immersed in a
matrix of the electropositive species. In many cases the struc-
ture of these polyanions can be predicted according to the
Zintl rule. On the other hand, so-called octet compounds are
formed at compositions where each of the polyvalent metal
atoms receives a sufficient number of electrons from the al-
kali metal atoms to obtain the desired octet shell. Due to
sterical restrictions often only one of these compounds is
found, with the light ͑and correspondingly small͒ alkali met-
als driving the alloys towards formation of the octet com-
pound and the heavy ones towards the formation of Zintl
compounds.
For most of the systems exhibiting extrema in the physi-
cal properties at one or both of these compositions in the
solid phase, these extrema are found in the liquid phase as
well.1 Neutron diffraction studies validate the conclusion that
polyanions survive the melting process.2
The phase diagram of KSb exhibits maxima at the equi-
atomic and at the K3Sb composition, and in the liquid phase
these compositions are characterized by maxima in the
Darken excess stability function.3,4
In contrast, the systems with heavy alkali metals and
bismuth exhibit congruently melting compounds at the com-
positions M3Bi and MBi2 and not at the MBi composition.
A maximum in the electrical resistivity is found for liquid
M3Bi ͑pronounced for Li, Na, and K, weak for Rb and Cs͒,
II. EXPERIMENT
Antimony or bismuth ͑at least 99.999%͒ were added to
molten potassium or rubidium ͑at least 99.95%͒ in small
amounts because of exothermic reactions. The mixtures were
heated to 950 K in an aluminum oxide crucible, and the
resulting brittle alloys were ground and filled into a sample
cell. Due to reactions with the air and moisture of both prod-
ucts and educts, all steps were carried out inside an argon-
filled glove box ͑Ͻ2 ppm O2, Ͻ2 ppm H2O͒.
Details of the experimental setup and data treatment are
published elsewhere.11,12 Briefly, the neutron diffraction ex-
periments were carried out on the SLAD instrument of the
Studsvik Neutron Research Laboratory, Sweden (␭
ϭ1.1 Å). The
Q
range covered was 0.36 ÅϪ1ϽQ
Ͻ10.47 ÅϪ1. The sample was contained in a specially de-
signed molybdenum cell within a custom made high-
temperature high-pressure autoclave. The differential scatter-
ing cross sections (d␴/d⍀) have been determined up to
temperatures of 1800 K, and the structure factors have been
obtained according to
5
0021-9606/2000/112(17)/7551/6/$17.00
7551
© 2000 American Institute of Physics
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7552
J. Chem. Phys., Vol. 112, No. 17, 1 May 2000
K. Hochgesand and R. Winter
FIG. 1. Static structure factor S(Q) of liquid K–Sb. Dots are the experi-
mental data points, the line is the equally spaced spline used for the RMC
simulations. The column graph represents a calculated neutron diffraction
pattern of the solid phase ͓LiAs type with lattice constants aϭ7.18 Å, b
ϭ6.97 Å, cϭ13.40 Å, ␤ϭ115.1° ͑Ref. 13͔͒.
FIG. 3. Static structure factor S(Q) of liquid Rb–Bi. Dots are the experi-
mental data points, the line is the equally spaced spline used for the RMC
simulations. The column graph represents a calculated neutron diffraction
pattern of the solid compound RbBi2 ͓MgCu2 type with lattice constant a
ϭ9.50 Å ͑Ref. 17͔͒.
d␴
␴
␴
total
coherent
ϭ
S Q͒Ϫ1͒ϩ
͑ ͑
,
͑1͒
ͩ ͪ
partial preservation of structural characteristics during the
melting process. Compared to the structure factor of liquid
Cs–Sb,14 the first peak is clearly more pronounced, whereas
the second peak around 2 ÅϪ1 is of comparable height ͑1.61
for K–Sb at 650 K, 1.67 for Cs–Sb at 600 K͒. One could
conclude from the different scattering cross sections of the
alkali metals—assuming a similar structure of both alloys—
that the first peak is essentially due to Sb correlations, as the
weight of the partial structure factor SSbSb(Q) is larger in the
case of K–Sb. Even for the lowest temperature measured we
do not find distinct oscillations beyond the second peak of
S(Q). Please note that the sample container broke during the
1773 K measurement. Because of the resulting poor statistics
this S(Q) was not used as input for RMC simulations.
The structure factor of liquid K–Bi ͑Fig. 2͒ at 850 K
exhibits a prepeak at about Qϭ1.17 ÅϪ1 and a main peak at
about Qϭ2.05 ÅϪ1. According to the rough approximation
Qdϭ7.7, a characteristic distance dϭ6.6 Å can be estimated
from the position of the prepeak. Again we tend to assign it
to the appearence of Bi polyanions. The phase diagram of
KBi15 at the equiatomic composition exhibits an eutectic
mixture of the compounds KBi2 and K4Bi5. The stoichiom-
etry of the latter is still not confirmed, and the crystal struc-
ture is unknown. The column graph in Fig. 2 ͑bottom͒ rep-
resents the neutron diffraction pattern of solid KBi2. The
position of the prepeak corresponds approximately to the
͑111͒ diffraction peak, but there are no diffraction peaks cor-
responding to the main peak. However, x-ray diffraction pat-
terns of the potassium-richer solid phases show a number of
diffraction peaks in this region,16 so solving the crystal struc-
tures of these phases would be desireable to calculate the
neutron diffraction patterns.
d⍀
4␲
4␲
are the coherent and total scattering
where ␴coherent ,␴
total
cross sections.
III. RESULTS AND DISCUSSION
Figures 1–3 show the structure factors of liquid K–Sb,
K–Bi, and Rb–Bi over a wide temperature range up to 1800
K. The lowest temperatures were chosen little above the cor-
responding melting points ͑see Table I͒. For K–Sb ͑Fig. 1͒
we find a pronounced first sharp diffraction peak ͑so-called
‘‘prepeak’’͒ at Qϭ1.06 ÅϪ1 which is indicative of chemical
short-range order, and a main peak at Qϭ2.1 ÅϪ1. The po-
sition of the prepeak corresponds well to an ensemble of
intense diffraction peaks of the solid phase,13 suggesting the
The structure factor S(Q) of Rb–Bi ͑Fig. 3͒ at 673 K
displays several sharp peaks, indicating an incomplete melt-
ing of the sample at this temperature. The S(Q) did not
change with time, suggesting the coexistence of a solid and a
liquid phase. This is in reasonable agreement with the pub-
FIG. 2. Static structure factor S(Q) of liquid K–Bi. Dots are the experi-
mental data points, the line is the equally spaced spline used for the RMC
simulations. The column graph represents a calculated neutron diffraction
pattern of the solid compound KBi2 ͓MgCu2 type with lattice constant a
ϭ9.60 Å ͑Ref. 15͔͒.
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J. Chem. Phys., Vol. 112, No. 17, 1 May 2000
Structure of liquid alloys K–Sb, K–Bi, and Rb–Bi
7553
TABLE I. Liquid state number densities 1␳/nmϪ3 as determined by the RMC simulations of the scattering data
at the corresponding experimental conditions ͑temperature T/K, pressure p/bar͒. In addition, the melting tem-
peratures Tm are given.
K–Sb
K–Bi
Rb–Bi
1
1
1
T
p
␳
T
p
␳
T
p
␳
673
850
1073
1273
1573
1800
2
3
8
20
44
76
21.0
19.5
18.5
17.0
14.0
11.5
673
850
1073
1273
1573
1800
4
4
13
26
53
96
-
923
1073
1273
1573
1773
14
20
22
38
50
19.5
19.0
18.0
16.0
14.5
19.5
18.5
17.5
15.5
13.0
Tmϭ878 K
Tmϭ628 K
Tmϭ649 K
lished phase diagram, showing that the melting point of the
equiatomic composition is not far below the temperature
here. Note that the components in the solid at this composi-
tion are still uncertain.17 The compounds under consideration
are RbBi2, RbBi, and Rb4Bi5. The existence of RbBi ͑pro-
posed from EMF measurements9͒ is yet unconfirmed, as is
the stoichiometry of Rb4Bi5. The structure of RbBi2 is
solved, and the column graph in Fig. 3 shows the calculated
neutron diffraction pattern. The peak in the experimental
S(Q) at about 2.2 ÅϪ1 and the shoulder at about 1.85 ÅϪ1
might correspond to those of the diffraction pattern, but not
the peak at 2.0 ÅϪ1. The dashed line indicates the position of
an experimental x-ray diffraction peak of the equiatomic
solid, thus indicating the presence of a more rubidium-rich
compound.
smaller Q values with increasing temperature can be ob-
served for both alloys, indicating an increase in average dis-
tances between the polyanionic clusters. Furthermore, the
heights of both prepeak and main peak decrease, indicating a
gradual loss of structural order at high temperatures. Al-
though less pronounced, the same temperature dependence
of S(Q) is observed for liquid K–Sb.
From S(Q) one obtains the total pair correlation func-
tion g(r) by Fourier transformation:
1
sin Qr͒
͑
g r͒ϭ1ϩ
͑
Q2 S Q͒Ϫ1
͓ ͑
dQ.
͑2͒
͔
͵
2 1
2␲
␳
Qr
20
To avoid truncation problems reverse methods ͑MCGR͒
have been applied but deviations in our case are small be-
tween direct and reverse methods of calculating g(r). For
multicomponent systems the total structure factor is a linear
combination of the pairwise contributions from different
types of atoms, i.e., the partial structure factors Sij(Q):
At 850 K a prepeak at about Qϭ1.08 ÅϪ1 and a main
peak at about Qϭ2.05 ÅϪ1 are conspicuous, the prepeak
being much less pronounced than that for liquid K–Bi. From
the position of the prepeak a characteristic real-space dis-
tance of dϭ7.1 Å can be calculated. It can be concluded that
polyanions appear in liquid Rb–Bi as well and they are sepa-
rated farther from each other due to the increasing size of the
alkali metal compared to K–Bi. They are separated even
more when going to Cs–Bi,18 where dϭ7.3 Å was deter-
mined. Another hint of the presence of polyanions is the
increase in the height of the prepeak in the order Rb–Bi,
Cs–Bi, and K–Bi: The weight of the partial Bi–Bi structure
factor SBiBi(Q) to the total S(Q) increases with decreasing
scattering cross section of the alkali metals Rb–Cs–K. Thus,
if the prepeak can be assigned to Bi–Bi correlations mainly,
its pronounciation in S(Q) should follow the observed order.
Furthermore, a systematic trend towards larger Q values
in the prepeak position ͑Table II͒ is evident for the alloys of
alkali metals with polyvalent metals, when going to the right
of the periodic table. That the Bi alloys are subject to this
trend, again points towards the occurence of polyanions in
the liquid Bi alloys.
S Q͒ϭ
͑
w S Q͒.
͑3͒
͑
͚
ij ij
ij
In the same way the total pair correlation function can be
expressed as a combination of the partial pair correlation
functions gij(r):
g r͒ϭ
͑
w g r͒.
͑4͒
͑
͚
ij ij
ij
The weighting factors wij arise from the corresponding neu-
tron coherent scattering lengths bij and concentrations ͑mole
fractions͒ xij ͑see Table III͒:
2
w ϭb b x x / x b ϩx b
͒
j j
.
͑5͒
͑
ij
i
j
i
j
i
i
TABLE II. Position of the prepeak of S(Q) for the equiatomic liquid alloys
at temperatures close to the melting point.
Alloy
Peak positions
References
18 and 19
18
18
18 and 2
18
This work
This work
Cs–Tl
K–Tl
Cs–Pb
K–Pb
Cs–Bi
0.74/0.72 ÅϪ1
0.80 ÅϪ1
We find that the structure factor of liquid K–Sb changes
remarkably little with temperature, but the temperature range
accessible to investigation with our equipment was limited to
an interval of 650 K. For liquid K–Bi and Rb–Bi, we were
able to measure S(Q) over a much larger temperature inter-
val of 1127 K, enabling us to investigate systematic tempera-
ture effects. A clear shift of the prepeak maximum towards
0.92 ÅϪ1
0.96 ÅϪ1
1.06 ÅϪ1
K–Bi/Rb–Bi
K–Sb
1.17/1.08 ÅϪ1
1.06 ÅϪ1
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7554
J. Chem. Phys., Vol. 112, No. 17, 1 May 2000
K. Hochgesand and R. Winter
TABLE III. Neutron coherent scattering lengths b of the components ͑Ref.
21͒ and weighting factors wij of the partial functions for the different alloys.
K–Sb
K–Bi
Rb–Bi
b͑Bi͒ϭ8.53 fm
b͑Sb͒ϭ5.57 fm
b͑K͒ϭ3.67 fm
b͑Rb͒ϭ7.09 fm
0.158
0.479
0.363
0.090
0.421
0.489
0.206
0.496
0.298
wMM
2•wMPM
wPMPM
The covalent intracluster Sb–Sb or Bi–Bi distances
cause a sharp first peak of g(r) for the alloys of Sb or Bi
with Cs.14,18 When trying to analyze g(r) of K–Sb, K–Bi,
and Rb–Bi11,22 in terms of their different pair contributions
we face the problem that an assignment of peaks to particular
pair contributions is not possible due to the small size of the
alkali atoms. The first peak is probably composed of contri-
butions from M–M–, M–Bi–, and Bi–Bi–correlations.
Compared to K–Bi, for Rb–Bi a shift of the first peak to-
wards larger r values is obvious. This might be partly due to
increased distances of the first coordination sphere, but the
effect is rather large considering the similar densities of both
alloys. More important seems to be the increased scattering
power of Rb compared to K which causes an increasing
weight of the M–M–correlations. These correlations prob-
ably make up the right shoulder of the first peak of g(r).
We decided to perform RMC simulations20 of the data to
derive the various contributions to the total S(Q)’s and
g(r)’s, to assess what kind of structural features are in agree-
ment with the scattering data, and to refine the so far un-
known densities of liquid K–Bi and Rb–Bi at the thermody-
namic conditions chosen ͑Table I͒. The cutoff radius of the
different atomic species has to be considered carefully, as it
depends on the degree of charge transfer as well as on the
kind of bonding present in the given alloy. Tegze and
Hafner23 showed in their ab initio molecular dynamics ͑MD͒
simulations that a transfer of valence electrons from M to
PM orbitals occurs, but with still a high probability of local-
ization close to the M atom. This leads us to the assumption,
that the radius for the alkali metals is far greater than the
ionic radius. However, to avoid an unjustified exclusion of
FIG. 5. Partial structure factors Sij(Q) of liquid K–Bi from the RMC simu-
lation without nearest neighbor constraint.
closer distances, we applied rather soft cutoff constraints for
the minimum distances between the atoms in the simulation.
We used the ionic radii for the alkali metals and the covalent
radii for the polyvalent metal atoms ͑for all atom pairs
PMPM, MPM, MM: 2.5 Å for liquid K–Sb, 2.7 Å for liquid
K–Bi, 2.8–2.9 Å for liquid Rb–Bi͒.
The partial structure factors ͑see Fig. 4 for K–Sb, Fig. 5
for K–Bi, data for Rb–Bi are not shown͒ indeed confirm that
the prepeak is mostly due to PM–PM correlations, with little
contributions from PM–M correlations. This is obvious up to
the highest temperatures measured, revealing the persistence
of polyanions over the full temperature range. In the case of
liquid K–Sb, only the Sij(Q)’s of the lowest temperature are
shown in Fig. 4 because of the small temperature range ex-
plored. The partial pair correlation functions for K–Sb and
K–Bi are displayed in Figs. 4 and 6. The partial g(r)’s of
the Bi alloys exhibit distinct peaks for the first coordination
sphere, shifted towards larger distances with increasing
atomic size. The first peak in gBiBi(r) remains rather sharp,
even up to 1800 K for both alloys. In contrast, the peak in
gRbRb(r) flattens with increasing temperature, and the peak
in gKK(r) vanishes completely. At 1800 K barely any hint
for an ordered short-range structure can be drawn from
gKK(r). Whereas it is not possible for these alloys to resolve
very sharp features in the partial g(r)’s, such as a clear
splitting of the first peak of gPMPM(r) into an intracluster and
FIG. 4. Partial structure factors Sij(Q) ͑lower panel͒ and partial pair corre-
lation functions gij(r) ͑upper panel͒ of liquid K–Sb at 923 K from the RMC
simulation without nearest neighbor constraint.
FIG. 6. Partial pair correlation functions gij(r) of liquid K–Bi from RMC
simulation without nearest neighbor constraint.
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J. Chem. Phys., Vol. 112, No. 17, 1 May 2000
Structure of liquid alloys K–Sb, K–Bi, and Rb–Bi
7555
TABLE IV. Fraction of onefold and twofold coordinated PM atoms result-
ing from the simulations with ͑a͒ ‘‘dumbbell constraint’’ and ͑b͒ ‘‘chain
constraint.’’
K–Sb
K–Bi
Rb–Bi
͑a͒ onefold
͑a͒ twofold
͑b͒ onefold
͑b͒ twofold
0.81
0.00
0.24
0.43
0.88
0.01
0.18
0.41
0.80
0.00
0.20
0.39
ber of PM dimers—this constraint induces the maximum
number of dumbbells in a model configuration with its struc-
ture factor being in agreement with the scattering data; and
͑b͒ ‘‘chain constraint:’’ configurations with PM atoms neigh-
bored by two other PM atoms being favored, this constraint
induces the maximum number of atoms in chain structures.
Note that we found it impossible to model the data assuming
a significant number of threefold coordinated PM atoms, thus
proving the absence of significant three-dimensional struc-
tural features in these systems ͑in other liquid Zintl alloys,
such as K–Pb, Cs–Pb, and Na–Sn, networklike structures
are found at conditions close to their melting point͒. For
these simulations we chose a maximum nearest neighbor dis-
tance of 3.0 Å for Sb atoms, respectively 3.2 Å for Bi atoms,
for covalent bonding between the PM atoms.
FIG. 7. Fraction f(n) of Bi atoms in liquid K–Bi as a function of the
number of Bi neighbors n within 3.4 Å over the complete temperature
range. Inset: Quotient of the average coordination numbers
n up to a
͗ ͘
distance r at 1800 K and 673 K ͑the horizontal line represents the quotient
of the bulk densities͒. Results are from RMC simulation without nearest
neighbor constraint.
intercluster peak, in gSbSb(r) of K–Sb there is an indication
for such splitting into peaks at around 2.9 Å and 3.6 Å. We
attribute the peak at 2.9 Å to Sb–Sb–correlations of co-
valently bonded Sb.
The results obtained for all three alloys show remarkably
similar fractions of PM atoms with a given coordination
number ͑Table IV͒. For the simulation with the ‘‘dumbbell
constraint,’’ between 80% and 88% onefold coordinated at-
oms are found with barely any twofold coordinated ones.
Applying the ‘‘chain constraint’’ 39%–43% of the polyva-
lent metal atoms are double coordinated. The tendency to
form chains or dimers thus seems to be similar in these al-
loys regardless of whether the polyvalent metal is Sb or Bi.
Figure 8 ͑left panel͒ shows the partial pair correlation func-
tions of liquid K–Bi being derived from the different simu-
lations. The first peak in gBiBi(r) is clearly split into an in-
tracluster and an intercluster part due to the applied
constraints. The striking feature is the following: Despite the
difference in f(n) values of models originating from simu-
Furthermore, we analyzed the structural models obtained
from the RMC simulations of S(Q) near the melting point
with respect to the fraction f(n) of PM atoms with a fixed
number n of neighboring atoms of the same kind within a
maximum distance dPM . We have chosen dBiϭ3.4 Å ͑re-
spectively dSbϭ3.3 Å͒ to take into account predominantly
neighbors that are able to form covalent bonds in the poly-
valent metal atom clusters. f(n) displays a clear maximum
for atoms with one neighbor only, a considerable amount of
atoms with two neighbors, and very few higher coordinated
atoms only. There is no significant difference between f(n)
of liquid K–Bi, Rb–Bi, and K–Sb. These results indicate
that these alloys contain only few networklike structural fea-
tures or three-dimensional clusters, instead consist predomi-
nantly of short chains and dimers. For liquid K–Bi, f(n) is
shown in Fig. 7 for all temperatures to demonstrate the small
temperature dependence found for f(n). Only for the highest
temperatures a slight increase in the number of zerofold co-
ordinated Bi atoms is visible, stressing again the stability of
covalent intracluster bonds up to 1800 K. The results ob-
tained for liquid Rb–Bi are very similar and therefore not
shown here. These findings correspond well to the increase
in the relative height of the first peak of gPMPM(r) with in-
creasing temperature. From the inset in Fig. 7 it can be de-
duced that this temperature stability of coordination is indeed
short ranged. The average coordination number at 1800 K is
smaller compared to the one at 673 K at distances exceeding
significantly the covalent bond length, and finally scales with
the bulk density for distances larger than 6.5 Å.
To distinguish between the formation of chains and
dimers, we performed RMC simulations with two different
nearest-neighbor constraints; ͑a͒ ‘‘dumbbell constraint:’’
configurations with PM atoms neighbored by one other PM
atom being favored above configurations with a lower num-
FIG. 8. Comparison of partial pair correlation functions gij(r) of liquid
K–Bi ͑left panel͒ and fractions f(n) of Bi atoms as a function of the number
of Bi neighbors n ͑right panel͒ from RMC simulations with different nearest
neighbor constraints.
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7556
J. Chem. Phys., Vol. 112, No. 17, 1 May 2000
K. Hochgesand and R. Winter
lations with different constraints ͑right panel in Fig. 8͒, the
gij(r)’s are practically indistinguishable. This result implies
that the structure factor does not contain enough information
to make a clear-cut decision whether an alloy prefers forma-
tion of short chains or dumbbells. Even the use of isotopic
substitution experiments seems not to be very helpful here,
as the advantage is the firm determination of the partials
only. The problem for distinguishing between a set of rather
similar structures remains—at least in this case. This prob-
lem could probably be solved using ab initio MD simula-
tions. A study on solid alloys of alkali metals and both Sb
and Bi23 explains the strong differences in the bonding be-
havior of the Sb and the Bi alloys by the more extended
nature of the Bi 5p orbitals destabilizing chain structures
compared to Sb. A recent ab initio MD study on liquid
K–Sb24 gives an average number of Sb atoms in chain frag-
ments of about 5, which is in good agreement with the chain-
length that can be calculated from the coordination numbers
of the ‘‘chain constraint’’–RMC simulation of our scattering
data. They also compared experimental structure factors with
structure factors resulting from their MD configurations, and
found a good agreement. Therefore we consider it as essen-
tial to perform an ab initio MD simulation also for liquid Bi
alloys to explore conformational differences between Sb and
Bi alloys.
showing the stability of the short-ranged structural features
up to the highest temperatures measured. Whereas the Bi–
Bi–correlations persist, the partial pair correlation functions
of the alkali atoms reveal a loss of correlations at high tem-
peratures, pointing to a structure made up of small Bi polya-
nions embedded in a randomly distributed alkali atom back-
ground.
ACKNOWLEDGMENTS
Financal support from the BMBF and the EC TMR–LSF
program is gratefully acknowledged. Many thanks to the
staff of NFL for help during the experiment.
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The static structure factors of the liquid alloys K–Sb,
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