Table of contents

Terms responsible for Brillouin scattering in molecular crystals are derived in dipole approximation by a canonical transformation. Certain divergent series originating in the rigid infinite lattice assumption are rendered convergent once this assumption is relaxed.

The frequency against wave vector dispersion relations for the symmetry directions ( zeta 00), ( zeta zeta 0), and ( zeta zeta zeta ) in silver are computed on the basis of the lattice dynamical model of Sharma and Joshi (1963 and 1964). The calculations are in fair agreement with the experimental results of Drexel et al. (1969). obtained from neutron spectrometry.

Low-temperature series for the Ising model show a marked lattice dependence and a recent analysis by Guttmann (1969) has revealed a pattern of spurious singularities which are sensitive to the coordination number of the lattice. The present paper attempts a configurational analysis of these series. Taking account of Cayley tree configurations with proper volume exclusion, it is found that good approximations are obtained for all the singularities in zero magnetic field. The form of the singularities in a nonzero field is also discussed.

The measured peak positions of electronic absorption bands of substitutional H- ions in alkaline earth fluorides are compared with the results of a point-ion calculation.

Magnetophonon extrema are reported for the first time in the Hall coefficient. With weak electric fields and high lattice temperatures, minima are found at the resonant fields with n-type InSb and InAS but maxima are found at these fields with n-type GaAs. Under hot electron conditions at low lattice temperatures, magnetophonon peaks are also observed in the all coefficient with GaAs.

By Green function methods. The density of electronics states in the potential field of randomly distributed impurities, and a magnetic field of arbitrary strength, is calculated. Analytical and graphical results are presented for high and low densities of impurities, including a low density of hydrogenic potentials.

For pt. III, see abstr. A21890 of 1970. A new low-temperature expansion variable for the Ising model is given. Expansions in the new variable, x=1-tanh(J/kT), then converge right up to the critical point. Power series in the new variable are derived, and then analysed by the Pade method and the method of N-point fits. For the spontaneous magnetization of the Ising model in three dimensions. beta =0.312+or-0.002 for the simple cubic lattice, beta =0.3125+or-0.0015 for the body-centred cubic lattice, and beta =0.312+or-0.004 for the face-centred cubic lattice. For the low-temperature susceptibility gamma =1.30+or-0.02, gamma =1.28+or-0.04, and gamma '=1.29+or-0.04 for the simple cubic, body-centred cubic and face-centred cubic lattices respectively. For the low-temperature specific heat the authors estimate ¹/₁₆<or= alpha =0.2 for all three lattices.

The relative probability of observing an enhanced conductivity in extrinsic and intrinsic semiconductors due to the Poole-Frenkel lowering of activation energy at high electric fields is compared with the probability of the competing process of impact ionization avalanche. It is concluded that the Poole-Frenkel process is only likely to be seen in low mobility crystalline solids.

A study has been made of small-angle (1*10^-4-8*10^-3 rad) electron scattering in thin films of evaporated carbon for a series of incident electron energies (30-80 keV). The angular distribution of the electrons scattered in such films has been interpreted in terms of plural scattering of the incident electrons within the specimen film. The plural scattering calculations were based on both the free atom theory and the Bohm-Pines plasma oscillation theory. The two sets of theoretical calculations both agree with experiment to within a deviation of 20% for angles of scattering in the range 5*10^-4-5*10^-3 rad and for films thinner than about 1000AA.

For pt. I, see abstr. A48149 of 1968. A study of the temperature dependence of critical opalescence in the Bi-Ga system has been made for solutions of five different concentrations, by means of the inelastic scattering of slow neutrons. At each concentration the spectra of neutrons scattered from the solution are separable into a Q-dependent quasi-elastic region and an inelastic region largely independent of Q. The former are associated with scattering from the concentration fluctuations and the latter with the high frequency cooperative modes of the system. The inelastic regions of the spectra are largely independent of temperature and the concentration of the solution, whereas the elastic regions are sensitive to both these parameters. The critical indices eta and delta are evaluated.

The formalism is developed for determining the band-structure contributions to the first- and second-order elastic shear constants of hexagonal close-packed metals in terms of the normalized energy-wavenumber characteristic of the optimized model potential theory. A method of calculating the internal strain or inner displacement contribution to ¹/₂(c₁₁-c₁₂) is also derived, and the results show that it is significant. Two calculations have been made, one including a correction for exchange and correlation, and the other neglecting it. The fuller version for beryllium and magnesium gives. The results for zinc and cadmium appear disastrous, but detailed analysis shows that this may be rectified by modifying the normalized energy-wavenumber characteristic.

See also abstr. A11887 of 1970. The lattice dynamics of magnesium fluoride has been studied using a rigid ion model with short-range central axially symmetric forces and long-range Coulomb forces. In order to get the symmetry required by the elastic constants of the crystal it was found necessary to minimize the potential function against every structural parameter of the crystal. The elastic constants and the dispersion relations for the phonons propagating along ( zeta 00), (00 zeta ) and ( zeta zeta 0) are computed and compared with the experimental values. The wave vector dependence of the dipolar modes is discussed.

An isolated T_g ion in a lattice gives rise to a strain distribution via the Jahn-Teller effect. Two such ions in a lattice appear to have a mutual energy of interaction, owing to the Jahn-Teller coupling. The form which this takes and the resulting properties of the pair are studied using the transformation method recently introduced to deal with orbital triplets, combined with an elastic continuum description of the lattice. Two cases are considered, depending on the relative magnitudes of the spin-orbit coupling and the interaction energy. In particular it is shown that if the interaction is large compared with spin-orbit interaction the properties of a pair of ions are quite different from those of the isolated ions.

A difficulty in the present perturbative schemes for calculating correlation at metallic densities is shown to be caused by a pole in the complex-coupling-constant plane entering the unit circle at e²=-e²₀, a consequence of the bound state which occurs when the electron-electron interaction is reversed. A remedy is proposed and applied, resulting in a renormalized interaction which is spin dependent, has no divergences appearing at metallic densities, and for which an analytic expression can be found.

Using the electron tunnel technique the authors studied superconducting alloy films of SnIn in magnetic fields perpendicular to the surface. Measurements of the function f( eta ) introduced by Maki (1964 and 1965) to take account of the decreased effects of screening currents for thin films are in good general agreement with theory. Measurements of the second generalized Ginzburg-Landau parameter are compared with the theoretical predictions of Eilenberger (1967). Some disparity is found between theory and experiment, the results being in general agreement with those of French and Lowell (1968) on bulk specimens on NbMo alloys.

Electrical conductivity and Hall effect measurements have been made on a series of synthetic p-type semiconducting diamonds in the temperature range 80 to 450K. The dominant conductivity mechanism at low temperatures is shown to be impurity conduction, and effects have been isolated due both to impurity-band conduction and to hopping transport between neutral and ionized acceptor centres. The activation energies associated with the latter processes are much lower than the acceptor ionization energy, and the variation with temperature of the onset of impurity conduction as a function of the neutral acceptor concentration accounts for the wide range of activation energies reported for synthetic diamonds by previous authors.

A method has been developed for calculating the effective complex permittivity of a solid dielectric arising from the motion of charge carriers which are blocked at the electrodes. The method makes use of computer simulation of the motion of the charge carriers and is valid for high voltages. Results are given of calculations carried out for a simple model with charge carriers of only one sign mobile. Diffusion effects are neglected. The effective complex permittivity is then found to depend on only two parameters. The dielectric dispersion is found to exhibit a well-defined loss peak whose frequency can, show a strong voltage dependence.

A general expression for the nuclear magnetic resonance spin-echo signal in a ferromagnet is derived. Spin echoes stimulated from hyperfine field distributions in Co alloys are interpreted in terms of the analysis, and the observed behaviour of spin-echo shape as a function of excitation conditions is shown to be consistent with the predictions. The theoretical expression is used to obtain the conditions under which measurement of the spin-echo amplitude as a function of excitation frequency can be expected to reflect the hyperfine field distribution in a ferromagnet.

Quite large discrepancies are found when crystal field splittings are fitted to a one-particle potential V= Sigma Aⁿ_my_nm. It is suggested that the parametrization of the experimental data can be improved by introducing an additional potential which represents the two particle correlation induced by the environment. This separates the problem of describing the discrepancies from the problem of explaining them in terms of specific mechanisms. A formal development of the correlation crystal field concept is given, and suggestions are made regarding the treatment of experimental data. Some possible generalizations of this concept are also discussed.

Carbon is a common impurity, present as an acceptor, in GaP. The fundamental of the local vibrational mode of ¹²C in GaP has been identified at 606.2 cm^-1 at 20 K and the identification has been confirmed by investigating the isotope shift in ⁴C-doped crystals. An earlier tentative identification of a gap mode of As in GaP at 270.0 cm^-1 at 20 K has been confirmed.

A detailed study has been made of the variations in the structure of the blue and green edge emission of doped and undoped crystals of cadmium sulphide under Stokes and anti-Stokes excitation. A model to explain the results is proposed, in which the key feature is the state of ionization of the centre which makes the anti-Stokes excitation process possible. The model implies that this centre is the same as that which leads to the green edge emission and to deep centre luminescence during recombination.

The authors include Umklapp processes into the coupled exciton-photon (polariton) theory. Additional radiation field terms resonate at Bragg conditions but may also significantly change the character of any resonance at optical frequencies. Comprehensive treatment of the radiation field yields effective v-body intermolecular interactions which are fully retarded. The Lamb shift of the ground state is a natural consequence of the formalism. Polariton theory agrees with linear response if and only if Umklapp processes are included.

Crystallographic studies of Ba₂ NaNb₅O₁₅ have shown that the possible space groups are D⁶₂, C¹¹_2v and D¹⁹_2h. The coincidences between the infrared and Raman spectra support the conclusion, based on the ferroelectric properties of the crystal, that the space group is C¹¹_2v. The anomalous tantalum compound has a spectrum compatible with a similar structure. The vibrations are classified as internal modes of the Mo₆ octahedron (M=Nb, Ta) and lattice translations involving motion of the cation. Force constants are calculated for internal modes using the Wilson FG matrix method and for lattice modes using the Born-von Karman theory.

The study of polarized absorption spectra on the ab face of crystalline pyrene at 90K has been reported. Measurements on the a:b polarization ratio and vibrational analysis for the different absorption systems are presented. It has been found that the second absorption system could be analysed in terms of frequencies of totally symmetric vibrations, whereas many of the vibrations in the first absorption system could not be unambiguously assigned. The excimer fluorescence of crystalline pyrene has also been studied on the ab and bc' faces. From the analysis of the data it has been found that, while the major contribution to the excimer fluorescence is derived from the transition directed along the long axis of the monomer molecule, the contribution due to an out-of-plane polarized transition is not negligible.

Optical excitation of additively coloured CaF₂ crystals gives rise to population of a metastable excited ³ Sigma _u-type state of the M centre. The optical excitation spectrum of this state has been investigated. Measurement of the epr spectrum of the ³ Sigma _u state confirms a model proposed earlier by Beaumont and Hayes) for the M centre in CaF₂. The lifetime of the ³ Sigma _u state at 77K is 1.7 s. The temperature dependence of creation and of decay of the ³ Sigma _u state population has been investigated by optical and epr methods; the mechanisms of creation and decay are discussed.

The v₂ bending mode of the nitrite radical in NaNO₂ has been studied in detail at 77 and 300K. The spectrum at 77K shows four distinct bands, the most intense being the fundamental due to the mass configuration O¹⁶N¹⁴O¹⁶, and having an absorption peak at 829 cm^-1. Further bands, with shifts of -4.7 cm^-1, -10.1 cm^-1 and -19.5cm^-1 have been accurately measured, assigned to various isotopic species, and used to calculate and verify a set of force constants for this molecular system. The three shifted bands have been shown to be due to the mss configurations ¹⁶O¹⁵N¹⁶O, ¹⁷O¹⁴N¹⁶O, ¹⁸O¹⁴N¹⁶O, respectively. A harmonic force field potential function has been used which shows excellent agreement with results.

Results are presented of a study of x-ray and electron excited luminescence in all alkali halides in the temperature range 4K to 300K. Details are given of the spectral distribution and lifetimes associated with the luminescence bands at about 5K. The lifetime and peak intensities of some bands have been measured as a function of temperature giving parameters characterizing quenching processes. These parameters confirm that many luminescence transitions are nearly forbidden and that the quenching process involves internal radiationless transitions.

It is shown that the point-charge model used by Bates and Stevens (1969) to explain the main features of the epr linewidth transitions and low-temperature entropy anomalies in hexammine nickel halides also predicts critical behaviour at temperatures T_c which depend on the halide. The critical behaviour arises from ordering of NH₃ tetrahedra due to nearest-neighbour electrostatic interactions between point charges assigned to the protons of neighbouring (Ni(NH₃)₆)²⁺ clusters. The minimum free energy of the crystal is computed as a function of temperature and the critical behaviour is clearly demonstrated.

The theory of the V³⁺ ion in MgO is developed using a model which takes into account Jahn-Teller effects and tetragonal distortions in the cubic ground state ³T_1g. Reasonable numerical assumptions using published data lead to values of the various parameters which are consistent with recently published acoustic parametric resonance results. The Ham reduction factor is deduced to be approximately 0.15 and the energy level diagram for the low-lying states of the V³⁺ ion is obtained.