Structure of liquid caesium-bismuth alloys studied by neutron diffraction

Article abstract of DOI:10.1063/1.480612

Neutron diffraction experiments were carried out for two liquid alloys with compositions CsBi and Cs₃Bi₂. The results indicate that probably polyanions with an average number of about two Bi atoms per cluster are formed. This result

Full text of DOI:10.1063/1.480612

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Structure of liquid caesium–bismuth alloys studied by neutron diffraction
S. A. van der Aart, V. W. J. Verhoeven, P. Verkerk, and W. van der Lugt
Citation: The Journal of Chemical Physics 112, 857 (2000); doi: 10.1063/1.480612
View online: http://dx.doi.org/10.1063/1.480612
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/112/2?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 112, NUMBER 2
8 JANUARY 2000
Structure of liquid caesium–bismuth alloys studied by neutron diffraction
S. A. van der Aart, V. W. J. Verhoeven, and P. Verkerka)
Interfacultair Reactor Instituut, Delft University of Technology, 2629 JB Delft, The Netherlands
W. van der Lugt
Solid State Physics Laboratory, University of Groningen, 9747 AG Groningen, The Netherlands
͑Received 3 August 1999; accepted 15 October 1999͒
Neutron diffraction experiments were carried out for two liquid alloys with compositions CsBi and
Cs3Bi2. The results indicate that probably polyanions with an average number of about two Bi atoms
per cluster are formed. This result contrasts with that for liquid Cs–Sb, which contains larger chains
as polyanions. © 2000 American Institute of Physics. ͓S0021-9606͑00͒52102-3͔
I. INTRODUCTION
crystal structure and the electronic structure of Li3Bi are pre-
served in the liquid. In the sequence Li–Bi to Rb–Bi a sec-
ond maximum at 40% Bi gradually appears, and for liquid
Cs–Bi only the latter has survived.17,18 In many cases of
ionic alloys of alkali metals with post-transition polyvalent
metals there is a strong relation between the crystal structure
and the liquid structure.4,19 In the case of Cs–Bi the resistiv-
ity data would indicate that the ͑unknown͒ structure of the
compound Cs3Bi2 is somehow preserved in the liquid. There
is, however, no trace of the Laves phase (CsBi2) in the re-
sistivity measurements. According to Tegze and Hafner20 the
solid Laves compounds are metallic due to a surplus of elec-
trons, provided by the alkali atoms, on the otherwise cova-
lent Bi network. Measurements of the Darken stability func-
tion of liquid Rb–Bi, which behaves very similar to Cs–Bi,
suggest a compound at 50%, which is inconsistent with the
resistivity measurements.21 Cs–Sb exhibits a plateaulike
maximum in the electrical resistivity between 35% and 50%
Cs, which indicates that not only the Zintl compound CsSb
plays a role in the liquid.22 Tegze and Hafner20 made a com-
prehensive theoretical investigation of the electronic struc-
ture of alkali-pnictide alloys. They attribute the difference
between Sb and Bi alloys to the strong relativistic effects on
the Bi orbitals.
Summarizing, the behavior of the Cs–Bi alloys is con-
fusing, particularly around the eutectic composition. The
present investigation constitutes an attempt to shed some
light on the situation. Attention was focused on two compo-
sitions near the eutectic. Cs3Bi2 was chosen because there
exists a solid compound of that composition, while CsBi was
chosen for comparison with CsSb. As in this class of alloys,
anion configurations ͑often Zintl ions͒ play an important
role; neutron diffraction was chosen as the experimental
technique. The occurrence of polyanions is often accompa-
nied by a superstructure in the liquid, which shows up as a
prepeak ͑‘‘first sharp diffraction peak’’͒ in the structure fac-
tor.
In some respects the physical and chemical properties of
the liquid Cs–Bi system are not well understood. The phase
diagram1 exhibits a deep eutectic at approximately 50% in
between the congruently melting compounds Cs3Bi and
CsBi2. The crystal structure of Cs3Bi can be described as an
NaTl lattice ͑two interpenetrating diamond lattices͒ with
one-quarter of the lattice sites occupied by Bi.2 Each Bi atom
is in its first coordination shell completely surrounded by Cs
atoms, in accordance with the electronegativity difference
between the two components ͑1.23 on the Pauling scale͒.
CsBi2 forms a Laves (MgCu2) structure.2 The Bi atoms form
a network of vertex-sharing tetrahedra; the bonding is not in
accordance with the rules for Zintl phases.3–5 Furthermore,
there exists evidence for a compound Cs3Bi2 and a com-
pound with approximate composition Cs5Bi4. The structure
of neither of them could be determined.6 Cs3Bi2 is peritecti-
cally melting, or nearly so. The phase diagram of the K–Bi7
and Rb–Bi8 systems are very similar to that of Cs–Bi.
From their relative positions in the Periodic Table one
would expect a strong similarity between Bi and Sb and
between their corresponding alloys. Indeed, such similarities
are found for Tl and In and for Pb and Sn, which belong to
the same two periods as Bi and Sb. In contrast, the physical
and chemical properties of Bi and its alloys differ apprecia-
bly from those of Sb and its alloys.
In the phase diagrams of K–Sb, Rb–Sb, and Cs–Sb con-
gruently melting equiatomic compounds occur.9–11 The Sb
ions in these compounds form tellurium-like infinite spiral
chains in accordance with the rules for Zintl ion
formation.12,13 In the corresponding Bi systems these equi-
atomic compounds do not appear, but have given way to
deep eutectics. There are strong indications that fragments of
the Sb chains are preserved in the liquid state of the
alkali–Sb alloys.14,15 According to ab initio calculations the
average length of a chain in liquid KSb is approximately five
atoms.15
The resistivities of liquid Li–Bi alloys exhibit a distinct
maximum at 25% Bi,16 suggesting that the essentials of the
First, we describe experimental details. Next, the experi-
mental data are analyzed by means of the reverse Monte
Carlo ͑RMC͒ technique and with a scaling model.
a͒
Electronic mail: verkerk@iri.tudelft.nl
0021-9606/2000/112(2)/857/7/$17.00
857
© 2000 American Institute of Physics
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858 J. Chem. Phys., Vol. 112, No. 2, 8 January 2000
TABLE I. Composition of the Cs–Bi samples.
van der Aart et al.
As monochromator we used Cu ͑220͒ to select a wavelength
of 0.11 nm. An oscillating collimator strongly reduced back-
ground scattering. There are four detector banks, each con-
taining three Reuter–Stokes 3He linear position-sensitive de-
tectors with an active length of 60 cm. To cover the gaps
between the four detector banks the detector box can rotate
over 10°.
Sample
w
Bi(g)
Composition ͑at. %͒
wCs(g)
Cs3Bi2
CsBi
3.150
4.725
3.002
3.002
Cs59.98Bi40.02
Cs50.02Bi49.98
The angular range is 2°Ͻ2␪Ͻ125°, corresponding to
II. EXPERIMENT
A. Samples
an available range of momentum transfer
k
ϭ4–93.6 nmϪ1. Each measurement was divided in several
runs in order to check the stability of the system. The beam
size was 3.5ϫ1 cm2.
A cylindrical cell with a 0.6-mm-thick wall, 7 mm inner
diameter, and 50 mm length was used. The cell is made of
the alloy Ti0.68Zr0.32, which has zero coherent scattering
length and produces completely incoherent background scat-
tering without Bragg peaks. Furthermore, Ti–Zr is corrosion
resistant against liquid alkali metals. However, the tempera-
ture should be kept below 800 °C, at which temperature the
Ti–Zr alloy starts to soften and recrystallization can occur
leading to Bragg peaks. Special care has to be taken to seal
the cell leak tight, in particular at high temperatures. We use
a knife edge and a screw lid to close the cell as described in
Ref. 23. Because the knife edge is made of the same material
as the cell there were no problems due to thermal expansion.
The cell was tested and proved to be leak proof at high
temperature.
During the measurements the reactor power varied from
37 MW during the empty can measurement to 47 MW dur-
ing the sample and vanadium measurements. It turned out
this was not well corrected for by the monitor in the incident
beam, probably due to saturation of the monitor. The empty
can measurement needed to be corrected for the difference in
monitor efficiency at the respective reactor powers ͑3.6%͒.
The samples were measured at 550 °C. Cs3Bi2 was mea-
sured for 9 h in 13 runs, alternating the detector positions.
This sample was heated up in the SLAD furnace where we
could see from the diffraction pattern the bismuth melt at
271 °C, and immediately after that we saw new Bragg peaks
appear at different positions. At around 440 °C these Bragg
peaks disappeared. CsBi was measured for 11 h in 16 runs.
Corrections for attenuation, background, multiple scat-
tering, and inelasticity ͑Placzek͒ were applied and the data
were normalized by means of a vanadium measurement to an
absolute value for the scattered intensity. The data correc-
tions and normalization were performed using the program
CORRECT, which is available at the NFL.25
After normalization, using first estimates of the unknown
number densities ͑␳ϭ16.3 nmϪ3 for Cs3Bi2, and ␳ϭ17.8
nmϪ3 for CsBi͒, the scattering level for large k turned out to
be 0.453 b for Cs3Bi2 ͑using a filling fraction of the sample
of 0.79 as estimated from x-ray photographs͒ and 0.481 b for
CsBi ͑filling fraction of 0.94͒. The theoretically expected
levels are 0.478 and 0.519 b, respectively. The difference is
attributed to uncertainties in the density. The density has a
noticeable effect only on the normalization, the effect on the
multiple scattering correction is negligible. We therefore
multiplied the data by a factor to obtain the theoretically
expected scattering level, which is equivalent to choosing
number densities of 15.4 and 16.5 nmϪ3 for Cs3Bi2 and CsBi,
respectively.
The following metals were used for the preparation of
the samples:
͑a͒ Cs: vial 99.98%, Cabot ͑Revere, USA͒.
͑b͒ Bi: ingots 99.999%, Ventron GmbH ͑Karlsruhe, Ger-
many͒.
The samples were prepared in an argon-filled glovebox with
O2 and H2O levels that are typically lower than 1 ppm.
Ti and Zr both have a poor resistance against liquid
bismuth.24 However, it is conceivable that the Cs–Bi mixture
is less corrosive than the pure elements, because there is a
strong compound formation. This is, for instance, indicated
by the fast reaction between liquid Cs and solid Bi chunks.
Unfortunately, no information on the corrosiveness of the
Cs–Bi alloy is available. But after the measurements there
were no indications for corrosion of the cell material.
Proper amounts of metal were transferred to the sample
cell. After closing, the cell was heated up to 650 °C. Near the
melting point of bismuth ͑271 °C͒ the heating was done very
slowly in order to avoid a sudden fierce reaction which could
destroy the cell. After measuring Cs3Bi2 the cell was opened
in a glovebox and extra bismuth was added for the CsBi
measurements. The cell was closed again with a new knife
edge. The compositions of the samples are given in Table I.
The resulting experimental structure factors S(k) of
Cs3Bi2 and CsBi at 550 °C are shown in Fig. 1. They show
prepeaks at kϭ10.9 and 10.7 nmϪ1, respectively. Measure-
ments on the Cs–Sb system by Lamparter, Martin, and
Steeb14 show that the prepeak remains at about the same
B. Neutron diffraction
The experiments were performed on SLAD ͑Studsvik
Liquids and Amorphous Materials Diffractometer͒ at the
NFL ͑Neutronforskningslaboratoriet͒ in Studsvik, Sweden.
SLAD has a medium resolution (⌬k/kϷ0.01) and a rela-
tively high count rate. This resolution is sufficient in view of
the broad features in the structure factor of a liquid material.
position for CsSb and Cs65Sb35, namely 9.5 and 9.7 nmϪ1
,
respectively. This contrasts with the Cs–Tl case,26 where the
prepeak increases in height and the position shifts to higher k
with increasing Cs concentration.
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J. Chem. Phys., Vol. 112, No. 2, 8 January 2000
Structure of liquid Cs–Bi alloys
859
TABLE II. Pair distances in crystalline alkali-Bi and alkaline earth–Bi al-
loys.
Pair
Alloy
Distance ͑nm͒
Reference
Bi–Bi
(cryptKϩ)2͑Bi4)2Ϫ
Ca11Bi10
Ca14MnBi11
Sr14MnBi11
Ba14MnBi11
KBi2
0.2936, 0.2941
0.315, 0.320
0.3335
0.3425
0.3498
28
29
30
30
30
31
2
0.335
0.345
CsBi2
Cs3Bi
0.658
2
Cs–Bi
Cs–Cs
Cs3Bi
CsBi2
0.403
0.404
2
2
Cs3Bi
CsBi2
0.403
0.423
2
2
FIG. 1. Structure factors S(k) of liquid Cs3Bi2 ͑shifted vertically by ϩ1͒ and
CsBi at 550 °C. Dots: experimental results; solid line: MCGR fit.
III. ANALYSIS AND INTERPRETATION
consideration, because they most probably do not pertain to
atoms in contact. Unfortunately, we could not find more data
on Cs–Cs and Cs–Bi distances.
A. Total pair distribution function and crystallographic
data
The total pair distribution functions of both Cs3Bi2 and
CsBi exhibit distinct peaks at 0.30 and 0.39 nm ͑Fig. 2͒. The
crystallographic data leaves us little choice for the first one:
It should be attributed to Bi–Bi pairs. It is remarkable that
the distance in the liquid is in the range of the shorter dis-
tances found in the solid. This indicates a strong covalent
bond. The maximum of the second peak is situated very
close to the Bi–Cs and Cs–Cs distances in the solid, but this
peak is sufficiently broad to have appreciable values already
at 0.35 nm. Therefore, it can, within the limits given by the
crystallographic data, accommodate Bi–Bi pair distances as
well.
27
By means of the program MCGR we obtained from the
experimental S(k) the total pair distribution functions defined
by
ϱ
1
sin kr
g r͒ϭ1ϩ
k2 S k͒Ϫ1
dr
͑1a͒
͑
͑
͕
͖
͵
2
kr
0
2␲ ␳
with the inverse:
ϱ
sin kr
S k͒ϭ1ϩ4␲␳
͑
r2 g r͒Ϫ1
dr.
͑1b͒
͑
͕
͖
͵
kr
0
By iteration using Eq. ͑1b͒ we fitted a smooth g(r) to the
experimental data with the constraint that g(r)ϵ0 for r
Ͻ0.26 nm. The results for S(k) and g(r) are given in Figs. 1
and 2.
For the interpretation of g(r) it is useful to give some
pair distances in crystalline alkali–Bi and alkaline earth–Bi
alloys, see Table II. The largest distances for Bi–Bi and
Cs–Cs ͑0.658 and 0.423 nm, respectively͒ are left out of
B. RMC, partial structure factors
In order to obtain more insight we have estimated the
partial pair distribution functions and partial structure factors
by means of the reverse Monte Carlo method32 ͑RMC͒. The
differential cross section d␴/d⍀ contains a weighted sum of
the Faber–Ziman partial structure factors, A␣␤(k):
1 d␴
N d⍀
␴
s
ϭ
c b c b
A k͒Ϫ1 ϩ
͓ ͑
␣␤
,
͑2͒
͔
͚
␣
␣
␤
␤
␣,␤
4␲
with c␣ the concentration and b␣ the average coherent scat-
tering length of component ␣, and ␴ the total scattering
s
cross section of the alloy. The normalized weight factors
w␣␤ϭc b c b / b 2, with b ϭ͚ c b , are given in
͗ ͘
͗ ͘
␣
␣
␤
␤
␣ ␣ ␣
Table III. They are calculated using bCsϭ5.42 fm and bBi
ϭ8.531 fm.
TABLE III. Weight factors w␣,␤ for the partial structure factors A␣,␤(q)
and partial pair distribution functions g␣,␤(r).
Alloy
wCs,Cs
wCs,Bi
wBi,Bi
0.2381
0.1509
0.4997
0.4751
0.2622
0.3740
FIG. 2. Total pair distribution functions g(r) for liquid Cs3Bi2 ͑shifted ver-
tically by ϩ01͒ and CsBi at 550 °C, as obtained by Fourier transform of the
experimental data by means of MCGR.
Cs3Bi2
CsBi
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