Table of contents

A new approximate theory relating the radial distribution function to the pair interaction potential is applied to the calculation of an effective pair potential for neon by use of the recent structure factor measurements of de Graaf and Mozer (see abstr. A82693 of 1971). The approximation is constrained to reproduce the correct pressure and internal energy.

The temperature dependence of the frequencies of the TO and LO A₂-type modes in the alpha and beta phases of quartz has been deduced from an infrared reflectivity study by using a four-parameter dispersion model. An attempt is made to understand the critical behaviour of most of the frequencies in the alpha phase at the approach of the alpha - beta transition.

Various alternatives to the Balian-Werthamer model of the B phase of superfluid ³He are considered. The linear NMR properties of a certain f-wave state of axial symmetry are shown to be very similar to those required by experiment.

Hydrostatic pressure resistivity measurements up to 15 kbar at 300K have been made on n-type single crystals of ZnSiP₂ and CdSiP₂. Results are consistent with recent theoretical conduction band structures. In both cases the pressure characteristics can be analysed in terms of the lowest conduction band minima not having direct Gamma _1C properties. For CdSiP₂ results indicate that more than one conduction band minimum is close in energy at atmospheric pressure. An increase in resistivity with pressure is observed for CdGdAs₂ implying that the Gamma _1C minimum is lowest in energy.

The critical spin-spin correlation function of the Ising model in a magnetic field and below the critical temperature has been calculated up to and including terms of order epsilon ².

EPR spectra have been recorded from SrF₂ crystals containing Yb, Er or Sm immediately after their growth, or following oxidation and/or hydrogen diffusion treatments. New spectra were observed for Sm³⁺-H^-(i), Sm³⁺-O^2-(T₂) and Er³⁺-O^2-(T₂) defects. No T₁ centres (or T₃ centres) involving RE³⁺O₄^2-F^- groups were detected.

A simple form for the partial dynamic structure factors in a molten binary salt, based on Mori's memory function formalism and satisfying the usual moment sum rules, is proposed and applied in numerical calculations for a rigid-ion model of molten sodium chloride. Suitable linear combinations of the partial density fluctuations, having the character of acoustic- and optic-type collective motions at long wavelength and of independent particle behaviour of the two components at short wavelength and of independent particle behaviour of the two components at short wavelength, lead to an approximate diagonalization of the matrix of dynamic structure factors. The corresponding longitudinal current spectra, at any given wavevector, peak at different frequencies even though no well defined structure corresponding to optic-type motions would be present in the neutron scattering spectrum for wavevectors q>or approximately=1AA^-1.

For a variety of crystal types (orthorhombic, hexagonal, and monoclinic) it is shown that the conditions which must be applied to force constants in rigid ion models to ensure the correct symmetry of the elastic constants can be related to derivatives of the Madelung constant. The derivatives are of two types: (i) with respect to internal lattice parameters; and (ii) with respect to combinations of unit cell parameters which leave the crystal type unchanged and which keep the volume constant. If the short-range interactions are assumed to be central then the symmetry conditions are identical to the constraints which stabilize the crystal energy with respect to the above deformations; but this identity only holds for central interactions.

The minimization of the Landau free energy functional for p-wave pairing near T_c has been studied using a combination of analytic and numerical procedures. Eleven phases have been identified, each of which is stable in some domain of the parameters of the functional. Six of these phases have not been described before.

Normalized LEED intensity-voltage data have been obtained for the (100) surface of MgO prepared by cleavage in-situ. Corrections for the variation of primary current with energy and for varying optical attenuation of the grids as beams move across the screen have both been applied. Variations in surface potential with primary energy have been estimated using the position of the L_2.3VV peak in the Auger spectrum. Data are given for four beams at normal incidence, the specular beam in two azimuths and at angles of incidence of 5, 10, 15 and 20 degrees and the (10) beams at one azimuth and the same angles of incidence.

Using the layer-by-layer approach to low-energy electron diffraction (LEED) the authors explain how to symmetrize the beam scattering matrix for layers. The coincidence structure formed by the layers may be dense or open and may possess any of the 17 two-dimensional space group symmetries. The beams of the electron field become diffracted by the layers in a manner determined by von Laue's diffraction conditions. These conditions turn out to arrange the beams in mutually independent bundles. After establishing the transformation properties of bundles of beams under the point group part of the two-dimensional space group the authors derive a scheme for finding symmetrized combinations of interacting beams. The formalism is applied to the layer-KKR method for LEED calculation. In particular the symmetrization of the beam patterns created by three overlayer structures on surfaces of face-centred cubic crystals are described: the primitive 2*2 structure and the ( square root 2* square root 2)45 degrees structure on the (100) surface together with the ( square root 3* square root 3)30 degrees structure on the (111) surface.

Antimony has been evaporated under ultrahigh vacuum conditions on to an atomically clean tungsten (110) surface at 300K. The structural changes occurring from submonolayer up to 60 mean monolayers coverage, have been monitored using reflection high-energy electron diffraction. Deposition under these conditions yielded a series of submonolayer structures followed by a spontaneous change of symmetry at a coverage of theta approximately=2 from two-fold to four-fold symmetry. Further deposition caused the growth of two types of long, thin three-dimensional islands of antimony, one similar to bulk antimony, the other an abnormal FCC phase with the same lattice constant. Both types of islands grew with their pseudocubic (100) face parallel to the (110) substrate and the relaxation from perfect four-fold symmetry was detected by the RHEED. Subsequent electron microscopic examination of the thicker films confirmed the structural results deduced from the RHEED experiments.

A vibrating sample magnetometer was used to study the de Haas-van Alphen effect in degenerate n-type InSb samples with carrier concentration in the range 6*10²¹ to 2*10²³m^-3, and in two degenerate n-type InAs samples with carrier concentrations 4*10²² and 4.5*10²³m^-3. The carrier scattering lifetime was obtained for all the samples and is compared with a Born approximation calculation of the scattering by ionized impurities. Measurements were made in a number of the samples of the carrier cyclotron mass, which are compared with the band structure, and of the phase and amplitude of the oscillations, which are compared with the Lifshitz-Kosevich theoretical formula.

It is shown that electron-electron interactions do not alter the high-field Hall coefficient and related properties of the electron gas.

A quantum theory of acoustic parametric interaction in piezoelectric semiconductors is developed. The rate of acoustic sum frequency generation is expressed in terms of the nonlinear conductivity coefficient gamma , which is obtained for arbitrarily degenerate electron statistics by solving the equation of motion for the one-electron density operator to second order in the wave amplitudes. An anomalous variation of gamma is found to occur when the acoustic wavenumber becomes comparable with the characteristic electron wavenumber. This anomaly, which is associated with the cut-off of the linear acoustoelectric coupling, gives rise to an enhancement of the acoustic parametric interaction. In particular it becomes possible for acoustic sum frequency signals to be efficiently generated on the high-frequency side of the cut-off of the linear acoustoelectric coupling. Using X-ray diffraction techniques, this effect was observed in the piezoelectrically amplified sound flux of a highly doped GaAs single crystal.

The dilute Ising model in a transverse field which is related to phase transitions in a number of dilute systems has been studied by series expansion techniques to obtain the susceptibility for the face-centred cubic lattice. The surface of critical points in the temperature-concentration-transverse field space is obtained together with some indication of the critical exponent gamma .

The excitation of the diluted Heisenberg antiferromagnet are studied using the coherent potential approximation (CPA) by extending the work of Harris et al. for the ferromagnet. The Green functions of the system are described in terms of an effective medium which is determined self-consistently using the CPA equation to treat the scattering of a vacancy and its neighbours. Results of calculations for the spectral weight function and for the density of states are presented. When compared with previous theories the present work is generally found to be more satisfactory. Comparison is also made with neutron scattering data for (Mn_1-xZn_x)F₂ and excellent agreement is found.

The excitation spectrum is derived for a system consisting of arrays of lone spins and strongly coupled pairs. The problem was treated with a conventional spin-wave formalism in two models: (i) every spin was treated individually as in normal antiferromagnets, and (ii) the pairs were treated as rigid entities. The two models lead to similar acoustic spin-wave energies and thermal properties but optic energies for model (i) are found to be unphysical in the sense of being unbound with the strength of the stronger interaction.

The symmetry properties of coupled magnetoelastic waves can be exploited to enable selection rules to be determined for the lifting of accidental degeneracy between a phonon and a magnon with the same wavevector, k, the cause of the lifting of the degeneracy being the magnon-phonon interactions. The lifting of these degeneracies can be studied experimentally, principally by using inelastic neutron-scattering techniques. The author studies group theoretically the magnon-phonon interactions in antiferromagnetic FeCl₂ and determine selection rules for magnon-phonon interactives for wavevectors directed along the special lines of symmetry in the Brillouin zone of this material.

The electrical conductivity sigma , dielectric constant epsilon ' at 450 kHz and magnetic susceptibility chi _m have been measured perpendicular to the c axis in EuWO₄ single crystals for temperatures from approximately 300K to approximately 1000K. It has been shown that large-polaron band-type conduction is effective from 500-680K. Conversion of large polarons into small polarons takes place in the range 680<T<725K. For T>725K, the conduction is due to a hopping mechanism of small polarons. The possible conduction mechanisms for T<500K are also discussed. The dielectric constant variation with T follows the trend of the conductivity variation. The variation of magnetic susceptibility chi _m with T is typical of a ferrimagnetic-type material with T_N=232K. For T>500K, the Curie-Weiss law is obeyed. Molecular-field theory has been used to explain the results. Possible magnetic interactions are logically discussed.

Acoustic paramagnetic resonance experiments have been made on calcium fluoride crystals doped with cerium, neodymium and samarium using longitudinal ultrasonic waves at about 9.4 GHz. Strong resonances have been observed for each of these three ions and are attributed to transitions within the Gamma ₈ ground state of the trivalent ions. In the case of Ce³⁺ the cubic crystal-field interaction must be taken to second order to account for the resonance. For Nd³⁺ a first-order crystal-field calculation will explain the resonance while for Sm³⁺ the crystal-field calculation must be taken to second order and the Jahn-Teller effect invoked to explain the resonance.

Non-Lorentzian diffusion-broadened Mossbauer lines are reported for two different systems: (i) SnO₂ particles in silicon grease; and (ii) Fe(C₅H₇O₂)₃ dissolved in 1,3-propanediol. Both results are discussed as superpositions of Lorentzians each representing a particular situation of a Mossbauer nucleus. A model for the interpretation of the SnO₂ result is presented. Agreement is found assuming that rotational diffusion of the SnO₂ particles is dominating.

The system V_1-xFe_xO₂ was investigated in the region 0<x<or=0.04 with the Mossbauer effect technique. Both stoichiometric and non-stoichiometric material was studied. The results indicate that trivalent iron is present in all cases. The different crystallographic phases in the system were distinguished through their Mossbauer spectra. The spectra obtained in M1 phase material, which has a small impurity concentration, suggest the presence of impurity-induced structural distortions, depending on the history of the samples. In oxygen-deficient samples, shear planes are formed in which Fe³⁺ ions preferentially occupy the cation positions.

The Kramers-Kronig transforms relating the real and imaginary parts of the dielectric susceptibility have been used both on empirical functions and on experimental data. Good agreement is found between measured values of the imaginary part and those calculated from measured values of the real part of the susceptibility.

Calculations have been made of the spontaneous cross section of spin-flip Raman scattering in InSb. The electron occupancy of the conduction-band Landau states is accounted for in order to evaluate the cross section for the resonant conditions that occur for 5 mu m pumping at low magnetic fields. It is shown that quantum oscillations in the cross section are a major cause of irregularities observed in spin-flip Raman-laser output powers. Calculations of the cross sections for double-cyclotron and double-cyclotron spin-flip scattering are also presented.

The calculation of radiative transition probabilities between two rare earth energy levels using the Judd-Ofelt approach is extended to include J mixing. The theory is used to explain a purely radiative transition in Eu³⁺ when situated in two different host materials. Next the theory is applied to the ⁴S_11/2 transition of Er³⁺ in Y₂O₃ and YAlO₃ where it is concluded that inter-J mixing only has a small effect on the radiative probability. Non-radiative multiphonon decay in this system is considered and it is suggested that, for rare earth systems having a large energy separation to the next lowest level, decay involves emission of phonons with different energies.

The influence of rare-earth (RE) impurities as well as the host ions in the thermoluminescence (TL) of CaSO₄ phosphors has been studied in detail by recording the TL glow curves, TL emission spectra and electron spin resonance (ESR) spectra of a number of gamma-irradiated CaSO₄ samples doped individually with different elements of the lanthanide series. It is concluded that: (i) Dy and Tm are the most efficient activators of TL in CaSO₄ and follow the well known concentration quenching law; (ii) radicals like SO₄^-, SO₃^-, O₃^-, etc., produced by gamma irradiation, form stable trapping sites of varying activation energies which are responsible for the multipeak TL glow curves exhibited by CaSO₄ phosphors; (iii) the temperatures of occurrence of the various glow peaks remain remarkably constant irrespective of the RE dopant and are directly proportional to the activation energies of the respective traps; and (iv) the TL emission spectra correspond to the fluorescence emission of RE³⁺ ions. A possible model for the process of TL in CaSO₄ (RE) is also discussed.

Photoemission spectra have been recorded for the dichalcogenides of several metals in groups IVA and IVB, using incident photon energies of 21.2, 40.8 and 48.4 eV. Considerable structure is resolved in the valence bands which are based mainly on chalcogen p orbitals. An interpretation given in terms of a simple LCAO model is in qualitative agreement with recent band structure calculations.

For pt.I, see ibid., vol.7, no.23, 4416 (1974). Photoemission spectra have been recorded for several of the dichalcogenides of group VA and VIA transition metals, using incident photon energies in the range 16.8-48.4 eV. The transition between octahedral and trigonal prismatic coordination in group VA, is accompanied by changes both in the p-electron and d-electron derived valence bands. The results are discussed in the light of recent band structure calculations, and the observation of charge density waves in some of these materials.