Table of contents

A structural model is proposed with regions consisting of identical two-dimensionally perfect layers, stacked randomly on top of one another such that bonds in adjacent layers are in either diamond-like (staggered) or wurtzite-like (eclipsed) configurations. The model has perfect tetrahedral coordination everywhere throughout such regions and is consistent with electron microscopy results and with the observed diffraction data, especially those features corresponding to the diamond (1,1,1) and (2,2,0), (3,1,1) peaks.

It is shown that the surface energy and curvature energy of electron-hole droplets both have a positive sign, and that they depend strongly on the gradient terms in the density functional expansion.

A linear response expression for the isothermal local resistivity is derived with the many-variable projection technique of Mori (1965). The isothermal local resistivity is given by a force-force response function, and it is inverse to the isothermal local electric conductivity. The resistivity expression is obtained by inversion of the Kubo conductivity formula.

The 'average nuclear effective charge' Z, defined previously by the authors, is shown to be applicable to A^IIB^VI semiconductors. The cohesive energy, heat of formation, lowest-energy gap, microhardness and melting point are found to be linearly related to Z.

It is shown that the two-dimensional q-component Potts model is equivalent to a staggered ice-type model. It is deduced that the model has a first-order phase transition for q>4, and a higher-order transition for q<or=4. The free energy and latent heat at the transition are calculated.

The longitudinal correlation function of the Heisenberg ferromagnet is evaluated using the Dyson-Maleev transformation and also by spin operators. Its correctness is analysed through the violation of kinematical interaction.

A series of sidebands shifted by +or-n omega _T from the main nuclear magnetic resonance line is predicted for systems of small interacting molecular groups undergoing tunnelling rotation at frequency omega _T.

The dynamic structure factor, S(q, omega ), for liquid sodium is investigated by means of a generalized hydrodynamic approach, using a computed fourth moment, measured values of transport coefficients (as far as possible) and the experimentally determined specific heat ratio C_P/C_V. This ratio has characteristically a value of 1.1 to 1.3 for liquid metals, near their melting points, and the importance of its proximity to unity in determining the shape of the dynamic structure factor is stressed, as is the need for accurate experimental results for S(q, omega ) in liquid metals.

Calculations of the electronic structure of the F centre in KMgF₃ are reported and their results compared with experiment. The hyperfine interaction of the ground state with the nearest F^- ion is predicted to be 70 G, in good agreement with the experimental result of 60 G. The energy for optical absorption to the E_u excited state is given by a point-ion calculation as 4.4 eV, compared with the observed 4.6 eV. The predicted spin-orbit splitting of the excited state is 57 cm^-1, close to the experimental value of 60 cm^-1.

The elastic constants of DySb near its 9.5 K phase transition are calculated using a simple model for the states of the Dy ions. Good agreement with experiment is obtained above the transition but there are large discrepancies in the low temperature phase. It is argued that his disagreement is not a consequence of the model for the states.

Results are presented for the velocity of sound for liquid Cu-Sn alloys accurate to 0.2% for temperature up to 1400 degrees C. The adiabatic and isothermal compressibilities are calculated from these data plus other thermodynamic data. The almost linear dependence on composition of the isothermal compressibility is not predicted by a simple extension to alloys of the Ascarelli model for the compressibility of pure metals. The partial structure factors at zero wavevector a_ij(0) are calculated from available thermodynamic data and are found to be strongly dependent on composition. Comparison with the a_ij(0) calculated from models of binary mixtures shows that the composition dependence arises both from the size difference and the finite interaction between the Cu and Sn components. It is deduced from the a_ij(0) that Cu-Sn correlations are favoured over Cu-Sn correlations for compositions centred around 75 at% Cu.

Hall's prediction (see abstr. 4065 of 1973) that first sound will be generated when second sound is incident normally on an array of vortex lines in rotating superfluid helium is tested experimentally with a cylindrical resonator rotating on its side. No coupling was detected at any temperature. The measurements indicate that Hall's parameter C' is at least an order of magnitude smaller than the predicted value of 1.8 at 1.34 K. Second sound absorption measurements show that even at the highest rotation speed of 6.2 rads s^-1 the vortex line density is less than the large cavity limit 2 omega / kappa .

In a previous publication an exact expression was given for the Hartree potential in a perfect solid. The screen charge round a particular ion was expressed in terms of an effective dielectric tensor. The diagonal components of this tensor are examined using a simple model of the electronic states in a semiconductor.

An analysis is given of the behaviour of two-centre parameters used in the semi-empirical tight-binding method, as a function of inter-atomic separation, and for various values of the principal atomic quantum numbers. It is found that, in certain cases, the use of free atom wavefunctions to calculate these parameters can lead to their nonphysical behaviour. Numerical calculations are presented which show when this problem occurs and an example demonstrates that it can be a problem in actual calculations. Various methods to overcome this difficulty are discussed. A modification of the semi-empirical tight binding method is given which eliminates the nonphysical behaviour of the parameters, and makes it possible to perform detailed band calculations using suitable localized functions.

A study is made of the electronic structure of a network with arbitrary disorder using free-electron and tight-binding models. In the free-electron model, propagator techniques are used to describe the probability distribution of the wavefunction's logarithmic derivative along an arbitrary path in the network. The tight-binding model is developed by analogy to the free-electron model. In both models coupled self-consistent integral equations are found to describe steady-state probability distributions when the effects of closed loops in the network are ignored. A discussion of the equivalence of the two models is given.

The valence and conduction bands of diamond were calculated by the augmented plane wave (APW) method for the points of higher symmetry of the Brillouin zone. The calculations were carried out for four different approximations to the exchange energy. The convergence of the method was studied, and a limited study of the self- consistency in the potential was made. Very good results were obtained using a non-muffin-tin potential between APW spheres, instead of a constant. The correlation effects appear to be of importance, and very good results were obtained making an approximate self- consistency in the dielectric constant. On the other hand, self-consistency in the crystal potential was shown to be of minor importance for diamond.

A study of the electronic levels associated with the divacancy in silicon is reported. The extended Huckel theory is shown to reproduce the band structure of silicon. The electronic levels of the divacancy are calculated by considering a periodic array of large unit cells each containing 62 atoms; a 64 atom perfect cell with two atoms removed to form the divacancy. The results are found to be in qualitative agreement with the results of EPR and infrared absorption measurements.

For part I. see abstr. A44035 of 1973. The method developed in the authors' previous paper is applied to a calculation of the ground state energy and wavefunction of the deep donor oxygen in GaP. 21*48 sampling points, 2 valence bands and 2 conduction bands are used in the expansion for the impurity wavefunction Psi . A ground state energy of 0.696 eV from the bottom of the conduction band is obtained. A plot of mod Psi (r) mod ² and also of the wavevector dependence of the probability density are presented and compared with those for other impurities in GaP. It is found that the ground state of GaP:O is dominated by contributions from the secondary conduction band minima and it is suggested that this result may explain the pressure coefficients of some deep centres in many-valley semiconductors.

A random-phase approximation is used to investigate an Ising system with spin-phonon interactions. It is found that at sufficiently high temperatures the correlation functions develop an oscillatory behaviour. These results are discussed with reference to earlier work on disorder points.

The magnetic ordering of Ce_0.8 Tb_0.2 Ru₂ has been investigated by neutron scattering above and below the superconducting transition point at 2.6 K. Ferromagnetic short range ordering has been found with a correlation length of 15.6 AA at 1.5 K. No significant difference between the ordering in the normal and in the superconducting phase has been observed.

It is shown that a mechanism exists which gives rise to narrow lines of paramagnetic resonance absorption of longitudinal sound waves, transverse sound waves and temperature waves in a liquid in spite of the rotational diffusion. The observation conditions for these resonances are discussed. The interaction of the molecular orientation with the fluctuations of shear stresses has been found to affect significantly the spin-lattice relaxation rate in a liquid.

It is demonstrated unambiguously that a single methyl group can be responsible for two well resolved minima in the temperature dependence of its proton spin-lattice relaxation time. The analysis of seven infrared absorption bands verifies that these minima are due to (i) hindered threefold reorientation of the methyl group and (ii) transitions of the methyl group between its ground and first excited torsional state. The investigations were made on the isolated methyl group in p-tert-butyltoluene, which was found to have a threefold potential barrier hindering its reorientation of amplitude (4.13+or-0.07)kJ mole^-1.

Multiplication measurements, in which the photocurrent in a Schottky diode is measured as a function of electric field, have been used to obtain information on impact processes at deep impurities in ZnSe. For ZnSe:Mn one sees multiplication governed by impact transfer of electrons from the impurity to the conduction band. At higher fields, band-to-band impact ionization occurs. For ZnSe:Cu, the impurity concentration is not high enough for one to see a contribution to the multiplication from impact ionization. A theory of the multiplication as a function of field is presented and shown to be in agreement with the ZnSe:Mn data.

The double ENDOR method has been used to measure the relative signs of the hyperfine interactions of the unpaired hole in Tm²⁺ (4f¹³) with (a) the ¹⁶⁹Tm nucleus, and (b) the ¹⁹F ligand nuclei in CaF₂. The sign of the interaction (a) is known from theory, hence the measurement determines the sign of the interaction (b); both components A₂ and A_p are found to be positive. It has been shown that information about the relative signs of two hyperfine parameters may be obtained in a double ENDOR experiment only if the ENDOR signals are essentially transient, or have a significant transient component. The proportion of transient component is somewhat adjustable by suitable choice of experimental conditions. Rapid spin diffusion tends to decrease the proportion of transient component and hence tends to frustrate measurements of relative signs of hyperfine parameters.

For part I see Phys. Rev. B, vol.4, 2757 (1973). The model takes the origin of the far-infrared lines as transitions corresponding to the quantized translational motion of the impurity in the matrix cage, and then considers the effect of various perturbing mechanisms on it. It is found that the theory can explain the multiplet structure for the KCl-⁶Li⁺ and KCl-⁷Li⁺ systems in terms of a (111) displacement direction of the impurity ion. The unexplained results are discussed in terms of the recent trend of work in this field, and the results are compared with those of other existing models. For the NaCl-Li⁺ system also, an attempt has been made to explain the observed doublet structures and their relative intensities in terms of the present theory. However, a correct explanation could not be achieved. This indicates that this system is probably not an example of an off-centred impurity.