We have analyzed the NMR spectra of a series of 19 di-halobenzenes having Cs or C₂v symmetry dissolved in a special mixture of nematic liquid crystals, i.e., 55 wt% 1132/EBBA-d₂. This mixture has the unique feature that dideuterium dissolved in it experiences a zero average electric field gradient. Therefore one can assume that for this mixture the contribution to the molecular order due to the interaction between the average electric field gradient and the quadrupole moment of the molecule can be neglected. It has been suggested that the orientational order also depends on the size and shape of the solutes and a model has been used to calculate the order parameters. Another model relates the ordering to the molecular polarizability anisotropy. A description of the ordering of molecules having Cs symmetry requires 3 independent order parameters and thus provides a strong test for the different models of orientational order. Comparisons are made between our experimentally determined order parameters and the theoretical values obtained using the size and shape, and the polarizability models. Very good agreement is obtained for the size and shape model. However, it is found that any mechanism, involving a molecular property which is approximately bond additive, can not predict the differences found between the ortho- and meta-dihalobenzenes. Consequently, a poor agreement results from the polarizability model when a bond-additive scheme is used to calculate the molecular polarizability. Further investigation of the correlation between order parameters and solute molecules suggests that the molecular shape dominates the orientational behavior. / Science, Faculty of / Chemistry, Department of / Graduate

The crystal structure of diferrocenyl ketone has been analyzed using Fe(Kα) X-radiation. The molecule is symmetrical about a 2-fold axis passing through the carbonyl bond. Coordinates of the iron atom were determined from two Patterson-Harker sections and coordinates of the remaining atoms were derived from subsequent three dimensional Fourier summations. Structure refinement was carried out using (block-diagonal) least squares with allowances for anisotropic temperature vibration. The R value derived from the final coordinates is 0.09. The cyclopentadienyl rings not bonded to the keto group are vibrating more than those which are; when this is taken into account the iron atom lies midway between the cyclopentadienyl rings which are planar and 3.30 Å apart. The carbon bond lengths in these rings are all the same length (1.45 Å) and the conformation of one ring with respect to the other is almost eclipsed. The intermolecular contacts are all of normal length. The molecular dimensions of anti-8-tricyclo [3,2,1,0²˒⁴] octyl p-bromobenzenesulphonate and anti-7-norborneny1 p-bromo-benzoate have been measured to assist in the interpretation of the solvolytic reactivity in norbornane derivatives. Data were collected (Cu(Kα) radiation) by counter methods in both cases; the structures were determined using the heavy atom-Patterson method and refinements were carried out using differential syntheses and (block-diagonal) least squares. The discrepancy factors derived from the final coordinates are 0.09 and 0.18 respectively. The norbornane and norbornene skeletons have symmetry m and the bond lengths are normal. The bond angles at the methylene bridge are 97° and 96° respectively, the other angles are all less than the tetrahedral angle. The angles between the planes formed by different parts of the skeleton are identical in both cases. Bond lengths and angles in the remainders of both molecules are of normal dimensions. The configuration of the cyclopropyl methylene group in anti-8- tricycle [3,2,1,0²˒⁴] octyl p-bromobenzenesulphonate is exo to the norbornane skeleton. The results indicate that there is insufficient variation in the methylene bridge bond angles to account for the difference in solvolytic reactivity. The crystal and molecular structure of ochotensine methiodide has been investigated in order to determine the chemical structure of the molecule. The data were recorded photographically using Cu(Kα) radiation and a Weissenberg equi-inclination camera; estimation of the intensities was carried out by visual methods and interfilm scales were derived from corresponding symmetry related structure amplitudes. 845 independent reflections were measured in this way. The position of the iodine atom was determined from a three dimensional Patterson function and the positions of the remaining atoms from three subsequent three-dimensional Fourier maps. Refinement of the temperature and atomic parameters was carried out by (block diagonal) least squares; the final R value was 0.11. The analysis has shown that the structure of ochotensine is similar to that postulated for ochotensimine and the position of the phenolic group on ring A has been determined. A difference synthesis was carried out to verify the positions of the atoms. The bond lengths and angles are normal but several short intermolecular contacts were observed. The planes of the two benzene rings are inclined at an angle of 94°. / Science, Faculty of / Chemistry, Department of / Graduate

Spin-lattice relaxation times have been measured in metal single crystals with a pulsed nuclear magnetic resonance apparatus at both room and liquid nitrogen- temperatures. The values obtained for aluminum and vanadium agreed well with the values given in the literature for powdered samples. The niobium value was slightly lower than the most reliable powder value, possibly because of impurities. Measurements were made on isotopically pure tin to see if any anisotropy could be detected in the spin-lattice relaxation time. No anisotropy could be detected, but the crystal orientation used was so unfavourable that an anisotropy of less than about 50% could not be detected. The spin-spin relaxation time was measured in the isotopically pure tin for five different magnetic field orientations. These showed that exchange narrowing occurred. With a suitable choice of operating conditions, the apparatus measured the equivalent of the absorption mode in steady state nuclear magnetic resonance as a function of magnetic field orientation. This was combined with the spin-spin measurements to give the complete orientation dependence of the latter. These measurements gave a value of (2.1±0.3)Kc/s. for the pseudo-exchange constant in tin. The pseudo-dipolar second moment was found to be twice the dipolar second moment. Spin echoes were observed in the isotopically pure tin and were used to measure the spin-spin relaxation time. These gave values which were much shorter than those measured by free induction decays. The reason for this was not determined. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In this thesis the problem of an electron in a crystal in the presence of a uniform magnetic field is investigated using group theory method. A group of operators [ symbol omitted ] commuting with the Hamiltonian of an electron in the presence of a uniform magnetic field and a crystal electric potential is constructed. This group is homomorphic to the group [ symbol omitted ] (a magnetic space group) of space time transformations that leave the magnetic field and the crystal electric potential invariant. The property of the subgroup [ symbol omitted ] of [ symbol omitted ] that under the above homomorphism is mapped onto the lattice [ symbol omitted ] of [ symbol omitted ] is studied in detail. It turns out the structure of [ symbol omitted ] depends on the magnitude and the orientation of the magnetic field, so that, in fact one has to deal with an infinite class of groups. In particular, it is useful to divide this infinite class of groups into two subclasses: one subclass is then referred to as corresponding to "rational" magnetic fields, the other as corresponding to "irrational" magnetic field. The group [ symbol omitted ] is a generalisation of the "magnetic translation group" recently introduced by Zak for the special case of a symmetric gauge. He also constructed "physical" irreducible representations of the "magnetic translation group" for the special case of a "rational" magnetic field. In this case a group [ symbol omitted ] always has a maximal Abelian subgroup with a finite index. (The term "physical" representation simply means a representation which can be generated by functions of spatial coordinates.) In this thesis no such restriction is introduced: the "physical" irreducible representations of [ symbol omitted ] are also constructed for the case of irrational magnetic field, in which case the index of a maximal Abelian subgroup is always infinite; the "physical" irreducible representations are then always infinite dimensional. Using a complete set of Landau functions the basis functions generating "physical" irreducible representations of [ symbol omitted ] are found for the special case when the crystal is simple cubic and the magnetic field is parallel to a lattice vector. It turns out when the field is "irrational" the basis functions are countably infinite sets of Landau functions, and the energy spectrum depends only on one of the parameters labelling the "physical" irreducible representations of [ symbol omitted ]. The problem of perturbation produced by a weak periodic potential on the Landau levels for a free electron in a magnetic field is also considered. In this connection we make plausible the validity of certain quite general selection rules for an arbitrary periodic potential. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

X-irradiated cyanoacetylurea CNCH₂CONHCONH₂ and x-irradiated dicyandiaraide NCNC(NH₂)₂ single crystals were studied,by Electron Spin Resonance. Two radical species were formed when cyanoacetylurea, CNCH₂CONHCONH₂, was irradiated with x-rays. One was a π-electron radical, CNCHCONHCONH₂, and the other a σ-electron radical, CNCH₂CONHCONH . The σ electron radical was found to have a large, isotropic proton coupling tensor and an anisotropic nitrogen coupling tensor very similar to those of H₂NCOCH₂CONH . The π-electron radical had similar proton and nitrogen coupling tensors as CNCHCOOH which was formed in γ-irradiated cyanoacetic acid. In x-irradiated dicyandiamide crystals, the main species formed was shown to be NCNC(NH₂)NH, having also a large, isotropic proton coupling tensor, and hyperfine interactions with two nitrogen coupling nuclei were also observed and measured. ESR studies were carried out both at room and at liquid nitrogen temperatures. The effect of temperature on the spectra is discussed. INDO-SCF-LCAO-MO calculations were carried out for a model compound HCONH , with the amide proton assuming different inplane and out of plane positions. The spin density was found to vary over a wide range and could be used to interpret the large proton coupling of the dicyandiamide radical. MO calculations were also performed on the radical NCCHCOO ̄. The calculated results correlate fairly satisfactorily with the observed ones. Comparison of the direction of the unpaired electron p-orbital symmetry axis with bond directions and with normals to the fragment planes showed that while malonamide radical, H₂NCOCH₂CONH was a genuine σ-electron radical, dicyandiamide radical, NCNC(NH₂)NH was most likely a π-electron radical. / Science, Faculty of / Chemistry, Department of / Graduate

A numerical analysis of radiative heat transfer in a liquid encapsulant Czochralski gallium arsenide crystal puller is developed. The heat transfer and equivilent ambient temperature of each surface element are calculated using the Gebhart radiative model. The effective ambient temperature, to which each surface element is radiating, is found to vary indicating that assuming a constant ambient temperature for all surfaces (simplified radiative model) is incorrect. The importance of including the middle and top cylinders of the growth chamber in numerical analysis of radiative heat transfer in the system is evaluated in the study. The upper section could be replaced by one isothermal surface without significant change of the effective ambient temperature distribution. Fluid flow and heat transfer in the GaAs melt, crystal and encapsulant are calculated using a three dimensional axisymmetric finite difference code which includes the detailed radiative model. The mathematical modelling of the fluid and heat flow describes steady state transport phenomena in a three dimensional solution domain with latent heat release at the liquid/solid interface. The predicted flow and temperature fields using the detailed radiative model differ considerably from the predicted fields using the simplified model. The simplified model shows high axial and low radial temperature gradients in the crystal near the encapsulant region; the axial gradient decreases and the radial gradient increases with increasing distance from the encapsulant top. The detailed model shows a high radial temperature gradient in the crystal near the crystal-encapsulant-ambient junction and nearly flat isotherms in the top half of the crystal. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The spectrum of 1,3-dichloro-2-ethenylbenzene partially oriented in nematic liquid crystalline solvents has been analysed using a number of complimentary nuclear magnetic resonance (NMR) techniques. The analysis of this spectrum poses a considerable problem due to its complexity and the uncertain geometry and orientation of the molecule. The technique of multiple quantum NMR (MQNMR) has the capability of tremendously simplifying complex spectra. The multiple quantum spectrum was measured and proved very useful in the analysis but unavoidable resolution difficulties in the MQNMR experiment prevented a complete solution of the problem using this spectrum alone. While the spectrum of 1,3-dichloro-2-ethenylbenzene is dominated by only a few large interactions, the lines are split by relatively small dipolar couplings and the limited resolution available in the multiple quantum spectrum makes the determination of the smaller couplings difficult. To overcome this difficulty a frequency selective excitation of the multiple quantum spectrum was adapted and developed. After testing the experiment on the relatively simple spectrum of 1,1,2-trichloroethane dissolved in a nematic solvent, this selective experiment was applied to the much more complex spectrum of 1,3-dichloro-2-ethenylbenzene where it proved capable of directly measuring the small couplings in the spectrum without interference from any of the larger interactions. This information contributed greatly to the eventual analysis of the spectrum. MQNMR experiments can be very time consuming and as a result the spectroscopist must frequently make do with very limited time domain signals from which the spectrum must be extracted. This creates a number of difficulties when the signals are analysed with the fast Fourier transform (FFT), the standard method of spectral analysis used in NMR. With these problems in mind, the suitability of MQNMR time domain signals for analysis by a method of spectral estimation due to Burg, commonly called the maximum entropy method (MEM), was examined. By testing Burg's MEM with the MQNMR spectra of a number of different solutes partially oriented in nematic phases, it was found to be a useful adjunct to the FFT when dealing with MQNMR interferograms. While some care is required in its application, this method of spectral analysis should find important uses in the estimation of MQNMR spectra. Solution of the spectrum yielded information on the molecular geometry and the orientation of the 1,3-dichloro-2-ethenylbenzene in the nematic solvents used. While an extensive analysis of molecular geometry proved impossible, the information on molecular orientation was examined in terms of two different models. The orientation data shows excellent agreement with a recently developed model for orientation based upon the shape of the solute. / Science, Faculty of / Chemistry, Department of / Graduate

Two sets of structures were determined by X-ray crystallographic techniques, one of maleic anhydride (2,5-furandione) and the other of 4-phenyl-4-p-bromophenylcyclohex-2-en-1-one and its photoproduct, trans-5-phenyl-6-p-bromophenylbicyclo[3.1.0]hexan-2-one. Analysis of maleic anhydride included a room temperature redetermination of the crystal structure. This was done to improve parameters and simplify comparison of the room temperature and low temperature data. The structure determination at 104k resulted in the location of bonding electrons in the double bond. Thermal motions of both sets of data showed that translational motion was greatest along an axis parallel to the carbonyl bonds. Libration was found to be greatest about this axis also. The second set of structures was done to examine the migration pattern of aryl groups upon irradiation of a diarylcyclohexenone. The major photoproduct was formed by migration of the p-bromophenyl group. The resulting bicyclohexanone had the aryl groups trans to each other. / Science, Faculty of / Chemistry, Department of / Graduate

In order to test the apparently conflicting predictions of some current theories of strain hardening, slip line length measurements were made on a series of oriented copper single crystals, identically prestrained at 673°K, polished and incrementally strained at temperatures between 573°K and 4.2°K; slip lines formed during low temperature increments were found to be longer than those formed during strain increments at higher temperature (Garner and Alden, 1974). The result is shown to be in conflict with any theory of strain hardening in which slip lines are blocked by specific obstacle configurations, such as Lomer-Cottrell barriers, ribbons of converted pile-ups or dislocation cell walls. In contrast, the result is shown to be consistent with theories of strain hardening in which slip lines are blocked by statistical interaction between expanding glide loops and forest dislocations, on the condition that, within the framework of such a theory, the glide loops are able to expand athermally over a newly available free area of slip plane, after a thermally activated process. Two possible thermally activated processes are discussed. A unified view of slip lines properties is presented which is shown to provide a self-consistent explanation of the temperature variation of slip line length, slip band formation, the existence of multipole carpets and the variation of flow stress with temperature. The statistical aspects of this interpretation were investigated further by obtaining 77°K microstrain curves from a series of oriented copper single crystals, prestrained at temperatures between 1000°K and 77°K, to produce dislocation microstructures with differing degrees of regularity, yet with approximately the same overall density. The forest dislocation microstructures of an identically prepared series of crystals were examined using a dislocation etch on the primary slip plane. A statistical sampling technique was devised, which was used to measure local dislocation densities. In addition, new parameter is introduced, namely the ratio of the sampled standard deviation, to mean local dislocation density, which quantifies the degree of regularity of a dislocation micro-structure. All microstructures were found to have a smaller degree of regularity than a random distribution. For crystals prestrained at temperatures above 293°K, at any given fraction of the 77°K yield stress, the amount of microstrain was found to increase as the microstructures became less regular. Crystals prestrained at and below 293°K exhibited the Haasen-Kelly effect, which was attributed to restricted source operation. However, once sources begin to operate, the amount of microstrain anticipated from the degree of regularity was indeed detected. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

There are a number of interesting and as yet unresolved problems concerning the dissolution rates and solubilities of various drugs. It seems clear that the inherent properties of crystals (i.e. surface and bulk structure and properties) and their relationship to solubility and dissolution rate need to be more clearly understood before explanations for these observations can be offered. The approach taken in this study to the problem of dissolution is to consider the method of preparation and its effect on crystal structure. This study attempts to show that, in addition to properties of the solid state such as polymorphism, solvation and degree of crystallinity, the dissolution kinetics may be affected by: a) the anisotropic nature of crystalline solids and hence crystal habit b) the type and number of crystal defects incorporated into a crystal during growth. Inorganic salts such as nickel sulfate hexahydrate (NiSO₄ α 6H₂O) and potassium perchlorate (KCIO₄) provided suitable model, crystalline materials as they grew as large, well-formed crystals with distinct habits. KCIO₄ crystals could be easily cleaved and etched and grew with relatively low dislocation densities. The dissolution anisotropy of NiSO₄ a 6H₂O crystals was studied using a single crystal dissolution method by measuring the movement of the (111) and (112) crystal faces with time in a flowing solvent using a travelling microscope. The observed apparent rate constant, Kobs for the (112) face was greater than for the (111) face at all flow rates but anisotropy was less pronounced at the lower flow rates, The apparent rate constants for the transport and surface controlled reactions, Kt and Kr were of the same order of magnitude suggesting that the overall dissolution reaction was under mixed control at the lower flow rates. Activation energies were slightly higher than the normal range for transport processes. Kr (112) > Kr (111) indicating that anisotropy was probably due to differences in the rate of the surface reaction. At high flow rates there was a change to a predominantly surface controlled reaction. It is likely that dissolution anisotropy is due to the differences in activation energy for the two faces. The effect of habit modification on the dissolution rate of NiSO₄ a 6H₂0 in 60% v/v ethanol was studied using a rotating basket method. Bipyramidal crystals were grown in a fluidized-bed crystallizer and platy crystals were recrystallized from supersaturated solutions of nickel sulfate containing small amounts of gelatin. Acicular crystals were prepared by the topotactic dehydration of acicular crystals of NiSO₄.7H₂O. DSC thermograms of platy and acicular habits were similar but differed from the bipyramidal habit probably due to differences in vapor pressures exerted by the habits. The observed dissolution rate constant, K'obs. for the bipyramidal and acicular crystals was similar and greater than the platy habit at both low and high rotation rates, the difference being less pronounced at the lower rotation speed. At the high rotation speed dissolution was under mixed transport-surface control . The difference in K' obs must be due to different values of the overall surface energy of the crystals. KCIO₄ crystals were grown in silica gels and the crystals from three growth levels (and hence grown at different rates) were cleaved, etched and the dislocation etch pits counted using a differential interference contrast microscope. Crystals grown at the fastest rate had the highest mean dislocation densities and the highest K'obs values as determined using the rotating basket method. Conversely, crystals grown at the lowest rate had a low mean dislocation density and low K'obs values. The differences in K'obs were not due to impurities but to differences in the energy content of crystals resulting from the incorporation of differing numbers of dislocations into the crystals. / Pharmaceutical Sciences, Faculty of / Graduate