Table of contents

Neutron scattering measurements of the quasi-elastic scattering at temperatures above the structural phase transition in SrTiO₃ show that the scattering arises from the interior of the specimen and is not associated with the surfaces as suggested by X-ray scattering measurements.

A relativistic generalisation of the Hohenberg-Kohn-Sham theory of the inhomogeneous non-relativistic electron gas is presented. In a local scheme, where the results of the homogeneous electron gas are used as input, a self-consistent one-particle Dirac-like equation is derived. When only 'exchange' energy is used as an approximation, the usual Slater's rho ^1/3 theory is shown to need a relativistic correction.

An analysis of the augmented space method has been carried out to determine the reason for its failure to reproduce the resonance modes in a one-dimensional disordered system. The question as to whether it is more efficient to carry out the ensemble average in augmented space or in real space is also discussed.

The authors have investigated the Fedro-Wilson theory (1975) to obtain a hierarchy of differential equations for the correlation functions. An approximation is suggested for the truncation of the hierarchy of equations. The result is applied to the weakly correlated Hubbard model to calculate the quasi-particle energy.

The electronic response including electron-phonon matrix elements in a simple tight-binding model is calculated for the 'd_z2' sub-band in 2H-NbSe₂. This function, in contrast to the bare response, shows a peak in the region of the charge density wave (CDW) wavevector. It is therefore concluded that the CDW is driven not simply by Fermi surface nesting but rather by a combination of matrix element effects and weak nesting.

Extends the author's previous work (see ibid., vol.10, p.L649 (1977)) to a form offering an unconventional direct way of computing the current density under high electric field conditions.

The noise power spectrum of the voltage fluctuations in a resistor network near the percolation threshold is found in a mean-field approximation. The magnitude of the noise is increased over that in the perfect network and shows an interesting frequency dependence.

The thermodynamics at low temperatures of an Ising spin system with random ferromagnetic and antiferromagnetic bonds is considered. It is shown that the replica method leads to expansions for the free energy and correlation functions in terms of the amount of frustration. At low temperatures in two dimensions the Toulouse sum over minimal strings is obtained. An estimate for the entropy at zero temperature and equally probable ferromagnetic and antiferromagnetic bonds is obtained.

It is proved that Girvin's method (see ibid., vol.11, p.L427 (1978)) for the calculation of the two-spin correlation function of the three-dimensional Ising model is based on the same approximation made by Frank and Mitran (1978).

The apparent absence of S_z=O spin waves in a recent neutron scattering experiment on an anisotropic antiferromagnetic chain system is explained, and further experiments are suggested.

A high-temperature series for the spin-glass order-parameter susceptibility is presented for n-component spins on a d-dimensional hypercubic lattice. The coupling between neighbouring spins is taken to be a Gaussian random variable. The series is analysed for the cases of XY(n=2) and Heisenberg (n=3) spins. In each case the transition temperature falls to zero near four dimensions, indicating that there is no Edwards-Anderson order in less than four dimensions.

Electron spin resonance has been observed in the lowest optically excited state of the F_A(Mg) centre in CaO by detecting F_A(Mg)-band phosphorescence peaking at 689 nm. The ODMR spectrum is axially symmetric about the (100) axis; transferred hyperfine structure due to ²⁵Mg(I=⁵/₂) confirms that a nearest-neighbour cation site of the F-centre is occupied by an Mg²⁺ impurity ion.

The technique of using ultrasonic modulation to measure strain effects in solids has been extended to the study of the quadrupole splitting of ²⁷Al in Al₂O₃ by NMR. The advantages and limitations of the strain modulation technique for NMR are discussed.

The dispersion of the surface state electron bands has been measured for the Gamma J' direction of the reconstructed cleaved (111) silicon surface, using angle resolved photo-electron spectroscopy. The excellent agreement obtained with the surface band calculations of Pandey and Phillips (1975) is taken as strong evidence for the validity of the surface structure deduced by them.

For pt.I see ibid., vol.11, p.3749 (1978). A representation of the velocity autocorrelation function in terms of the longitudinal and transverse momentum current densities is applied to models of liquid argon and liquid sodium. Results for the contributions of the current components to both correlation functions and frequency spectra are presented. The existence of collective density excitations for wavelengths down to one or two atomic spacings is shown to be correlated with the oscillatory behaviour of the velocity correlation function. It is also argued that the formation of a peak in the frequency spectrum, at a frequency well below the Einstein frequency is indirect evidence that the liquid can sustain the propagation of shear wave modes.

The authors extend the formalism of the scattering intensity due to Yonezawa and Birman (1977) which is based on a random stacking model for tetrahedrally bonded amorphous semiconductors. The extension is carried out by relaxing, step by step, several aspects of long-range order inherent in the original random stacking model. By so doing, they can extract microscopic information about the structures which is reflected in macroscopic quantities. By removing some long-range order, they are actually modifying the model so that it better simulates realistic amorphous systems. They apply the modified formalism to the calculation of the diffraction pattern and the radial distribution function for amorphous silicon.

For crystals in which inner displacement is possible there exists a group of tensors whose members (called inner elastic constants) are derivatives of the energy with respect to at least one component of inner displacement. A consistent, simple tensorial notation is introduced for the six types that arise when the energy of deformation is expanded to third order in the strain. Each inner elastic constant is shown to be composed of a sum of more fundamental interlattice tensors. An account is given of the basic definitions of inner displacement, of the expansion of the energy in terms of partial and inner elastic constants, of extra equilibrium conditions, of the decomposition of the total elastic constants into parts dependent on different orders of internal strain and, finally, of the relationship between this formalism and that of lattice dynamics in the limit of zero wavevector.

The symmetry of inner elastic constants depends on the symmetry of the fundamental interlattice tensors from which they are built up. The number of independent interlattice tensors and their symmetries are determined by considering transformations of the interlattice index using a representation of the space group in which the not-purely-translational elements correspond to permutations. The method is explained and illustrated in detail. The non-zero components of the interlattice tensors are determined by standard methods and results are tabulated for the six species of tensor under consideration.

Near the commensurate-incommensurate transition the incommensurate phase is characterised by the formation of 'discommensurations' or phase solitons. The authors consider the coupling to an elastic strain along the wavevector describing the modulation. The solitons induce a highly non-homogeneous soliton-like strain. The measurable macroscopic strain is proportional to the phase-soliton density. The transition remains second order in contrast to previous expectations.

Two consequences of Gibbs-Bogoliubov variational theory are examined as applied to liquid argon: the choice of a hard-sphere reference system leads to an equation of state if the packing fraction is used as the variational parameter, the non-ideal part of the entropy is only a function of eta . Calculations are performed along the freezing and vapour-pressure lines. Excellent agreement with experimental results is obtained if the Lennard-Jones potential is regarded as an effective pair potential and its parameters are appropriately chosen, and for the hard-sphere reference system the empirical radial distribution function proposed by Verlet and Weis (1972) is used together with the Helmholtz free energy derived from the Carnahan and Starling equation of state (1969).

The authors present a method, based on the thermoelastic effect, which makes possible a new kind of direct experimental evaluation of the Gruneisen gamma parameter. A thermodynamic relation is used, relating isentropic temperature and volume variations in the elastic regime, during tensile tests. Unavoidable viscous effects are taken into account within the frame of the linear thermodynamics of irreversible phenomena on the basis of previous work.

The angular distribution of phonons transmitted through the interface between liquid He and a single crystal of NaF has been measured in both directions. There are two channels; a q/sub ///-conserving channel and a non-classical channel which carries most of the energy at high phonon frequencies. However, the ratio of the energy carried in these two channels is quite different in the two directions for similar heater powers. At low powers the differences are due to the low characteristic temperature of the phonons injected into the He by a thin-film metal heater. At high power the differences are attributed to the saturation of the transmission channels from He to a solid.

Using a time-dependent generalisation of the Hohenberg-Kohn-Sham formalism the energy functional is shown to be calculable by an iteration technique. The proposed method yields approximations for the particle density and the dynamic density response function of the interacting electron system; excited energy states and non-stationary time-dependent problems can also be investigated. As an example for practicability of the formalism a simple approximation for the 1s2s states of the helium atom is presented.

Transition metals are known to have phase shifts showing resonant behaviour in the d wave, but with the phase changing by less than pi on passing through the resonance, sometimes rising to little more than ¹/₂ pi . It is shown that this behaviour can be accounted for within Hubbard's theory of the phase shift, and may be explained either in terms of a strongly energy-dependent width, Gamma varies as kappa ⁵, or in terms of a repulsive contribution to the pseudopotential at energies above the resonance.

A means whereby the convergence of a recently developed Green function method useful in the calculation of localised defect electronic energy levels can be optimised is described. The results of the optimisation procedure are presented for two examples of realistic neutral defect potentials. In particular, an optimised value for the position of the one-electron t₂ state of the unrelaxed silicon vacancy is calculated. The level is found to be in the upper half of the forbidden gap, a result by implication consistent with the idea of substantial lattice relaxation effects. Some observations concerning the role of the form of the real and Fourier space impurity/defect potentials employed in this type of calculation are made.

The thermoelectric power S(T) of MnAs_1-xP_x compounds has been measured in the temperature range from 5K to 350K and for compositions between x=0 and x=0.1. In addition to diffusion thermopower several anomalies are observed. Phonon drag effects may be responsible for a maximum below 30K while other anomalies are related to magnetic phase transitions or to particular scattering mechanisms which have been inferred from resistivity measurements.

Experimental results are presented for the electrical conductivity, optical absorption and photoconductivity of evaporated germanium and silicon, bombarded at 14K with self-ions and measured in situ. The conductivity in the ohmic region follows the Mott T^-1/4 law (1969) extremely well, with ion bombardment increasing the conductivity by many orders of magnitude and decreasing the slope of the T^-1/4 plots consistently. By using the hopping conduction model of Apsley and Hughes (1975), it is possible to determine independently the radius and density of the localised states at the Fermi level.

Photoexcited electrons and holes in 2H-PbI₂ are studied by measurements of the Hall effect magnetoconductivity and cyclotron resonance. Transport by holes is dominant below 20K under long-wavelength illumination. Electron transport is dominant under white light illumination below 20K and under all illumination conditions above 20K. Hole mobility is anisotropic with 2< mu _{perpendicular to c}/ mu /sub //c/<4. The mobility of electrons above 30K, when limited by optical phonon scattering may be fitted by an effective band mass of 0.55 m₀ where m₀ is the mass of the free electron. Cyclotron resonance at 137 GHz gives a polaron mass m/sub ///m_{perpendicular to} )¹2/=(0.68+or-0.16)m₀, or a band mass (m_b//m_{b perpendicular to} )¹2/=(0.46+or-0.15)m₀.

The susceptibility of a quantum X-Y model in a transverse field Gamma is studied in the vicinity of the multicritical point ( Gamma _c,T=0). For dimensions d between two and four we obtain a Hartree type approximation an equation for the corresponding crossover function which is solvable analytically in three dimensions. The critical line Gamma _c(T)- Gamma _c(0) approximately T^psi is asymptotically described by the shift exponent psi =d/2 in accord with self-consistent spin wave theory. For the variable of the crossover scaling function T/( Gamma - Gamma _c(T))^phi one obtains the crossover exponent phi =(4-d)/2 which is characteristic for the Gaussian multicritical point. A dimensional-analysis argument suggests that this is valid beyond the approximation.

A perturbation expansion about the atomic limit of the Anderson model is formulated in the limit of infinite conduction bandwidth. Terms up to second order in Delta are constructed in various temperature regimes; non-logarithmic terms are explicitly given. Particular care is taken to expose the structure of perturbation theory in the valence fluctuation limit. An expression for the Kondo temperature is obtained and compared with numerical results. The structure of the expansion is commented on in the light of scaling theory.

Measurement of the magnetic susceptibility of powder samples of heavy rare-earth (Tb, Dy, Ho, Er, Tm and Yb) tungstates have been reported in the temperature range 300 to 900K. Curie-Weiss law behaviour has been observed for all samples. The Curie constant, paramagnetic Curie temperature and magneton number for the magnetic ions have also been evaluated for each material.

The g_eff=30/7 isotropic signal in the EPR of high-spin Fe³⁺ compounds is discussed for both tetragonal rhombic crystal fields by reference to the resonance in calcium tungstate. The Fe³⁺/CaWO₄ EPR signals are shown to arise from Fe³⁺ in two slightly different interstitial sites in the crystal; the crystal field in both sites is predominantly rhombic. Highly anisotropic signals arising from transitions within the other two Kramers' doublets were positively identified leading to an unambiguous calculation of the spin Hamiltonian parameters. The results are likely to be of great value in analysing similar Fe³⁺ spectra in crystals of biological importance.

The EPR spectra of synthetic and natural samples of chromium-doped beryllium aluminium silicate (emerald) show a large number of resonance lines in addition to those arising from isolated Cr³⁺ ions occupying Al³⁺ sites. The angular and temperature dependence of the spectra indicate that most of the additional lines arise from three types of exchange-coupled pairs of Cr³⁺ ions occupying first, second and third nearest neighbour Al³⁺ sites, with antiferromagnetic exchange coupling constants of approximately 2.260, 0.195 and 0.026 cm^-1 respectively. The spectra have been fitted with a spin Hamiltonian which includes anisotropic bilinear exchange, Zeeman and crystal field terms. Dynamic strain experiments for the first nearest-neighbour Cr³⁺ ion pair suggest that the magnetostriction contribution to the biquadratic exchange is negligible, and so the upper limit of 1% refers to intrinsic biquadratic exchange.

The Raman scattering of light from the ferroelectric fluctuations of the uniaxial ferroelectric lead germanate is analysed and found to be well described by models for which the self-energy has appreciable dispersion at frequencies comparable with the soft-mode linewidth. A model is developed to calculate the self-energy arising from phonon-density fluctuations of the modes belonging to the same branch. The model shows that this contribution to the self-energy of the soft mode is particularly large if the modes with which it is interacting are overdamped. In detail, however, the model suggests that close to T_c there is an appreciable contribution to the Raman scattering from the interference terms between the one- and two-phonon scattering.