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The electrical resistivities of liquid KSn and CsSn alloys
] O U R N A L OF
Journal of Non-Crystalhne Solids 156-158 (1993) 293-296 North-Holland
~
U
The electrical resistivities of liquid K-Sn and Cs-Sn alloys R. X u , T. d e J o n g e a n d W. v a n d e r L u g t Sohd State Phystcs Laboratory, Unwerstty of Gronmgen, Nqenborgh 4, 9747AG Gronmgen, The Netherlands
The electrical res~stivlty, p, of llqmd K-Sn and Cs-Sn alloys has been measured as a function of composition and temperature The reslstivities of both systems exhibit very sharp peaks close to the equlatomlc composition At the same compos~tmn, the temperature dependence of the res~stwlty has a deep mlmmum The maximum reslstw~t~esare 3100 and 14200 i~ll cm respectively. Comparison with the L1-Sn and Na-Sn alloys and with the alkah-lead systems strongly suggests that Zintl ions are formed in the liqmd
1. Introduction
2. Experimental
The electrical resistivities of liquid K - S n and C s - S n were determined experimentally as part of a systematic investigation of the resistivities of liquid alkali-lead and alkali-tin alloys [1-4]. The physical interest of the present work is to confirm the expected similarity between the liquid alkali-tin alloys and the corresponding alkali-lead alloys. The alkali-lead alloys form a classical example of a set of systems changing from simple ionic ( L i - P b ) to clustered configurations ( K - P b , R b - P b and Cs-Pb). Ideally, the clusters are (Pb4)4- tetrahedra ('Zintl' compounds). This transition has been confirmed by a large variety of experimental results (electrical resistivity, neutron diffraction, inelastic neutron scattering, thermodynamic properties), for which we refer to some review papers [5-7]. The clust e r e d - n o n - c l u s t e r e d transition has been described theoretically by G e e r t s m a [8-10]. Earlier investigations on alkali-tin systems [4,11-15] showed that they most probably also form a category of alloys which are precisely described by G e e r t s m a ' s model. The present m e a s u r e m e n t s aim at further verifying this supposition.
A m o n g the alkali-tin and alkali-lead alloys, the K - S n and C s - S n systems are the most difficult from an experimental point of view and earlier attempts were not quite successful. The experimental problems are a consequence of strong evaporation, high corrosivity and the need of high temperatures (1200 K). For K - S n alloys, the metal tube method was used. For experimental details, we refer to refs. [16,17]. Since we expected the resistivities of the C s - S n system to be much higher than those of the K - S n system, a four-probe method was adopted. The experimental set-up was the same as previously used for the liquid C s - P b system [2]. The R b - S n system has not been investigated because one may safely assume that the results are intermediate between those for K - S n and Cs-Sn. The inaccuracy in the values for the resistivities is estimated to be + 2% for K - S n and + 5 % for Cs-Sn.
Correspondence to. Dr W. van der Lugt, Sohd State Physics
Laboratory, Unwersity of Groningen, Nuenborgh 4, 9747 AG, Gronmgen, The Netherlands. Tel.' + 31-50 634 828. Telefax +31-50 634 825
3. Results Figure 1 gives the resistivities of K - S n alloys plotted as a function of composition. The experiments cover the entire concentration range. Figure 2 gives the resistivities of C s - S n alloys. The measurements exhibit a gap between 7 and 40
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V All rights reserved
294
R Xu et al. / Electrical reststwmes of hqutd K-Sn and Cs-Sn alloys
at.% Sn, where, as a consequence of experimental difficulties, no reliable data could be obtained. Both systems exhibit a high and sharp peak at a composition of 50 at.% Sn of either component. The maximum resistivity values are far beyond the purely metallic range; that for Cs-Sn is higher than in any other alkali-lead or alkali-tin system.
4. Discussion
We show below that the observed maximum resistivities and the positions of these maxima (interpreted as stoichiometric compositions) fit nicely into Geertsma's model. Anticipating this discussion, we assume that at least a fraction of the atoms occurs in tetrahedra ( S n 4 ) 4 - . Geertsma's model is based largely on analogies between solid-state and liquid-state structures. It should be noticed that the equiatomic liquid compound in the Cs-Sn system does not correspond to a congruently melting solid compound. Rather, the congruently melting compound and the top of the liquidus is to be found at 60 at.% Sn [18], whereas the solid Zintl compound in the crystalline state does not exist at higher temperatures, probably because of packing problems. We assume that the liquid is more flexible to accommodate the sizeable cesium atoms. The same situation occurs in some alkali-T1 and alkali-In alloys, where we have concluded to the existence of fragmented Zintl ions in liquid alloys with K, Rb and Cs, while there are no corresponding crystalline compounds [3,19-21]. Table 1 lists for all alkali-lead and alkali-tin systems the maximum resistivity values and the compositions and the temperatures for which they are obtained. Evidently the resistivities increase monotonically with the size of the alkali metal. Also there is a shift in the peak position between the Li compound and the K compound. Na-Pb and, more clearly, Na-Sn are transition cases exhibiting side peaks (see also figs. 3 and 4). Geertsma has interpreted the results in terms of the strength of the covalent-metallic interaction between the lead or tin atoms, respectively [8]. The non-clustering equiatomic case was represented by a CsCl-type configuration. The inter-
action between atoms on the same tetrahedral clusters is called U, the interaction between nearest atoms on two neighbouring clusters is V, that in the CsC1 configuration is T. Important for the stability is the ratio U/V. A large U stabilizes the clustered configuration. Electron transfer is mainly determined by hopping between tetrahedral clusters. A low V corresponds to a high resistivity in the clustered configuration. Now V is largely determined by the size of the alkali atoms pushing the lead or tin atoms apart. Consequently with increasing size of the alkali atom V decreases, the resistivity, p, increases and the clustered configuration becomes more stable. This is all in agreement with the data in table 1. Table 1 also shows that the resistivities of the tin alloys are systematically higher than those of the corresponding lead alloys. Probably the density of states in the covalent pseudogap, determined largely by the electronic structure of the
K-Sn •
.W-
550 °C
A 650 °C 0 700 oC
E U
*
850 ° C
[] 900 °C C) v2
.>
*
°~
u) ~p n0
1
[]
6
oxrl
4(A
e0
I 20
I 40
I 60
0 I 80
100
Sn c o n c e n t r a t i o n in at.gS Fig. 1 The reslshvity, p, of liqmd K - S n alloys as a function of composition at the temperatures indicated m the figure
R Xu et al / Electncal resatmtzes of bquld K-h
Table 1 The values of p and dp/dT at compound-forming tions for the alkali-Pb and alkali-Sn systems
composl-
C,,, (at.% Pb or Sn)
T PC)
Ll-Pb Na-Pb K-Pb Rb-Pb Cs-Pb
20.5 22.5 50.0 50.0 500
730 400 575 601 620
440 460 980 2200 7000
- 0.48 - 0.78 - 4.60 -18 - 115
[31 Dl [31 Dl El
LI-Sn
20 0 23.0 43 0 50.0 50.0
775 440 490 850 900
850 570 880 3100 14200
- 2.10 - 1.50 - 4.70 -30 - 130
[41 141 [41
System
Na-Sn
K-Sn Cs-Sn
Ref.
dp/dT
&fl
295
and Cs-Sn alloys
Na-Sn _____-
cm) (~a cm/ K-‘1
present present
tetrahedra, is smaller in (Sn,j4- than in (Pb4j4-. Then the resistivity results follow from the Kubo-Greenwood formula. As shown in figs. 3 and 4, the resistivity results exhibit a qualitative similarity for these two sets
0
20
40
Sn concentratiI7
100
in a?%
Fig. 3 The resistivitles, p, of hqmd alkah-Sn alloys near the hqmdus temperature
Cs-Sn l 15
* G -i *
x
c
.L
‘;._ ti
oz
5
I
750 Oc
A 800 ‘C 0 850%
*
*
900 OC
0
94OY
0 0
*
0
go O 0
I I
0
Sn concentration
in at.%
Fig 2. The reslstmlty, p. of hqmd Cs-Sn alloys as a function
of composltlon at the temperatures
indicated in the figure.
of systems. However, going from the Li systems to the Cs systems, the transition from non-clustered to clustered (observed as a transition from octet compound to equiatomic compound) sets 1s slightly earlier for the tin alloys (where in NaSn the octet and the nearly-equiatomic compound give rise to resistivity maxima of almost equal magnitude), than for the lead alloys (where in Na-Pb the clustered compound is only marginally visible in the resistivity results). This is a consequence of U being slightly larger for Sn than for Pb, because the Sn atoms are smaller than the Pb atoms. So all the experimental data excellently fit Geertsma’s model, This success is, however, qualified by the recognition that this model is an obvious idealization, since it supposes that all the lead or tin atoms participate in the clusters. This is highly improbable. Closer investigation, both theoretical and experimental, of the chemical
296
R. Xu et al /Electrtcal reststwtttes of hqutd K-Sn and Cs-Sn alloys
resistivity measurements. This work forms part of the research programme of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research on Matter (FOM)) and was made possible by financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organisation for Scientific Research (NWO)).
LI-Pb No-Pb K-Pb
"-"5
E U
Rb-Pb
:L4 Ca-Pb
0
References
1
0
0
I 20
I 40
I 60
80
100
Pb concentrotion in ot.gS Fig 4. The resistlv]tles, p, of liqmd alkah-Pb alloys near the liquldus temperature
equilibrium is necessary for a better understanding of this problem.
5. Conclusions Measurements of the resistivities of liquid K-Sn and Cs-Sn alloys are in agreement with predictions from earlier measurments on alkalilead and alkali-tin alloys. More particularly, the stoichiometry as derived from the resistivity measurements indicates Zintl ion formation. Further, the resistivities increase monotonically from LiSn to Cs-Sn. All these results confirm Geertsma's model. The authors acknowledge with thanks the technical assistance of Mr F. van der Horst, J.F.M. Wieland, R. Kinderman and H. Bron during the
[1] V T Nguyen and J E Enderby, Phdos Mag. 35 (1977) 1013. [2] J A. Meijer, G J B. Vinke and W. van der Lugt, J Phys F16 (1986) 845 [3] J.A Meuer, W Geertsma and W van der Lugt, J Phys F15 (1985) 899. [4] C. van der Marel, A.B. van Oosten, W. Geertsma and W. van der Lugt, J Phys. F12 (1982) 2349. [5] W. van der Lugt and W Geertsma, Can J Phys. 65 (1987) 326 [6] M-L. Saboungl, G.K. Johnson, D L Price and H.T J Re0ers, High Temp. Sci 26 (1990) 335. [7] W van der Lugt, Phys Scr. T39 (1991) 372. [8] W Geertsma, J Dljkstra and W van der Lugt, J. Phys. F14 (1984) 1833 [9] W Geertsma, J Phys. C18 (1985) 2461 [10] W. Geertsma, J. Phys.: Condens. Matter 2 (1990) 8517. [11] C. van der Marel, W. Geertsma and W van der Lugt, J. Phys F10 (1980) 2305. [12] C van der Marel, P.C. Stem and W. van der Lugt, Phys Lett 95A (1983) 451. [13] S Takeda, S. Matsunaga and S. Tamakl, J. Phys. S o c Jpn 53 (1984) 1448 [14] S. Takeda and S. Tamakl, J Phys F18 (1988) IA5. [15] H T.J Reljers, M.-L Saboungl, D L. Price and W van der Lugt, Phys. Rev. B41 (1990) 5661 [16] R Xu, R ganderman and W van der Lugt, J. Phys.: Condens. Matter 3 (1991) 127 [17] R. Xu, R.A de Groot and W. van der Lugt, J Phys Condens. Matter 4 (1992) 2389 [18] T B Massalski, J L Murray, L H. Bennet, H. Baker and L Kaprzak, Binary Alloy Phase Diagrams (American Society for Metals, Metals Park, OH, 1986). [19] M. Kltajlma and M. Shlmoji, in: Llqmd Metals, Inst Phys Conf Series 30 (1977) 226. [20] R. Xu and W. van der Lugt, these Proceedings, p 289 [21] W. van der Lugt and R. Xu, m. Recent Developments m the Physics of Flmds (Adam Hdger, Bristol, 1992) p F249.
Journal of Non-Crystalhne Solids 156-158 (1993) 293-296 North-Holland
~
U
The electrical resistivities of liquid K-Sn and Cs-Sn alloys R. X u , T. d e J o n g e a n d W. v a n d e r L u g t Sohd State Phystcs Laboratory, Unwerstty of Gronmgen, Nqenborgh 4, 9747AG Gronmgen, The Netherlands
The electrical res~stivlty, p, of llqmd K-Sn and Cs-Sn alloys has been measured as a function of composition and temperature The reslstivities of both systems exhibit very sharp peaks close to the equlatomlc composition At the same compos~tmn, the temperature dependence of the res~stwlty has a deep mlmmum The maximum reslstw~t~esare 3100 and 14200 i~ll cm respectively. Comparison with the L1-Sn and Na-Sn alloys and with the alkah-lead systems strongly suggests that Zintl ions are formed in the liqmd
1. Introduction
2. Experimental
The electrical resistivities of liquid K - S n and C s - S n were determined experimentally as part of a systematic investigation of the resistivities of liquid alkali-lead and alkali-tin alloys [1-4]. The physical interest of the present work is to confirm the expected similarity between the liquid alkali-tin alloys and the corresponding alkali-lead alloys. The alkali-lead alloys form a classical example of a set of systems changing from simple ionic ( L i - P b ) to clustered configurations ( K - P b , R b - P b and Cs-Pb). Ideally, the clusters are (Pb4)4- tetrahedra ('Zintl' compounds). This transition has been confirmed by a large variety of experimental results (electrical resistivity, neutron diffraction, inelastic neutron scattering, thermodynamic properties), for which we refer to some review papers [5-7]. The clust e r e d - n o n - c l u s t e r e d transition has been described theoretically by G e e r t s m a [8-10]. Earlier investigations on alkali-tin systems [4,11-15] showed that they most probably also form a category of alloys which are precisely described by G e e r t s m a ' s model. The present m e a s u r e m e n t s aim at further verifying this supposition.
A m o n g the alkali-tin and alkali-lead alloys, the K - S n and C s - S n systems are the most difficult from an experimental point of view and earlier attempts were not quite successful. The experimental problems are a consequence of strong evaporation, high corrosivity and the need of high temperatures (1200 K). For K - S n alloys, the metal tube method was used. For experimental details, we refer to refs. [16,17]. Since we expected the resistivities of the C s - S n system to be much higher than those of the K - S n system, a four-probe method was adopted. The experimental set-up was the same as previously used for the liquid C s - P b system [2]. The R b - S n system has not been investigated because one may safely assume that the results are intermediate between those for K - S n and Cs-Sn. The inaccuracy in the values for the resistivities is estimated to be + 2% for K - S n and + 5 % for Cs-Sn.
Correspondence to. Dr W. van der Lugt, Sohd State Physics
Laboratory, Unwersity of Groningen, Nuenborgh 4, 9747 AG, Gronmgen, The Netherlands. Tel.' + 31-50 634 828. Telefax +31-50 634 825
3. Results Figure 1 gives the resistivities of K - S n alloys plotted as a function of composition. The experiments cover the entire concentration range. Figure 2 gives the resistivities of C s - S n alloys. The measurements exhibit a gap between 7 and 40
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V All rights reserved
294
R Xu et al. / Electrical reststwmes of hqutd K-Sn and Cs-Sn alloys
at.% Sn, where, as a consequence of experimental difficulties, no reliable data could be obtained. Both systems exhibit a high and sharp peak at a composition of 50 at.% Sn of either component. The maximum resistivity values are far beyond the purely metallic range; that for Cs-Sn is higher than in any other alkali-lead or alkali-tin system.
4. Discussion
We show below that the observed maximum resistivities and the positions of these maxima (interpreted as stoichiometric compositions) fit nicely into Geertsma's model. Anticipating this discussion, we assume that at least a fraction of the atoms occurs in tetrahedra ( S n 4 ) 4 - . Geertsma's model is based largely on analogies between solid-state and liquid-state structures. It should be noticed that the equiatomic liquid compound in the Cs-Sn system does not correspond to a congruently melting solid compound. Rather, the congruently melting compound and the top of the liquidus is to be found at 60 at.% Sn [18], whereas the solid Zintl compound in the crystalline state does not exist at higher temperatures, probably because of packing problems. We assume that the liquid is more flexible to accommodate the sizeable cesium atoms. The same situation occurs in some alkali-T1 and alkali-In alloys, where we have concluded to the existence of fragmented Zintl ions in liquid alloys with K, Rb and Cs, while there are no corresponding crystalline compounds [3,19-21]. Table 1 lists for all alkali-lead and alkali-tin systems the maximum resistivity values and the compositions and the temperatures for which they are obtained. Evidently the resistivities increase monotonically with the size of the alkali metal. Also there is a shift in the peak position between the Li compound and the K compound. Na-Pb and, more clearly, Na-Sn are transition cases exhibiting side peaks (see also figs. 3 and 4). Geertsma has interpreted the results in terms of the strength of the covalent-metallic interaction between the lead or tin atoms, respectively [8]. The non-clustering equiatomic case was represented by a CsCl-type configuration. The inter-
action between atoms on the same tetrahedral clusters is called U, the interaction between nearest atoms on two neighbouring clusters is V, that in the CsC1 configuration is T. Important for the stability is the ratio U/V. A large U stabilizes the clustered configuration. Electron transfer is mainly determined by hopping between tetrahedral clusters. A low V corresponds to a high resistivity in the clustered configuration. Now V is largely determined by the size of the alkali atoms pushing the lead or tin atoms apart. Consequently with increasing size of the alkali atom V decreases, the resistivity, p, increases and the clustered configuration becomes more stable. This is all in agreement with the data in table 1. Table 1 also shows that the resistivities of the tin alloys are systematically higher than those of the corresponding lead alloys. Probably the density of states in the covalent pseudogap, determined largely by the electronic structure of the
K-Sn •
.W-
550 °C
A 650 °C 0 700 oC
E U
*
850 ° C
[] 900 °C C) v2
.>
*
°~
u) ~p n0
1
[]
6
oxrl
4(A
e0
I 20
I 40
I 60
0 I 80
100
Sn c o n c e n t r a t i o n in at.gS Fig. 1 The reslshvity, p, of liqmd K - S n alloys as a function of composition at the temperatures indicated m the figure
R Xu et al / Electncal resatmtzes of bquld K-h
Table 1 The values of p and dp/dT at compound-forming tions for the alkali-Pb and alkali-Sn systems
composl-
C,,, (at.% Pb or Sn)
T PC)
Ll-Pb Na-Pb K-Pb Rb-Pb Cs-Pb
20.5 22.5 50.0 50.0 500
730 400 575 601 620
440 460 980 2200 7000
- 0.48 - 0.78 - 4.60 -18 - 115
[31 Dl [31 Dl El
LI-Sn
20 0 23.0 43 0 50.0 50.0
775 440 490 850 900
850 570 880 3100 14200
- 2.10 - 1.50 - 4.70 -30 - 130
[41 141 [41
System
Na-Sn
K-Sn Cs-Sn
Ref.
dp/dT
&fl
295
and Cs-Sn alloys
Na-Sn _____-
cm) (~a cm/ K-‘1
present present
tetrahedra, is smaller in (Sn,j4- than in (Pb4j4-. Then the resistivity results follow from the Kubo-Greenwood formula. As shown in figs. 3 and 4, the resistivity results exhibit a qualitative similarity for these two sets
0
20
40
Sn concentratiI7
100
in a?%
Fig. 3 The resistivitles, p, of hqmd alkah-Sn alloys near the hqmdus temperature
Cs-Sn l 15
* G -i *
x
c
.L
‘;._ ti
oz
5
I
750 Oc
A 800 ‘C 0 850%
*
*
900 OC
0
94OY
0 0
*
0
go O 0
I I
0
Sn concentration
in at.%
Fig 2. The reslstmlty, p. of hqmd Cs-Sn alloys as a function
of composltlon at the temperatures
indicated in the figure.
of systems. However, going from the Li systems to the Cs systems, the transition from non-clustered to clustered (observed as a transition from octet compound to equiatomic compound) sets 1s slightly earlier for the tin alloys (where in NaSn the octet and the nearly-equiatomic compound give rise to resistivity maxima of almost equal magnitude), than for the lead alloys (where in Na-Pb the clustered compound is only marginally visible in the resistivity results). This is a consequence of U being slightly larger for Sn than for Pb, because the Sn atoms are smaller than the Pb atoms. So all the experimental data excellently fit Geertsma’s model, This success is, however, qualified by the recognition that this model is an obvious idealization, since it supposes that all the lead or tin atoms participate in the clusters. This is highly improbable. Closer investigation, both theoretical and experimental, of the chemical
296
R. Xu et al /Electrtcal reststwtttes of hqutd K-Sn and Cs-Sn alloys
resistivity measurements. This work forms part of the research programme of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research on Matter (FOM)) and was made possible by financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organisation for Scientific Research (NWO)).
LI-Pb No-Pb K-Pb
"-"5
E U
Rb-Pb
:L4 Ca-Pb
0
References
1
0
0
I 20
I 40
I 60
80
100
Pb concentrotion in ot.gS Fig 4. The resistlv]tles, p, of liqmd alkah-Pb alloys near the liquldus temperature
equilibrium is necessary for a better understanding of this problem.
5. Conclusions Measurements of the resistivities of liquid K-Sn and Cs-Sn alloys are in agreement with predictions from earlier measurments on alkalilead and alkali-tin alloys. More particularly, the stoichiometry as derived from the resistivity measurements indicates Zintl ion formation. Further, the resistivities increase monotonically from LiSn to Cs-Sn. All these results confirm Geertsma's model. The authors acknowledge with thanks the technical assistance of Mr F. van der Horst, J.F.M. Wieland, R. Kinderman and H. Bron during the
[1] V T Nguyen and J E Enderby, Phdos Mag. 35 (1977) 1013. [2] J A. Meijer, G J B. Vinke and W. van der Lugt, J Phys F16 (1986) 845 [3] J.A Meuer, W Geertsma and W van der Lugt, J Phys F15 (1985) 899. [4] C. van der Marel, A.B. van Oosten, W. Geertsma and W. van der Lugt, J Phys. F12 (1982) 2349. [5] W. van der Lugt and W Geertsma, Can J Phys. 65 (1987) 326 [6] M-L. Saboungl, G.K. Johnson, D L Price and H.T J Re0ers, High Temp. Sci 26 (1990) 335. [7] W van der Lugt, Phys Scr. T39 (1991) 372. [8] W Geertsma, J Dljkstra and W van der Lugt, J. Phys. F14 (1984) 1833 [9] W Geertsma, J Phys. C18 (1985) 2461 [10] W. Geertsma, J. Phys.: Condens. Matter 2 (1990) 8517. [11] C. van der Marel, W. Geertsma and W van der Lugt, J. Phys F10 (1980) 2305. [12] C van der Marel, P.C. Stem and W. van der Lugt, Phys Lett 95A (1983) 451. [13] S Takeda, S. Matsunaga and S. Tamakl, J. Phys. S o c Jpn 53 (1984) 1448 [14] S. Takeda and S. Tamakl, J Phys F18 (1988) IA5. [15] H T.J Reljers, M.-L Saboungl, D L. Price and W van der Lugt, Phys. Rev. B41 (1990) 5661 [16] R Xu, R ganderman and W van der Lugt, J. Phys.: Condens. Matter 3 (1991) 127 [17] R. Xu, R.A de Groot and W. van der Lugt, J Phys Condens. Matter 4 (1992) 2389 [18] T B Massalski, J L Murray, L H. Bennet, H. Baker and L Kaprzak, Binary Alloy Phase Diagrams (American Society for Metals, Metals Park, OH, 1986). [19] M. Kltajlma and M. Shlmoji, in: Llqmd Metals, Inst Phys Conf Series 30 (1977) 226. [20] R. Xu and W. van der Lugt, these Proceedings, p 289 [21] W. van der Lugt and R. Xu, m. Recent Developments m the Physics of Flmds (Adam Hdger, Bristol, 1992) p F249.