Ionic Conductivity in Liquid Sn Se, Sb Se and Bi Se Alloys

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(1)Materials Transactions, Vol. 43, No. 9 (2002) pp. 2235 to 2242 c 2002 The Japan Institute of Metals. Ionic Conductivity in Liquid Sn–Se, Sb–Se and Bi–Se Alloys Ryoki Uejyo, Osamu Uemura, Takeshi Usuki and Yasuo Kameda Department of Material and Biological Chemistry, Faculty of Science, Yamagata University, Yamagata 990-8560, Japan Simultaneous measurements of ionic and electronic conductivities around the stoichiometric composition have been carried out on liquid Sn–Se, Sb–Se and Bi–Se alloys by applying the residual potential theory. The ionic conductivity, σi , in liquid Sn–Se and Sb–Se alloys increases with increasing temperature, while, in liquid Bi–Se alloys, it decreases with increasing temperature. The isothermal σi in liquid Sn–Se and Sb–Se alloys at higher temperatures exhibits a minimum at the stoichiometric composition of SnSe and Sb2 Se3 , respectively, and, on the other hand, it shows a maximum at Bi2 Se3 in liquid Bi–Se alloys. Values of σi at SnSe, Sb2 Se3 and Bi2 Se3 near the melting temperature are 7.40 Sm−1 at 1173 K, 0.448 Sm−1 at 893 K and 45.3 Sm−1 at 993 K, respectively, which are about two orders of magnitude smaller than the corresponding electronic conductivities, σe . The value of σi of liquid Bi2 Se3 , which is the largest among three liquids, is roughly comparable to that for ionic liquid alloys such as Ag and Tl-chalcogenides. In contrast, liquid Sb2 Se3 indicates the smallest σi due to the strong covalent bonding between unlike atoms. The minimum of the σi -isotherm at SnSe and Sb2 Se3 in liquid Sn–Se and Sb–Se alloys also reflect the covalent nature in these liquids. (Received April 25, 2002; Accepted July 5, 2002) Keywords: liquid metal-chalcogen alloy, ionic conductivity, electronic conductivity, liquid structure, magnetic susceptivility. 1. Introduction It has been well known that liquid metal-chalcogen alloys exhibit common semiconducting behaviors at the stoichiometric composition, such as deep minima of the electronic conductivity, σe , and electronic paramagnetic susceptibility, χe , and a reverse of the sign in the thermoelectric power, S.1) These behaviors have successfully been interpreted in the term of the electronic localization theory based on the strong scattering regime for electrons.1) Usuki, one of the present authors, has firstly measured the ionic conductivity, σi , over a whole range of composition in Tl–Se liquid alloys, and observed a sharp maximum of σi at the stoichiometric composition of Tl2 Se.2) The coexistence of σe -minimum and σi maximum at the stoichiometeric composition has also been found in liquid Ag–TlSe and Ag–Te alloys.3, 4) In these systems, it has been considered that the effect of the electron-ion cross conduction caused mainly by the electrostatic interactions, which disturbs smooth migration of mobile ions, is the smallest at the stoichiometric composition, where electrons are strongly localized. However, the conflicting result has recently been reported in liquid Ag–Se alloys, where both σe and σi exhibit steep maxima at the stoichiometric composition of Ag2 Se, although both maxima gradually disappear with increasing temperature.5, 6) The simultaneous appearance of σe - and σi -maxima can not be explained in terms of the ion-electron interaction effect. The authors have suggested that unusual ionic and electronic conductions observed in liquid Ag–Se alloys are closely related to the inherent structure of liquid Ag2 Se, which maintains the local atomic configuration in the fast-ion crystalline phase (α-Ag2 Se), particularly, just above the melting temperature.4) Information on σi in liquid metal-chalcogen alloys containing polyvalent metals are very scarce at present. This paper reports observed results of σi , together with those of σe , in the stoichiometric composition range in liquid Sn–Se, Sb–Se and Bi–Se alloys, applying the residual potential method. We also. explore the relationship between the ionic conduction and liquid structure in these alloys. 2. Experimental Procedures Purities of Sn, Sb, Bi and Se used were all better than 99.99%. Alloys with the required composition were prepared by enclosing together elemental components into an evacuated fused quartz ampoule and mixing thoroughly in the molten state. The fused quartz d.c. conductivity cell with four tungsten electrodes was used for the measurement of σi and σe , which is identical to that in our previous measurement.2, 3) The electrodes were cleaned in advance by the electrolysis in a dilute solution of NaOH. The molten alloy was inserted in the cell under the Ar atmosphere of about 0.1 MPa. The cell constant was determined at room temperature, using purified liquid Hg. The temperature of the sample was measured by the calibrated CA thermocouple attached to the central position of the sample. σi and σe were separately obtained by employing the residual potential theory developed by Yokota.7) Essential details of the theory are described as below. A constant d.c. current is applied to the sample across the electrodes. When mobile ions in the alloy participate in the conduction together with electrons, we can observe the potential decay process immediately after switching on and off. σe is directly obtained from the steady-state potential, VS , according to the relation, VS = jl/σe , where j and l denote the current density and distance between electrodes, respectively. σi relates to the residual potential at the instant of switching off, Vr0 , through the equation of Vr0 / Vs = σi /(σi + σe ). Thus, if Vr0 is enough large to be deduced from the potential decay curve, σi can be calculated from the ratio of Vr0 / Vs . The magnetic susceptibility, χ , of alloys was measured by the Faraday method, using the torsion balance. Details for the measurement have been discribed previously.8).

(2) 2236. R. Uejyo, O. Uemura, T. Usuki and Y. Kameda. 3. Experimental Results Figure 1 shows the temperature dependence of σi in liquid Sn–Se, Sb–Se and Bi–Se alloys, respectively. Usuki has pointed out in liquid Tl–Se alloys that the temperature change of σi near the stoichiometric composition does not necessarily follow the simple thermal activation process. The present σi at the stoichiometric composition of SnSe in liquid Sn–Se. alloys depends little on temperature. In liquid Bi–Se alloys σi has rather the negative temperature dependence at any composition covered, being consitent with that observed around Ag2 Se in liquid Ag–Se alloys.4) Composition dependences of σi in liquid Sn–Se, Sb–Se and Bi–Se alloys are summarized in Fig. 2. Most of σi , which have been hitherto observed in liquid metal-chalcogen alloys, take the sharp maximum at the stoichiometric composi-. Fig. 1 1/T plots of ionic conductivities, σi , in liquid Sn–Se (a), Sb–Se (b) and Bi–Se (c) alloys, respectively..

(3) Ionic Conductivity in Liquid Sn–Se, Sb–Se and Bi–Se Alloys. 2237. Both temperature and composition dependences of isothermal σe in liquid Sn–Se, Sb–Se and Bi–Se alloys are given in Figs. 3 and 4, respectively. Although σe in liquid metalchalcogen alloys usually exhibits a minimum at the stoichiometric composition due to the electron localization,1) the minimum of σe in liquid Sb–Se and Bi–Se alloys is less clear owing to extremely low values of σe at the Se-rich side. 4. Discussions 4.1 Ionic conductivity Assuming that all metallic atoms in the alloy are fully ionized and participate in the ionic conduction, the number density, n i , and mobility µi , of metal i can easily be calculated using the observed σi , through equation, σi σi µi = = , (1) eni eρ0 x i where x i and ρ0 denote the atomic fraction of metal i and average number density of atoms in the alloy, respectively. Table 1 lists calculated results of µi in liquid Sn–Se, Sb– Se and Bi–Se alloys, respectively. The value of µi at SnSe and Sb2 Se3 are considerably smaller than that reported in liquid monovalent metal-chalcogen alloys with the ionic feature (e.g., 358 × 10−10 at Ag2 Se (1173 K),4) 62 × 10−10 at Ag2 Te (1233 K),4) and 78 × 10−10 m2 V−1 s−1 at Tl2 Se (713 K),2) respectively). Therefore, liquid SnSe and Sb2 Se3 cannot be classsified as the ionic liquid and are different from liquid silver-chalcogenides. On the other hand, liquid Bi2 Se3 has the same order of magnitude of µi as liquid silver-chalcogenides. It has often been pointed out that the temperature change. Table 1 Values of ionic transport parameters (σi , n i , µi ,) in liquid Sn–Se (1173 K), Sb–Se (1013 K) and Bi–Se (1013 K) alloys, respectively.. Fig. 2 Compositional plots of ionic conductivities, σi , in liquid Sn–Se (a), Sb–Se (b) and Bi–Se (c) alloys, respectively.. tion.2–4) The maximum of σi at Bi2 Se3 in liquid Bi–Se alloys in Fig. 2(c) is such an example. Nevertheless, the minimum of σi is observed at SnSe in liquid Sn–Se, and at Sb2 Se3 at higher temperatures in Sb–Se alloys.. composition/ at%M. σi / S·m−1. ni / 1028 m−3. µi / 10−10 m2 ·V−1 s−1. Sn–Se system 52 51 50 49 48 47 45 43. 16.8 13.2 7.40 8.01 9.09 13.3 11.4 10.5. 1.74 1.71 1.68 1.64 1.60 1.57 1.51 1.45. 30.1 24.1 13.8 15.2 17.8 26.4 23.6 22.7. Sb–Se system 57 50 47.5 45 40 37.5 35 Bi–Se system 50 43 40 37.5 35. 7.81 3.78 1.63 1.27 0.821 1.02 0.939 19.6 31.7 41.3 28.5 16.0. 1.79 1.57 1.49 1.40 1.25 1.17 1.09 14.7 1.26 1.18 1.09 1.04. 9.07 5.03 2.23 1.89 1.37 1.81 1.80 27.7 52.3 72.8 54.4 32.0.

(4) 2238. R. Uejyo, O. Uemura, T. Usuki and Y. Kameda. Fig. 3 1/T plots of electronic conductivities, σe , in liquid Sn–Se (a), Sb–Se (b) and Bi–Se (c) alloys, respectively.. of σi in liquid metal-chalcogen alloys does not obey the simple thermal activation process because of the effect of the electron-ion cross conduction due to the electrostatic interactions. This effect disturbs smooth migration of mobile ions. Particularly, this effect appears in the temperature dependence of σi at the stoichiometric composition, because the electron localization rapidly weakens with increasing temperature. In fact, it has been observed in liquid monovalent metal-chalcogen alloys that the temperature dependence of σi at the stoichiometric composition is relatively small due to the. cancellation of the thermal activation and ion-electron cross conduction effects. Similarly, the temperature dependence of σi at SnSe and Sb2 Se3 in liquid Sn–Se and Sb–Se alloys becomes smaller than that at other compositions. However, in liquid Bi–Se alloys, strong negative dσi /dT is observed at all compositions covered, which can not be explained at present. The similar negative dσi /dT has been observed at Ag2 Se in liquid Ag–Se alloys.4) Usuki et al. have interpreted the negative temperature coefficient of σi in liquid Ag2 Se, in connection with the significant change of the local atomic configu-.

(5) Ionic Conductivity in Liquid Sn–Se, Sb–Se and Bi–Se Alloys. 2239. Fig. 5 A sketch of the crystalline lattice of Sb2 Se3 .. Now we discuss the relationship between the magnitude of σi (or µi ) and short-range structure, by using structural data of liquid Sb2 Se3 and Bi2 Se3 .9, 10) The crystalline structure of Bi2 Se3 is a distorted NaCl type with the partial ionic nature, in which one Bi atom is surrounded by three Se atoms in the intralayer and one Se atom in the neighboring layer (the shorter Bi–Se distance) and 2.5 Se in the neighboring layer (the longer one).11) Crystalline Sb2 Se3 has the same structure type, but the shorter bonds are considerably covalent, while, the bonding between neighboring layers is much looser. Then, crystalline Sb2 Se3 seems to be constructed by dimmer molecules, Sb4 Se6 , as described in Fig. 5.12) That is to say, it possesses the covalent (3+3) folded structure rather than the ioninc (4 + 2) folded one. Neutron diffraction measurements have been made by the authors’ group for liquid Sb2 Se3 at 943, 993 and 1043 K, and liquid Bi2 Se3 at 1073 K. Pair distribution functions, g(r), are represented in Fig. 6.9, 10) Provided that the local structural order is unchanged in liquid and crystalline states, the longer Sb (or Bi)-Se bond distance should fall at a little shorter r side of the valley between the first and second peaks in g(r). This valley of g(r) is much shallower in liquid Bi2 Se3 than that in liquid Sb2 Se3 , this means that the contribution of the longer Bi–Se most be significant, whereas, that of the longer Sb–Se one is almost absent. We now investigate the contribution of Sb (or Bi)-Se bonds in both liquid Sb2 Se3 and Bi2 Se3 by the least squares fit of the model function to the observed structure factor, S(Q). The following model structure factor, S model (Q), was employed, ci n ij f i f j sin(Qrij ) 1 2 S model (Q) = , 2 exp − lij Q 2 Qrij ci f i (2). Fig. 4 Compositional plots of electronic conductivities, σe , in liquid Sn–Se (a), Sb–Se (b) and Bi–Se (c) alloys, respectively.. ration caused by the thermal energy.4) At present, it does not seem to be legitimate to neglect the structural effect for discussing the ionic conduction in liquid metal-chalcogen alloys.. where ci , f i and n ij are the concentration of atom i, coherent form factor of atom i, and number of atoms j around a given atom i, respectively. Parameters lij and rij in eq. (2), denote the root mean square displacement and bond distance of i– j pairs, respectively. In the present fit, we assumed that the ratio of the longer bond distance of Sb (or Bi)-Se pairs to the shorter one remains constant upon melting, e.g., the same ratio in liquid and crystalline states. Then, only n ij , besides lij , becomes variable in the present fit. Table 2 shows the calculated result of structural parameters.

(6) 2240. R. Uejyo, O. Uemura, T. Usuki and Y. Kameda. isotherm at Sb2 Se3 in Fig. 2(b) becomes deeper with increasing temperature may correspond to the enhancement of the molecular feature at higher temperatures. Crystalline SnSe has high- and low-temperature phases, both of which are distorted NaCl types.13, 14) However, the low-temperature phase is more directional and more covalent compared with the high-temperature one. According to the neutron diffraction measurement by Itoh et al.,15) the nearest neighbor distance and coordination number in liquid SnSe (283 pm and 3.4, respectively) determined from the position and area of the first peak in g(r) are not closer to those in the high-temperature phase (300 pm and 5.0, respectively), but to those in the low-temperature one (285 pm and 3.0, respectively).13, 14) Possibly, the minimum of the σi -isotherm at SnSe in liquid Sn–Se alloys in Fig. 2(a) may reflect the covalent nature in the liquid state.. Fig. 6 Pair distribution functions, g(r ), in liquid Sb2 Se3 at 943, 993 and 1043 K, and in liquid Bi2 Se3 at 1073 K, respectively.. Table 2 Structural parameters within the first two nearest neighbor distances in liquid Sb2 Se3 and liquid Bi2 Se3 calculated through the least squares fit. r (short)/ pm. r (long)/ pm. n (short). n (long). Liquid Sb2 Se3 943 K 993 K 1043 K Crystal. rSbSe 273 270 270 270. rSbSe 325 324 324 324. n SbSe 3.1 3.1 3.0 3.0. n SbSe 1.8 1.7 1.5 3.5. Liquid Bi2 Se3 1073 K Crystal. rBiSe 280 286. rBiSe 322 330. n BiSe 4.2 4.0. n BiSe 2.3 2.5. for both liquids, together with the corresponding ones in the crystal. An agreement of the parameters in liquid and crystalline Bi2 Se3 encourages us to believe the presence of some kind of crystalline ionic order in the liquid state. The parameters for liquid Sb2 Se3 denote that the nearest neighbor covalent Sb–Se bonds within intra-dimmers in Fig. 5 remain strengthened as in crystalline state, and, on the other hand, the longer Sb–Se bonds are considerably lost on melting and are further weakened with increasing temperature (a rapid decrease of n SbSe on melting in the Table 2), that is, the molecular feature with Sb4 Se6 dimers is enhanced. This structural change may relate to the smaller µ3+ Sb in liquid Sb2 Se3 in Table 1. Further, the tendency that the minimum of σi -. 4.2 Electronic conductivity The σe -isotherm in liquid metal-chalcogen alloys generally exhibits a deep minimum at the stoichiometric composition due to the occurrence of the electron localization.1) However, the minimum of σe at Sb2 Se3 and Bi2 Se3 in liquid Sb–Se and Bi–Se alloys in Figs. 4(b) and (c) is less clear owing to low values of σe at the Se-rich side. We have attempted to confirm the occurrence of the electron localization at the stoichiometric composition in the present liquid alloys through the measurement of the magnetic susceptibility, χ , the results are shown in Fig. 7. When conduction electrons are strongly localized at the stoichiometric composition, the observed χ should exhibit the diamagnetic maximum there, corresponding to a rapid decrease in the electronic paramagnetic contribution. The diamagnetic peak obviously appeared at the stoichiometric composition in these alloys as shown in Fig. 7. The degree of the electron localization can be quantitatively expressed in terms of the g-factor, which is the ratio of the density of electronic states at the Fermi level, E F , to the free electron value. According to the strong scattering regime for electrons,16) σe can be described as follows, e2 (3) ak2 g 2 , 3π 2 h F where a is the interatomic distance corresponding to the lowest value of the electron mean free path (a ∼ = 300 pm for liquid selenides), and kF is the Fermi wave vector.17) Assuming that the number of conduction electrons is taken to be two per atom for Sn, three per atom for Sb and Bi, respectively, and two electrons per atom are supplied into the conduction band for Se, we can find g(1173 K) ∼ = 0.20 at SnSe, ∼ 0.03 at Sb Se and g(993 K) g(893 K) ∼ = 0.42 at Bi2 Se3 , = 2 3 respectively, using the observed σe . g 1/3 has been taken as the criterion for the electronic localization.16) Therefore, it appears that electrons in liquid Sb2 Se3 are the most localized, reflecting the strong covalent bonds between unlike atoms. The degree of the atomic ionization in the alloy can be investigated using observed temperature dependences of σe and χ . According to the strong scattering regime for electrons,1) the following relation is established between σe and χ , through an implicit factor, N (E F ) (N (E F ): the number density of electronic states at E F ), σe =.

(7) Ionic Conductivity in Liquid Sn–Se, Sb–Se and Bi–Se Alloys. Fig. 7 Compositional plots of magnetic susceptibilities, χ, in liquid Sn–Se (●), Sb–Se (■) and Bi–Se (▲) alloys, respectively.. 2241. Fig. 9 The composition dependence of χd (solid lines) in liquid Sn–Se (●), Sb–Se (■) and Bi–Se (▲) alloys, respectively. χd,ion is given as the broken line in the figure.. line, when the alloy composition approaches the stoichiometric one. The result indicates that metallic ions in the latter two alloys are not fully ionized at the stoichiometric composition. The estimation for the atomic ionization at the stoichiometric composition does not conflict with structural and bonding features in these liquid alloys. 5. Conclusion. 1/2. Fig. 8 The relationship between χ and σe. in liquid Sn–Se alloys.. 1. χ = χd + Cσe2 ,. (4). where χd represents the total diamagnetic contribution by bound electrons in the alloy. The proportional constant C depends on the electronic band structure and scattering mecha1/2 nism of electrons. For example, plots of χ vs σe in liquid Sn–Se alloys are shown in Fig. 8, from which we can get the 1/2 value of χd by the extrapolation of lines to the σe = 0 axis. Figure 9 gives plots of χd vs. composition in liquid Sn–Se, Sb–Se and Bi–Se alloys, together with χd,ion calculated from the ionic model; χd,ion = cM χM(+) + (1 − cM )χSe2− . 2+. 3+. 3+. 2−. (5). Ionic susceptibilities of Sn , Sb , Bi and Se were taken from the table of Selwood.18) The value of χd at Bi2 Se3 in liquid Bi–Se alloys is found near the χd,ion line, while, that in liquid Sn–Se and Sb–Se alloys far away from the χd,ion. The ionic conductivity, σi , and electronic conductivity, σe , in the stoichiometric composition range in liquid Sn–Se, Sb– Se and Bi–Se alloys have been measured simultaneously by applying the residual potential theory. The results can be summarized as follows, (1) σi in liquid Sn–Se and Sb–Se alloys increases with increasing temperature, but, in liquid Bi–Se alloys, it decreases with increasing temperature. (2) The σi -isotherm in liquid Sn–Se alloys, and that at high temperatures in liquid Sb–Se alloys exhibit a minimum at stoichiometric compositions of SnSe and Sb2 Se3 , respectively. In stead, in liquid Bi–Se alloys, it shows a maximum at the stoichiometric composition of Bi2 Se3 , similar to the case of ionic liquid alloys such as Ag–Se and Tl–Se. (3) Magnitudes of σi in liquid SnSe, Sb2 Se3 and Bi2 Se3 are found to be 7.40 (1173 K), 0.488 (893 K) and 45.3 Sm−1 (993 K), respectively, which are about two orders of magnitude smaller than σe in the corresponding liquids. (4) σi in liquid Bi2 Se3 is roughly close to that in liquid Tl2 Se and Ag2 Se with the structural ionicity. On the other hand, liquid SnSe and, particularly, liquid Sb2 Se3 indicate much lower σi because of its covalent nature..

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