An analytical method of determining the higher-dimensional lattice associated with an aperiodic structure is presented. The Moore-Penrose generalized matrix-inversion procedure has been utilized to overcome the problem arising due to the number of physical basis vectors being more than that of the linear equations relating these vectors to higher-dimensional lattice basis vectors.

The conformational and electronic properties of flexible conducting polymer chains are investigated. As a starting point a general Hamiltonian for conjugated flexible chains is presented. The π electrons are described in terms of a Hubbard model confined to the chain modeled by (random) walks. One main result is that electronic degrees greatly affect the conformation which is shown explicitly for a melt of conjugated polymers. The presence of electrons leads to a significant stiffening (rigidification) of the chains, i.e., the effective persistence length is increased. The other important point is the effect of the conformation of the chain on the electron-electron interaction. This leads to a weak disorder-induced localization of the electrons. An effective pair potential is derived using Feynman-graph techniques.

Structure changes in amorphous ${\mathrm{Pd}}_{52}$${\mathrm{Ni}}_{32}$${\mathrm{P}}_{16}$ upon relaxation were modeled by means of reverse Monte Carlo (RMC) simulations using neutron-diffraction data from M. Schaal, P. Lamparter, and S. Steeb [Z. Naturforsch. Teil A 43, 1055 (1988)] as input for the RMC program. Two states after annealing (2 h at 570 K and 2 h at 607 K) and the as-quenched state were successfully modeled. The resulting three-dimensional models of the structure were inspected for changes in the nearest-neighbor coordinations (short-range order) and for changes at larger interatomic distances (medium-range order) upon relaxation. It was found that the short-range order is affected by annealing, resulting in, for instance, a sharpening of the Voronoi volume distribution. These results were found to agree with interpretations of experimental atomic mobility studies. The effect of annealing on multibody correlation functions for medium-range distances is much less pronounced than that for the short-range distances, and the two appear to be largely decoupled from one another. These results, together with the observed annealing effect on the decay rate of the peaks of the reduced radial distribution function, suggest that medium-range ordering is not merely a reflection of short-range ordering, but has its origin in a change in propagation of disorder in the structure. Medium-range ordering can therefore be treated as a separate effect of annealing.

Orientationally disordered crystals possess translational order while retaining rotational and conformational degrees of freedom. Because these materials exhibit a glasslike transition, they are of great theoretical and experimental interest as model systems for structural glasses. We present detailed measurements of the complex dielectric susceptibility ɛ(ω,T) of the orientationally disordered phase of cyclo-octanol. The frequency dependence (${10}^{\mathrm{-}3}$–${10}^4$ Hz) of the real and imaginary parts of ɛ are fit to Cole-Davidson and Kohlrausch-Williams-Watts shape functions to extract values for the peak frequency and width exponents as functions of temperature. The temperature dependence of the peak frequency is described by a Vogel-Tamman-Fulcher form with ${\mathit{T}}_0$=92.4 K for the Cole-Davidson fit and 94.7 K for the Kohlrausch-Williams-Watts fit. The correlation between the width exponent and fragility is consistent with the behavior of other glasses and glasslike materials. The data also obey a scaling form proven successful for a variety of organic glass formers. Both analyses demonstrate the close similarity of the transition in orientationally disordered cyclo-octanol to the structural glass transition and confirm that cyclo-octanol is an ideal candidate for further theoretical and experimental treatment as a model glass.

ac and dc conductivities of fast-ion conducting x${\mathrm{Na}}_2$S+(1-x)${\mathrm{B}}_2$${\mathrm{S}}_3$ glasses in the composition range 0.001≤x≤0.1 were analyzed using the Almond-West formula σ(ν)=${\mathrm{\sigma }}_{\mathrm{dc}}$[1+(ν/${\nu }_{\mathit{H}}$${)}^{\mathrm{\alpha }}$]. The hopping frequency for free charge carriers ${\nu }_{\mathit{H}}$, the dc conductivity ${\mathrm{\sigma }}_{\mathrm{dc}}$, and their respective activation energies were determined. The concentration of free charge carriers evaluated from the conductivities and estimated mobilities is in good agreement with the overall content of sodium cations in the glasses and it is proposed that this supports the concept of a strong and not weak electrolyte model for these fast-ion conducting glasses.

We propose a combination of the generalized augmented-space theorem and the recursion method of Haydock et al. to study short-ranged ordering effects in binary alloys. We apply this technique to a tight-binding linear muffin-tin orbitals study of 50-50 AgPd and 50-50 paramagnetic FeNi and predict ordering in the former and segregation in the latter. This is in qualitative agreement with earlier embedded-cluster methods.

We present a detailed analysis of the nature of electronic eigenfunctions in one-dimensional quasiperiodic chains based on a clustering idea recently introduced by us [Sil et al., Phys. Rev. B 48, 4192 (1993)], within the framework of the real-space renormalization-group approach. It is shown that even in the absence of translational invariance, extended states arise in a class of such lattices if they possess a certain local correlation among the constituent atoms. We have applied these ideas to the quasiperiodic period-doubling chain, whose spectrum is found to exhibit a rich variety of behavior, including a crossover from critical to an extended regime, as a function of the Hamiltonian parameters. Contrary to prevailing ideas, the period-doubling lattice is shown to support an infinity of extended states, even though the polynomial invariant associated with the trace map is nonvanishing. Results are presented for different parameter regimes, yielding both periodic as well as nonperiodic eigenfunctions. We have also extended the present theory to a multiband model arising from a quasiperiodically arranged array of δ-function potentials on the atomic sites. Finally, we present a multifractal analysis of these wave functions following the method of Godreche and Luck [J. Phys. A 23, 3769 (1990)] to confirm their extended character.

The elastic and total (energy-integrated) structure factors for glassy selenium have been measured by means of neutron spectroscopy within the temperature range 15 K≤T≤310 K. The correlated nature of the atomic vibrations gives rise to marked features in the total (energy-integrated) inelastic structure factors defined as the difference between the total and elastic intensities. Also, both structure factors show rather distinct dependences with temperature, which are discussed in some detail.

Polarized Raman-scattering spectra are obtained from oriented single crystals of yttria-doped ${\mathrm{CeO}}_2$. The temperature and dopant dependencies of Raman spectra strongly suggest that many structures in the Raman spectra of yttria-doped ${\mathrm{CeO}}_2$ are induced by the defect space including an ${\mathrm{O}}^{2\mathrm{-}}$ vacancy. The contribution to the frequency distributions of Raman-active modes from the whole Brillouin zone are estimated from the imaginary part of the simple projection of the phonon displacement-displacement Green’s functions of undoped ${\mathrm{CeO}}_2$ crystals onto several defect spaces. The observed spectra are well explained by the linear combination of the calculated frequency distributions from the defect space consisting of the four metal ions and from that consisting of the six next-nearest-neighbor ${\mathrm{O}}^{2\mathrm{-}}$ ions surrounding an ${\mathrm{O}}^{2\mathrm{-}}$ vacancy. Brillouin-scattering spectra of ${\mathrm{CeO}}_2$ are also measured in order to calculate the phonon-dispersion curves of ${\mathrm{CeO}}_2$. The dependencies of type and concentration of defect space on dopant concentration in doped ${\mathrm{CeO}}_2$ are also discussed.

The Frenkel-Kontorova (FK) model of edge dislocation is analyzed. Solutions of the continuum limit of the FK model [the sine-Gordon (SG) equation] are obtained in a form convenient for investigation of dynamics of a large number of interacting dislocations. We consider, based on these solutions, some nonstationary processes: dislocation generation, diffusion of dislocations, and crack-dislocation interaction. Simple relations connecting the velocity of plastic deformation, density and velocity of dislocations, and the force of interaction between dislocations are obtained. The nucleation of dislocations at a moving crack tip is described.

This paper deals with the problem of interimpurity transport of quasiparticles (electron, exciton, etc.) in condensed media. A realistic situation is simulated by the simple two-level model interacting with an environment whose influence is described by a set of harmonic oscillators. The model is general enough to include most of the situations of interest by a convenient choice of parameters. A variational approach is developed which enables one to formulate the set of evolution equations for the variables describing the essential system properties in practically the whole parameter space, which consists of the coupling constant and the adiabaticity parameter (representing the ratio of the interimpurity-transfer integral to the phonon bandwidth). It was found that the parameter space (plane of the coupling constant vs adiabaticity parameter) is divided into two regions with quite distinct physical properties. In the first one the dynamics is dominated by the quantum nature of the phonon subsystem and the localization transition is achieved through the reduction of the effective transfer integral. In the second, the so-called symmetry-breaking region, the classical nature of the phonon field prevails. Therefore, the dynamics and localization are described by the discrete nonlinear Schrödinger equation. The symmetry breaking itself is induced by nature of the phonon field, which, in the strong coupling limit, behaves classically. The results are presented in such a form that it allows for the precise determination of the system behavior for any set of realistic system parameters, enabling comparison with previous results.

The nonlinear response of a two-component composite is studied. The first component is assumed to be nonlinear and obeys a current-voltage (I-V) characteristic of the form I=${\mathrm{g}}_1$V+${\mathrm{\chi }}_1$${\mathrm{V}}^3$, while the second component is linear with I=${\mathrm{g}}_2$V, where ${\mathrm{g}}_1$ and ${\mathrm{g}}_2$ are linear conductances of the constituents and ${\mathrm{\chi }}_1$ is the nonlinear susceptibility. The volume fractions of the two components are p and q, respectively, and p+q=1. Near the percolation threshold, we identify two important limits: (i) the conductor-insulator (N/I) limit in which ${\mathrm{g}}_2$=0 and (ii) the superconductor-conductor (S/N) limit in which ${\mathrm{g}}_2$=∞. For the S/N case and below the percolation threshold (q<${\mathrm{q}}_{\mathrm{c}}$), the crossover voltage ${\mathrm{V}}_{\mathrm{c}}$, defined as the voltage at which the linear and nonlinear response become comparable, is found to have a power-law dependence ${\mathrm{V}}_{\mathrm{c}}$≈(${\mathrm{q}}_{\mathrm{c}}$-q${)}^{\mathrm{v}\prime }$ as the percolation threshold is approached from below. For the N/I limit and above the percolation threshold (p>${\mathrm{p}}_{\mathrm{c}}$), the crossover current ${\mathrm{I}}_{\mathrm{c}}$ is found to have a similar dependence ${\mathrm{I}}_{\mathrm{c}}$≈(p-${\mathrm{p}}_{\mathrm{c}}$${)}^{\mathrm{w}}$ as the percolation threshold is approached from above. By a connection between the nonlinear response of the random nonlinear composite problem and the relative conductance fluctuations of the corresponding random linear composite problem, the exponents w and v′ are found to be w=(κ+t)/2 and v′=(κ′+s)/2, respectively where κ and κ′ are noise exponents and t and s are conductivity exponents. Previously derived bounds and estimates on κ and κ′ were used to give reasonable estimates of the exponents w and v′. For a small but finite ratio h of poor to good conductances and right at the percolation threshold, the linear and nonlinear response functions are found to cross over from the fractal (h=0) to homogeneous (h=1) behavior. The scaling functions of the crossover voltage and current are obtained within the effective-medium approximation and numerical simulations. An excellent agreement with general scaling arguments is found.

The concept of separation of diffusional and drift flows, i.e., the postulate that the total mass flow is a sum of diffusion flux and translation only, is applied for the general case of diffusional transport in an r-component compound (process defined as interdiffusion in a one-dimensional mixture). The equations of local mass conservation (continuity equations), the appropriate expressions describing the fluxes (drift flux and diffusional flux), and momentum conservation equation (equation of motion) allow a complete quantitative description of diffusional transport process (in one-dimensional mixture showing constant concentration) to be formulated. The equations describing the interdiffusion process (mixing) in the general case where the components diffusivities vary with composition are derived. If certain regularity assumptions and a quantitative condition (concerning the diffusion coefficients—providing a parabolic type of the final equation) are fulfilled, then there exists the unique solution of the interdiffusion problem. Good agreement between the numerical solution obtained with the use of Faedo-Galerkin method and experimental data is shown. An effective algebraic criterion allows us to determine the parabolic type of a particular problem. A condition for the ‘‘up-hill diffusion’’ in the three component mixture is given and a universal example of such effect is demonstrated. The results extend the standard Darken approach. The phenomenology allows the quantitative data on the dynamics of the processes to be obtained within an interdiffusion zone.

Longitudinal-acoustic and -optic phonons along the three main symmetry directions in Si were investigated by coherent neutron inelastic scattering. While the determination of phonon frequencies is a routine task, the complementary information on the phonon eigenvectors contained in the intensities of the observed phonon groups is exploited only rarely. The main reasons are problems with correct normalization and reliability of the data, caused by frequent occurrence of spurious peaks. In the present study we addressed this problem by restricting the experiment to scans fulfilling conditions for good resolution so that most of the observed phonon peaks could be resolved from the spurious ones. The inelastic structure factors were then extracted from several sets of integrated intensities, observed at different Q and ω values, and fitted by appropriate models with common scale factors in order to obtain detailed information on eigenvector phases and amplitudes in elliptically polarized modes. The observed eigenvectors and frequencies were found in good agreement with results of ab initio calculations.

Using the 93.31-keV Mössbauer resonance in ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$ the anisotropy of the Lamb-Mössbauer factor (LMF), the quadrupole interaction, and the isomer shift in ${\mathrm{ZnF}}_2$ single crystals have been investigated between 1.1 and 4.2 K. The anisotropy of the LMF is large: ${\mathit{f}}_{\mathit{x}}$=(2.4±0.1)%, ${\mathit{f}}_{\mathit{y}}$=(2.3±0.2)%, and ${\mathit{f}}_{\mathit{z}}$=(1.4±0.2)%. The main component of the electric-field gradient (EFG) tensor ${\mathit{V}}_{\mathit{z}\mathit{z}}$=+(2.18±0.22)×${10}^{17}$ V/${\mathrm{cm}}^2$ and η=0.29±0.03 is derived. ${\mathit{V}}_{\mathit{z}\mathit{z}}$ is perpendicular to the c axis. Using a force-constant model (shell model) which includes short-range interactions we solved the eigenvalue problem of the dynamic matrix and quantitatively reproduced the anisotropy of the LMF. Within the same model we calculated the second-order Doppler shift. We performed ab initio Hartree Fock (HF) cluster calculations to give a detailed interpretation of the various electronic contributions to the EFG’s at the Zn and F sites and to the s electron density at the Zn nucleus (isomer shift). The covalent part of the chemical bond essentially determines all hyperfine interactions. The agreement between HF calculations and experiment is very good.

On the basis of a model similar to that of Su, Schrieffer, and Heeger, we investigate transitions between bipolaron and polaron states in doped heterocycle polymers such as polypyrrole, polythiophene, and polyselenophene. The dopant impurity is assumed to be located between chains, and the interchain coupling is due to the electron hopping which is assumed to be confined to nearest-neighboring carbon groups around the counterion. The electron-electron interaction described by a Hubbard-type Hamiltonian is also included in our calculation. It is shown that the system may be in a bipolaron state or a state of a polaron pair of spin triplet (singlet) nature. We find that the interchain coupling has little influence on the stability of a bipolaron. Transitions from a bipolaron to a pair of polarons can be induced by a strong electron-electron interaction, which is also responsible for the energy difference between the singlet and triplet polarons states.

A microscopic quantum electrodynamical (QED) theory is developed for representing the dynamics of excitation transfer in a dielectric medium between individual species, such as atoms or molecules, at various separations, including both near- and far-zone distances. The theory, built on explicit QED consideration of the time evolution, fully incorporates medium-induced energy renormalizations and damping corrections for the transfer species. In addition, it embodies the local field and screening contributions which have already been featured in a previous paper devoted to the rate description. The influence of the medium is also manifest in the relativistic time-lag (reflecting the delay of the initial arrival of the excitation at the acceptor molecule), which is now shown to be characterized by the group velocity of the light. The phase velocity features in the distance-dependent retardation in phase of the transition matrix element. The theory extends to different transfer regimes. Following a general analysis, the paper reexamines the rate regime, where not only the transition matrix element but also the molecular excitation frequencies for the transfer species are modified by the medium. Another non-rate-regime, occurring in situations that lack an intrinsic molecular density of states, displays oscillatory dynamics over short transfer distances. These oscillations are suppressed by monomolecular damping in the long-range case: here the transfer process is cast in terms of transfer probabilities, rather than rates. In all situations the characteristic parameters of the process properly reflect the influence of the medium, though it is apparent that in the limiting case of an infinitely dilute medium the present results are consistent with those previously obtained for the vacuum case.

The phonon frequencies at the Γ point, the Born effective charges, and the dielectric permittivity tensors of ${\mathrm{TiO}}_2$ rutile are calculated using the variational density-functional perturbation theory. The calculated phonon frequencies agree with experiment within a few percent. We analyze the corresponding theoretical eigenvectors as well as the interaction of the vibration modes with the electric field. The Born effective charges of ${\mathrm{TiO}}_2$ rutile are much larger than the nominal charges of ${\mathrm{Ti}}^{4+}$ and ${\mathrm{O}}^{2\mathrm{-}}$ ions, as well as those of ${\mathrm{SiO}}_2$ stishovite despite the structural similarity. A giant LO-TO splitting is observed for ${\mathit{E}}_{\mathit{u}}$ and ${\mathit{A}}_{2\mathit{u}}$ modes. The O ions in rutile as well as in stishovite are found to have a counterintuitive reversed electronic polarization near the nuclei. The calculated large, anisotropic static dielectric permittivity tensors as well as electronic dielectric permittivity tensors also compare favorably with experiments.

Low-temperature conductivity and diffusivity of the generalized Frenkel-Kontorova model, which takes into account realistic (anharmonic) interaction of particles subjected to a periodic substrate potential, are investigated analytically in the framework of a phenomenological approach which treats a system of strongly interacting atoms as a system of weakly interacting quasiparticles (kinks). Using phenomenology of the ideal kink gas, where the low-temperature ground state of the chain is described as that consisting of ‘‘residual’’ kinks supplemented by thermally excited kinks, we describe the ground state of the system as a hierarchy of consequently ‘‘melted’’ kink lattices. System dynamics is then described in terms of the kink dynamics. The motion equation for a single kink is reduced to a Langevin-type equation which is investigated with the help of the Kramers theory. In this way, we qualitatively analyze dependence of the susceptibility, conductivity, and chemical diffusivity of the chain on the concentration of atoms in the chain. The model leads to a series of effects which we expect are related to the experimentally observed phenomena in several quasi-one-dimensional systems, in particular, superionic conductors and anisotropic layers of atoms adsorbed on crystal surfaces.

We present a phemomenological approach to the lattice-dynamical properties of various SiC polytypes. A generalized bond-charge model is applied to the cubic and hexagonal polytypes 3C, 6H, 4H, and 2H. The long-range microscopic electric field of ions and bond charges is fully taken into account via an Ewald technique. The short-range elastic interactions are described by bending and stretching forces between ions and bond changes. The force constants and effective charges are fit to phonon frequencies known from Raman and luminescence measurements. The reliability of the model is tested not only for the frequencies but also for the eigenvectors by comparison with results of ab initio calculations for 3C- and 2H-SiC. We show that the anisotropy in the uniaxial hexagonal polytypes is mainly due to the nonanalyticity of the Coulomb forces. The corresponding frequency splittings are related to slight changes of the bond charges in dependence on the bond orientation. Differences in the elastic forces parallel and nonparallel to the hexagonal axis are only necessary to stabilize the zone-boundary phonons. The trends of the resulting frequencies and density of states are discussed versus the percentage hexagonality. Consequences of the different phonon dispersions for the elastic properties of the 3C, 6H, 4H, and 2H polytypes are considered. We speculate about possible mechanisms of polytype stabilization by the lattice vibrations.