Table of contents

Evidence is presented which tends to support the suggestion by grimes and collett (1971) that MgCr₂O₄ should be referred to the space group f4?3m rather than the one usually used. Refinement of integrated intensity data according to f4?3m symmetry gave a value of the temperature factor b of 0.4 aa²-a value more in keeping with that derived from infrared measurements on the material.

Measurement of the thermal conductivity of InSb and InSb containing 500 and 2000 ppm Ga have been made in the temperature range 0.5 to 70K. The results show the existence of a resonance scattering mode, having a resonant frequency of 5.8*10^-12 rads^-1 but this is attributed to a residual impurity and not to the Ga defect. There is no resonance interaction between phonons and Ga defects in InSb.

The multiple-scattering approach has been used to determine the electronic structure and orbital charge distributions for clusters of iron, nickel and copper atoms in a configuration of a simple stepped surface. The density of states at the fermi energy is by far the largest in the case of iron, and the relatively inert copper is distinguished by the absence of pronounced charge lobes present at the step in the other elements. For all three elements, the stepped surface shows a variety of bonding orbitals not present on the flat surface.

A new renormalization group transformation for ising spin systems is proposed. Using a cluster approximation, the exponent nu is estimated to be 0.9899 for the square lattice and 1.0191 for the triangular, compared with the exact value of nu=1.

A simple molecular field theory of the spin glass phase is presented using only conventional methods to make the approximations and philosophy transparent. Using a heisenberg model with random exchange constants one finds an ordering temperature proportional to the root mean square exchange and a cusp in the susceptibility at that temperature. These results are in accord with experiment.

See also ibid., vol.8, no.10, p.l208 (1975). A simple molecular field theory of the spin glass phase is presented which utilizes a local stability condition for the orientation of each spin. The order parameter is taken to be the magnitude of the spin regardless of its orientation. The initial susceptibility exhibits a cusp at an ordering temperature proportional to the root mean square exchange and is similar to the powder susceptibility of a simple antiferromagnetic below this temperature.

A proof based on microscopic theory is given for the existence of a T² ln T term in the temperature dependence of the susceptibility of normal paramagnetic metals and Fermi liquids. Comparison with experiments on Pd, YCo₂, LuCo₂, U₂C₃, He³ and Ni₃Ga is discussed.

The electron paramagnetic resonance of Ni⁺¹ in CuGaS₂ has been observed at 5k and 35 ghz. The measurements yield an axially symmetric g tensor with g_?=1.9185(15) and g_?=2.3243(10). First-order anisotropic orbital reduction factors were found to be k_??0.62 and k_??0.90.

Aspects of the applications of the Kronig-Kramers relations in dielectric and viscoelastic theory and in electrical network analysis are discussed.

Magnetic and stress properties have been studied of the F centres appearing in the tetragonal BaClF crystal: the f(F^-) and the f(Cl^-) centres. The results have been analysed by the method of moments extended to the tetragonal symmetry. The excited state orbital lande factor is found to be close to zero for both centres and the spin-orbit splitting is determined. The introduction of second order spin-orbit mixing allows evidence to be given for the existence of k states associated to the f(F^-) centre. The temperature shift of the F band is shown to be due mostly to the thermal expansion of the lattice. The analysis of higher order moments of absorption, magnetic circular dichroism and stress linear dichroism spectra leads to the determination of the dynamic electron-lattice coupling parameters which are used to explain the shape of the two bands in terms of a Jahn-Teller interaction.

The effect of oxidizing heat treatment reducing heat treatment and of gamma-irradiation on the thermal conductivity of cr-doped mgo is investigated. Estimates of the proportion of chromium in the divalent state after each treatment are obtained.

An analysis has been made of the change in thermal conductivity that occurs when the frequencies of two resonant phonon-scattering processes become equal, a situation which is termed a frequency crossing. The analysis is applicable when the effective width of the scattering processes is small compared with the spectral width of the thermal phonons. The frequency-crossing effect, which is an incoherent effect, is due to the non-linear relation between the strength of the scattering and the thermal conductivity, and can give rise to sharp changes in conductivity. Brief consideration is also given to analogous effects which are expected to occur in heat pulse work. A method is suggested for producing an amplitude-modulated component of narrow spectral width from a heat current, which might have application as a 'monochromatic' phonon source.

An experimental investigation has been made of the size and width of the sharp maxima in the thermal conductivity of Al₂O₃ containing Fe²⁺ ions that occur when two of the resonant scattering frequencies present are made equal-frequency crossings. The crossings are brought about or resolved by applying a magnetic field. Two crossings were studied and the temperature and angular dependence of the size and width of the maxima were found to be in reasonable agreement with a recent analysis.

An analysis is given of the changes that occur in the thermal conductivity of a solid containing resonant phonon scattering centres when there are crossings or anticrossings of levels involved in the scattering. At a level crossing, the changes are due to interference between the scattering processes involving the two levels. At a level anticrossing, the two levels repel because of the coupling between them and the changes in conductivity are due to the effects of state mixing as well as to interference. The effects of both types of crossing are discussed in the two limiting cases of weak and strong resonant scattering in comparison with the other scattering rates present. Observation of these effects can in principle provide rather accurate spectroscopic information about the positions of energy levels. In addition, information should be obtainable on the eigenstates and on the lifetimes of the levels involved.

Some of the remarkable NMR properties are discussed of superfluid ³He-a contained in a slab thinner than a certain characteristic thickness (=10^-3 cm) with a static magnetic field applied perpendicular to the slab. Below a characteristic field (=20 g) there appear two transverse resonance lines. Above it there is one line with a negative shift. The integrated absorption (Kramers-Kronig sum rule) is larger than that in the bulk. These effects provide a useful means to measure the susceptibility anisotropy. Similar phenomena occur in the bulk when there is a superflow. The resonance frequencies are obtained as functions of the flow velocity.

LEED and AES studies were performed on the clean and oxidized Zn and O faces of a ZnO crystal. Clean surfaces were obtained by ar bombardment and anneal. The surface structure of the clean (0001)Zn face depended on the annealing temperature: if it was below a certain 'transition temperature' (=600 degrees C for our sample), the surface was unreconstructed and displayed a (1*1) LEED pattern. For annealing temperatures higher than 600 degrees C, the Zn face underwent reconstruction and exhibited a (sqroot3*sqroot3) pattern, which was retained even after extended exposure to oxygen. The clean (0001)o face displayed a (1*1) pattern, with lines indicative of steps. When this surface was annealed above 600 degrees C, there was no sign of reconstruction. The (1*1) pattern was retained after exposure to oxygen. After oxygen adsorption, no chemical shift in the Zn or A Auger transitions could be detected on either the (0001)Zn or the (0001)o surface.

The configuration-averaging theory of Mookerjee (see abst. A38777, a43969 of 1973) using a disorder field is put here in an equivalent picture of an electron interacting with a fermion field. This provides a more physical background to the mathematically abstruse formalism and also provides a justification to the CPA and cluster cpas proposed by Bishop and Mookerjee (see abstr. A60719 of 1974).

In a previous paper (see abstr. A76748 of 1974) the expansion of the irreducible self-energy of an electron gas was studied and found to give unreliable results for the satellites of the one-electron spectra function. This was due to the incorrect analytic properties of the corresponding green function. These results are confirmed and extended by studying a simple model (s-model) which allows the nature of different approximation schemes to be demonstrated clearly. A consistent iterative expansion method for the green function is also developed, which, in addition to giving a one-electron green function with correct analyticity and a spectral function fulfilling the sum rule, is computationally simple enough to be used for an electron gas and possibly for simple metals. The method gives quite reasonable results for the s-model when developed to second order in the screened interaction. From comparison with other electron gas calculations it is concluded that the method should also give reasonable results for an electron gas.

A systematic discussion of various choices of the localized functions for constructing the bloch sums for LCAO calculations is presented. By generalizing the basis functions, improvement of efficiency and extension of the domain of applicability of the lcao method can be accomplished. The use of extended basis sets containing a series of single-gaussian bloch sums not only yields energy bands of accuracy comparable to those of the method of augmented plane waves, but also enables one to handle the highly excited states. For calculating the filled bands and lower conduction bands the basis functions formed by the optimized orbitals give considerably better results than those with the free-atom orbitals. To reduce the computational work, one can introduce the truncated orbitals by gradually damping the atomic wavefunctions beyond a certain distance, typically the mid-point to the second nearest neighbours. Specific calculations are given for the cases of lithium and diamond-type crystals.

It is shown that for electronic surface problems in a tetrahedrally coordinated solid it is possible to reduce a four-orbital sp³ tight-binding model to an equivalent one-orbital s model. This is the surface analogue of the Weaire-Thorpe transformation (1971) for the bulk. One example of the transformation, which is a reasonably good representation of (111) surface of silicon, is carried out in detail. It exhibits four bands of surface states-two of them almost totally overlapping-in the valence-band region and one band of dangling-bond surface states in the optical gap. The calculation is for the whole two-dimensional Brillouin zone and compares satisfactorily with other calculations.

The electronic surface structure has been studied of a binary compound in the zincblende structure with GaAs as a prototype. Two models are presented: (i) a one-orbital s-like model and (ii) a three-parameter four-orbital sp³ model. Various kinds of surface states are found and analysed: dangling bonds, back bonds and intrinsic atomic-like states. Both surfaces, the (111)-ga and the (1?1?1?)-as, are discussed and their similarities and differences emphasized. Comparison with experiment yields good qualitative agreement.

The matrix elements of the spin and orbital magnetic moment density operators are calculated using spherical tensors and racah algebra. The formulae are derived in the nusljm basis and supplementary results for the extension to the nusm_slm_l representation are given. The simple relationship between magnetic moment density, scattering operator and intermediate scattering operator is investigated and a procedure for the transition from the intermediate scattering operator to the magnetic moment density is derived. The results are applied to fef₂ as a specific example.

The basic theory of ferromagnetic resonance is considered and the shifts in resonance field that can arise from misalignment are calculated. Single-crystal samples are considered and two types of misalignment are noted: firstly, that of applied field with respect to the sample, and secondly, that of crystallographic axis with respect to the sample. A two degree error introduces a resonance field shift of the order of 0.1%.

The generating function of the optical line shape of impurity absorption is obtained, including both displacement of equilibrium positions of normal oscillators and the change of their frequencies. The line shape is investigated by the saddle-point method. It is shown that the frequency effect considerably changes the Gaussian line shape in the centre of the band and the Urbach constants in the long-wave edge. Urbach's rule also describes the long-wave wing for forbidden transitions reduced by lattice vibrations.