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Anion reorientation in Na3PO4
ELSEVIER
Physica B 241 243 (1998) 338-340
Anion reorientation in Na3PO4 D. Wilmer a'*, R.D. Banhatti a, J. Fitter b, K. Funke a, M. Jansen c, G. Korus c, R.E.
Lechner b
a Institutfiir Physikalische Chemie, Sehloflplatz 4/7, D-48149 Miinster, Germany b Hahn-Meitner-lnstitut, Glienieker Str. 100, D-14109 Berlin, Germany c lnstitutfiir Anorganische Chemie, Domagkstr. 1, D-53121 Bonn, Germany
Abstract The reorientational motion of phosphate anions in the high-temperature phase of Na3PO 4 has been investigated with a coherent quasielastic neutron-scattering experiment. Our study aimed at clarifying the relevance of the so-called "paddle-wheel" mechanism, i.e., the influence of the anion motion on the translational Na + ion conduction. In the Q range between 0.3 and 2.3 A- 1, the data could be fitted by the sum of a 6 function and a single Lorentzian whose width exhibits an Arrhenius behavior with an activation energy of 0.184eV. We have calculated Sq(Q, co), the coherent quasielastic structure factor of the oxygen ions, based on several models. A comparison of the model predictions with our experimental data shows that only three oxygen atoms per anion are rotationally mobile. The experiment yields an additional small maximum around 1.5 ,~- 1, which appears more pronounced at higher temperatures. Its position on the Q scale suggests that sodium ions, further away from the center of rotation, are involved in the reorientational anion motion. © 1998 Elsevier Science B.V. All rights reserved.
Keywords: Coherent quasielastic neutron scattering; Paddle-wheel mechanism; Rotator phases; Ionic conduction
1. Introduction Sodium orthophosphate undergoes a first-order phase transition at 598 K. The high-temperature form (H-Na3PO4) is both a plastic phase and a good sodium ion conductor [1,2]. The orientationally disordered P O 3- anions form an F C C lattice in which the sodium cations occupy all the tetrahedral and octahedral interstices [1]. H-Na3PO4 exhibits a considerable cationic conductivity (about 1 0 - 3 f U l c m -1 at 600K). Since anionic rotational disorder and high cationic *Corresponding author. Tel.: +49 251 832 3436; fax: +49 251 832 9138; e-mail: [email protected].
mobility are both observed above the phase transition temperature, it has been suggested that the rotational motion of the translationally fixed tetrahedral PO43- anions enhances the sodium ion transport [3]. Due to the lack of vacancies and free space for the sodium ion hopping, H-Na3PO4 is a very good candidate for a study of the interplay of anion rotation and cation hopping, i.e. the importance of the "paddle-wheel" mechanism.
2. Experimental QNS experiments were performed with the timeof-flight spectrometer N E A T at the Hahn-Meitner-
0921-4526/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved PI1 S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 5 7 9 - 6
339
D. Wilmer et al. /Physica B 241--243 (1998) 338-340
Institut [4]. Spectra have been taken at nine temperatures between 300 and 973K. The incident wavelength of 5.1 A resulted in an elastic resolution of about 100 ~teV (FWHM).
3. Results and discussion
~,~ 1 . 0 09 08 ~ 0.7 ~ 0.6 1,2 1.1
i
i
i
i
~
i
i
~
0.5 0.4
The spectra taken from H-Na3PO4 consist of incoherent elastic scattering from Na (only slightly decreasing with increasing Q; at the selected resolution of 100 ~teV, the cationic translational motion is too slow to be distinguished from the elastic scattering) and coherent quasielastic scattering from oxygen nuclei due to the phosphate reorientation. The spectra are easily fitted by a combination of a 5-function and a single Lorentzian, broadened by convolution with the resolution function. The quasielastic line width h~-I does not depend on Q (indicating the localized character of the observed rotational motion), but increases with temperature in an Arrhenius-type fashion, see Fig. 1. The activation energy is 0.184eV. Our model calculations concentrate on the quasielastic structure factor. Experimental values obtained at three different temperatures are shown in Fig. 2. Oxygen being an exclusively coherent scatterer, we need to consider models for the quasielastic part of the coherent structure factor, Sq(Q, co). Assuming that correlations between different anions may be neglected [5,6], we have calculated Sq(Q, ~o) based on four different models for the anion reorientation: (i) isotropic rotational diffusion (four mobile ions), (ii) rotational jump diffusion around the Cz-axis (four mobile ions), (iii) continuous rotational diffusion and (iv) rotational jump diffusion around the Cs-axis (three mobile ions). All models predict single Lorentzians in the Q range under study. In Fig. 2, we have scaled the quasielastic intensity predicted by the models using the measured elastic intensity at low temperature (473 K, Q--* 0), which is considered to be entirely due to incoherent sodium scattering. Considering that there is no adjustable parameter for the quasielastic structure factor, the agreement between models (iii), (iv) and the experimental data is surprising; models (i) and (ii) do not give a satisfactory fit. We may conclude that in
0.3
0.2 1.0
I
I
I
I
I
I
I
1.1
1.2
1.3
1.4 1 0 0 0 KI'I-
1.5
1.6
1.7
1.8
Fig. 1. Arrhenius plot for the quasielastic neutron scattering line width, expressed as r 1, measured at Q = 2.16,~ 1. The activation energy is 0.184 eV.
12.0
10.0
three mobile ions -four mobile ions ..... 973 K o 673 K + 613K c3
8.0
6.0
/ o
4.0
2.0
~
0.0 0.0
0.5
~-
,
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Q/A-1 Fig. 2. Quasielastic structure factor of H-Na3PO 4 at three different temperatures. Model curves have been scaled according to the incoherent elastic scattering measured at 473 K.
agreement with the X-ray data of quenched samples of Na3PO4[-1], the disorder and rotational reorientation of the phosphate ions is mainly represented by a circular motion of three oxygen atoms. This does not exclude other types of anion reorientations, which, if they exist, are simply too slow to be detected in our study. Interestingly, the experiment yields an additional small maximum around 1.5 A-1, see Fig. 2, which seems to become more pronounced as the temperature is increased. Its position on the Q scale suggests that sodium ions, further away from the
340
D. Wilmer et al. / Physica B 241 243 (1998) 338 340
center of rotation, are involved in the reorientational m o t i o n of some of the anions.
4. Conclusions As part of a larger study on the importance of the "paddle-wheel" mechanism, we have succeeded in determining the dynamics and geometry of the anion reorientation in H-Na3PO4. The quasielastic neutron scattering shows that this reorientation is restricted to a circular m o t i o n a r o u n d one of the C3-axes, performed by only three of the four oxygen atoms. The dynamics can be described by a single time constant ~ which is thermally activated with an energy of 0.184 eV.
Acknowledgements T w o of the authors (R.D.B., D.W.) are grateful for support by the Alexander von H u m b o l d t F o u n dation.
References [1] D.M. Wiench, M. Jansen, Z. Anorg. Allg. Chem 461 {1980) 101. [2] H. Hruschka, E. Lissel, M. Jansen, Solid State Ion. 28 30 (1988) 159. [3] M. Jansen, Angew. Chem. 103 (1991) 1574. [4] R.E. Lechner, R. Melzer, J. Fitter, Physica B 226 (1996) 86. [5] D.L. Price, M.L. Saboungi, Phys. Rev. B 44 (1991i 7289. [6] D.A. Neumann et al., Phys. Rev. Lett. 67 (1991~ 3808.
Physica B 241 243 (1998) 338-340
Anion reorientation in Na3PO4 D. Wilmer a'*, R.D. Banhatti a, J. Fitter b, K. Funke a, M. Jansen c, G. Korus c, R.E.
Lechner b
a Institutfiir Physikalische Chemie, Sehloflplatz 4/7, D-48149 Miinster, Germany b Hahn-Meitner-lnstitut, Glienieker Str. 100, D-14109 Berlin, Germany c lnstitutfiir Anorganische Chemie, Domagkstr. 1, D-53121 Bonn, Germany
Abstract The reorientational motion of phosphate anions in the high-temperature phase of Na3PO 4 has been investigated with a coherent quasielastic neutron-scattering experiment. Our study aimed at clarifying the relevance of the so-called "paddle-wheel" mechanism, i.e., the influence of the anion motion on the translational Na + ion conduction. In the Q range between 0.3 and 2.3 A- 1, the data could be fitted by the sum of a 6 function and a single Lorentzian whose width exhibits an Arrhenius behavior with an activation energy of 0.184eV. We have calculated Sq(Q, co), the coherent quasielastic structure factor of the oxygen ions, based on several models. A comparison of the model predictions with our experimental data shows that only three oxygen atoms per anion are rotationally mobile. The experiment yields an additional small maximum around 1.5 ,~- 1, which appears more pronounced at higher temperatures. Its position on the Q scale suggests that sodium ions, further away from the center of rotation, are involved in the reorientational anion motion. © 1998 Elsevier Science B.V. All rights reserved.
Keywords: Coherent quasielastic neutron scattering; Paddle-wheel mechanism; Rotator phases; Ionic conduction
1. Introduction Sodium orthophosphate undergoes a first-order phase transition at 598 K. The high-temperature form (H-Na3PO4) is both a plastic phase and a good sodium ion conductor [1,2]. The orientationally disordered P O 3- anions form an F C C lattice in which the sodium cations occupy all the tetrahedral and octahedral interstices [1]. H-Na3PO4 exhibits a considerable cationic conductivity (about 1 0 - 3 f U l c m -1 at 600K). Since anionic rotational disorder and high cationic *Corresponding author. Tel.: +49 251 832 3436; fax: +49 251 832 9138; e-mail: [email protected].
mobility are both observed above the phase transition temperature, it has been suggested that the rotational motion of the translationally fixed tetrahedral PO43- anions enhances the sodium ion transport [3]. Due to the lack of vacancies and free space for the sodium ion hopping, H-Na3PO4 is a very good candidate for a study of the interplay of anion rotation and cation hopping, i.e. the importance of the "paddle-wheel" mechanism.
2. Experimental QNS experiments were performed with the timeof-flight spectrometer N E A T at the Hahn-Meitner-
0921-4526/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved PI1 S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 5 7 9 - 6
339
D. Wilmer et al. /Physica B 241--243 (1998) 338-340
Institut [4]. Spectra have been taken at nine temperatures between 300 and 973K. The incident wavelength of 5.1 A resulted in an elastic resolution of about 100 ~teV (FWHM).
3. Results and discussion
~,~ 1 . 0 09 08 ~ 0.7 ~ 0.6 1,2 1.1
i
i
i
i
~
i
i
~
0.5 0.4
The spectra taken from H-Na3PO4 consist of incoherent elastic scattering from Na (only slightly decreasing with increasing Q; at the selected resolution of 100 ~teV, the cationic translational motion is too slow to be distinguished from the elastic scattering) and coherent quasielastic scattering from oxygen nuclei due to the phosphate reorientation. The spectra are easily fitted by a combination of a 5-function and a single Lorentzian, broadened by convolution with the resolution function. The quasielastic line width h~-I does not depend on Q (indicating the localized character of the observed rotational motion), but increases with temperature in an Arrhenius-type fashion, see Fig. 1. The activation energy is 0.184eV. Our model calculations concentrate on the quasielastic structure factor. Experimental values obtained at three different temperatures are shown in Fig. 2. Oxygen being an exclusively coherent scatterer, we need to consider models for the quasielastic part of the coherent structure factor, Sq(Q, co). Assuming that correlations between different anions may be neglected [5,6], we have calculated Sq(Q, ~o) based on four different models for the anion reorientation: (i) isotropic rotational diffusion (four mobile ions), (ii) rotational jump diffusion around the Cz-axis (four mobile ions), (iii) continuous rotational diffusion and (iv) rotational jump diffusion around the Cs-axis (three mobile ions). All models predict single Lorentzians in the Q range under study. In Fig. 2, we have scaled the quasielastic intensity predicted by the models using the measured elastic intensity at low temperature (473 K, Q--* 0), which is considered to be entirely due to incoherent sodium scattering. Considering that there is no adjustable parameter for the quasielastic structure factor, the agreement between models (iii), (iv) and the experimental data is surprising; models (i) and (ii) do not give a satisfactory fit. We may conclude that in
0.3
0.2 1.0
I
I
I
I
I
I
I
1.1
1.2
1.3
1.4 1 0 0 0 KI'I-
1.5
1.6
1.7
1.8
Fig. 1. Arrhenius plot for the quasielastic neutron scattering line width, expressed as r 1, measured at Q = 2.16,~ 1. The activation energy is 0.184 eV.
12.0
10.0
three mobile ions -four mobile ions ..... 973 K o 673 K + 613K c3
8.0
6.0
/ o
4.0
2.0
~
0.0 0.0
0.5
~-
,
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Q/A-1 Fig. 2. Quasielastic structure factor of H-Na3PO 4 at three different temperatures. Model curves have been scaled according to the incoherent elastic scattering measured at 473 K.
agreement with the X-ray data of quenched samples of Na3PO4[-1], the disorder and rotational reorientation of the phosphate ions is mainly represented by a circular motion of three oxygen atoms. This does not exclude other types of anion reorientations, which, if they exist, are simply too slow to be detected in our study. Interestingly, the experiment yields an additional small maximum around 1.5 A-1, see Fig. 2, which seems to become more pronounced as the temperature is increased. Its position on the Q scale suggests that sodium ions, further away from the
340
D. Wilmer et al. / Physica B 241 243 (1998) 338 340
center of rotation, are involved in the reorientational m o t i o n of some of the anions.
4. Conclusions As part of a larger study on the importance of the "paddle-wheel" mechanism, we have succeeded in determining the dynamics and geometry of the anion reorientation in H-Na3PO4. The quasielastic neutron scattering shows that this reorientation is restricted to a circular m o t i o n a r o u n d one of the C3-axes, performed by only three of the four oxygen atoms. The dynamics can be described by a single time constant ~ which is thermally activated with an energy of 0.184 eV.
Acknowledgements T w o of the authors (R.D.B., D.W.) are grateful for support by the Alexander von H u m b o l d t F o u n dation.
References [1] D.M. Wiench, M. Jansen, Z. Anorg. Allg. Chem 461 {1980) 101. [2] H. Hruschka, E. Lissel, M. Jansen, Solid State Ion. 28 30 (1988) 159. [3] M. Jansen, Angew. Chem. 103 (1991) 1574. [4] R.E. Lechner, R. Melzer, J. Fitter, Physica B 226 (1996) 86. [5] D.L. Price, M.L. Saboungi, Phys. Rev. B 44 (1991i 7289. [6] D.A. Neumann et al., Phys. Rev. Lett. 67 (1991~ 3808.