Correlation between thermal vibration and conductivity in La0.9Sr0.1B0.9Mg0.1O3−δ, B=Al, Ga and Sc
Introduction
The conductivity and structure of La0.9Sr0.1B0.9Mg0.1O3−δ, B=Al, Ga, and Sc have been investigated by several groups [1], [2], [3], [4], [5], [6] in the search for new materials for electrolytes in solid oxide fuel cells (SOFC). The aim is to understand the conduction mechanism in order to be able to predict conduction behaviour in these and other perovskite-type oxides. La0.9Sr0.1Ga0.9Mg0.1O3−δ has the highest oxide ion conductivity of the three materials and has no significant electronic contribution. La0.9Sr0.1Sc0.9Mg0.1O3−δ has mixed oxide ion and proton conductivity. La0.9Sr0.1Sc0.9Mg0.1O3−δ and La0.9Sr0.1Al0.9Mg0.1O3−δ have significantly lower conductivities than La0.9Sr0.1Ga0.9Mg0.1O3−δ and exhibit p-type electronic conduction at oxygen partial pressures between 10−5 and 1 atm. In order to contribute to the understanding of the conduction mechanism and, thereby, the following difference in oxide ion conductivity, the influence of thermal vibration on conduction has been investigated here.
The materials investigated are called perovskites according to their overall structure. The general formula unit is given as ABO3 where A and B, as in this case, may be partly substituted by A′ and B′. Perovskites are made up of a cubic close packing of A-cations and oxide ions accommodating B-cations in oxygen octahedral interstitials. Due to structural restrictions, the migrating oxide ion has to pass through a triangle defined by two A-site ions and one B-site ion. Fig. 1 shows this triangle that defines the radius of a circle, rcrit, which just touches the circles representing the cations [7]. The simple assumption has been that the larger rcrit the higher the conductivity due to less disturbance of the lattice. This means that the conductivity of La0.9Sr0.1Sc0.9Mg0.1O3−δ should be higher than the conductivity of La0.9Sr0.1Ga0.9Mg0.1O3−δ and this is not the case. Furthermore, the variation in rcrit is small compared to the difference in conductivity [8]. However, a crystal lattice is not a rigid lattice and therefore, correlated thermal motions of the ions must play a part in allowing the oxide ion to migrate. Dynamic informations on atomic thermal motion cannot be derived from elastic scattering data. However, information on the space- and time-averaged atomic thermal motion are obtainable and have contributed successfully to the understanding of the conduction mechanisms in systems of cation conductors [9], [10], [11]. Willis and Pryor [12] describe formalisms capable of providing an analytical description of scattering from atomic densities smeared by anharmonic vibration or positional disorder. In the most commonly applied models, non-Gaussian terms are added to the Gaussian density description in the crystal structure refinement. Such models involve a large number of parameters, which may be reduced by symmetry restrictions imposed by the atomic site symmetry. However, crystal structure refinement including anharmonic contributions to the thermal parameters for atoms with low positional symmetry involve a large number of refinable parameters, which are extremely elaborate to perform, especially from powder diffraction data. In addition, systematic errors from data collection and correlation with positional parameters affect the outcome.
In the following, a different method is used—the method applied by Ranløv and Nielsen [13] for investigations of thermal motion in oxide ion conductors. A direct method is used to calculate nuclear difference densities between observations at different temperatures. Detailed information on atomic thermal displacements is extracted by resolving the observed density differences into spherical harmonics. An important property of the difference synthesis is that they are less affected by series truncation arising from the limited number of observations and errors due to strong correlation with other parameters during refinement are avoided.
Section snippets
Nuclear densities and spherical harmonics
Nuclear densities can be calculated in different ways according to the feature that is investigated. In order to obtain information on the thermal vibrations, nuclear difference density maps, Δρ, are synthesised from the following [13]:
The subscripts 1 and 2 refer to room temperature observation and high temperature observations, respectively. V is the unit cell volume; H is the reciprocal lattice vector and r is the positional vector. T
Experimental
Powders were prepared by the glycine nitrate method [14]. The obtained powders were ball milled for one h, then divided in two and calcined at 1000 and 1200 °C for 4 h in order to obtain a bimodal grain size distribution in order to obtain a better packing of the powder when preparing samples. The calcined powder was ball milled again. The crystallinity and purity of the resulting powders were tested by XRD using a STOE θ/θ diffractometer with CuKα radiation.
Time-of-flight neutron diffraction
Isotropic temperature factors
The spherical contribution to the difference density or the isotropic temperature factor, obtained from Eq. (4), increases, as expected, with temperature. This is consistent with the isotropic temperature factors obtained from the Rietveld refinement [18]. However, the difference in the temperature factors changes with atomic position. The temperature factors are plotted as a function of temperature for each position in Fig. 3, Fig. 4, Fig. 5. The results obtained by Ranløv and Nielsen [13] on
Discussion and conclusion
The rotation of the anharmonic contribution of the La/Sr site in La0.9Sr0.1Sc0.9Mg0.1O3−δ could explain the flattening of the conductivity curve at high temperature. The increased density is in a plane perpendicular to the vector between O(1) and O(2). Meaning that at high temperature, the passage between the oxygen sites is partly blocked.
The largest increase in atomic vibration is found for the oxygen positions. This is in good agreement with the fact that the oxide ions are the migrating
Acknowledgements
Steve Hull and Ron Smith, instruments scientists at the POLARIS diffractometer at ISIS, UK, are thanked for their help in data acquisition. The EPSRC is thanked for providing access to neutron scattering facilities.
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