Table of contents

The application of the empirical pseudopotential method to the study of the electronic and optical properties of the germanium polytypes is investigated. It is found that there is sufficient arbitrariness inherent in the interpolation of the available empirical data for the germanium form factor to allow significant uncertainties in the predicted band structure. An independent augmented plane wave calculation of the band structure appropriate to the hypothetical germanium wurtzite structure suggests a new interpolation for the germanium pseudopotential form factor.

The structure of alpha -phase potassium nitrate (KNO₃) has been determined at room temperature (25 degrees C) and closer to the alpha to beta transition temperature at 100 degrees C, from three-dimensional neutron diffraction data. The present results indicate that the potassium atoms experience small but significant displacements, predominantly along the (001) direction, as the temperature is increased. They also suggest that the NO₃ groups are nonplanar, with the plane of the oxygen atoms making a small angle to the a-b face of the unit cell. Analysis of the atomic anisotropic thermal parameters, obtained from the least-squares refinements, suggests that the RMS vibrational amplitudes of the potassium atoms increase along the (001) direction as the temperature increases.

Total, elastic and inelastic scattering measurements have been made on liquid gallium over the temperature range 272 K to 375 K. The total scattering, giving the structure factor S(Q), is only slightly temperature-dependent but elastic diffraction measurements with special reference to values of the scattering vector Q near the main peak in S(Q) (Q₀=2.52 AA^-1) show an appreciable increase in the peak intensity as the temperature is reduced, although no change in the position of the peak is seen. The quasi-elastic scattering measured at Q₀ is shown to have a Lorentzian frequency profile whose width increases by some 45% over the temperature range. The rate of change of this width is 0.00143+or-0.0001*10¹² Hz K^-1 at 300 K. This gradient is more than twice that calculated by the T^1/2 law for free atoms.

Aligned anisotropic defects in a solid cause different changes in macroscopic dimensions and in lattice parameters along the different crystal axes. A simple general method is given for relating these differences to the microscopic forces associated with the individual defects. Explicit results are given for isotropic, cubic and hexagonal host lattices.

Optical and spin resonance properties have been calculated for the self trapped hole (V_k centre) in CaF₂, SrF₂ and BaF₂. The electronic properties are regarded as those of an F₂^- molecular ion whose internuclear spacing has been changed by the crystalline environment, and evidence is given that this is a good approximation. The spacing is obtained from a detailed lattice relaxation calculation allowing motion of many neighbours to the defect. The results are not sensitive to the different interatomic potentials used. Good agreement with experiment is obtained for optical transition energies and linewidths and for spin resonance parameters.

For pt. I, see ibid., vol.6, 229 (1973). The activation energies for the hopping motion of a self trapped hole (V_k centre) have been calculated for CaF₂, SrF₂ and BaF₂. The estimates use the well known small polaron model, together with the microscopic model used successfully for the static properties in the previous paper. The results are in reasonable agreement with observation. Unfortunately, the only data available refer to temperatures so low that simple thermal activation is not expected, and the most serious approximation appears to be the relation of the calculated and observed parameters. In CaF₂ 90 degrees jumps are not observed, in contrast to all simple theories. Possible explanations are discussed; chemical bonding between the V_k ions and the nearest axial anions is not adequate, but a modification of the corresponding repulsive interaction has the correct properties.

Exciton diffusion allows excitons created some distance beneath the surface to contribute to sputtering and causes the sputtering efficiency to peak at a higher bombarding electron energy than would be expected if no diffusion occurred. Measurements of this peak energy for KI and KI containing 0.1% Tl indicate exciton diffusion ranges 21 and 13 nm. In KI:Tl a reduction in sputtering efficiency and a lower peak energy are consistent with the model of exciton diffusion, the Tl⁺ ions acting as recombination centres. The exciton trapping cross section of thallium ions which can be estimated in this model is comparable with the ionic size of Tl⁺.

Recent work of the author (abstr. A64846 of 1972) on the acoustic attenuation due to the spin-phonon interaction in a concentrated paramagnetic crystal with spin ¹/₂ is applied to the geometry of interest for an acoustic-wave rotation experiment. It is shown that the intrinsic linewidth due to the spin-phonon interaction should not prevent observation of acoustic-wave rotation. A region of the coupled mode spectrum exists where the attenuation due to the intrinsic linewidth is negligible but yet the angle of rotation should be measurable even in the case of paramagnetic ions only weakly coupled to the lattice.

A device simulation method derived from a numerical method for solving the Boltzmann transport equation is described. It is essentially exact, in particular free from the assumption that electrons respond instantaneously to changes of electric field. A key feature is the representation of the k dependence of the free carrier distribution by an expansion in a set of basis functions. Reasonable accuracy can be obtained for a fairly small number of basis functions, leading to high computational efficiency compared with alternative exact simulation methods.

Hall effect measurements to 90 kbar at 295 K on two single crystals of InAs are described. The zincblende to rock salt structure phase transition was at 69+or-2 kbar, and the high pressure phase was metallic. In the zincblende phase, results gave limiting values of E(L_1c- Gamma _1c)>or=0.40 eV and E(X_1c- Gamma _1c)>or=0.75 eV for the sub-band energy gaps in the conduction band. Two impurity levels situated 0.70 and 0.61 eV above the valence band maximum at atmospheric pressure were observed with pressure coefficients of 0+or-1*10^-6 eV bar^-1 and +6+or-1*10^-6 eV bar ^-1 respectively. The levels are interpreted as being possibly associated with the higher lying conduction band states. The use of the mobility variations with pressure is shown to be a powerful method of determining the dominant scattering mechanisms at different carrier concentrations.

Hall measurements to 120 K at 50 kbar have been carried out for electrons in the )100), X_1c, satellite valleys in epitaxial and bulk grown GaAs for carrier concentrations in the range 10¹⁴-10¹⁸ cm^-3. Two distinct impurity levels have been found to be associated with the X_1c minima; estimates of activation energies 0.145+or-0.02 eV and 0.066+or-0.01 eV have been obtained for carrier concentrations near 10¹⁵ cm^-3. The activation energies of these levels decreased with increasing carrier concentration. Theoretical analysis of mobility-temperature curves has shown intervalley scattering to be dominant for purer samples while for the heavily doped bulk grown samples space-charge scattering becomes more important. A best estimate of the (X_1c-X_1c) deformation potential field, D_xx, of 0.8*10⁹ eV cm^-1 for a deformation potential E₁ of 5.0 eV has been obtained.

It is shown that exchange core polarization of a closed shell ion (Li⁺) having nonzero overlap with a neighbouring paramagnetic ion (O^-) is a reasonable mechanism to explain observed negative transferred contact interactions if overlap is considered not only on the shortest (Li⁺-O^-) path but also on indirect ones.

The study of the optical absorption of Ni²⁺ in ZnO and cubic, hexagonal and 6H polytype ZnS with polarized light has yielded an identification of all the expected zero phonon lines of the ³T₂ crystal field term. Static crystal field theory is inadequate to explain the observed splittings in ZnO, but this can be explained by the dynamic Jahn-Teller effect involving moderately strong electron-phonon coupling. Phonon sidebands observed in ZnS are interpreted on the basis of the one-phonon spectrum of ZnS.

In the first of this series of four papers in which two-magnon processes and their manifestation in light and neutron scattering from Heisenberg antiferromagnets are studied, general expressions for the temperature dependent electric and magnetic dynamical susceptibilities are derived. The method employed is based on an equation of motion technique and a decoupling scheme which in essence is equivalent to a t matrix approximation in a perturbation expansion in terms of the magnon density. Kinematical effects and spin wave damping are neglected. The method is considered to be valid for the temperature regime where the usual spin wave theory is applicable, that is roughly up to ⁹/₁₀T_N. Applying this method to evaluate the electrical susceptibility for light absorption and scattering, the temperature dependent cross sections are obtained and for neutron scattering the longitudinal dynamical susceptibility evaluated.

The temperature dependence of the two-magnon light scattering cross sections (derived in ibid., vol.6, 323, 1973), is examined for the rutile structure Heisenberg antiferromagnets NiF₂, FeF₂ and CoF₂. Although the temperature dependence of the peak position in the Raman scattering cross section is predominantly determined by the temperature dependence of the magnon frequency, it is found that taking into account the temperature variation of the effective magnon-magnon interaction yields a closer agreement with experiment. The temperature dependence of the peak width and height can be accounted for by including the magnon damping and properly treating the temperature variation of the sublattice magnetization which appears as an overall factor in the scattering cross section.

The neutron scattering cross section for two-magnon excitations and spin density fluctuations (derived in ibid., vol.6, 323, 1973) is examined for the rutile structure Heisenberg antiferromagnet CoF₂. Spin density fluctuations are found to result in a featureless cross section for all frequencies ranging from 0 to the top of the magnon-hole band. The two-magnon scattering cross section is evaluated and plotted for scattering off the Gamma (Q=(2 pi /a) (1,0,0)) and X(Q=(2 pi /a)(1.5,0,0)) points. Describing CoF₂ in terms of an effective spin ¹/₂ Heisenberg hamiltonian, which apart from an anisotropic exchange interaction contains an effective anisotropy field, good quantitative agreement with existing experimental data is achieved. Magnon- magnon interaction does not play any significant role in Gamma point scattering.

One and two magnon correlations are examined within the framework of standard perturbation theory using a Hollstein-Primakoff spin wave representation. Within the RPA this method reproduces the results obtained by the equation of motion technique in ibid., vol.6, 323 (1973), provided it is carried out in a certain selfconsistent way. A step by step comparison of the two methods throws new light onto the physical implications involved in the different approximations which seem to be favoured by the two techniques. The present method has in general an advantage over the equation of motion method in casting its results in terms which are easily physically interpretable. This allows the derivation of a simple expression for the neutron scattering cross section in terms of merely three q- omega dependent functions which describe certain free two-magnon correlation functions.