Table of contents

The author adopts the canonical form, in which bond Hamiltonians are diagonalised first, the nearest-neighbour bond-bond coupling being the major correction. Several examples (for which a complete quantum mechanical solution can be found) are analysed, the procedures being no more difficult than for classical anharmonic dynamics.

Neutron incoherent inelastic scattering measurements on H₂O are reported. Two bands, seen at 290 meV and 360 meV had not been resolved before in a neutron scattering experiment. The width of the stretching mode is much less than in previous neutron measurements and in close agreement with optical data.

The total cross section for the scattering of acoustic phonons by a two-dimensional electron gas is sensitive to the electron temperature in the 1-10K regime where experiments are performed. The temperature dependence of the phase-space integral modifies both the size and the temperature dependence of the phonon scattering, but only explains a part of the discrepancy between theory and experiment.

Calculates the critical exponent of percolation conductivity t for two- and three-dimensional networks by using a finite-size scaling technique. In two dimensions the authors obtain t=1.264+or-0.054, in excellent agreement with the recent transfer-matrix calculation of Derrida and Vannimenus (t=1.28+or-0.03, 1982). In three dimensions the finite-size scaling technique yields t=1.87+or-0.04, in very good agreement with the available experimental data as well as the series expansion estimate of Fisch and Harris (t=1.95+or-0.03, 1977). The results lend support to the recent conjecture of Alexander and Orbach (1982) that relates t to the correlation length exponent v and the percolation probability exponent beta .

The authors have studied the angular dependence of the photoemission from surface states located around the Gamma point in the two-dimensional Brillouin zone on Ag(111) and Ag-Mn(111) random alloys. They report intensity and dispersion relations and conclude that the E_F-L₂' gap and the neck radius at the L point on the Fermi surface increase as Mn is added to Ag.

The static 360 degrees kink in a planar ferromagnet with an in-plane field becomes energetically unstable when the strength of the applied field exceeds one-third of the anisotropy field. The search for a soft dynamic eigenmode of the kink yields, however, a negative result. One finds that in the undamped chain the role of the soft eigenmode is taken over by the perturbation which carries the static kink into a neighbouring one, and the role of the soft-mode frequency is taken over by the velocity difference with respect to neighbouring kinks. When spin damping is included, one does find a soft relaxation mode: attenuation of the velocity of the neighbouring kinks gives rise to a perturbation which may be described as a superposition of the Goldstone mode and a relaxation mode. For the moving kinks a similar situation occurs, but in this case the inclusion of damping would make the kink nonstationary. It is therefore not obvious how the dynamic stability of a moving kink can be defined.

The effect of pressure up to 130 kbar on the valence state of Eu in Eu₄Bi₃ has been studied by ¹⁵¹Eu Mossbauer spectroscopy. It is shown that Eu remains divalent in the investigated pressure range.

The authors study the statistical mechanics of the two-component Coulomb lattice gas in three dimensions, with the aim of obtaining an approximate overall description of its thermodynamic properties. The method consists of the Pade extrapolation of the series expansion of the free energy in powers of kappa a, where a is the lattice parameter and kappa is the Debye screening wavevector. The authors show how to recast the usual diagrammatic expansion for the interaction free energy into a form suitable for extracting the series expansion and evaluate the terms up to order ( kappa a)⁶ for the simple cubic lattice. According to the resulting form for the free energy, the Coulomb lattice gas exhibits a liquid-vapour critical point. The position of this critical point corresponds quite closely to that predicted by Stell et al. (1976) for the restricted primitive model of ionic liquids.

A lattice dynamical model based on a potential function is used to obtain the phonon dispersion relations in various phases of KNbO₃. It is observed that the soft mode in each of the cubic, tetragonal and orthorhombic phases could be simulated by proper choice of a crucial parameter in the short-range part of the potential function. The calculated phonon dispersion relations agree reasonably well with the available experimental data from neutron scattering in the various phases.

The O-D stretching modes between 220 and 330 meV (1800-2600 cm^-1) have been observed in heavy ice in the hexagonal structure by means of coherent neutron scattering. Observation of the modes at these high energies was made possible by using the constant-Q spectrometer on the Harwell electron Linac. A simple procedure was followed to assign peaks within the same branch. No appreciable dispersion in the branches was observed within the present accuracy (+or-10 meV, +or-80 cm^-1).

A detailed procedure leading to the evaluation of the explicit anharmonic contributions to the phonon frequency shift and the linewidth to the lowest order is described for a molecular crystal. An application is then made to obtain numerical results for phonon frequency shifts and the linewidths in deuterated naphthalene. The assumptions are made that the molecules behave as rigid units and the intermolecular potential is a pairwise sum of the atom-atom potentials. Using a 6-exp potential, and the potential parameters provided by Kitaigorodski (1973), the results for all the external modes at the Gamma points (q=0) are presented and compared with the available experimental data. Keeping in view the inadequacy of many of the measured results, and the fact that there is only a fair agreement between the measured and calculated harmonic phonon frequencies with the chosen potential, the results from the calculation presented here for phonon shifts and linewidths are very encouraging. An attempt made to compare the results from the three sets of potential parameters-those of Kitaigorodski, Mackenzie et al. (1977) and Williams (1966, 1967)-reveals the superiority of Williams's parameters.

Proton mobility has been established in solid hydrazine sulphate through coulometric, conductivity, IR, DSC and TGA studies. The electrical conductivity has been measured on pressed pellets in the frequency range from 100 Hz to 100 kHz in the temperature range 300-500K. The frequency dependence of the conductivity has been explained on the basis of a 'variable-potential-barrier' model. The DC conductivity has been estimated from the complex admittance (B-G) plots. The sigma against 1/T curves show a sudden increase in conductivity at about 480K which has been attributed to a structural phase transition. A possible mechanism for proton transport has also been suggested and discussed vis-a-vis NMR studies reported in part II of this paper.

For pt.I see ibid., vol.16, no.16, p.3081 (1983). The proton mobility has been observed in hydrazine sulphate (H₂H₆SO₄) from NMR studies. The linewidth has been measured as a function of temperature. It shows a sudden line narrowing at 150K indicating that the H⁺ are mobile at temperatures higher than this. Further, a minor hump in the linewidth curve is obtained at 228K which indicates a structural change. The relaxation time measurement (T₁ and T₂) also confirms the above conclusion. From the linewidth data at different temperatures, the jump attempt frequency is estimated to be about 10¹¹ s^-1. The low attempt frequency of about 10¹¹ s^-1 is nearly the proton tunnelling frequency suggesting H⁺ motion.

Electroreflectance spectra in PbS, PbSe and PbTe are presented. Band population effects are exploited to establish the separation of bands at the L point. The separations for the three salts in order of increasing anion atomic number are found to be L(3)-L(6): 2.4, 2.1 and 1.8 eV; L(4)-L(6): 2.4, 1.9 and 1.2 eV; L(5)-L(7): 2.0, undetermined and 1.5 eV; L(5)-L(8); 3.0, undetermined and 2.0 eV. In addition, the measurements show that an earlier suggestion by the authors regarding the parity of states at the L point is incorrect. This now brings the results into agreement with the accepted picture of the lead salts and they find good agreement between their experimental results and first-principles theoretical calculations.

The absolute half widths of the excited states of the Wannier-exciton-ionised-donor complex in CdS due to their decay into free-exciton and free-hole continua are calculated. The computed half width of the 4S state of the complex is in very good agreement with the experimental value for the only observed excited state. The results strongly support the authors' earlier interpretation which rationalised the absence of the 2S and 3S states of the complex in experimental spectra in terms of the short lifetimes of these states.

The interband contribution to epsilon ₂( omega ) has been calculated for TiN and ZrN using the LCAO energy eigenvalues and eigenvectors, resulting from an LCAO fit to self-consistent APW band structures of these compounds. The k-dependence of the transition moments and lifetime broadening has been approximately taken into account. The theoretical epsilon ₂^b( omega ) curves are compared with experimental epsilon ₂^b( omega ) curves resulting from measurements of the optical constants. General agreement between theory and experiment is satisfactory, although some peaks in the theoretical curves are shifted by 0.5-1 eV to higher energies with respect to experimental findings.

The field theoretical renormalisation group method, which correctly describes the critical as well as the multicritical (at zero temperature) behaviours of the quantum mechanical d-dimensional Ising model in a transverse magnetic field, is proposed. Due to the introduction of the additional renormalisation the singularities associated with zero temperature have been removed. The crossover scaling form of the inverse correlation length and longitudinal susceptibility are considered for the following spatial dimensions d:2<d<3, d=3 and 3<d<4. For 2<d<3, d=3 and 3<d<4 the calculations are performed to the first order in 3-d and 4-d, respectively.

A simple modification of the real-space renormalisation group method is used to discuss critical behaviour of site diluted spin-¹/₂ Ising and Heisenberg ferromagnets in two and three dimensions. The critical parameters and critical exponents are evaluated, and are shown to be in good agreement with the exact results and series calculations for site-diluted Ising ferromagnets on the square and triangular lattices. Good values of the critical parameters have also been obtained for the site-diluted Heisenberg and Ising models in two and three dimensions using the Migdal-Kadanoff approximation (1976).

The magnetic phase diagram of the system ZnCr_2xGa_2-2xO₄ has been experimentally determined by using low-field DC and AC susceptibility measurements, neutron diffraction experiments and Mossbauer spectroscopy. A spin glass behaviour has been found in the concentration range 0.40<or=x<0.85; this behaviour is a result of the frustration inherent in the octahedral spinel sublattice with antiferromagnetic interactions only.

Two magneto-structural phase transitions of MnAs between three phases; ferromagnetic and undistorted phase, paramagnetic and distorted phase, paramagnetic and undistorted phase; are consistently explained by a simple model Hamiltonian without an assumption of high- and low-spin states for Mn atoms. An operator is introduced to describe the distortion of the crystal, and an exchange interaction of each Mn atom pair is expressed in terms of the operator. Thus a coupled Hamiltonian for the crystal distortion and the magnetic ordering is obtained in a molecular field approximation. It is shown from the calculated result that the three phases are realised and an anomalous temperature dependence of a paramagnetic susceptibility is explained. In the presence of an external magnetic field, this model yields a field-induced transition, which is qualitatively in agreement with experimental results. Significant features of temperature dependences of the specific heat and the lattice constant are also explained by the present calculation.

The author has measured the dependence of the photoluminescence spectrum of the isoelectronic trap AgBr:LI on the iodine concentration N in the range 4.3*10¹⁴ cm^-3<or=N<or=3.2*10¹⁹ cm^-3 and in the limit of low excitation densities. This range of concentrations corresponds to 41.1>or=r_s>or=0.97, where r_s is practically the average distance between iodine impurities measured in Bohr radii (20 AA) of the iodine bound exciton. The following characteristic quantities have been considered in detail as a function of the concentration: position and halfwidth of the zero-phonon A line, position of the B line, the intensity ratio I_B/I_A of the two components of the zero-phonon line and the ratio of the luminescence intensities at 2.38 eV (position of the iodine pair line) and at 2.51 eV (maximum of the single-iodine phonon-assisted emission). The data are explained as being due to an interaction between pairs of iodine impurities. Either one iodine impurity is excited (i.e. carries a bound exciton) and interacts with an iodine impurity in its ground state, or less frequently, both iodine impurities are excited simultaneously. Good agreement is found between the resonant energy transfer model and the experimental data. For r_s<1.4 an abrupt change in the single iodine spectrum occurs which is believed to be due to the appearance of a new phonon-assisted transition, whereby the phonon which is forbidden by symmetry in the single impurity bound exciton transitions becomes allowed due to the reduction in symmetry as a consequence of the interaction.