Phase behavior of complex superprotonic solid acids

Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb3H(SO4)2-RbHSO4 system, Rb3H(SeO4)2-Cs3H(SeO4)2 solid solution system, and Cs6(H2SO4)3(H1.5PO4)4. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.

Rb3H(SO4)2 is an atypical member of the M3H(XO4)2 class of compounds (M = alkali metal or NH4+ and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb3H(SO4)2-RbHSO4 system have revealed the disproportionation products to be Rb2SO4 and the previously unknown compound Rb5H3(SO4)4. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs5H3(SO4)4 [2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.

The compounds Rb3H(SeO4)2 and Cs3H(SeO4)2, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.

The compound Cs6(H2SO4)3(H1.5PO4)4 is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH2PO4) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H2O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs6(H2SO4)3(H1.5PO4)4 undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.

References

[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.

[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.

[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).

Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.

Effects of particle size ratio on single particle motion in colloidal dispersions

The motion of a single Brownian particle of arbitrary size through a dilute colloidal dispersion of neutrally buoyant bath spheres of another characteristic size in a Newtonian solvent is examined in two contexts. First, the particle in question, the probe particle, is subject to a constant applied external force drawing it through the suspension as a simple model for active and nonlinear microrheology. The strength of the applied external force, normalized by the restoring forces of Brownian motion, is the Péclet number, Pe. This dimensionless quantity describes how strongly the probe is upsetting the equilibrium distribution of the bath particles. The mean motion and fluctuations in the probe position are related to interpreted quantities of an effective viscosity of the suspension. These interpreted quantities are calculated to first order in the volume fraction of bath particles and are intimately tied to the spatial distribution, or microstructure, of bath particles relative to the probe. For weak Pe, the disturbance to the equilibrium microstructure is dipolar in nature, with accumulation and depletion regions on the front and rear faces of the probe, respectively. With increasing applied force, the accumulation region compresses to form a thin boundary layer whose thickness scales with the inverse of Pe. The depletion region lengthens to form a trailing wake. The magnitude of the microstructural disturbance is found to grow with increasing bath particle size -- small bath particles in the solvent resemble a continuum with effective microviscosity given by Einstein's viscosity correction for a dilute dispersion of spheres. Large bath particles readily advect toward the minimum approach distance possible between the probe and bath particle, and the probe and bath particle pair rotating as a doublet is the primary mechanism by which the probe particle is able to move past; this is a process that slows the motion of the probe by a factor of the size ratio. The intrinsic microviscosity is found to force thin at low Péclet number due to decreasing contributions from Brownian motion, and force thicken at high Péclet number due to the increasing influence of the configuration-averaged reduction in the probe's hydrodynamic self mobility. Nonmonotonicity at finite sizes is evident in the limiting high-Pe intrinsic microviscosity plateau as a function of bath-to-probe particle size ratio. The intrinsic microviscosity is found to grow with the size ratio for very small probes even at large-but-finite Péclet numbers. However, even a small repulsive interparticle potential, that excludes lubrication interactions, can reduce this intrinsic microviscosity back to an order one quantity. The results of this active microrheology study are compared to previous theoretical studies of falling-ball and towed-ball rheometry and sedimentation and diffusion in polydisperse suspensions, and the singular limit of full hydrodynamic interactions is noted.

Second, the probe particle in question is no longer subject to a constant applied external force. Rather, the particle is considered to be a catalytically-active motor, consuming the bath reactant particles on its reactive face while passively colliding with reactant particles on its inert face. By creating an asymmetric distribution of reactant about its surface, the motor is able to diffusiophoretically propel itself with some mean velocity. The effects of finite size of the solute are examined on the leading order diffusive microstructure of reactant about the motor. Brownian and interparticle contributions to the motor velocity are computed for several interparticle interaction potential lengths and finite reactant-to-motor particle size ratios, with the dimensionless motor velocity increasing with decreasing motor size. A discussion on Brownian rotation frames the context in which these results could be applicable, and future directions are proposed which properly incorporate reactant advection at high motor velocities.

Probing the thermodynamic properties of mantle rocks in solid and liquid states

Our understanding of the structure and evolution of the deep Earth is strongly linked to knowledge of the thermodynamic properties of rocky materials at extreme temperatures and pressures. In this thesis, I present work that helps constrain the equation of state properties of iron-bearing Mg-silicate perovskite as well as oxide-silicate melts. I use a mixture of experimental, statistical, and theoretical techniques to obtain knowledge about these phases. These include laser-heated diamond anvil cell experiments, Bayesian statistical analysis of powder diffraction data, and the development of a new simplified model for understanding oxide and silicate melts at mantle conditions. By shedding light on the thermodynamic properties of such ubiquitous Earth-forming materials, I hope to aid our community’s progress toward understanding the large-scale processes operating in the Earth’s mantle, both in the modern day and early in Earth’s history.

Investigations of charge-carrier dynamics at semiconductor/liquid interfaces

Theoretical and experimental investigations of charge-carrier dynamics at semiconductor/liquid interfaces, specifically with respect to interfacial electron transfer and surface recombination, are presented.

Fermi's golden rule has been used to formulate rate expressions for charge transfer of delocalized carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. The treatment allows comparison between charge-transfer kinetic data at metallic, semimetallic, and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been determined from experimental data for charge transfer at metallic electrodes. The maximum rate constant (i.e., at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10^-17-10^-16 cm⁴ s^-1, which is in excellent agreement with prior theoretical models and experimental results for charge-transfer kinetics at semiconductor/liquid interfaces.

Double-layer corrections have been evaluated for semiconductor electrodes in both depletion and accumulation conditions. In conjuction with the Gouy-Chapman-Stern model, a finite difference approach has been used to calculate potential drops at a representative solid/liquid interface. Under all conditions that were simulated, the correction to the driving force used to evaluate the interfacial rate constant was determined to be less than 2% of the uncorrected interfacial rate constant.

Photoconductivity decay lifetimes have been obtained for Si(111) in contact with solutions of CH₃OH or tetrahydrofuran containing one-electron oxidants. Silicon surfaces in contact with electrolyte solutions having Nernstian redox potentials > 0 V vs. SCE exhibited low effective surface recombination velocities regardless of the different surface chemistries. The formation of an inversion layer, and not a reduced density of electrical trap sites on the surface, is shown to be responsible for the long charge-carrier lifetimes observed for these systems. In addition, a method for preparing an air-stable, low surface recombination velocity Si surface through a two-step, chlorination/alkylation reaction is described.

I. Spectroscopic observation of discrete sites in simple liquids. II. Infrared intensity perturbations of hydrogen halide fundamentals in liquid xenon. III. Rotation of HCl in solid rare gases.

Part I

The spectrum of dissolved mercury atoms in simple liquids has been shown to be capable of revealing information concerning local structures in these liquids.

Part II

Infrared intensity perturbations in simple solutions have been shown to involve more detailed interaction than just dielectric polarization. No correlation has been found between frequency shifts and intensity enhancements.

Part III

Evidence for perturbed rotation of HCl in rare gas matrices has been found. The magnitude of the barrier to rotation is concluded to be of order of 30 cm^(-1).

Study of Solid-Phase Reactions of metals on GaAs

To make stable and reproducible contacts to GaAs, metals which react with GaAs in the solid-phase should be favored. In this study, contacts formed employing Pd/TiN/Pd/Ag, Pd:Mg/TiN/Pd:Mg/Ag and Ru/TiN/Ru/Ag are studied. The TiN layer is included to investigate its application as diffusion barrier in these metallizations. Contacts to n-GaAs are rectifying and the value of barrier height is modified upon annealing. Contacts to p-GaAs are initially rectifying but exhibit ohmic behaviour after annealing. The modifications in the electrical properties are attributed to the solid-phase reaction of metal and GaAs. The integrity of the contacts relies critically on the success of TiN to prevent the intermixing of Ag overlayer and the underlying layers. At elevated annealing temperatures (450°C), TiN fails to function as a diffusion barrier. As a result, the properties of the contact deteriorates.

Experimental study on inertial effects in liquid-solid flows

This thesis presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Reynolds (defined by the shear rate and particle diameter) and Stokes numbers, ranging from 3 ≤ Re ≤ 1.6 × 10³ and 0.4 ≤ St ≤ 195. The experiments use a specifically designed Couette cylindrical rheometer that allows for probing the transition from transporting a pure liquid to transporting a dense suspension of particles. Measurements of the shear stress are presented for a wide range of particle concentration (10 to 60% in volume) and for particle to fluid density ratio between 1 and 1.05. The effective relative viscosity exhibits a strong dependence on the solid fraction for all density ratios tested. For density ratio of 1 the effective viscosity increases with Stokes number (St) for volume fractions (φ) lower than 40% and becomes constant for higher φ. When the particles are denser than the liquid, the effective viscosity shows a stronger dependance on St. An analysis of the particle resuspension for the case with a density ratio of 1.05 is presented and used to predict the local volume fraction where the shear stress measurements take place. When the local volume fraction is considered, the effective viscosity for settling and no settling particles is consistent, indicating that the effective viscosity is independent of differences in density between the solid and liquid phase. Shear stress measurements of pure fluids (no particles) were performed using the same rheometer, and a deviation from laminar behavior is observed for gap Reynolds numbers above 4× 10³, indicating the presence of hydrodynamic instabilities associated with the rotation of the outer cylinder. The increase on the effective viscosity with Stokes numbers observed for mixtures with φ ≤ 30% appears to be affected by such hydrodynamic instabilities. The effective viscosity for the current experiments is considerably higher than the one reported in non-inertial suspensions.

Phase transitions from the solid state of monatomic elements

The principle aims of this thesis include the development of models of sublimation and melting from first principles and the application of these models to the rare gases.

A simple physical model is constructed to represent the sublimation of monatomic elements. According to this model, the solid and gas phases are two states of a single physical system. The nature of the phase transition is clearly revealed, and the relations between the vapor pressure, the latent heat, and the transition temperature are derived. The resulting theory is applied to argon, krypton, and xenon, and good agreement with experiment is found.

For the melting transition, the solid is represented by an anharmonic model and the liquid is described by the Percus-Yevick approximation. The behavior of the liquid at high densities is studied on the isotherms kT/∈ = 1.3, 1.8, and 2.0, where k is Boltzmann's constant, T is the temperature, and e is the well depth of the Lennard-Jones 12-6 pair potential. No solutions of the PercusYevick equation were found for ρσ³ above 1.3, where ρ is the particle density and σ is the radial parameter of the Lennard-Jones potential. The liquid structure is found to be very different from the solid structure near the melting line. The liquid pressures are about 50 percent low for experimental melting densities of argon. This discrepancy gives rise to melting pressures up to twice the experimental values.

I. Site effects and exciton structure in molecular crystals - Benzene. II. The first and second triplet states of solid benzene

The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C₆H₆, C₆H₅D, m-C₆H₄D₂, p-C₆H₄D₂, sym-C₆H₃D₃, C₆D₅H, and C₆D₆ in either a C₆H₆ or C₆D₆ host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C₆H₆, C₆D₆, and sym-C₆H₃D₃; c) the orientational effect for the isotopes without a trigonal axis in both the ¹B_2u electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.

To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.

A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be^-Cr - A/r⁶ ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.

In part II the location and identification of the benzene first and second triplet states (³B_1u and ³E_1u) is given.