The first INS study on proton-conducting perovskites was done by Karmonik et al.

[53] who investigated vibrational proton-dynamics in SrCe0 .95M0.05O3S (M — Sc, Ho, Nd). The INS spectra of the materials are reprinted in Fig. 9.8a and reveal O-H wag modes at around 115 (Sc) and 105 (Ho) meV. For the Nd-doped equivalent, the O-H wag band overlaps with a band at * 80 meV. It appears that the frequency of the O-H wag mode shifts to higher wavenumbers with decreasing size of the dopant cation (Nd! Ho! Sc), indicating that this band is related to protons in the vicinity of such atoms [53]. This behaviour was later validated by Yildrim et al.

[54] , who performed lattice-dynamics calculations on a л/2 x л/2 x 1 supercell of SrCeO3, replacing one Ce by Sc + H to give a supercell of Sr8Ce7ScHO24, whose composition is close to that of the real material. In particular, the authors calculated the vibrational spectrum for the hydrogen at the undoped (U) and doped (D) site and by comparing the experimental and calculated spectra (Fig. 9.8b) it could be confirmed that the O-H wag mode at * 120 meV indeed is associated with protons close to dopant (Sc) atoms, whereas the O-H wag mode at lower frequency, *80 meV, is associated with protons in the vicinity of host-lattice Ce atoms [54].

More recently, Karlsson et al. [55] addressed the question of how the O-H wag frequency depends on the dopant concentration. Specifically, the authors performed a systematic INS study of the BaInxZr1_xO3_x/2 (x = 0.20, 0.50, and 0.75) system, which exhibits an average cubic Pm3m symmetry independent of the In concen­tration. The INS spectra are shown in Fig. 9.9a. It can be seen that the O-H wag vibrations show up as a strong, broad, band between approximately 600 and 1,300 cm-1, whilst the peak-fit analysis presented in Fig. 9.9b shows that this band can be decomposed into three Gaussian components. Figure 9.9c shows the In concentration dependence of the relative intensities of the three peak fitted Gaus — sians. A significant redistribution of intensity amongst the three Gaussians as the In concentration is varied can be observed (the total integrated-intensity of the O-H wag band increases linearly with increasing In concentration [55]). Most interest­ingly, there is an increased contribution from the two high-frequency components to the overall spectrum, reflected by a band broadening towards higher frequencies, whereas the width and position of each individual Gaussian are found to be essentially independent of the In concentration [55]. The increase in total intensity of the O-H wag band results from the increasing concentration of protons in the sample, whereas the increased contribution of the high-frequency modes is due to an increased fraction of protons in more or less strongly hydrogen-bonding con­figurations [55]. The formation of strong hydrogen-bonds is believed to be the result of dopant atoms and/or oxygen vacancies in the vicinity of the protons, which act as charged defects, pushing the proton towards a neighbouring oxygen and increasing the tendency for hydrogen-bond formation [55]. However, the presence of such strongly hydrogen-bonding configurations may equally well be the result of tilts and/or rotations of oxygen octahedra induced by doping at the acceptor-atom site, which is of purely static origin [56]. Whatever the case, the formation and breaking of hydrogen bonds are crucially important for long-range proton transport, since proton transfer is a hydrogen-bond mediated process. Thus, information about the nature of hydrogen bonds, which can be derived from the O-H stretch and O-H wag frequencies, and how they link to the structural and dynamical details of the material, is highly valuable. Moreover, O-H stretch and O-H wag mode fre­quencies are useful in computer simulations, where they are utilized as prefactors in transition-state models to estimate the rates of proton transfer and — OH reorien­tational motion, respectively [57].

Further information about the behaviour of protons in the perovskite lattice may be derived from the temperature dependence of the INS spectra. In this regard, Karlsson et al. [55] performed a variable-temperature study on BaZr1-xInxO3_x/2 (x = 0.20). The INS spectra measured at T = 30, 100, 200, and 300 K are shown in Fig. 9.9d. As can be seen the spectra measured at the four different temperatures look essentially the same, which suggests that there is only a small change of the Debye-Waller factor as the temperature is raised from 30 to 300 K, i. e. the total root mean-square displacement, UT, increases only slightly within this temperature range [55]. The weak temperature-dependence of UT indicates that there is no particular difference between the proton dynamics in this material at 30 and 300 K.

Since it is unlikely that the protons undergo long-range diffusion at 30 K, it follows that this is also the case at 300 K. This is in agreement with the generally low proton-conductivity for barium zirconates at these temperatures [26, 52].