NSE offers a unique opportunity to obtain information about dynamical processes on different timescales, e. g. from the elementary processes of the proton-conduction mechanism occurring on the picosecond timescale to the long-range translational diffusion of protons occurring on the nanosecond timescale, simultaneously. Despite these advantages, the first application of NSE to investigate proton-conducting ceramics was relatively recent, in 2010 when Karlsson et al. [65] reported proton dynamics in hydrated BaY010Zr0.90O2.95. Figure 9.10a shows the intermediate­scattering function, I(Q, t), at different temperatures (521-650 K) at the Q-value of 0.3 A-1, within the time-range of 0.2-50 ns. The I(Q, t) is characterized by a decay with time, which is related to the proton motions in the material. In particular, from the shape of this decay and how it depends on temperature and momentum transfer, hQ, information about the mechanistic detail of proton motions, such as the timescale, activation energy, and spatial geometry, can be obtained.

From Fig. 9.10a, it can be seen that the I(Q, t) is described well by a single exponential function (solid lines) with a relaxation time s and a relaxation rate s-1 that exhibits a Q2-dependence (inset), which indicates that the relaxational decay is related to long-range translational diffusion. To further justify a result obtained using a single exponential function, the authors modelled the scattering function, Icalc.(Q, t), using a kinetic model based on first-principles calculations. Figure 9.10b shows these results for momentum transfers Q = 0.3, 0.5, 2.0 A-1, as well as for the long-range diffusion limit Q! 0, at a temperature T = 563 K. In the latter case, the scattering function is given by a single exponential with a characteristic relaxation rate s-1(Q) = DQ2, where D is the diffusion constant. Since the

7calc.(Q, t)s are plotted against Q2t they collapse onto a single curve in the long — range regime and this can be seen in Fig. 9.10b up to at least Q = 0.5 A-1. These results suggest that the long-range translational diffusion of protons occurs and on this basis, a diffusion coefficient assuming a s-1(Q) = DQ2 dependence was extracted. Temperature-dependent results are shown in the Arrhenius plot in Fig. 9.10c, from which it is evident that the diffusion constant is consistent between different temperatures, showing that the analysis is physically reasonable. Included in this figure is also the diffusion constant extracted from conductivity experiments and derived from first-principles calculations. It is evident that the diffusion con­stant obtained from NSE and conductivity experiments are comparable, which implies that already on a length-scale as short as * 20 A the effect of potential local traps or other “imperfections’’ in the structure that can be expected to affect the proton dynamics, has averaged out. That is, there are no new features revealed on a larger length-scale that have not been experienced by the proton on the shorter length-scale probed by NSE. However, by extending the Q range to higher Q values it should be possible to observe the crossover from single-exponential behaviour at low Q values, typical for long-range proton diffusion, to a more complex behaviour at larger Q values, suggesting that several processes are taking place. Further work along these lines is likely to give answers to questions like how the type and concentration of dopant atoms correlate with the macroscopic proton-conductivity, which as discussed above is a topic of some controversy.

Several researchers claim that the dopant atoms act as localized trapping-centres where the proton spends an extended time before it diffuses further throughout the material. This view was first introduced by Hempelmann et al. [32, 33] on the basis of their QENS data for SrYb0 05Ce0.95O2.975, which could be described by a so — called “two-state” model, suggesting that the proton migration takes place through a sequence of trapping and release events (Fig. 9.11 (left)). This view later found support from muon spin relaxation experiments [66] and computational studies of proton dynamics in perovskite-type oxides [34, 67-70], and most recently from a combined thermogravimetric and a. c. impedance spectroscopy study [71], as well as from luminescence spectroscopy measurements [72]. Converse to this picture, Kreuer et al. [73, 74] proposed that the dopant atoms may affect the proton transport in a more nonlocal fashion (Fig. 9.11 (right)). This suggestion is based on con­ductivity data for Y-doped BaCeO3 [73, 74], which shows that the proton conductivity increases with dopant level, but not as a result of a decrease of the pre­exponential factor, D0, in the expression for the diffusivity D = D0exp(—Ea/kBT) as anticipated by the two-state model, but rather as a result of an increased activation energy, Ea [73, 74].[13] Moreover, Mulliken population analyses of the electron densities at the oxygens showed that the additional negative charge introduced by

the dopants is distributed rather homogeneously over the oxygen lattice, which results in stronger bonding of the protons with increased proton-transfer barriers in general [73].

Irrespective of whether the dopant atoms influence the proton diffusion in a spatially restricted way or more non-locally, further QENS investigations using time-of-flight, backscattering, and spin-echo methods, is likely the only way to experimentally elucidate the mechanistic detail of proton dynamics in proton­conducting perovskites. Such information is crucial for the development of strat­egies for the strategic design of new materials with conductivities beyond the current state-of-the-art materials and hence are critical for future breakthroughs in the development of intermediate-temperature fuel-cell technology.