Table of contents

The validity of mean field models for phase transitions is discussed, and examples are given for dilute random systems of anisotropic defects interacting with long range elastic strain fields. The distribution of internal fields, and not merely the moments, is calculated.

Calculations of the equilibrium axial ratios of beryllium, magnesium, zinc and cadmium based on the optimized model potential are compared. The condition for a large axial ratio is examined. A recent empirically determined change in the normalized energy- wavenumber characteristic in the structure region for zinc and cadmium helps to satisfy this condition and consequently improves the axial ratio prediction.

The results of an acoustic paramagnetic resonance study of x-irradiated ruby using longitudinal ultrasonic waves at 9.1-9.6 ghz are presented. Most resonances are attributed to the cr²⁺ ion which is very strongly coupled to the lattice and is subject to a dynamic jahn-teller effect. Four principal resonances are observed with the magnetic field along the c axis at approximately 6.3 kg, 7.7 kg, 11.4 kg and 15.8 kg. These split up into several components as the field is turned away from the c axis. The results are in broad agreement with the theory of bates and dixon (1969). Lines due to other centres are observed.

Several papers have reported the observation of transitions induced by acoustic resonance between s_z= +or- 1 of an s=1 ion (with s_z=0 well removed). The standard spin hamiltonian formalism is expected to account for the observations, but difficulties have been encountered in its perturbation treatment. A technique which circumvents these is described. It leads naturally to a description of s_z= +or- 1 as a doublet with fictitious spin=¹/₂. The new spin hamiltonian has an unusual form, and the wider issue of the symmetry property of spin hamiltonians is raised.

The earlier work on harmonic raman ion-lattice interaction processes is extended to systems with an arbitrary number of ionic energy levels. The weisskopf-wigner linewidth-lifetime relation (that the full width is the sum of the inverse lifetimes of the two states) is valid only for those linewidth contributions arising from raman processes in which there is a net electronic transition, that is, processes which contribute to depopulation rates. This includes the usual three level raman processes and the semidiagonal process, but not the self energy raman process; for the latter process, transition probability amplitudes combine coherently.

The properties of a conduction electron in a ferromagnetic crystal (magnetic polaron) have been investigated. The magnetic spins are treated within the idealized boson representation. At absolute zero a large number of terms in the perturbation expansion are zero and the remainder can be summed exactly. For strong coupling it is demonstrated that, for certain total spin states, slight narrowing of the conduction electron bandwidth can occur. This narrowing depends on the magnitude of the atomic spin in the form of a factor 2s/2s+1.

Measurements of the thermal expansion coefficients of monoclinic nicl₂.6h₂o in the temperature range 2-9.5k are reported. The results show complex behaviour associated with antiferromagnetism below 5.34 k. Assuming a general strain dependent hamiltonian for an anisotropic system, it is shown that the excess thermal expansion of magnetic origin should be proportional to the magnetic specific heat for systems ordering at low temperatures. Although the hamiltonian appropriate to nicl₂.6h₂o does not appear to be of this form, the observed approximate proportionality between the largest thermal expansion coefficients and the magnetic specific heat below the neel temperature is used to obtain phenomenological magnetostriction constants.

Two peaks are observed in tan delta against frequency isothermals in cobalt doped potassium chloride crystals in the temperature range 100 degrees C to 200 degrees C and frequency range 10² Hz to 10⁵ Hz. The low and high frequency peaks have been labelled as A and B, respectively. The logarithm of peak frequencies plotted against 1/T gave straight lines for both the peaks. The values of the activation energy calculated from the slope of the straight lines are 0.83+or-0.06 eV and 0.85+or-0.06 eV for the A and B peaks respectively. None of the A and B peaks were found to be due to Maxwell-Wagner losses or interfacial polarization.

The magnetoresistance of three samples of high purity n-type insb(n_d-n_a varying from 5*10¹³ to 5*10¹⁴ cm^-3) is studied at lattice temperatures of 11 and 20 k with electric field strengths sufficient (>100 mv cm^-1) to heat the electron distribution appreciably above the temperature of the lattice and at magnetic field strengths such that the effect of landau quantization is apparent. Two distinct types of magnetophonon extrema are observed, each having a different dependence on electric field and temperature. The first consists of a series of minima which are only observed when the electron temperature is in excess of about 20 k and which arises from the emission of long wavelength longitudinal optical (lo) phonons.

The scaling laws derived by a complicated space-time approach for the Kondo problem in previous work are rederived by a cutoff renormalization technique used previously in the theory of superconductivity.

A semiconducting diamond was irradiated at ambient temperature with 1 mev electrons. The dependence of the resistivity on the dose is consistent with annealing of the radiation damage during the course of the irradiation. The resistivity was then measured as a function of isochronal annealing in the range 200 to 1400 degrees C. The results suggest the presence of a number of annealing mechanisms. At 1400 degrees C the recovery was complete. The same specimen was then irradiated with 1 mev electrons at 77k. The variation of the resistivity with the dose was consistent with diamond being a partially compensated p-type semiconductor. The resistivity as a function of isochronal annealing in the range 100 to 1450 degrees C once again indicated the presence of a number of distinct processes.

The time dependent Ginzburg-Landau equation is used to calculate the anomalous contribution to the conductivity of a dirty superconducting film due to thermodynamic fluctuations above the critical field. Expressions are obtained for the conductivity along the film and also in the surface sheath case above H_c3. It is found that sigma varies as d^-3(H²-H_c//²)^-1, sigma varies as d^-1(H-H_{c perpendicular to} )^-1, sigma varies as (H-H_c3)^-1. The conductivity is calculated for a thin film in an inclined field, to get an interpolation formula between the parallel and perpendicular field results.

The matrix element of the electron-ion interaction in the rigid ion model is examined critically in a one-dimensional formulation of this well known problem. It is found to be very significantly different from one of the standard expressions for it found in the literature. The error in the standard derivation seems to have stemmed from the use of a simplifying assumption at an inappropriate stage. Consequently, the electron-phonon coupling constant should be much smaller in magnitude than what it is believed to be.

New de haas-van alphen data are presented for dilute alloys of tin and lead in indium. These data support the conclusion that the very low frequency oscillations observed in pure indium arise from electron orbits around the junction regions of the third zone ring of beta-arms. A pseudopotential calculation indicates that the rigid band model is not always adequate to explain fermi surface changes in dilute alloys. An alternative model is suggested which gives good agreement with the present data. It is shown that the variation of superconducting transition temperature in these alloys can be explained qualitatively in terms of overlap of the fermi surface into regions of the third zone only.

Measurements have been made of the ionization coefficient as a function of electrical field in znse. Hole and electron ionization coefficients are equal within the limits of the experiments. The results obtained are consistent with baraff's theory. Values of the scattering length lamda lie in the range 25-50 aa. An empirical relation has been found between lamda and the concentration of ionized impurities. The results are discussed in terms of the band structure of znse. The ionization coefficients are consistent with those of similar materials.

Many no phonon lines in diamond are found to have the spectral intensity distribution i(v)=a(b+(v-v₀)²)^-2 in the limit of low temperature. This distribution lies midway between the lorentzian and gaussian shapes and is close to a voigt function with lorentzian and gaussian components l/g=0.5. Detailed measurements on the width, energy and shape of the 503 nm line produced by the electron irradiation and annealing of a series of type i diamonds have shown that the width and exact energy are partly dependent on the concentration of impurity nitrogen. This, and other evidence, suggests the nitrogen is predominantly in the form of small aggregates, rather than platelets. With this assumption, the width, exact energy and lineshape may be closely related to the strain field produced by the nitrogen.

The cold neutron time of flight technique has been used to study the diffusive motions of hydrogen in the beta -phase of palladium hydride. The quasielastic scattering was measured at 20 degrees C, 100 degrees C, 150 degrees C and 200 degrees C. The data were found to be well predicted by Lorentzians broadened by the appropriate resolution function. In contrast to the results obtained by Skold and Nelin in the alpha -phase, the dependence of the broadening on momentum transfer was not as predicted by the Chudley-Elliot model for jumps between octahedral sites. It was, however, well fitted by a modal which included the possibility of jumps between octahedral and tetrahedral interstitial sites as well as octahedral ones. The resultant diffusion coefficients were described by the expression D=1.1*10^-3 exp (-3380/RT) cm² s^-1.

Oxygen ion vacancies, which absorb light at 250 nm, are observed in 'pure' mgo after irradiation with 0.23-29 mev electrons. The threshold energy for anion vacancy formation is observed to occur at 0.33 mev; this corresponds to a displacement energy t_d=60 ev. Energy independent damage is observed below the threshold energy. Zero phonon lines are observed at wavelengths of 361.5, 1044.5 and 1342.5 nm in crystals irradiated at electron energies greater than 1.6 mev. Optical bleaching experiments suggest that these lines are associated with trapped electron centres. The energy dependence of the growth rate of the 1044.5 nm line confirms that intrinsic defect aggregates are involved, anion divacancies being the most probable.

Recent experiments in which a crystal was exposed to an electron beam and laser light are treated here by quantum mechanical scattering theory. Diffraction patterns oscillating with the laser frequency are predicted in agreement with experimental results. Three effects are considered: (i) scattering due to laser induced crystal oscillations; (ii) scattering from the crystal with subsequent deflection by the laser field; (iii) the inverse of (ii). The latter two processes seem to be dominant. Periodic modulation of the intensity with increasing distance to the screen is predicted.