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Electrical resistivities of liquid KBi and CsBi alloys
Journal of Non-Crystalline Solids 117/118 (1990) 355-358
355
North-Holland
ELECTRICAL RESISTIVITIES OF LIQUID K-Bi AND Cs-Bi ALLOYS J.A. MEIJER and W. van der LUGT Solid State Physics Laboratory, Materials Science Centre,University of Groningen, Melkweg i , 9718 EP, Groningen, the Netherlands. i.
INTRODUCTION
using the metal tube method. The use of thin-
In the course of our investigation of
walled stainless steel tubes allowed
e l e c t r i c a l transport properties of l i q u i d ionic
measurements up to 5000 NQcmwith a r e l a t i v e
compound forming alloys the e l e c t r i c a l
error of no more than 2.5%.
r e s i s t i v i t i e s of alloys of the K-Bi and Cs-Bi
In f i g . i the r e s i s t i v i t y p of l i q u i d K-Bi
systems have been investigated experimentally. A
alloys is plotted as a function of composition
p a r t i c u l a r point of interest in ionic alloys is
c at d i f f e r e n t temperatures. Data originating
the p o s s i b i l i t y of poly-anion formation. As
from Freyland as quoted by Egan7 are included.
GeertsmaI has pointed out, in many of the ionic
Near the octet composition our data suffer from
alloys systems there is a competition between
an uncertainty of about i% in the composition,
octet and "clustered" compounds. In some alloys
as a consequence of evaporation of the a l k a l i
systems polyanions probably occur as w e l l -
metal. The p(c) curve has a very d i s t i n c t
defined units called Zintl ions 2 of which the
maximum at the octet composition, with a small
(Pb4)4- ion is the best known example. In other
shoulder between 40 and 50 at.%. Fig. 2 gives
systems the configuration of the polyanions is
the temperature dependence, dlnp/dT, which
less clearly defined and may change with
exhibits a d i s t i n c t minimum at the octet
composition 3. P a r t i c u l a r l y in the Cs-Sb system
composition; dlnp/dT is strongly negative
evidence has been found for the existence of
around the minimum, as is usual for ionic
variable-size fragments of negatively charged,
alloys.
t e l l u r i u m - l i k e chains of antimony atoms.4,5
Fig. 3 shows the r e s i s t i v i t y of the Cs-Bi
Therefore, alkali-bismuth alloys were considered
system. Results obtained by Steinleitner8 and
interesting candidates for further
quoted in his thesis have been included. The
investigations of this phenomenon. However the
two sets of data f i t very well. The peak at the
phase diagrams of the alkali-bismuth alloys
octet composition found in K-Bi has here given
d i f f e r strongly from those of the a l k a l i -
way to a broad maximumcentered at 40 at.% Bi.
antimony alloys. The K-Bi and Cs-Bi phase
The maximumr e s i s t i v i t y value is 4600 NQcm. at
diagrams exhibit octet compounds K3Bi and Cs3Bi
550 C. In f i g . 4 the temperature derivative
at the a l k a l i - r i c h side and compounds KBi 2 and
dlnp/dT has been plotted for Cs-Bi. Also here
CsBi 2 at the bismuth-rich side. The octet
the maximum in p corresponds to a minimum in
compound is reflected also in the excess
dp/dT. Note the peculiar behaviour of the
s t a b i l i t y6 of K-Bi which has i t s main peak at
equiatomic alloy: though the r e s i s t i v i t y is
the composition K3Bi.
2000 NQcm, dlnp/dT is nearly zero.
2. MEASUREMENTS
3. DISCUSSION
The r e s i s t i v i t y measurements were carried out 0022-3093/90/$03.50 (~) Elsevier Science Publishers B.V. (North-Holland)
In e i t h e r system around the r e s i s t i v i t y
J.A. Meijer, W. van der Lugt / Electrical resistivities of liquid K-Bi and Cs-Bi alloys
356
x
10 -3 2.5
+
r +
2000
+ •
0
++
K-
0
0.0
+~W 0
x o
P (jJ~cm:
# +
1000
300 450 600 700
"C °C °C °C
dlnp/dT (I/K)
++4-+
8
x o
0
-2.5
+
300 450 600 700
°C °C °C °C
,W(, 0
-5.0
0 K
2'0
,4'0
6'0
8'0
Bi
20
CBi (at. %)
40
BO
80
CB~ (at .%)
FIGURE 1 R e s i s t i v i t y , p, of l i q u i d K-Bi alloys at temperatures indicated in the figure.
FIGURE 2 Temperature derivative, dp/dT, of the r e s i s t i v i t y of l i q u i d K-Bi alloys at the indicated temperatures.
maximum the r e s i s t i v i t i e s exceed those
compound.l,11,12,13
characteristic for the nearly-free-electron
Bi
The occurrence of polyanions in bismuth
regime. According to the c l a s s i f i c a t i o n given by
alloys was f i r s t conjectured by Steinleitner8.
Mott and Davis9 the highest r e s i s t i v i t i e s in Cs-
The r e s i s t i v i t y maximum in Cs-Bi is much
Pb even correspond to the regime of
broader than that in K-Pb or Cs-Pb. This can be
localization.
explained in the following way. The Zintl ion
In Li-Bi Steinleitner et al. 10 report a
corresponding to Pb- is a f i n i t e unit,
r e s i s t i v i t y maximumat the octet composition. In
tetrahedral (Pb4)4~ isoelectronic with the
K-Bi the maximum is at the same composition but
molecule As4. The ideal Zintl ion corresponding
i t is probably broader and is accompanied by a
to Bi- is l i k e l y to be a chalcogenide-like
weak shoulder at higher Bi concentrations. In
i n f i n i t e chain. Such chains have indeed been
Cs-Bi the maximumhas shifted d e f i n i t e l y to more
observed14 in the solid compound CsSb but they
Bi-rich compositions. This behaviour is similar
can not exist in the l i q u i d . Therefore we
to that in the sequence Li-Pb, Na-Pb and K-Pb11
expect that fragments of such chains occur in
and can be explained in the same way: with
the l i q u i d . Then extra electrons are needed to
increasing size of the a l k a l i atom the clustered
saturate the dangling bonds. This explains that
configuration becomes more stable than the octet
the maximumr e s i s t i v i t y does not occur at the
J.A. Meijer, W.
I
I
I
van d e r
Lugt / Electrical resistivities of liquid K-Bi
2
1
and
Cs-Bi alloys
357
i
x CO-z I 0 0
4000
•
P
x * o +
[JJOcm:
400 550 600 B50
0 dlnp/dT
"C °C "C °C
•
®
@
400 550 600 650
°C "C °C °C
X
(h/K) -I oi w
-2
2000
x w o +
-3
-4 W
0
Cs
'
2'0
'
4'0
CBi
'
6'0
'
8'0
'
Bi
-5 Cs
2b
(at .%)
'
40
'
sb
'
Bb
Bi
CBi (at .%)
FIGURE 3 R e s i s t i v i t y , p, of l i q u i d Cs-Bi alloys at temperatures indicated.
FIGURE 4 Temperature derivative, dp/dT, of the r e s i s t i v i t y of l i q u i d Cs-Bi alloys at the indicated temperatures.
equiatomic composition, but at 40 at.% Bi. As
strongly negative, because with increasing
the fragments may have variable length the
temperature the ionic order breaks up and the
stoechiometry is not uniquely defined and
system becomes more metallic. In l i q u i d CsSb,
accordingly the maximum is broad.
however, the temperature derivative is indeed
Similar conclusions have been drawn for the
almost zero. For the moment we cannot propose
Cs-Sb alloys by Redslob et al. 4 and by Lamparter
any conduction mechanism explaining this
et al. 5 when analyzing t h e i r r e s i s t i v i t y and
behaviour.
neutron d i f f r a c t i o n data, respectively. Finally we discuss the equiatomic l i q u i d alloy CsSb. The measured r e s i s t i v i t y is 2000
ACKNOWLEDGEMENTS This work forms part of the research
pQcm, corresponding to the category of diffusive
programme of the Stichting voor Fundamenteel
motion of electrons in the c l a s s i f i c a t i o n by
Onderzoek der Materie (Foundation for
Mott and Davis9. According to t h e i r description
Fundamental Research on Matter (FOM)) and was
for this category the temperature dependence
made possible by financial support from the
should be almost zero. In practice, in a l l ionic
Nederlandse Organisatie voor Wetenschappelijk
alloys near the stoechiometric composition the
Onderzoek (Netherlands Organization for
temperature derivative of the r e s i s t i v i t y is
S c i e n t i f i c Research (NWO)).
J.A. Meijer, W. van der Lugt / Electrical resistivities of liquid K-Bi and Cs-Bi alloy~
358
REFERENCES 1 W. Geertsma, J.Dijkstra and W.van der Lugt, J.Phys. F: Metal Phys. 14 (1984) 1833. 2
E. Busmann, Z.Anorg. Allg. Chemie, 313 (1961) 90.
3 J.A. Meijer, P.Kuiper, C.van der Marel and W.van der Lugt, Z. Phys. Chem. Neue Folge 156 (1988) 623. 4
H. Redslob, G. Steinleitner and W. Freyland, Z. Naturforsch. 27a (1982) 587.
5 P. Lamparter, W.Martin and S.Steeb, Z. Naturforsch. 38a (1983) 329. 6 A.Petric, A.D. Pelton and M.-L. Saboungi J.Phys. F: Metal Phys. 18 (1988) 1473. 7 J.J. Egan, High Temp. Sci. 19 (1985) 111. 8
G. Steinleitner, Thesis, Marburg 1978.
9
N.F. Mott and E.A. Davis, Electronic Processes in Non-crystalline Materials, Clarendon Press, Oxford 1979.
10 G. Steinleitner, W.Freyland and F.Hensel, Ber.Bunsenges. 79 (1975) 1186. 11 J.A. Meijer, W. Geertsma and W. van der Lugt, J. Phys.F: Metal Phys. 15 (1985) 899. 12 J.A. Meijer, G.J.B. Vinke and W. van der Lugt, J. Phys.F: Metal Phys. 16 (1986) 845. 13 W. van der Lugt and W. Geertsma, Can. J. Phys. 65 (1987) 326. 14 H.-G. von Schnering, W. H~nle and G. Krogull Z. Naturforsch. 34b (1979) 1678.
355
North-Holland
ELECTRICAL RESISTIVITIES OF LIQUID K-Bi AND Cs-Bi ALLOYS J.A. MEIJER and W. van der LUGT Solid State Physics Laboratory, Materials Science Centre,University of Groningen, Melkweg i , 9718 EP, Groningen, the Netherlands. i.
INTRODUCTION
using the metal tube method. The use of thin-
In the course of our investigation of
walled stainless steel tubes allowed
e l e c t r i c a l transport properties of l i q u i d ionic
measurements up to 5000 NQcmwith a r e l a t i v e
compound forming alloys the e l e c t r i c a l
error of no more than 2.5%.
r e s i s t i v i t i e s of alloys of the K-Bi and Cs-Bi
In f i g . i the r e s i s t i v i t y p of l i q u i d K-Bi
systems have been investigated experimentally. A
alloys is plotted as a function of composition
p a r t i c u l a r point of interest in ionic alloys is
c at d i f f e r e n t temperatures. Data originating
the p o s s i b i l i t y of poly-anion formation. As
from Freyland as quoted by Egan7 are included.
GeertsmaI has pointed out, in many of the ionic
Near the octet composition our data suffer from
alloys systems there is a competition between
an uncertainty of about i% in the composition,
octet and "clustered" compounds. In some alloys
as a consequence of evaporation of the a l k a l i
systems polyanions probably occur as w e l l -
metal. The p(c) curve has a very d i s t i n c t
defined units called Zintl ions 2 of which the
maximum at the octet composition, with a small
(Pb4)4- ion is the best known example. In other
shoulder between 40 and 50 at.%. Fig. 2 gives
systems the configuration of the polyanions is
the temperature dependence, dlnp/dT, which
less clearly defined and may change with
exhibits a d i s t i n c t minimum at the octet
composition 3. P a r t i c u l a r l y in the Cs-Sb system
composition; dlnp/dT is strongly negative
evidence has been found for the existence of
around the minimum, as is usual for ionic
variable-size fragments of negatively charged,
alloys.
t e l l u r i u m - l i k e chains of antimony atoms.4,5
Fig. 3 shows the r e s i s t i v i t y of the Cs-Bi
Therefore, alkali-bismuth alloys were considered
system. Results obtained by Steinleitner8 and
interesting candidates for further
quoted in his thesis have been included. The
investigations of this phenomenon. However the
two sets of data f i t very well. The peak at the
phase diagrams of the alkali-bismuth alloys
octet composition found in K-Bi has here given
d i f f e r strongly from those of the a l k a l i -
way to a broad maximumcentered at 40 at.% Bi.
antimony alloys. The K-Bi and Cs-Bi phase
The maximumr e s i s t i v i t y value is 4600 NQcm. at
diagrams exhibit octet compounds K3Bi and Cs3Bi
550 C. In f i g . 4 the temperature derivative
at the a l k a l i - r i c h side and compounds KBi 2 and
dlnp/dT has been plotted for Cs-Bi. Also here
CsBi 2 at the bismuth-rich side. The octet
the maximum in p corresponds to a minimum in
compound is reflected also in the excess
dp/dT. Note the peculiar behaviour of the
s t a b i l i t y6 of K-Bi which has i t s main peak at
equiatomic alloy: though the r e s i s t i v i t y is
the composition K3Bi.
2000 NQcm, dlnp/dT is nearly zero.
2. MEASUREMENTS
3. DISCUSSION
The r e s i s t i v i t y measurements were carried out 0022-3093/90/$03.50 (~) Elsevier Science Publishers B.V. (North-Holland)
In e i t h e r system around the r e s i s t i v i t y
J.A. Meijer, W. van der Lugt / Electrical resistivities of liquid K-Bi and Cs-Bi alloys
356
x
10 -3 2.5
+
r +
2000
+ •
0
++
K-
0
0.0
+~W 0
x o
P (jJ~cm:
# +
1000
300 450 600 700
"C °C °C °C
dlnp/dT (I/K)
++4-+
8
x o
0
-2.5
+
300 450 600 700
°C °C °C °C
,W(, 0
-5.0
0 K
2'0
,4'0
6'0
8'0
Bi
20
CBi (at. %)
40
BO
80
CB~ (at .%)
FIGURE 1 R e s i s t i v i t y , p, of l i q u i d K-Bi alloys at temperatures indicated in the figure.
FIGURE 2 Temperature derivative, dp/dT, of the r e s i s t i v i t y of l i q u i d K-Bi alloys at the indicated temperatures.
maximum the r e s i s t i v i t i e s exceed those
compound.l,11,12,13
characteristic for the nearly-free-electron
Bi
The occurrence of polyanions in bismuth
regime. According to the c l a s s i f i c a t i o n given by
alloys was f i r s t conjectured by Steinleitner8.
Mott and Davis9 the highest r e s i s t i v i t i e s in Cs-
The r e s i s t i v i t y maximum in Cs-Bi is much
Pb even correspond to the regime of
broader than that in K-Pb or Cs-Pb. This can be
localization.
explained in the following way. The Zintl ion
In Li-Bi Steinleitner et al. 10 report a
corresponding to Pb- is a f i n i t e unit,
r e s i s t i v i t y maximumat the octet composition. In
tetrahedral (Pb4)4~ isoelectronic with the
K-Bi the maximum is at the same composition but
molecule As4. The ideal Zintl ion corresponding
i t is probably broader and is accompanied by a
to Bi- is l i k e l y to be a chalcogenide-like
weak shoulder at higher Bi concentrations. In
i n f i n i t e chain. Such chains have indeed been
Cs-Bi the maximumhas shifted d e f i n i t e l y to more
observed14 in the solid compound CsSb but they
Bi-rich compositions. This behaviour is similar
can not exist in the l i q u i d . Therefore we
to that in the sequence Li-Pb, Na-Pb and K-Pb11
expect that fragments of such chains occur in
and can be explained in the same way: with
the l i q u i d . Then extra electrons are needed to
increasing size of the a l k a l i atom the clustered
saturate the dangling bonds. This explains that
configuration becomes more stable than the octet
the maximumr e s i s t i v i t y does not occur at the
J.A. Meijer, W.
I
I
I
van d e r
Lugt / Electrical resistivities of liquid K-Bi
2
1
and
Cs-Bi alloys
357
i
x CO-z I 0 0
4000
•
P
x * o +
[JJOcm:
400 550 600 B50
0 dlnp/dT
"C °C "C °C
•
®
@
400 550 600 650
°C "C °C °C
X
(h/K) -I oi w
-2
2000
x w o +
-3
-4 W
0
Cs
'
2'0
'
4'0
CBi
'
6'0
'
8'0
'
Bi
-5 Cs
2b
(at .%)
'
40
'
sb
'
Bb
Bi
CBi (at .%)
FIGURE 3 R e s i s t i v i t y , p, of l i q u i d Cs-Bi alloys at temperatures indicated.
FIGURE 4 Temperature derivative, dp/dT, of the r e s i s t i v i t y of l i q u i d Cs-Bi alloys at the indicated temperatures.
equiatomic composition, but at 40 at.% Bi. As
strongly negative, because with increasing
the fragments may have variable length the
temperature the ionic order breaks up and the
stoechiometry is not uniquely defined and
system becomes more metallic. In l i q u i d CsSb,
accordingly the maximum is broad.
however, the temperature derivative is indeed
Similar conclusions have been drawn for the
almost zero. For the moment we cannot propose
Cs-Sb alloys by Redslob et al. 4 and by Lamparter
any conduction mechanism explaining this
et al. 5 when analyzing t h e i r r e s i s t i v i t y and
behaviour.
neutron d i f f r a c t i o n data, respectively. Finally we discuss the equiatomic l i q u i d alloy CsSb. The measured r e s i s t i v i t y is 2000
ACKNOWLEDGEMENTS This work forms part of the research
pQcm, corresponding to the category of diffusive
programme of the Stichting voor Fundamenteel
motion of electrons in the c l a s s i f i c a t i o n by
Onderzoek der Materie (Foundation for
Mott and Davis9. According to t h e i r description
Fundamental Research on Matter (FOM)) and was
for this category the temperature dependence
made possible by financial support from the
should be almost zero. In practice, in a l l ionic
Nederlandse Organisatie voor Wetenschappelijk
alloys near the stoechiometric composition the
Onderzoek (Netherlands Organization for
temperature derivative of the r e s i s t i v i t y is
S c i e n t i f i c Research (NWO)).
J.A. Meijer, W. van der Lugt / Electrical resistivities of liquid K-Bi and Cs-Bi alloy~
358
REFERENCES 1 W. Geertsma, J.Dijkstra and W.van der Lugt, J.Phys. F: Metal Phys. 14 (1984) 1833. 2
E. Busmann, Z.Anorg. Allg. Chemie, 313 (1961) 90.
3 J.A. Meijer, P.Kuiper, C.van der Marel and W.van der Lugt, Z. Phys. Chem. Neue Folge 156 (1988) 623. 4
H. Redslob, G. Steinleitner and W. Freyland, Z. Naturforsch. 27a (1982) 587.
5 P. Lamparter, W.Martin and S.Steeb, Z. Naturforsch. 38a (1983) 329. 6 A.Petric, A.D. Pelton and M.-L. Saboungi J.Phys. F: Metal Phys. 18 (1988) 1473. 7 J.J. Egan, High Temp. Sci. 19 (1985) 111. 8
G. Steinleitner, Thesis, Marburg 1978.
9
N.F. Mott and E.A. Davis, Electronic Processes in Non-crystalline Materials, Clarendon Press, Oxford 1979.
10 G. Steinleitner, W.Freyland and F.Hensel, Ber.Bunsenges. 79 (1975) 1186. 11 J.A. Meijer, W. Geertsma and W. van der Lugt, J. Phys.F: Metal Phys. 15 (1985) 899. 12 J.A. Meijer, G.J.B. Vinke and W. van der Lugt, J. Phys.F: Metal Phys. 16 (1986) 845. 13 W. van der Lugt and W. Geertsma, Can. J. Phys. 65 (1987) 326. 14 H.-G. von Schnering, W. H~nle and G. Krogull Z. Naturforsch. 34b (1979) 1678.