Table of contents

The energy band structure of LiH in the selfconsistent Hartree-Fock approximation has been computed, and the state density for this solid computed directly by a new band model. Evidence is found for a strong optical absorption 'resonance' which should be present in the Li-K-shell spectrum and occurs about 13 eV beyond the onset of K-shell absorption.

The dependence of the delay time of a new switching effect (switching to a lower conductance) on the applied electric field, the transverse magnetic field and the pulse repetition frequency in liquid selenium is studied. With two different techniques-(a) reducing the pulse time below the delay time; (b) reducing the pulse voltage below the switching voltage-the conductivity expiration after switching to low conductance could be obtained.

Changes in the calorimetric and NMR properties of CoCl₂.6H₂O, LiCuCl₃.2H₂O, MnF₂ and azurite in the immediate vicinity of T_N are attributed to a distinct intermediate stage in the antiferromagnetic ordering process. It is pointed out that Pippard's thermodynamic relations may be applicable, even though the transitions are formally of first order. The thermal behaviour of NiCl₂.6H₂O below T_N appears to be in accord with Pippard's first relation, but a definitive test of the present thesis calls for additional experimental work.

The spontaneous staggered polarization P₀ of the two-dimensional F model is reported. At the critical temperature, P₀ has an essential singularity, both P₀ and all its derivatives with respect to temperature vanishing.

With a suitable definition, magnons can exist in a magnetically disordered medium with any wavelength at sufficiently low temperature, but they can only be observed by neutron scattering at small wavelengths. The neutron inelastic scattering cross section is accurately calculated at low temperature in a special model for one- and two-dimensional media.

A thermal mixing of the ¹⁹F and ⁷Li Zeeman reservoirs in lithium fluoride containing F centres has been observed at high magnetic fields and low temperatures (g beta H>kt), and its rate measured as a function of NMR frequency and electronic polarization. The mixing, much faster than spin-lattice relaxation, is through the electronic spin-spin reservoir.

The H3 zero-phonon line in diamond is generally broader when measured in absorption than in emission. It is shown that a nonradiative energy transfer from the H3 centres to nitrogen impurity accounts qualitatively for this behaviour.

The lineshape function for the transitions ²P_1/2 to ²P_3/2 of the Tl⁰ atom in KCl is investigated in the limit of large spin-orbit interaction using the semiclassical Franck-Condon approximation. The parity-forbidden transitions are made allowed by the odd-parity mode T_1u. The interaction of the ²P_3/2 state with the E_g mode causes splitting in the absorption band. One can interpret differences in the features of the two observed bands as a result of the ²P-²P_3/2 mixing.

Thin films of ZnS_xTe_1-x have been grown in the composition range 0<x<1. The optical energy gap and the lattice parameters of these alloys have been measured, and the energy gap bowing is compared with previous theoretical estimates. The bowings estimated from the dielectric model of Van Vechten are recalculated, and it is shown that disorder is unimportant. The dependence of the bowing on lattice constant is investigated, and is shown to be consistent with pseudopotential theory.

The memory function associated with the velocity autocorrelation has been calculated from the equation of motion of a test atom and by decoupling the statistical average in such a way that the collective effects of the system are also included. The self diffusion coefficient of liquid sodium has been computed from the present formulation and compared with the value obtained from Helfand's expression for the memory function, which excluded the collective effects of the system.

The relations between the localized potential method in the theory of the electron-phonon interaction and classical lattice dynamics have been investigated. The well known rigid ion approximation in lattice dynamics has been re-discussed. Long range multipole interactions in various semiconductor crystals have been studied.

Lattice dynamical theory for long optical phonons in the diamond structure is presented. The long range quadrupole interaction is taken into account. An estimate is made of the quadrupole interaction constant for germanium.

A method is described for identifying essential stationary points in the electronic energy bands or the lattice vibration spectrum E_j(k) of a crystalline solid with space group G. It is noted that E_j(k), considered as a function of k, possesses the symmetry of a certain symmorphic space group G' and the relationship between G and G' is identified. In addition to essential stationary values it is also possible to identify certain points at which the derivative of E_j(k) vanishes for only a restricted number of directions. The results are tabulated and a comparison is made with the method and results of Kudryavtseva.

The work of a previous paper (ibid. vol.6, 826 of 1973) on the identification of essential stationary points in the electronic energy bands or the lattice vibration spectrum of a non-magnetic crystalline solid is extended in this paper to the case of a magnetic crystalline solid with symmetry which has to be described by one of the black and white space groups.

A new method is presented for calculating the surface specific heat of a crystal lattice in the harmonic approximation. As an illustration it is applied to an isotropic elastic continuum with stress-free boundaries and the result is in agreement with previous authors. The method clearly shows the contributions to the surface specific heat from the various types of mode that can exist in the presence of a surface and, in particular, how the contribution from the bulk modes is closely related to the difference between the form of these modes in a semi-infinite and an infinite crystal.

The through-bond interaction of two H atoms on (100) tungsten has been calculated in a surface molecule approximation using both Anderson's and Hubbard's hamiltonians, and assuming a linear W_zH local geometry for chemisorbed hydrogen. There is a short range repulsion preventing two such adsorbed H atoms from occupying adjacent sites amounting to 0.020 Ryd for Anderson's model, and 0.010 Ryd for that of Hubbard.

A study is made of the electronic structure of a network by adapting the free-electron model. In this model, a tight-binding structure is represented by free electrons constrained to move upon lines joining the bonded atoms of the network. A Boltzmann equation is then derived for the joint probability distribution of the wavefunction and its logarithmic derivative. In the Fokker-Planck approximation this equation reduces to that derived by Halperin for a one-dimensional random white-gaussian noise potential. This model strongly suggests that localization persists in a network long after percolation is possible.

For pt.I see abstr. A57179 of 1972. A unified formalism for describing the transverse and longitudinal magnetophonon effects is developed from a resolvent perturbation expansion of the high magnetic field Kubo formula for conductivity to include the effects of Landau level collision broadening. A kinetic equation is derived for the longitudinal magnetoconductivity and solved for a non-polar optic phonon scattering model in the limits of zero and strong level broadening. Conditions for observing maxima or minima in the resistivity are obtained in these limits. Strong damping is shown to lead to minima displaced to the low field side of the resonance fields B=m omega ₀/eP where omega ₀ is the LO phonon frequency and P is an integer. The theory is consistent with experimental data on III-V semiconductors due to Straddling.

For pt.II see abstr. A8428 of 1973. A detailed theoretical discussion is given of the Jahn-Teller theory of a ground state orbital doublet in a trigonal environment. In particular, the isoelectronic ions Cr²⁺ and Mn³⁺ in Al₂O₃ are studied and it is found that the site symmetry may be approximated to C_3v. A cluster model is used to evaluate the coefficients in the hamiltonian describing the spin system which is derived using symmetry arguments. Various approximations in the theory are discussed in detail. It is shown that the system is characterized by four parameters. The more important are the inversion splitting delta and lambda ²/ Delta . Data previously obtained by APR experiments when the magnetic field is along the c axis are used to obtain estimates for the parameters for Cr²⁺. The best fit to the data is obtained by taking the anharmonic coefficient B to be positive, delta approximately 3.0 cm^-1. and lambda ²/ Delta approximately 0.6 cm^-1 An energy level diagram appropriate to Cr²⁺ in constrained sites in Al₂O₃ is also given.

Low temperature series expansions for the Ising model with spin S=1 and S=³/₂ are derived for a number of two and three dimensional lattices. For each spin-lattice combination the critical point is estimated, and then the critical exponents beta and gamma ' with their corresponding critical amplitudes are also estimated. The principal conclusion is that there is no compelling evidence to suggest that the above critical exponents differ from their S=¹/₂ values.

The isobaric temperature dependence of the low frequency dielectric response of KTaO₃ and SrTiO₃ is reported for the range 2-300 K together with its isothermal pressure dependence for hydrostatic pressures up to 12 kbar in the range 77-300 K. The results are used to show that the paraelectric phase of these materials is stabilized by strong interactions of the soft mode through the quartic anharmonicity. The low frequency anharmonic self energy of the soft mode in both materials dominates both the thermal strain and the harmonic contribution, this latter being imaginary. At temperatures above 290 K it appears that second order quartic interactions may be becoming important. A comparison with the theoretical calculations of Cowley for SrTiO₃ shows reasonable agreement with the rate of increase with temperature of both the thermal strain and the anharmonic self energy contributions to the soft mode.