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This thesis is concerned with the properties of transition metals in High Pressure High Temperature synthetic diamond. They have been studied using the following techniques: optical and electron paramagnetic resonance spectroscopies, and a local density approximation code to model various defect centres. Experimental studies of recently-discovered lines, attributed to Co-N complexes in diamond, are presented. Under uniaxial stress, it is found that a zero-phonon line at 2.367 eV has its optical transition from an E- to A_1-ground state at a defect with trigonal symmetry. Another line at 2.135 eV arises at a defect with monoclinic I symmetry. EPR work has revealed the first Co-related EPR centre - O4. This has monoclinic I symmetry, and, because of hyperfine interaction that results in a broadening of the spectral features, it is concluded that nitrogen is also present. Next, cobalt in diamond has been modelled. Using the ab-initio local density code, AIMPRO, many different cobalt-related structures in diamond have been examined, ranging from the isolated atom to complexes with several nitrogens. The empirical model developed by Ludwig and Woodbury is useful in describing these defects. The defects that have been studied experimentally have also been modelled theoretically. For the 2.367 eV system, a Co-N complex with spin zero has been found to be the most likely candidate for the defect centre. Finally, some optical and modelling work have been combined on nickel-nitrogen complexes in diamond. The S2 and S3 luminescence systems are present in natural and synthetic diamond and have been tentatively correlated with the EPR NE3/2 defect systems. Uniaxial stress results indicate that the centres are of low symmetry - typically triclinic. This agrees with the EPR work. Some complementary modelling investigating these systems further supports these results. The thesis is concluded with some discussions and suggestions for further work.

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The series of compounds which crystallize in the orthorhombic Pbnm distortion of the perovskite structure has proved a lucrative source of experiments in solid state physics. In the general formula ABO₃, either or both the metallic ions may be magnetic and since the two site symmetries are also different this provides several different degrees of complication. The main study in this thesis is of the two members GdAlO₃ and DyAlO₃ in which the B site is occupied by the diamagnetic aluminium ion. We therefore only have to consider the interactions of the rare earth ions with each other and with their surroundings. Three types of experimental measurements have been carried out. Specific heat measurements in the range 0.5°K to 20°K were performed in a conventionally designed He³ cryostat using a germanium resistance thermometer. Measurements of the magnetic moment and most of the magnetic susceptibility measurements were carried out by a ballistic method and the induced signal measured on an integrating digital voltmeter. Applied magnetic fields up to 90kOe were available for use in the moment experiments. The temperature range 0.4°K to 4.2°K could be covered using pumped He³ or He⁴. Susceptibility measurements in the pumped liquid hydrogen range and some measurements in the liquid He⁴ range were carried out using a mutual inductance technique. The most prominent feature of the specific heat measurement on GdAlO₃, was a lambda anomaly peaked at 3.870°K which we take to be the ordering temperature. Around 1°K there is another smaller bump which is a Shottky anomaly due to the crystal field splitting. The total entropy under the magnetic part of the specific heat was measured to be R ln8 showing that the Gd³⁺ ion is in its ⁸S_7/2 ground state. Measurement of the magnetic susceptibility of GdAlO₃, along the three orthorhombic axes showed results similar to that expected for a simple two sublattice antiferromagnet with the b-axis as the direction of magnetic alignment. Above the Néel temperature there was very little anisotropy. As expected for an antiferromagnet with small anisotropy, the phenomenon of "spin flop" was observed in the magnetic moment measurement along the b-axis. The critical field was found to be 11.58kOe. Magnetic saturation was achieved along the a, b and c-axes at 45.6kOe, 39.5kOe and 44.4kOe respectively with an isotropic saturation moment within 1% of 7 Bohr magnetons per atom. Prom a simple molecular field theory analysis of these experiments we obtain the values 21.0kOe for the exchange field and 2.7kOe for the anisotropy field. Closer analysis reveals that the anisotropy is mainly due to the crystal field interaction and the principal axis is canted at ±38° to the b-axis in the a-b plane for the two different magnetic sites. This means that the ordering mode is really divided into four sublattices with hidden canting in an A_xG_y configuration following the notation of Bertaut. At low temperatures the G_y component, which corresponds to antiparallel nearest neighbours, is dominant showing why many of the properties could be explained on the basis of a simple two sublattice antiferromagnet. The sublattice magnetization was calculated in several different ways and helped show that the internal consistency of molecular field theory is much better than its accuracy in ab initio calculations. Using results from the moment experiments along the b-axis the magnetic phase diagram on the H-T plane was plotted. The value of the nearest neighbour exchange constant was evaluated from results of several different experiments using the Heisenberg model and a best value of J/k = -0.067°K obtained. Prom the consistency of the results it was concluded that second nearest neighbour exchange is negligible. Specific heat measurements on DyAlC₃ below 8°K showed only a lambda anomaly peaked at the Néel point of 3.53°K. The entropy under the specific heat was measured to be almost R ln2 showing that the Dy³⁺ ion is in the lowest lying Kramers' doublet of the ⁶H_15/2 ground state. Thus the Dy³⁺ is well described by an effective spin of andfrac12; and this gives rise to very anisotropic interactions with its surroundings. Optical measurements have shown that one g-value is very much larger than the other two so we expect it to behave to a good approximation as an Ising system. The susceptibility measurements below the Néel temperature confirm this belief, with the susceptibility decreasing with decreasing temperature along both the a- and b-axes. The ratio of the two measurements remains constant at a value corresponding to tan²33° showing that the canting angle is ±33° to the b-axis. The susceptibility along the c-axis is very small and almost temperature independent. The moment measurements in the a-b plane all showed the phenomenon of "spin flip" or reversal of the direction of a sublattice, expected in an anisotropic antiferromagnet. Measurements at an arbitrary angle showed two flips due to the magnetically inequivalent sublattices and the angular dependence could be explained well using dipole interactions alone. Although the magnetic ordering is due mainly to dipole interactions it is shown that there is a significant antiferromagnetic exchange interaction with J/k~-1°K between nearest neighbours along the c-axis. Susceptibility measurements were carried out on four series of rare earth compounds of the general formulae RNbO₄, R₃NbO₇, R₂TiO₅ and R₂Ti₂O₇ as well as several other members of the RAlO₃ family. Half of the compounds showed ordering transitions but further detailed work could not be carried out because of the difficulty in obtaining suitable specimens.

The major emphasis of this thesis relates to the calculation of the electronic structure of the isolated vacancy in the diamond and silicon crystal using the defect molecule approach. The electronic energy levels from an undistorted vacancy calculation are corrected, to a first approximation, for symmetric relaxation and Jahn-Teller distortion effects. The electronic properties of the undistorted neutral divacancy in diamond are also determined. A description of a dynamic relaxation program developed to estimate the displacement of atoms surrounding a point defect in the diamond-type crystal as the result of distortion effects is also reported. A discussion of the theoretical methods available for the calculation of the electronic structure of point defects in diamond-type crystals and the reasons for choosing the defect molecule approach is presented in section 1.2 of <strong>Chapter 1</strong>. In the remainder of the chapter the experimental evidence available for the existence of single vacancies, divacancies and the interstitial atom in irradiated diamond and silicon crystals is briefly reviewed. <strong>Chapter 2</strong> contains a detailed account of the fundamental aspects of the defect molecule method first proposed by Coulson and Kearsley. The limitations as well as the advantages of this method are discussed and the modifications made to the model in the present study are outlined. The basic formal relationships required for the calculation of the electronic structure of the undistorted vacancy in its various charge states are developed within this framework. The results of applying this method to a calculation for the single isolated vacancy in the diamond crystal are presented and discussed in <strong>Chapter 3</strong>. Four possible charge states of the vacancy; namely, the single positive, the neutral, the single negative and the double negatively charged state are considered. An investigation of the sensitivity of the relative ordering of the energy levels for the various centres to two different choices of basis functions to represent the 2s and 2p orbitals on the tons in the crystal is undertaken. For the neutral vacancy the ¹E electronic level is predicted to be the ground state of this centre with the ³T₁ level the first excited state when simple Slater-type functions are chosen for the 2s and 2p orbitals. However, when the atomic Hartree-Fock functions proposed by Clementi are employed the order of these two levels is inverted. A simple model to examine the influence of delocalizing the electronic wave-function of the defect electrons on the relative ordering of the lowest levels is presented in section 3.5. For the neutral vacancy no change in the ordering of the lowest levels results when a reasonable amount of delocalisation is incorporated. For the negatively charged centre the ⁴A₂ level is reinforced as the lowest electronic level. The calculation for the electronic structure of the uto- distorted neutral divacancy in the diamond crystal using a modified antisymmetrized molecular orbital method, based upon the bond method, is reported in <strong>Chapter 4</strong>. Using simple Slater-type functions for the 2s and 2p orbitals the ³A_2g level is predicted to be the ground state of this centre, with spin- and orbitally-allowed transitions to the ³A_1u level corresponding to optical absorption in the u-v region of the spectrum. In <strong>Chapter 5</strong> the development of a dynamic relaxation method which enables the displacement of the atoms surrounding a point defect in the diamond-type lattice to be determined free from the constraints of previous models is described. The method relies upon having a valence-force potential function which includes non-central as well as central force terms to describe the interactions between the atoms of the perfect crystal. The interaction between the defect electrons is simulated by applying external forces to the atoms nearest the defect. The method is applicable to a wide range of systems; however, here it has been applied only to the neutral single vacancy in the diamond and silicon crystal which undergoes a tetragonal distortion as a result of the nature of the rebonding forces. Displacements of the atoms in the vicinity of the defect are much greater for the silicon crystal than for the diamond crystal. It has been demonstrated that the displacement of atoms which are fifth neighbour to the defect is greater than that for third or fourth neighbours. As a by-product of the calculation the formation energy of the single vacancy has been evaluated. The theory of the Jahn-Teller effect, to first order, for the degenerate levels of the vacancy system is developed in <strong>Chapter 6</strong> using the rigid atom approximation proposed by Lidiard and Stoneham. The differences between the method used in the present calculation and that developed by Lannoo and co-workers is discussed. The extent of Jahn-Teller splitting for all the lowest levels of the various centres is determined. Contrary to previous suggestions the values obtained for the splittings were found to be insensitive to the choice of basis functions for the valence orbitals. A correction to the lowest energy levels for the symmetry relaxation of the atoms nearest the defect is also made. This latter modification was different for various electronic levels belonging to a particular charge state of the vacancy and consequently is very important in determining the relative ordering of the lowest levels. This is again contrary to what has previously been tacitly assumed. The corrected electronic structure of the neutral vacancy suggests that this centre is not responsible for the GR1 band observed in irradiated diamonds as the ³T₁ level is predicted to be the ground state of this centre from all calculations. On the basis of this work it is also unlikely that this band is associated with the negatively charged vacancy; however, this possibility cannot be definitely eliminated. The electronic structure for the four possible charged states of the single vacancy in the silicon crystal is determined in <strong>Chapter 7</strong>. The atomic Hartree-Fock functions proposed by Clementi are used to approximate the 3s and 3p orbitals on the silicon atoms in the crystal. Using both an unmodified and a modified antisymmetrized molecular orbital theory it has been demonstrated that electron-electron interaction terms and configuration mixing effects are important in determining the lowest levels of each centre. Again the energy levels resulting from the undistorted calculation are corrected for symmetric relaxation and Jahn-Teller distortion effects. The modified theory predicts ground state levels for the various centres which have the same total spin as those suggested by Watkins from his electron spin resonance experiments. The roost important findings and their implications on further work in this area are reported in a final general discussion.

The atomization of a liquified gas propellant, as a means of dispersing a powdered drug or non-volatile solute, was investigated. Atomization was achieved by passing the propellant through a two-orifice nozzle assembly. A number of properties of the system were shown to be predictable with reasonable accuracy, in terms of the nozzle dimensions and thermodynamic properties of the propellant, together with minor empirical factors. The properties that could be predicted were the mass flow-rate, the pressure of the propellant in the expansion chamber between the two orifices, the quality, or mass fraction evaporated, of the propellant in the expansion chamber, and the initial velocity of the spray. By application of the principle of momentum conservation the axial velocity decay of the gaseous component of the resultant spray and to a certain extent the particulate component of the spray could also be predicted. In addition to the above fundamental relationships, an empirical expression for the mass median diameter of the residual aerosol of a non-volatile solute dissolved in the propellant was determined. Information thus obtained is of assistance in the optimisation of the design of liquified gas aerosol generators as a means of administering a drug by inhalation.

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