Table of contents

The elastic constants (in units of 10¹¹ dyn cm^-2) of Na beta -alumina as measured by inelastic neutron scattering are c₁₁=33.8, c₃₃=24.5, c₄₄=5.0 and c₁₂=14.3, c₄₄ varies with the substitution of other ions for Na, with c₄₄=5.6, 6.2 and 7.3 for Ag, K and Rb respectively. A dispersionless phonon mode observed at 5-6 meV for q>0.2 rlu is attributed to the Na motion, but its energy is not in agreement with Raman and far-infrared measurements.

LEED data from the stable 1*1 structure formed by exposing alpha -Fe(001) to oxygen at room temperature have been compared with full dynamical calculations. The oxygen atoms are found to lie at 0.53+or-0.06 AA above the surface in the four-fold hollows, and the spacing between the first and second iron layers is increased by about 7.5% to 1.54+or-0.06 AA.

Four different n>or=4 component Hamiltonians describing phase transitions in certain physical systems are derived. The corresponding critical behaviour is studied using the exact renormalization group in d=4- epsilon dimensions. In particular, although TbD₂, Nd and K₂IrCl₆ have different symmetries, their critical behaviour is described by the same anisotropic n=6 Hamiltonian and is predicted to correspond to the same fixed point. For three Hamiltonians, no stable fixed point exists.

The time-dependent backflow of charge around a moving ion in a model molten salt, reported by Hansen and McDonald (1974) is analysed in terms of the flow of mass and charge associated with a cation-anion pair. Simple parametrizations of the data are given by the memory function approach.

Measurements of the conductivity characteristics of Cu_xS-ZnS:Mn,Cu film heterojunctions provide quantitative evidence for the existence of Wannier-Stark levels. Corresponding peaks in the electroluminescence characteristics are also ascribed to the electron-phonon resonance states by Wannier (1960). It is suggested that temperature effects may be relatively unimportant.

An exact probabilistic treatment of conduction properties of random Bethe resistor lattices is presented. In the special case of substitutional disorder where a faction 1-p of resistors is removed, the known exact results for the conductance and voltage correlations in the critical region p to p_c are readily given. The simplicity of the method allows a generalization to the case where the remaining fraction p of resistors also has an arbitrary distribution. The case where each element of the lattice is composed of several independently distributed resistive and reactive parts is also discussed.

The d.c. hopping conductivity, sigma , of magnetically frozen electrons is calculated using a critical exponent approximation. When the density of states is constant near the Fermi level sigma is proportional to exp(-T₀/T)^0.4) where T₀ depends on the magnetic field.

A correlation is shown to exist between ligand polarizabilities and the intrinsic spin-Hamiltonian parameter b₄, and a possible mechanism giving this relationship is discussed.

The dynamic properties of an easy-plane magnetic chain with exchange energy J and single-ion anisotropy A<<J display a gradual transition from the easy-plane to the isotropic behaviour at T approximately=(AJ)¹2/. The temperature-dependent strength of the one-magnon excitation in CsNiF₃, reflects this transition.

The identification of the F centre in KCN is reported. It is shown that a correlation exists between the EPR spectrum of the F centre and the optical F band at 585 nm.

Certain solids exhibit anomalously high ionic conductivities at temperatures appreciably below their melting points; this phenomenon is sometimes referred to as superionicity, and is associated with development of disorder in a component sublattice. This effect has been studied in the fluorites SrCl₂, BaF₂ and PbF₂ and in AgI, using Raman and Brillouin scattering. In the fluorites the disorder occurs in the anion sublattice and in AgI in the cation sublattice. At the transition to the highly conducting phase, the emergence of a broad low-frequency response has been observed; simultaneously, there is a dramatic softening of elastic constants.

For pt.I see ibid., vol.8, p.89 (1975). Calculations are reported of the memory function associated with the longitudinal current correlations along with some results for the density fluctuation spectrum for a model of liquid rubidium. The latter are compared with the information about the dynamics of density fluctuations obtained from molecular dynamics computations and neutron scattering experiments on the liquid near its melting point. The fourth frequency moment has played an essential role in generalized hydrodynamic or viscoelastic theories of the dynamic structure factor. However, the fourth moment is infinite for the rigid core potential and yet the rigid sphere fluid is frequently used as a model for real liquids. It is argued that a theory of the density fluctuation spectrum of a liquid should accurately describe the short-range collision processes, so that the rigid core limit can be recovered, even if this can only be achieved, as with the present approach, at the expense of the fourth moment condition.

Phonon dispersion curves of trigonal selenium were measured as 300K. Determination of acoustic branches was performed for the directions ( zeta 00), ( zeta zeta 0) and (00 zeta ), where good agreement with ultrasonic data was found. All six optic modes could be measured in the directions ( zeta 00), ( zeta zeta 0), (00 zeta ), (¹/₃¹/₃ zeta ) and ( zeta zeta ¹/₂). The low symmetry of Se required close interaction of theory and experiment. Several successively more elaborate models were developed which are dealt with in paper II. A valence force field (VFF) model which assumes partly covalent interchain bonding yielded good agreement in the acoustic and lower optic regime. The upper optic modes showed an important dispersion indicating the existence of long-range forces. They were treated within the framework of the shell model.

For pt.I see ibid., vol.8, p.3725 (1975). Phonon dispersion curves of trigonal selenium (Se) were studied using a valence force field model (VFFM) and a shell model (SM) with anisotropic core-shell coupling constants. The interchain coupling of the VFFM arises largely from forces representing interactions between adjacent bonds, suggesting covalent interchain bonding. Long range forces exist especially along the chains for the SM, which also gives correct values for the LO-TO splitting of the i.r. active A₂ and E₂ modes and the associated effective charges and also the low and high-frequency dielectric constants.

An exact variational principle involving the density-of-eigenstates function is derived. This variational principle differs from previously published conjectures, and has been applied to two different types of band-tailing problems in order to demonstrate its usefulness. A closely related variational ansatz concerning the complex self-energy of a random medium is then formulated, and is shown, under the appropriate circumstances, to lead to the CPA approximation as well as to cluster generalizations of this approximation. It is shown that such cluster generalizations can accurately reproduce some computer-generated density of states.

The electronic properties of spiral chains of Se atoms, in which the bond length, bond angle, and dihedral angle are the same for every atom, are investigated in the nearest-neighbour interaction approximation and are equivalent to those of a linear chain containing one atom per unit cell. The basis set used consists of one s and three p orbitals per atom. This model gives a good description of the overall features of the densities of valence states of the amorphous and crystalline forms because of their one-dimensional nature. The differences between the densities of valence states of the amorphous and crystalline forms can be explained by a change in the sign of the (pp pi ) interaction between the bonding p orbitals on adjacent sites. Although the s-p hydridization of each p band is estimated to be only 5%, the s bands strongly influence their shape.

The electronic valence-band structure and the density of states for the FCC molecular ortho-hydrogen crystal has been calculated by the molecular tight-binding method, using different approximations. It has been found that the band parameters depend significantly on the quality of the molecular wavefunction at large separations from the nuclei. The functions arising from the limited-basis-set SCF procedure have been found to be rather poor. Much better functions are those obtained by fitting the exact SCF orbital. It has been shown that the Fock matrix elements should be calculated with an accuracy of the order of at least S (where S denotes the intermolecular overlap integral). The contribution of the second neighbours to the band structure has been found to be very small compared with that of the first neighbours.

The self-consistent OPW method has been applied to investigate the electronic spectrum of the ideal 1T phase of TiS₂. Both valence and core state energies are presented. Bonding properties are discussed in terms of the self-consistent charge densities. Exchange-correlation effects and crystal parameter refinements are shown to have a minor influence on the optical gap of about 1 eV. It is concluded that the electronic properties of real TiS₂ crystals in the neighbourhood of the Fermi level do not seem to be determined by properties of the 1T phase alone.

Previously reported small non-random differences between the calculated and experimental conductivity of NaCl doped with Sr²⁺ in the temperature range 660-1050K are shown to be attributable to a single extrinsic process which immobilizes a small number of cation vacancies below about 723K. Impurity-vacancy dipole interactions with internal fields is considered as a viable process, and a theoretical analysis of the electrical interaction is developed. A size effect, deformation dependence and crystal-orientation dependence in the residual conductivity are implicated.

Surface roughness scattering is calculated for carriers in ellipsoidal energy bands. The purpose is to identify which dimension of the Fermi surface determines the degree of roughness which is required to produce diffuse reflection. It is concluded that the surface corrugations must be deep enough so that (k^{perpendicular to} -k_R^{perpendicular to} ) xi ₀ is comparable to unity, where xi ₀ is the RMS bump height and k^{perpendicular to} and k_R^{perpendicular to} are the initial wavevector and reflected wavevector in the sense defined by Price (1969).

Local densities of states inside and outside a metal surface are calculated and discussed for the simple square-step potential and the planar uniform background model. Quantitative results for the narrowing of the energy width of the occupied electron states outside the surface are presented. The relevance of the results for experiments on the electron capture by deuterons scattered at surfaces and for ion-neutralization spectroscopy is discussed.

In the presence of trapping, the usual electron and hole ionization coefficients alpha and beta are inadequate to describe the multiplication processes. The usual theory has then to be generalized and four ionization coefficients have to be introduced. The paper shows how this can be achieved and the key results of earlier workers, who assumed no trapping, are obtained as special cases. Some evidence for a trapping effect is seem in low-field ionization measurements.

Neutron inelastic scattering experiments have been performed to measure the crystal-field splitting of the ⁵I₈ ground state multiplet corresponding to the Ho³⁺ ion in Ho_cY_1-cAg compounds. The resulting crystal-field parameters turn out to be independent of the rare earth concentration. Additional information has been obtained on the strength of the molecular field. The parameters derived from the neutron experiments give an excellent description of the magnetic properties of HoAg.

Spin-correlation functions are calculated for the exactly soluble model of a one-dimensional array of classical spins interacting via a Heisenberg exchange and a single-site anisotropy of the form B(S^z)². Analytic results are obtained in the limit low temperatures, and numerical results presented for general temperatures. For B positive, the spins align in the xy plane at low temperatures, with the inverse correlation length k_z tending to a value proportional to B¹2/. For B negative, alignment occurs along the z direction at low temperatures. The divergence of the susceptibility chi _z is of the form exp (constant/temperature).

Dynamic properties of classical one-dimensional magnets with ferro- or antiferromagnetic exchange coupling and single-site anisotropy B(S^z)² are discussed in terms of a theory which utilizes exact expressions for static spin correlation functions e.g. the wavevector-dependent susceptibility. The theory is shown to provide a quantitative interpretation of the dispersion and damping of collective modes observed in the ferromagnetically coupled compounds CsNiF₃. Marked differences are predicted between the dynamic properties of ferro- and antiferromagnetically coupled models. A gap in the dispersion of the out-of-plane collective mode at low temperatures for antiferromagnetic coupling leads to the persistence of a zone-boundary mode up to moderate temperature with only a small anisotropy. The associated lineshape is studied as a function of wavevector and temperature, and the intensity is found to decrease rapidly with temperature.

The results of ESR studies of the exchange-coupled pairs in (NPr₄)₃Cr₂Cl₉ are presented. In this material the (Cr₂Cl₉)^3- anion shows ESR spectra from all the manifolds to different total spin (J=1, 2, 3). A large deviation from the Lande interval rule is found which can be represented in terms of an exchange Hamiltonian H= Delta ₁(S₁.S₂)- Delta ₂(S₁.S₂)²+ Delta ₃(S₁.S₂)³ with Delta ₁/k=16.1K, Delta ₂/k=3.8K and Delta ₃/k=0.71K. Comparisons with previous studies of this anion in different crystals show that the magnetic properties of (Cr₂Cl₉)^3- are closely similar, despite differences in crystal structure and symmetry.

An explanation based on exchange forces is proposed for the antiferromagnet-ferromagnet transition in Dy which is in good agreement with the available experimental results. Contrary to the usual idea that the driving mechanism is the magnetostriction and anisotropy in the basal plane of the HCP structure it is shown that the exchange forces are mainly responsible for the transition. Magnetoelastic, anisotropy and applied magnetic field energies only provide the delicate balance of energy necessary to assist the exchange forces for the transition. These energies only amount to a relatively small fraction (<20%) of the total driving energy.

In diopside two different EPR spectra of Mn²⁺ were observed. Each spectrum has been fully interpreted and all fine structure spin-Hamiltonian constants are given. Mn²⁺ was seen in both possible substitutional sites M1 and M2. The pseudo-symmetry of the fourth-order term of the spin Hamiltonian has been studied and has been compared to the crystal field calculated on the basis of a point-charge model. From this comparison it was possible to distinguish the spectrum due to the Mn²⁺ in M1 from that produced by Mn²⁺ in M2. It is seen that the environment of Mn²⁺ in M1 has a good pseudo-cubic symmetry, while the M2 site, when occupied by Mn²⁺, is highly distorted.

The fourth-order differential equations for the transverse displacement of a dielectric inhomogeneous plate in an electric field are solved analytically and the acoustic response is expressed in terms of an equivalent electrical circuit. Its components are determined experimentally from the flexure resonance characteristics and the polarization moment is deduced from the data. Polarization moments are reported for KH₂PO₄, KD₂PO₄, KH₂AsO₄ SrTiO₃ and BaTiO₃. These moments are analysed in terms of the space-charge model involving drift and diffusion and a mismatch of electron affinity at the interface. For narrow depletion layers, the moments are proportional to the plate thickness. For deep depletion of carrier exhaustion throughout the sample, a third-power dependence of the moment on plate thickness is predicted.

The method of linear response theory used by Barker and Loudon (1972) to study bulk polaritons is adapted to study surface polaritons propagating along the interfaces of a thin film. Response functions are derived and used to determine the thermally-excited fluctuations in the electric fields and vibrational amplitudes. The forward-scattering cross section is shown to be much larger than the backward-scattering cross section for both branches of surface modes. The ratio of the forward scattering cross section for surface polaritons to the bulk scattering cross section decreases with increasing film thickness. Numerical results are presented for thin films of InSb and GaP.

The optical absorption and luminescence spectra of chromium ions in the LiGa₅O₈ spinel are investigated. Measurements are made in the temperature range 1.6-300K. The absorption spectra consist of broad (split into three) spin-allowed bands connected with the transitions ⁴A₂ to ⁴T₂ and ⁴A₂ to a⁴T₁, and sharp lines connected with spin-forbidden transitions from the ground state ⁴A₂ to the excited states ²E, ²T₁ and ²T₂. The results from absorption measurements together with the results of EPR measurements are interpreted in the framework of crystal-field theory.

Crystals of silicon which were pure, and either monocrystalline or polycrystalline, or were doped with oxygen, or with carbon and oxygen have been irradiated at room temperature with fast neutrons to doses in the range 10¹⁵-10²⁰ n⁰ cm^-2. After irradiation, measurements were made of the strengths of the induced electronic absorption due to divacancies at 1.7 mu m and that due to band tailing below fundamental edge ( lambda =1.05 mu m) together with the vibrational one-phonon absorption below the Raman frequency omega _R (band mode) and intrinsic local-mode features just above omega _R. These features were independent of the degree of crystal perfection and the presence of impurities. Annealing studies showed a major stage near 150 degrees C when all the divacancies were lost; the anneal temperature decreased systematically with increasing n degrees dose and was reduced further in the polycrystalline samples, but was unaffected by the impurities.