Neutron powder diffraction and difference maximum entropy method analysis of protium- and deuterium-dissolved BaSn0.5In0.5O2.75+α
Graphical abstract
A novel method, difference maximum entropy method (MEM) analysis of the neutron diffraction data, is proposed for revealing the detailed structure around hydrogen atoms in proton-conducting oxides. This MEM analysis uses the differences between the structure factors of protium- and deuterium-dissolved crystals and improves the spatial resolution of the MEM mapping around the hydrogen atoms.
Introduction
Some perovskite oxides with dopant cations and oxide ion vacancies absorb water vapor in a humid atmosphere to release mobile hydrogen ions (protons) into the structure, thereby becoming proton conductors. BaZr1−xMxO3−x/2, BaCe1−xMxO3−x/2, and SrCe1–xMxO3–x/2 (M: dopant) are examples of this class of materials. These materials are not only of fundamental interest, but also of practical interest because of their potential application to protonic devices including fuel cells [1].
In previous studies, we performed neutron powder diffraction experiments on D2O-dissolved BaSn0.5In0.5O2.75 at 10–473 K [2], [3], and D2O-dissolved BaZr0.5In0.5O2.75 at 10 K [4]. Analyzing the data by the Rietveld method and the maximum entropy method (MEM), we found that the deuterium atoms were located at, or close to, the 12h site in the Wyckoff notation of the cubic perovskite structure (space group , see Fig. 1). In other words, the O–H bond was directed (roughly) along the bisector of the edges of the adjacent MO6 (M: Sn, Zr, In) octahedra. (We refer to such a hydrogen site as a bisector site.)
Recently, using neutron powder diffraction, Ahmed et al. [6], Kendrick et al. [7], and Azad et al. [8] found that hydrogen atoms occupied the bisector site in BaZr0.5In0.5O3−y at 5 K, La0.73Ba0.27ScO2.865-0.135(H/D)2O at 4.2 K, and BaCe0.4Zr0.4Sc0.2O2.90-0.10D2O at 5–500 K, respectively. Some computational studies [9], [10], [11], [12], [13], [14], [15], [16] for similar materials also suggested the bisector site as a hydrogen atom position. These results indicate that the occupation of the bisector site by hydrogen atoms is common in many proton-conducting perovskite oxides.
However, there are still questions about the detailed structure around hydrogen atoms in BaSn0.5In0.5O2.75+α and BaZr0.5In0.5O2.75+α, because the results of the Rietveld and MEM analyses were somewhat inconsistent [2], [3], [4]. The Rietveld analysis showed that the deuterium atoms in BaSn0.5In0.5O2.75+α were located at the 48n site, slightly off the {100} planes; the O–D bonds tilted towards the oxygen atoms second nearest to the deuterium atoms. On the other hand, the MEM analysis using the structure factors determined by the Rietveld analysis showed that deuterium atoms were distributed around the 12h site on the {100} planes; there were few, if any, O–D bonds that tilted towards the second nearest oxygen atoms. In addition, the MEM analysis yielded small, yet finite, scattering length density between the normal sites of oxygen and deuterium. It appeared that a significant number of oxygen and/or deuterium atoms deviated from their normal sites to be distributed over the interstitial regions.
Both the O–H tilting suggested by the Rietveld analysis and the O/H deviation suggested by the MEM analysis can be attributed, at least qualitatively, to asymmetric local environments arising from charged defects such as dopant cations and/or oxygen vacancies [14], [17]. They are often accompanied by the formation of hydrogen bonds between the hydrogen atoms and the second nearest oxygen atoms [14]. These hydrogen bonds will help hydrogen atoms jump between oxygen atoms; on the other hand, they will hinder the rotation of hydrogen atoms around oxygen atoms. In other words, they have the opposing effects of enhancing and suppressing hydrogen diffusion. Thus it is important to elucidate the detailed structure around the hydrogen atoms to understand the hydrogen diffusion mechanism.
Recently, MEM has been used to investigate static and dynamic disorder in ionic conductors [18], and so one might think that the result of the MEM analysis is more reliable than that of the Rietveld analysis. However, the results of our MEM analysis seemed to suffer from the relatively long wavelength (182.3 pm) of the neutrons used in the experiments [4]. This leads to a lack of data for a d-spacing less than 90–100 pm and limits the spatial resolution of the three-dimensional map deduced by MEM for scattering length density distribution.
The most straightforward approach to improve the spatial resolution is to use shorter wavelength neutrons. Actually, neutrons with a wavelength of 116.3 pm are also available at the diffractometer we used (high resolution powder diffractometer (HRPD), Japan Atomic Energy Agency). However, their flux density is an order of magnitude smaller than that of 182.3 pm neutrons, making experiments using them rather impractical.
Therefore, in the present paper, we propose a new method that we call difference MEM analysis, which uses the differences between the structure factors of protium- and deuterium-dissolved crystals. After describing basic equations for difference MEM analysis, we demonstrate by simulation that it effectively improves the spatial resolution of MEM mapping around hydrogen atoms as well as provides the distribution of hydrogen atoms alone. We then apply it to the actual neutron diffraction data of protium- and deuterium-dissolved BaSn0.5In0.5O2.75+α, and discuss hydrogen distribution in it.
Section snippets
Basic equations for difference MEM analysis
Let us consider protium- and deuterium-dissolved, but otherwise identical, crystals. The structure factors of these crystals areandrespectively, where ρH(r), ρD(r), and ρ′(r) are the neutron scattering length densities at a point r due to protium atoms, deuterium atoms and other constituent atoms, respectively; hK is a reciprocal lattice vector and V means the integration is
Sample preparation
The BaSn0.5In0.5O2.75 samples were prepared by the solid-state reaction of BaCO3 (99.99% pure, Rare Metallic Co., Japan), SnO2 (99.99% pure, Kojundo Chemical Laboratory Co., Japan), and In2O3 (99.99% pure, Rare Metallic Co.) powders. These raw materials were mixed with an agate mortar, pressed into pellets and heated at 1473 K for 20 h in air. They were ground to powder, pressed into pellets again and heated at 1673 K for 40 h in air and for 5 h in dry oxygen flow.
X-ray diffraction (RINT2200, Rigaku
Simulation of (difference) MEM analysis
Figs. 2(a1)–(a3) are isosurface representations of the three-dimensional distribution of the neutron scattering length density in a model structure, i.e., BaSn0.5In0.5O2.75-0.188D2O that has the crystal structure parameters given in Table 1. They have 48 spherical areas at the positions where deuterium atoms have been placed.
Figs. 2(b)–(f) show the distribution ρ2,MEM deduced by ordinary MEM analysis from the structure factors of the model structure and their simulated errors. When structure
Conclusions
Difference MEM analysis of the neutron powder diffraction data of H2O- and D2O-dissolved BaSn0.5In0.5O2.75 indicates that the O–D bonds mostly tilt towards the second nearest oxygen atoms. The large atomic displacement parameters and modulated diffuse background strongly suggest that there is local structural disorder in water-dissolved BaSn0.5In0.5O2.75. However, no significant scattering length densities are seen in the interstitial regions of the difference MEM map; the non-zero scattering
Acknowledgment
This work was partly supported by the 21st Century COE Program “Isotopes for the Prosperous Future.”
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