A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Doctor of Philosophy School of Physics 2017 / Different experimental techniques have clearly demonstrated that the predominant intrinsic point defects in ionic barium fluoride are anion Frenkel pairs. Positron annihilation technique is utilized in obtaining Doppler broadening and positron lifetime spectra in the temperature range 300 - 900 K. Doppler broadening quantifies the defects whereas positron lifetime components elaborate on the nature of defects. Theoretical approach by density functional theory (DFT) and the generalized gradient approximation (GGA) in the calculation of electron-positron momentum density (or Doppler broadening) spectra at 0 K show that the positron annihilations decay predominantly with barium valence electrons, especially the 5p and 6s electrons and to a lesser extent with core electrons. These annihilations contribute towards the electron-positron momentum density. The annihilations with valence electrons partly contribute toward the short positron lifetime component. The positron-electron annihilations in barium atoms increase steadily with temperature. At 693 K, the annihilation fraction due to the Ba-atom when the anionic Frenkel is formed is found to be 84.44% compared to 15.56% for the fluorine atom. These annihiltions become part of a larger bulk positron-electron annihilations which form a short positron lifetime component. It is also noted that for F-divacancy at 693 K, the annihilation fraction due to 5p and 6s valence electrons in Ba increases by 2.13% to 86.57% indicating the role of defect clusters in the annihilation process. The long positron lifetime decreases in the temperature range from 500 ps at 300 K to 402 ps at 711 K, corresponds to a fractional increase of 22% in the temperature range 300 K to 693 K. The long positron lifetime component is attributed to a delocalized positronium which quickly annihilates through the pick-off (spin conversion) process. Pick-off process seems to be the dominant processes in the long positron lifetime component. The self-diffusion, at all temperature ranges, of cations Ba2+ in barium fluoride is several orders of magnitude smaller than that of F− which has a diffusion constant of 10−9 m2/s at 300 K. Therefore the contribution of cations in superionic conductivity in the temperature range can be ignored. This is also supported by the absence of third lifetime component which is an indication that only anionic vacancies, F−, are generated in the temperature range. The variation of the lattice constant with temperature as determined by X-ray diffraction becomes a major factor in the determination of S-parameters as a function of temperature hence it can reveal the critical temperature at which the formation of anion Frenkel defects commences before entering superionic region. The disordering of fluorine sublattice is found to deviate from linear behaviour at a temperature of 580 K (S-parameter of 0.50622 and lattice constant of 0.623 nm) without observing any appreciable superionic conductivity. X-ray diffraction technique provides a lattice constant of 0.625 nm at 693 K (corresponding to S-parameter of 0.50776) through which an appreciable small activity in conduction is first observed. This is demonstrated through the correlation between the lattice constants and conductivity values at elevated temparatures. This effectively means that lattice constant increases exponentially with temperature. Ilmenite (FeT iO3) which is an ionic conductor in which a permanent dipole moment can be formed by local changes in the environment of Ti4+ ion. It was used to test the validity the positron annihilation spectroscopy in a completely different environment of this corundum structure of space group R-3. The observed long positron lifetime components in comparison with theoretical calculations clearly show that these long positron lifetime components emanate from positron annihilations at metallic vacancies Fe2+. M¨ossbauer pressure effect confirms the increase of Fe3+ at high pressure. At ambient conditions (pressure and temperature), the ratio Fe3+/Fe2+ is small but gradually increase as the pressure increase. The relative intensity clearly shows a dramatic increase of the Fe3+ component with pressure. Further test was carried out using variable positron beam on a 100 keV Ar+ implanted LiF in the fluence range of 1012 − 1016 ions/m2. In the process of ion implantation on alkali halides, ion vacancies in the form of F centers are formed. Using the penetration depth profile, S-parameter at different incident positron beams from 0.03 to 25 keV energies identifies the concentration of defects. This identification was also confirmed by optical absorption which clearly identified the F-band at 242 nm and F2-band at 444 nm. / MT2018

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This thesis describes results obtained using high resolution electron microscopy, acoustic microscopy and chemical analysis to study the structure and properties of the superionic β-aluminas. The acoustic microscopy and chemical analysis results relate solely to sodium β- and β -alumina, which are used as the solid state electrolyte in the sodium/sulphur cell. The high resolution electron microscopy results cover sodium β- and β-alumina as well as a number of ion-exchanged β-aluminas. The β-alumina structure consists of spinel-like blocks separated by the so-called conduction planes. The conduction planes have a low density, and contain all the mobile cations. Lattice images of sodium β- and β-alumina, silver β-alumina, ammonium/hydronium β-alumina, gadolinium β -alumina and divalent and trivalent europium β -alumina are presented and discussed. A hitherto unreported long-period structure in sodium β-alumina is shown, as is superlattice ordering in the divalent and trivalent β-aluminas. Defects in these materials are also discussed. The most common damage mode in the β -aluminas, due to electron beam irradiation, is the loss of the mobile-ion containing planes, and the subsequent collapse and shear of the structure to form broad defect spinel blocks. It is shown that collapse vectors determined for sodium β-alumina can also be applied to ammonium/hydronium β-alumina. Two further damage modes observed in this β-alumina are also discussed. A damage mode has been observed in sodium B-alumina and silver β-alumina which involves the extrusion of material to the crystal surface. Electron diffraction patterns from the extruded material have been indexed. The acoustic microscope has been used to examine bulk sodium β/β-alumina electrolyte tube specimens. Images of rectangular features present in the tubes (approximately 40um in length) are presented and the possible nature of the features is discussed.

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Diffusion is a fundamental process which plays a crucial role in many processes occurring in nature. It is governed by the Fickian laws of diffusion. The laws of diffusion explain how diffusive flux is related to the concentration gradient. However, diffusion occurs even when there is no concentration gradient. Chapter 1 introduces diffusion and related concepts such as random walk, Brownian motion, etc. Present understanding with relation to ionic conduction and diffusion in polar solvents and the anomalies observed in the variation of ionic conductivity with ionic radii has also been discussed. Walden’s rule states that the product of limiting ionic conductivity and viscosity is constant for a given ion in different solvents and it is inversely proportional to ionic radius in a given solvent. However, experimental observations indicate that in a given solvent limiting ionic conductivities show an increase followed by a decrease with increase in ionic radii. This is often referred to as the breakdown of Walden’s rule. Several theories have been proposed in the past to explain the breakdown in Waldens rule. Solvent-berg model, continuum based theories and microscopic theories are some of theories that have been proposed. These theories are discussed briefly. The limitations in these theories are also outlined. There are several computer simulation investigations of ions in water and these are discussed. Also described is diffusion of hydrocarbons in zeolites. Various interesting observations such as window effect, nest effect, single file diffusion and the levitation effect are discussed. In Chapter 2, we have analysed the experimental ionic conductivity data as a function of the ionic radius for monovalent cations and anions in aqueous solution. Molecular dynamics simulations on LiCl and CsCl dissolved in water are also reported. The results suggest that the activation energy is responsible for the anomalous dependence of ionic conductivity on ionic radii. It is seen that ions with high conductivity posses low activation energy. The reason for the variation of activation energy with ionic radii are explained in terms of Derouane’s mutual cancellation of forces or levitation effect. This provides an alternative to the existing theories. Experimental limiting ionic conductivity, λ0 of different alkali ions in water shows markedly different dependences on pressure. Existing theories such as that of Hubbard-Onsager are unable to explain this dependence on pressure of the ionic conductivity for all ions. Experimental ionic conductivity data shows that smaller ions such as Li+ exhibit a monotonic increase in λ0 with pressure. Intermediate sized ions such as K+ exhibit an increase in λ0 followed by a decrease at still higher pressures. Larger ions such as Cs+ exhibit a monotonic decrease in λ0 with increase in pressure. In the present thesis, we have explored this intriguing behaviour shown by alkali ions in water in the next few chapters. In Chapter 3, we report molecular dynamics investigation of potassium chloride solution (KCl) at low dilution in water at several pressures between 1 bar and 2 kbar. Two different potential models have been employed. One of the models successfully reproduces the experimentally observed trend in ionic conductivity of K+ ion in water over 0.001-2 kbar range at 298K. We also propose a theoretical explanation, albeit at a qualitative level, to account for the dependence of ionic conductivity on pressure in terms of the previously studied Levitation Effect. A number of properties of the solvent in the hydration shell are also reported. In Chapter 4, residence times of water in the solute and water hydration shell are reported for KCl in water as a function of pressure. Two different approaches – Impey, McDonald and Madden’s approach as well as the recently proposed stable state picture (SSP) of Laage and Hynes yield somewhat different values for the residence times. The latter suggests that the hydration shell is more labile. As pressure is varied, the analysis suggests drastic changes in the hydration shell around water and little or no change in the hydration shell of the ions at higher pressures. The residence times τIMM as well as τSSP show a decrease with increase in pressure upto 1.5 kbar and a small increase beyond this pressure. This correlates with the dependence of the ionic conductivity of potassium ion on pressure. Similar correlation is also seen for chloride ion between ionic conductivity and residence time in hydration shell. However, no such correlation is seen in the case of water. We also report variation of residence time as a function of t∗, the minimum time that a water has to leave the hydration shell to be excluded from it. In Chapter 5, a molecular dynamics study of LiCl dissolved in water is reported at several pressures between 1 bar and 4 kbars at 240K. Structural properties such as radial distribution function, distribution of the angle between ion-oxygen and dipole vector of water in the hydration shell, angle between ion-oxygen and OH vector, oxygen-ion oxygen angle for water in the hydration shell, mean residence times by two different approaches are reported. Self-diffusivity of both Li+ and Cl− exhibit an increase with pressure in agreement with the experimentally observed trend. We also report the velocity autocorrelation function as a function of pressure. We show that the changes in these can be understood in terms of the levitation effect. For the first time we report the self part of the intermediate scattering function, Fs(k, t), at different pressures. These show for Li+ at small wavenumber k, a bi-exponential decay with time at low pressures. At higher pressures when the ionic conductivity is high, Fs(k, t) exhibits a single exponential decay. We also report wavenumber dependence of the ratio of the full width at half maximum to 2Dk2. These changes in these properties can be accounted for in terms of the levitation effect. The changes in the void structure of water with pressure plays a crucial role in the changes in ionic conductivity of both the ions. In Chapter 6, a detailed molecular dynamics study of self-diffusivity of model ions in water is presented as a function of pressure. First, we have obtained the dependence of self-diffusivity on ionic radius for both cations and anions by varying the radius of the ion, rion. Self-diffusivity exhibits an increase with ionic radius when rion is small and reaches a maximum at some intermediate value, before decreasing with increase in rion for rion > . The velocity autocorrelation function for different sizes of cations as well as anions suggest that the ion with maximum self-diffusivity has facile motion with little back scattering. These trends can be understood in terms of the levitation effect which relates the dependence of self-diffusivity on ionic radius to the bottleneck radius of the pore network provided by the solvent or water. The ratio ζ, defined as the full width at half maximum of the self part of the dynamic structure factor at wavenumber k to its value (2Dk2) at k = 0 is seen to increase with k for ions far away from the diffusivity maximum while a decrease with k is observed for ions closer to the diffusivity maximum. Calculations have also been carried out at pressures of 0.001, 2 and 4 kbars to obtain the variation of ionic conductivity with pressure for model ions of several different sizes. It is shown that for small ions (rion < ), self-diffusivity increases with pressure or exhibits an increase followed by a decrease. In contrast, we show that whenever ionic radius is large, (rion > ), a decrease in self-diffusivity with increase in pressure is seen. We suggest that there is a relation between the dependence of self-diffusivity on ionic radius and its dependence on pressure. The nature of this relationship arises through the levitation effect. Increase in pressure leads to decrease in the bottleneck radius, thus increasing the levitation parameter. For small ions (rion < ), this will lead to increase in diffusivity whereas for large ions (rion > ) this will lead to decrease in diffusivity. For small ions (rion < ), the increase in pressure leads to lowered back scattering in the velocity autocorrelation function. In contrast to this, for large ions (rion ≥ ), any increase in pressure leads to increase in back scattering in the velocity autocorrelation function. For the 1.7 °A anion, the ratio ζ is seen to exhibit a minimum at intermediate k and increase with k at large k for 0.001 kbar pressure. This changes to a less pronounced minimum at 2 kbars and by 4 kbars to a nearly monotonically decreasing function of k. These changes suggest, in agreement with the predictions of the levitation effect, the approach of the bottleneck radius to values similar to that of the ionic radius of 1.7 °A on increasing pressure to 4 kbars. Thus, this work offers an unification in our understanding of the dependence of ionic conductivity on ionic radius and pressure. It is seen that when the ionic radius is varied the numerator of the expression for levitation parameter is varied whereas by varying the pressure, the denominator is varied. The variation of diffusivity with density of the host medium and degree of disorder of the host medium is explored in Chapter 7. The system consists of a binary mixture of a relatively smaller sized solute (whose size is varied) and a larger sized solvent interacting via Lennard-Jones potential. Calculations have been performed at three different reduced densities of 0.7, 0.8 and 0.933. These simulations show that diffusivity exhibits a maximum for some intermediate size of the solute when the solute diameter is varied. The maximum is found at the same size of the solute at all densities which is at variance with the prediction of the levitation effect. In order to understand this anomaly, we have carried out additional simulations in which we have varied the degree of disorder at constant density and find that the diffusivity maximum gradually disappears with increase in disorder. We have also carried out simulations in which we have kept the degree of disorder constant but changed only the density. We find that the maximum in diffusivity is now seen to shift to larger distances with decrease in density. In these simulations we have characterized the disorder by constructing the minimal spanning tree. These results are in excellent agreement with the predictions of the levitation effect. They suggest that the effect of disorder is to shift the maximum in diffusivity towards smaller solute radius while that of the decrease in density is to shift it towards larger solute radius. Thus, in real systems where the degree of disorder is lower at higher density and vice versa, the effect due to density and disorder have opposing influences. These are confirmed by the changes seen in the velocity autocorrelation function, self part of the intermediate scattering function and activation energy. In Chapter 8 we report a molecular dynamics study of the dependence of diffusivity of the cation on cation radii in molten superionic salt containing iodine ion. In this study, we have employed modified Parinello-Rahman-Vashistha interionic pair potential proposed by Shimojo et al (F. Shimojo and M. Kobayashi, J. Phys. Soc. Jpn 60, 3725 (1991)). Our results suggest that the diffusivity of the cation exhibits an increase followed by a decrease as the ionic radius is increased. Several other properties like velocity auto correlation function, intermediate scattering function, activation energy are reported. The next two chapters deal with diffusion of hydrocarbon isomers containing aromatic moiety. Chapter 9 reports structure, energetics and dynamic properties of the three isomers of trimethyl benzene in β-zeolite. Monte Carlo and molecular dynamics simulations have been performed at 300K. Of the three isomers, it is observed that 1,2,4-trimethyl benzene(124 TMB) shows fast dynamics inside the channels of β-zeolite. It is seen that both translational and rotational diffusivities are in the order D (124 TMB) > D (123 TMB) > D (135 TMB). 124 TMB seems to perform jumps between perpendicular channels more frequently whereas 123 and 135 isomers experience more hindrance to these jumps. It is also shown that there is a lower energetic barrier for 124 TMB across the window that separates two perpendicular channels in β-zeolite. Reorientational correlation functions suggest that reorientation of C6 axis (axis perpendicular to the plane of the phenyl ring) is highly restricted in case of 135 TMB. Reorientation of C2 axis (axis on the plane of the phenyl ring) seems to be more facile than that of C6 axis in case of both 123 TMB and 135 TMB. And interestingly, C6 and C2 axis reorientations are equally facile in case of 124 TMB. Chapter 10 presents molecular dynamics simulation results carried out on an equimolar binary mixture of cumene (isopropyl benzene) and pseudo-cumene (1,2,4-trimethyl benzene) in zeolite-NaY at four different temperatures. We compare different structural, energetic and dynamic properties of cumene and pseudo-cumene in zeolite-NaY. Our results suggest that both translational and rotational diffusivities are higher for cumene as compared to pseudo-cumene. Potential energy landscapes show that there is an energetic barrier for diffusion past the 12 MR window plane that separates two neighboring super cages. Such an energetic barrier is large for pseudo-cumene (3 kJ/mol) as compared to that of cumene (1.5 kJ/mol). Activation energies corresponding to both translational and rotational diffusion suggest that pseudo-cumene encounters larger energetic barriers for both translation and rotation as compared to cumene. Reorientational correlation functions suggest that reorientation of C2 axis is more facile than that of C6 axis in case of both cumene and pseudo-cumene. Activation energies corresponding to reorientational relaxations suggest that C6 axis encounters larger energetic barriers as compared to C2 axis in case of both cumene and pseudo-cumene. Chapter 11 discusses the main conclusions of the thesis and directions for future work.

Functional materials, particularly metal oxides, have been the focus of much attention in solid state chemistry for many years and impact every aspect of modern life. The approach adopted in this thesis to access desirable functionality for enhanced fundamental understanding is via modifying existing materials by deploying reducing synthetic procedures. This work spans several groups of inorganic crystalline materials, but is unified by the development of new properties within host compounds of particular relevance to solid oxide fuel cell technology, which allow interstitial oxide ion conduction at elevated temperatures. The Ca₁₂Al₁₄O₃₂e₂ electride was successfully synthesized by replacing the mobile extra-framework oxygen ions with electrons acting as anions. The high concentration of electrons in the C12A7 electride gives rise to an exceptionally high electronic conductivity of up to 245 S cm⁻¹ at room temperature. Making use of the high density of electrons in Ca₁₂Al₁₄O₃₂e₂ electride, the strong N-N bonds in N₂ was found to be broken when heating Ca₁₂Al₁₄O₃₂e₂ in a N₂ atmosphere. A reaction between silicate apatites and the titanium metal yielded another completely new electride material La₉.₀Sr₁.₀(SiO₄)₆O₂.₄e₀.₂ which was found to be a semiconductor. To fully understand the role of oxygen interstitials in silicate apatites, high-resolution transmission electron microscopy (HRTEM) was employed as the main technique in probing how the oxygen nonstoichiometry is accommodated at the atomic level. Atomic-resolution imaging of interstitial oxygen in La₉.₀Sr₁.₀(SiO₄)₆O₂.₅ proved to be a success in this thesis. Substitution of oxygen in 2a and interstitial sites with fluoride ions in La[subscript(8+y)]Sr[subscript(2- z)](SiO₄)₆O[subscript(2+(3y-2z)/2)] (0<y<2, 0<z<2) could be an approach to enriching the functionalities in the apatite structure. A wide range of fluoride substitution levels was tolerated in La[subscript(10-x)]Sr[subscript(x)](SiO₄)₆O[subscript(3-1.5x)]F[subscript(2x)] (x= 0.67, 1, 1.5, 2) and AC impedance measurements were found in support of a tentative conclusion that fluoride ions could be mobile in fluorinated apatites. The last part of this thesis was focused on a new class of fast oxide ion conductors based on Ge₅P₆O₂₅ whose performance was superior to both La₉.₀Sr₁.₀(SiO₄)₆O₂.₅ and Ca₁₂Al₁₄O₃₃ in the low temperature range.