Table of contents

Attention is drawn to two edge effects, which if neglected, introduce substantial error in the analysis of electrical conductivity data for ionic crystals. Firstly, where the area of the electrodes does not exceed the total specimen area the effect of field fringing must be accounted for, and secondly, because of the importance of surface conduction the use of guard electrodes is essential to ensure that the conductance measured is that of the crystal bulk alone. A simple expression for the field fringing correction is developed for the first case, and in the second it is shown that the suppression of surface conductivity results in a decrease in the calculated enthalpy of motion of a cation vacancy and an increase in the calculated enthalpy of formation of a Schottky vacancy pair.

Resonant structure in the photomagnetic EMF of n- and p-Ge at liquid helium temperatures reveals two distinct energy relaxation mechanisms for the intrinsically excited electrons. The first arises from capture of hot electrons by ionised donors accompanied by the emission of an LO phonon, the second involves inelastic scattering of electrons by excitation or de-excitation of natural or acceptor impurities. The strength of the series associated with LO phonon emission shows directly that hot electrons play an important role in the transport properties of intrinsically photoexcited Ge at low temperatures.

Band theory methods are used to study the form of the Bloch waves excited in a crystal by a beam of high-energy electrons. Because of absorption, the effective Hamiltonian is non-Hermitian and the branch points usually encountered in band theory at complex K can therefore occur at real K. Under systematic diffracting conditions, it is found that a branch point is either close to the centre of the Brillouin zone or close to the zone boundary at a particular incident beam energy E_b which is close to the critical voltage. However, despite the divergence of the excitation amplitudes of the Bloch waves near a branch point, calculations have failed to display any diffraction effects which can be clearly ascribed to the branch point itself. Similarly, branch points can occur near a zone axis critical voltage under cross-grating diffraction conditions. To facilitate the calculations, a simple approximation is used to estimate the optical potential in the effective Hamiltonian.

Acoustic phonon dispersion curves have been measured by neutron inelastic scattering in phases I and II of solid deuteromethane (CD₄), yielding elastic constants C_II=3.08+or-0.20, C₁₂=2.14+or-0.24 and C₄₄=1.58+or-0.06 (in units of 10¹⁰ dyn cm^-2) in phase I. The elastic constants in phase II are about 10% higher. Longitudinal acoustic phonons in the (111) direction indicate life-time broadening. While no well defined librational excitations were observed, there is evidence that inelastic 'shoulders' in the neutron spectra are due to damped librations.

The Van der Waals contribution to the binding energy of the noble metals for both FCC and HCP structures is calculated. It is shown that the Van der Waals forces will give noble metals a more stable FCC structure than HCP, the energy difference being about 0.02 eV atom^-1. A comparison of binding energy is made with recent calculations by Rehr, Zaremba and Kohn (1975). There is general agreement between the many-body estimate in the present paper and their pairwise interaction model results.

The satellite resonances of Gd³⁺ in (Lu_0.99,Sc_0.01)PO₄ were investigated using a variable-frequency EPR spectrometer in the frequency range of 2.0 to 12.4 GHz. Besides the tetragonal spectrum typical for Gd³⁺ in pure LuPO₄, two satellite spectra were extracted, both described by a spin-Hamiltonian or orthorhombic symmetry. These two spectra were interpreted as spectra of Gd³⁺ ions, whose surroundings were distorted by neighbouring Sc³⁺ ions. For one spectrum a specific configuration of the Gd³⁺ and Sc³⁺ ions in the crystal could be assigned. For the other spectrum there are two possible configurations. The experiments demonstrated that even small local distortions in the surroundings of the Gd³⁺ ion could be detected by EPR. If a better understanding of the mechanism of the ground-state splitting of Gd³⁺ is reached, such experiments may be useful to study local distortions in detail.

Evidence is presented which indicates that radiation damage can be photochemically introduced in MnF₂ and RbMnF₃ crystals. At 77K radiation-induced defect-manganese complexes are formed which not only enhance the oscillator strength of the manganese optical transitions, but also act as terminal emission points for manganese excitons. Energy transfer to these defects occurs above 40K. The radiation-induced defects are shown to have annealing stages at 200K and about 300K in MnF₂ and very little stable damage is found for 300K irradiations. On the other hand, the RbMnF₃ 300K irradiation does produce a significant amount of stable damage.

The phonon dispersion curves of cuprous chloride have been determined at 4.2K by inelastic neutron scattering. The curves are very similar to those for the isomorphous CuBr and CuI. They are analysed within the shell model formalism, which permits the calculation of derived quantities such as one- and two-phonon densities of states, Debye temperature and amplitudes in the Debye-Waller factor for the individual ion. The frequencies of the phonons are not very temperature dependent: 6% renormalisation for some optic modes between 4.2K and 300K, but the peak intensity or the visibility is rapidly decreasing with increasing temperature, indicating the strong anharmonicity of CuCl.

The critical properties of a quantum-mechanical X-Y model in a transverse magnetic field are calculated. At zero temperature near the critical field Gamma _c a Gaussian type behaviour is observed for dimensions higher than two. The exponent which describes the rescaling of frequencies is here z=2. For d<2 a renormalisation group treatment produces a non-trivial fixed point. However, the exponents remain unchanged to first order in epsilon =2-d.

Pyridinium pentasilver-hexaiodide, (C₅H₅NH)Ag₅I₆, is a solid electrolyte with a very high conductivity of the Ag⁺ ions, comparable to those of the best ionic conductors such as AgI and RbAg₅I₆. Far-infrared experiments (FIR) show the existence of very low frequency optical modes with h(cross) omega approximately=2-3 meV. The lack of structure in the incoherent neutron scattering experiments in this energy range strongly suggests that these low frequency modes are of prime importance for the conduction mechanism: the low frequency z polarised mode can be regarded as a 'quasi-attempt' mode for jumps of Ag⁺ ions from 4c-sites into adjacent empty 4c-sites along channels formed by face-sharing iodide octahedra.

The motion of negative ions in superfluid ³He when acted on by a field is calculated using a model in which the cross-section is taken to be constant. The theory is developed for both the A and B-phase It is argued that the scattering processes can be treated as being elastic for temperatures close to the transition temperature. The theory is in good agreement with experimental results for the B-phase of superfluid ³He for velocities in excess of the critical velocity. It is possible to estimate the energy gap from the data. The theory is not in agreement with experimental results for lower velocities. This implies that the momentum transfer cross-section is smaller than in the normal phase for quasiparticle scattering processes.

Relaxation of the orientation of the order parameter and the total spin of ³He-A following a sudden small rotation of an applied magnetic field is discussed. Explicit formulae to describe the relaxation are obtained in terms of the spin and the orbital relaxation constants without any assumption on their relative magnitudes. The criterion for applicability of the theoretical formula used by Paulson, Krusius and Wheatley (1976) in analysing their data is deduced.

Insulators such as SiO₂ are not normally photosensitive except perhaps in the vacuum ultraviolet range. A photoresponse in the visible range can be stimulated by illuminating a dye in intimate contact with the surface of the insulator. This paper describes preliminary experiments on metal-SiO₂-dye-metal sandwich structures. The induced photoconductivity has been measured as a function of wavelength, polarity and magnitude of the applied field using steady-state and pulse techniques. Relatively large electron currents are observed with a time response limited by instrumental factors. Estimates have been made of the quantum efficiency of electron injection under steady-state and pulse conditions. The phenomenon has possible device applications.

The temperature dependence of DC conductivity in the high-temperature range in transition metal oxide glasses containing MoO₃, WO₃ and V₂O₅ is presented. Molybdenum phosphate glass has been investigated with MoO₃ contents varying from 60 to 85 mol% while vanadium and tungsten phosphate glasses have been examined for one composition only. The conductivity of a molybdenum phosphate glass is considerably lower than that of tungsten and vanadium phosphate glasses of similar composition while the activation energy is higher for the molybdenum glass. The DC conduction in molybdenum phosphate glasses can be considered to be due to hopping of polarons and is consistent with the reported results of other transition metal ion phosphate glasses.

When a surface is made, ¹/₄ of an electronic state is removed at band edges for each value of the wavevector parallel to the surface. This is shown by using a mode-counting argument, and also by the matching Green function method in which the change in density of states is given in terms of surface values of the bulk and vacuum Green functions. The removal of ¹/₄ of a state at the bottom of the band, with the requirement of charge neutrality, leads to the surface phase-shift rule.

The behaviour of thermodynamical quantities near the critical points of Ising Hamiltonians with many-spin interactions is investigated. A critical analysis of the Griffiths and Wood (1974) numerical calculation is performed demonstrating that the critical behaviour of Ising systems is determined by pair rather than many-spin interactions.

Electronic absorption spectra are reported for crystals of CdCl₂ doped with Fe(II) in the ratios 1:5.5, 1:11 and 1:30. Bands in the region 20000-24000 cm^-1 are studied as a function of temperature and magnetic field. Their intensities, polarisations and concentration dependence suggest that they are due to ferromagnetically coupled in-plane pairs of Fe(II) ions and that they are allowed by the exchange-induced electric dipole mechanism.

The relative intensities and the energies of the electric dipole absorption spectra of MnCl₂.2H₂O (V-lines in the 27000 cm^-1 region) are investigated as functions of temperature with polarised light. Their magnetic field dependence is also studied both in paramagnetic and ordered state. It is confirmed from the angular dependence of Zeeman patterns in the b plane that the principal axes x', y' and z of g-values in the excited states are obtained by rotating the crystallographic axes c, a' and b by pi /4 around b(z). The preferred spin axis in the spin-flop region is also found to coincide with the a (or a') axis. The values of exchange fields in the ground and excited state are determined from the observed exchange splittings and g-values. Experimental results suggest that the observed line spectra are all magnon sidebands.

For pt.I see ibid., vol.10, no.20, p.4089 (1977). Absorption lines of MnCl₂.2H₂O corresponding to ⁶A_1g to ⁴T_2g(II) transition and their Zeeman effects are studied theoretically in the magnetically ordered phase under the ligand- and molecular-field approximation. All the lines are interpreted as magnon sidebands. The energy, polarisation, relative intensity and external field dependence show fair agreement with experiment. The principal axes x', y' and z of an orthorhombic field around Mn²⁺ in the excited state do not coincide with the crystal symmetry axes c, a', b and are rotated by pi /4 around b(z). The large and negative value of the tetragonal field around the y' axis is assumed to explain the polarisation of the lowest two Kramers doublets. To understand the small splitting of the lowest Kramers doublet (V₁, V₂) in H//y', a relatively large value for the magnitude of molecular field in the excited state mod mu _BH'_E mod has to be chosen.

For pt.II see ibid., vol.10, no.20, p.4103 (1977). The external magnetic field dependence of intensities of two absorption lines near 27000 cm^-1 of MnCl₂.2H₂O in the paramagnetic phase is studied theoretically by means of a molecular-field approximation. These lines are magnon sidebands and are considered to be the lowest two Kramers doublets of ⁴T_2g(II) state of Mn²⁺ in the cubic field. Calculations are made for two cases. In the first case, the external field H is parallel to b and the field dependence of the intensities is studied. In the second, the external field H is the b plane and angular dependence of the intensities of the two Kramers doublets with E perpendicular to b polarisation is examined. The agreement between theory and experiment is good except for the polarisation E//b in the case H//b.

A re-analysis for earlier magnetostriction measurements on dysprosium is presented. Domain effects have been corrected for using the phase theory. The re-analysed results for the temperature dependence of the magnetostriction constants and of the magnetocrystalline anisotropy energy are in reasonable agreement with theoretical predictions and the results of other experimental workers. For T to 0K it is found that lambda ^{gamma ,2}=(10.6+or-0.2)*10^-3 and K₆⁶=(-1.4+or-0.2)*10⁶ Jm^-3.

The allowed and forbidden hyperfine transitions of the S-state ion Mn²⁺ have been observed in single crystals of sodium beta -alumina. Manganese was incorporated in the beta -alumina during its synthesis. The observed spectrum is shown to arise from three overlapping spectra which are due to manganese ions occupying different sites in the spinel-like blocks. The values of g, A and D are evaluated for Mn²⁺ in each of the occupied sites. The distribution of manganese within the beta -alumina is shown to be different from that obtained during diffusion doping.

Proton reorientation tunnelling in many NH₄⁺ salts gives a frequency independent minimum in both T₁ and T_{1 rho} at the transition to classical relaxation at about 40-70K. The average tunnel frequency is approximately: f₁ approximately=4*10⁹Ti_{1( rho )min,} (Hz when T₁ or T_{1 rho} is in s). Tunnel frequencies are derived from T₁ and T_{1 rho} measurements on NH₄ClO₄, cubic and trigonal (NH₄)₂SiF₆, (NH₄)₂SnCl₆, (NH₄)₂Ce(NO₃)₆, (NH₄)₂Cr₂O₇ and literature data, and compared with tunnel frequencies calculated from barrier heights.

The Zeeman relaxation of protons in two NH₄ClO₄ samples with natural (0.015%) and 0.1% deuteron concentrations was studied at the proton resonance frequencies 18 MHz and 22 MHz in the temperature range from 4.2 to 30K. The effect of deuterons on the relaxation becomes observable below 20K and increases with decreasing temperature. The additional minima observed in the proton relaxation time below 20K are shown to be characteristic of pure NH₄ClO₄. The non-exponentiality of the relaxation bears some resemblance to the relaxation in the presence of paramagnetic impurity centres.

The results of the normal-incidence reflectivity measurements performed between 3.8 and 28 eV on tin diselenide crystals (SnSe₂) are given. The analysis of the reflectivity data according to band structure calculations and photoemission results (XPS and UPS) provides fundamental information about electron and optical properties of SnSe₂. For the interpretation of the reflectivity structures the most probable direct interband transitions are proposed.

A detailed analysis of the electronic and vibronic structure in the absorption spectrum of CdCl₂:Co²⁺ single crystals near 18800 cm^-1 is presented. Sharp features in the spectrum which have been attributed by earlier workers to pure electronic transitions are shown to be vibronic in origin and due to a local vibrational model at the Co²⁺ site. Zeeman studies in magnetic fields up to 13 T applied perpendicular and parallel to the trigonal c-axis have yielded g-values within the ²T_1g(²H) multiplet. Comparison with earlier studies of the isomorphous system CdBr₂:Co²⁺ indicates that, unlike the bromide, the wavefunctions of the trigonal-field-split Gamma ₈⁺ level in ²T_1g(²H) remain nearly pure octahedral in the chloride.

Effective charges, q, in ternary and complex systems are estimated. The semiempirical method of Suchet (1965) is extended to ternary compounds such as manganites and ferrites while the semi-experimental method of Gianturco and Coulson (1968) is applied to complex Co-Zn ferrites and cobalt complexes. An attempt is made to obtain correlation between the estimated values of q and the measured chemical shifts, Delta E. It is found that although the effective charge governs the chemical shift, its magnitude is profoundly affected by the cation distribution in spinels. A comparison of the values of q obtained from the Suchet's method with those estimated from Gianturco and Coulson's method for the same family of compounds shows good agreement.