Local structure of water studied by Compton scattering

This thesis presents a novel application of x-ray Compton scattering to structural studies of molecular liquids. Systematic Compton-scattering experiments on water have been carried out with unprecedented accuracy at third-generation synchrotron-radiation laboratories. The experiments focused on temperature effects in water, the water-to-ice phase transition, quantum isotope effects, and ion hydration. The experimental data is interpreted by comparison with both model computations and ab initio molecular-dynamics simulations. Accordingly, Compton scattering is found to provide unique intra- and intermolecular structural information. This thesis thus demonstrates the complementarity of the technique to traditional real-space probes for studies on the local structure of water and, more generally, molecular liquids.

Applications of dimensional reduction to electroweak and QCD matter

When heated to high temperatures, the behavior of matter changes dramatically. The standard model fields go through phase transitions, where the strongly interacting quarks and gluons are liberated from their confinement to hadrons, and the Higgs field condensate melts, restoring the electroweak symmetry. The theoretical framework for describing matter at these extreme conditions is thermal field theory, combining relativistic field theory and quantum statistical mechanics. For static observables the physics is simplified at very high temperatures, and an effective three-dimensional theory can be used instead of the full four-dimensional one via a method called dimensional reduction. In this thesis dimensional reduction is applied to two distinct problems, the pressure of electroweak theory and the screening masses of mesonic operators in quantum chromodynamics (QCD). The introductory part contains a brief review of finite-temperature field theory, dimensional reduction and the central results, while the details of the computations are contained in the original research papers. The electroweak pressure is shown to converge well to a value slightly below the ideal gas result, whereas the pressure of the full standard model is dominated by the QCD pressure with worse convergence properties. For the mesonic screening masses a small positive perturbative correction is found, and the interpretation of dimensional reduction on the fermionic sector is discussed.

Characterisation of cellulose- and lignin-based materials using x-ray scattering methods

Wood is an important material for the construction and pulping industries. Using x-ray diffraction the microfibril angle of Sitka spruce wood was studied in the first part of this thesis. Sitka spruce (Picea sitchensis [Bong.] Carr.) is native to the west coast of North America, but due to its fast growth rate, it has also been imported to Europe. So far, its nanometre scale properties have not been systematically characterised. In this thesis the microfibril angle of Sitka spruce was shown to depend significantly on the origin of the tree in the first annual rings near the pith. Wood can be further processed to separate lignin from cellulose and hemicelluloses. Solid cellulose can act as a reducer for metal ions and it is also a porous support for nanoparticles. By chemically reducing nickel or copper in the solid cellulose support it is possible to get small nanoparticles on the surfaces of the cellulose fibres. Cellulose supported metal nanoparticles can potentially be used as environmentally friendly catalysts in organic chemistry reactions. In this thesis the size of the nickel and copper containing nanoparticles were studied using anomalous small-angle x-ray scattering and wide-angle x-ray scattering. The anomalous small-angle x-ray scattering experiments showed that the crystallite size of the copper oxide nanoparticles was the same as the size of the nanoparticles, so the nanoparticles were single crystals. The nickel containing nanoparticles were amorphous, but crystallised upon heating. The size of the nanoparticles was observed to be smaller when the reduction of nickel was done in aqueous ammonium hydrate medium compared to reduction made in aqueous solution. Lignin is typically seen as the side-product of wood industries. Lignin is the second most abundant natural polymer on Earth, and it possesses potential to be a useful material for many purposes in addition to being an energy source for the pulp mills. In this thesis, the morphology of several lignins, which were produced by different separation methods from wood, was studied using small-angle and ultra small-angle x-ray scattering. It was shown that the fractal model previously proposed for the lignin structure does not apply to most of the extracted lignin types. The only lignin to which the fractal model could be applied was kraft lignin. In aqueous solutions the average shape of the low molar mass kraft lignin particles was observed to be elongated and flat. The average shape does not necessarily correspond to the shape of the individual particles because of the polydispersity of the fraction and due to selfassociation of the particles. Lignins, and especially lignosulfonate, have many uses as dispersants, binders and emulsion stabilisers. In this thesis work the selfassociation of low molar mass lignosulfonate macromolecules was observed using small-angle x-ray scattering. By taking into account the polydispersity of the studied lignosulfonate fraction, the shape of the lignosulfonate particles was determined to be flat by fitting an oblate ellipsoidal model to the scattering intensity.

Thermal expansion of caesium bromide

The temperature variation of the coefficient of thermal expansion of caesium bromide has been computed in quasiharmonic approximation and compared with the experimental results.

Debye-Waller factors of caesium halides

The Debye-Waller factors of 133Cs in three caesium halides at 4.2°K and of 129I ion in caesium iodide at 80°K are calculated and compared with experimental results.

Non-Linear vibration of an elastic string

Equations proposed in previous work on the non-linear motion of a string show a basic disagreement, which is here traced to an assumption about the longitudinal displacement u. It is shown that it is neither necessary nor justifiable to assume that u is zero; and also that the velocity of propagation of u disturbances in a string is different from that in an infinite medium, although this difference is usually negligible. After formulating the exact equations of motion for the string, a systematic procedure is described for obtaining approximations to these equations to any order, making only the assumption that the strain in the material of the string is small. The lowest order equations in this scheme are non-linear, and are used to describe the response of a string near resonance. Finally, it is shown that in the absence of damping, planar motion of a string is always unstable at sufficiently high amplitudes, the critical amplitude falling to zero at the natural frequency and its subharmonics. The effect of slight damping on this instability is also discussed.

The vibration spectrum of rutile

The long-wave lattice dynamics of rutile has been studied using a rigid ion model. The vibration frequencies for the zero wavevector have been calculated using the expressions for the frequencies of the normal modes derived group theoretically. The observed Raman and infrared frequencies have been explained.

Large deflections of rectangular plates

Approximate solutions for the non-linear bending of thin rectangular plates are presented considering large deflections for various boundary conditions. In the case of stress-free edges, solutions are given for von Kármán's equations in terms of the stress function and the deflection of the plate. In the case of immovable edges, equations are constructed in terms of the three displacements and these are solved. The solution is given by using double series consisting of the appropriate Beam Functions which satisfy the boundary conditions. The differential equations are satisfied by using the orthogonality properties of the series. Numerical results for square plates with uniform lateral load indicate good convergence of the series solution presented here.

The buoyant plume above a heat source

The boundary-layer type conservation equations of mass, momentum and energy for the steady free turbulent flow in gravitational convection over heat sources are set up for both two-dimensional and axisymmetric cases. These are reduced to ordinary differential equations in a similarity parameter by suitable transformations. The three classical hypotheses of turbulent diffusion-the Constant Exchange Coefficient hypothesis, Prandtl's Momentum Transfer theory and Taylor's Vorticity Transfer theory-are then incorporated into these equations in succession. The resulting equations are solved numerically and the results compared with some experimental results on gravitational convection over heat sources reported by Rouse et al.

A general treatment of two dimensional plane flows, for a micropolar fluid

In this paper we have studied the flow of a micropolar fluid, whose constitutive equations were given by Eringen, in two dimensional plane flow. In two notes, we have discussed the validity of the boundary condition v=a ω and its effect on the entire flow field. We have restricted our study to the case when Stokes' approximation is valid, i. e. slow motion for it is difficult to uncouple the equations in the most general case.

The Path to a Porous Semiconductor Multilayer

Thin films are the basis of much of recent technological advance, ranging from coatings with mechanical or optical benefits to platforms for nanoscale electronics. In the latter, semiconductors have been the norm ever since silicon became the main construction material for a multitude of electronical components. The array of characteristics of silicon-based systems can be widened by manipulating the structure of the thin films at the nanoscale - for instance, by making them porous. The different characteristics of different films can then to some extent be combined by simple superposition. Thin films can be manufactured using many different methods. One emerging field is cluster beam deposition, where aggregates of hundreds or thousands of atoms are deposited one by one to form a layer, the characteristics of which depend on the parameters of deposition. One critical parameter is deposition energy, which dictates how porous, if at all, the layer becomes. Other parameters, such as sputtering rate and aggregation conditions, have an effect on the size and consistency of the individual clusters. Understanding nanoscale processes, which cannot be observed experimentally, is fundamental to optimizing experimental techniques and inventing new possibilities for advances at this scale. Atomistic computer simulations offer a window to the world of nanometers and nanoseconds in a way unparalleled by the most accurate of microscopes. Transmission electron microscope image simulations can then bridge this gap by providing a tangible link between the simulated and the experimental. In this thesis, the entire process of cluster beam deposition is explored using molecular dynamics and image simulations. The process begins with the formation of the clusters, which is investigated for Si/Ge in an Ar atmosphere. The structure of the clusters is optimized to bring it as close to the experimental ideal as possible. Then, clusters are deposited, one by one, onto a substrate, until a sufficiently thick layer has been produced. Finally, the concept is expanded by further deposition with different parameters, resulting in multiple superimposed layers of different porosities. This work demonstrates how the aggregation of clusters is not entirely understood within the scope of the approximations used in the simulations; yet, it is also shown how the continued deposition of clusters with a varying deposition energy can lead to a novel kind of nanostructured thin film: a multielemental porous multilayer. According to theory, these new structures have characteristics that can be tailored for a variety of applications, with precision heretofore unseen in conventional multilayer manufacture.

Dynamics of Stick-Slip: Some Universal and Not So Universal Features

Stick-slip is usually observed in driven dissipative threshold systems. In these set of lectures, we discuss, some generic and system specific features of stickslip systems by considering a few examples wherein there has been some progress in understanding the associated dynamics. In most stick slip systems, both at low and high drive rates, the system slides smoothly, but within a window of drive rates, the motion becomes intermittent; the system alternately “sticks” till the stress builds up to a threshold value, and then “slips” when the stress is rapidly released. This intermittent motion can be traced to the existence of an unstable branch separating the two resistive branches in the force-drive-rate relation. While the two resistive branches are experimentally measurable, the unstable branch is usually not measurable and is only inferred.

A semi-classical model of the electron containing tachyonic matter

It is shown that the mass of the electron could be conceived as the energy associated with its spinning motion and the angular velocity is such that the linear velocities at the surface exceed the velocity of light; this in fact accounts for its stability against the centrifugal forces in the core region.