Switchable lanthanide fluorescence probes in homogenous molecular diagnostics

The number of molecular diagnostic assays has increased tremendously in recent years.Nucleic acid diagnostic assays have been developed, especially for the detection of human pathogenic microbes and genetic markers predisposing to certain diseases. Closed-tube methods are preferred because they are usually faster and easier to perform than heterogenous methods and in addition, target nucleic acids are commonly amplified leading to risk of contamination of the following reactions by the amplification product if the reactions are opened. The present study introduces a new closed-tube switchable complementation probes based PCR assay concept where two non-fluorescent probes form a fluorescent lanthanide chelate complex in the presence of the target DNA. In this dual-probe PCR assay method one oligonucleotide probe carries a non-fluorescent lanthanide chelate and another probe a light absorbing antenna ligand. The fluorescent lanthanide chelate complex is formed only when the non-fluorescent probes are hybridized to adjacent positions into the target DNA bringing the reporter moieties in close proximity. The complex is formed by self-assembled lanthanide chelate complementation where the antenna ligand is coordinated to the lanthanide ion captured in the chelate. The complementation probes based assays with time-resolved fluorescence measurement showed low background signal level and hence, relatively high nucleic acid detection sensitivity (low picomolar target concentration). Different lanthanide chelate structures were explored and a new cyclic seven dentate lanthanide chelate was found suitable for complementation probe method. It was also found to resist relatively high PCR reaction temperatures, which was essential for the PCR assay applications. A seven-dentate chelate with two unoccupied coordination sites must be used instead of a more stable eight- or nine-dentate chelate because the antenna ligand needs to be coordinated to the free coordination sites of the lanthanide ion. The previously used linear seven-dentate lanthanide chelate was found to be unstable in PCR conditions and hence, the new cyclic chelate was needed. The complementation probe PCR assay method showed high signal-to-background ratio up to 300 due to a low background fluorescence level and the results (threshold cycles) in real-time PCR were reached approximately 6 amplification cycles earlier compared to the commonly used FRET-based closed-tube PCR method. The suitability of the complementation probe method for different nucleic acid assay applications was studied. 1) A duplex complementation probe C. trachomatis PCR assay with a simple 10-minute urine sample preparation was developed to study suitability of the method for clinical diagnostics. The performance of the C. trachomatis assay was equal to the commercial C. trachomatis nucleic acid amplification assay containing more complex sample preparation based on DNA extraction. 2) A PCR assay for the detection of HLA-DQA1*05 allele, that is used to predict the risk of type 1 diabetes, was developed to study the performance of the method in genotyping. A simple blood sample preparation was used where the nucleic acids were released from dried blood sample punches using high temperature and alkaline reaction conditions. The complementation probe HLA-DQA1*05 PCR assay showed good genotyping performance correlating 100% with the routinely used heterogenous reference assay. 3) To study the suitability of the complementation probe method for direct measurement of the target organism, e.g., in the culture media, the complementation probes were applied to amplificationfree closed-tube bacteriophage quantification by measuring M13 bacteriophage ssDNA. A low picomolar bacteriophage concentration was detected in a rapid 20- minute assay. The assay provides a quick and reliable alternative to the commonly used and relatively unreliable UV-photometry and time-consuming culture based bacteriophage detection methods and indicates that the method could also be used for direct measurement of other micro-organisms. The complementation probe PCR method has a low background signal level leading to a high signal-to-background ratio and relatively sensitive nucleic acid detection. The method is compatible with simple sample preparation and it was shown to tolerate residues of urine, blood, bacteria and bacterial culture media. The common trend in nucleic acid diagnostics is to create easy-to-use assays suitable for rapid near patient analysis. The complementation probe PCR assays with a brief sample preparation should be relatively easy to automate and hence, would allow the development of highperformance nucleic acid amplification assays with a short overall assay time.

Utilization of steelmaking waste materials for production of calcium carbonate (CaCO3)

The steel industry produces, besides steel, also solid mineral by-products or slags, while it emits large quantities of carbon dioxide (CO2). Slags consist of various silicates and oxides which are formed in chemical reactions between the iron ore and the fluxing agents during the high temperature processing at the steel plant. Currently, these materials are recycled in the ironmaking processes, used as aggregates in construction, or landfilled as waste. The utilization rate of the steel slags can be increased by selectively extracting components from the mineral matrix. As an example, aqueous solutions of ammonium salts such as ammonium acetate, chloride and nitrate extract calcium quite selectively already at ambient temperature and pressure conditions. After the residual solids have been separated from the solution, calcium carbonate can be precipitated by feeding a CO2 flow through the solution. Precipitated calcium carbonate (PCC) is used in different applications as a filler material. Its largest consumer is the papermaking industry, which utilizes PCC because it enhances the optical properties of paper at a relatively low cost. Traditionally, PCC is manufactured from limestone, which is first calcined to calcium oxide, then slaked with water to calcium hydroxide and finally carbonated to PCC. This process emits large amounts of CO2, mainly because of the energy-intensive calcination step. This thesis presents research work on the scale-up of the above-mentioned ammonium salt based calcium extraction and carbonation method, named Slag2PCC. Extending the scope of the earlier studies, it is now shown that the parameters which mainly affect the calcium utilization efficiency are the solid-to-liquid ratio of steel slag and the ammonium salt solvent solution during extraction, the mean diameter of the slag particles, and the slag composition, especially the fractions of total calcium, silicon, vanadium and iron as well as the fraction of free calcium oxide. Regarding extraction kinetics, slag particle size, solid-to-liquid ratio and molar concentration of the solvent solution have the largest effect on the reaction rate. Solvent solution concentrations above 1 mol/L NH4Cl cause leaching of other elements besides calcium. Some of these such as iron and manganese result in solution coloring, which can be disadvantageous for the quality of the PCC product. Based on chemical composition analysis of the produced PCC samples, however, the product quality is mainly similar as in commercial products. Increasing the novelty of the work, other important parameters related to assessment of the PCC quality, such as particle size distribution and crystal morphology are studied as well. As in traditional PCC precipitation process, the ratio of calcium and carbonate ions controls the particle shape; a higher value for [Ca2+]/[CO32-] prefers precipitation of calcite polymorph, while vaterite forms when carbon species are present in excess. The third main polymorph, aragonite, is only formed at elevated temperatures, above 40-50 °C. In general, longer precipitation times cause transformation of vaterite to calcite or aragonite, but also result in particle agglomeration. The chemical equilibrium of ammonium and calcium ions and dissolved ammonia controlling the solution pH affects the particle sizes, too. Initial pH of 12-13 during the carbonation favors nonagglomerated particles with a diameter of 1 μm and smaller, while pH values of 9-10 generate more agglomerates of 10-20 μm. As a part of the research work, these findings are implemented in demonstrationscale experimental process setups. For the first time, the Slag2PCC technology is tested in scale of ~70 liters instead of laboratory scale only. Additionally, design of a setup of several hundreds of liters is discussed. For these purposes various process units such as inclined settlers and filters for solids separation, pumps and stirrers for material transfer and mixing as well as gas feeding equipment are dimensioned and developed. Overall emissions reduction of the current industrial processes and good product quality as the main targets, based on the performed partial life cycle assessment (LCA), it is most beneficial to utilize low concentration ammonium salt solutions for the Slag2PCC process. In this manner the post-treatment of the products does not require extensive use of washing and drying equipment, otherwise increasing the CO2 emissions of the process. The low solvent concentration Slag2PCC process causes negative CO2 emissions; thus, it can be seen as a carbon capture and utilization (CCU) method, which actually reduces the anthropogenic CO2 emissions compared to the alternative of not using the technology. Even if the amount of steel slag is too small for any substantial mitigation of global warming, the process can have both financial and environmental significance for individual steel manufacturers as a means to reduce the amounts of emitted CO2 and landfilled steel slag. Alternatively, it is possible to introduce the carbon dioxide directly into the mixture of steel slag and ammonium salt solution. The process would generate a 60-75% pure calcium carbonate mixture, the remaining 25-40% consisting of the residual steel slag. This calcium-rich material could be re-used in ironmaking as a fluxing agent instead of natural limestone. Even though this process option would require less process equipment compared to the Slag2PCC process, it still needs further studies regarding the practical usefulness of the products. Nevertheless, compared to several other CO2 emission reduction methods studied around the world, the within this thesis developed and studied processes have the advantage of existing markets for the produced materials, thus giving also a financial incentive for applying the technology in practice.

Application and development of numerical methods for the modelling of innovative gas cooled fission reactors

Innovative gas cooled reactors, such as the pebble bed reactor (PBR) and the gas cooled fast reactor (GFR) offer higher efficiency and new application areas for nuclear energy. Numerical methods were applied and developed to analyse the specific features of these reactor types with fully three dimensional calculation models. In the first part of this thesis, discrete element method (DEM) was used for a physically realistic modelling of the packing of fuel pebbles in PBR geometries and methods were developed for utilising the DEM results in subsequent reactor physics and thermal-hydraulics calculations. In the second part, the flow and heat transfer for a single gas cooled fuel rod of a GFR were investigated with computational fluid dynamics (CFD) methods. An in-house DEM implementation was validated and used for packing simulations, in which the effect of several parameters on the resulting average packing density was investigated. The restitution coefficient was found out to have the most significant effect. The results can be utilised in further work to obtain a pebble bed with a specific packing density. The packing structures of selected pebble beds were also analysed in detail and local variations in the packing density were observed, which should be taken into account especially in the reactor core thermal-hydraulic analyses. Two open source DEM codes were used to produce stochastic pebble bed configurations to add realism and improve the accuracy of criticality calculations performed with the Monte Carlo reactor physics code Serpent. Russian ASTRA criticality experiments were calculated. Pebble beds corresponding to the experimental specifications within measurement uncertainties were produced in DEM simulations and successfully exported into the subsequent reactor physics analysis. With the developed approach, two typical issues in Monte Carlo reactor physics calculations of pebble bed geometries were avoided. A novel method was developed and implemented as a MATLAB code to calculate porosities in the cells of a CFD calculation mesh constructed over a pebble bed obtained from DEM simulations. The code was further developed to distribute power and temperature data accurately between discrete based reactor physics and continuum based thermal-hydraulics models to enable coupled reactor core calculations. The developed method was also found useful for analysing sphere packings in general. CFD calculations were performed to investigate the pressure losses and heat transfer in three dimensional air cooled smooth and rib roughened rod geometries, housed inside a hexagonal flow channel representing a sub-channel of a single fuel rod of a GFR. The CFD geometry represented the test section of the L-STAR experimental facility at Karlsruhe Institute of Technology and the calculation results were compared to the corresponding experimental results. Knowledge was gained of the adequacy of various turbulence models and of the modelling requirements and issues related to the specific application. The obtained pressure loss results were in a relatively good agreement with the experimental data. Heat transfer in the smooth rod geometry was somewhat under predicted, which can partly be explained by unaccounted heat losses and uncertainties. In the rib roughened geometry heat transfer was severely under predicted by the used realisable k − epsilon turbulence model. An additional calculation with a v2 − f turbulence model showed significant improvement in the heat transfer results, which is most likely due to the better performance of the model in separated flow problems. Further investigations are suggested before using CFD to make conclusions of the heat transfer performance of rib roughened GFR fuel rod geometries. It is suggested that the viewpoints of numerical modelling are included in the planning of experiments to ease the challenging model construction and simulations and to avoid introducing additional sources of uncertainties. To facilitate the use of advanced calculation approaches, multi-physical aspects in experiments should also be considered and documented in a reasonable detail.

Development of an HTR-10 model in the Serpent reactor physics code

The use of exact coordinates of pebbles and fuel particles of pebble bed reactor modelling becoming possible in Monte Carlo reactor physics calculations is an important development step. This allows exact modelling of pebble bed reactors with realistic pebble beds without the placing of pebbles in regular lattices. In this study the multiplication coefficient of the HTR-10 pebble bed reactor is calculated with the Serpent reactor physics code and, using this multiplication coefficient, the amount of pebbles required for the critical load of the reactor. The multiplication coefficient is calculated using pebble beds produced with the discrete element method and three different material libraries in order to compare the results. The received results are lower than those from measured at the experimental reactor and somewhat lower than those gained with other codes in earlier studies.

Superkondensaattoreiden valmistus selluloosageeleistä ja hiilimustasta

Tässä työssä tavoitteena oli selvittää selluloosageelien soveltuvuutta superkondensaattorien elektrodimateriaaliksi. Superkondensaattoreiden elektrodit valmistetaan yleensä hyvin huokoisesta hiilimateriaalista. Näin ollen selluloosageeliin joukkoon sekoitettiin sähkönjohtavuutta parantamaan hiilimustaa. Kirjallisessa osassa keskityttiin superkondensaattorin toimintaperiaatteeseen, rakenteeseen ja yleisimmin käytössä oleviin elektrodimateriaaleihin. Yksityiskohtaisemmin paneuduttiin selluloosan käyttöön superkondensaattorien rakennemateriaalina. Kokeellisessa osassa valmistettiin erilaisia selluloosageelejä ja tämän jälkeen elektrodeja hiilimusta-selluloosageeli-seoksesta. Eri sekoitustapojen vaikutusta elektrodin sähköisiin ominaisuuksiin tarkasteltiin sekoittamalla hiilimustaa selluloosageeliin kahdella eri tavalla; korkeapainehajottajalla ja sekoittimella. Tämän lisäksi selvitettiin myös eri kuivaustapojen ja kuivauslämpötilojen vaikutusta elektrodiarkkien ominaisuuksiin. Arkkien sähköiset ominaisuudet määritettiin syklistä voltammetriaa (SV) käyttäen. Saavutetut tulokset osoittivat, että selluloosageelin valmistus on yksi kriittisimmistä kohdista elektrodimateriaalin valmistuksessa. Riittävä entsyymikäsittely vaaditaan, jotta saadaan muodostettua sopiva geeli, johon hiilimusta-partikkelit saadaan takertumaan. Hiilimustan sekoitustavalla sekä elektrodiarkin kuivauslämpötilalla ja – tavalla on myös suuresti vaikutusta elektrodin sähköisiin ominaisuuksiin.

Leijukattilan savukaasujen loppulämpötilan hallinta

Nykyaikaista leijukattilaa voidaan ohjata ja säätää erilaisten säätöpiirien ja sekvenssien kautta erittäin tarkasti. Toiminnot on optimoitu parhaan hyötysuhteen saavuttamiseksi ja kunnossapitokustannusten minimoimiseksi. Tehokkaasta automaatiosta ja nykyaikaisista laitevalinnoista huolimatta leijukattiloissa on usein yksi osa-alue, jota ei pystytä hallitsemaan tehokkaasti. Useilla voimalaitoksilla savukaasu poistuu liian korkeassa lämpötilassa viimeiseltä lämpöpinnalta. Kun kattilahyötysuhdetta tarkastellaan epäsuoralla menetelmällä, savukaasuhäviö on merkittävin tekijä kaikista häviöstä. Tässä diplomityössä on etsitty mahdollisuuksia savukaasun loppulämpötilan hallintaan kattilan ajoarvojen muutoksella sekä lämpöpintoja muuttamalla. Tutkimus keskittyy Järvi-Suomen Voima Oy:n Ristiinan voimalaitokselle. Tutkimus on tehty yhteistyössä laitoksen omistajien Pohjolan Voima Oy:n, UPM-Kymmene Oyj:n sekä laitetoimittaja Valmet Oyj:n kanssa.

Effect of drying temperature on quality of β-glucan in white oat grains

Oats have received attention because of their nutritional characteristics, especially their high-quality content of β-glucan. The drying process reduces water content; therefore they can be preserved for long periods. However, high-temperature drying process may affect the physical, chemical, and functional properties of the grains. The objective of this study was to evaluate the effect of different drying temperatures on β-glucan quality in oat grains. Grains of oats (Avena sativa, L.), cultivar Albasul, harvested at harvest moisture content of 23% were submitted to stationary drying at air temperatures of 25, 50, 75, and 100 ºC until they reached 13% moisture content. The β-glucan content was determined in samples of oat grains and extraction was performed using water as solvent at 90 ºC. The β-glucan extract was evaluated for water holding capacity, water retention capacity, capacity of displacement, and gelation properties. Stationary of oat grains at air temperatures above 25 ºC decreased the water holding capacity, whereas the content of β-glucan and the water retention capacity of β-glucan extract was affected at temperatures above 50 ºC. Physical changes such as increased gelation capacity of the β-glucan extract occurred following drying at air temperature over 75 ºC.

Impact of different drying parameters on color, β-carotene, antioxidant activity and minerals of apricot (Prunus armeniacaL.)

Abstract Apricot is one of the fruits dried by using different methods, such as sun, convective or microwave drying. The effects of drying methods on the components of this fruit differ depending upon the temperature or time parameters. In this research, the impacts of convective, microwave and microwave–convective drying techniques on color, β-carotene, minerals and antioxidant activity of apricots were investigated. The color values (L*, b*,ΔEab, h° and C*ab) of dried fruit were decreased, while the a* values increased. Compared with a fresh sample, the dried apricots showed a 1.4-3.9-fold proportional increase in β-carotene based on the increment of dry matter. The samples dried at high temperature and microwave levels, at 75 °C+90 watt and 75 °C+160 watt, showed lower antioxidant activity. Of the different drying treatments, the microwave-convective method (50 °C+160 watt) obtained a higher β-carotene content while maintaining antioxidant activity with a short drying time.

Drying soybean seed using air ambient temperature at low relative humidity

Under subtropical and tropical environments soybean seed (Glycine max (L.) Merrill) are harvested early to avoid deterioration from weathering. Careful after-harvest drying is required and is an important step in maintaining the physiological quality of the seed. Soybean seed should be harvested when the moisture content is in a range of 16-20%. Traditional drying utilizes a high temperature air stream passed through the seed mass without dehumidification. The drying time is long because the system is inefficient and the high temperature increases the risk of thermal damage to the seed. New technology identified as heat pipe technology (HPT) is available and has the unique feature of removing the moisture from the air stream before it is passed through the seed mass at the same environmental temperature. Two studies were conducted to evaluate the performance of HPT for dry soybean seed. In the first study the seeds were dried from 17.5 to 11.1% in 2 hours and 29 minutes and in the second sudy the seeds were dried from 22.6 to 11.9% in 16 hours and 32 minutes. This drying process caused no reduction in seed quality as measured by the standard germination, tetrazolium-viability, accelerated aging and seedling vigor classification tests. The only parameter that indicated a slight seed quality reduction was tetrazolium vigor in the second study. It was concluded that the HPT system is a promising technology for drying soybean seed when efficiency and maintenance of physiological quality are desired.

Drying peanut seed using air ambient temperature at low relative humidity

The moisture content of peanut kernel (Arachis hypogaea L.) at digging ranges from 30 to 50% on a wet basis (w.b.). The seed moisture content must be reduced to 10.5% or below before seeds can be graded and marketed. After digging, peanuts are cured on a window sill for two to five days then mechanically separated from the vine. Heated air is used to further dry the peanuts from approximately 18 to 10% moisture content w.b. Drying is required to maintain peanut seed and grain quality. Traditional dryers pass a high temperature and high humidity air stream through the seed mass. The drying time is long because the system is inefficient and the high temperature increases the risk of thermal damage to the kernels. New technology identified as heat pipe technology (HPT) is available and has the unique feature of removing the moisture from the air stream before it is heated and passed through the seed. A study was conducted to evaluate the performance of the HPT system in drying peanut seed. The seeds inside the shells were dried from 17.4 to 7.3% in 14 hours and 11 minutes, with a rate of moisture removal of 0.71% mc per hour. This drying process caused no reduction in seed quality as measured by the standard germination, accelerated ageing and field emergence tests. It was concluded that the HPT system is a promising technology for drying peanut seed when efficiency and maintenance of physiological quality are desired.

Calculation of the magnetic field penetration depth for high-Tc cuprate superconductors based on the Interlayer Pair Tunneling model /

In this work, the magnetic field penetration depth for high-Tc cuprate superconductors is calculated using a recent Interlayer Pair Tunneling (ILPT) model proposed by Chakravarty, Sudb0, Anderson, and Strong [1] to explain high temperature superconductivity. This model involves a "hopping" of Cooper pairs between layers of the unit cell which acts to amplify the pairing mechanism within the planes themselves. Recent work has shown that this model can account reasonably well for the isotope effect and the dependence of Tc on nonmagnetic in-plane impurities [2] , as well as the Knight shift curves [3] and the presence of a magnetic peak in the neutron scattering intensity [4]. In the latter case, Yin et al. emphasize that the pair tunneling must be the dominant pairing mechanism in the high-Tc cuprates in order to capture the features found in experiments. The goal of this work is to determine whether or not the ILPT model can account for the experimental observations of the magnetic field penetration depth in YBa2Cu307_a7. Calculations are performed in the weak and strong coupling limits, and the efi"ects of both small and large strengths of interlayer pair tunneling are investigated. Furthermore, as a follow up to the penetration depth calculations, both the neutron scattering intensity and the Knight shift are calculated within the ILPT formalism. The aim is to determine if the ILPT model can yield results consistent with experiments performed for these properties. The results for all three thermodynamic properties considered are not consistent with the notion that the interlayer pair tunneling must be the dominate pairing mechanism in these high-Tc cuprate superconductors. Instead, it is found that reasonable agreement with experiments is obtained for small strengths of pair tunneling, and that large pair tunneling yields results which do not resemble those of the experiments.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

On the anharmonic, multi-phonon, Debye-Waller contributions to the phonon-limited resistivity of metals : applications to Na and K

The anharmonic, multi-phonon (MP), and Oebye-Waller factor (OW) contributions to the phonon limited resistivity (;0) of metals derived by Shukla and Muller (1979) by the doubletime temperature dependent Green function method have been numerically evaluated for Na and K in the high temperature limit. The anharmonic contributions arise from the cubic and quartic shift of phonons (CS, QS), and phonon width (W) and the interference term (1). The QS, MP and OW contributions to I' are also derived by the matrix element method and the results are in agreement with those of Shukla and Muller (1979). In the high temperature limit, the contributions to;O from each of the above mentioned terms are of the type BT2 For numerical calculations suitable expressions are derived for the anharmonic contributions to ~ in terms of the third and fourth rank tensors obtained by the Ewald procedure. The numerical calculation of the contributions to;O from the OW, MP term and the QS have been done exactly and from the CS, Wand I terms only approximately in the partial and total Einstein approximations (PEA, TEA), using a first principle approach (Shukla and Taylor (1976)). The results obtained indicate that there is a strong pairwise cancellation between the: OW and MP terms, the QS and CS and the Wand I terms. The sum total of these contributions to;O for Na and K amounts to 4 to 11% and 2 to 7%, respectively, in the PEA while in the TEA they amount to 3 to 7% and 1 to 4%, respectively, in the temperature range.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .