A field modulated super-regenerative spectrometer was constructed. The theory of its operation was developed and put to test by observing the pure quadrupole resonance of Chlorine 35 in Para - di-chlorobenzene powder at room temperature. The spectrometer's operation is closely related to the quadrupole transient effects. So another experiment was done to measure the amplitude and the decay time constant of Free Induction Signal in Para-di-chlorobenzene as a function of pulse width and magnetic field, using a pulsed r.f. transmitter, constructed for this purpose, The results of this experiment were then applied to the theory of the spectrometer to explain its behaviour. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Nuclear magnetic resonance and infra-red studies have been made of various clathrate compounds. The purpose of the investigations was to examine the extent of molecular motion which the enclathrated molecule^ may undergo. It has been shown that the benzene molecule in the clathrate with Nickel Ammonium Cyanide rotates about the six-fold axis at room temperature. The existence of shifts in the infra-red spectrum of the enclosed molecule has been confirmed but the assignment of the absorption bands at 1573 cm-¹ and 1165 cm-¹ as the Raman active E[subscript 2g] vibrations is incorrect. Studies on the quinol clathrates of methane, fluoroform, methyl alcohol and methyl cyanide and the clathrate of sulphur hexafluoride in Dianin's compound (4-p-hydroxyphenyl-2,2,4-trimethyl chroman) infer that isotropic motion of the enclathrated molecues occurs at 77°K. The infra-red spectra of these clathrates and of quinol 0-d₂ have been examined. Nuclear magnetic resonance investigations of molecular motion in weak charge transfer complexes are reported. In the dioxane complexes of bromine and mercuric chloride the structure is rigid at room temperature. In the complexes with antimony trichloride and silver perchlorate the dioxane molecule is reorienting about the O-O axis at 298°K but is rigid at 77°K. Rotation of the benzene ring at 25°C in the complex AgClO₄.C₆H₆ suggests that the reported distortion of the benzene ring may be incorrect. At low temperatures the agreement between the theoretical and and experimental second moments shows that the essential features of the structure are correct. The implication of the infra-red studies of other workers are discussed. Reorientation of both aromatic rings in the complex of benzene and hexafluorobenzene occurs down to low temperatures. The potential barrier hindering rotation of the hexafluorobenzene molecule is estimated to be 1.1 kcal/mole. / Science, Faculty of / Chemistry, Department of / Graduate

In 1930, Bloch derived a formula for the temperature-dependence of the spontaneous magnetisation of a ferromagnetic substance (in the sense of the well-known Heisenberg model) valid asymptotically as the temperature T tends to zero. In 1936, Kramers rederived Bloch's formula using an entirely new approximate method. In 1937, Opechowski applied Kramers’ method to obtain, in addition to Bloch's T³′²-term in the expression for the magnetisation, two additional terms, in T² and T⁵′². In 1956, Dyson found a rigourous method for dealing with this problem. His result shows that there is no T²-term and the T⁵′²-term has a coefficient different from that found by Opechowski. In this thesis, some possibilities are investigated of modifying Kramers' method. In particular, the question is considered, which assumptions in Kramers' method are responsible for the above mentioned discrepancies. In Kramers' method, the partition function of the Heisenberg model is identified with the largest term in its power series expansion. The calculation of the largest term is in turn reduced to a certain random walk problem. This reduction of the problem to a random walk problem involves certain assumptions which we have not tried to modify in this thesis. What is new is a careful discussion of, and improvement on the solution of the random walk problem. The improved method of solving this problem leads to a cubic equation in P¹′², where P is a certain parameter with no single physical meaning. In chapters 6 and 7, a first approximation is obtained by omitting the term in P³′². The resulting quadratic equation in P¹′² leads to an expression for the spontaneous magnetisation containing no term in T² as in Dyson's formula. The solution of the complete cubic equation unfortunately leads to an expression for the spontaneous magnetisation, in which the term in T² reappears again. One obtains again Opechowski's result, except for a small modification of the coefficient of the T⁵′²-term; this is due to a better approximation for the factorials occuring in the calculations. This fact shows that Kramers’ random walk problem constitutes too crude an approximation of the actual problem. After the writing of this thesis was completed, Professor Opechowski found a way of modifying Kramers' method. The calculation of the partition function in the modified method is reduced to a slightly different random walk problem. The expression for the spontaneous magnetisation becomes then identical with Dyson's up to the T⁷′²-term inclusive. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A fifteen inch magnetic spectrometer using its fringing field to achieve double focusing has been developed and made ready for experimental work. Its power supply delivers continuously variable currents from 0-100 amperes. The current is stable to one part in ten thousand, being regulated by a transistor amplifier which drives a bank of parallel output power transistors. Interlocks are provided to protect the components against foreseeable hazards. The vacuum and detecting systems are complete, and the spectrometer has been tested with various alpha sources. The best resolution obtained was .57 per cent, but there should be much better resolving power inherent in the spectrometer, unrevealed because the sources used were fairly large. A resolution measurement of scattered protons when the beam from the Van de Graaff is put in to the spectrometer should determine the resolution more accurately. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Nuclear magnetic resonance studies in single crystals of thallium have been performed for the first time. The resonance frequency, line width and second moment were studied as a function of crystal orientation with respect to the magnetic field. The Knight shift parameters were determined at liquid helium and liquid nitrogen temperatures. The anisotropic Knight shift results were in disagreement with the results obtained on powder specimens by other workers. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The purpose of this work was to investigate experimentally the effects of an externally applied magnetic field on free diffusion of saccharides in aqueous solution. The diffusion coefficients of simple saccharides (deoxyribose, D(-)ribose, D(+)xylose, D-glucose, D-galactose, D(-)fructose, lactose, sucrose, maltose, raffinose) diffusing through a 0.4 micron pore diameter Nuclepore membrane were measured in applied magnetic field strengths ranging from zero to 1.1 T. The applied magnetic field strength was the only variable in these experiments. The initial saccharide concentration difference across the membrane was one percent by weight. The experiments were conducted at a constant temperature of 25 ±0.1° C. The diffusion coefficient was obtained by means of a modified Rayleigh interferometer-laser system. A Rayleigh interferometer measured refractive index profiles of dilute saccharide solutions contained in a diffusion cell. Refractive index profiles were converted to concentration profiles which were then used to calculate mass fluxes and the corresponding binary diffusion coefficients. A study of saccharide-water interactions indicates that these interactions are very complex in nature and that saccharide hydration depends not only on the number of equatorial hydroxyl (e-OH) groups in a saccharide molecule but also on their spatial orientation. The saccharide-water solutions exhibit properties that are considered to be the result of two factors (1) the elongated (non-spherical) shape of the oligosaccharides (2) effect of monosaccharides on the local water structure (i.e their ability to either enhance or destroy the local water structure). The observed magnetic field effect on diffusion coefficients of saccharides shows a strong dependency on these two factors. A decrease in binary diffusion coefficients ranging from two to eighteen percent has been observed for applied magnetic fields up to 1.1 T. The diffusion coefficients evaluated at zero field strength (earth's magnetic field) agreed with literature values to within one percent. The noted decrease in diffusivity of monosaccharides (ribose, xylose, galactose, glucose) becomes larger with an increase in the number of equatorial hydroxyl (e-OH number) groups in the saccharide molecule. This is because an increase in e-OH number increases the microviscosity of the saccharide molecule (structure making or stabilising effect). Deoxyribose and fructose, on the other hand, are considered to be structure breakers. The observed decrease in diffusivity for these saccharides induced by the applied magnetic field seem to be the result of a general stabilizing effect of the applied field on the originally less stable saccharide-water solution. The effect of applied magnetic field on the binary diffusion coefficients of oligosaccharides (sucrose, lactose, maltose, raffinose) correlates with the e-OH numbers as well. In this case, however, the observed decrease in diffusivities is due directly to the orientation of these molecules by the externally applied magnetic field (Cotton-Mouton effect). The same membrane was used to study one complete saccharide system, six runs, (made possible by the changes introduced into the design of diffusion cell and diffusion cell holder in this work) so that variation between membranes would not be a factor. The new experimental procedure resulted in significant reduction in data scatter and highly improved measurement accuracy. Finally, it was shown that the membrane only presented an area reduction to diffusion i.e. the transport process through the membrane followed the assumption of free diffusion. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

This thesis is concerned with tolerances for magnetic field imperfections in the TRIUMF cyclotron set by the betatron oscillation resonances v[formula omitted] = 1.0, v[formula omitted] – v[formula omitted] = 1.0 and v[formula omitted] = 1.5. These resonances, encountered during acceleration, can lead to undesirable growth in the amplitudes of the betatron oscillations. We first derive equations of motion that take into account non-linear terms and field imperfections, and show how resonance conditions may occur. These conditions were simulated in our orbit codes and numerical calculations were made to determine the tolerances they impose on the magnetic field. We have made a detailed investigation of the effect on the behaviour of the beam of first harmonic bumps at radii less than 150 in. The first harmonic tolerance of 0.1 G to produce an increase in the radial amplitude of 0.1 in. is in agreement with analytical calculations. We have also shown that this tolerance, too small to be seen in the magnetic field survey, may be achieved by suitable adjustments in the harmonic coil settings. Tolerances on the second harmonic imperfection are also presented. To determine the tolerances set by the coupled resonance v[formula omitted] – v[formula omitted] = 1.0, we have simulated a first harmonic twist in the median plane. The results show that, for high current poor resolution experiments, the magnitude of the twist on entering the resonance is of no importance, provided the amplitudes of the radial and vertical betatron oscillations are not much larger than the estimate of 0.2 in. For high resolution experiments, the tolerances on the slope of the twist are of the order of a few mrad. Analytical estimates of these tolerances are also presented. Finally, we have determined that the v[formula omitted] = 1.5 resonance sets an upper limit to the gradient of the third harmonic of about 0.2 G/in., which produces a 20% increase in the radial betatron amplitude. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Satellite lines originating from the first nearest neighbours have been observed on the Al²⁷ N.M.R. spectrum in dilute single crystal samples of Al-Mn and Al-Cr. The field and orientation dependence of the satellite position has revealed the quadrupole coupling constant and asymmetry parameter of [formula omitted] = 60 ± 1kHz and [formula omitted] = -0.01 ± 0.005 for Al-Cr, and [formula omitted] = 19 ± 1kHz, [formula omitted] = -0.08 ± 0.02 for Al-Mn. An anisotropic magnetic perturbation of ∆ K[₁₁₁] = -0.05 ± 0.01% and ∆ K[₀₀₁] = -(0.07 ± 0.1)% in Al-Mn is attributed to a spin density perturbation at the impurity sites. The Al-Cr results agree with those of Janossy and Gruner [18] and Minier and Berthier [22]. The satellite line observed in the Al-Mn system was also seen by Launois and Alloul [2], with approximately the same values of [formula omitted] and ∆ K. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis is concerned with three aspects of magnetic properties in solids. 1. The mean square value <I(I + 1)> of the proton angular momentum per molecule has been measured to be 3.73 ± 0.18 in solid CH₄ at 4.2 K . The experiment was done by measuring the ratio of the proton magnetic resonance free induction decay signal to that of ¹³C at the same frequency in a sample containing 53% ¹³CH₄ . The measured value of <I(I + 1)> differs appreciably from the high temperature value of <I(I + 1)> =3 and from the value of <I(I + 1)> = 6 when all the molecules are converted into the A spin symmetry species. Experiments at lower temperatures using a sample containing 0.002% O₂ impurity indicated that there may be a slight increase in the value of <I(I + 1)> between 4.2 K and 2.45 K . The presence of 0.05% O₂ impurity shortened the time constant for conversion of CH₄ between different symmetry species. The interpretation of measurements of <I(I + 1)> in the presence of large amounts of O₂ impurities is complicated by changes in the NMR line shapes. These complications are discussed in terms of the theoretical results obtained in the second part of the thesis. 2. The NMR line shape inhomogeneously broadened by paramagnetic impurities in solids was investigated theoretically using the statistical method of Margenau. The general expression for the Fourier transform of the line shape function was derived. The lattice can be divided into an inner spherical cut-off region and its complement. Impurities inside the cut-off region give rise to satellite lines and impurities outside determine the shape of the main line and satellite lines. Detailed numerical calculations were performed for a f.c.c. lattice when the impurities are (a) classical magnetic dipoles, (b) spin 1/2 systems and (c) spin 1 systems. An asymmetry in the line shape is predicted at finite temperatures. The peak intensity is shifted from the centre by an amount linear in the impurity concentration and in the magnitude of the magnetic moment and the overall line shape adjusts itself in such a way to give a vanishing first moment about the centre. The line shape is always Lorentzian at the centre and Gaussian in the wings. It depends on the impurity concentration. At low concentrations, the main line and the satellite lines have the same shape which is predominantly Lorentzian. The shape of a powdered sample is also discussed. 3. General expressions are derived for the first two terms in the expansion of the specific heat of a paramagnetic salt in powers of T⁻¹. It is assumed that the interaction between the paramagnetic ions consists of magnetic dipole and isotropic exchange interactions, and that the g-tensor of each ion is axial and has the same orientation for all ions. The general formulae are evaluated numerically for cerium magnesium nitrate. Comparison with the experimental data of Mess and coworkers indicated that the exchange parameter corresponds to a ferromagnetic interaction. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A series of isomeric, six-membered, cyclic phenyl phosphate esters has been obtained by column chromatography of the mixtures of isomers obtained by reaction of phenyl phosphorodichloridate with appropriate 1,3-diols. The conformational analysis of the isomers was undertaken using both ¹ʜ and ³¹p n.m.r.. The basic conformation of the 2 oxo-2-phenoxy-1,3,2-dioxaphosphorinane ring system is that of a "flattened-chair". The thermodynamic free energy difference between "chair" conformations is sufficiently large for the basic ring to exist essentially in one favoured conformation, rationalized to have an axial phenoxy substituent. The stereospecific nature of Jpoch has been confirmed by using ¹ʜ n.m.r. to determine conformations. Long-range, ⁴J, ³¹p- ¹ʜ coupling constants have been found to be stereospecific in nature and useful in facilitating assignment of conformations for methyl-substituted-2-oxo-2-phenoxy-l,3,2-dioxaphosphorinanes. Similar ring systems having different substituents at phosphorus have been studied and the conformations of these derivatives are seen to differ depending on the nature of the phosphorus substituent. The conformation of a cyclic nucleotide has been determined from its ³¹p n.m.r. spectrum. The use of computer programming techniques and hetero-nuclear double resonance techniques, greatly facilitated the analysis of the n.m.r. spectra discussed. An interesting deceptively-simple type of ABX n.m.r. spectrum has been found for many of these cyclic phosphate derivatives and the explicit analysis of this system is presented. / Science, Faculty of / Chemistry, Department of / Graduate