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Studies of ionic conductivity and structural phase transitions of Na3H(SO4)2 crystal
Solid State Ionics 110 (1998) 277–281
Studies of ionic conductivity and structural phase transitions of Na 3 H(SO 4 ) 2 crystal a b a R.H. Chen*, Ren-June Wang , T. Fukami , C.S. Shern a
b
Department of Physics, National Taiwan Normal University, Taipei, 117, Taiwan Department of Physics and Earth Sciences, College of Science, University of the Ryukyus, Okinawa 903 -O1, Japan Received 16 December 1997; accepted 27 March 1998
Abstract The complex electrical impedance of Na 3 H(SO 4 ) 2 along the b m -axis has been measured from 258C to 3168C in the frequency range 4 kHz–40 MHz. The temperature dependence of the electrical conductivity shows remarkable changes in the temperature range 1608C–2608C. The sample crystal becomes a fast ionic conductor above 2608C. The conduction mechanisms of proton and sodium ions in the different phases are analyzed in detail with respect to the structural features of the sample crystal. 1998 Elsevier Science B.V. All rights reserved. Keywords: Na 3 H(SO 4 ) 2 ; Ionic conductivity; Structural phase transition
1. Introduction The crystal structure of Na 3 H(SO 4 ) 2 was reported to be monoclinic with space group P2 1 / c at room temperature by Catti et al. [1]. The crystal has cell ˚ b m 5 9.648(1) A, ˚ cm 5 dimensions a m 5 8.648(1) A, 0 ˚ 9.143(1) A and bm 5 108.77(1) and there are four molecules in a unit cell [1]. A high-temperature structural phase transition of Na 3 H(SO 4 ) 2 has been found independently at 513 K by Bose et al. [2] and at 533 K by Moskvich et al. [3] in an NMR experiment. The crystal structure of Na 3 H(SO 4 ) 2 in the high-temperature phase has been studied by Chen et al. via X-ray diffraction [4]. The crystal system was transformed from the monoclinic room-temperature phase to hexagonal high temperature phase. The possible space groups are that are proposed are
¯ P6 3 / mmc, P6 3 mc or P62c in high-temperature phase. The reorientation of SO 4 groups and the disorder of both H and Na atoms are proposed [4]. No detailed structural analysis has yet been performed at high temperature. It has been found that some hydrogen-bonded crystals with general formula M 3 H(XO 4 ) 2 (M 5 Rb, Cs, NH 41 and X 5 S, Se) undergo structural phase transitions above room temperature and become fast ionic conductors in the high temperature phases [5– 7]. But the structure of Na 3 H(SO 4 ) 2 is not isomorphous with them in both room- and high-temperature phases. In this paper, we report the results of electrical impedance measurement of the sample crystal. The mechanism of electrical conduction in the sample crystal is also studied.
*Corresponding author. E-mail: [email protected] 0167-2738 / 98 / $19.00 1998 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 98 )00135-0
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R.H. Chen et al. / Solid State Ionics 110 (1998) 277 – 281
2. Experimental Colorless sample crystals of Na 3 H(SO 4 ) 2 were grown from the aqueous solutions containing 3:1 mole fraction of Na 2 SO 4 and H 2 SO 4 by slow evaporation at room temperature. Transparent plates with a (010) predominant face were obtained. The b m -axis is perpendicular to the crystal plate. The measured density using the floating methods was 2.402 g cm 23 . A single domain crystal of 3 mm 3 1.5 mm with thickness 0.75 mm is cut from a swallow-tail twin for the impedance measurement. The sample crystal was pasted with silver paster on (010) plates as electrodes. The complex impedance of the specimens was measured at the frequency range of 4 kHz to 40 MHz with a HP4194A impedance analyzer interfaced to a IBM compatible PC. The impedance measurements were carried out in the temperature interval 258C–3168C. The temperature of the sample crystal was controlled by a Huber high temperature attachment with a precision of 618C.
3. Results and discussions From the obtained impedance data, the typical semicircles of the impedance plot are observed. The equivalent circuit for the sample crystal is proposed to be close to the parallel combination of resistance and capacitance of bulk crystal. The sample impedance ( $ 10 6 V) at low frequencies and at temperatures below 2008C is too large for accurate measurements with our impedance analyzer. The DC conductivity is not extracted. Though the results are plotted at some high frequencies, the frequency dependence is consistent. Fig. 1 shows the result of the temperature dependence of electrical conductivity for the sample crystal at several frequencies. As the temperature is raised, the electrical conductivity decreases slightly until around 1608C and then it increases with increasing temperature. Before 1608C, the sample crystal behaves well as a typical insulator. The conductivity increases drastically near the transition point. The electrical conductivity increased about two order of magnitude from the room-temperature phase to high temperature phase. The conductivity increases with increasing temperature again in the region of high temperatures.
Fig. 1. Temperature dependence of the AC electrical conductivity of sample crystal along the b m -axis at several frequencies.
The temperature dependence of ionic conductivity is usually given by the Arrhenius equation
s T 5 A exp(2Eg /KB T )
(1)
where Eg is the activation energy of the migration ion, k B is the Boltzmann constant, T is absolute temperature and A is the preexponential factor. On the basis of Eq. (1), ln(s T ) versus 1000 /T at several AC frequencies is plotted in Fig. 2. An increasing of slope is observed above 1608C and the slopes change discontinuously at about 2328C. The former temperature (|1608C) shifts to a higher temperature as the frequency is increased. It indicated that the ion mobility in the crystal of this phase is effected by the applied frequencies. The obtained activation energies are 0.19 eV, 0.21 eV, 0.29 eV and 0.36 eV (18.3 kJ mole 21 –34.6 kJ mole 21 ) for the decreasing applied AC frequencies. Fig. 3a shows the crystal structure of the sample crystal in the room temperature phase as determined by Catti et al. [1]. The crystal cell is outlined alternatively in different ways by the b m 2, [101] m 2 ¯ m 2 axes. The dimensions of and half of the [101] ˚ 10.368 A ˚ and 7.233 A ˚ this cell are 9.648(1) A,
R.H. Chen et al. / Solid State Ionics 110 (1998) 277 – 281
279
Fig. 2. Arrhenius plot of the ionic conductivity for the sample crystal at several frequencies.
respectively and the axes are closely perpendicular to each other. There are four chemical formulas in such a cell. Two nonequivalent SO 4 groups are linked by the shortest hydrogen bond as compared with the other members of the general chemical formula of M 3 H(XO 4 ) 2 [1]. The length of the hydrogen bonds ˚ The hydrogen bond is are O? ? ?O52.432(2) A. ˚ and H? ? ?O5 asymmetric with O–H51.156(3) A ˚ 1.276 A and the angle of O–H? ? ?O is 179.1(2)8, as evaluated from neutron diffraction data [8]. The projection of the atomic positions onto the plane containing b m - and [101] m -axes is given in Fig. 3b. We assume that the reorientation of SO 4 takes place and the hydrogen bonds are broken gradually at temperatures above 160 8C. The proton ions are relatively free to move between the neighboring SO 4 groups. Hence, the proton ions make the main contribution to the electrical conductivity of Na 3 H(SO 4 ) 2 in this intermediated phase. Moskvich et al. had also found that the electrical conduction of Na 3 H(SO 4 ) 2 is caused by the proton diffusion in this phase by the NMR studies [3]. Although the ionic conductivity measurements would reflect the structure change, the crystal structure of Na 3 H(SO 4 ) 2 in the temperature range of 1608C to 2328C is not well established and reported yet.
Fig. 3. (a) Schematic drawing of the crystal structure of Na 3 H(SO 4 ) 2 , as determined by Catti et al. [1], but shown in the different cell dimensions; (b) Same as (a) but the projection is ¯ m -axis. The decimal numbers indicate the approxialong the [101] ¯ m. mate heights of the atoms in terms of the half length of [101]
The structure of Na 3 H(SO 4 ) 2 transforms to the hexagonal system in the high-temperature phase as studies by X-ray diffraction have shown [4]. The b h* -axis of the high-temperature phase is found along the b m -axis (or b *m ) of the room-temperature phase. The direction of the c h -axis points closely along the ¯ m and then the a h direction is close direction of [101] to the [101] m direction [4]. The likely crystal structure in the high-temperature phase as proposed by Chen et al. [4] is given in Fig. 4a. The unit cell ˚ and c h 57.18(7)A ˚ [4]. dimensions are a h 55.37(5) A There is one formula unit in this hexagonal cell. The structure is changed by the reorientation and / or the dynamical orientational disorder up and down of SO 4 groups as the temperature is raised [4]. The dy-
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R.H. Chen et al. / Solid State Ionics 110 (1998) 277 – 281
Fig. 4. (a) The proposed crystal structure of Na 3 H(SO 4 ) 2 in the high temperature phase [4]. One of the sodium atoms, Na(3), is disordered in two positions and the hydrogen atom is dynamically disordered in six positions as shown in the figure; (b) Same as (a) but the crystal structure is projected onto the (001) plane. The jump paths of the proton ions between neighboring disordered positions are shown by arrows.
namically disordered model of SO 4 tetrahedra has been proposed in other sulfate crystals, such as the high-temperature form of K 2 SO 4 and Na 2 SO 4 [9,10]. The discrepancy from the Arrhenius behavior at the temperatures around 2468C is also observed in Fig. 2. The incomplete onset of dynamical disorder of up and down of SO 4 may show the electrical conductivity behavior in this temperature range. The sulfur atoms of the SO 4 groups are at the special positions (2 / 3, 1 / 3, 1 / 4) and (1 / 3, 2 / 3, 3 / 4). Two sodium atoms, Na(1) and Na(2), are located at (0, 0, 0) and (0, 0, 1 / 2) respectively, while the third sodium atom, Na(3), is disordered at the positions of (2 / 3, 1 / 3, 3 / 4) and (1 / 3, 2 / 3, 1 / 4). The position of the hydrogen atom was unable to be determined in the work of Chen et al. [4]. We proposed that the hydrogen atom is statistically disordered at six
positions as shown in Fig. 4a. The hydrogen atom still links two SO 4 tetrahedra which are near neighbors but the bonding is much weaker than that of the room-temperature phase. The thermal effect increases the number of possible proton sites and activates the concentration of possible vacancy sites. As the electric field is applied along the b m -axis of the sample crystal, the high electrical conductivity is caused by jumps of proton ions onto these new possible positions. The proton ion migration paths within the layers of z50 and z51 / 2 are shown in Fig. 4b. Beside the hydrogen diffusion, the sodium ions are also possibile ions for migration through the crystal. The contribution of the sodium ions to the electrical conductivity in the high-temperature phase is also verified by the NMR study of ionic motion in Na 3 H(SO 4 ) 2 crystal [3]. The value of the electrical conductivity in the high-temperature phase is |10 2 3 S cm 2 1 . It is about ten times larger than those found in the high temperature phases of K 2 SO 4 and Na 2 SO 4 crystals [11,12]. The activation energies as measured from Fig. 2 in the high-temperature phase are 0.32 eV, 0.32 eV, 0.32 eV, and 0.35 eV (|31.5 kJ mole 21 ) which are almost independent of the applied frequencies. The electrical contribution of the third disordered sodium ion, Na(3), in the c h -direction will be more or less hindered by the surrounding SO 4 groups. Unfortunately, the conductivity measurement along some other axis is somewhat difficult to do in the present studies. The comparison of the electrical conductivity along the different directions has not been made. The high-temperature form of Na 3 H(SO 4 ) 2 crystal is optically turbid and disrupts easily and the crystal cannot return to its initial form as the temperature is lowered from the high temperature. The measurements have not been carried out on cooling back to low temperature. It is suggested that the structural phase transition around 2468C is very drastic. Further studies on the structure and transition mechanism of every phase in the sample crystal are still required.
Acknowledgements This research was supported by the National Science Council, Republic of China (Project No. NSC 85-2112-M003-009).
R.H. Chen et al. / Solid State Ionics 110 (1998) 277 – 281
References [1] M. Catti, G. Ferraris, G. Ivaldi, Acta Cryst. B 35 (1979) 525. [2] M. Bose, K. Roy, A. Ghoshray, Proc. Nucl. Phys. Solid State Phys. Sym. 24C (1981) 393. [3] Y.N. Moskvich, A.M. Polyakov, A.A. Sukhovsky, Ferroelectrics 81 (1988) 197. [4] R.H. Chen, S.C. Chen, T.M. Chen, Phase Transitions 53 (1995) 15. [5] A.I. Baranov, I.P. Makarova, L.A. Muradyan, A.V. Tregubchenko, L.A. Shuvalov, V.I. Simonov, Sov. Phys. Crystallogr. 32(3) (1987) 400. [6] B.V. Merinov, A.I. Baranov, L.A. Shuvalov, Sov. Phys. Crystallogr. 35(2) (1990) 200.
281
[7] K. Furukawa, S. Akaloshi, T. Fukami, K. Hukuda, J. Phys. Soc. Jpn. 59 (1990) 4560. [8] W. Joswig, H. Fuess, G. Ferraris, Acta Cryst. B 38 (1982) 2798. [9] M. Miyake, H. Morikawa, S.I. Iwai, Acta Cryst. B 36 (1980) 532. [10] S.E. Rasmussen, J.E. Jorgensen, B. Lundtoft, J. Appl. Cryst. 29 (1996) 42. [11] B.K. Choi, Y.H. Cho, H.K. Lee, J. Phys. Chem. Solids 54 (1993) 197. [12] B.K. Choi, D.J. Lockwood, Phys. Rev. B 40 (1989) 4683.
Studies of ionic conductivity and structural phase transitions of Na 3 H(SO 4 ) 2 crystal a b a R.H. Chen*, Ren-June Wang , T. Fukami , C.S. Shern a
b
Department of Physics, National Taiwan Normal University, Taipei, 117, Taiwan Department of Physics and Earth Sciences, College of Science, University of the Ryukyus, Okinawa 903 -O1, Japan Received 16 December 1997; accepted 27 March 1998
Abstract The complex electrical impedance of Na 3 H(SO 4 ) 2 along the b m -axis has been measured from 258C to 3168C in the frequency range 4 kHz–40 MHz. The temperature dependence of the electrical conductivity shows remarkable changes in the temperature range 1608C–2608C. The sample crystal becomes a fast ionic conductor above 2608C. The conduction mechanisms of proton and sodium ions in the different phases are analyzed in detail with respect to the structural features of the sample crystal. 1998 Elsevier Science B.V. All rights reserved. Keywords: Na 3 H(SO 4 ) 2 ; Ionic conductivity; Structural phase transition
1. Introduction The crystal structure of Na 3 H(SO 4 ) 2 was reported to be monoclinic with space group P2 1 / c at room temperature by Catti et al. [1]. The crystal has cell ˚ b m 5 9.648(1) A, ˚ cm 5 dimensions a m 5 8.648(1) A, 0 ˚ 9.143(1) A and bm 5 108.77(1) and there are four molecules in a unit cell [1]. A high-temperature structural phase transition of Na 3 H(SO 4 ) 2 has been found independently at 513 K by Bose et al. [2] and at 533 K by Moskvich et al. [3] in an NMR experiment. The crystal structure of Na 3 H(SO 4 ) 2 in the high-temperature phase has been studied by Chen et al. via X-ray diffraction [4]. The crystal system was transformed from the monoclinic room-temperature phase to hexagonal high temperature phase. The possible space groups are that are proposed are
¯ P6 3 / mmc, P6 3 mc or P62c in high-temperature phase. The reorientation of SO 4 groups and the disorder of both H and Na atoms are proposed [4]. No detailed structural analysis has yet been performed at high temperature. It has been found that some hydrogen-bonded crystals with general formula M 3 H(XO 4 ) 2 (M 5 Rb, Cs, NH 41 and X 5 S, Se) undergo structural phase transitions above room temperature and become fast ionic conductors in the high temperature phases [5– 7]. But the structure of Na 3 H(SO 4 ) 2 is not isomorphous with them in both room- and high-temperature phases. In this paper, we report the results of electrical impedance measurement of the sample crystal. The mechanism of electrical conduction in the sample crystal is also studied.
*Corresponding author. E-mail: [email protected] 0167-2738 / 98 / $19.00 1998 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 98 )00135-0
278
R.H. Chen et al. / Solid State Ionics 110 (1998) 277 – 281
2. Experimental Colorless sample crystals of Na 3 H(SO 4 ) 2 were grown from the aqueous solutions containing 3:1 mole fraction of Na 2 SO 4 and H 2 SO 4 by slow evaporation at room temperature. Transparent plates with a (010) predominant face were obtained. The b m -axis is perpendicular to the crystal plate. The measured density using the floating methods was 2.402 g cm 23 . A single domain crystal of 3 mm 3 1.5 mm with thickness 0.75 mm is cut from a swallow-tail twin for the impedance measurement. The sample crystal was pasted with silver paster on (010) plates as electrodes. The complex impedance of the specimens was measured at the frequency range of 4 kHz to 40 MHz with a HP4194A impedance analyzer interfaced to a IBM compatible PC. The impedance measurements were carried out in the temperature interval 258C–3168C. The temperature of the sample crystal was controlled by a Huber high temperature attachment with a precision of 618C.
3. Results and discussions From the obtained impedance data, the typical semicircles of the impedance plot are observed. The equivalent circuit for the sample crystal is proposed to be close to the parallel combination of resistance and capacitance of bulk crystal. The sample impedance ( $ 10 6 V) at low frequencies and at temperatures below 2008C is too large for accurate measurements with our impedance analyzer. The DC conductivity is not extracted. Though the results are plotted at some high frequencies, the frequency dependence is consistent. Fig. 1 shows the result of the temperature dependence of electrical conductivity for the sample crystal at several frequencies. As the temperature is raised, the electrical conductivity decreases slightly until around 1608C and then it increases with increasing temperature. Before 1608C, the sample crystal behaves well as a typical insulator. The conductivity increases drastically near the transition point. The electrical conductivity increased about two order of magnitude from the room-temperature phase to high temperature phase. The conductivity increases with increasing temperature again in the region of high temperatures.
Fig. 1. Temperature dependence of the AC electrical conductivity of sample crystal along the b m -axis at several frequencies.
The temperature dependence of ionic conductivity is usually given by the Arrhenius equation
s T 5 A exp(2Eg /KB T )
(1)
where Eg is the activation energy of the migration ion, k B is the Boltzmann constant, T is absolute temperature and A is the preexponential factor. On the basis of Eq. (1), ln(s T ) versus 1000 /T at several AC frequencies is plotted in Fig. 2. An increasing of slope is observed above 1608C and the slopes change discontinuously at about 2328C. The former temperature (|1608C) shifts to a higher temperature as the frequency is increased. It indicated that the ion mobility in the crystal of this phase is effected by the applied frequencies. The obtained activation energies are 0.19 eV, 0.21 eV, 0.29 eV and 0.36 eV (18.3 kJ mole 21 –34.6 kJ mole 21 ) for the decreasing applied AC frequencies. Fig. 3a shows the crystal structure of the sample crystal in the room temperature phase as determined by Catti et al. [1]. The crystal cell is outlined alternatively in different ways by the b m 2, [101] m 2 ¯ m 2 axes. The dimensions of and half of the [101] ˚ 10.368 A ˚ and 7.233 A ˚ this cell are 9.648(1) A,
R.H. Chen et al. / Solid State Ionics 110 (1998) 277 – 281
279
Fig. 2. Arrhenius plot of the ionic conductivity for the sample crystal at several frequencies.
respectively and the axes are closely perpendicular to each other. There are four chemical formulas in such a cell. Two nonequivalent SO 4 groups are linked by the shortest hydrogen bond as compared with the other members of the general chemical formula of M 3 H(XO 4 ) 2 [1]. The length of the hydrogen bonds ˚ The hydrogen bond is are O? ? ?O52.432(2) A. ˚ and H? ? ?O5 asymmetric with O–H51.156(3) A ˚ 1.276 A and the angle of O–H? ? ?O is 179.1(2)8, as evaluated from neutron diffraction data [8]. The projection of the atomic positions onto the plane containing b m - and [101] m -axes is given in Fig. 3b. We assume that the reorientation of SO 4 takes place and the hydrogen bonds are broken gradually at temperatures above 160 8C. The proton ions are relatively free to move between the neighboring SO 4 groups. Hence, the proton ions make the main contribution to the electrical conductivity of Na 3 H(SO 4 ) 2 in this intermediated phase. Moskvich et al. had also found that the electrical conduction of Na 3 H(SO 4 ) 2 is caused by the proton diffusion in this phase by the NMR studies [3]. Although the ionic conductivity measurements would reflect the structure change, the crystal structure of Na 3 H(SO 4 ) 2 in the temperature range of 1608C to 2328C is not well established and reported yet.
Fig. 3. (a) Schematic drawing of the crystal structure of Na 3 H(SO 4 ) 2 , as determined by Catti et al. [1], but shown in the different cell dimensions; (b) Same as (a) but the projection is ¯ m -axis. The decimal numbers indicate the approxialong the [101] ¯ m. mate heights of the atoms in terms of the half length of [101]
The structure of Na 3 H(SO 4 ) 2 transforms to the hexagonal system in the high-temperature phase as studies by X-ray diffraction have shown [4]. The b h* -axis of the high-temperature phase is found along the b m -axis (or b *m ) of the room-temperature phase. The direction of the c h -axis points closely along the ¯ m and then the a h direction is close direction of [101] to the [101] m direction [4]. The likely crystal structure in the high-temperature phase as proposed by Chen et al. [4] is given in Fig. 4a. The unit cell ˚ and c h 57.18(7)A ˚ [4]. dimensions are a h 55.37(5) A There is one formula unit in this hexagonal cell. The structure is changed by the reorientation and / or the dynamical orientational disorder up and down of SO 4 groups as the temperature is raised [4]. The dy-
280
R.H. Chen et al. / Solid State Ionics 110 (1998) 277 – 281
Fig. 4. (a) The proposed crystal structure of Na 3 H(SO 4 ) 2 in the high temperature phase [4]. One of the sodium atoms, Na(3), is disordered in two positions and the hydrogen atom is dynamically disordered in six positions as shown in the figure; (b) Same as (a) but the crystal structure is projected onto the (001) plane. The jump paths of the proton ions between neighboring disordered positions are shown by arrows.
namically disordered model of SO 4 tetrahedra has been proposed in other sulfate crystals, such as the high-temperature form of K 2 SO 4 and Na 2 SO 4 [9,10]. The discrepancy from the Arrhenius behavior at the temperatures around 2468C is also observed in Fig. 2. The incomplete onset of dynamical disorder of up and down of SO 4 may show the electrical conductivity behavior in this temperature range. The sulfur atoms of the SO 4 groups are at the special positions (2 / 3, 1 / 3, 1 / 4) and (1 / 3, 2 / 3, 3 / 4). Two sodium atoms, Na(1) and Na(2), are located at (0, 0, 0) and (0, 0, 1 / 2) respectively, while the third sodium atom, Na(3), is disordered at the positions of (2 / 3, 1 / 3, 3 / 4) and (1 / 3, 2 / 3, 1 / 4). The position of the hydrogen atom was unable to be determined in the work of Chen et al. [4]. We proposed that the hydrogen atom is statistically disordered at six
positions as shown in Fig. 4a. The hydrogen atom still links two SO 4 tetrahedra which are near neighbors but the bonding is much weaker than that of the room-temperature phase. The thermal effect increases the number of possible proton sites and activates the concentration of possible vacancy sites. As the electric field is applied along the b m -axis of the sample crystal, the high electrical conductivity is caused by jumps of proton ions onto these new possible positions. The proton ion migration paths within the layers of z50 and z51 / 2 are shown in Fig. 4b. Beside the hydrogen diffusion, the sodium ions are also possibile ions for migration through the crystal. The contribution of the sodium ions to the electrical conductivity in the high-temperature phase is also verified by the NMR study of ionic motion in Na 3 H(SO 4 ) 2 crystal [3]. The value of the electrical conductivity in the high-temperature phase is |10 2 3 S cm 2 1 . It is about ten times larger than those found in the high temperature phases of K 2 SO 4 and Na 2 SO 4 crystals [11,12]. The activation energies as measured from Fig. 2 in the high-temperature phase are 0.32 eV, 0.32 eV, 0.32 eV, and 0.35 eV (|31.5 kJ mole 21 ) which are almost independent of the applied frequencies. The electrical contribution of the third disordered sodium ion, Na(3), in the c h -direction will be more or less hindered by the surrounding SO 4 groups. Unfortunately, the conductivity measurement along some other axis is somewhat difficult to do in the present studies. The comparison of the electrical conductivity along the different directions has not been made. The high-temperature form of Na 3 H(SO 4 ) 2 crystal is optically turbid and disrupts easily and the crystal cannot return to its initial form as the temperature is lowered from the high temperature. The measurements have not been carried out on cooling back to low temperature. It is suggested that the structural phase transition around 2468C is very drastic. Further studies on the structure and transition mechanism of every phase in the sample crystal are still required.
Acknowledgements This research was supported by the National Science Council, Republic of China (Project No. NSC 85-2112-M003-009).
R.H. Chen et al. / Solid State Ionics 110 (1998) 277 – 281
References [1] M. Catti, G. Ferraris, G. Ivaldi, Acta Cryst. B 35 (1979) 525. [2] M. Bose, K. Roy, A. Ghoshray, Proc. Nucl. Phys. Solid State Phys. Sym. 24C (1981) 393. [3] Y.N. Moskvich, A.M. Polyakov, A.A. Sukhovsky, Ferroelectrics 81 (1988) 197. [4] R.H. Chen, S.C. Chen, T.M. Chen, Phase Transitions 53 (1995) 15. [5] A.I. Baranov, I.P. Makarova, L.A. Muradyan, A.V. Tregubchenko, L.A. Shuvalov, V.I. Simonov, Sov. Phys. Crystallogr. 32(3) (1987) 400. [6] B.V. Merinov, A.I. Baranov, L.A. Shuvalov, Sov. Phys. Crystallogr. 35(2) (1990) 200.
281
[7] K. Furukawa, S. Akaloshi, T. Fukami, K. Hukuda, J. Phys. Soc. Jpn. 59 (1990) 4560. [8] W. Joswig, H. Fuess, G. Ferraris, Acta Cryst. B 38 (1982) 2798. [9] M. Miyake, H. Morikawa, S.I. Iwai, Acta Cryst. B 36 (1980) 532. [10] S.E. Rasmussen, J.E. Jorgensen, B. Lundtoft, J. Appl. Cryst. 29 (1996) 42. [11] B.K. Choi, Y.H. Cho, H.K. Lee, J. Phys. Chem. Solids 54 (1993) 197. [12] B.K. Choi, D.J. Lockwood, Phys. Rev. B 40 (1989) 4683.