Effects of self energy of the ions on the double layer structure and properties at the dielectric interface

Although numerous theoretical efforts have been put forth, a systematic, unified and predictive theoretical framework that is able to capture all the essential physics of the interfacial behaviors of ions, such as the Hofmeister series effect, Jones-Ray effect and the salt effect on the bubble coalescence remain an outstanding challenge. The most common approach to treating electrostatic interactions in the presence of salt ions is the Poisson-Boltzmann (PB) theory. However, there are many systems for which the PB theory fails to offer even a qualitative explanation of the behavior, especially for ions distributed in the vicinity of an interface with dielectric contrast between the two media (like the water-vapor/oil interface). A key factor missing in the PB theory is the self energy of the ion.

In this thesis, we develop a self-consistent theory that treats the electrostatic self energy (including both the short-range Born solvation energy and the long-range image charge interactions), the nonelectrostatic contribution of the self energy, the ion-ion correlation and the screening effect systematically in a single framework. By assuming a finite charge spread of the ion instead of using the point-charge model, the self energy obtained by our theory is free of the divergence problems and gives a continuous self energy across the interface. This continuous feature allows ions on the water side and the vapor/oil side of the interface to be treated in a unified framework. The theory involves a minimum set of parameters of the ion, such as the valency, radius, polarizability of the ions, and the dielectric constants of the medium, that are both intrinsic and readily available. The general theory is first applied to study the thermodynamic property of the bulk electrolyte solution, which shows good agreement with the experiment result for predicting the activity coefficient and osmotic coefficient.

Next, we address the effect of local Born solvation energy on the bulk thermodynamics and interfacial properties of electrolyte solution mixtures. We show that difference in the solvation energy between the cations and anions naturally gives rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The miscibility of the mixture can either increases or decreases depending on the competition between the solvation energy and translation entropy of the ions. The interfacial tension shows a non-monotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations, and decreases approximately as the square root of the salt concentration for dilute solutions, which is in agreement with the Jones-Ray effect observed in experiment.

Next, we investigate the image effects on the double layer structure and interfacial properties near a single charged plate. We show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. The image charge effect is then studied for electrolyte solutions between two plates. For two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like- charge attraction.

Then, we study the inhomogeneous screening effect near the dielectric interface due to the anisotropic and nonuniform ion distribution. We show that the double layer structure and interfacial properties is drastically affected by the inhomogeneous screening if the bulk Debye screening length is comparable or smaller than the Bjerrum length. The width of the depletion layer is characterized by the Bjerrum length, independent of the salt concentration. We predict that the negative adsorption of ions at the interface increases linearly with the salt concentration, which cannot be captured by either the bulk screening approximation or the WKB approximation. For asymmetric salt, the inhomogeneous screening enhances the charge separation in the induced double layer and significantly increases the value of the surface potential.

Finally, to account for the ion specificity, we study the self energy of a single ion across the dielectric interface. The ion is considered to be polarizable: its charge distribution can be self-adjusted to the local dielectric environment to minimize the self energy. Using intrinsic parameters of the ions, such as the valency, radius, and polarizability, we predict the specific ion effect on the interfacial affinity of halogen anions at the water/air interface, and the strong adsorption of hydrophobic ions at the water/oil interface, in agreement with experiments and atomistic simulations.

The theory developed in this work represents the most systematic theoretical technique for weak-coupling electrolytes. We expect the theory to be more useful for studying a wide range of structural and dynamic properties in physicochemical, colloidal, soft-matter and biophysical systems.

High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.

Stopping power of gases for heavy ions

Pulse-height and time-of-flight methods have been used to measure the electronic stopping cross sections for projectiles of ¹²C, ¹⁶O, ¹⁹F, ²³Na, ²⁴Mg, and ²⁷Al, slowing in helium, neon, argon, krypton, and xenon. The ion energies were in the range 185 keV ≤ E ≤ 2560 keV.

A semiempirical calculation of the electronic stopping cross section for projectiles with atomic numbers between 6 and 13 passing through the inert gases has been performed using a modification of the Firsov model. Using Hartree-Slater-Fock orbitals, and summing over the losses for the individual charge states of the projectiles, good agreement has been obtained with the experimental data. The main features of the stopping cross section seen in the data, such as the Z₁ oscillation and the variation of the velocity dependence on Z₁ and Z₂, are present in the calculation. The inclusion of a modified form of the Bethe-Bloch formula as an additional term allows the increase of the velocity dependence for projectile velocities above v_o to be reproduced in the calculation.

Zn-VI/Cu2O Heterojunctions for Earth-Abundant Photovoltaics

The need for sustainable energy production motivates the study of photovoltaic materials, which convert energy from sunlight directly into electricity. This work has focused on the development of Cu₂O as an earth-abundant solar absorber due to the abundance of its constituent elements in the earth's crust, its suitable band gap, and its potential for low cost processing. Crystalline wafers of Cu₂O with minority carrier diffusion lengths on the order of microns can be manufactured in a uniquely simple fashion — directly from copper foils by thermal oxidation. Furthermore, Cu₂O has an optical band gap of 1.9 eV, which gives it a detailed balance energy conversion efficiency of 24.7% and the possibility for an independently connected Si/Cu₂O dual junction with a detailed balance efficiency of 44.3%.

However, the highest energy conversion efficiency achieved in a photovoltaic device with a Cu₂O absorber layer is currently only 5.38% despite the favorable optical and electronic properties listed above. There are several challenges to making a Cu₂O photovoltaic device, including an inability to dope the material, its relatively low chemical stability compared to other oxides, and a lack of suitable heterojunction partners due to an unusually small electron affinity. We have addressed the low chemical stability, namely the fact that Cu₂O is an especially reactive oxide due to its low enthalpy of formation (ΔH_f⁰ = -168.7 kJ/mol), by developing a novel surface preparation technique. We have addressed the lack of suitable heterojunction partners by investigating the heterojunction band alignment of several Zn-VI materials with Cu₂O. Finally, We have addressed the typically high series resistance of Cu₂O wafers by developing methods to make very thin, bulk Cu₂O, including devices on Cu₂O wafers as thin as 20 microns. Using these methods we have been able to achieve photovoltages over 1 V, and have demonstrated the potential of a new heterojunction material, Zn(O,S).

Energy loss of light ions channeling in silicon

Experimental measurements of rate of energy loss were made for protons of energy .5 to 1.6 MeV channeling through 1 μm thick silicon targets along the <110>, <111>, and <211> axial directions, and the {100}, {110}, {111}, and {211} planar directions. A .05% resolution automatically controlled magnetic spectrometer was used. The data are presented graphically along with an extensive summary of data in the literature. The data taken cover a wider range of channels than has previously been examined, and are in agreement with the data of F. Eisen, et al., Radd. Eff. 13, 93 (1972).

The theory in the literature for channeling energy loss due to interaction with local electrons, core electrons, and distant valence electrons of the crystal atoms is summarized. Straggling is analyzed, and a computer program which calculates energy loss and straggling using this theory and the Moliere approximation to the Thomas Fermi potential, V_TF, and the detailed silicon crystal structure is described. Values for the local electron density Z_loc in each of the channels listed above are extracted from the data by graphical matching of the experimental and computer results.

Zeroth and second order contributions to Z_loc as a function of distance from the center of the channel were computed from ∇²V_TF = 4πρ for various channels in silicon. For data taken in this work and data of F. Eisen, et al., Rad. Eff. 13, 93 (1972), the calculated zeroth order contribution to Z_loc lies between the experimentally extracted Z_loc values obtained by using the peak and the leading edge of the transmission spectra, suggesting that the observed straggling is due both to statistical fluctuations and to path variation.

Imaging the earth with ambient noise and earthquakes

In this thesis, I develop the velocity and structure models for the Los Angeles Basin and Southern Peru. The ultimate goal is to better understand the geological processes involved in the basin and subduction zone dynamics. The results are obtained from seismic interferometry using ambient noise and receiver functions using earthquake- generated waves. Some unusual signals specific to the local structures are also studied. The main findings are summarized as follows:

(1) Los Angeles Basin

The shear wave velocities range from 0.5 to 3.0 km/s in the sediments, with lateral gradients at the Newport-Inglewood, Compton-Los Alamitos, and Whittier Faults. The basin is a maximum of 8 km deep along the profile, and the Moho rises to a depth of 17 km under the basin. The basin has a stretch factor of 2.6 in the center decreasing to 1.3 at the edges, and is in approximate isostatic equilibrium. This "high-density" (~1 km spacing) "short-duration" (~1.5 month) experiment may serve as a prototype experiment that will allow basins to be covered by this type of low-cost survey.

(2) Peruvian subduction zone

Two prominent mid-crust structures are revealed in the 70 km thick crust under the Central Andes: a low-velocity zone interpreted as partially molten rocks beneath the Western Cordillera – Altiplano Plateau, and the underthrusting Brazilian Shield beneath the Eastern Cordillera. The low-velocity zone is oblique to the present trench, and possibly indicates the location of the volcanic arcs formed during the steepening of the Oligocene flat slab beneath the Altiplano Plateau.

The Nazca slab changes from normal dipping (~25 degrees) subduction in the southeast to flat subduction in the northwest of the study area. In the flat subduction regime, the slab subducts to ~100 km depth and then remains flat for ~300 km distance before it resumes a normal dipping geometry. The flat part closely follows the topography of the continental Moho above, indicating a strong suction force between the slab and the overriding plate. A high-velocity mantle wedge exists above the western half of the flat slab, which indicates the lack of melting and thus explains the cessation of the volcanism above. The velocity turns to normal values before the slab steepens again, indicating possible resumption of dehydration and ecologitization.

(3) Some unusual signals

Strong higher-mode Rayleigh waves due to the basin structure are observed in the periods less than 5 s. The particle motions provide a good test for distinguishing between the fundamental and higher mode. The precursor and coda waves relative to the interstation Rayleigh waves are observed, and modeled with a strong scatterer located in the active volcanic area in Southern Peru. In contrast with the usual receiver function analysis, multiples are extensively involved in this thesis. In the LA Basin, a good image is only from PpPs multiples, while in Peru, PpPp multiples contribute significantly to the final results.

Long-term natural acidification of upland sites in Cumbria: Evidence from post-glacial lake sediments

Studies by the Freshwater Biological Association over the last 25 years have supplied data relevant to the levels of acidity in local soils and water before the onset of industrial pollution and current interest in acid rain. This article reviews published analysis from cores of lake sediments, in or near the catchment of the River Duddon. Electron spin resonance spectra of humic acids and iodine values confirm evidence from pollen analysis for a history of progressive acidification of the source material of lake sediments since before 5000 radiocarbon years, in upland catchments of the Lake District. Processes involved included: removal of basic ions from soils by rainfall, the effects of which were intensified by removal by man of deciduous forest; acidification of soils and waters by decomposition products of Calluna and further acidification of waters by Sphagnum species which colonized habitats where drainage became impeded by paludification processes.

Studies of noble gases in meteorites and in the earth

The isotopic and elemental abundances of noble gases in the solar system are investigated, using simple mixing models and mass-spectrometric measurements of the noble gases in meteorites and terrestrial rocks and minerals.

Primordial neon is modeled by two isotopically distinct components from the interstellar gas and dust. Neon from the gas dominates solar neon, which contains about ten times more ²⁰Ne than ²²Ne. Neon from the dust is represented in meteorites by neon-E, with ²⁰Ne/²²Ne less than 0.6. Isotopic variations in meteorites require neon from both dust and gas to be present. Mixing dust and gas without neon loss generates linear correlation lines on three-isotope and composition-concentration diagrams. A model for solar wind implantation predicts small deviations from linear mixing, due to preferential sputtering of the lighter neon isotopes.

Neon in meteorites consists of galactic cosmic ray spallation neon and at least two primordial components, neon-E and neon-S. Neon was measured in several meteorites to investigate these end- members. Cosmogenic neon produced from sodium is found to be strongly enriched in ²²Ne. Neon measurements on sodium-rich samples must be interpreted with care so not to confuse this source of ²²Ne with neon-E, which is also rich in ²²Ne.

Neon data for the carbonaceous chondrite Mokoia show that the end member composition of neon-Si in meteorites is ²⁰Ne/²²Ne = 13.7, the same as the present solar wind. The solar wind composition evidently has remained constant since before the compaction of Mokoia.

Ca, Al-rich inclusions from the Allende meteorite were examined for correlation between neon-E and oxygen or magnesium isotopic anomalies. ²²Ne and ³⁶Ar enrichments found in some inclusions are attributed to cosmic- ray-induced reactions on Na and Cl, not to a primordial component. Neon-E is not detectably enriched in Allende.

Measurements were made to determine the noble gas contents of various terrestrial rocks and minerals, and to investigate the cycling of noble gases between different terrestrial reservoirs. Beryl crystals contain a characteristic suite of magmatic gases including nucleogenic ²¹Ne and ²²Ne from (α,n) reactions, radiogenic ⁴⁰Ar, and fissiogenic ^131-136Xe from the decay of K and U in the continental crust. Significant concentrations of atmospheric noble gases are also present in beryl.

Both juvenile and atmospheric noble gases are found in rocks from the Skaergaard intrusion. The ratio ⁴⁰Ar/³⁶Ar (corrected for in situ decay of ⁴⁰K) correlates with δ¹⁸O in plagioclase. Atmospheric argon has been introduced into samples that have experienced oxygen-isotope exchange with circulating meteoric hydrothermal fluids. Unexchanged samples contain juvenile argon with ⁴⁰Ar/³⁶Ar greater than 6000 that was trapped from the Skaergaard magma.

Juvenile and atmospheric gases have been measured in the glassy rims of mid-ocean ridge (MOR) pillow basalts. Evidence is presented that three samples contain excess radiogenic ¹²⁹Xe and fission xenon, in addition to the excess radiogenic ⁴⁰Ar found in all samples. These juvenile gases are being outgassed from the upper-mantle source region of the MOR magma. No isotopic evidence has been found here for juvenile primordial noble gases accompanying the juvenile radiogenic gases in the MOR glasses. Large argon isotopic variations in a single specimen provide a clear indication of the late-stage addition of atmospheric argon, probably from seawater.

The Skaergaard data demonstrate that atmospheric noble gases dissolved in ground water can be transferred into crustal rocks. Subduction of oceanic crust altered by seawater can transport atmospheric noble gases into the upper mantle. A substantial portion of the noble gases in mantle derived rocks may represent subducted gases, not a primordial component as is often assumed.

Dynamical models for the Earth's geoid

The Earth's largest geoid anomalies occur at the lowest spherical harmonic degrees, or longest wavelengths, and are primarily the result of mantle convection. Thermal density contrasts due to convection are partially compensated by boundary deformations due to viscous flow whose effects must be included in order to obtain a dynamically consistent model for the geoid. These deformations occur rapidly with respect to the timescale for convection, and we have analytically calculated geoid response kernels for steady-state, viscous, incompressible, self-gravitating, layered Earth models which include the deformation of boundaries due to internal loads. Both the sign and magnitude of geoid anomalies depend strongly upon the viscosity structure of the mantle as well as the possible presence of chemical layering.

Correlations of various global geophysical data sets with the observed geoid can be used to construct theoretical geoid models which constrain the dynamics of mantle convection. Surface features such as topography and plate velocities are not obviously related to the low-degree geoid, with the exception of subduction zones which are characterized by geoid highs (degrees 4-9). Recent models for seismic heterogeneity in the mantle provide additional constraints, and much of the low-degree (2-3) geoid can be attributed to seismically inferred density anomalies in the lower mantle. The Earth's largest geoid highs are underlain by low density material in the lower mantle, thus requiring compensating deformations of the Earth's surface. A dynamical model for whole mantle convection with a low viscosity upper mantle can explain these observations and successfully predicts more than 80% of the observed geoid variance.

Temperature variations associated with density anomalies in the man tie cause lateral viscosity variations whose effects are not included in the analytical models. However, perturbation theory and numerical tests show that broad-scale lateral viscosity variations are much less important than radial variations; in this respect, geoid models, which depend upon steady-state surface deformations, may provide more reliable constraints on mantle structure than inferences from transient phenomena such as postglacial rebound. Stronger, smaller-scale viscosity variations associated with mantle plumes and subducting slabs may be more important. On the basis of numerical modelling of low viscosity plumes, we conclude that the global association of geoid highs (after slab effects are removed) with hotspots and, perhaps, mantle plumes, is the result of hot, upwelling material in the lower mantle; this conclusion does not depend strongly upon plume rheology. The global distribution of hotspots and the dominant, low-degree geoid highs may correspond to a dominant mode of convection stabilized by the ancient Pangean continental assemblage.

High frequency wave propagation in the earth: theory and observation

The wave-theoretical analysis of acoustic and elastic waves refracted by a spherical boundary across which both velocity and density increase abruptly and thence either increase or decrease continuously with depth is formulated in terms of the general problem of waves generated at a steady point source and scattered by a radially heterogeneous spherical body. A displacement potential representation is used for the elastic problem that results in high frequency decoupling of P-SV motion in a spherically symmetric, radially heterogeneous medium. Through the application of an earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as a Weyl integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle:

1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), the critically refracted wave reduces to the classical head wave for flat, homogeneous layers.

2) For gradients more negative than critical, the amplitude of the critically refracted wave decays more rapidly with distance than the classical head wave.

3) For positive, null, and gradients less negative than critical, the amplitude of the critically refracted wave decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.

These theoretical results applied to published amplitude data for P-waves refracted by the major crustal and upper mantle horizons (the Pg, P*, and Pn travel-time branches) suggest that the 'granitic' upper crust, the 'basaltic' lower crust, and the mantle lid all have negative or near-critical velocity gradients in the tectonically active western United States. On the other hand, the corresponding horizons in the stable eastern United States appear to have null or slightly positive velocity gradients. The distribution of negative and positive velocity gradients correlates closely with high heat flow in tectonic regions and normal heat flow in stable regions. The velocity gradients inferred from the amplitude data are generally consistent with those inferred from ultrasonic measurements of the effects of temperature and pressure on crustal and mantle rocks and probable geothermal gradients. A notable exception is the strong positive velocity gradient in the mantle lid beneath the eastern United States (2 x 10^-3 sec^-1), which appears to require a compositional gradient to counter the effect of even a small geothermal gradient.

New seismic-refraction data were recorded along a 800 km profile extending due south from the Canadian border across the Columbia Plateau into eastern Oregon. The source for the seismic waves was a series of 20 high-energy chemical explosions detonated by the Canadian government in Greenbush Lake, British Columbia. The first arrivals recorded along this profile are on the Pn travel-time branch. In northern Washington and central Oregon their travel time is described by T = Δ/8.0 + 7.7 sec, but in the Columbia Plateau the Pn arrivals are as much as 0.9 sec early with respect to this line. An interpretation of these Pn arrivals together with later crustal arrivals suggest that the crust under the Columbia Plateau is thinner by about 10 km and has a higher average P-wave velocity than the 35-km-thick, 62-km/sec crust under the granitic-metamorphic terrain of northern Washington. A tentative interpretation of later arrivals recorded beyond 500 km from the shots suggests that a thin 8.4-km/sec horizon may be present in the upper mantle beneath the Columbia Plateau and that this horizon may form the lid to a pronounced low-velocity zone extending to a depth of about 140 km.

Using Earth Deformation Caused by Surface Mass Loading to Constrain the Elastic Structure of the Crust and Mantle

Surface mass loads come in many different varieties, including the oceans, atmosphere, rivers, lakes, glaciers, ice caps, and snow fields. The loads migrate over Earth's surface on time scales that range from less than a day to many thousand years. The weights of the shifting loads exert normal forces on Earth's surface. Since the Earth is not perfectly rigid, the applied pressure deforms the shape of the solid Earth in a manner controlled by the material properties of Earth's interior. One of the most prominent types of surface mass loading, ocean tidal loading (OTL), comes from the periodic rise and fall in sea-surface height due to the gravitational influence of celestial objects, such as the moon and sun. Depending on geographic location, the surface displacements induced by OTL typically range from millimeters to several centimeters in amplitude, which may be inferred from Global Navigation and Satellite System (GNSS) measurements with sub-millimeter precision. Spatiotemporal characteristics of observed OTL-induced surface displacements may therefore be exploited to probe Earth structure. In this thesis, I present descriptions of contemporary observational and modeling techniques used to explore Earth's deformation response to OTL and other varieties of surface mass loading. With the aim to extract information about Earth's density and elastic structure from observations of the response to OTL, I investigate the sensitivity of OTL-induced surface displacements to perturbations in the material structure. As a case study, I compute and compare the observed and predicted OTL-induced surface displacements for a network of GNSS receivers across South America. The residuals in three distinct and dominant tidal bands are sub-millimeter in amplitude, indicating that modern ocean-tide and elastic-Earth models well predict the observed displacement response in that region. Nevertheless, the sub-millimeter residuals exhibit regional spatial coherency that cannot be explained entirely by random observational uncertainties and that suggests deficiencies in the forward-model assumptions. In particular, the discrepancies may reveal sensitivities to deviations from spherically symmetric, non-rotating, elastic, and isotropic (SNREI) Earth structure due to the presence of the South American craton.

Concentrations of major ions in the stream water of the River Duddon, England, 1970-1974 [Dataset]

This dataset provides raw data of chemical analyses made during studies on seasonal variations of some major ions in the stream water of the River Duddon in Cumbria. Measurements of sodium, calcium, potassium, magnesium and chloride ions and pH were taken at 5 stations in the River Duddon between January 1970 and August 1974.

Concentrations of major ions in the stream water of the upper basin of the River Duddon, England, 1972-1974 [Dataset]

This dataset provides raw data of chemical analyses made during studies on seasonal variations of some major ions in the stream water of the upper basin of the River Duddon in Cumbria. Measurements of sodium, calcium, potassium, magnesium and chloride ions and pH were taken at 26 stations in the River Duddon basin between 1972 and 1974.

Major ions in 25 frequently sampled tarns in the English Lake District (1954-56, 1974-1976) [Dataset]

This dataset provides raw data of chemical analyses made during studies on seasonal variations of 25 frequently sampled tarns in Cumbria. Measurements of sodium, calcium, potassium, magnesium, pH, chloride ions, alkalinity, sulphite, strong acids and nitrate were taken between 1954 and 1956 and between 1974-1976.

Concentrations of major ions in 182 tarns in the English Lake District (1953-1978) [Dataset]

This dataset provides raw data of chemical analyses made during studies on seasonal variations of 182 tarns in the English Lake District, Cumbria. Measurements of sodium, calcium, potassium, magnesium, pH, chloride ions, alkalinity, sulphite, strong acids and nitrate were taken between 1953 and 1978.