Table of contents

We study a system of one-dimensional t-J models coupled to a ladder system. A special choice of the interaction between neighbouring rungs leads to an integrable model with supersymmetry, which is broken by the presence of rung interactions. We analyse the spectrum of low-lying excitations and the ground-state phase diagram at zero temperature.

In this work we show how to calculate the equilibrium and non-equilibrium charge fluctuations in a gated normal mesoscopic conductor which is attached to one normal lead and one superconducting lead. We then consider an example where the structure is placed in a high magnetic field, such that the transport is dominated by edge states. We calculate the equilibrium and non-equilibrium charge fluctuations in the gate, for a single edge state, comparing our results to those for the same system, but with two normal leads. We then consider the specific example of a quantum point contact and calculate the charge fluctuations in the gate for more than one edge state.

Recent measurements of the atomic structure of supercooled liquid B, Ni, Si and Zr show a short-range structure similar to that of the nucleating crystalline phases. As the liquids are supercooled, the coordination numbers and interatomic distances increase, decrease or remain essentially constant to approach the values characteristic of the crystals that nucleate from the liquid. Further support for the present observations comes from prior results on Ga, Ge and Pd. This observed correlation between supercooled liquid and crystalline structures provides new insight into nucleation phenomena. The trends in the experimental results and the relationship between the short-range structural properties of supercooled elemental liquids and their crystalline counterparts are discussed.

A fundamental modification is considered of the well-known Fredrickson-Andersen (FA) n-spin facilitated kinetic Ising model for studying the glass transition in supercooled liquids, in which the up spins correspond to a liquid-like state A and the down states to a solid-like state B. In our general model, which we call the n-spin cluster facilitated kinetic Ising model, a spin can flip from one state to the other (i.e. is facilitated) only if in the cluster containing the spin and those adjacent to it there are at least n up spins. Thus, in contrast to the FA model, it is easier for an up spin to flip than for one in the down state, which is the physically reasonable motivation for considering this class of models and leads to very different properties. In this communication, we consider the simplest case, namely n = 1, for which both a qualitative analysis and computer simulations show that as the temperature of the system decreases, the fraction f_A of spins in state A when the system is in a metastable steady state decreases until it reaches zero at a critical temperature T_c, and the mean relaxation time of the system's memory function increases rapidly as T_c is approached.

This special section of Journal of Physics: Condensed Matter contains papers that were presented during a workshop held in Lyon (France) at CECAM (Centre Européen de Calcul Atomique et Moléculaire), 28 - 30 June 1999. The meeting brought together scientists with computational, theoretical, and experimental interests and expertise in the field of effective interactions and phase transitions in colloidal suspensions. Attended by about 30 participants from 11 countries, the workshop comprised 22 talks accompanied by intensive discussions. In recent years colloidal suspensions have been a focus of growing cross-disciplinary attention from the condensed matter physics, physical chemistry, and chemical engineering communities. The unprecedented tunability of interparticle interactions, a correspondingly rich and unusual display of thermodynamic phases, and deep analogies with atomic condensed matter systems have fueled intense scientific inquiry. Recent advances in theoretical, computational, and experimental methods have helped to illuminate the basic nature of microscopic interactions and their influence on macroscopic phenomena. Significant progress has been achieved especially in the area of thermodynamic phase transitions. Theoretical approaches such as density-functional theory and thermodynamic perturbation theory, combined with a variety of simulation techniques, have yielded important insights particularly into first-order phase transitions and the stability of ordered phases. Experimental developments such as total internal reflection microscopy have greatly improved the quantitative analysis of the effective interactions. Charge-stabilized colloids and colloids mixed with adsorbed and non-adsorbing polymers were a particular focus of the meeting. The statistical method of obtaining effective interactions between colloidal particles is to integrate out the microscopic degrees of freedom of particles such as counter-ions, co-ions, and polymers. Although the formal methods are similar, the results are quite different for charged colloids and colloid-polymer mixtures, giving rise to a diversity of phase transition scenarios. The present volume highlights and summarizes some important recent developments in this field. The workshop organizers wish to thank the contributing authors and to acknowledge generous support from CECAM and from the ESF-Programme SIMU (Challenges in Molecular Simulations: bridging the length and time scale gap). Last but not least, they thank the CECAM director, Professor M Mareschal, for his hospitality, and Ms E Crespeau for her excellent local organization.

H Löwen (Universität Düsseldorf, Germany) A R Denton (Acadia University, Canada) J K G Dhont (University of Utrecht, The Netherlands)

We calculate phase diagrams of low-salt suspensions of charged colloidal particles using a recently proposed effective one-component Hamiltonian for the colloids (van Roij R, Dijkstra M and Hansen J-P 1999 Phys. Rev. E 59 2010). This Hamiltonian consists of the purely repulsive pairwise Derjaguin, Landau, Verwey, and Overbeek (DLVO) potential and density-dependent volume terms. The latter play a crucial role in driving phase transitions at salt concentrations of the order of 10 µM or lower. We find phase diagrams that exhibit gas-liquid coexistence with upper and lower critical points, and, for sufficiently large surface charge densities, upper and lower gas-liquid-solid triple points. A connection between the Debye-Hückel theory for simple electrolytes and the DLVO theory for colloidal suspensions is made.

Charge-stabilized colloidal suspensions can be conveniently described by formally reducing the macroion-microion mixture to an equivalent one-component system of pseudo-particles. Within this scheme, the utility of a linear response approximation for deriving effective interparticle interactions has been demonstrated (Grimson M J and Silbert M 1991 Mol. Phys.74 397). Here the response approach is extended to suspensions of finite-sized macroions and used to derive explicit expressions for (1) an effective electrostatic pair interaction between pseudo-macroions and (2) an associated volume energy that contributes to the total free energy. The derivation recovers precisely the form of the DLVO (Derjaguin, Landau, Verwey, and Overbeek) screened Coulomb effective pair interaction for spherical macroions and makes manifest the important influence of the volume energy on thermodynamic properties of deionized suspensions. Excluded-volume corrections are implicitly incorporated through a natural modification of the inverse screening length. By including the nonlinear response of counterions to macroions, the theory may be generalized to systematically investigate effective many-body interactions.

Depletion forces in colloidal systems are known to be entirely attractive, as long as the background of macromolecules is small enough that an ideal gas approach is valid. At higher densities, however, structural correlation effects of the macromolecules which lead to additional repulsive parts in the depletion interaction, have to be taken into account. We have measured the depletion interaction between a single polystyrene sphere and a wall in the presence of non-ionic polymer coils. Although the polymer volume fraction is very small, our results clearly show the existence of repulsive parts, leading to a large over-estimation of correlation effects in a hard sphere liquid. The possible explanation of this discrepancy by additionally considering the role of van der Waals forces is discussed.

We study the phase behaviour and structure of model colloid-polymer mixtures. By integrating out the degrees of freedom of the non-adsorbing ideal polymer coils, we derive a formal expression for the effective one-component Hamiltonian of the colloids. Using the two-body (Asakura-Oosawa pair potential) approximation to this effective Hamiltonian in computer simulations, we determine the phase behaviour for size ratios q = _p/_c = 0.1, 0.4, 0.6, and 0.8, where _c and _p denote the diameters of the colloids and the polymer coils, respectively. For large q, we find both a fluid-solid and a stable fluid-fluid transition. However, the latter becomes metastable with respect to a broad fluid-solid transition for q0.4. For q = 0.1 there is a metastable isostructural solid-solid transition which is likely to become stable for smaller values of q. We compare the phase diagrams obtained from simulation with those of perturbation theory using the same effective one-component Hamiltonian and with the results of the free-volume approach. Although both theories capture the main features of the topologies of the phase diagrams, neither provides an accurate description of the simulation results. Using simulation and the Percus-Yevick approximation we determine the radial distribution function g(r) and the structure factor S(k) of the effective one-component system along the fluid-solid and fluid-fluid phase boundaries. At state-points on the fluid-solid boundary corresponding to high colloid packing fractions (packing fractions equal to or larger than that at the triple point), the value of S(k) at its first maximum is close to the value 2.85 given by the Hansen-Verlet freezing criterion. However, at lower colloid packing fractions freezing occurs when the maximum value is much lower than 2.85. Close to the critical point of the fluid-fluid transition we find Ornstein-Zernike behaviour and at very dilute colloid concentrations S(k) exhibits pronounced small-angle scattering which reflects the growth of clusters of the colloids. We compare the phase behaviour of this model with that found in studies of additive binary hard-sphere mixtures.

In this article we introduce depletion in asymmetric mixtures within the context of density functional theory. As in the definition of the interaction potentials, it is convenient to work in a semi-grand ensemble at constant chemical potential of the small particles. The free-energy functional can then be mapped onto that of a one-component effective fluid. This method is applied to the fluid of parallel hard cubes, which is studied in the limit of infinite asymmetry. The phase behaviour of this fluid is shown and discussed in terms of the general phase behaviour of additive mixtures of hard particles.

Sterically stabilized colloidal dispersions, such as PMMA, have long been regarded as archetypal realizations of hard spheres and hard-sphere mixtures. Indeed, this is precisely what is found in studies of these systems as a function of the volume fraction, at constant temperature. However, a much richer behaviour - which goes beyond what is expected from just hard spheres - is found as a function of both volume fraction and temperature T. For instance, sterically stabilized colloids are known to exhibit both upper (high-T) and lower (low-T) two-phase behaviour, such that the former is temperature sensitive but the latter is not.

We review model calculations based on a double Yukawa potential that exhibits some of the rich phase behaviour found experimentally, and predicting other behaviour which has not yet been found by experiment. Both the former and latter show a degree of similarity to the phase behaviour of polymer solutions. We also present preliminary results for the phase behaviour of bidisperse model sterically stabilized colloids.

In this paper, we explore the similar behaviour of the Yukawa and power law systems at crystallization. This is done within the context of our density functional theory model, the modified weighted density approximation with a static solid reference state. Some issues we probe include the stable solid crystalline structure at equilibrium, the fractional change in density upon crystallization, the Lindemann ratio of the equilibrium solid and the magnitude of the first peak of the structure factor at freezing. We find many similarities between these two classes of potentials. We also compare our findings with computer simulation and experimental results. While the theoretical and simulation results in general agree, there exists some discrepancies between these results for the Yukawa system and the experimental findings for colloidal suspensions.

We have reinvestigated the structural and thermodynamic properties of the square-well and the square-shoulder system using two different theoretical frameworks, i.e., the optimized random-phase approximation and the Rogers-Young integral equation. We discuss the limits of applicability of the respective concepts and compare the results with `exact' Monte Carlo simulation results and with data obtained from a semi-analytic method proposed by Nezbeda for narrow wells. Using these correlation functions, we study in the framework of the modified-weighted-density approximation the isostructural solid-solid transition predicted for narrow wells and narrow shoulders.

We develop a density functional theory for a system of penetrable spheres that interact with a constant pair potential energy if their separation distance is smaller than their diameter. As sufficient input, just the geometrical properties of the particles and the exactly known statistical behaviour of the system under strong confinement are needed. The theory predicts the bulk fluid properties in good agreement with computer simulations and better than liquid integral theories, as well as the freezing transition to a multiply occupied face-centred-cubic lattice. It becomes exact in the limits of strong confinement and high temperature, and coincides with a successful hard-sphere theory for zero temperature.

The idealized mode-coupling theory (MCT) is applied to colloidal systems interacting via short-range attractive interactions of Yukawa form. At low temperatures, MCT predicts a slowing down of the local dynamics and ergodicity-breaking transitions. The non-ergodicity transitions share many features with the colloidal gel transition, and are proposed to be the source of gelation in colloidal systems. Previous calculations of the phase diagram are complemented with additional data for shorter ranges of the attractive interaction, showing that the path of the non-ergodicity transition line is then unimpeded by the gas-liquid critical curve at low temperatures. Particular attention is given to the critical non-ergodicity parameters; this is motivated by recent experimental measurements. An asymptotic model is developed, valid for dilute systems of spheres interacting via strong short-range attractions, and is shown to capture all aspects of the low-temperature MCT non-ergodicity transitions.

The nature of anisotropic fluctuation modes in an ordered system is analysed using general symmetry arguments. It is shown that the anisotropic fluctuation modes in a periodic phase can be classified using a wave vector within the irreducible Brillouin zone and a band index. The spatial profiles of the fluctuation modes are described by Bloch functions. These general features enable a study of the stability and kinetic pathway of complex ordered polymeric structures to be carried out. The utility of the theory is illustrated using the Landau-Brazovskii theory of weak crystallization.

Fe-Co-based amorphous alloys were studied by x-ray diffraction and anomalous x-ray diffraction methods for a range of sample compositions and preparation methods. The main structural characteristics at short- and medium-range scales were investigated. The presence of chemical ordering with preferred Co-Co and Fe-Fe homonuclear correlations and partial Fe-rich phase separation, suggested from previous extended x-ray absorption fine-structure experiments, were clearly in evidence.

First-principles molecular dynamics simulations of liquid selenium for three different densities at the temperatures 1770 and 1870 K are presented. Whereas the densities for 1770 K have been chosen to correspond to pressures at which recent x-ray diffraction experiments were performed, the densities for 1870 K are related to pressures close to the critical point in the p-T phase diagram. For the lower temperature, close agreement with the most recent x-ray data is found in structure factors and pair distribution functions. For the higher temperature, the structure factors get large at low wavelengths close to the critical point. This indicates a highly compressible liquid as would be expected within the critical regime.

The change in topology with increasing temperature of liquid GeSe₂ was studied by using neutron diffraction to measure the Bhatia-Thornton number-number partial structure factor, S_NN(Q), where Q is the scattering vector. As the temperature is raised from 800 to 1100 °C there is a broadening but little other change in the peaks describing the local coordination environment. There is, however, a collapse of the intermediate range atomic ordering of the network associated with the Ge-Ge correlations as manifest by a substantial reduction in the height of the first sharp diffraction peak and a shift in its position from 0.99(1) to 1.05(1) Å^-1. The changes in the structure with increasing temperature mimic those observed as the composition of liquid GeSe₂ is changed to the GeSe stoichiometry by the addition of germanium. The significance of the results for recent Car-Parinello type ab-initio molecular dynamics simulations is briefly discussed.

We have measured, using the pulsed neutron source ISIS, the total neutron cross section of liquid para-hydrogen in the vicinity of the triple point. The experimental results compare only qualitatively with the results of the Young and Koppel theory. However, a much better agreement is found once modifications are included in the model which effectively take into account the intermolecular interactions.

Liquid selenium undergoes a phase transition towards a metallic phase when sufficient pressure is applied. We performed an x-ray diffraction experiment at the ID30 beamline of the ESRF at the wavelength of 0.149 Å to investigate the local order of the metallic liquid. The diffraction pattern of liquid Se has been recorded with the large-volume Paris-Edinburgh cell between (20 °C, 3 GPa) and (1650 °C, 4.1 GPa). The local order of the metallic liquid selenium is found to be close to that of liquid tellurium. In particular, the coordination number Z increases with temperature from 2.6 to 3.0.

A model based on the existence of two different competing local structures in water is described. It is shown that it can explain the transition between fragile and strong behaviour that supercooled water undergoes at around 220 K. The high-temperature behaviour is similar to that observed in standard fragile glass formers. The strong behaviour at low temperatures is associated with the existence of a remanent configurational entropy arising from the possibility of locally choosing between the two possible environments.

The melting-freezing phase transition of gallium confined within Vycor glass was studied by NMR, resistance and acoustic techniques. A single although broadened ⁷¹Ga NMR line corresponding to melted gallium was observed in contrast to lineshapes found until now for liquid gallium in porous matrices. A difference between results obtained using the three methods was explained by formation of various confined solid gallium modifications. A depression of the freezing and melting phase transition temperatures and a pronounced hysteresis in the melting-freezing processes were found and are discussed. Heterogeneous nucleation was suggested to explain the dependence of crystallization on temperatures of pre-warming. Irreversible melting was observed for the second gallium modification.

Physical properties of the ideal Bose gas with non-integer dimensions between D = 2 and D = 3 are theoretically investigated. Calculation shows that there exists a hierarchy of condensation transitions with changing fractional dimensionality. The results obtained on the specific heat and the condensed density in non-integer dimensions are similar to those for liquid helium-4 in porous media. This results suggest that the geometrical factor may be important for the physical properties of liquid helium-4 in porous media.

We examine the transverse and longitudinal components of the drag force upon a straight vortex line due to the scattering of liquid ⁴He excitations. For this purpose, we consider a recently proposed Hamiltonian that describes the dissipative motion of a vortex, giving an explicit expression for the vortex-quasiparticle interaction. The dissipative coefficients involved are obtained in terms of the reservoir correlation function. Most of our explicit calculations are concerned with the range of temperatures below 0.4 K, for which the reservoir is composed of phonon quasiparticle excitations. We also discuss some important implications for the determination of possible scattering processes leading to dissipation, on the basis of the values of the vortex mass found in the literature.

Dielectric measurements have been performed on a series of samples consisting of poly-(acrylonitrile) (PAN) mixed with the plasticizers ethylene carbonate (EC) and propylene carbonate (PC) in various proportions. The spectra obtained show characteristic features such as a linear ln() variation, a horizontal inflection point and double minima, which are predicted within the A₄-scenario of the mode-coupling theory. We find very good agreement with the theoretical results in the relevant frequency range. The experimental spectra are found to satisfy a scaling behaviour, and the resulting master curves are in good agreement with the theoretical predictions.

Dielectric measurements of an epoxy resin, N, N-diglycidyl-4-glycidyloxyaniline, have been carried out in the supercooled and glassy phase over a broad frequency range (10²-6 ×10⁹ Hz). The measurements reveal electrical transport due to ionic impurities as well as three different dipolar relaxations - in addition to the - and -relaxation, a slower ´-relaxation is recognized, whose loss peak is disclosed after subtraction of the dc conductivity contribution. The glass transition is found to affect markedly the secondary relaxation, whose strength and shape parameters change across T_g. The major inference from the results concerns the existence of a transition in the dynamics, occurring some tens of degrees above T_g, in the vicinity of the temperature T_S where the peaks of the - and -relaxations merge. Evidence in favour of such a transition is given by: (i) the change in the temperature dependence of the -relaxation time; (ii) independently, the change in the temperature dependence of the dc conductivity; (iii) the breakdown of the Debye-Stokes-Einstein model, replaced at lower temperatures by a fractional regime.

Concerning the ´-process, it shows a Vogel-Fulcher behaviour with the same temperature T₀ as the -relaxation but, unlike this last, it is not involved in a splitting phenomenon with the -relaxation. Several hypotheses concerning the nature of the ´-process are explored.

The electrical resistivity, , was measured for the melt of a typical III-V semiconductor system, Ga-Sb, by the direct-current four-probe method. Similarly to the case for solid substitutional alloys, the Nordheim rule almost establishes the concentration dependence of . That is, a rather parabolic form of was obtained as a function of composition; is the deviation of the resistivity from the linear law relating the resistivities of the pure components, liquid Ga and liquid Sb. In spite of this rather simple behaviour of the concentration dependence of itself, its temperature coefficient, d/dT, shows a clear minimum at the eutectic composition and even a negative temperature coefficient was observed near the eutectic point. This negative d/dT may be the first indication for the existence of particular hidden structure, related to concentration fluctuations, in the liquid near the eutectic point. In addition, this strange behaviour of d/dT was discussed on the basis of the effective-medium theory.

We extend the spectral theory used for the calculation of the effective linear response functions of composites to the case of a polycrystalline material with uniaxially anisotropic microscopic symmetry. As an application, we combine these results with a non-linear decoupling approximation as modified by Ma and co-workers, to calculate the third-order non-linear optical susceptibility of a uniaxial polycrystal, assuming that the effective dielectric function of the polycrystal can be calculated within the effective-medium approximation.

The temperature and time dependences of the density of molten indium antimonide are measured by using an improved Archimedean technique, in which a single-bob probe with two equivalent arms is applied. In the measurement, the influence of the surface tension of the melts and the buoyancy of the protecting gas can be eliminated. The accuracy of the measured density is about 0.05%. The temperature dependence of the density shows a negative linear tendency in the range from 780 K to 960 K, and the coefficient of temperature dependence of the density -d/dT is 6.542 × 10^-1 kg m^-3 K^-1. The density is 6.582 × 10³ kg m^-3 at the melting point. The volumetric thermal expansion coefficient of the melt increases linearly upon heating. The time dependence of the density shows that the liquid InSb is quite stable at a temperature just a little above the melting point and at higher temperatures, and that the transition from the lower-coordination-number state to the higher-coordination-number state will be completed at exactly the moment when the transition from the solid state to liquid state is entirely complete.

In the Al-Pd-Ru system, a structurally ordered icosahedral phase has been successfully produced near the composition Al₇₃Pd₁₅Ru₁₂ by heat treatment at 1273 K for several hours. The x-ray diffraction patterns of the Al-Pd-Ru i-phase are very sharp, indicating that the i-phase is quite stable and that samples of high structural quality are attainable by appropriate heat treatment in this system. Prolonged annealing at 1273 K, however, results in phase transformation into the 1/0 cubic approximant (a = 1.5 nm). Also, we found the formation of a 2/1 cubic approximant phase (a = 2.0 nm) near the composition Al₇₁Pd₁₉Ru₁₀ when samples were annealed at 1173 K for one hour.

The temperature dependence of the resistivity of the i-phase is significantly large and the resistivity ratio R (R = _{12 K}/_{300 K}) reaches as high as 2.5, comparing well to that seen in the ordered Al-Cu-Ru i-phase. The resistivity and its temperature dependence for the 2/1 approximant phase are quite similar to those for the i-phase, exhibiting a large resistivity ratio R~1.6, in contrast with the metallic behaviour of the 1/0 cubic approximant phase. These results indicate that the characteristic length which determines the temperature dependence of the resistivity is somewhere between 1.5 and 2.0 nm and suggest that the long-range quasiperiodicity beyond the length scale is of less significance as far as the electrical properties are concerned.

The potential wells seen by hydrogen in several interstitial sites in the C-15 Laves phase compounds, ZrTi₂ (ZT), ZrCr₂ (ZC) and TiCr_1.85 (TC), have been investigated using incoherent inelastic neutron scattering (IINS) data. Parameters describing the harmonic terms in the H-potential well in the three compounds are obtained from the first localized hydrogen vibrations as measured by the IINS technique. The H-potential well is created by the sum of the pairwise potentials between the hydrogen and the four metallic atoms forming the different types of tetrahedral site which are labelled g (A₂B₂), e (AB₃) or b (B₄) in the C-15 structure. A Born-Mayer potential has been used to model these pairwise interactions, with parameters determined from the IINS. The resulting overall potential energy surface describes well the observed site occupancies and the diffusional behaviour of H in the ZC and TC compounds. On the other hand, due to the higher H content of the ZT sample, H-H interactions have to be included in the model for a proper description of the energy potential well in this compound. The potential energy surface enables us to identify the different diffusion paths of H in the C-15 structure and hence to infer the different time scales of H diffusion (localized and long-range diffusion) that have recently been shown to exist in these compounds (Skripov A V et al 1996 J. Phys.: Condens. Matter8 L319-24; 1997 J. Alloys Compounds253/254 432-4).

In this paper, an isothermal three-parameter equation of state (EOS) of solid is presented in the form V/V₀ = f(P). The proposed EOS uses three parameters expressible in terms of B₀, B´₀ and B´´₀, denoting bulk modulus and its first and second pressure derivatives at zero pressure. The new EOS is applied to the isotherms of ionic, metallic, quantum and rare-gas solid, with pressures ranging from zero to variable maximum pressures of up to 1 TPa ( = 10 Mbar). The fits are uniformly excellent, and equally excellent is the agreement of the fitted parameters B₀ and B´₀ with experimental values. Deviations between data points and fits are computed and compared with the successful EOSs of similar form from the literature, and the drastic superiority of our new model is demonstrated. Further, the proposed model is applied to the isotherms of metals at ultrahigh pressures, with B₀ and B´₀ constrained to experimental values. An inter-comparison of results obtained from different EOSs, including the universal formulations, shows that our new form yields a superior fit.

Nuclear magnetic resonance measurements of the proton spin-lattice relaxation rate in C15-type HfMo₂H_0.4 have been performed over the temperature range 20-420 K and the resonance frequency range 13-90 MHz. The temperature dependence of the relaxation rate is found to exhibit two peaks. This is consistent with a coexistence of two types of H hopping with different frequency scales. The experimental results are analysed to evaluate the parameters of hydrogen motion and the electronic (Korringa) contribution to the relaxation rate. Our results support the idea that the ratio of the characteristic frequencies of the two types of H motion in C15 compounds AB₂ is related to the ratio of the metallic radii of elements A and B.

The long-range and short-range motion of lithium ions into an electrochemically intercalated Li_3xLa_2/3-xTiO₃ (LLTO) sintered pellet has been studied by ac impedance spectroscopy and ⁷Li solid state nuclear magnetic resonance (NMR). The temperature dependence of the dc conductivity and the intercalation ratio dependence of the chemical shift, the relative intensity of the resonance line, the spin-lattice and the spin-spin relaxation times of ⁷Li NMR experiments are indicative of polaron formation at the initial stage of intercalation. The total dc conductivity measured in the temperature range 45-600 K and the shape of the impedance diagrams show that after intercalation the conductivity is both ionic and electronic in nature. However for temperatures lower than 300 K the total conductivity is mainly dominated by the electronic one and for temperatures higher than 400 K the total conductivity is dominated by the ionic one. Moreover at low temperatures, when electronic conductivity dominates, the temperature dependence of the conductivity agrees well with a polaron model for conduction in these intercalated oxides.

The NMR experiments clearly show that the resonance peak decreases strongly as intercalation occurs. This is explained by a coupling between the electronic and the Li⁺ nuclear spins leading to an unobservability of some Li⁺ nuclei in NMR. The other Li⁺ nuclei, which do not interact directly with the electronic spins, are responsible for the observed NMR signal. If the static effect of the intercalation is weak and leads to a very small chemical shift variation, variable temperature ⁷Li NMR spin-lattice and spin-spin relaxation measurements show that the presence of electrons acts essentially on the dynamics of the Li⁺ nuclei through the lattice modification induced by the polaron formation. At the beginning of the intercalation the inverse of the relaxation time T₁ of the observed Li⁺ nuclei decreases by one order of magnitude. At the same time the linewidth of the resonance peak (1/T₂) decreases abruptly. The motion of the lithium ions is sharply enhanced. For further intercalation, 1/T₁ decreases and the linewidth of the central peak increases indicating that the variations of the relaxation times are mostly governed by the variations of the spectral densities of the Li⁺ motion. Consequently, the lithium motion decreases gradually as intercalation proceeds. These results are in good agreement with a lattice modification due to polaron formation during intercalation.

We investigated the magnetic properties of the following approximants of quasicrystals in the Al(Si)-Pd-Mn system: two cubic compounds, 1/1-Al₆₈Pd₁₁Mn₁₄Si₇ and 2/1-Al₇₀Pd₂₄Mn₆, and three orthorhombic compounds ´-Al_71.9Pd_23.5Mn_4.6, T-Al_73.1Pd_5.2Mn_21.7, and T-Al_78.5Pd_4.9Mn_16.6. No magnetic Mn atoms are present in the 2/1 and ´ phases or in the Mn-poor T phase. In contrast, a fraction of the Mn atoms carry magnetic moments in the Mn-rich T phase in which a spin-glass transition occurs at 14 K, and in the 1/1 phase in which a ferromagnetic transition occurs at 8.8 K. The crystallographic sites responsible for the magnetism were identified from spin-polarized band-structure calculations; this allows us to discuss the origin of magnetism in both approximant and quasicrystal structures.

A first-principles pseudopotential study of neutral self-interstitial defects in silicon is reported, together with calculations for Pandey's concerted exchange mechanism for self-diffusion. The energies and structures of the fully relaxed hexagonal, tetrahedral, split-110, `caged' (Clark S J and Ackland G J 1997 Phys. Rev. B 56 47), split-100, and bond-centred interstitials are calculated using supercells with up to 128 + 1 atoms. We present results obtained using the local density approximation (LDA) and the PW91 generalized gradient approximation (GGA) for the exchange-correlation energy. Both the LDA and PW91-GGA functionals give the hexagonal and split-110 defects as the lowest-energy self-interstitials. The hexagonal and split-110 defects are essentially degenerate in energy with formation energies of about 3.3 eV (LDA) and 3.80 eV (PW91-GGA). Energy barriers are studied by calculating saddle-point structures using a simple `ridge-walking' method. The energy barrier for a diffusive jump between the hexagonal and split-110 interstitial sites is calculated to be 0.15 eV (LDA) and 0.20 eV (PW91-GGA) and the barrier between neighbouring hexagonal sites is 0.03 eV (LDA) and 0.18 eV (PW91-GGA), but we have not found a low-energy path between split-110 interstitial sites. The results suggest that self-interstitial diffusion in silicon occurs via diffusive jumps between the hexagonal sites and between hexagonal and split-110 defects.

For the case of finite lifetime broadening the standard Kubo formula for the optical conductivity tensor is rederived in terms of Green's functions by using contour integrations, whereby finite temperatures are accounted for by using the Fermi-Dirac distribution function. For zero lifetime broadening, the present formalism is related to expressions well known in the literature. Numerical aspects of how to calculate the corresponding contour integrals are also outlined.

We report measurements of the temperature (40 K T 200 K) and polarization (z(yy)x,z(xz)x) dependence of the integrated intensities of quasi-elastically scattered laser light ( = 514.5 nm) in a wavenumber interval of 0±3 cm^-1 around the Rayleigh line at the different phase transitions in single crystals of BCCD. Large anomalies (central peaks) are observed at the transitions into the ferroelectric, the various commensurate (c,c´), and the incommensurate phases. The widths of the anomalies on the temperature scale are large in the regions of quasi-harmonic modulation of the structure, but narrow and distinct in the region of square-wave modulation in the solitonic phase of BCCD, where also unusual shapes on the T-axis are observed. The scattering phenomena at low temperatures are interpreted hypothetically as due to fluctuations caused by the formation or rearrangement of domain walls (solitons) in the lattice near the transitions between commensurate phases and by the variation in soliton density. The cc´ transitions are of the order-disorder type.

The potential of a one-dimensional lateral superlattice screened by two-dimensional electron gas located in close proximity is found. The periodic potential created by the superlattice affects the kinetic and optical properties of the electron system. The magnetoreflectance, Faraday rotation angle and ellipticity of the reflected electromagnetic field are calculated.

We study the ground state of the model Hamiltonian of the trimerized S = 1/2 quantum Heisenberg chain Cu₃Cl₆(H₂O)₂2H₈C₄SO₂ in which a non-magnetic ground state was observed recently. This model consists of stacked trimers and has three kinds of coupling constant describing the couplings between spins: the intra-trimer coupling constant J₁ and the inter-trimer coupling constants J₂ and J₃. All of these constants are assumed to be antiferromagnetic. By use of an analytical method and physical considerations, we show that there are three phases on the ₂ - ₃ plane (₂J₂ / J₁, ₃J₃ / J₁): the dimer phase, the spin-fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists an excitation gap between the twofold-degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in Cu₃Cl₆(H₂O)₂·2H₈C₄SO₂. We also obtain the phase diagram on the ₂ - ₃ plane from the numerical diagonalization data for finite systems by use of the Lanczos algorithm.

Electron spin-resonance (ESR) spectra of Cr³⁺ ions in LiSr_xCa_1-xAlF₆ crystals with x = 0, 0.5, 0.8, and 1 have been measured at X-band microwave frequencies in the temperature range 1.3-300 K. The intense ESR lines from Cr³⁺ ions in these crystals have been fitted to a trigonal spin Hamiltonian to determine values of the g-tensor (g,g) and zero-field splitting, 2D. The principal g-values (gg1.974) are almost the same in all cases whereas 2D increases sequentially for x = 0, 0.5, 0.8, and 1. The value of |2D| for Cr³⁺:LiCaAlF₆ decreases gradually as the temperature is increased from 1.3 K to 300 K. Over this same temperature range the value of |2D| for Cr³⁺:LiSrAlF₆ increases. The ESR spectra for Cr³⁺ in LiSr_0.5Ca_0.5AlF₆ and LiSr_0.8Ca_0.2AlF₆ are inhomogeneously broadened by discrete centres with pseudo-trigonal symmetry, different configurations of which correspond to the random occupation of the second-nearest-neighbour cation sites by Ca²⁺ and Sr²⁺ ions.

Previously a many-body coherent potential approximation (CPA) was used to study the double-exchange (DE) model with quantum local spins S, both for S = 1/2 and for general S in the paramagnetic state. This approximation, exact in the atomic limit, was considered to be a many-body extension of Kubo's one-electron dynamical CPA for the DE model. We now extend our CPA treatment to the case of general S and spin polarization. We show that Kubo's one-electron CPA is always recovered in the empty-band limit and that our CPA is equivalent to dynamical mean-field theory in the classical spin limit. We then solve our CPA equations self-consistently to obtain the static magnetic susceptibility in the strong-coupling limit. As in the case of the CPA for the Hubbard model, we find unphysical behaviour in at half-filling and no magnetic transition for any finite S. We identify the reason for this failure of our approximation and propose a modification which gives the correct Curie-law behaviour of at half-filling and a transition to ferromagnetism for all S.

The calculation of the low-damping Kramers escape rate (in the context of magnetic relaxation of single-domain ferromagnetic particles i.e. superparamagnetism) for non-axially-symmetric potentials of the magneto-crystalline anisotropy (which is of importance in view of recent experiments on the superparamagnetic relaxation time of individual small ferromagnetic particles) is considered in detail (in view of the intricate mathematical manipulations which are required) using the uniform expansion of the transition rate method proposed by Matkowsky et al (1984 J. Stat. Phys.35 443) which has been adapted to spins by Klik and Gunther (1990 J. Stat. Phys.60 473). The results agree with those of Klik and Gunther (up to a factor of 2) and with later calculations of the escape rate using the original Kramers energy diffusion method.

A novel method for analysing complex ⁵⁷Fe Mössbauer spectra has been successfully applied to nanostructured Fe_86-xCu₁Nb_xB₁₃ (x = 5, 7). This method provides an objective model describing the measured spectra. This model consists of the largest meaningful number of lines, given by the `quality' of the measured spectrum, i.e. by the criterion that all line parameters should be well defined. Using this method the temperature dependence of the mean hyperfine fields and the fractions of Fe atoms in different sites of the FeCuNbB samples are derived in the temperature range from 300 K to 700 K. In contrast to conventional methods for determining the hyperfine field distributions in magnetic alloys this approach allows us to evaluate the resulting hyperfine field distributions with indication of their mean-square deviations. The analysis results in detailed information about the iron nanograins, the amorphous residual phase and the so-called interface zone.

A tetragonal phase with a = 9.778 Å and c = 11.516 Å is formed in the Nd_0.33(Fe_0.75Al_0.25)_0.67 alloy after melt spinning and short period annealing at 873 K. The tetragonal phase is probably metastable and transforms slowly into the stable -Nd₃Fe_7-xAl_x phase during heat treatment at 873 K. This phase is antiferromagnetic with a Néel temperature of 260±5 K. Metamagnetism is observed at a temperature of 140 K or below. The magnetic properties have been characterized using a vibrating sample magnetometer and Mössbauer spectroscopy. Magneto-resistivity of up to 7.2% is accompanied by metamagnetism. At room temperature, 1% of the magneto-resistivity is measured in the paramagnetic state.

The earlier-described master equation approach to the configurational kinetics of non-equilibrium alloys is used to study kinetic features of `multivariant' orderings for which more than two types of ordered domain are possible. To this end we make extensive simulations of various phase transformations involving D0₃-type orderings for a number of alloy models. The microscopic structure of various antiphase boundaries in the D0₃ phase is also studied. A consistent approach to describing the effect of elastic forces on microstructural evolution is outlined and used to study the kinetics of a multivariant ordering accompanied by alloy decomposition. Our simulations reveal a number of peculiar kinetic features of multivariant orderings, many of them agreeing well with experimental observations.

The earlier-described master equation approach to configurational kinetics of non-equilibrium alloys is applied to study L1₂-type orderings in FCC alloys. We describe the kinetic tetrahedron cluster-field method which generalizes a similar method used for equilibrium systems to the case of non-equilibrium alloys. The method developed is used to simulate A1 L1₂ and A1 A1+L1₂ transformations after a quench of an alloy from the disordered A1 phase to the single-phase L1₂ state or the two-phase A1+L1₂ state for a number of alloy models with both short-range and long-range interactions. Simulations of the A1 L1₂ transition show a sharp dependence of the microstructural evolution on the type of interaction, and particularly on the interaction range. The simulations also reveal a number of peculiar features in both the transient microstructures and the transformation kinetics, many of them agreeing well with experimental observations. Microstructural evolution under A1 A1+L1₂ transition was found to be less sensitive to the type of the finite-range (`chemical') interaction, while in the presence of elastic interaction this evolution shows a number of specific features which were earlier discussed phenomenologically by Khachaturyan and co-workers and are illustrated by our simulations. We also consider the problem of the occurrence of a transient congruent ordering under A1 A1+L1₂ transformation and discuss the microstructural features of this stage.