Table of contents

By using the condition of perfect screening in a liquid metal A-B alloy for ion A, ion B and electron e separately, the structure factors S_ee, S_Ae and S_Be in the long-wavelength limit are related to the measured partial structure factors of the ions, S_AA, S_BB and S_AB. The relations are illustrated by calculating S_ee, S_Ae and S_Be for Na-K.

A mechanism is proposed in terms of electrostatic and strain factors, for the formation of the interstitial anion clusters predicted from neutron diffraction work. Support is provided for the hypothesis by calculations using the HADES program for defect formation energies in ionic crystals. The calculations further indicate that the trivalent substitutional should be largely confined to the sites of maximum electrostatic stabilization with respect to the cluster.

A simple derivation of a critical value of U/W in the Hubbard model (U is the intra-atomic interaction, W the bandwidth) is presented, and its implications on the character of the Fermi distribution function above the transition is discussed. It is also shown that the Hubbard criterion can be rewritten in a form completely equivalent to the Mott instability criterion for the metal-nonmetal transition.

It is argued that the band gap in amorphous semiconductors is maximized if the structure is as homogeneous as possible.

Recent re-evaluation of diffraction data from cubic spinel compounds has suggested that in many cases the crystal structure is properly referred to the noncentrosymmetrical space group F43m. This symmetry provides the possibility of antiferroelectric behaviour which may resolve previous theoretical difficulties concerning the very high dielectric constant observed at low frequencies with certain spinel ferrites.

A recent analysis of Mossbauer hyperfine interaction data for the octahedral 3d (t_2g⁵) Fe III complex in K₃Co_1-xFe_x(CN)₆ led to values of the contact field constant differing in sign and order of magnitude from free-ion estimates (see abstr. A68613 of 1972). This was interpreted in terms of a covalent expansion of the 3d electron wavefunctions to a degree previously unsuspected. It is shown that the analysis was based on several theoretical misconceptions and as a result is incorrect.

The authors are concerned with extraction of structural information from LEED intensity measurements by comparison with dynamical calculations for trial structures. The technique is illustrated by the system of sodium on a nickel (100) surface. Experiments are described; resolution is investigated and found to be about +or-0.1 AA. The top layer of a clean nickel (100) surface is shown to be dilated by not more than 0.15 AA and the determination of the sodium nickel distance of 2.9 AA reported earlier by Andersson and Pendry is described in greater detail.

It is shown that the long wavelength limit of the partial structure factors a₁₁, a₁₂ and a₂₂ contains direct information on the non-ideality of the mixture. In particular, the energy of interchanging an A atom and a B atom in two pure substances A and B is reflected rather directly, as is the difference in atomic volumes between atoms A and B. To illustrate the way the non-ideality is reflected in the partial structure factors, the authors have adopted the model of conformal solutions. They demonstrate that the interchange energy referred to above is directly related to the combination 2a₁₂-a₁₁-a₂₂ of the partial structure factors, which is a simple function of c(1-c) in this theory, c being the concentration. The model is applied to Na-K alloys, recently analysed thermodynamically by McAlister and Turner. It is able to explain the principal features of their results. On the other hand, the model is inappropriate for the other case, K-Hg they considered, presumably because the differences in the forces between different species are too large.

Ge 3 and Ge 4 are two high pressure crystal phases of germanium which have some of the structural features believed to be present in amorphous germanium. The atomic arrangements and electronic and optical properties of Ge 3 and Ge 4 are calculated. The properties of Ge 3 are found to show many similarities to those of amorphous germanium.

The energies of formation of the Schottky and two cationic Frenkel defects have been calculated in gamma -CuCl (ZnS structure) by the method of Mott and Littleton. The values obtained are 2.27 eV for the Schottky defect and 1.05 eV and 2.62 eV for Frenkel defects with octahedral and tetrahedral interstitials respectively.

Measurements of the thermal conductivity of 'pure' Al₂O₃ and Al₂O₃ doped with Mg have been made in the temperature range 1.3-100 K, both before and after gamma -irradiation at approximately 77 K. Within the experimental errors, the gamma -irradiation had no effect on the thermal conductivity of the 'pure' Al₂O₃-in contrast to results reported earlier. Al₂O₃:Mg shows resonant phonon scattering at approximately 19 K which is removed by gamma -irradiation treatment and replaced by resonant phonon scattering at approximately 8 K and approximately 100 K, caused by Cr²⁺ ions present as an impurity. The gamma -irradiated state is unstable, annealing at room temperature within a few hours. The phonon scattering at approximately 19 K is tentatively interpreted in terms of scattering by Fe⁴⁺-which has not been previously observed in Al₂O₃.

The one-band hamiltonian for an electron in an open finite tight-binding chain in a uniform external electric field is exactly diagonalized. The exact energy eigenvector components are given in terms of the Lommel polynomials and the energy spectrum, for a chain of N atoms, corresponds to the zeros of the Lommel polynomial of degree N. From this general eigenvalue problem solution, limiting cases of the model are investigated. In the infinite N limit, with fixed field strength and hopping parameter, for all eigenvalues bounded with respect to the centre of the spectrum, the components of the eigenvectors converge to Bessel functions whose order is determined by the energy. An asymptotic analysis shows that these bounded eigenvalues converge quite rapidly to a Wannier-Stark ladder when N to infinity . The results can be applied to the study of certain new one-dimensional solids.

A theory of the free carrier absorption in acoustoelectric domains is developed by using a generalized current equation and the Poisson equation. The theory is compared with microwave absorption measurements. Using the relative values of the frequency distribution of the acoustic flux in the domains obtained by Brillouin scattering, the absolute values of the AC acoustic potential have been determined from these experiments. The obtained values of the acoustic potential show that gain saturation is not caused by carrier bunching but by parametric conversion processes.

Application of the f-sum rule to a proposed inverted band structure for PbPo yields calculated values of longitudinal and transverse effective masses as follows: for electrons, (m_l*)=0.040, (m_t*/m)=0.024; for holes, (m_t*/m)=0.045, (m_t*/m)=0.028.

The effect of interactions between the magnetic moments which exchange scatter tunnelling electrons is to depress the conductance below the logarithmic temperature and voltage behaviour which is found for junctions with low concentrations of magnetic moments. Interactions make the scattering inelastic and this curtails some of the processes, in a similar way that an external field does. The interactions are replaced by a distribution of internal fields and the effect of interactions found using both theoretical and measured values of G(V,H,T). The results are qualitatively similar and show that the effect of interactions can make G(V) independent of V for eV <or approximately=kT_H where T_H is a temperature that characterizes the strength of the interactions. At higher concentrations of magnetic moments or at lower temperatures G(V) has a minimum at V=0. The temperature dependence of G(V=0) shows a maximum which shifts from T=0 to T approximately T_H in the presence of interactions. Such behaviour has recently been found in Ti doped Al/Al oxide/Ag junctions.

A theoretical study of the tunnelling phenomenon through a metal-insulator-metal junction containing paramagnetic impurities is made. The dependence of the conductance on magnetic impurities inside the electrode near the interface and magnetic impurities inside the barrier has been analysed. The impurity-impurity interaction between the paramagnetic impurities inside the barrier has also been considered. It is found that one can explain the conductivity peak and the giant resistance peak at zero bias by just changing the concentration of the paramagnetic impurities in the barrier of the same junction, as experimentally observed.

The electrical transport coefficients of a thin metal or semiconductor film in a magnetic field perpendicular to the film surface are studied. It is shown that the dependence of these coefficients on magnetic field and film thickness can be characterized by an analytic function of a complex variable. This result is subject to fairly restrictive assumptions on the Fermi surface and bulk scattering but the surface scattering can be extremely general. Similar results hold for the thermal and thermoelectric transport coefficients, and, in the case of semiconductors, for the high frequency conductivity (cyclotron resonance). Possible applications of the results are discussed.

It is shown that approximate relativistic radial wavefunctions can be constructed from nonrelativistic wavefunctions by allowing for nl to n'l configuration interaction due to the spin-orbit coupling. This construction is used to demonstrate that the dominant contribution to the relativistic crystal field is not due to the mechanism which has frequently been proposed (i.e. the anisotropy of the electrostatic potential). A new model is employed to estimate the contribution of overlap and covalency effects to the relativistic crystal field, and the role of this field in splitting the ground state of Gd³⁺ is discussed. The method used by the author could be employed to calculate relativistic effects in the many cases where solutions of the relativistic Hartree-Fock equations are not readily available.

The d⁴ configuration in an octahedral ligand field is considered. The optical absorption spectrum of Ru⁴⁺ is calculated by taking into account the ligand-field, electrostatic and spin-orbit interactions and using all the strong-field states of the ground configuration t⁴₂ as well as those arising from the first excited configuration t³₂e. The matrix elements of the magnetic moment operator (L+2S) were calculated between the ground state A₁ and all the T₁ states belonging to the two configurations. These matrix elements and the wavefunctions of the energy levels were used to calculate the magnetic susceptibility of Ru⁴⁺ in cubic coordination. It was found that the effect of the t³₂e configuration on both the energy levels and the magnetic susceptibility is very large and, therefore, cannot be ignored. The covalency of the t₂ and e orbitals was also included in the calculations of the susceptibility. It was found that there is not much difference in the degree of covalency of these orbitals, and also the delocalization of the electrons is fairly small.

The magnetic structures and ordered moments of NdN, NdP, NdAs, and NdSb with NaCl structure have been determined by means of line profile analysis of neutron diffraction powder patterns. NdN orders ferromagnetically at 4.2 K, which is characteristic of most 4f nitrides. The other neodymium monopnictides in contrast to the type II magnetic structures of heavy rare earths show FCC (BCT) type I antiferromagnetism at low temperatures. Except for NdBi and NdSb the ordered magnetic moments are reduced considerably below the free ion value because of crystal field effects and due to comparably weaker magnetic exchange interactions. The experimental and calculate neutron magnetic form factors of Nd³⁺ (dipole and M_J=J approximations) are in reasonable agreement. The measured powder intensities do not show conclusive evidence for anisotropy of the form factor related to the asymmetry of the magnetization distribution. The observed magnetic structures are discussed in the context of molecular field theory, and exchange constants have been determined. The neutron scattering amplitude of neodymium was refined to b_Nd=0.75(1)*10^-12cm.

The spin wave modes of a metallic ferromagnet are studied using a short range interaction between the electrons, in the random phase approximation (RPA). Besides confirming known properties of the undamped spin waves found for momentum less than a certain value p₁ (such as the existence of negative velocity spin waves) the authors find that the amplitude of the spin waves, relative to the non-spin wave contribution to the transverse spin correlation function, is a monotonic decreasing function of the wavenumber going from unity at p=0 to zero at p=p₁. For p>p₁, decay of spin waves into Stoner excitations becomes possible and the spin waves are damped. The dynamical transverse susceptibility was studied by analytic continuation. Two branches of complex poles are found for relative magnetization xi <1. (one branch for xi =1).

Measurements upon single crystal samples with composition Y₃Fe_5-xSi_xO₁₂, where x=0.02 and 0.034, confirm that, under different experimental conditions, two distinct types of photoinduced change in the magnetocrystalline anisotropy occur. The first type is distinguished by a change in the symmetry of the specimen in which the various (111) directions become inequivalent; the change depends upon the crystallographic orientation of the electric vector, E, of the irradiating infrared beam. The second type is not dependent upon the orientation of E and inequivalence of (111) directions is not involved. It is more important at low doping levels, persists to higher temperature and is irreversible, except by heating the sample. The specimen with x=0.02 shows both types of effect whereas that with x=0.034 exhibits essentially only the first type. Both types of change are explained by photoinduced valence exchange, which allows the displacement of Fe²⁺ ions between inequivalent lattice sites.

EPR studies of K₂PbCu(NO₂)₆ as a function of temperature as well as under uniaxial stress conditions are reported. The lattice parameters in the two tetragonal phases below 280 K are measured, and changes with temperature are observed in the surfaces of a crystal viewed under a microscope. These results are explained in terms of a domain structure below 280 K which is related to a cooperative Jahn-Teller effect. Each domain consists of tetragonally compressed copper sites whose tetragonal axes are parallel. The g values are consistent with a tetragonally compressed environment for the Cu²⁺ ion, in which the states transforming as 3z²-r² and x²-y² are mixed by the vibrational motion of the ligands.

The relative permittivity and loss factor of thiourea, in a frequency range from 1.6 Hz to 20 MHz, have been examined carefully throughout the temperature region in which phase transitions occur. The narrow ferroelectric region, phase III, has been studied more thoroughly than previously and the existence of additional distinct ferroelectric regions within phase II has been established. In each of the ferroelectric regions, there is dispersion in the permittivity and dependence of the permittivity on DC bias field.

Measurements have been made on the effect of an applied electric field on the 5742 AA zero-phonon emission line of the F centre in CaO. Results are interpreted taking account of both electronic polarization (Stark effect) and of ionic effects (electrostriction). It is shown that the latter are essential for the understanding of the overall effect. The measurements allow a determination of the position of ³S relative to ³P. E(³S)-E(³P) approximately=1200 cm^-1 to 1500 cm^-1. On the basis of this result the theory of the electric field effect on the zero-phonon line of the absorption of the F⁺ centre in CaO is re-examined.

The electron-beam excited visible luminescence of copper in zinc telluride is reported and explained as being due to transitions from the conduction band into localized levels of Cu²⁺ ions which are situated on cation sites.

A mathematical formulation of a recent proposal by Walsh, Lightowlers and Collins for a thermoluminescence process involving the capture and annihilation of holes at donor-acceptor pairs is given. Theoretical expressions are developed which, besides furnishing a check on the model, permit various parameters such as the Bohr radius of the shallowest centre to be evaluated from observations of the thermoluminescence glow.

A treatment of tunnel luminescence is described which accounts for the apparent anomaly associated with the rapid decrease of the emission intensity in the early stages of the decay in terms of a weak preferential pairing of the donors and acceptors. The implications of the analysis for the wider issue of the experimental detection of preferential pairing effects is discussed.