Table of contents

A local description of stable 2D random packing of equal discs maximising the randomness is given. The authors neglect all correlation due to non-local geometrical effects thus arriving at a mean-field-like treatment of the problem. Bounds for the mean coordination of each disc are derived and shown to be incompatible with earlier results obtained by Williams (1985).

The measurement of the thermal diffusivity D_T of the glassy Ge₂₀Te₈₀ alloy obtained by rapid quenching from the melt was carried out using a ruby laser flash technique. A glass-supercooled-liquid transition was manifested by a lambda -form in D_T, as the alloy was heated from room temperature to around 200 degrees C. Thus the thermal and hydrodynamic evidence of the transition was observed, for the first time, for the amorphous semiconducting and metallic materials within a narrow temperature range around the glass transition temperature. The crystalline-to-amorphous phase transformation in the Ge-Te alloy gave rise to an abrupt fall in D_T for the semiconducting Ge₂₀Te₈₀ glass (i.e., 2.0*10^-3 approximately 5.5*10^-3 cm² s^-1), which is very small compared to that (around 1.5*10^-2 cm² s^-1) for the crystalline Te+GeTe mixture. Since D_T in the first approximation is proportional to the electron mean free path, it may become short and the conduction process can be regarded as strong scattering of electrons in the glass. The production of the metastable crystalline solid in the equilibrium phase consisting of the crystalline Te and GeTe solids was confirmed by the sharp Bragg-type maxima observed in the X-ray scattering from the Ge₂₀Te₈₀ glass heated above the crystallisation temperature and by the experimental data on D_T for the same sample.

The authors study the behaviour of the scaling stiffness coefficient in the vicinity of the spin-glass-paramagnet phase transition. They derive a novel generalisation of the Widom scaling relation for the vanishing of the scaling stiffness coefficient at the critical point. The scaling stiffness coefficient is a useful equilibrium parameter that distinguishes between the spin glass and paramagnetic phases. It can further be used for defining a stiffness coherence length that may play the role of a correlation length for spin glasses.

It is argued that a charge introduced (either as an impurity or a quasi-particle) into a two-dimensional conductor exhibiting a quantised Hall conductance can be screened only if an additional local magnetic field generated by local currents produced by the charge is included. Furthermore, screening cannot occur if the conductor is a thin inversion layer, but it will occur if it is a three-dimensional system (e.g., a layered compound).

The selection rule in the quantum Hall effect is derived from the generalised spin statistics connection. For a two-dimensional fermion system, a necessary condition to have the quantum Hall effect at a filling factor v=p/q (p and q are mutual primes) is exp(ipq pi )=exp(ip² pi ); hence q must be an odd integer. For a two-dimensional boson system, a necessary condition to have the quantum Hall effect at v=p/q is exp(ipq pi )=1, hence a filling factor v with both odd p and q is excluded from the quantum Hall effect, but other filling factors are possible candidates.

The authors low-temperature data for variable-range-hopping conductivity in lightly doped, compensated n-InP gives: sigma = sigma ₀ exp(-(T₀/T)^s) with 0.21<s<0.28. This indicates that the corresponding Mott law for this conductivity mechanism, now established for two-dimensional structures is also an adequate description for three-dimensional systems.

Intercalated iron in nontronite is found to increase the magnetic ordering temperature of the iron in the 2:1 layers considerably. The effect is explained by a magnetic bridging between iron atoms in the layers by the intercalated iron.

Recent developments in the theory of spin glasses due to the discovery of the hierarchical structure of different degrees of freedom are used for the construction of Ising spin memory models. A new learning algorithm is proposed. This algorithm permits one to construct an 'ordered' spin glass and therefore to memorise an exponential number of hierarchically ordered images.

The dynamics of the trimethyloxosulphonium (TMOS) ion is studied in the three solid phases of TMOS-iodide, (CH₃)₃SOI, using both the time-of-flight and back-scattering incoherent quasi-elastic neutron scattering (IQNS) over the temperature range 120-373K. It is shown that, on the 10^-10-10^-12 s timescale accessible to the experiment, the molecular motions consist of 120 degrees C jumps of the methyl groups about their respective threefold axes. Conversely, whole-cation reorientations were found to be too slow to produce any quasi-elastic broadening, as predicted from NMR. The strongly intramolecular nature of the potential acting on methyl groups is clearly shown by the absence of discontinuity in the temperature evolution of the related correlation time which is found to follow the unique Arrhenius law: tau _M(s)=(1.05*10^-12) exp( Delta H_M/RT) with barrier height Delta H_M equal to 10.6 kJ mol^-1.

The annealing behaviour of defects produced in KI by gamma -irradiation at 198K has been studied by optical absorption and Raman scattering techniques. During isochronal annealing, the major optical absorption features, the F band and the double-peaked V band decay at 338K in unison with the 113 cm^-1 Raman peak attributed to I₃^- interstitial halogen complexes. This identifies the I₃^- complexes as the major centres complementary to the F centres and responsible for the V band. Isothermal and isochronal annealing studies indicate second-order kinetics for the 338K stage and an activation energy of 1.4 eV. The other substantial Raman feature observed at 173 cm^-1 and attributed to I_n^- (n=5 . . .) halogen complexes is shown to decay at 378K, but is not obviously correlated with any optical absorption feature. It is suggested that these defects are associated with interstitial dislocation loops on their precursors.

The dependence of ultrasound attenuation and velocity on magnetic field was measured in bismuth-antimony alloys containing from 0 to 12.8% of antimony. The field was parallel or perpendicular to the trigonal axis of the sample. The quantum oscillations appear in semimetallic samples. The changes of attenuation in semiconducting samples are due to the transition to the metallic state.

The complementary variation principle is used to obtain sequences of lower and upper bounds on the phonon thermal conductivity. In comparison with previous work the present analysis has the advantage that the two parts of the collision operator are taken to be non-commutative. The convergence of the sequences of lower and upper bounds as well as the best way of decomposing the collision operator in each case are explored in a more rigorous and general manner than has been done hitherto.

For pt.II see ibid., vol.18, p.3191 (1985). Using a Bethe-lattice approach the differential conductivity is calculated numerically on the basis of the tight-binding model of parts I and II of this series. Both hopping and tunnelling contributions to the transport are obtained within a small-polaron picture, treated to lowest order in the electron-phonon coupling. The results agree qualitatively and nearly quantitatively with the analytical theory of I, based on a mode-coupling approximation. In contrast to the latter no ad hoc assumption about the density of states has to be made, leading to a consistent phase diagram in the static limit.

The authors present a numerical analysis of the Stark-Wannier states in finite Kronig-Penney crystals extended to the complex field plane. Exponential stability in the infinite crystal limit for any fixed complex field value f is verified. The energies E_n.j(f) of such states are all connected through sequences of couples of branch points of the Bender-Wu type approaching symmetrically the real axis. On the other hand, near f=0 in the complex directions they have a smooth behaviour and it is possible to compute the first terms of the asymptotic power series.

The behaviours of the memory function determined from an integral equation and of the chemical potential lead to the quantised Hall effect in two dimensions.

In the coherent-state representation the quantum mechanical calculation of thermomagnetic current fluctuations in a non-degenerate semiconductor is done by the introduction of an effective Hamiltonian. The results obtained are applicable to the study of noise in electron instruments.

The fluctuating valence state of Sm₃Se₄ has been investigated by measurements of ultrasonic dispersion and AC conductivity. A pronounced frequency dependence of the elastic constants and ultrasonic attenuation near 120K is observed, which is caused by the thermally activated hopping of 4f electrons. The AC resistivity also shows marked frequency and temperature dependences, which are governed by the 4f hopping conduction and the thermally assisted quantum mechanical tunnelling among the localised states in the randomly distributed potentials. The 4f hopping rate determined by the present experiments has the activation-type temperature dependence, tau = tau ₀ exp(E₀/kT), where tau ₀=2.4*10^-13 s and the activation energy is E₀=0.14 eV.

By using the TDPAC technique the authors were able to detect the structural changes suffered by the InSe compound when submitted to a switching process. this was done by measuring the thermal dependence of the nuclear quadrupole frequencies in both electric states of the sample. In the off state, one of the frequencies remains constant through the whole temperature range. The other, instead, follows a linear dependence up to 80K and then the well known T^3/2 relationship. In the on state only one frequency appears, which has a linear dependence with temperature.

The dynamics of quantum systems subject to dissipation is a subject of fundamental importance which has recently been of great interest due to its relation to macroscopic quantum phenomena, In particular the behaviour of the magnetic flux trapped in a SQUID is an example of this. The authors derive the quantum mechanical analogue of the Fokker-Planck equation which describes such systems. The major difference between the quantum and classical Fokker-Planck equations arises from the presence of a quantum mechanical memory term.

The authors study some ground-state properties and the thermodynamics of the fully frustrated simple cubic lattice with classical XY and Heisenberg spins. Using an algorithm which minimises local energies, we find twelve ground-state periodic spin configurations for the XY case, while the degeneracy is probably infinite for the Heisenberg case. The groundstate energy is found to be equal to - square root 3J for both cases, with the same local-field strength for all spins, making the sublattices thermodynamically equivalent in contrast to the Ising case. Various physical quantities are calculated using a Monte Carlo technique. The results show a second-order phase transition in both the XY and Heisenberg cases. Critical exponents are calculated and a crossover is observed.

The AC susceptibility and the low-field magnetisation measurements on the disordered spinel system Zn_xCo_1-xFeCrO₄ (x=0.0, 0.2, 0.4, 0.5, 0.8) are reported. The X-ray analysis shows that the lattice parameter shows a minimum at x=0.5, indicating a redistribution of the cations in the A and B sites on introduction of Zn²⁺. The low-field AC susceptibility and DC magnesidation indicate two transitions for x=0.0 and 0.2 while only one for x>or=0.4. The high-temperature peak in chi corresponds to a ferrimagnetic transition at T_N. The magnetic phase below the lower-temperature peak at T_f could be considered as that of clusters of spins randomly frozen. This state is characterised by strong irreversibility in low DC fields, rapid decay of remanence on increasing the temperature and saturation in rather low applied magnetic fields. For T_f<T<T_N the ferrimagnetic state observed for x<<0.4 is unstable. For larger x, short-range order exists for T>>T_f. For T_f<T<2T_f the interacting groups of spins could be considered to be in a liquid-like state, from which they freeze into random directions at T_f. A suggestive phase diagram is also discussed.

A microscopic drop of a polar liquid in equilibrium with its vapour has been simulated. The Stockmayer potential, Lennard-Jones plus point dipole, gives the simplest realistic polar liquid. The static dielectric constant as a function of radius, epsilon (R),, is evaluated and corresponds quite well to a tanh, or Fermi, function of the radius with a mean position, R_epsilon , and a width, D_epsilon , similar to the values, R_h, and D, for the density profile but displaced by a fraction of a molecular diameter towards the liquid. there appears to be no satisfactory theory for this dielectric profile (which must be the same for a plane surface) at present available.

A model of resonant Raman scattering of molecules weakly adsorbed at semiconductor surfaces is resolved exactly. Full spatial dispersion and polaronic effects due to the vibration-electron coupling are embodied in the theory. Well known previous results are recovered when the coupling between the interatomic vibration and the excited electron of the molecule tends to zero. The role of polaronic effects in the resonant Raman response is also discussed.

The authors report here high-resolution infrared measurements at 1.7K on KI single crystals doped with NO₂^- ions. At very low concentrations of approximately 10¹⁷ NO₂^- ions cm^-3, they have observed a multiplet structure with the antisymmetric stretching vibration nu ₃ of the NO₂^- ion arising due to tunnelling motion of the ion among the twelve equilibrium potential wells in the KI lattice. At relatively higher concentrations of the NO₂^- impurities (10^-19 ions cm^-3), several extra sharp and distinct bands have been observed in the region of the antisymmetric stretching vibration of the NO₂^- ions in KI at 1.7K. This structure has been interpreted in terms of mutual interaction effects between the transition dipole moments during the nu ₃ vibrations of the nearby nitrite ions in pairs and triplet clusters. Several ion pairs and triplet clusters were considered and their vibrational spectrum has been calculated using a model of coupled harmonic oscillators. From these studies, the authors have obtained the magnitude of the transition dipole moment mu _i=0.248 D during the nu ₃ vibration of the NO₂^- ion doped in KI.