Sodium ion diffusion in solid solutions of sodium orthophosphate and sodium sulphate
Introduction
A number of simple inorganic crystalline materials like Li2SO4 and LiNaSO4 exhibit high-temperature modifications with both fast cation conductivity and anion rotational disorder. They may thus be termed fast ion conducting rotor phases.
Tracer diffusion measurements on these rotor phases (see [1] for a collection of diffusion data) revealed some peculiarities. In contrast to our expectation, various dopant cations show fast diffusion in these materials, more or less irrespective of their radii. In LiNaSO4, e.g., Na+ and Li+ show nearly equal diffusivities although the cross-section of the sodium ion is nearly twice as large as the one of the lithium ion.
It has, therefore, been suggested that a special cation conduction mechanism is operative in these phases, the key feature being that the rotational motion of the translationally fixed tetrahedral anions enhances the cation transport by some sort of dynamic coupling of these two motions.
There was a vigorous debate between the proponents of this so-called “paddle-wheel” mechanism [2], [3], [4], [5], [6] and those who favor an explanation in terms of a percolation-type mechanism, emphasizing the role of the increased volume in the high-temperature phase [7], [8], [9], [10], [11]. Part of the controversy was due to the fact that the term “paddle-wheel” mechanism was used in a variety of meanings [12].
Sodium orthophosphate (Na3PO4) undergoes a first-order phase transition at 598 K. The high-temperature form (α-Na3PO4)2 contains orientationally disordered PO43− anions and can thus be classified as a rotor phase [13]. The anions form an fcc lattice while the sodium cations occupy all the tetrahedral and octahedral interstices. Na3PO4 exhibits a considerable conductivity (about at 600 K) [15], which is entirely due to the mobility of sodium ions [12]. The low temperature form is tetragonal with space group [16]. Na3PO4 has several attractive properties as a model system for studying the complex ion dynamics in ion conducting rotor phases:
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The high-temperature rotor phase is stable over a wide temperature range between about 600 K and the melting point (literature values between 1613 and 1856 K) [17], [18].
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In contrast to the most prominent ion conducting rotor phase, Li2SO4, where the octahedral holes of the fcc anion arrangement are typically vacant, all octahedral and tetrahedral cation sites are occupied in Na3PO4. Under these circumstances, one would expect an increased probability for detecting a dynamic cation–anion coupling.
In order to determine the relevance of the dynamic coupling in rotor-phase fast-ion conductors, it is highly desirable to examine the dynamics of cations and anions in entirely dynamic experiments. Time-of-flight quasielastic neutron scattering has successfully been used to reveal the details of the anion reorientational motion in Na3PO4 [19] and in with x=0.1 and x=0.5 [20]. In these experiments, the quasielastic broadening was found to be solely due to the coherent scattering of oxygen atoms involved in the anion rotational motion, while the elastic contribution was attributed to incoherent sodium scattering.
In this paper, we present results of high-resolution quasielastic backscattering experiments capable of resolving the quasielastic broadening due to the sodium ion hopping. The analysis of the quasielastic linewidths, determined as functions of both momentum transfer and temperature, reveals a complete picture of the cation transport mechanism in .
Section snippets
Theory
Quasielastic neutron scattering experiments exhibit the broadening of the elastic scattering caused by non-periodic, i.e., diffusive motions in the sample as a function of momentum transfer, .
The classical model for random jump diffusion on Bravais lattices via nearest neighbour sites was derived by Chudley and Elliott (CE) in 1961 [21], see also [22], [23]. The CE model predicts a single Lorentzian for the incoherent dynamic structure factor, . In the case of polycrystalline
Sample preparation
Powder samples of pure Na3PO4 were obtained by solid state reaction of Na2CO3 and Na4P2O7 [15]. Equimolar amounts of Na2CO3 and Na4P2O7 were thoroughly mixed and fired at 1073 K for two days, reground and fired at 1273 K for another two days. Samples of with x=0.1 and x=0.5 were prepared by adding the respective amount of dry Na2SO4 to the previously synthesised Na3PO4, mixing, firing (1373 K, two days), regrinding and firing twice (1373 K, two days).
Sample purity was confirmed
Results and discussion
For all samples, quasielastic broadening could be observed in a temperature range of about 300 K. Since sodium transport is enhanced in the solid solutions due to their higher concentration of vacancies, it is not surprising to detect quasielastic scattering already at 550 K for x=0.5, while in pure Na3PO4 (x=0.0) the line broadening could only be observed beyond 773 K.
Our data analysis was performed in several steps. At the first stage, we applied a phenomenological fit, i.e., we fitted a
Conclusion
High-resolution quasielastic neutron scattering experiments have been performed on solid solutions of Na3PO4 and Na2SO4 in order to to examine the sodium hopping motion. The obtained data were analysed in terms of the Q-dependent linewidths using a model for jumps between different types of site on an fcc lattice. It turned out that for all composition of our study, the sodium hopping motion is dominated by jumps between tetrahedrally coordinated sites over a distance of half the fcc lattice
Acknowledgements
We have profited by stimulating discussions with K. Funke, H. Eckert, A. Putnis, R.D. Banhatti, and H.-Ch. Freiheit. Financial support by the Deutsche Forschungsgemeinschaft in the framework of the Sonderforschungsbereich 458 and by the Fonds der Chemischen Industrie is gratefully acknowledged. We thank B. Frick (IN16 instrument responsible) for his advice during the experiment. O. Losserand (IN16 instrument technician) also contributed considerably to the success of the experiment. Finally, we
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