Table of contents

In nondilute alloys, the proximity of magnetic ions can induce resonant states in the Rudermann-Kittel electron scattering. This effect is treated in a generalized coherent potential approximation and the exchange energy enhancement produced by such states is shown explicitly.

A new quantity, the isothermal pressure derivative of the liquid structure factor, is introduced into the distribution function theory of simple liquids. It is shown how the triplet correlation function and certain other quantities may be expressed in terms of this experimental quantity and the usual liquid structure factor. From experimental measurements of the liquid structure factor and its pressure derivative in rubidium, carbon tetrachloride and argon, the authors have studied the triplet correlation function and, where possible, measured its range. In addition the Born-Green, hypernetted chain and Percus-Yevick equations are written as relationships between the structure factor and its pressure derivative.

A method of calculating the velocity autocorrelation function psi (t) in a monatomic classical liquid is developed, using directly the equation of motion of an atom in a liquid and a procedure which involves decoupling a statistical average. This leads to an equation of the form (d/dt) psi (t)+ integral ₀^td tau K(t- tau ) psi ( tau )=0 and gives a prescription for calculating the 'memory' function K(t) in terms of the interatomic potential, the static pair correlation function and the selfcorrelation function G_s. Within the Gaussian approximation, G_s depends on psi (t) and the calculation therefore gives an approximately selfconsistent means of determining the latter. The first approximation to the solution, which involves replacing G_s by its ideal gas value, leads to the well known linear trajectory approximation for the diffusion coefficient and indicates that the method will give results which supersede this approximation.

A stimulated spin echo method has been used to measure the spin diffusion coefficient of liquid He³ for temperatures between 0.026 K, and 0.22 K, and the results fitted over a limited range to the line (DT*²)^-1=((6.67+or-0.4)-(24.1+or-4)T*)*10⁵ s cm^-2 K^-2.

The kinetics of saturation of F⁺ centre production have been studied in MgO after reactor irradiation. Although both vacancy and interstitial clusters are formed at high neutron dose, saturation does not result from clustering but is more probably caused by spontaneous recombination of vacancies and interstitials when these are separated by less than 18 nearest-neighbour distances. The production of interstitials and vacancies during irradiation results in growth of both the macroscopic and unit-cell dimensions of the crystals. Comparison of these changes suggest that below about 3*10¹⁹ nvt Frenkel defects are formed. At the lowest doses (<3*10¹⁷ nvt) the mean dilatation per Frenkel pair is estimated to be approximately 8 atomic volumes. At high doses (about 3*10¹⁹ nvt) Frenkel defects migrate to form interstitial clusters. Since this corresponds to the conversion of Frenkel defects to Schottky defects, the mean dilatation per interstitial decreases from approximately nine atomic volumes to one atomic volume.

When MgO crystals are subjected to reactor irradiation after annealing in hydrogen, large differences in the colour centre concentration are observed compared with unannealed crystals. These are believed to be due to vacancies diffusing to large lenticular voids produced in MgO crystals by the annealing treatment. Thus for doses less than 10¹⁹ nvt there is an excess of interstitial defects over vacancies which leads to an inequality between the growth of the macroscopic and unit-cell dimensions of the crystals. Detailed analysis of the changes in defect concentration, lattice parameter and density gives an estimated volume contraction per single vacancy of the order of 1 atomic volume. The formation of F⁺ centre/cation vacancy pairs (F_c⁺ centres) on annealing below 550 degrees C proceeds with an activation energy of only 0.96+or-0.2 eV. Since this is much lower than the activation energy for cation vacancies to migrate, it is suggested that this corresponds to the activation energy for the aggregation of close pairs of defects.

Cadmium doped alkali halide crystals were quenched, X- irradiated at room temperature and subsequently investigated by magneto-optical methods. An optical absorption band of Cd⁺ has been identified at 342 nm in NaCl, 332 nm in KCl, 336 nm in KBr and 345 nm in KI. This band has been assigned to a transition of the type ²S to ²P and the spin-orbit coupling constant in ²P state of the transition has been found by magnetic circular dichroism measurements to be 743 cm^-1 in NaCl, 845 cm^-1 in KCl, 513 cm^-1 in KBr and 263 cm^-1 in KI. The Cd⁺ ion is created as a result of reduction of Cd²⁺ by the irradiation. The interaction of the Cd⁺ ion with the crystal environment is discussed.

It is shown that the lattice Green function for the body centred cubic lattice with isotropic nearest neighbour interactions can, in principle, be evaluated exactly in terms of complete elliptic integrals. The asymptotic behaviour of the Green function is analysed, and applications of the results in lattice statistics are briefly discussed.

Measurements of the ultrasound attenuation near the Neel point in MnF₂ were performed at two different frequencies simultaneously and a temperature dependence of the attenuation maximum was detected. The absorption 'peaked' at higher temperatures the lower the sound frequency, obeying an approximately linear relation in the frequency range 1-7*10⁷ Hz, with a temperature variation of 3+or-1.5*10^-2 K. These results are in qualitative agreement with the phenomenological theory of Landau and Khalatnikov, and with resonant absorption of ultrasound by a 'soft' magnon mode.

By the application of electric and transverse magnetic fields n-InSb bars are acoustoelectrically excited at 77 K. The build-up of acoustical domains is sampled by 35 GHz helicon transmission through small parts of the specimen. A decrease of helicon amplitude and increase of wavelength is observed with growing acoustical excitation. This phenomenon is explained by the theoretical treatment of microwave propagation through acoustoelectrically excited semiconductors. Here a periodical structure is assumed with two layers of different carrier concentration within one acoustical wavelength, representing carrier bunching in the piezoelectric field. Calculations of microwave propagation parallel to the plane of the layers yield the experimentally observed 'wave guide' effects. Furthermore the experiments indicate a nucleation of the acoustical domain in the high field region near the cathode, where the domain propagates as a region of slightly enhanced electric field. Bunching becomes effective at 9-12 mm from the cathode.

Thermoreflectance measurements have been made on a series of (InGa)P epitaxial layers. The direct spin-orbit optical transitions are observed at all concentrations. The indirect transition is seen in the indirect gap material, which occurs about 65 mol.% GaP, through a process involving thermotransmission through the layer and a reflection at the substrate.

The electron-phonon interaction in a metal or semiconductor was expressed in terms of the matrix elements of the 'localized potentials', the localized potential being equal to the displacement of the jth nucleus of the basis multiplied by some vector field W^j. The symmetry properties of the W^j fields and some sum rules for these fields were investigated. The results were applied, in particular, to the long range multipole interactions in semiconductors; it was shown that the W^j field decreases-for increasing distance from the displaced nucleus-no faster than this distance to the power of minus four (which corresponds to the octupole interaction). The symmetry properties of the matrix elements of the W^j fields were studied in both the Bloch and Wannier representations.

The ground- and excited-state energies of the F-centre in the sodium chloride lattice have been calculated using a Hartree-Fock and pseudopotential formalism. The free-ion Hartree-Fock-Slater orbitals and potential of Na⁺ and Cl^- ions were used. A static undistorted ion model has been considered for the vacancy. The significant features of the calculation are (i) the exchange and pseudopotential have been treated as nonlocal terms; (ii) an energy-dependent pseudopotential Hamiltonian is used and (iii) the point-group symmetry of the vacancy potential is taken into account.

A derivation is given of the dispersion relation for excitations from the spin-density wave ground state. Working in the random phase approximation, and taking a single tight binding electronic band with a delta function interaction between electrons, the author finds three types of collective mode, of which one is longitudinal and two transverse. Calculation shows that the former has a linear dispersion relation for small wave vectors, and is probably a zero-sound excitation modified by the magnetic ordering. One of the transverse modes is also linear in behaviour, and is identified as a spin wave excitation. The other behaves as omega = omega ₀+Aq² for small q, where omega ₀ lies in the energy gap; on examining the approach to the ferromagnetic limit, it is demonstrated that omega ₀ approaches zero, and the mode goes over smoothly into a ferromagnetic spin wave.

Electrical conductivity measurements on n-type InSb in the temperature range 0.27-4.2 K and in magnetic fields up to 10 kG have been made. The results indicate a strong magnetic field dependence for the conductivity, with an activation energy depending on magnetic field. These results are discussed in the light of the recently proposed wigner transition which is appropriate to the highly compensated samples used in this work. The magnitude of the activation energy and the role of the first excited state of the impurity centre are also briefly considered.

The trigonal field and spin-orbit interaction matrices for the d² configuration have been calculated in the 'strong field' scheme, using the irreducible tensor operators of the site symmetry group. These matrices were used to calculate the energy levels of V³⁺ ion in a alpha -Al₂O₃ (corundum) in the intermediate coupling scheme. The effective Hamiltonian appropriate to the T₁ manifold was used to calculate the value of g/sub /// and g_{perpendicular to} . Analytical expressions for the trigonal field splitting of the t²₂³T₁ term, the ground state ³A₂ splitting under the combined effect of the trigonal field and the spin-orbit interaction, g/sub /// and g_{perpendicular to} have been obtained.

A study has been made of the energy loss of electrons in evaporated amorphous films of germanium for a range of incident electron energies (30-60 keV) and specimen thicknesses (200-800 AA). These spectra have been corrected for instrumental resolution effects and plural electron scattering. The spectrum exhibits a 16.2 eV plasmon loss and an X-ray absorption edge at 32 eV; this edge had been previously masked by plural electron scattering. The mean free path for inelastic electron scattering averaged over all loss processes in the region 2-50 eV, is determined from the single scattering profiles for germanium. The mean free path values so determined were 350, 415 and 470 AA for incident electron energies 30, 45 and 60 keV respectively.

Observations of the influence of (111) uniaxial stress on free carrier absorption in n-type germanium for infrared radiation polarized parallel or perpendicular to stress are reported. In particular very large dichroic ratios are observed at 77 K. The corresponding energy splitting of the multivalley conduction band states is measured directly using a differential spectroscopic technique. The results are explained according to the electron transfer model and yield a mass times relaxation time anisotropy of 26+or-3.

The thermoluminescence of X-ray irradiated KBr and KBr:Cu crystals has been studied in the temperature range 300-510 K. Four glow peaks with first order kinetics are observed at 359, 377, 392 and 409 K for a warming rate 40 K min^-1. The trap depths for the above peaks are respectively 0.86, 0.97, 1.00 and 1.05 eV. The 377 K peak is related to the presence of Cu⁺ ions in the crystal. Based on the identification of the filled traps with F-centres in different local environments, the thermal excitation energy of the F-centres to the relaxed excited state is deduced to be 1.7 eV for KBr ( and 2.0 eV for KCl).

Deformation-induced and optically stimulated thermoluminescence peaks associated with new electron traps have been observed from KCl. It is suggested that the traps may be small anion-cation vacancy clusters produced by the jogged motion of dislocations during plastic deformation.

EPR measurements have been made of Ce nearest and second nearest neighbour pairs in europium, yttrium and lutecium ethyl sulphates. The information obtained from these measurements has been used, in conjunction with previous data on pure cerium ethyl sulphate, to obtain the elements of the interaction tensors. This sheds new light upon the interaction mechanisms. It is shown that the large nondipolar interaction cannot be due to exchange or electric quadrupole-quadrupole interactions alone, but is due mainly to virtual phonon exchange, with interaction parameters more than an order of magnitude larger than those hitherto calculated using a simple Debye model for the phonon spectrum and orbit- lattice coupling parameters estimated from the static crystal field.

The existing data on the interactions between a large number of different pairs of rare earth ions in ethyl sulphates is surveyed as a whole, and some comparisons are made with similar data for LaCl₃ and LaBr₃. Such an analysis of all of the data enables one to draw much firmer conclusions about the interaction mechanisms than a discussion of the results for any particular pair of ions. It is shown that exchange contributes very little to the interaction, and that electric multipole-multipole interaction contributions are negligible. This suggests that the sizeable nondipolar contribution to the interaction should be attributed to virtual phonon exchange (VPE). Estimates of this interaction based upon standard theories show that the interaction must be enhanced by a factor of 40-50 in order to agree with the experimental measurements. That this enhancement factor remarkably consistent for all of the data, and that one can invent a plausible model to account for the enhancement factor in terms of contributions from optical phonon modes, indicates that VPE interaction is the appropriate mechanism.