Table of contents

Persistent non-linear oscillations-breathers-are studied in a dimerised one-dimensional electron phonon system as a function of an alternating on-site potential +or- alpha . Dimerisation is present if alpha < Delta _O, where 2 Delta _O is the electronic gap in the ground state. The authors show the existence of breathers in the adiabatic limit by both analytic expansions and numerical dynamics. For alpha >or=0.3 Delta _O however, the breathers become progressively unstable towards pattern doubling. Semi-classical quantisation also shows an instability at alpha <or approximately=0.75. Delta _O. Electron-hole excitations form a kink-anti-kink pair for all alpha < Delta _O, and are accompanied by a breather when alpha <or approximately=0.2 Delta _O.

The behavior of non interacting electrons is studied in two-dimensional disordered systems under a perpendicular magnetic field. The strong-field limit is examined, in which scattering between Landau bands may be neglected. It is shown that the form of the two-particle spectral function is severely restricted by a general inequality for certain eigenfunction correlations, together with the requirements of average translational and rotational invariance. Consequences are: there cannot exist bands of extended states (in the diffusion sense) with finite energy width; and either the exponent nu <or=¹/₂ (which has been predicted previously, but violates the Harris condition) or the exponent eta >O (which would be new in two-dimensional localisation).

The band-to-band impact ionisation rate has been found in ZnS from measurements of the multiplication of the photocurrent in Schottky diodes. The ionisation coefficient varies with field approximately as alpha _O exp(-b/E) with b approximately=1.3*10⁷ V cm^-1.

The two-particle bound states spectrum in generalised quantum 1D ferromagnets is studied in detail. It is shown that the behaviour inherent in integrable models with S>or=1 is realised on a whole surface in a space of Hamiltonian's parameters.

The positive muon is a unique microscopic probe. When it is implanted in condensed matter, the evolution of its spin polarisation may be readily monitored to give information on the crystallographic or molecular sites it occupies, the local fields it experiences and the time dependence of these fields. This article describes the experimental techniques in current use, and the manner in which the muon behaviour is characterised. The implications for solid state and chemical physics are discussed. The comparison between muon and proton behaviour in similar circumstances is emphasised. For chemical aspects, the equivalent comparison is between muonium and hydrogen, with muonium considered as a radioactive light isotope. Examples of studies are reviewed for magnetic materials, for metals and metal hydrides, for semiconductors and ionic crystals, and for certain organic materials and liquids. Novel information is obtained on topics including spin dynamics, dynamic correlations and critical phenomena, the localisation and quantum mobility of light interstitial particles, charge screening, the local electronic structure of hydrogen-like defect centres, hyperfine interactions, various kinetic and dynamic isotope effects and the role of vibrational effects, including zero-point motion, in determining molecular structure. Comparisons are drawn with studies by other techniques, notably magnetic resonance. Techniques and applications appropriate to pulsed muon sources are considered. The major achievements to date and the potential for future developments and new science are identified.

A theory of electron scattering by longitudinal plasmons in binary metallic super-lattices is considered. The theory is based on the dispersive hydrodynamic jellium model applied to both superlattice components. This allows a straightforward derivation of the dispersion relation and permits the quantisation of the superlattice longitudinal plasmon field. For application to electron energy-loss spectroscopy (EELS) the coupling of this field to electrons is taken as the canonically transformed interaction Hamiltonian which readily incorporates the effects of the finite screening lengths of the superlattice metallic components. For a typical metallic superlattice the cross section as a function of energy loss is derived, and is shown to predict a number of scattering peaks corresponding to zone-folded longitudinal plasmons due to the superlattice macroscopic periodicity. It is suggested here that an experiment employing conventional EELS techniques should reveal this folding of longitudinal plasmons in metallic superlattices.

The authors extend the model of phase III biphenyl (introduced by Heine and Price in 1985), based on enmeshed rotation of phenyl rings of neighbouring molecules, by including an intramolecular potential in the form of a double well: V_intra=¹/₂AQ²+¹/₄BQ⁴ where Q is the twist of one ring. Within this model, they study both the transition to the incommensurate phase and the possibility that this may be biphenyl's ground state as some experiments have indicated. They build up a coherent picture of biphenyl which includes the following physical properties: (i) the possibility of lack of lock-in as T to O; (ii) squaring up of the modulation as T drops below T_c; (iii) an optimal twist angle for the molecule in the solid (5.1 degrees ) that is lower than that in the vapour phase (21 degrees ); and (iv) the temperature of a notional I-III transition (which should be very close to the temperature of the actual I-II transition). This picture agrees both qualitatively and quantitatively with experimental results.

The authors discuss in detail the incommensurate phase II of biphenyl, in which the modulation vector is not along one major direction of the reciprocal lattice. This double incommensurateness is due to the interplay of the molecules' twists, translations and librations. They calculate the intermolecular interactions by computer modelling and analyse their implications. Calculations are carried out to demonstrate that this model explains the double incommensurateness. Furthermore they clarify the ambiguity concerning the structure of the modulation in phase II, and prove that it must be 'stripe'-like rather than 'quilt'-like. The implications of this result for the transition between phases II and III are discussed.

The influence of pressure on the phase transitions in biphenyl is discussed in detail. It is shown that a simple model, containing a harmonic intermolecular as well as a double-well-shaped intramolecular potential, can account for the experimentally observed phase transitions and their temperature dependence. The vanishing of the phase transition I-II at higher pressure and the transition temperature T_I-II at atmospheric pressure are used to give an estimate of the parameters of the intramolecular potential. These two estimates will prove to be sufficient to explain all the characteristic features of the phase transitions. Furthermore it is shown that the incommensurate phase III in biphenyl at low pressure must be metastable but there is a higher-pressure range in which the stable structure at zero temperature is incommensurate, presumably the phase II as observed. Finally the dependence of the transition temperatures from phase I to II and from phase II to III on pressure is calculated and the results compared with experiment.

A model is set up for the description of the chemisorption of a CO molecule on specifically Ni, Pd and Pt surfaces. This is based on the molecular 2 pi * and 5 sigma levels lying within the metal bands, the former above the Fermi level and the latter well below. Broadening of the former into a virtual bound state which can overlap the Fermi level then leads to a situation in which it is demonstrated that one can obtain strong indirect interactions between CO molecules. The amplitude and the phase of the long-range oscillatory form B cos(2K_Fr+Q)/r⁵ for separation r between the CO molecules are thereby estimated. The results of this model are then compared with an analysis made of thermal desorption as a function of coverage for CO on Pt. Immediately the strong scattering situation predicted by the above model is revealed, with a phase shift of between pi /4 and pi /2 and a large amplitude B.

The lithiated spinels Li_yMg(Yb₂)X₄, X=S or Se and y approximately=0.8, have been compared with the parent spinels via the following physical measurements: electron paramagnetic resonance. AC and DC electrical conductivity, high-pressure electrical conductivity and magnetic susceptibility. The lithiated compounds are shown to be of mixed valence with a partially occupied Yb³⁺/²⁺:4f^13/14 redox couple located well below the bottom of the Yb 5d conduction band. In contrast to intermediate-valence compounds, these mixed-valence compounds behave magnetically as their non lithiated analogues Mg(Yb₂)X₄, but with a dilution of the magnetic Yb³⁺:4f¹³ ion due to transfer of one electron per lithium ion to the host to create diamagnetic Yb²⁺:4f¹⁴ ions. The small-polaron motional enthalpy is Delta H_m<or=0.23 eV in Li_yMg(Yb₂)S₄ and Delta H_m<or=0.14 eV in Li_yMg(Yb₂)Se.

The energy of a one-dimensional domain wall (Bloch or Neel) at low and high temperatures is calculated approximately for the application of an external magnetic field along the hard direction. Following Aharoni (1966), Bulaevskii and Ginzburg (1964), the wall is found to vanish at a critical field value h=h_c, the wall energy varying as (h_c-h)³2/. At high temperatures, in an applied magnetic field h which tends to zero, the magnetisation profile of the wall is calculated as a function of T-T* (where T*<T_c is the temperature for the transition to a linear wall). The susceptibility is shown numerically to diverge as (T-T*)^-1. This agrees with Lajzerowicz and Niez (1976) who argue that the linear transition should be of a second order.