Table of contents

The rate, nu , of nucleation of vortices by negative ions in liquid helium under high pressures is calculated as a function of the electric field, E, applied to the ions. Measurements of nu (E) and nu (E), the drift velocity of ions, give sufficient information to determine the critical velocity required to form vortex rings and the rate at which these vortex rings are produced. This critical velocity is found to be 58.9+or-0.5 ms^-1 for negative ions at 25 bar.

The drift velocity nu of negative ions has been measured in He II near 1K, under a pressure of 25 bar, for electric fields E up to 17 kV cm^-1. Beyond E_c1, the critical field for creation of stable charged vortex rings, a second critical field E_c2 has been observed at which nu passes through a minimum and then starts to increase again. Numerical values of the rate nu at which rings are nucleated and of the rate P at which the ions escape from the rings again when E>or=E_c2 are calculated from the experimental data.

It is explicitly demonstrated how the uniqueness theorem applies to the problem of the scattering of atoms from corrugated, hard surfaces. It is also shown how the alternative solutions claimed in earlier work are algebraically related.

The activation energy of carrier transport in solids is examined and shown to be a conductivity average of the magnitude of the energies of the carriers, in contrast to the thermopower energy, SeT, which is a similar average of the absolute values of the same energies. For the case of a single majority carrier in a semiconductor it is shown that the difference between the thermopower energy and the activation energy is not due to the form of the density of allowed states but to the temperature dependence of the mobility of the carriers.

For a model it is proved with the help of the Bogoljubov inequality that the isothermal local resistivity, given by the force-force correlation function, is greater than zero. This fact elucidates the contradictory points existing in the literature.

A detailed theoretical study is undertaken of the influence of the relevant intermolecular interactions in the splitting of fundamental stretching (internal) modes in hydrogen halide crystals. The molecular exciton theory of Davydov has been used. Lattice sums have been carried out till good convergence is obtained. It is observed that the exchange interaction can be neglected in these crystals. The induction forces have a small contribution in the splitting, while the contribution from the dispersion forces is almost negligible. But the dipole-dipole interaction alone cannot account for the splitting of the internal mode and the quadrupole-quadrupole interaction must be taken into account. This is true since in these crystals the molecules possess a large value of the quadrupole moment and its first derivative with respect to the vibrational coordinate.

In an interacting spin-phonon system, coherences in the phonon scattering from different ions lead to coupled spin-phonon modes. The lifetime of the excitations is calculated for a fully concentrated crystal containing ions with S=¹/₂. The poles of the phonon Green function are related directly to those of the generalized spin susceptibility for which a diagrammatic expansion in terms of a polarization matrix M is presented. Averages of time-ordered products of spin operators that occur are expressed in terms of semi-invariants and evaluated using the Vaks diagrammatic technique. Inclusion of the diagrams in the expansion of M to second order lead away from resonance, to a phonon lifetime consistent with that obtained in previous treatments using the drone-fermion representation. A new feature of the present method however is that a partial summation of M to all orders, at least at low temperatures, is possible that enables the lifetime of the coupled excitations to be found over the entire frequency range. Results for the lifetime of the excitations close to the spin resonance frequency are presented.

For pt.II see ibid., vol.8, p.2382 (1975). Dynamical LEED I(V) calculations have been performed for the MgO(100) surface for eight different off-normal incidence geometries. Using parameters identical to those which were found to give good agreement with experiment at normal incidence, similar good agreement is found over all the forty-eight spectra comprising the extended set of data. The result found previously, which was that the MgO(100) surface is little distorted from a simple termination of the bulk crystal, is confirmed, thereby emphasizing the value of the more economical normal incidence analysis.

A self-consistent Hartree method has been developed for the dynamics of quantum impurities in harmonic crystals. The authors have obtained and formally solved at very low temperatures the eigenvalue equation which determines the frequencies of the crystal in resonance with the impurity and the localized frequencies of transition of the impurity coupled with the crystal. This theory is applied to the problem of the interaction of Rayleigh waves with a gas of mobile non-interacting atoms adsorbed on a crystal surface. The attenuation of Rayleigh waves due to the surface contamination of helium is calculated for an epitaxial layer of argon on copper as a function of the wavelength and temperature.

Sodium and sulphur on an (001) nickel surface are investigated in the c(2*2)S-c(2*2)Na, c(2*2)S-p(2*2)Na, and p(2*2)S-p(2*2)Na configurations. Sulphur always sits in hollows 1.3 AA from the nickel surface. Sodium always lies above hollows in the nickel substrate 2.5 AA from the substrate, but prefers to maximize the number of sulphur nearest neighbours.

The coherent potential approximation has been generalized to incorporate the effects of the local environment in the energy spectrum of disordered alloys described by the simple tight-binding approximation. The effective medium has been characterized by an effective local potential Sigma ₁ and an effective hopping integral Sigma ₂ between the nearest neighbours though the off-diagonal elements of the alloy Hamiltonian are not assumed to be disordered in the present calculation. The density of states has been calculated for a binary alloy A_xB_1-x having diamond lattice structure.

The linear combination of muffin-tin orbitals (LMTO) method, developed by Andersen (see Phys. Rev. B, vol.12, p.3060 (1975)) and applied previously to the electronic properties of bulk materials, has been used to calculate energy eigenvalues and charge distributions for small clusters of atoms. For a muffin-tin potential (spherically symmetrical within touching spheres surrounding the atoms, constant between them), the method reproduces accurately the results of multiple-scattering (KKR) calculations. The LMTO method has, however, several marked advantages: (1) computational times are much less; (2) false roots of the secular matrix do not occur; (3) improved convergence of eigenfunctions and energies can readily be obtained. These points are examined in detail for the clusters C₂, Al₅Na and Al₅O.

The intermediate spin-correlation function (S*_-q(0).S_q(t)) for classical linear chains of up to 120 antiferromagnetically coupled spins has been obtained by computer simulation as a function of wavevector q and time t. The spin correlations are calculated directly in reciprocal space. Chains in thermal equilibrium at 0.13, 0.24 and 0.44 times the molecular field transition temperature T_m=2JS(S+1)/3k have been analysed in detail at 21 wavevectors. Spin-wave frequencies and damping constants have been estimated using a fitted interpolation function. Appreciable deviations from a sinusoidal dispersion curve of linear spin-wave theory are found even at 0.13 T_m. Fourier transforms of the results to give the neutron-scattering function S(q, omega ) are presented and are shown to be in excellent agreement with the experimental results of Hutchings et al.

The magnon energy in itinerant-electron ferromagnets is calculated taking the spin-orbit interaction into account. A model of multiple narrow bands is considered with the intra-atomic-intraband and intra-atomic-interband Coulomb interactions as well as the intra-atomic exchange integrals as the coupling constants of the model. The Hamiltonian of the spin-orbit interaction is taken in the tight-binding approximation. Calculations are based on the RPA and an effective Hamiltonian for magnons is introduced. General formulae for the magnon energy are applied to nickel. It is argued that the largest contributions from spin-orbit coupling to the magnon energy come from regions in the Brillouin zone where the Gamma L direction intersects the Fermi surface. A two-band tight-binding model is chosen to simulate the band structure of nickel in that region.

The temperature dependence of the specific heat of Co²⁺, Fe²⁺ and Mn²⁺ perchlorates have been studied using a heat-pulse technique. It is found that all three compounds have a lambda -shaped C_p against T dependence around the transition point. In addition it is shown from the analysis of the critical region data that the phase transition has a second-order origin.

The NMR spectra of the protons in some methyl groups show temperature dependences at low temperatures where hindered rotation is thought to be ineffective. A theory based on the density matrix formalism is presented here for this effect. A rotational barrier having three-fold symmetry is assumed, and an equivalent spin Hamiltonian is assigned to each torsional level for the methyl group. Thermally activated transitions between the torsional levels cause the spin system to experience a fluctuating Hamiltonian. It is shown that in the limit of large rates of transition between the torsional levels, the NMR spectrum is determined by the time average Hamiltonian. The important parameter turns out to be the average of the tunnelling splitting over the thermally populated torsional levels.

Cyclotron resonance has been observed on n-Ge samples of varying doping concentrations with the radiation of an HCN laser. A shift of the transverse-mass resonance with increasing temperature has been found. This is explained by the increasing population of higher Landau levels which are not equally spaced due to the nonparabolicity of the conduction band. It seems that the use of a value of 2.2 eV for the direct gap epsilon _G(L₁,L_3') at the L-point of the Brillouin zone underestimates the nonparabolicity as already observed in magnetopiezotransmission experiments.

The non-parabolicities of the transverse effective masses m_{perpendicular to} * for the lowest conduction band minima are measured in silicon and germanium by means of cyclotron resonance at submillimeter wavelengths. For silicon a 2+or-1% increase in m_{perpendicular to} * at 10 meV into the band is found, whereas for germanium an 8+or-4% increase at 50 meV is measured. A recent report by Fink and Braunstein (Solid St. Commun., vol.15, p.1627 (1974)) that the cyclotron resonance scattering time in germanium decreases by up to a factor of five in going from a measuring frequency of 35 GHz to 891 GHz is shown not to occur for high-purity samples of silicon and germanium.

Cyclotron resonance of the holes in p-GaAs is reported at wavelengths of 2.2 mm and 337 mu m and at liquid nitrogen temperatures. The conditions under which hole cyclotron-resonance measurements can be interpreted as being dominated by classical light and heavy holes are investigated by means of complimentary cyclotron-resonance studies in p-Ge at 337 mu m wavelengths over the temperature range 70-200K. When the ratio of photon energy to thermal energy (h(cross) omega /kT) is about 0.6, weak quantum structure can be observed and the heavy-hole lines observed in certain directions can be shifted from the classical k=0 values by as much as 10%. The bare masses for the light and heavy holes in GaAs, after nonparabolicity and polaron corrections have been carried out, are found.

A self-consistent formula, which corrects a persistent mistake in the literature, has been developed for the optical joint density-of-states (OJDS) function. A way of linking valence- and conduction-bands densities of states to produce an average density or optically linked states function (ADOLS) for comparison with the OJDS function in the case of certain covalent materials has been suggested and successfully applied to existing data on amorphous As. New results on the quantitative OJDS functions of some transition-metal dichalcogenides have also been presented and discussed.