Table of contents

We study the strain-induced morphological instability at the submonolayer coverage stage of heteroepitaxial growth on a vicinal substrate with regularly spaced steps. We study the regime in which diffusion along the film edge is the dominant mechanism of transport of matter. We perform a linear stability analysis and determine for which conditions of coverage a flat front is unstable and for which conditions it is stable. We discuss the effect of step energy. Our results predict that when the thin film covers less than one-half of the terraces the flat front is unstable. For very small coverage, the front will spontaneously break into a regular array of islands. We obtain expressions for the aspect ratio, the size and the spacing of the islands forming this array. This opens the possibility of inducing the spontaneous formation of an array of two-dimensional quantum structures with the desired size and spacing by controlling the cutting angle of the vicinal surface and the fraction of the surface covered by the material.

Irradiation of 3.5 GeV Xe ions was performed at room temperature on Czochralski-grown (CZ) and floating zone Si(100) single crystals with different fluences 1.0×10¹² and 1.0×10¹³ Xe cm^-2. All the irradiated samples were investigated by infrared spectroscopy at room temperature. For the first time, vacancy-oxygen (VO) complexes were found experimentally in CZ-Si during high-energy heavy ion irradiation. A depth profile of the IR spectra, the distribution of VO concentration and the interstitial oxygen were successfully obtained along the irradiation depth. The concentration of VO and interstitial oxygen were quantitatively analysed. The effects of electronic excitation and nuclear collision upon the VO production are also discussed in this letter.

A new method, metal vapour vacuum arc ion source implantation, has been developed to synthesize Er-doped Si-rich SiO_x thin films under relatively low implanted ion energies and very high doses. An Er concentration as high as ~10²¹ atoms cm^-3 in the Si oxide layer can be reached. Reflection high-energy electron diffraction and cross section transmission electron microscopic observations show that the excess Si atoms in the SiO₂ matrix cluster and crystallize gradually into nano-size grains with an average size of 4.5 nm during the rapid thermal annealing process after dual-implantation. The sample emits a 1.54 µm wavelength luminescence signal, the intensity of which decreases by only a factor of two as the measuring temperature increases from 77 K to 300 K, showing very weak temperature quenching.

The Bethe-Salpeter equation for two-dimensional excitons in the presence of a strong external constant magnetic field is solved in the lowest-Landau-level approximation. It is shown that the constant magnetic field leads to the generation of an energy gap in the exciton spectrum.

Many materials containing colloids or polymers are polydisperse: they comprise particles with properties (such as particle diameter, charge, or polymer chain length) that depend continuously on one or several parameters. This review focuses on the theoretical prediction of phase equilibria in polydisperse systems; the presence of an effectively infinite number of distinguishable particle species makes this a highly non-trivial task. I first describe qualitatively some of the novel features of polydisperse phase behaviour, and outline a theoretical framework within which they can be explored. Current techniques for predicting polydisperse phase equilibria are then reviewed. I also discuss applications to some simple model systems including homopolymers and random copolymers, spherical colloids and colloid-polymer mixtures, and liquid crystals formed from rod- and plate-like colloidal particles; the results surveyed give an idea of the rich phenomenology of polydisperse phase behaviour. Extensions to the study of polydispersity effects on interfacial behaviour and phase separation kinetics are outlined briefly.

On the basis of the lattice-gas Hubbard model, which is the extension of the original Hubbard model for a crystal to the lattice-gas system, the thermodynamic properties of expanded alkali fluids are investigated to clarify how electron correlation, which causes the metal-non-metal transition in these fluids, influences their thermodynamic behaviours near the critical point of the liquid-vapour (LV) transition, and especially at the transition itself. The thermodynamic potential is calculated in a self-consistent combination of approximations: the molecular-field approximation for treating random atomic arrangements and the single-site coherent-potential approximation due to Yonezawa and Watabe for dealing with electron correlation. The results calculated for the equation of state are analysed in detail and it is pointed out that the peculiar behaviour of the LV transition observed for fluid caesium could be caused by the effects of electron correlation.

Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble. However, as recent work shows, although its extension to the canonical ensemble (CE) is not straightforward, work in nanopore systems could certainly benefit from a mesoscopic DFT in the CE. The stumbling block is the fixed N constraint which is responsible for the failure in proving the interchangeability of density profiles and external potentials as independent variables. Here we prove that, if in the CE the correlation functions are stripped of their asymptotic behaviour (which is not in the form of a properly irreducible n-body function), the HKSM theorem can be extended to the CE. In proving that, we generate new hierarchies of N-modified distribution and correlation functions with the same formal structure that the more conventional ones have (but with the proper irreducible n-body behaviour) and show that, if they are employed, either a modified external field or the density profiles can indistinctly be used as independent variables. We also write down the N-modified free energy functional and prove that the thermodynamic potential is minimized by the equilibrium values of the new hierarchy, completing in this way the extension of the HKSM theorem to the CE.

An explanation is proposed for a non-unique dependence of the dynamic contact angle on the wetting speed observed experimentally for some liquid-solid systems at low wetting speeds. The key idea is that the flow pattern near the wetting line, which follows from previously developed theory, suggests the possibility of a microscopic mass flux from the three-phase-interaction zone into the bulk thus causing `imperfect rolling' of the spreading liquid. The resultant `starvation' of the liquid-solid interface gives rise to a higher value of the contact angle. The above flow pattern turns into the regular one at a certain wetting speed thus determining the region where the metastable regimes of wetting can be observed.

Recently the study of liquid drainage through foams has generated considerable experimental and theoretical research. This research has usually made the assumptions that the liquid content is very low and that the viscous resistance is limited to occurring within either the Plateau borders or vertices.

This paper presents a foam drainage model that not only describes the low-liquid-content extreme, but also takes account of liquid content effects. These include the increase in the foam volume with increasing liquid content and the increase in the liquid flowrate in the Plateau borders over the average flowrate brought about by the presence of vertices. The relative importance of the Plateau borders and vertices to viscous loss within the foam is also made dependent on the liquid content of the foam.

This model is verified experimentally for two surfactant types and various bubble sizes using a standard forced drainage system.

We relate the frequency of the scissors mode to the moment of inertia of a trapped Bose gas at finite temperature in a semi-classical approximation. We apply these theoretical results to the data obtained in our previous study of the properties of the scissors mode of a trapped Bose-Einstein condensate of ⁸⁷Rb atoms as a function of the temperature. The frequency shifts that we measured show quenching of the moment of inertia of the Bose gas at temperatures below the transition temperature - the system has a lower moment of inertia than that of a rigid body with the same mass distribution, because of superfluidity.

Large-scale copper nanowires have been fabricated by potentiostatic electrochemical deposition (ECD) of copper sulphate solution within the nanochannels of porous anodic alumina templates. Scanning electron microscopy, transmission electron microscopy, selected-area electron diffraction and x-ray diffraction techniques were used to characterize the copper nanowires obtained. It is found that the individual copper nanowires are dense and continuous, with uniform diameters (60 nm) along the entire lengths of the wires (30 µm). The single-crystal and polycrystal copper nanowires can be prepared by choosing suitable applied potentials in the copper ECD processes. Moreover, the formation of copper oxides in nanochannels is also discussed in detail. The investigation results reveal that a lower overpotential is necessary to fabricate copper nanowires with fine crystalline structures by the potentiostatic ECD technique.

A Cu/ZrW₂O₈ metal matrix composite was thermally cycled between 298 and 591 K while being subjected to x-ray diffraction in transmission using high-intensity synchrotron radiation. The reversible allotropic phase transformations of ZrW₂O₈ between its two low-pressure phases and its high-pressure phase were observed within the composite bulk as a function of temperature. This observation gives experimental proof of the existence of the reversible pressure-induced phase transformation, which had been inferred indirectly from dilatometry in a previous investigation and assigned to the large thermal mismatch stresses in the composite. The volume fraction of each ZrW₂O₈ compound was determined from the measured diffracted intensity, and the thermal expansion behaviour of the composite was then calculated. Good agreement was found with the experimental dilatometric curve reported in a recent investigation.

The structures of tungsten trioxide, WO₃, have been studied in fine temperature steps, from room temperature to 1000 °C, by means of very high-resolution neutron powder diffraction. It was confirmed that the sample used was single-phase monoclinic in space group P2₁/n at room temperature. In addition to this monoclinic structure, the structures observed were an orthorhombic structure in Pbcn from about 350 to 720 °C, another monoclinic structure in P2₁/c from about 720 to 800 °C, a tetragonal structure in space group P4/ncc from 800 to 900 °C, and above 900 °C a second tetragonal structure in P4/nmm. The transformation from the Pbcn orthorhombic to the P2₁/c monoclinic structure was certainly discontinuous, and indeed just above 720 °C two-phase mixtures were observed. The other transitions were continuous or nearly so, all three being apparently tricritical in nature. The sequence of phases, and nature (continuous or otherwise) of the transitions between them, can be well understood by reference to the results from a group theoretical analysis.

Crystal structures of binary alloys of Sn with In, Hg and Ga were studied under pressure with diamond-anvil cells and energy-dispersive diffraction of synchrotron radiation. The ambient-pressure simple hexagonal (sh) phase in In-Sn alloys becomes unstable under pressure above 13 GPa and decomposes into the mixture of two phases: the body-centred tetragonal (bct) phase and hexagonal close-packed (hcp) phase with compositions ~15 and ~25 at.% In, respectively. The hcp/bct phase boundary shifts towards Sn with increasing pressure. A similar behaviour was found for the sh phase in Hg-Sn alloys, where the hcp phase occurs at higher pressure. Another bct phase with an axial ratio similar to that in In occurs under pressure in the Hg-Sn alloy system at the composition ~50/50.

A sh phase was also found in the Ga-Sn alloy system near 80 at.% Sn at pressures above 11 GPa after heating to 150 °C, showing a similarity to the ambient-pressure sh phases in In-Sn and Hg-Sn alloys.

Structural sequences of phases in binary alloys are discussed with respect to the valence electron concentration of the alloys, taking into account the results of the present and previous structural high-pressure studies on Sn-based and related alloys.

The compound In₅Bi₃ decomposes at pressure 15 GPa and temperature 150 °C into two phases of different compositions. Each phase represents a tetragonal distortion of the body-centred cubic phase, one with axial ratio c/a>1 and the other with c/a<1. These phases follow the Bain path - a tetragonal distortion of the cubic structure on the way from face-centred cubic to body-centred cubic, observed for tetragonal phases of In and Sn alloys as a function of composition (or electron concentration) at ambient and high pressure. Ambient-pressure stoichiometic compounds in the In-Bi alloy system are replaced under pressure by a sequence of metallic random phases with the structure determined by the electron concentration.

In order to find out more about the suppression of ferromagnetic (FM) interactions in Sr_1-xLa_xRuO₃, electronic structures and magnetic properties have been investigated upon changing x from 0.0 to 0.5, using an XRD method with Rietveld analysis, a SQUID magnetometer and a DV-Xα computational method. In comparison with magnetic properties in Sr_1-xCa_xRuO₃, FM interactions in Sr_1-xLa_xRuO₃ are found to be suppressed very rapidly against x. Neither structural distortion nor cation-size disorder can account for such rapid suppression. Instead, this may be attributed to the effect of La-O hybridization created by La substitution for Sr. This hybridization effect weakens the FM order around Ru ions and, as a result, the long-range FM states are suppressed even if x is small. The DV-Xα cluster method was employed to estimate the energy difference between the up and down spin density of states in SrRuO₃ and Sr_0.5La_0.5RuO₃. This calculation predicts that Sr_1-xLa_xRuO₃ contains La-O hybridization which suppresses FM interaction even at small x.

We present numerical renormalization group (NRG) calculations for a single-impurity Anderson model with a linear coupling to a local phonon mode. We calculate dynamical response functions, spectral densities, dynamic charge and spin susceptibilities. Being non-perturbative, the NRG is applicable for all parameter regimes. Our calculations cover both weak and strong electron-phonon coupling for zero and finite electron-electron interaction. We interpret the high- and low-energy features and compare our results to atomic limit calculations and perturbation theory. In certain restricted parameter regimes for strong electron-phonon coupling, a soft phonon mode develops inducing a very narrow resonance at the Fermi level.

This work investigates the effect of hydrostatic pressure on the excitation and emission spectra, as well as on the lifetime, of Al₂O₃:Ti³⁺ at room temperature. The aim is to establish correlations between the pressure-induced band shifts and the corresponding local structural changes undergone by the TiO₆ complex. A blue-shift of 8.52 and 6.86 cm^-1 kbar^-1 was found for the lower (E₁) and upper (E₂) energy components of the excitation band at 17760 and 20500 cm^-1, respectively, and blue-shifts of 5.93 and 5.40 cm^-1 kbar^-1 for the two overlapping bands of the emission spectrum located at 12680 and 14210 cm^-1. We explain these results on the basis of a reduction of the TiO₆ Jahn-Teller distortion upon increasing the pressure. In contrast, the increase of the overall Stokes shift, which is mainly associated with electron-vibration coupling to the totally symmetric a_1g vibration, is explained by the increase of the excited-state stabilization energy, S_a1gℏω_a1g, with increasing pressure.

The luminescence lifetime is also found to be pressure dependent, varying from 2.6 µs at ambient conditions to 3.2 µs at 80 kbar. This increase is caused by a diminution of the transition oscillator strength that is related to the odd-vibration assistance mechanism. The softening of the transition mechanism is interpreted in terms of the blue-shift experienced by the O^2- to Ti³⁺ charge-transfer transition energy upon increasing the pressure.

We have studied the effect of pressure on the stretching and bending modes of (PO₄)^3- molecular groups in undoped Li₃PO₄ and (MnO₄)^3- groups in Mn⁵⁺-doped Li₃PO₄ using Raman spectroscopy and luminescence. The high-pressure Raman spectroscopy study confirmed an irreversible phase transition from the high-temperature phase to the low-temperature phase, observed in our previous high-pressure luminescence study (Riedener T, Shen Y R, Smith R J and Bray K L 2000 Chem. Phys. Lett. 321 445) and further characterized the rate and irreversibility of the phase transition. We observed and analysed vibronic transitions occurring in the ¹E emission of Mn⁵⁺ in both phases. A stronger vibronic transition associated with the bending mode is interpreted in terms of an E⊗e Jahn-Teller coupling. Bulk and local compressibilities were predicted from variations of the energies of the (PO₄)^3- and (MnO₄)^3- stretching modes with pressure.

We calculate the binding energies for shallow impurities in multiple V-groove GaAs/AlGaAs quantum wires using a variational technique. The carrier ground states are calculated by an effective potential method together with a suitable coordinate transformation which allows the decoupling of the two-dimensional wavefunction. We present results as a function of impurity position in each wire of multiple quantum wire structures. The dependence of the donor binding energies on the parameters of the wire is discussed. We demonstrate that the interaction between the wires and the symmetry of the impurity wavefunction both have a significant effect on the binding energies in multiple quantum wires.

The magnetoresistance (MR) was measured in films of amorphous indium oxide at the region of weak-strong localization crossover (WSLC). The change from positive to negative MR was observed commonly in the samples as temperature increased, passing through 8-10 K, which falls within the WSLC region of each sample. The observed MR is fitted to a formula composed of the intrastate interaction and the delocalization (DL) terms. The fitting results show that the intrastate interaction term remains up to the high limit of the WSLC region, above which the weak localization is valid, while the DL effect is evident down to the low limit of the WSLC region, below which the strong localization prevails. Temperature dependences of the fitting parameters show qualitative agreement with theoretical expectations.

For a class of quasi-one-dimensional clusters, by using exact diagonalization, we study the effect of side spins on the spin-spin correlations on the chain. Our calculations show that side spins added in the same sublattice can effectively strengthen the spin-spin correlations in the large-distance region and make the change tend to flatten. It is exactly proved that periodically adding side spins can set up magnetic long-range order in the ground state. We also investigate the effect of the density of side spins on correlation strength. The case where two sublattices have different localized spins is discussed.

A new numerical method, recently developed to study ground states of the Falicov-Kimball model (FKM), is used to examine the effects of correlated hopping on the ground-state properties of this model in two dimensions. It is shown that the ground-state phase diagram as well as the picture of metal-insulator transitions found for the conventional FKM (without correlated hopping) are substantially changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition, even in the strong-coupling limit, where the ground states of the conventional FKM are insulating for all f-electron densities.

We have determined the dependence of the exchange coupling on both the thickness of the antiferromagnetic (AF) layer (t_AF) and that of the ferromagnetic (FM) layer (t_FM) in a Fe₅₀Mn₅₀/permalloy bilayer, where the thickness of the FeMn layer varies from 0.5 to 32 nm with a fixed permalloy layer of 30 nm, and that of the permalloy layer varies from 3.5 to 45 nm with the uniform FeMn layer fixed at 10 nm. For t_AF>3 nm, the exchange field H_ex varies as 1/t_AF^0.3 at both 80 and 300 K, whereas the coercivity does not vary with t_AF. The dependence of H_ex on t_FM displays a behaviour varying as 1/t_FM^0.9, and H_C a behaviour varying as 1/t_FM^1.7 which is close to the theoretical prediction based on a random field at the interface of a FM/AF bilayer.

We have measured the magnetization, low-temperature heat capacity and electrical resistivity of the binary quasicrystal YbCd_5.7 and its crystalline approximant, cubic YbCd₆. Magnetization data reveal that Yb ions are divalent in both compounds. The coefficient of the linear term in the heat capacity, γ, is 51 and 7.5 mJ mol^-1 K^-2 in YbCd₆ and YbCd_5.7, respectively. The heat capacity data thus reveal a significant reduction in the electronic density of states in the quasicrystalline phase. However, the Debye temperatures of the two compounds are comparable; 144 and 138 K, respectively. The electrical resistivity of YbCd₆ shows typical metallic behaviour while the resistivity of YbCd_5.7, larger than that of YbCd₆, is characterized by a negative temperature coefficient below 300 K with a peak around 50 K.

⁷Li nuclear magnetic resonance relaxation times T₁, T_1ρ and T₂ versus temperature are reported in the 150-900 K temperature range for the lithium lanthanum titanate Li_3xLa_2/3-x□_1/3-2xTiO₃ perovskite-type fast-ionic conductors. The presence of Li⁺ ions of two kinds with slightly differing environments is displayed in these experiments. These ions exhibit two different motions: a fast one with a characteristic frequency around 100 MHz at 350 K and a slow one whose frequency is around 60 kHz at 280 K. These two different Li⁺ species cannot be differentiated by means of the fast motion (only one T₁ is observed from the experiments), but only by means of the slow ones (two T_1ρ and two T₂ are observed). These motions are respectively attributed to Li⁺ motion inside the A-cage of the perovskite structure formed by the oxygen ions and to Li⁺ hops between the cages. T₁- and T_1ρ-studies also performed on the ⁶Li nucleus clearly show that just dipolar nuclear interaction is responsible for Li⁺ relaxation. This result is at variance with what has been previously put forward for the relaxation process in these compounds.

The low-frequency or π dielectric relaxation in (K, Li)TaO₃ crystals is considered. An analysis of available experimental data on the influence of the bias field on the relaxation frequency enabled a value of the dipole moment of flipping polar elements to be determined for the first time. It is affirmed that they are most probably pairs of rigidly coupled dipoles (dimers) created by off-centre Li ions. The asymmetry changing the Arrhenius law for the mean relaxation time is emphasized and discussed. The dimer concentration and the dimer contribution to the dielectric permittivity are estimated.

Using Brillouin scattering, we have measured the velocity angular dispersion of the surface and bulk acoustic waves in X-cut and 36° Y-cut LiTaO₃. The complete set of twelve independent acoustic physical constants at hypersonic frequencies is evaluated using a simultaneous fit to only the velocity angular dispersion data on both surface Rayleigh and bulk acoustic waves. In comparison to physical constants determined in the ultrasonic frequency range, our acoustic constants yield better agreement between theory and experiment for the angular dispersion of the surface Rayleigh and second leaky wave velocities. Additionally, computation based on these acoustic constants has accurately predicted the velocity angular dispersion of the bulk waves and their scattering coefficients.

The Lamb shift observed by analysing the antiresonances in the absorption spectra of Cr³⁺-doped glass systems has been studied. A discrepancy in the sign of the experimentally measured shifts and theoretical predictions is found. The experimental behaviour can be explained if we assume a site dependence of coupling between ²E and ⁴T₂ levels. The proposed model yields positive values for shifts in accordance with the experimental results.

The earlier-developed master equation approach and kinetic cluster methods are applied to study the kinetics of L1₀-type orderings in alloys, including the formation of twinned structures characteristic of cubic-tetragonal-type phase transitions. A microscopical model of interatomic deformational interactions is suggested which generalizes a similar model of Khachaturyan for dilute alloys to the physically interesting case of concentrated alloys. The model is used to simulate A1→L1₀ transformations after a quench of an alloy from the disordered A1 phase to the single-phase L1₀ state for a number of alloy models with different chemical interactions, temperatures, concentrations, and tetragonal distortions. We find a number of peculiar features in both transient microstructures and transformation kinetics, many of them agreeing well with experimental data. The simulations also demonstrate the phenomenon of an interaction-dependent alignment of antiphase boundaries in nearly equilibrium twinned bands which seems to be observed in some experiments.

We use exact diagonalization and the modified Lanczos method to study the finite-energy and finite-momentum spectral weight of the longitudinal and transverse spin excitations of the anisotropic zig-zag ladder. We find that the spin excitations form continua of gapless or gapped spinons in the different regions of the phase diagram. The results obtained are consistent with a picture previously proposed that in the anisotropic case there is a transition from a gapped regime to a gapless regime, for small interchain coupling. In the gapless regime we find a sharp low-energy peak in the structure function for the transverse spin excitations, consistent with a finite stiffness.

The magnetic properties of nanomaterials made by embedding cobalt nanocrystals in a copper matrix have been studied using a SQUID magnetometer. The remanent magnetization at temperatures down to 1.8 K and the RT (room temperature) field-dependent magnetization of 1000- and 8000-atom (average-size) cobalt cluster samples have been measured. In all cases it has been possible to relate the morphology of the material to the magnetic properties. However, it is found that the deposited cluster samples contain a majority of sintered clusters even at cobalt concentrations as low as 5% by volume. The remanent magnetization of the 8000-atom samples was found to be bimodal, consisting of one contribution from spherical particles and one from touching (sintered) clusters. Using a Monte Carlo calculation to simulate the sintering it has been possible to calculate a size distribution which fits the RT superparamagnetic behaviour of the 1000-atom samples. The remanent magnetization for this average size of clusters could then be fitted to a simple model assuming that all the nanoparticles are spherical and have a size distribution which fits the superparamagnetic behaviour. This gives a value for the potential energy barrier height (for reversing the spin direction) of 2.0 µeV/atom which is almost four times the accepted value for face-centred-cubic bulk cobalt. The remanent magnetization for the spherical component of the large-cluster sample could not be fitted with a single barrier height and it is conjectured that this is because the barriers change as a function of cluster size. The average value is 1.5 µeV/atom but presumably this value tends toward the bulk value (0.5 µeV/atom) for the largest clusters in this sample.

Arrays of Fe_1-xCo_x (0.0⩽x⩽0.92) nanowires have been prepared by an electrochemical process, co-depositing Fe and Co atoms into the pores of anodic aluminium; their compositions were determined by atomic absorption spectroscopy. Transmission electron microscope results show that the nanowires are regularly spaced and uniform in shape with lengths of about 7.5 µm and diameters of 20 nm. The x-ray diffraction indicates a texture in the deposited nanowires. For the composition below 82 at.% cobalt, the nanowires had a body-centred-cubic structure with a [110] preferred orientation. For the 92 at.% cobalt sample, the alloy exhibited a mixture of bcc and face-centred-cubic structure. The room temperature ⁵⁷Fe Mössbauer spectra of the arrays of Fe_1-xCo_x nanowires have second and fifth absorption lines of the six-line pattern with almost zero intensity, indicating that the internal magnetic field in the nanowires lies along the long axis of the nanowire. The maximum values of the hyperfine field (B_hf = 36.6±0.1 T) and isomer shift (IS = 0.06±0.01 mm s^-1) occur for 44 at.% cobalt. The variations of the isomer shift and the linewidths with composition indicate that the Fe_1-xCo_x alloy nanowires around the equiatomic composition are in an atomistic disordered state.

Brillouin-zone (BZ) integrations in systems with two-dimensional periodicity are discussed in the context of a method wherein the BZ is divided into simplices (triangles), and band energies and properties contributions are represented by quadratic interpolations based on six data points on the edges of each simplex. This paper describes a straightforward and easily implemented algorithm for identifying the paths bounding the occupied portion(s) of each simplex, and (in contrast to earlier work by others) provides completely analytic expressions, in closed form, for evaluating properties integrals over the occupied regions.

As was shown earlier (Dzero M O, Gor'kov L P and Zvezdin A K 2000 J. Phys.: Condens. Matter12 L711), the properties of the first-order valence phase transition in YbInCu₄ over a wide range of magnetic fields and temperatures can be perfectly described on the basis of a simple entropy transition for free Yb ions. Within this approach, the crystal-field effects have been taken into account and we show that the phase diagram in the B-T plane acquires some anisotropy with respect to the direction of an external magnetic field.

In the frame of the long-wavelength Heisenberg model, the magnonic bandgaps and the selective transmission in a serial loop structure, made of loops pasted together with segments of finite length, are investigated theoretically. The loops and the segments are assumed to be one-dimensional ferromagnetic materials. Using a Green function method, we obtained closed-form expressions for the band structure and the transmission coefficients for an arbitrary value of the number N of loops in the serial loop structure. It was found that the gaps originated from the periodicity of the system. The width of these forbidden bands depends on the structural and compositional parameters. We also present analytical and numerical results for the transmission coefficient through a defective geometry where the length of one finite branch has been modified. It was demonstrated that the presence of this defect in the structure can give rise to localized states inside the gaps. We show especially that these localized states are very sensitive to the size of the loops and to the periodicity as well as to the length and the location of the defect branch.

A discrete two-dimensional model of a ferroelastic lattice has been employed to study the equilibrium shapes of needle domains at different depths below the surface. We have found that the trajectory of the needle tip follows the theoretically predicted form of a quadratic function. A high-symmetry high-temperature region is identified, extending from the tip of a needle below the surface, and created as a result of elastic interaction between the needle tip and the surface, giving rise to possible unexpected surface topographies. A configuration where the needle tip touches the surface initially, is found to evolve into two kinked domain walls that move away from each other.