Table of contents

The dispersion relation for the transverse acoustic phonon mode propagating along (110) polarized along (110) in TeO₂ has been measured at P=1 atm, P_c( approximately=9.0 kbar), and 2P_c where P_c is the tetragonal-to-orthorhombic structural transition pressure. Complete softening of the mode at P_c is restricted to the q to 0 limit while at finite wavevectors there is a nearly constant energy shift of the dispersion curve of approximately=-0.1 meV between 1 atm and P_c and approximately=+0.25 meV between P_c and 2P_c. Measurements of the order parameter are consistent with a mean field of a pressure-induced elastic instability.

Results are presented of a new calculation of the surface states at the (110) surface of GaAs. By using Koster-Slater parameters fitted to bulk optical and photoemission data, the surface band structure has been calculated with a LCAO method. The main conclusion is the existence of two surface bands, one inside the band gap at about 1 eV from the top of the valence band and the other a few tenths of an eV below it. The results show good agreement with the available experimental data.

A high resolution study has been made of the two-roton Raman scattering from liquid ⁴He at T=0.6K and SVP. This experiment shows conclusively that roton-roton interactions are necessary to explain the spectrum. From the shape of the two-roton peak the two-roton binding energy is estimated to be 0.22+or-0.07K. An intrinsic zero temperature linewidth of the pair equal to 0.11+or-0.01K has been found.

Percolation theory is considered as the limit J>>k_BT of a dilute Ising model. The thermodynamic and correlation scaling arguments for the Ising model are shown to give corresponding scaling laws for the cluster size distribution and the pair-connectivity respectively.

In the conformal solutions model for liquid mixtures the deviation of the concentration-concentration correlation function S_cc(q) from its value c(1-c) in an ideal solution is given by the Fourier transform of the product of the radial distribution function g(r) and the pair potential phi (r) of the reference liquid. The form of S_cc(q) is calculated for choices of the reference liquid appropriate to: (a) a liquid mixture of rare gas atoms and (b) some liquid metal alloys. As yet there is no suitable experimental data on an alloy for which the conformal solution model is known to be applicable, but it is shown that the data of Ruppersberg (1973) on Li-Pb alloys can be usefully interpreted in the light of the results presented. Some comments are also made on Cu₆Sn₅.

Electromigration theories have brought increasing recognition that lattice inhomogeneities in metals produce spatial variations in current flow and in the associated transport field. It is shown, through a semiclassical one-dimensional model, that the spatial variations of carrier density near a lattice defect can produce strong local variations in the field required for current flow. This particular source of field inhomogeneity does not seem to have been recognized in earlier discussions.

Analytical expressions are derived for the stacking-fault contrast from phonon-scattered electrons. Phonon scattering is taken into account to first order and the elastic scattering from the defect is considered dynamically. Stacking-fault contrast profiles are calculated in a two beam approximation and a comparison is made with the experimental results of Kamiya and Nakai (see abstr. A58444 of 1971). Methods are developed to determine the character of the fringes where the fault meets the foil surfaces. Contrary to the situation in perfect crystals, phonon scattering processes, where the wavevector normal to the foil is not conserved, play an important role in the contrast formation in crystals with defects.

The elastic properties of the four scheelite structure crystals CaMoO₄, SrMoO₄, PbMoO₄ and CaWO₄ are compared. Attention is given to the orientation dependence of the elastic behaviour and to how this is related to the atomic arrangement. With respect to the conventional definition of the XYZ axial set employed for scheelites the stiffness constant C₁₆ is negative in all four materials.

Normal modes of vibration in vitreous SiO₂, GeO₂ and BeF₂ are discussed from the point of view of the relative phase of motion of neighbouring atoms in the system. The notion of a phase quotient is introduced, as a criterion for determining the extent to which modes are acoustic or optical in character. Use of the phase quotient, in conjunction with normal mode assignments derived in an earlier paper, enables one to make tentative predictions about the infrared activity of the different spectral bands. The results are in substantial agreement with available experimental data.

Calculations of the surface energy of eleven liquid metals are presented. These are based on the recently proposed pseudo-atom theory of Evans (see abstr. A72625 of 1974). The results are in good agreement with experiment for the alkali metals but overestimate the magnitude of the surface energy for several of the polyvalent metals.

The APW energy bands are fitted using the Slater-Koster LCAO method (1954). With this interpolation scheme partial densities of states are derived which allow in interpretation of the binding mechanism of NbC and NbN. These compounds are shown to be d-type superconductors.

A method is devised by which the effects of phonon and impurity scattering on the exciton spectrum of an insulator may be investigated. In the simplest case, that of a direct band gap, the form of the dielectric function for an energy omega near to the band gap is shown. The effects of the phonon and impurity scattering are contained in the renormalized mass function and the renormalized energy gap function. These functions, both complex, represent single-particle properties of the electron and hole and may be determined from the conduction- and valence-band Green functions.

Neutron inelastic scattering experiments have been performed on a polycrystalline sample of ErAG to obtain information on the crystal field level structure and on the exchange interaction. The measurements in the paramagnetic phase yield the crystal field parameters W=-0.040+or-0.002 meV and chi =0.42+or-0.02 which correspond to a Gamma ₈⁽³⁾ ground state with an overall splitting of 190K. The paramagnetic molecular field parameter is lambda _P=(-1.4+or-0.2)*10²³ Oe² erg^-1. From the measurements in the ordered states we obtain the molecular field parameters lambda _c=(1.07+or-0.03)*10²⁴ Oe² erg^-1 and lambda _i(1.11+or-0.06)*10²⁴ Oe² erg^-1 in the commensurate and incommensurate region, respectively. These parameters give an excellent description of the magnetic properties of ErAg. From the measured molecular field parameters three exchange integrals have been calculated.

A critical exponent associated with arbitrary hyperspherical harmonic perturbations of a generalized Heisenberg spin system is calculated to order epsilon ³ as well as 1/n. Some previous results and many new ones are contained as particular cases. High harmonic interactions are found to be generally irrelevant in the phase transition region, confirming the extent of universality.

The atom positions in antiferromagnetic and ferroelectric BiFeO₃ have been obtained by profile analysis of powder neutron diffraction data collected ant 4.2K and 293K. The sublattice magnetization also determined at 4.2K, has been used to obtain a covalency parameter sum, A_sigma ²+2A_pi ²+A_s²=13.4+or-0.5%. An experiment to obtain further information about the neutron magnetic form factor, by complete separation of the nuclear and magnetic contributions using polarization analysis, is described.

The lineshape of the A band in KBr:In⁺ and KCl:In⁺ has been measured as a function of temperature from about 16K to room temperature. The shape of the A band is well accounted for at low temperatures by a model that allows for spin-orbit coupling, vibrational coupling of the mod A), mod B) and mod C) states, and the dynamical Jahn-Teller effect in the perturbed mod A) state. The principal factor governing the lineshape is the coupling with modes of T_2g symmetry but agreement with the experimental results is much improved by a convolution of this calculated lineshape with a Gaussian function which represents the interaction with modes of A_1g symmetry. The model fails, however, to account satisfactorily for the relative peak heights of the two components of the A band at high temperatures.

For pt.I see ibid., vol.8, p.851 (1975). The lineshape of the C band in KBr:In⁺ has been measured as a function of temperature from 21K to room temperature. The band does not display obvious fine structure at any temperature but the appearance at the higher temperatures of two shoulders in addition to the main peak indicates a triplet structure. The lineshape of the C band is accounted for quantitatively in terms of a model that includes spin-orbit coupling, vibrational coupling to the mod A) and mod B) 11 0BC 2K state. The asymmetry of the C band is due to the states, the dynamical Jahn-Teller effect due to the trigonal T_{2 gamma} modes and coupling to modes of A_1g symmetry, in the perturbed mod C) state. The asymmetry of the C band is due to the quadratic terms in the Hamiltonian and although such terms would also arise from a difference in force constants in the ground and excited states, it is not necessary to introduce this effect to account for the lineshape in KBr:In⁺.

Using high-resolution far-infrared spectroscopy the vibrational properties of the Er³⁺-F^- tetragonal complex in CaF₂ has been studied at low temperatures. Three principal resonant peaks are observed in the absorption spectrum at 75.38, 91.6 and 107 cm^-1. From polarization measurements on Er³⁺-F^- dipoles aligned in a static electric field, the broad 107 cm^-1 peak is found to consist of two components centred at 106 and 109 cm^-1, corresponding to vibrations of the Er³⁺ ion parallel and perpendicular to the tetragonal axis respectively. The sharp 91.6 cm^-1 line is polarized perpendicular to the tetragonal axis and is assigned to a librational mode of the complex. Induced displacement of the charge-compensating F^- ion by X-ray irradiation at low temperature causes a decrease in the intensity of this mode, which tends to support the assignment.

Results are presented of photoemission calculations for hexagonal (wurtzite) CdSe based on the empirical pseudopotential band structure of Bergstresser and Cohen (1967). A rough approximation to account for electron-electron scattering is incorporated into the theory. The energy distributions of photoemitted electrons are calculated, assuming both direct and nondirect optical transitions, and the results are compared to the data of Shay and Spicer (1968). Prominent structures are identified.