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Conduction path of the sodium ion in Na3InCl6 studied by X-ray diffraction and 23Na and 115In NMR
Solid State Ionics 176 (2005) 823 – 829 www.elsevier.com/locate/ssi
Conduction path of the sodium ion in Na3InCl6 studied by X-ray diffraction and 23Na and 115In NMR Koji Yamada*, Keiji Kumano, Tsutomu Okuda Graduate School of Science, Hiroshima University, Department of Chemistry, Kagamiyama 1-3, 739-8526 Higashi-Hiroshima, Japan Received 18 July 2004; received in revised form 16 October 2004; accepted 20 October 2004
Abstract The crystal structure of Na3InCl6 was determined at 200 K by the single-crystal X-ray analysis. The crystal belongs to a trigonal system in which an isolated InCl63 anion and two crystallographically nonequivalent sodium ions Na(1) and Na(2) are confirmed. At 450 K, however, the Rietveld analysis suggested that a new site was occupied by the sodium ion forming vacancies at the original positions. In accordance with this observation, the 23Na NMR spectrum using a single crystal showed a coalescence phenomenon of the two crystallographically different peaks at around 400 K. These observations support the dynamical chemical exchange between Na(1) and Na(2) through newly occupied Na(3) site. Although the ionic conductivity for this compound was not so high (2105 S cm1 at 500 K), the conduction path for the sodium ions was able to be proposed clearly. D 2004 Elsevier B.V. All rights reserved. Keywords: Single-crystal NMR; Sodium ion conductor; X-ray diffraction; Conduction mechanism; Ternary halide
1. Introduction The ternary chlorides Li2MIICl4 have been studied extensively because of their high lithium ion conductivity [1–6]. Especially Li2MgCl4 having spinel structure shows the high conductivity ~101 S cm1 at 673 K [1]. The mechanism of the high ionic conductivity for these ternary chlorides has been investigated by X-ray or neutron diffraction technique [1–5] and high-resolution solid-state 7Li NMR [6]. On the other hand, ternary chlorides Li3MIIIX6 (X=Cl, Br) have been also investigated and the highest ionic conductivity among them was reported for Li3InCl6 (0.2 S cm1 at 573 K) [7–10]. We synthesized new lithium ion conductor Li3InBr6 and reported that this crystal undergoes a superionic phase transition at 314 K with the high conductivity of about 103 S cm1 at 330 K [11–13]. Although no structural analyses were reported on the low-temperature phase,
* Corresponding author. Tel.: +81 82 424 7418; fax: +81 82 424 0727. E-mail address: [email protected] (K. Yamada). 0167-2738/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2004.10.016
our 81Br NQR spectrum suggested the existence of an isolated InBr63 anion. On the other hand, our preliminary DSC measurement suggested the positional disorder not only In3+ but Li+ above T tr. With increasing temperature, however, this two-dimensional order is destroyed gradually and its powder pattern becomes quite similar to that of LiBr except some superlattice reflections. These superlattice reflections correspond to a lattice constant twice as that of the LiBr f.c.c. lattice [13]. This finding may suggest that the cationic site of the rock salt structure can be replaced by In3+ keeping an electroneutrality rule, 3Li+=In3++25. A quite similar phenomenon was reported in the NaCl–CdCl2 system, in which not only Na2CdCl4 but 6NaCl–CdCl 2 was reported [14]. The latter compound was known as a Suzuki phase and the structure was identified to be a f.c.c. lattice with the lattice constant twice as that of NaCl in which two Na+ is replaced by Cd2+ and vacancy. Kanno et al. [15] reported similar structure for Li6MCl8 (M=FeII and CoII). If trivalent cations can be introduced keeping the rock salt structure, high ionic conductivity is expected. Hence,
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we have interested in the cationic conductors having rock salt structure especially for the system between alkali halides and InX3 (X: Cl and Br) because the ionic radius of In3+ is quite similar to that of Li+. The main purpose of this study is to develop new ionic conductors and understand the relationship between structure and conductivity for A3BX6 halides. In this report, the conduction mechanism of the sodium ion in Na3InCl6 will be discussed on the basis of the structure and the singlecrystal 23Na NMR.
2. Experimental 2.1. Sample preparation Single crystal of Na3InCl6 was synthesized from the melt using a Bridgman furnace. Although Na3InCl6 was reported to be an incongruent melting compound [7], a transparent part of the grown crystal was proved to be a single crystal of Na3InCl6 by means of the X-ray analysis and also by the 23Na and 115In NMR. In this study, polycrystalline samples were also prepared from the single crystal. 2.2. X-ray diffraction A single crystal suitable for the X-ray diffraction was selected from the broken pieces of the large single crystal. Because of the slight hygroscopic property of the compound, the crystal was covered by paraffin oil and the intensity data were collected at 200 K with an Oxford Cryostream cooler. All measurements were made by a Mac Science DIP2030 imaging-plate diffractometer with monochromatized Mo Ka radiation (k=0.71069 2). The crystallographic data and details of the structural determinations for Na3InCl6 are summarized in Table 1. The powder X-ray diffraction was observed using a Rigaku Rint PC diffractometer with a homemade variable temperature attachment. Structural parameters at 298 and 450 K were refined by a Rietveld method [16]. 2.3. Conductivity and NMR measurements Impedance measurement was performed by a complex impedance method using a cylindrical ceramic cell with two stainless electrodes. A computer-controlled system with a GP–IB interface was used for the measurement. The frequency range covered was 42 Hz–5 MHz using HIOKI 3522 LCR meter. 23Na and 115In NMR were observed using a single crystal and a polycrystalline sample by means of a homemade pulsed spectrometer at 6.4 T which corresponds to 71.74 MHz for 23Na and 59.44 MHz for 115In. A singlepulse sequences followed by a Fourier transformation was
Table 1 Crystallographic Data for Na3InCl6 at 200 K Temperature Formula weight Diffractometer Wavelength Crystal size Crystal system a c V Space group Z value D calc l 2h max No. of reflections measured Structure solution Refinement Least squares weights No. observations (IN0.00r(I)) No. variables Residuals: R 1 (IN2.0r) Residuals: wR 2 (IN0.0r) Max shift/error in final cycle Max peak in final diff map Min peak in final diff map
200(1) K 396.51 Mac Science DIP2030 0.71069 2 0.10.10.15 mm trigonal 6.8915(1) 2 12.3820(4) 2 509.27(2) 23 P-31c (#163) 2 2.586 g cm3 39.40 cm1 55.98 Total: 2151 Unique: 415 Direct method (SIR92) Full-matrix least-squares on F 2 P w( Fo2Fc2)2 415 18 0.024 0.072 0.000 0.44e/23 1.13e/23
applied for all measurements. Typical dead time of our spectrometer was ca. 3 As.
3. Results and discussion 3.1. Single-crystal X-ray analysis on Na3InCl6 at 200 K Fig. 1 and Table 2 show the structure and the structural parameters for Na3InCl6, respectively. The crystal belongs to a trigonal system with space group P-31c (# 163). In this trigonal crystal, the chloride ions form a hexagonal close packing (hcp) perpendicular to the c-axis, in contrast to the cubic close packing (ccp) of the bromide ions found in Li3InBr6 [13]. As Fig. 1(a) shows, there are two crystallographically different cationic layers at z=1/4 (3/4) and c1/ 2, the former contains both In3+ and Na+(1) and later contains only Na+(2). All these cations locate on the special high symmetry positions 32 or 3 and the coordinations around these cations are shown in Fig. 1(c). The InCl63 anion distorts only slightly along the three-fold axis from the regular octahedron. Na(1) and Na(2) also form NaCl6 octahedron, however, the distortion at the Na(2) site along three-fold axis is remarkable probably due to the electrostatic repulsion between In3+ and Na+. No positional disorder was found at the cationic sites at 200 K. 3.2. Conductivity and DSC measurement Fig. 2 plots the conductivity against 1/T together with our previous data on Li3InBr6. The conductivity of the
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Fig. 1. Crystal structure of Na3InCl6 at 200 K. (a) Drawing perpendicular to the c-axis and (b) parallel to the c-axis. (c) The coordination geometry around the cations.
present compound was 104 times lower than that of Li3InBr6 even at 450 K. The activation energy for the conduction was estimated to be 70.9(5) kJ mol1 from the linear portion of the rT against 1/T plot below 500 K. The conductivity and its temperature behavior for Na3InCl6 agreed well to that reported previously [7]. No anomalous behavior was observed on the DSC curve up to 600 K. These findings suggest that this crystal exhibit no phase transition keeping the hcp of the chloride ions up to at least 600 K. As will be described below, however, the onset of the sodium ion diffusion was detected at around 400 K as a NMR chemical exchange phenomenon using a single crystal of Na3InCl6. 3.3.
115
In NMR
Since Na3InCl6 belongs to a trigonal system in which all cations, In3+, Na+(1) and Na+(2), are located on the threefold axes, the quadrupole coupling tensors for these sites must be cylindrical (g=0) with their principal axes parallel to the crystal c-axis. The quadrupole coupling constant (e 2Qq/h) having axially symmetry can be easily determined from the rotational pattern around the one axis of the single crystal. Fig. 3 plots the frequency of the central transition
(m=1/2 X 1/2) of the 115In NMR as a function of the crystal rotation, h. Although 115In has nuclear spin I=9/2 and hence totally 9 allowed transitions are expected, only the central transition was measured as a function of h. As expected from the structure, only one central transition is observed. The frequency shift of the central transition due to the second-order quadrupole effect (g=0) can be expressed as [17]: mobs mL ¼ m2q =16mL ð I ð I þ 1Þ 4=3Þ
1 cos2 hsin2 / 9cos2 hsin2 / 1;
ð1Þ
where m L is the 115In Larmor frequency corresponding to the anionic species InCl63, m q=3(e 2Qq/h)/2I(2I1), / is the angle between the principal axis of the e 2Qq/h tensor and the rotation axis of the crystal, and h is the angle of the crystal rotation around the axis perpendicular to the external magnetic field H. The following parameters were obtained from the nonlinear least squares method, m L=59.4390(3) MHz, e 2 Qq /h =20.11(14) MHz and /=63.8(5). m L agrees very well to that observed for the cubic elpasolite Cs2KInCl6 which contains a regular
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Table 2 Structural parameters for Na3InCl6 at 200, 298 and 450 K Atom
Point sym.
(a) 200 In Cl Na(1) Na(2)
Kb 32 1 32 3
Atom
Point sym.
(b) 298 In Cl Na(1) Na(2)
Kc 32 1 32 3
(c) 450 In Cl Na(1) Na(2) Na(3) a
x
y
z
B eq/22a
0.6667 0.9520(2) 0.0000 0.6667
0.3333 0.6345(2) 0.0000 0.3333
0.2500 0.37025(8) 0.2500 0.5418(3)
0.66(1) 1.25(2) 1.27(7) 1.47(5)
x
y
z
B iso/22
Occ.
0.6667 0.9544(4) 0.0000 0.6667
0.3333 0.6375(5) 0.0000 0.3333
0.2500 0.3714(2) 0.2500 0.5443(4)
1.45(6) 2.2(1) 3.7(4) 2.6(2)
1.0 1.0 1.0 1.0
d
K 32 1 32 3 3
0.6667 0.9526(4) 0.0000 0.6667 0.3333 2
0.3333 0.6355(4) 0.0000 0.3333 0.6667 2
0.2500 0.3695(2) 0.2500 0.5470(4) 0.2500 2
2.44(6) 4.2(1) 4.5(2) 4.5 4.5
1.0 1.0 0.976(3) 0.976 0.073
Fig. 3. Central transition of the 115In NMR for Na3InCl6 as a function of the crystal rotation, h. A typical second-order quadruple effect with the axial symmetry was observed.
chemical shift anisotropy at the 115In site. Although the separation between two singularities decreased continuously with increasing temperature, no symmetry change was detected at the In site in the temperature range studied. 3.4.
23
Na NMR
2
B eq =8/3p (U 11 (aa*) +U 22 (bb*) +U 33(cc*) +2U 12 (aa*bb*)cosc +2U 13(aa*cc*)cosb+2U 23(bb*cc*)cosa. b Single crystal data. c Rietveld analysis, a=6.9040(3) 2, c=12.4024(4) 2 and R f =0.026. d Rietveld analysis, a=6.9412(3) 2, c=12.4602(4) 2 and R f =0.029.
octahedral InCl63 anion. Fig. 4 shows the temperature dependence of the 115In NMR using a polycrystalline sample together with the simulation based on the secondorder quadruple effect using the parameters derived from the single crystal data. The powder pattern shows a typical second-order quadrupole effect with g=0 and agrees well with the simulation suggesting the vanishingly small
Fig. 2. Electric conductivity of Na3InCl6 determined by the complex impedance method. For comparison, our previous data on Li3InBr6 is shown together [11–13].
In contrast to the 115In NMR, the first-order quadrupole effect was observed using a single crystal due to its small e 2Qq/h. Fig. 5 plots the splitting between a pair of satellite transitions (Dm=1/2 X 3/2 and 1/2 X 3/2) as a function of the crystal rotation. Two pairs of satellite transitions with the intensity ratio 2:1 were observed symmetrically around the
Fig. 4. 115In NMR using polycrystalline Na3InCl6 as a function of temperature. Powder pattern simulation based on the second-order quadruple effect is shown at the bottom.
K. Yamada et al. / Solid State Ionics 176 (2005) 823–829
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Fig. 5. 23Na NMR using single crystal of Na3InCl6. Splitting between a pair of satellite transitions is plotted against the crystal rotation.
central transition. We can assign the stronger pair to the Na(2) because the intensity must be proportional to the number of the equivalent position in the unit cell. Since both Na(1) and Na(2) have the axially symmetric e 2Qq/h tensors (g=0) with the principal axes parallel to the c-axis, the splitting (Dm) between a pair of the satellite transitions as a function of the crystal rotation (h) could be expressed as follows [17]: Dm ¼ mð1=2 X 3=2Þ mð 1=2 X 3=2Þ ¼ 2mq 3sin2 /cos2 h 1 =2;
ð2Þ
2
where m q=3(e Qq/h)/2I(2I1) with I=3/2, / is the angle between rotation axis and the principal axis of the e 2Qq/h tensor. Two sets of the numerical solutions were obtained for each site. However, referring to the / value estimated from the 115In NMR, the e 2Qq/h were determined uniquely
Fig. 7. (a) Temperature dependence of the 23Na NMR central transition using a polycrystalline sample of Na3InCl6. (b) FWHM line width as a function of temperature. Solid line represents the calculated line width using Eqs. (3) and (4).
to be 0.426(2) and 0.522(2) MHz for Na(1) and Na(2) site, respectively. Fig. 6 shows the temperature dependence of the satellite transitions observed at the low-frequency side of the central transition. These spectra were observed at a certain orientation at which the principal axis of the e 2Qq/h tensor is perpendicular to the external magnetic field. In this orientation, the separation between a pair of satellite peaks corresponds to (1/2)d e 2Qq/h, and hence the temperature dependence of them is shown in Fig. 6(b). It is interesting to note that the two crystallographically nonequivalent sites
Fig. 6. (a) Temperature dependence of the 23Na NMR using single crystal. Two peaks assigned to Na(1) and Na(2) are merged into one line at around 400 K. (b) Temperature dependence of the quadrupole coupling constant.
Fig. 8. Rietveld refinement plots at 298 and 450 K for Na3InCl6.
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order to confirm the chemical exchange between Na(1) and Na(2), the Rietveld analysis was performed at 298 and 450 K. 3.5. Powder X-ray diffraction and Rietveld analysis at 298 and 450 K
Fig. 9. Conduction path of the sodium ions in Na3InCl6. Newly occupied Na(3) site was confirmed at 450 K by the Rietveld analysis.
Na(1) and Na(2) merge into one line at ca. 400 K associated with the narrowing. This behavior shown in Fig. 6(b) is quite similar to that observed for a second-order phase transition. However, in this case, no phase transition was detected around this temperature region. Furthermore, no reasonable phase transitions could be considered since the crystal keeps the trigonal lattice in this temperature region. This coalescence of the two peaks may suggest the chemical exchange process between these two Na sites faster than the NMR timescale (~104 s). On the other hand, the motional correlation time of the sodium ion was estimated from the FWHM line width using a polycrystalline sample. As Fig. 7 shows, a featureless central transition (Dm=1/2 X 1/2) shows a motional narrowing at ca. 400 K suggesting the self diffusion of the Na+. The motional correlation time (s NMR) for the Na+ diffusion was evaluated by the following equation [18]: ð3Þ sNMR ¼ tan p DH 2 A2 =2 B2 A2 =2paDH; where A, DH, and B represent the line width at the temperature above, within and below the transition region, respectively, and a is a constant near unity. A and B were estimated from the graph to be 0.32 and 1.99 kHz, respectively. Assuming an Arrhenius equation for the s NMR, the following parameters were reduced. sNMR =s ¼ 3:5 1011 exp 46ð3Þ 103 =RT ð4Þ Eq. (4) indicates that 1/s NMR reaches 24 kHz at 400 K and this value is fast enough to explain the coalescence phenomenon shown in Fig. 6. However, the activation energy is smaller than that from the dc conductivity. In
Fig. 8 shows powder X-ray diffraction patterns observed at 298 and 450 K. The observed powder pattern at 298 K could be reproduced quite well using the structural parameters at 200 K except the lattice constants and the thermal parameters. On the other hand, the precise Rietveld analysis at 450 K suggested the formation of a new sodium site Na(3). Table 2 summarizes the refined occupancies at the three Na sites together with the structural parameters. On the basis of the 23Na NMR and the sodium ion occupancy at 450 K, a possible conduction path could be proposed connecting three crystallographically different Na sites as shown in Fig. 9. In a typical two-site chemical exchange process, two original NMR peaks do not shift but show only broadening at the beginnings. In this case, however, the peak position also shows temperature dependence because it is a function of e 2Qq/h which normally shows strong temperature dependence due to the lattice vibrations.
4. Conclusions The crystal structure of Na3InCl6 was determined at 200 K. This crystal belongs to a trigonal system and consists of an isolated InCl63 and two crystallographic Na+ sites. However, the Rietveld analysis at 450 K suggested the formation of the new Na+ site. Furthermore, the 23Na NMR using single crystal exhibit the chemical exchange phenomenon at around 400 K. Although the ionic conductivity for Na3InCl6 is not so high compared to Li3InCl6 or Li3InBr6, the conduction path of the sodium ion could be proposed by means of the Rietveld analysis and single-crystal NMR measurement.
References [1] W. Schmidt, H.D. Lutz, Ber. Bunsenges. Phys. Chem. 88 (1984) 720. [2] H.D. Lutz, P. Kuske, A. Pfitzner, Ber. Bunsenges. Phys. Chem. 93 (1989) 1340. [3] H.D. Lutz, M. Schneider, Ch. Wickel, Z. Kristallogr. 211 (1996) 8. [4] R. Kanno, Y. Takeda, A. Matsumoto, O. Yamamoto, R. Suyama, S. Kume, J. Solid State Chem. 75 (1988) 41. [5] R. Kanno, Y. Takeda, A. Takahashi, O. Yamamoto, R. Suyama, S. Kume, J. Solid State Chem. 71 (1987) 196. [6] R. Nagel, Th.W. Gross, H. Gunther, H.D. Lutz, J. Solid State Chem. 165 (2002) 303. [7] H.J. Steiner, H.D. Lutz, Z. Anorg. Allg. Chem. 613 (1992) 26. [8] A. Bohnsack, F. Stenzel, A. Zajonc, G. Balzer, M.S. Wickleder, G. Meyer, Z. Anorg. Allg. Chem. 623 (1997) 1067.
K. Yamada et al. / Solid State Ionics 176 (2005) 823–829 [9] A. Bohnsack, G. Balzer, M.S. Wickleder, H-U. Gqdel, G. Meyer, Z. Anorg. Allg. Chem. 623 (1997) 1352. [10] M.O. Schmidt, M.S. Wickleder, G. Meyer, Z. Anorg. Allg. Chem. 625 (1999) 539. [11] Y. Tomita, A. Fujii, H. Ohki, K. Yamada, T. Okuda, Chem. Lett. (1998) 223. [12] Y. Tomita, K. Yamada, H. Ohki, T. Okuda, Z. Naturforsch. 53a (1998) 466. [13] K. Yamada, K. Iwaki, T. Okuda, Y. Tomita, in: B.V.R. Chowdari, S.R.S. Prabaharan, M. Yahaya, I.A. Talib (Eds.), Solid State Ionics: Trends in the New Millennium, World Scientific, Singapore, 2002, p. 621.
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[14] K. Suzuki, J. Phys. Soc. Jpn. 16 (1961) 67. [15] R. Kanno, Y. Takeda, A. Takahashi, O. Yamamoto, R. Suyama, M. Koizumi, J. Solid State Chem. 71 (1987) 189; R. Kanno, Y. Takeda, M. Mori, O. Yamamoto, Chem. Lett. (1987) 1465. [16] F. Izumi, T. Ikeda, Mat. Sci. Forum 321 (2000) 198. [17] A. Abragam, Principles of Nuclear Magnetism, Oxford University Press, London, 1961, Chap. VII. [18] A. Abragam, Principles of Nuclear Magnetism, Oxford University Press, London, 1961, Chap. X.
Conduction path of the sodium ion in Na3InCl6 studied by X-ray diffraction and 23Na and 115In NMR Koji Yamada*, Keiji Kumano, Tsutomu Okuda Graduate School of Science, Hiroshima University, Department of Chemistry, Kagamiyama 1-3, 739-8526 Higashi-Hiroshima, Japan Received 18 July 2004; received in revised form 16 October 2004; accepted 20 October 2004
Abstract The crystal structure of Na3InCl6 was determined at 200 K by the single-crystal X-ray analysis. The crystal belongs to a trigonal system in which an isolated InCl63 anion and two crystallographically nonequivalent sodium ions Na(1) and Na(2) are confirmed. At 450 K, however, the Rietveld analysis suggested that a new site was occupied by the sodium ion forming vacancies at the original positions. In accordance with this observation, the 23Na NMR spectrum using a single crystal showed a coalescence phenomenon of the two crystallographically different peaks at around 400 K. These observations support the dynamical chemical exchange between Na(1) and Na(2) through newly occupied Na(3) site. Although the ionic conductivity for this compound was not so high (2105 S cm1 at 500 K), the conduction path for the sodium ions was able to be proposed clearly. D 2004 Elsevier B.V. All rights reserved. Keywords: Single-crystal NMR; Sodium ion conductor; X-ray diffraction; Conduction mechanism; Ternary halide
1. Introduction The ternary chlorides Li2MIICl4 have been studied extensively because of their high lithium ion conductivity [1–6]. Especially Li2MgCl4 having spinel structure shows the high conductivity ~101 S cm1 at 673 K [1]. The mechanism of the high ionic conductivity for these ternary chlorides has been investigated by X-ray or neutron diffraction technique [1–5] and high-resolution solid-state 7Li NMR [6]. On the other hand, ternary chlorides Li3MIIIX6 (X=Cl, Br) have been also investigated and the highest ionic conductivity among them was reported for Li3InCl6 (0.2 S cm1 at 573 K) [7–10]. We synthesized new lithium ion conductor Li3InBr6 and reported that this crystal undergoes a superionic phase transition at 314 K with the high conductivity of about 103 S cm1 at 330 K [11–13]. Although no structural analyses were reported on the low-temperature phase,
* Corresponding author. Tel.: +81 82 424 7418; fax: +81 82 424 0727. E-mail address: [email protected] (K. Yamada). 0167-2738/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2004.10.016
our 81Br NQR spectrum suggested the existence of an isolated InBr63 anion. On the other hand, our preliminary DSC measurement suggested the positional disorder not only In3+ but Li+ above T tr. With increasing temperature, however, this two-dimensional order is destroyed gradually and its powder pattern becomes quite similar to that of LiBr except some superlattice reflections. These superlattice reflections correspond to a lattice constant twice as that of the LiBr f.c.c. lattice [13]. This finding may suggest that the cationic site of the rock salt structure can be replaced by In3+ keeping an electroneutrality rule, 3Li+=In3++25. A quite similar phenomenon was reported in the NaCl–CdCl2 system, in which not only Na2CdCl4 but 6NaCl–CdCl 2 was reported [14]. The latter compound was known as a Suzuki phase and the structure was identified to be a f.c.c. lattice with the lattice constant twice as that of NaCl in which two Na+ is replaced by Cd2+ and vacancy. Kanno et al. [15] reported similar structure for Li6MCl8 (M=FeII and CoII). If trivalent cations can be introduced keeping the rock salt structure, high ionic conductivity is expected. Hence,
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we have interested in the cationic conductors having rock salt structure especially for the system between alkali halides and InX3 (X: Cl and Br) because the ionic radius of In3+ is quite similar to that of Li+. The main purpose of this study is to develop new ionic conductors and understand the relationship between structure and conductivity for A3BX6 halides. In this report, the conduction mechanism of the sodium ion in Na3InCl6 will be discussed on the basis of the structure and the singlecrystal 23Na NMR.
2. Experimental 2.1. Sample preparation Single crystal of Na3InCl6 was synthesized from the melt using a Bridgman furnace. Although Na3InCl6 was reported to be an incongruent melting compound [7], a transparent part of the grown crystal was proved to be a single crystal of Na3InCl6 by means of the X-ray analysis and also by the 23Na and 115In NMR. In this study, polycrystalline samples were also prepared from the single crystal. 2.2. X-ray diffraction A single crystal suitable for the X-ray diffraction was selected from the broken pieces of the large single crystal. Because of the slight hygroscopic property of the compound, the crystal was covered by paraffin oil and the intensity data were collected at 200 K with an Oxford Cryostream cooler. All measurements were made by a Mac Science DIP2030 imaging-plate diffractometer with monochromatized Mo Ka radiation (k=0.71069 2). The crystallographic data and details of the structural determinations for Na3InCl6 are summarized in Table 1. The powder X-ray diffraction was observed using a Rigaku Rint PC diffractometer with a homemade variable temperature attachment. Structural parameters at 298 and 450 K were refined by a Rietveld method [16]. 2.3. Conductivity and NMR measurements Impedance measurement was performed by a complex impedance method using a cylindrical ceramic cell with two stainless electrodes. A computer-controlled system with a GP–IB interface was used for the measurement. The frequency range covered was 42 Hz–5 MHz using HIOKI 3522 LCR meter. 23Na and 115In NMR were observed using a single crystal and a polycrystalline sample by means of a homemade pulsed spectrometer at 6.4 T which corresponds to 71.74 MHz for 23Na and 59.44 MHz for 115In. A singlepulse sequences followed by a Fourier transformation was
Table 1 Crystallographic Data for Na3InCl6 at 200 K Temperature Formula weight Diffractometer Wavelength Crystal size Crystal system a c V Space group Z value D calc l 2h max No. of reflections measured Structure solution Refinement Least squares weights No. observations (IN0.00r(I)) No. variables Residuals: R 1 (IN2.0r) Residuals: wR 2 (IN0.0r) Max shift/error in final cycle Max peak in final diff map Min peak in final diff map
200(1) K 396.51 Mac Science DIP2030 0.71069 2 0.10.10.15 mm trigonal 6.8915(1) 2 12.3820(4) 2 509.27(2) 23 P-31c (#163) 2 2.586 g cm3 39.40 cm1 55.98 Total: 2151 Unique: 415 Direct method (SIR92) Full-matrix least-squares on F 2 P w( Fo2Fc2)2 415 18 0.024 0.072 0.000 0.44e/23 1.13e/23
applied for all measurements. Typical dead time of our spectrometer was ca. 3 As.
3. Results and discussion 3.1. Single-crystal X-ray analysis on Na3InCl6 at 200 K Fig. 1 and Table 2 show the structure and the structural parameters for Na3InCl6, respectively. The crystal belongs to a trigonal system with space group P-31c (# 163). In this trigonal crystal, the chloride ions form a hexagonal close packing (hcp) perpendicular to the c-axis, in contrast to the cubic close packing (ccp) of the bromide ions found in Li3InBr6 [13]. As Fig. 1(a) shows, there are two crystallographically different cationic layers at z=1/4 (3/4) and c1/ 2, the former contains both In3+ and Na+(1) and later contains only Na+(2). All these cations locate on the special high symmetry positions 32 or 3 and the coordinations around these cations are shown in Fig. 1(c). The InCl63 anion distorts only slightly along the three-fold axis from the regular octahedron. Na(1) and Na(2) also form NaCl6 octahedron, however, the distortion at the Na(2) site along three-fold axis is remarkable probably due to the electrostatic repulsion between In3+ and Na+. No positional disorder was found at the cationic sites at 200 K. 3.2. Conductivity and DSC measurement Fig. 2 plots the conductivity against 1/T together with our previous data on Li3InBr6. The conductivity of the
K. Yamada et al. / Solid State Ionics 176 (2005) 823–829
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Fig. 1. Crystal structure of Na3InCl6 at 200 K. (a) Drawing perpendicular to the c-axis and (b) parallel to the c-axis. (c) The coordination geometry around the cations.
present compound was 104 times lower than that of Li3InBr6 even at 450 K. The activation energy for the conduction was estimated to be 70.9(5) kJ mol1 from the linear portion of the rT against 1/T plot below 500 K. The conductivity and its temperature behavior for Na3InCl6 agreed well to that reported previously [7]. No anomalous behavior was observed on the DSC curve up to 600 K. These findings suggest that this crystal exhibit no phase transition keeping the hcp of the chloride ions up to at least 600 K. As will be described below, however, the onset of the sodium ion diffusion was detected at around 400 K as a NMR chemical exchange phenomenon using a single crystal of Na3InCl6. 3.3.
115
In NMR
Since Na3InCl6 belongs to a trigonal system in which all cations, In3+, Na+(1) and Na+(2), are located on the threefold axes, the quadrupole coupling tensors for these sites must be cylindrical (g=0) with their principal axes parallel to the crystal c-axis. The quadrupole coupling constant (e 2Qq/h) having axially symmetry can be easily determined from the rotational pattern around the one axis of the single crystal. Fig. 3 plots the frequency of the central transition
(m=1/2 X 1/2) of the 115In NMR as a function of the crystal rotation, h. Although 115In has nuclear spin I=9/2 and hence totally 9 allowed transitions are expected, only the central transition was measured as a function of h. As expected from the structure, only one central transition is observed. The frequency shift of the central transition due to the second-order quadrupole effect (g=0) can be expressed as [17]: mobs mL ¼ m2q =16mL ð I ð I þ 1Þ 4=3Þ
1 cos2 hsin2 / 9cos2 hsin2 / 1;
ð1Þ
where m L is the 115In Larmor frequency corresponding to the anionic species InCl63, m q=3(e 2Qq/h)/2I(2I1), / is the angle between the principal axis of the e 2Qq/h tensor and the rotation axis of the crystal, and h is the angle of the crystal rotation around the axis perpendicular to the external magnetic field H. The following parameters were obtained from the nonlinear least squares method, m L=59.4390(3) MHz, e 2 Qq /h =20.11(14) MHz and /=63.8(5). m L agrees very well to that observed for the cubic elpasolite Cs2KInCl6 which contains a regular
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Table 2 Structural parameters for Na3InCl6 at 200, 298 and 450 K Atom
Point sym.
(a) 200 In Cl Na(1) Na(2)
Kb 32 1 32 3
Atom
Point sym.
(b) 298 In Cl Na(1) Na(2)
Kc 32 1 32 3
(c) 450 In Cl Na(1) Na(2) Na(3) a
x
y
z
B eq/22a
0.6667 0.9520(2) 0.0000 0.6667
0.3333 0.6345(2) 0.0000 0.3333
0.2500 0.37025(8) 0.2500 0.5418(3)
0.66(1) 1.25(2) 1.27(7) 1.47(5)
x
y
z
B iso/22
Occ.
0.6667 0.9544(4) 0.0000 0.6667
0.3333 0.6375(5) 0.0000 0.3333
0.2500 0.3714(2) 0.2500 0.5443(4)
1.45(6) 2.2(1) 3.7(4) 2.6(2)
1.0 1.0 1.0 1.0
d
K 32 1 32 3 3
0.6667 0.9526(4) 0.0000 0.6667 0.3333 2
0.3333 0.6355(4) 0.0000 0.3333 0.6667 2
0.2500 0.3695(2) 0.2500 0.5470(4) 0.2500 2
2.44(6) 4.2(1) 4.5(2) 4.5 4.5
1.0 1.0 0.976(3) 0.976 0.073
Fig. 3. Central transition of the 115In NMR for Na3InCl6 as a function of the crystal rotation, h. A typical second-order quadruple effect with the axial symmetry was observed.
chemical shift anisotropy at the 115In site. Although the separation between two singularities decreased continuously with increasing temperature, no symmetry change was detected at the In site in the temperature range studied. 3.4.
23
Na NMR
2
B eq =8/3p (U 11 (aa*) +U 22 (bb*) +U 33(cc*) +2U 12 (aa*bb*)cosc +2U 13(aa*cc*)cosb+2U 23(bb*cc*)cosa. b Single crystal data. c Rietveld analysis, a=6.9040(3) 2, c=12.4024(4) 2 and R f =0.026. d Rietveld analysis, a=6.9412(3) 2, c=12.4602(4) 2 and R f =0.029.
octahedral InCl63 anion. Fig. 4 shows the temperature dependence of the 115In NMR using a polycrystalline sample together with the simulation based on the secondorder quadruple effect using the parameters derived from the single crystal data. The powder pattern shows a typical second-order quadrupole effect with g=0 and agrees well with the simulation suggesting the vanishingly small
Fig. 2. Electric conductivity of Na3InCl6 determined by the complex impedance method. For comparison, our previous data on Li3InBr6 is shown together [11–13].
In contrast to the 115In NMR, the first-order quadrupole effect was observed using a single crystal due to its small e 2Qq/h. Fig. 5 plots the splitting between a pair of satellite transitions (Dm=1/2 X 3/2 and 1/2 X 3/2) as a function of the crystal rotation. Two pairs of satellite transitions with the intensity ratio 2:1 were observed symmetrically around the
Fig. 4. 115In NMR using polycrystalline Na3InCl6 as a function of temperature. Powder pattern simulation based on the second-order quadruple effect is shown at the bottom.
K. Yamada et al. / Solid State Ionics 176 (2005) 823–829
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Fig. 5. 23Na NMR using single crystal of Na3InCl6. Splitting between a pair of satellite transitions is plotted against the crystal rotation.
central transition. We can assign the stronger pair to the Na(2) because the intensity must be proportional to the number of the equivalent position in the unit cell. Since both Na(1) and Na(2) have the axially symmetric e 2Qq/h tensors (g=0) with the principal axes parallel to the c-axis, the splitting (Dm) between a pair of the satellite transitions as a function of the crystal rotation (h) could be expressed as follows [17]: Dm ¼ mð1=2 X 3=2Þ mð 1=2 X 3=2Þ ¼ 2mq 3sin2 /cos2 h 1 =2;
ð2Þ
2
where m q=3(e Qq/h)/2I(2I1) with I=3/2, / is the angle between rotation axis and the principal axis of the e 2Qq/h tensor. Two sets of the numerical solutions were obtained for each site. However, referring to the / value estimated from the 115In NMR, the e 2Qq/h were determined uniquely
Fig. 7. (a) Temperature dependence of the 23Na NMR central transition using a polycrystalline sample of Na3InCl6. (b) FWHM line width as a function of temperature. Solid line represents the calculated line width using Eqs. (3) and (4).
to be 0.426(2) and 0.522(2) MHz for Na(1) and Na(2) site, respectively. Fig. 6 shows the temperature dependence of the satellite transitions observed at the low-frequency side of the central transition. These spectra were observed at a certain orientation at which the principal axis of the e 2Qq/h tensor is perpendicular to the external magnetic field. In this orientation, the separation between a pair of satellite peaks corresponds to (1/2)d e 2Qq/h, and hence the temperature dependence of them is shown in Fig. 6(b). It is interesting to note that the two crystallographically nonequivalent sites
Fig. 6. (a) Temperature dependence of the 23Na NMR using single crystal. Two peaks assigned to Na(1) and Na(2) are merged into one line at around 400 K. (b) Temperature dependence of the quadrupole coupling constant.
Fig. 8. Rietveld refinement plots at 298 and 450 K for Na3InCl6.
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order to confirm the chemical exchange between Na(1) and Na(2), the Rietveld analysis was performed at 298 and 450 K. 3.5. Powder X-ray diffraction and Rietveld analysis at 298 and 450 K
Fig. 9. Conduction path of the sodium ions in Na3InCl6. Newly occupied Na(3) site was confirmed at 450 K by the Rietveld analysis.
Na(1) and Na(2) merge into one line at ca. 400 K associated with the narrowing. This behavior shown in Fig. 6(b) is quite similar to that observed for a second-order phase transition. However, in this case, no phase transition was detected around this temperature region. Furthermore, no reasonable phase transitions could be considered since the crystal keeps the trigonal lattice in this temperature region. This coalescence of the two peaks may suggest the chemical exchange process between these two Na sites faster than the NMR timescale (~104 s). On the other hand, the motional correlation time of the sodium ion was estimated from the FWHM line width using a polycrystalline sample. As Fig. 7 shows, a featureless central transition (Dm=1/2 X 1/2) shows a motional narrowing at ca. 400 K suggesting the self diffusion of the Na+. The motional correlation time (s NMR) for the Na+ diffusion was evaluated by the following equation [18]: ð3Þ sNMR ¼ tan p DH 2 A2 =2 B2 A2 =2paDH; where A, DH, and B represent the line width at the temperature above, within and below the transition region, respectively, and a is a constant near unity. A and B were estimated from the graph to be 0.32 and 1.99 kHz, respectively. Assuming an Arrhenius equation for the s NMR, the following parameters were reduced. sNMR =s ¼ 3:5 1011 exp 46ð3Þ 103 =RT ð4Þ Eq. (4) indicates that 1/s NMR reaches 24 kHz at 400 K and this value is fast enough to explain the coalescence phenomenon shown in Fig. 6. However, the activation energy is smaller than that from the dc conductivity. In
Fig. 8 shows powder X-ray diffraction patterns observed at 298 and 450 K. The observed powder pattern at 298 K could be reproduced quite well using the structural parameters at 200 K except the lattice constants and the thermal parameters. On the other hand, the precise Rietveld analysis at 450 K suggested the formation of a new sodium site Na(3). Table 2 summarizes the refined occupancies at the three Na sites together with the structural parameters. On the basis of the 23Na NMR and the sodium ion occupancy at 450 K, a possible conduction path could be proposed connecting three crystallographically different Na sites as shown in Fig. 9. In a typical two-site chemical exchange process, two original NMR peaks do not shift but show only broadening at the beginnings. In this case, however, the peak position also shows temperature dependence because it is a function of e 2Qq/h which normally shows strong temperature dependence due to the lattice vibrations.
4. Conclusions The crystal structure of Na3InCl6 was determined at 200 K. This crystal belongs to a trigonal system and consists of an isolated InCl63 and two crystallographic Na+ sites. However, the Rietveld analysis at 450 K suggested the formation of the new Na+ site. Furthermore, the 23Na NMR using single crystal exhibit the chemical exchange phenomenon at around 400 K. Although the ionic conductivity for Na3InCl6 is not so high compared to Li3InCl6 or Li3InBr6, the conduction path of the sodium ion could be proposed by means of the Rietveld analysis and single-crystal NMR measurement.
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