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) .

The measured variation of the Debye-Waller factor of aluminum from 295K to 815K by using the energy dispersive x-ray diffraction technique

The Energy Dispersive X-ray Diffraction System at Brock University has been used to measure the intensities of the diffraction lines of aluminum powder sample as a function of temperature. At first, intensity measurements at high temperature were not reproducible. After some modifications have been made, we were able to measure the intensities of the diffraction lines to 815K, with good accuracy and reproducibility. Therefore the changes of the Debye-Waller factor from room temperature up to 815K for aluminum were determined with precision. Our results are in good agreement with those previously published.

Thermodynamic properties and Debye-Waller factor of fee materials

We have calculated the equation of state and the various thermodynamic properties of monatomic fcc crystals by minimizing the Helmholtz free energy derived in the high temperature limit for the quasiharmonic theory, QH, and the lowest-order (cubic and quartic), 'A2, anharmonic terms of the perturbation theory, PT. The total energy in each case is obtained by adding the static energy. The calculation of the thermal properties was carried out for a nearest-neighbour central-force model of the fcc lattice by means of the appropriate thermodynamic relations. We have calculated the lattice constant, the thermal expansion, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the isothermal and adiabatic bulk moduli, and the Griineisen parameter, for the rare-gas solids Kr and Xe, and gold. Morse potential and modified Morse potential were each used to represent the atomic interaction for the three fcc materials. For most of the calculated thermodynamic properties from the QH theory, the results for Kr and Xe with the modified Morse potential show an improvement over the results for the Morse potential when compared with the experimental data. However, the results of the 'A 2 equation of state with the modified Morse potential are in good agreement with experiment only in the case of the specific heat at constant volume and at constant pressure. For Au we have calculated the lattice contribution from the QH and 'A 2 PT and the electronic contribution to the thermal properties. The electronic contribution was taken into account by using the free electron model. The results of the thermodynamic properties calculated with the modified Morse potential were similar to those obtained with the Morse potential. U sing the minimized equation of state we also calculated the Mossbauer recoilless fraction for Kr and Xe and the Debye-Waller factor (DWF) for Pb, AI, eu, Ag, and Au. The Mossbauer recoilless fraction was obtained for the above two potentials and Lennard-Jones potential. The L-J potential gives the best agreement with experiment for Kr. No experimental data exists for Xe. At low temperature the calculated DWF results for Pb, AI, and eu show a good agreement with experimental values, but at high temperature the experimental DWF results increase very rapidly. For Ag the computed values were below the expected results at all temperatures. The DWF results of the modified Morse potential for Pb, AI, eu and Ag were slightly better than those of the Morse potential. In the case of Au the calculated values were in poor agreement with experimental results. We have calculated the quasiharmonic phonon dispersion curves for Kr, Xe, eu, Ag, and Au. The calculated and experimental results of the frequencies agree quite well for all the materials except for Au where the longitudinal modes show serious discrepancies with the experimental results. In addition, the two lowest-order anharmonic contributions to the phonon frequency were derived using the Green's function method. The A 2 phonon dispersion curves have been calculated only for eu, and the results were similar to those of the QH dispersion curves. Finally, an expression for the Griineisen parameter "( has been derived from the anharmonic frequencies, and calculated for these materials. The "( results are comparable with those obtained from the thermodynamic definition.

An anharmonic contribution to the Helmholtz free energy O(lambda 6)

The anharmonic contributions of order A6 to the Helmholtz free energy for a crystal in which every atom is on a site of inversion symmetry, have been evaluated The cor~esponding diagrams in the various orders of the perturbation theory have been presented The validity of the expressions given is for high temperatures. Numerical calculations for the diagrams which contribute to the free energy have been worked out for a nearest-n~ighbour central-force model of a facecentered cubic lattice in the high-temperature limit and in the leading term and the Ludwig approximations. The accuracy of the Ludwig approximation in evaluating the Brillouin-zone sums has been investigated. Expansion for all diagrams in the high-temperature limit has been carried out The contribution to the specific heat involves a linear as well as cubic term~ We have applied Lennard-Jones, Morse and Exponential 6 types of potentials. A comparison between the contribution to the free energy of order A6 to that of order A4 has been made.

Étude de l’impact de la température et de l’humidité sur la survie et la dynamique de la ponte de la mouche du chou (Delia radicum L.)

Réalisé en cotutellle avec Gaétan Bourgeois et avec la participation de Guy Boivin, d'Agriculture et Agroalimentaire Canada, du Centre de Recherche et Développement en Horticulture à Saint-Jean-sur-Richelieu, QC J3B 3E6, Canada

Short Isora Fibre Reinforced Natural Rubber Composites

The present study deals with the short isora fibre reinforced natural rubber composites. In recent years there has been a tremendous advancement in the field of science and technology of short fibre reinforced polymer composites. The low density, high strength, high stiffness to weight ratio, excellent durability and design flexibility are the primary reasons for their use in many diversified fields such as air crafts, automobiles, marine industry etc. Compared to the various natural and synthetic fibres used as reinforcement for elastomer composites isora fibre is superior in many aspects. `Isora' is a natural lignocellulosic fibre which is easily available in South India especially in Kerala. The fibre is separated from the bark of the Helicteres isora plant by retting process. This fibre has excellent mechanical properties and is easily amenable to physical and chemical modifications. The study shows that composites with poor interfacial bonding tend to dissipate more energy than that with to interfacial bonding. The mechanical loss also can be related to interfacial bonding. The effect of chemical treatment of isora fibre on damping was also studied. Both in the low and high temperature region which indicates that this composite posseses low damping and hence good interfacial bonding characteristics. Hence these composites are better candidates for high damping applications. Composites with longitudinally oriented fibres showed high storage modulus than transversely oriented ones due to the effective stress transfer between fibre and matrix.

Optical Emission Diagnostics Of Laser Produced Plasma From Graphite And Yba2cu3o7

This thesis is entitled “OPTICAL EMISSION DIAGNOSTICS OF LASER PRODUCED PLASMA FROM GRAPHITE AND YBa2Cu3O7. The work presented in this thesis covers the experimental results on the plasma produced with moderately high power laser with irradiance range in between 10 GW cm 2 to 100 GW cm -2. The characterization of laser produced plasma from solid targets viz. graphite and high temperature superconducting material like YBa2Cu3O7 have been carried out. The fundamental frequency from a Q - switched Nd: YAG laser with 9 ns pulse duration is used for the present studies. Various optical emission emission diagnostic techniques were employed for the the characterization of the LPP which include emission spectroscopy, time resolved studies, line broadening method etc. In order to understand the physical nature of the LPP like recombination, collisional excitation and the laser interaction with plasma, the time resolved studies offer the most logical approach

The Effect of Glass Additives on the Microwave Dielectric Properties of Ba(Mg 1 /3Ta2/3)03 Ceramics

The effect of glass additives on the densification , phase evolution, microstructure and microwave dielectric properties of Ba(Mg1;3 Ta2i3)03 (BMT) was investigated . Different weight percentages of quenched glass such as B203 , Si02, B203-SiO2, ZnO-B203, 5ZnO-2B2O3, Al203-SiO2, Na20-2B203.10H20, BaO-B203-SiO2, MgO-B203-SiO2, PbO-B203-SiO2 , ZnO-B203-SiO2 and 2MgO-Al203-5SiO2 were added to calcined BMT precursor . The sintering temperature of the glass -added BMT samples were lowered down to 1300 °C compared to solid-state sintering where the temperature was 1650 °C. The formation of high temperature satellite phases such as Ba5Ta4O15 and Ba7Ta6O22 were found to be suppressed by the glass addition . Addition of glass systems such as B203, ZnO-B203, 5ZnO-2B203 and ZnO-B203-SiO2 improved the densification and microwave dielectric properties. Other glasses were found to react with BMT to form low-Q phases which prevented densification . The microwave dielectric properties of undoped BMT with a densification of 93 . 1 % of the theoretical density were Cr = 24 . 8, Tr = 8 ppm/°C and Q„ x f= 80,000 GHz. The BMT doped with 1.0 wt% of B203 has Q„ x f = 124,700GHz, Cr = 24.2, and T f = -1.3 ppm /°C. The unloaded Q factor of 0.2 wt% ZnO-B203-doped BMT was 136,500 GHz while that of 1.0 wt% of 5ZnO-2B203 added ceramic was Q„ x f= 141,800 GHz . The best microwave quality factor was observed for ZnO -B203-SiO2 (ZBS) glass-added ceramics which can act as a perfect liquid-phase medium for the sintering of BMT. The microwave dielectric properties of 0.2wt% ZBS-added BMT dielectric was Q„ x f= 152,800 GHz, F,= 25.5, and Tr = - 1.5 ppm/°C

Optical and Thermal Characterization of Dye Intercalated Montmorillonites and Rare Earth Doped Materials

Nondestructive photothermal methods as well as optical absorption and fluorescence spectroscopy are utilized to characterise three different materials, both thermally and optically. The possibility of using montmorillonite clay minerals, after textile waste-water treatment, is investigated for further applications. The laser induced luminescence studies and thermal characterisation of certain rare earth titanates prepared by self propagating high temperature synthesis method are also presented. Moreover, effort is made to characterise rare earth doped sol gel silica glasses with the help of these nondestructive techniques.

Unusual autofluorescence characteristic of cultured red-rain cells

The red cells found in the red rain in Kerala, India are now considered as a possible case of extraterrestrial life form. These cells can undergo rapid replication even at an extreme high temperature of 300 deg C. They can also be cultured in diverse unconventional chemical substrates. The molecular composition of these cells is yet to be identified. This paper reports the unusual autofluorescence characteristic of the cultured red rain cells. A spectrofluorimetric study has been performed to investigate this, which shows a systematic shift of the fluorescence emission peak wavelength as the excitation wavelength is increased. Conventional biomolecules are not known to have this property. Details of this investigation and the results are discussed.

Thermal transport across incommensurate phases in potassium selenate: photo-pyroelectric and calorimetric measurements

The thermal transport properties—thermal diffusivity, thermal conductivity and specific heat capacity—of potassium selenate crystal have been measured through the successive phase transitions, following the photo-pyroelectric thermal wave technique. The variation of thermal conductivity with temperature through the incommensurate (IC) phase of this crystal is measured. The enhancement in thermal conductivity in the IC phase is explained in terms of heat conduction by phase modes, and the maxima in thermal conductivity during transitions is due to enhancement in the phonon mean free path and the corresponding reduction in phonon scattering. The anisotropy in thermal conductivity and its variation with temperature are reported. The variation of the specific heat with temperature through the high temperature structural transition at 745 K is measured, following the differential scanning calorimetric method. By combining the results of photo-pyroelectric thermal wave methods and differential scanning calorimetry, the variation of the specific heat capacity with temperature through all the four phases of K2SeO4 is reported. The results are discussed in terms of phonon mode softening during transitions and phonon scattering by phase modes in the IC phase.

Recyclable Short Fibre Reinforced Plastics PP/Nylon and HDPE/Nylon composites

The study shows that standard plastics like polypropylene and high density polyethylene can be reinforced by adding nylon short fibres. Compared to the conventional glass reinforced thermoplastics this novel class of reinforced thermoplastics has the major advantage of recyclability. Hence such composites represent a new spectrum of recyclable polymer composites. The fibre length and fibre diameter used for reinforcement are critical parameters While there is a critical fibre length below which no effective reinforcement takes place, the reinforcement improves when the fibre diameter decreases due to increased surface area.While the fibres alone give moderate reinforcement, chemical modification of the matrix can further improve the strength and modulus of the composites. Maleic anhydride grafting in presence of styrene was found to be the most efficient chemical modification. While the fibre addition enhances the viscosity of the melt at lower shear rates, the enhancement at higher shear rate is only marginal. This shows that processing of the composite can be done in a similar way to that of the matrix polymer in high shear operations such as injection moulding. Another significant observation is the decrease in melt viscosity of the composite upon grafting. Thus chemical modification of matrix makes processing of the composite easier in addition to improving the mechanical load bearing capacity.For the development of a useful short fibre composite, selection of proper materials, optimum design with regard to the particular product and choosing proper processing parameters are most essential. Since there is a co-influence of many parameters, analytical solutions are difficult. Hence for selecting proper processing parameters 'rnold flow' software was utilized. The orientation of the fibres, mechanical properties, temperature profile, shrinkage, fill time etc. were determined using the software.Another interesting feature of the nylon fibre/PP and nylon fibre/HDPE composites is their thermal behaviour. Both nylon and PP degrade at the same temperature in single steps and hence the thermal degradation behaviour of the composites is also being predictable. It is observed that the thermal behaviour of the matrix or reinforcement does not affect each other. Almost similar behaviour is observed in the case of nylon fibre/HDPE composites. Another equally significant factor is the nucleating effect of nylon fibre when the composite melt cools down. In the presence of the fibre the onset of crystallization occurs at slightly higher temperature.When the matrix is modified by grafting, the onset of crystallization occurs at still higher temperature. Hence it may be calculated that one reason for the improvement in mechanical behaviour of the composite is the difference in crystallization behaviour of the matrix in presence of the fibre.As mentioned earlier, a major advantage of these composites is their recyclability. Two basic approaches may be employed for recycling namely, low temperature recycling and high temperature recycling. In the low temperature recycling, the recycling is done at a temperature above the melting point of the matrix, but below that of the fibres while in the high temperature route. the recycling is done at a temperature above the melting points of both matrix and fibre. The former is particularly interesting in that the recycled material has equal or even better mechanical properties compared to the initial product. This is possible because the orientation of the fibre can improve with successive recycling. Hence such recycled composites can be used for the same applications for which the original composite was developed. In high temperature recycling, the composite is converted into a blend and hence the properties will be inferior to that of the original composite, but will be higher than that of the matrix material alone.

Thermo-Structural Analysis of 3D Composites

Three dimensional (3D) composites are strong contenders for the structural applications in situations like aerospace,aircraft and automotive industries where multidirectional thermal and mechanical stresses exist. The presence of reinforcement along the thickness direction in 3D composites,increases the through the thickness stiffness and strength properties.The 3D preforms can be manufactured with numerous complex architecture variations to meet the needs of specific applications.For hot structure applications Carbon-Carbon(C-C) composites are generally used,whose property variation with respect to temperature is essential for carrying out the design of hot structures.The thermomechanical behavior of 3D composites is not fully understood and reported.The methodology to find the thermomechanical properties using analytical modelling of 3D woven,3D 4-axes braided and 3D 5-axes braided composites from Representative Unit Cells(RUC's) based on constitutive equations for 3D composites has been dealt in the present study.High Temperature Unidirectional (UD) Carbon-Carbon material properties have been evaluated using analytical methods,viz.,Composite cylinder assemblage Model and Method of Cells based on experiments carried out on Carbon-Carbon fabric composite for a temparature range of 300 degreeK to 2800degreeK.These properties have been used for evaluating the 3D composite properties.From among the existing methods of solution sequences for 3D composites,"3D composite Strength Model" has been identified as the most suitable method.For thegeneration of material properies of RUC's od 3D composites,software has been developed using MATLAB.Correlaton of the analytically determined properties with test results available in literature has been established.Parametric studies on the variation of all the thermomechanical constants for different 3D performs of Carbon-Carbon material have been studied and selection criteria have been formulated for their applications for the hot structures.Procedure for the structural design of hot structures made of 3D Carbon-Carbon composites has been established through the numerical investigations on a Nosecap.Nonlinear transient thermal and nonlinear transient thermo-structural analysis on the Nosecap have been carried out using finite element software NASTRAN.Failure indices have been established for the identified performs,identification of suitable 3D composite based on parametric studies on strength properties and recommendation of this material for Nosecap of RLV based on structural performance have been carried out in this Study.Based on the 3D failure theory the best perform for the Nosecap has been identified as 4-axis 15degree braided composite.

Studies on grain refinement and alloying additions on the microstructure and mechanical properties of Mg-8Zn-4Al alloy

MAGNESIUM ALLOYS have strong potential for weight reduction in a wide range of technical applications because of their low density compared to other structural metallic materials. Therefore, an extensive growth of magnesium alloys usage in the automobile sector is expected in the coming years to enhance the fuel efficiency through mass reduction. The drawback associated with the use of commercially cheaper Mg-Al based alloys, such as AZ91, AM60 and AM50 are their inferior creep properties above 100ºC due to the presence of discontinuous Mg17A112 phases at the grain boundaries. Although rare earth-based magnesium alloys show better mechanical properties, it is not economically viable to use these alloys in auto industries. Recently, many new Mg-Al based alloy systems have been developed for high temperature applications, which do not contain the Mg17Al12 phase. It has been proved that the addition of a high percentage of zinc (which depends upon the percentage of Al) to binary Mg-Al alloys also ensures the complete removal of the Mg17Al12 phase and hence exhibits superior high temperature properties.ZA84 alloy is one such system, which has 8%Zn in it (Mg-8Zn-4Al-0.2Mn, all are in wt %) and shows superior creep resistance compared to AZ and AM series alloys. These alloys are mostly used in die casting industries. However, there are certain large and heavy components, made up of this alloy by sand castings that show lower mechanical properties because of their coarse microstructure. Moreover, further improvement in their high temperature behaviour through microstructural modification is also an essential task to make this alloy suitable for the replacement of high strength aluminium alloys used in automobile industry. Grain refinement is an effective way to improve the tensile behaviour of engineering alloys. In fact, grain refinement of Mg-Al based alloys is well documented in literature. However, there is no grain refiner commercially available in the market for Mg-Al alloys. It is also reported in the literature that the microstructure of AZ91 alloy is modified through the minor elemental additions such as Sb, Si, Sr, Ca, etc., which enhance its high temperature properties because of the formation of new stable intermetallics. The same strategy can be used with the ZA84 alloy system to improve its high temperature properties further without sacrificing the other properties. The primary objective of the present research work, “Studies on grain refinement and alloying additions on the microstructure and mechanical properties of Mg-8Zn-4Al alloy” is twofold: 1. To investigate the role of individual and combined additions of Sb and Ca on the microstructure and mechanical properties of ZA84 alloy. 2. To synthesis a novel Mg-1wt%Al4C3 master alloy for grain refinement of ZA84 alloy and investigate its effects on mechanical properties.

Effect of deuteration on the electrical conductivity, dielectric constant and phase transitions in LiNH4SO4

Measurements of dc conductivity and dielectric constant show that deuteration causes an upward shift of the high temperature phase transition point from 186.5 to 191°C and a downward shift of the low temperature transition point from 10 to -1.5°C in LiNH4SO4. Mechanisms of phase transitions and of electrical transport in the crystal are discussed.