Table of contents

A simple mathematical interpretation of the principle of corresponding states is determined which is applicable to dispersions of loss tangent and permittivity for all well known distributions of relaxation times. The relationships obtained provide a useful technique for analysing incomplete dielectric data. This technique is demonstrated for results already published on thin films of silicon oxide. A brief review is given on present methods of analysing dielectric data with particular reference to the relevant graphical plots.

Some of the various modes of vibration in crystals correspond to a rotation of the ionic complex around a paramagnetic ion.

It can be seen that these modes of vibration can generate a spin relaxation mechanism by means of a modulation of the orientation of the axis of quantization of the orbital moment. Such a mechanism is studied in an octahedral complex where Ti³⁺ ions are included.

In previous papers we have described the process of `relaxation through modulating the orientation' and we have used the principles of the calculation of the relaxation probability on a simple model of the crystalline lattice.

The aim of the present paper is to study such a process of relaxation in a concrete case, that of the Ti³⁺ ions, included in an octahedral complex presenting a trigonal distortion, among which the crystalline potential is much stronger than that of the spin-orbit coupling.

An example of such a complex is titanium trisacetylacetonate. Our study will be divided into two parts: we very briefly recall in the first part the principles on which `relaxation through modulating the orientation' is based; in the second part we apply these principles to the types of crystals mentioned above.

The results of measurements of the spin-lattice relaxation properties of mixed single crystals of chromium and aluminium acetylacetonate are reported. Measurements were made at microwave frequencies (9·3 GHz) in the range of liquid helium temperatures. In dilute crystals, where the investigation was primarily concerned with the angular dependence of the relaxation time, satisfactory agreement with the single-ion theory was obtained by taking 2D = -1·18 cm^-1. In concentrated crystals a reduction of spin-lattice relaxation time was observed together with a weaker temperature dependence. At the highest concentration (10 molar% Cr) the relaxation time was independent of temperature in the range 1·6-4·2 °K. The results are interpreted in terms of a mechanism involving exchange-coupled pairs.

The electrostatic potential is derived for a crystalline array of extended charge distributions and in particular for extended multipoles. The potential for a crystalline array of point multipoles is then derived by the theorem developed previously.

Sputtered platinum electrodes are frequently used on alkali halide crystals for the measurement of dielectric constant and conductivity. In the course of such work large capacity enhancements were observed in several alkali halide crystals at temperatures of a few hundred degrees centigrade. Evidence is presented that the effect is due to an interaction between the electrodes and the crystal, so that results on such systems at high temperatures must be interpreted with care.

A model in which the conductivity is a linear function of depth through part of the crystal gives satisfactory agreement with the experimental results.

A general procedure has been devised for the analysis and prediction of electron energy-loss spectra which may be described in terms of two basic inelastic scattering processes, one being more probable than the other. The procedure is illustrated by its application to the analysis of the characteristic energy-loss spectra of evaporated Al films as seen by electron transmission. The procedure accounts for plural surface-volume and volume-volume scattering and the modifying effect of the finite resolution of the energy analyser. Good agreement is found between observed and calculated spectra (23-70 kev energy electrons) for energy losses less than about 70 ev. The method allows the determination of the important energy-loss distribution corresponding to a single-volume loss and provides a basis for estimating the importance of energy-loss processes not specifically accounted for in the fitting procedure.

The hyperfine interactions of single and of exchange-coupled pairs of Ir⁴⁺ ions in (NH₄)₂PtCl₆ have been investigated by ENDOR methods at 4 °K. Recent investigations of electron transfer between magnetic ions have suggested that a measurable difference may occur. Experimentally, however, the difference is found to be less than 0·15%. The hyperfine constants are determined to be negative, leading to a value K = 0·85±0·4 for the core polarization constant for 5d electrons. The nuclear dipole moments of ¹⁹³Ir and ¹⁹¹Ir are determined to be ¹⁹³μ = +0·162±0·006 nuclear magnetons and ¹⁹¹μ = +0·146±0·008 nuclear magnetons, in agreement with recent measurements by nuclear magnetic resonance in the pure metal. A hyperfine anomaly of ₁₉₁¹⁹³Δ = (0·20±0·30)% is found. The ratio of the nuclear quadrupole moments is determined to be ¹⁹³Q:¹⁹¹Q = 0·92±0·09.

Direct observation is reported of cross-relaxation between isolated Ir⁴⁺ ions in (NH₄)₂PtCl₆ and exchange-coupled triads. A bimodal microwave cavity was used in the experiments and a small change in the electron paramagnetic resonance signal at 33·1 GHz due to triads was observed when the single ion resonance was saturated by a microwave pulse at 9·86 GHz. The results are in agreement with those of Harris and Yngvesson. Effects due probably to larger clusters were also observed.

Paramagnetic resonance spectra attributed to three Fe³⁺:Cu associated centres A, B and C have been studied at 77 °K in cadmium sulphide single crystals. The results are explained with an orthorhombic spin Hamiltonian H = gβH. S + D{S_z² − fraction one-third S(S+1)} + E(S_x² − S_y²) with S = fraction five-twos,|E| <|D| and|D| > hv. The x and y axes of centres A and B lie in the 112, macron0 plane and the x axes for A and B make angles of 21·0° and 29·2° with the c axis respectively. The centre C is less well defined. The parameters D and E, taking g = 2·01, are estimated to within 5% for A as D = −0·537 cm⁻¹, E = 0·116 cm⁻¹ and for B as D = −0·372 cm⁻¹, E = 0·0845 cm⁻¹. The resonance is not photosensitive. The association between the Fe and Cu is a possible explanation of the killer action of Fe on the CdS:Cu luminescence.

The essential degeneracies that may arise in the electronic band structure of a magnetic metal have been investigated by Falicov and Ruvalds. Because of the existence of a spontaneous magnetic moment the operation of time reversal θ is no longer a symmetry operation of the crystal. However, the crystal still possesses some compound anti-unitary symmetry operations, ignored by Falicov and Ruvalds, which consist of products of θ with various space-group operations. It is shown that for face-centred cubic and body-centred cubic structures the inclusion of these extra anti-unitary operations leads to no extra degeneracy, but that in the hexagonal close-packed structure, for certain magnetization directions and for certain points and lines of symmetry on the top face of the Brillouin zone, these extra anti-unitary symmetry operations lead to additional degeneracies which were not noted by Falicov and Ruvalds.

The hyperfine Mössbauer spectra of ⁵⁷Fe, incorporated as a dilute impurity in ten different non-cubic metals, have been studied. The splittings in the absorption spectra are interpreted to be due to electric quadrupole interactions. In hexagonal close-packed metals quadrupole splittings appear to be related to the axial ratio c/a of the host.

A calculation of the electron energy bands in face-centred cubic γ-manganese arising from the 3d and 4s levels in the free atom has been carried out by the augmented plane wave method. The overall picture is of a nearly-free electron s band overlapping almost completely a d band of width 0·16 ryd. The width is small compared with those calculated for other face-centred cubic transition metals but the band has no pronounced dip and a value of 0·014 J mole⁻¹ deg K⁻² calculated for the electronic specific heat coefficient γ does not appear too large when compared with measurements for α- and β-Mn. (κ) curves, a density of states histogram and Fermi surface have been calculated but there is no experimental evidence for direct comparison with these.

It is shown how non-orthogonal sets of functions can be used to calculate the transport properties of electrons in a structurally disordered system of potential wells by means of a Boltzmann equation. The main modification introduced by using non-orthogonal functions as a representation is that the transition probability from a state s to a state sprime is given by 2π/h δ(H_ss − H_{sprime sprime}) [H − H_ss]_ssprime [H − H_{sprime sprime}]_{sprime s} where [H − H_ss]_ssprime is a matrix element of H − H_ss and H_ss is a diagonal matrix element of the Hamiltonian H. The construction of suitable representations for the cases of simple and noble liquid metals is described. The method provides a simple framework for developing a theory of liquid transition metals.

Using the `coherent-wave' approximation, it is shown how wave functions can be constructed for describing electrons in liquid transition metals. These wave functions can be simplified, along the lines developed by Heine, by Hubbard and by Jacobs for crystalline transition metals, making feasible the calculation of transport properties using a Boltzmann equation.

The thermal conductivity of pure nickel and a number of dilute Ni-Co, Ni-Fe, Ni-Cu and Ni-Pd alloys has been measured in the temperature range 2-100 °K. An attempted separation of the measured conductivity into its electronic and lattice components indicates rather large deviations from the thermal equivalent of Matthiessen's rule. These deviations are greatest in Ni-Co and smallest in Ni-Pd, suggesting a close correlation with the deviations from Mattheissen's rule itself observed previously in the same alloys and attributed to a spin-mixing mechanism. Below 15 °K these deviations are negligible so that the lattice conductivity can be evaluated. The values obtained are close to those found in noble metal alloys, and are not unusually low as observed in alloys of palladium and platinum.

The soft x-ray emission from solute atoms in dilute alloys is discussed. Using a simple model for an attractive impurity in a metal, the qualitative effects on the intensity of virtual bound and bound states round the impurity are fully investigated. The effect of localized s states is found to be different in character from that due to localized states with non-zero angular momentum. The simple model used enables the transition probabilities to be evaluated analytically; it is these quantities rather than the density of states which are responsible for the large distortions of the solute intensity profiles when there are virtual bound states.

An analysis of the high-frequency conductivity coefficients of a many-valley semiconductor shows that the anisotropy factors for the real and imaginary parts are different if the scattering time is not isotropic. Also the ratio of the real and imaginary parts are independent of mass anisotropy if the relaxation time is isotropic. On the other hand, the ratio becomes dependent on both mass and relaxation-time anisotropies when the scattering time is anisotropic. The results can be used to determine the relaxation-time anisotropy in a semiconducting crystal by high-frequency measurements.

The susceptibility of type II superconductors in low-frequency alternating current fields has been measured using a phase sensitive detector. Penetrations of magnetic field of between 300 Å and 500 μm can be measured and if it is assumed that a critical state exists the field profile across the specimen can be plotted on this scale. The response is linear at low amplitude and is consistent with a model based on the reversible oscillation of vortices in harmonic wells. It is not consistent with the signal predicted from `flux creep'. The effective potential wells are found to be harmonic up to their edges and only about 25 Å in radius. The resolution is sufficient to show that the surface current is not a critical state, but can be described by a single row of vortices pinned by the boundary of the specimen.

The ranges of electron states near a band edge in liquid chains have been found to depend not on an exponential decay factor, as previously believed, but on the `beat length' R of a related Bloch function. This leads to a new qualitative description of the eigenstates near the band edge of a liquid chain and gives a smooth transition to the band states. A method for determining the range R is given, and shown to agree with Monte Carlo computer calculations. These findings enable a correct application of the `local density' approximation - for example, to the determination of state densities. Some discussion is given of the relevance of the findings to work on real liquids, and on the Anderson model of a regular lattice with random potential strengths.

The saturation by weak alternating fields of dipolar-broadened paramagnetic resonance spectra has been studied in experiments on the electron resonance line of Ce³⁺ ions in (Ce_xLa_1-x)₂Mg₃(NO₃)₁₂24H₂O. Two crystals (x = 0·36 and 1·0) were examined at 1·4 °K using frequencies in the range 9·0-9·5 GHz. Saturation by a field of frequency ω₁ had little effect on the width of the line observed by recording the power absorbed as the Larmor frequency ω₀ was swept slowly through resonance. Measurement of the effect of the field on the absorption χdouble prime (ω) at other frequencies ω showed the saturation of χdouble prime (ω) to be linearly dependent on ω - ω₀, and to be homogeneous only when ω₁ = ω₀.

The results confirm the view of Provotorov that the spin system reaches only quasi-equilibrium states in which separate spin temperatures are associated with independent Zeeman and dipolar contributions to the energy. A simple theory, based on Provotorov's but making allowance for the effect of the `phonon bottleneck' on the spin-lattice relaxation, is developed and accounts both for the saturation in the steady state, and for certain transient phenomena observed during its development.

A model for magnetic resonance saturation due to Gill and Vinall is found to be in conflict with the second law of thermodynamics. The reason is ascribed to two incompatible assumptions on which the model is based.

Criticism by Clough of a model of magnetic resonance saturation used by Gill and Vinall is based on the erroneous assumption that a spin system with a dipolar-broadened resonance line is necessarily in thermal equilibrium internally.

It is shown that the isotropic Heisenberg model with an exchange interaction J(R) cannot be ferromagnetic or antiferromagnetic if the spherical model with an interaction|J(R)| does not exhibit a phase transition. From this result it follows that the isotropic Heisenberg model with J(R) = A/|R|^d+σ (where d is the dimensionality of the lattice, A > 0 and σ > 0) cannot be ferromagnetic for d < 3 if σ >or= d.

The electron spin resonance spectrum of magnetically isolated Cu²⁺ ions is observed in γ-irradiated copper acetate monohydrate, which when undamaged contains only exchange-coupled pairs of Cu²⁺ ions. It is proposed that a liberated hydrogen atom converts a water molecule to H₃O⁺, donating an electron to the nearby Cu²⁺ ion.