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Atomic level mechanism of proton transport in alkali metal hydrogen sulfate and selenate superionic conductors
Solid State Ionics 136–137 (2000) 223–227 www.elsevier.com / locate / ssi
Atomic level mechanism of proton transport in alkali metal hydrogen sulfate and selenate superionic conductors a, b B.V. Merinov *, U. Bismayer a
b
Institute of Crystallography of the Russian Academy of Sciences, Leninskii pr. 59, 117333 Moscow, Russia ¨ Hamburg, Grindelallee 48, D-20146 Hamburg, Germany Mineralogisch-Petrographisches Institut, Universitat
Abstract The mechanism of proton diffusion in alkali metal hydrogen sulfates and selenates is analysed. The latest X-ray diffraction investigations of these compounds show that a highly correlated dynamic disorder of the hydrogen bonds occurs in the superionic phases. The observed diffraction patterns result from dynamically twinned crystals, which consist of a symmetry-related number of domains. We discuss the ‘anomalous display of the dynamically disordered hydrogen atoms on the electron density maps’, which is observed in the superionic phases. New X-ray diffraction data allow the atomic level mechanism of proton transport in the alkali metal hydrogen sulfates and selenates to be elucidated in detail. 2000 Elsevier Science B.V. All rights reserved. Keywords: E. Proton conductors; Alkali sulfates; Alkali selenates, Ionic conductivity–proton
1. Introduction The observation of superionic conductivity in CsHSO 4 and CsHSeO 4 [1] led to an intensive study of similar anhydrous compounds as potential solid state proton conductors. It turned out that most of the MXAO 4 , M 3 X(AO 4 ) 2 and M 5 X 3 (AO 4 ) 4 crystals, where M 5 NH 4 , K, Rb, Cs; X 5 H, D; A 5 S, Se, undergo superionic phase transitions which are ferroelastic simultaneously. Transport properties of these alkali metal hydrogen sulfates and selenates are due to the appearance of a dynamically disordered hydrogen bond network in the superionic paraelastic phases [2–4]. Two basic steps, proton motion within a double-well hydrogen bond (intrabond motion) and *Corresponding author. Fax: 1 7-095-135-10-11. E-mail address: [email protected] (B.V. Merinov).
HAO 4 reorientation (interbond motion), can be distinguished in the proton transport mechanism [5]. However, this is an over-simplified representation of the proton diffusion in the above-mentioned compounds. Further detailed studies of these materials have allowed the mechanism of proton transport to be modelled. Recent X-ray diffraction single crystal studies of MXAO 4 , M 3 X(AO 4 ) 2 and M 5 X 3 (AO 4 ) 4 revealed some unusual phenomena which could be characterised as ‘the effect of anomalous display of dynamically disordered hydrogen atoms on electrondensity maps’ [6]. The detailed analysis of the electron-density distributions showed the presence of electron density peaks which correspond to dynamically disordered hydrogen atoms with position occupancies 1 / 6, 1 / 12 and even less. One would not expect an observation of a visible electron density, which is related to hydrogen atoms disordered over
0167-2738 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 00 )00314-3
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their crystallographic positions with such low occupancies. Nevertheless, in the structure determinations of the superionic phases of some MXAO 4 , M 3 X(AO 4 ) 2 and M 5 X 3 (AO 4 ) 4 crystals we could localise and even refine the positions of the disordered hydrogen atoms. This allows the atomic level mechanism of the superionic transport in alkali metal hydrogen sulfates and selenates to be elucidated. In this paper we try to answer the question: why are the dynamically disordered hydrogen atoms with extremely low occupancies clearly seen on the electron-density maps?
2. Dynamic twinning as the reason of the anomalous display of the hydrogen atoms As was mentioned above, the superionic phase transitions in MHAO 4 , M 3 H(AO 4 ) 2 and M 5 H 3 (AO 4 ) 4 are also ferroelastic. On cooling the paraelastic phases a high-symmetry axis is forbidden below the superionic phase transition temperature and ferroelastic low-symmetry domains related by the high-symmetry axis can be formed. The hydrogen bond network, which is dynamically disordered in the superionic phases, becomes ordered in the ferroelastic phases. Our latest X-ray diffraction studies showed that a highly correlated dynamic disorder of the hydrogen bonds is observed in the superionic phases of the alkali metal hydrogen sulfates and selenates [7]. This means that a change of the orientation of one hydrogen bond induces cooperative orientation changes of other hydrogen bonds and AO 4 tetrahedra within some crystal volume. The size of this volume is at least of an X-ray beam coherence length ( | 1 mm). Therefore, as for the light atoms, which participate in the hydrogen bond formation, the situation is similar as if the ferroelastic domains exist in the paraelastic phase but with dynamic character. The reorientation of the HAO 4 groups occurs relatively rarely if they are examined in the time scale of X-ray scattering [5,8], i.e. the residence time of the orientation states is much larger than the characteristic time of the process of X-ray scattering. Therefore, the observed diffraction patterns should be considered as resulting from twinned crystals, which consist of domains related by the corresponding high-symmetry axis. As
it is shown in [7], the above-mentioned domain twinning results in ‘amplification’ of the electron density at the hydrogen atom position. Such an interpretation allows the anomalous display of the dynamically disordered hydrogen atoms in the superionic paraelastic phases of the alkali metal hydrogen sulfates and selenates to be understood.
3. Atomic level mechanism of proton transport The anomalous display of the hydrogen atoms shows details of the proton diffusion mechanism. Three main components: thermal librations of the HAO 4 group, reorientations of the HAO 4 group and the hydrogen transfer from one potential minimum of the hydrogen bond to the other can be distinguished in the proton transport process. The first two components are clearly seen in Fig. 1 and the third component in Fig. 2. The atomic level mechanism of the superprotonic transport in the alkali metal hydrogen sulfates and selenates can be described as follows. During thermal vibrations of the oxygen atoms which participate in hydrogen bonding, and thermal librations of the HAO 4 groups as a whole, the hydrogen bonds are deformed and the corresponding potential curves are changed in time as well (see Fig. 3). Under certain conditions, when one of the neighbouring AO 4 tetrahedra is in a suitable position and the hydrogen bond becomes long enough, the existing hydrogen bond is broken and a new one is formed (Fig. 3b, c) — interbond motion. On the other hand, due to the same thermal processes there occur situations when the hydrogen bond becomes relatively short and the proton can overcome the potential barrier within the hydrogen bond and moves from one potential minimum to the other (Fig. 3d) — intrabond motion. Our calculations of the potential barriers for the interbond and intrabond motions from the X-ray data result in similarly quite low values (Figs. 4 and 5). However, we assume that the real potential barriers are higher by 30–50% than the calculated ones which are most probably underflowed because of the above-mentioned amplification of the electron density at the hydrogen atom position. The ammonium-containing members of the MHAO 4 , M 3 H(AO 4 ) 2 and M 5 H 3 (AO 4 ) 4 families of proton conductors have certain distinctions from the
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Fig. 1. The electron density section showing thermal vibration and reorientation motion of the acid hydrogen atom in the superionic phase ˚ – 3 , positive contours are represented by solid lines, negative contours by of Cs 3 H(SeO 4 ) 2 . Contour intervals are drawn at steps of 0.1 eA dashed lines and zero levels are omitted.
[Rb 0.57 (NH 4 ) 0.43 ] 3 H(SeO 4 ) 2 single crystal [7] shows that, most probably, the hydrogen atoms of one of the two crystallographically distinguished NH 4 groups also participate in the proton transport process by exchanging positions with the acid hydrogen atoms. The potential barrier for such motion is rather low (Fig. 6).
4. Conclusions
Fig. 2. The electron density of the acid hydrogen atom in the superionic phase of Cs 3 H(SeO 4 ) 2 in the hydrogen bond plane parallel to the z axis. Contour intervals, etc. as given for Fig. 1.
other alkali metal hydrogen sulfates and selenates due to the presence of the additional hydrogen atoms of the steric NH 4 ions. In the superionic phases of these compounds disorder of the ammonium groups is observed along with the HAO 4 disorder [9,10]. Our recent X-ray diffraction study of a mixed
1. X-ray diffraction single crystal studies of MXAO 4 , M 3 X(AO 4 ) 2 and M 5 X 3 (AO 4 ) 4 have revealed some unusual phenomena which could be characterised as the effect of anomalous display of dynamically disordered hydrogen atoms: the dynamically disordered hydrogen atoms with position occupancies 1 / 6, 1 / 12 and even less are clearly seen on the appropriate electron density maps. 2. Dynamic twinning of domains related by the corresponding high-symmetry axis is the reason of the anomalous display of the hydrogen atoms. 3. The dynamic twinning results from a highly correlated dynamic disorder of the hydrogen
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Fig. 4. The potential curve calculated for the interbond motion of the acid hydrogen atom in the superionic phase of Cs 3 H(SeO 4 ) 2 .
Fig. 5. The potential curve calculated for the intrabond motion of the acid hydrogen atom in the superionic phase of Cs 3 H(SeO 4 ) 2 .
Fig. 3. Sectors of the proton transport mechanism in the alkali metal hydrogen sulfates and selenates.
bonds, which is observed in the superionic phases of the alkali metal hydrogen sulfates and selenates. 4. From the study of the ammonium-containing M 3 H(AO 4 ) 2 compounds we found that the hydrogen atoms of the NH 4 groups also participate in the proton transport process by exchanging positions with the acid hydrogen atoms.
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References
Fig. 6. The potential curve calculated for the exchanged motion between acid and ammonium hydrogen atoms in the superionic phase of [Rb 0.57 (NH 4 ) 0.43 ] 3 H(SeO 4 ) 2 .
Acknowledgements Financial support from the Alexander von Humboldt Foundation is gratefully acknowledged.
[1] A.I. Baranov, L.A. Shuvalov, N.M. Schagina, Sov. Phys. Crystallogr. 29 (1984) 706. [2] B.V. Merinov, A.I. Baranov, L.A. Shuvalov, B.A. Maksimov, Sov. Phys. Crystallogr. 32 (1987) 47. [3] A.I. Baranov, I.P. Makarova, L.A. Muradyan, A.V. Tregubchenko, L.A. Shuvalov, V.I. Simonov, Sov. Phys. Crystallogr. 32 (1987) 400. [4] B.V. Merinov, A.I. Baranov, L.A. Shuvalov, Sov. Phys. Crystallogr. 35 (1990) 200. [5] R. Blinc, J. Dolinsek, G. Lahajnar, I. Zupanic, L.A. Shuvalov, A.I. Baranov, Phys. Status Solidi (b) 123 (1984) K83. [6] B.V. Merinov, Crystallography Reports 42 (1997) 906. [7] B.V. Merinov, G. Bourenkov, U. Bismayer, Phys. Status Solidi 218 (2000). [8] V.P. Dmitriev, V.V. Loshkarev, L.M. Rabkin, L.A. Shuvalov, Yu.I. Yuzyuk, Sov. Phys. Crystallogr. 31 (1986) 673. [9] M. Kamoun, M. Halouani, A. Daoud, Phase Transitions 9 (1987) 327. [10] J. Tritt-Goc, N. Pislewski, S.K. Hoffmann, M. Augustyniak, Phys. Status Solidi (b) 176 (1993) K13.
Atomic level mechanism of proton transport in alkali metal hydrogen sulfate and selenate superionic conductors a, b B.V. Merinov *, U. Bismayer a
b
Institute of Crystallography of the Russian Academy of Sciences, Leninskii pr. 59, 117333 Moscow, Russia ¨ Hamburg, Grindelallee 48, D-20146 Hamburg, Germany Mineralogisch-Petrographisches Institut, Universitat
Abstract The mechanism of proton diffusion in alkali metal hydrogen sulfates and selenates is analysed. The latest X-ray diffraction investigations of these compounds show that a highly correlated dynamic disorder of the hydrogen bonds occurs in the superionic phases. The observed diffraction patterns result from dynamically twinned crystals, which consist of a symmetry-related number of domains. We discuss the ‘anomalous display of the dynamically disordered hydrogen atoms on the electron density maps’, which is observed in the superionic phases. New X-ray diffraction data allow the atomic level mechanism of proton transport in the alkali metal hydrogen sulfates and selenates to be elucidated in detail. 2000 Elsevier Science B.V. All rights reserved. Keywords: E. Proton conductors; Alkali sulfates; Alkali selenates, Ionic conductivity–proton
1. Introduction The observation of superionic conductivity in CsHSO 4 and CsHSeO 4 [1] led to an intensive study of similar anhydrous compounds as potential solid state proton conductors. It turned out that most of the MXAO 4 , M 3 X(AO 4 ) 2 and M 5 X 3 (AO 4 ) 4 crystals, where M 5 NH 4 , K, Rb, Cs; X 5 H, D; A 5 S, Se, undergo superionic phase transitions which are ferroelastic simultaneously. Transport properties of these alkali metal hydrogen sulfates and selenates are due to the appearance of a dynamically disordered hydrogen bond network in the superionic paraelastic phases [2–4]. Two basic steps, proton motion within a double-well hydrogen bond (intrabond motion) and *Corresponding author. Fax: 1 7-095-135-10-11. E-mail address: [email protected] (B.V. Merinov).
HAO 4 reorientation (interbond motion), can be distinguished in the proton transport mechanism [5]. However, this is an over-simplified representation of the proton diffusion in the above-mentioned compounds. Further detailed studies of these materials have allowed the mechanism of proton transport to be modelled. Recent X-ray diffraction single crystal studies of MXAO 4 , M 3 X(AO 4 ) 2 and M 5 X 3 (AO 4 ) 4 revealed some unusual phenomena which could be characterised as ‘the effect of anomalous display of dynamically disordered hydrogen atoms on electrondensity maps’ [6]. The detailed analysis of the electron-density distributions showed the presence of electron density peaks which correspond to dynamically disordered hydrogen atoms with position occupancies 1 / 6, 1 / 12 and even less. One would not expect an observation of a visible electron density, which is related to hydrogen atoms disordered over
0167-2738 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 00 )00314-3
224
B.V. Merinov, U. Bismayer / Solid State Ionics 136 – 137 (2000) 223 – 227
their crystallographic positions with such low occupancies. Nevertheless, in the structure determinations of the superionic phases of some MXAO 4 , M 3 X(AO 4 ) 2 and M 5 X 3 (AO 4 ) 4 crystals we could localise and even refine the positions of the disordered hydrogen atoms. This allows the atomic level mechanism of the superionic transport in alkali metal hydrogen sulfates and selenates to be elucidated. In this paper we try to answer the question: why are the dynamically disordered hydrogen atoms with extremely low occupancies clearly seen on the electron-density maps?
2. Dynamic twinning as the reason of the anomalous display of the hydrogen atoms As was mentioned above, the superionic phase transitions in MHAO 4 , M 3 H(AO 4 ) 2 and M 5 H 3 (AO 4 ) 4 are also ferroelastic. On cooling the paraelastic phases a high-symmetry axis is forbidden below the superionic phase transition temperature and ferroelastic low-symmetry domains related by the high-symmetry axis can be formed. The hydrogen bond network, which is dynamically disordered in the superionic phases, becomes ordered in the ferroelastic phases. Our latest X-ray diffraction studies showed that a highly correlated dynamic disorder of the hydrogen bonds is observed in the superionic phases of the alkali metal hydrogen sulfates and selenates [7]. This means that a change of the orientation of one hydrogen bond induces cooperative orientation changes of other hydrogen bonds and AO 4 tetrahedra within some crystal volume. The size of this volume is at least of an X-ray beam coherence length ( | 1 mm). Therefore, as for the light atoms, which participate in the hydrogen bond formation, the situation is similar as if the ferroelastic domains exist in the paraelastic phase but with dynamic character. The reorientation of the HAO 4 groups occurs relatively rarely if they are examined in the time scale of X-ray scattering [5,8], i.e. the residence time of the orientation states is much larger than the characteristic time of the process of X-ray scattering. Therefore, the observed diffraction patterns should be considered as resulting from twinned crystals, which consist of domains related by the corresponding high-symmetry axis. As
it is shown in [7], the above-mentioned domain twinning results in ‘amplification’ of the electron density at the hydrogen atom position. Such an interpretation allows the anomalous display of the dynamically disordered hydrogen atoms in the superionic paraelastic phases of the alkali metal hydrogen sulfates and selenates to be understood.
3. Atomic level mechanism of proton transport The anomalous display of the hydrogen atoms shows details of the proton diffusion mechanism. Three main components: thermal librations of the HAO 4 group, reorientations of the HAO 4 group and the hydrogen transfer from one potential minimum of the hydrogen bond to the other can be distinguished in the proton transport process. The first two components are clearly seen in Fig. 1 and the third component in Fig. 2. The atomic level mechanism of the superprotonic transport in the alkali metal hydrogen sulfates and selenates can be described as follows. During thermal vibrations of the oxygen atoms which participate in hydrogen bonding, and thermal librations of the HAO 4 groups as a whole, the hydrogen bonds are deformed and the corresponding potential curves are changed in time as well (see Fig. 3). Under certain conditions, when one of the neighbouring AO 4 tetrahedra is in a suitable position and the hydrogen bond becomes long enough, the existing hydrogen bond is broken and a new one is formed (Fig. 3b, c) — interbond motion. On the other hand, due to the same thermal processes there occur situations when the hydrogen bond becomes relatively short and the proton can overcome the potential barrier within the hydrogen bond and moves from one potential minimum to the other (Fig. 3d) — intrabond motion. Our calculations of the potential barriers for the interbond and intrabond motions from the X-ray data result in similarly quite low values (Figs. 4 and 5). However, we assume that the real potential barriers are higher by 30–50% than the calculated ones which are most probably underflowed because of the above-mentioned amplification of the electron density at the hydrogen atom position. The ammonium-containing members of the MHAO 4 , M 3 H(AO 4 ) 2 and M 5 H 3 (AO 4 ) 4 families of proton conductors have certain distinctions from the
B.V. Merinov, U. Bismayer / Solid State Ionics 136 – 137 (2000) 223 – 227
225
Fig. 1. The electron density section showing thermal vibration and reorientation motion of the acid hydrogen atom in the superionic phase ˚ – 3 , positive contours are represented by solid lines, negative contours by of Cs 3 H(SeO 4 ) 2 . Contour intervals are drawn at steps of 0.1 eA dashed lines and zero levels are omitted.
[Rb 0.57 (NH 4 ) 0.43 ] 3 H(SeO 4 ) 2 single crystal [7] shows that, most probably, the hydrogen atoms of one of the two crystallographically distinguished NH 4 groups also participate in the proton transport process by exchanging positions with the acid hydrogen atoms. The potential barrier for such motion is rather low (Fig. 6).
4. Conclusions
Fig. 2. The electron density of the acid hydrogen atom in the superionic phase of Cs 3 H(SeO 4 ) 2 in the hydrogen bond plane parallel to the z axis. Contour intervals, etc. as given for Fig. 1.
other alkali metal hydrogen sulfates and selenates due to the presence of the additional hydrogen atoms of the steric NH 4 ions. In the superionic phases of these compounds disorder of the ammonium groups is observed along with the HAO 4 disorder [9,10]. Our recent X-ray diffraction study of a mixed
1. X-ray diffraction single crystal studies of MXAO 4 , M 3 X(AO 4 ) 2 and M 5 X 3 (AO 4 ) 4 have revealed some unusual phenomena which could be characterised as the effect of anomalous display of dynamically disordered hydrogen atoms: the dynamically disordered hydrogen atoms with position occupancies 1 / 6, 1 / 12 and even less are clearly seen on the appropriate electron density maps. 2. Dynamic twinning of domains related by the corresponding high-symmetry axis is the reason of the anomalous display of the hydrogen atoms. 3. The dynamic twinning results from a highly correlated dynamic disorder of the hydrogen
226
B.V. Merinov, U. Bismayer / Solid State Ionics 136 – 137 (2000) 223 – 227
Fig. 4. The potential curve calculated for the interbond motion of the acid hydrogen atom in the superionic phase of Cs 3 H(SeO 4 ) 2 .
Fig. 5. The potential curve calculated for the intrabond motion of the acid hydrogen atom in the superionic phase of Cs 3 H(SeO 4 ) 2 .
Fig. 3. Sectors of the proton transport mechanism in the alkali metal hydrogen sulfates and selenates.
bonds, which is observed in the superionic phases of the alkali metal hydrogen sulfates and selenates. 4. From the study of the ammonium-containing M 3 H(AO 4 ) 2 compounds we found that the hydrogen atoms of the NH 4 groups also participate in the proton transport process by exchanging positions with the acid hydrogen atoms.
B.V. Merinov, U. Bismayer / Solid State Ionics 136 – 137 (2000) 223 – 227
227
References
Fig. 6. The potential curve calculated for the exchanged motion between acid and ammonium hydrogen atoms in the superionic phase of [Rb 0.57 (NH 4 ) 0.43 ] 3 H(SeO 4 ) 2 .
Acknowledgements Financial support from the Alexander von Humboldt Foundation is gratefully acknowledged.
[1] A.I. Baranov, L.A. Shuvalov, N.M. Schagina, Sov. Phys. Crystallogr. 29 (1984) 706. [2] B.V. Merinov, A.I. Baranov, L.A. Shuvalov, B.A. Maksimov, Sov. Phys. Crystallogr. 32 (1987) 47. [3] A.I. Baranov, I.P. Makarova, L.A. Muradyan, A.V. Tregubchenko, L.A. Shuvalov, V.I. Simonov, Sov. Phys. Crystallogr. 32 (1987) 400. [4] B.V. Merinov, A.I. Baranov, L.A. Shuvalov, Sov. Phys. Crystallogr. 35 (1990) 200. [5] R. Blinc, J. Dolinsek, G. Lahajnar, I. Zupanic, L.A. Shuvalov, A.I. Baranov, Phys. Status Solidi (b) 123 (1984) K83. [6] B.V. Merinov, Crystallography Reports 42 (1997) 906. [7] B.V. Merinov, G. Bourenkov, U. Bismayer, Phys. Status Solidi 218 (2000). [8] V.P. Dmitriev, V.V. Loshkarev, L.M. Rabkin, L.A. Shuvalov, Yu.I. Yuzyuk, Sov. Phys. Crystallogr. 31 (1986) 673. [9] M. Kamoun, M. Halouani, A. Daoud, Phase Transitions 9 (1987) 327. [10] J. Tritt-Goc, N. Pislewski, S.K. Hoffmann, M. Augustyniak, Phys. Status Solidi (b) 176 (1993) K13.