The pressure dependence of the superconducting transition temperature (${\mathit{T}}_{\mathit{c}}$) has been determined up to ∼2.5 GPa for solid-solution In-Tl alloys with compositions between 31.5 and 36.5 at. % Tl. The cusp in ${\mathit{T}}_{\mathit{c}}$ as a function of composition, that has been associated with the fcc-fct phase boundary at zero pressure, is found to move to higher thallium concentrations with increasing pressure. This is interpreted as a pressure-induced stabilization of the fct phase resulting from changes in the Fermi surface–Brillouin zone boundary overlap.

Clear evidence for multielectron excitation channels involving 2p or 2s and 4f electrons has been discovered in x-ray-absorption L-edge spectra of several sixth-period elements. Measurements on liquid Pb and Bi, as well as in PbO, Pb(${\mathrm{CH}}_3$${\mathrm{CO}}_2$${)}_2$, and ${\mathrm{Bi}}_2$${\mathrm{O}}_3$ compounds are reported and compared with previous data on vapor Hg. Onset energies of the double-electron excitation channels are found to be in agreement with previously published self-consistent calculations. A weaker feature, which has been observed in several spectra, is assigned to a triple-electron excitation involving two strongly correlated 4f electrons. The importance of these findings for the extended x-ray-absorption fine structure structural analysis of sixth-period elements is discussed.

We have used differential scanning calorimetry and x-ray diffraction to study the crystalline phases of the 6,5-annulene isomer of ${\mathrm{C}}_{61}$${\mathrm{H}}_2$. At 308 K the methylenated fullerenes are orientationally disordered in a face-centered cubic lattice with lattice parameter 14.19±0.02 Å. Below ${\mathit{T}}_{\mathit{c}}$=290 K the symmetry is lowered to Pa3¯, a simple-cubic structure. At 20 K the lattice parameter is 14.06±0.02 Å, with substantial statistical disorder remaining. The transition temperature in ${\mathrm{C}}_{61}$${\mathrm{H}}_2$ is slightly higher than in ${\mathrm{C}}_{60}$O and higher still than in ${\mathrm{C}}_{60}$, but the three compounds exhibit orientationally ordering transitions between qualitatively similar phases.

A relativistic model for the extended x-ray-absorption fine structure, in which the energy loss of the emitted photoelectron is accounted for by using a complex energy-dependent exchange-correlation potential, has been developed. Relativistic curved-wave single-, double-, and triple-scattering formulas for excitation from any core hole have been found. The dominant single-scattering signal has been computed for the first shell at the ${\mathit{L}}_2$ and ${\mathit{L}}_3$ edges of Th (Z=90), Pt (Z=78), and Eu (Z=63) and at the K edge of Sr (Z=38) using this model. Comparisons of the relativistic scattering amplitudes of the Dirac model with the current standard Schrödinger curved-wave model reveal that the latter deviates from the more exact Dirac model by 20% above 240 eV for Th, by 15% above 240 eV for Pt, and by 10% above 140 eV for Eu. For lower energies, the deviations are as much as two times larger. Differences between the Dirac model ${\mathit{L}}_2$- and ${\mathit{L}}_3$-edge amplitudes occur below 240 eV for Th and Pt with values of 2% and 6%, respectively. For Eu, this difference diminishes to 4% and occurs only below 140 eV. In the case of the K edge of Sr, the Schrödinger single-scattering amplitude differs from the Dirac amplitude by 5% for energies above 95 eV. The spin dependence of the generalized Ramsauer-Townsend effect is also exhibited.

${}_{}{}^{113}{}_{}{}^{}\mathrm{Cd}$, ${}_{}{}^{109}{}_{}{}^{}\mathrm{Ag}$, and ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ nuclear-magnetic-resonance line-shape and Knight-shift measurements are reported for ${\mathrm{Ag}}_{53.5}$${\mathrm{Cd}}_{46.5}$ and ${\mathrm{Cu}}_{61}$${\mathrm{Zn}}_{39}$ over a temperature interval covering the martensitic phase transformation (MPT) displayed by these alloys. The changes observed in the line shape and width are explained in terms of the changes in atomic coordination and crystal symmetry occurring at the MPT. A small but non-negligible temperature dependence of the Knight shift is observed in the austenitic phase with small discontinuous changes at the transformation for all the nuclei investigated. The difference of resonance frequency of ${}_{}{}^{113}{}_{}{}^{}\mathrm{Cd}$ in the two phases has been utilized to obtain the curve of the percentage of martensite in the Ag-Cd alloy as a function of temperature during the thermoelastic transformation. It is shown that our growth curve reveals details which cannot be seen by dynamical methods such as differential scanning calorimetry.

We have started a study of quantum ferroelectrics and paraelectrics. Simple two-dimensional short-range lattice model Hamiltonians are constructed, keeping in mind the phenomenology of real perovskite systems, like ${\mathrm{SrTiO}}_3$ and ${\mathrm{KTaO}}_3$. Pertinent quantum tunneling phenomena, and the presence of an icelike constraint are demonstrated. The two simplest models, namely a plain quantum four-state clock model and a constrained one, are then studied in some detail. We show the equivalence of the former, but not of the latter, to a quantum Ising model. For the latter, we describe a very good analytical wave function valid in the special case of zero coupling (J=0). In order to study the full quantum statistical mechanics of these models, a path-integral Monte Carlo calculation is set up, and implemented with a technique, which even in the constrained case permits a good convergence for increasing time slice number m. The method is applied first to the unconstrained model, which serves as a check, and successively to the constrained quantum four-state clock model. It is found that in both cases a quantum phase transition at T=0 takes place at finite coupling J, between a ferroelectric and a quantum paraelectric state, even when the constraint hinders disordering of the ferroelectric state. These model paraelectric states have a finite excitation gap, and no broken symmetry. The possible role of additional (‘‘oxygen hopping’’) kinetic terms in making closer contact with the known phenomenology of ${\mathrm{SrTiO}}_3$is proposed.

Modulated differential scanning calorimetry of sublimed ${\mathrm{C}}_{70}$ shows clear evidence for four first-order transitions, two strong and two weak, which we associate with the two different molecular rotational degrees of freedom in majority (equilibrium) and minority (metastable) phases. The latter correspond to two different stacking sequences of close-packed layers, and their relative contributions to the thermal data correlate well with high-temperature x-ray powder-diffraction results. The upper (long axis tumbling) transition in the majority phase exhibits 50 K supercooling when scanned at 2 K/min. ${\mathrm{C}}_{60}$ impurities at the few % level depress the transition temperatures substantially.

A generally theoretical framework for predicting the coupled thermal-electrical-mechanical properties of inhomogeneous media is developed in terms of a Green’s-function method and perturbation theory. Taking a tranversely isotropic fiber-reinforced composite of the 4- or 6-mm symmetry class as a practical example, I discuss the general theoretical results, and give explicit expressions for the effective coupled thermal-electrical-mechanical properties. The pyroelectricity of ${\mathrm{BaTiO}}_3$-epoxy and CdS-epoxy composites is numerically analyzed. An enhanced pyroelectricity is predicted, and the numerical results show the interesting behavior of these materials.

Molecular-dynamics and energy-minimization calculations with nonadditive Lennard-Jones interactions are used to investigate the microstructure of amorphous ${\mathrm{Ni}}_{33}$${\mathrm{Y}}_{67}$. The interaction parameters are mainly determined from structural data on crystalline Ni-Y alloys at several compositions. The molecular dynamics results reproduce satisfactorily the neutron-diffraction measurements on the glass. Analysis of Voronoi polyhedra, radial, and angular distribution functions indicate that atomic coordination in the glass resembles that of the crystalline species. Distorted ${\mathrm{NiY}}_6$ trigonal prisms constitute the most common coordination in the simulated material.

A theory of quasiperiodic lattices that consist of three types of atoms, A, B, and C is introduced. First, we present the scaling transformations for construction of the ternary quasiperiodic lattices in terms of a substitution scheme. Since this substitution scheme has a group structure we call it the scaling group for the ternary quasiperiodic lattices. Second, we show that under the scaling transformations we are able to obtain the trace map for the ternary quasiperiodic lattices. It is a generalization of those for the binary quasiperiodic lattices.

The marked changes in the dielectric and thermal properties of vulcanized cis-1,4-polyisoprene due to different iodine doping levels are investigated. The results show strong evidences of formation of conjugated sequences of unsaturated double bonds in the vulcanized polyisoprene backbone, through visible and infrared spectroscopic data. The dependence of the electrical conductivity, specific heat, and of the Young’s modulus, upon doping, indicate the existence of a critical doping concentration for the onset of an order-disorder transition.

Formulas for calculating the characters of the representation matrices and the number of independent components of any physical-property tensor of quasicrystals have been derived by using group-representation theory, where the internal symmetry of the physical-property tensor was considered. As an example of their application, we have calculated the number of independent elastic constants up to cubic order for many of the quasicrystals discovered to date.

The low-temperature properties of the Coulomb glass, i.e., a disordered system with many electrons subject to long-range electron-electron interaction, are investigated by means of a Monte Carlo simulation. The Metropolis algorithm enables a systematic analysis of three-dimensional systems with up to 256 electrons on 512 sites within the standard lattice model for compensated doped semiconductors. We obtain the thermodynamical properties like the expectation value of the internal energy and the specific heat with high accuracy. A modification of the algorithm yields the spectrum of the low-energy many-electron excitations. The majority of these excitations is characterized by a correlated displacement of several electrons which often span the size of the entire system. A detailed analysis of the correlations corroborates the importance of variable-number hopping, while variable-range hopping is insignificant for low temperatures due to the lack of possible final states. Accordingly the density of states of the correlated many-electron excitations displays a soft gap in correspondence to the Coulomb gap known for the single-electron density of states.

We present the solutions to two simple models for the brittle failure of materials containing random flaws. These solutions provide support for simple scaling theories we had previously developed for more complex models, and refute recent claims that models with random dilution scale in a manner similar to a disorderless material. In particular, we find that for these models, the asymptotic size effect in the average strength is logarithmic, and the failure distribution is of an exponential of an exponential form (often with an algebraic prefactor). The method of solution is also interesting. The failure probability of the quasi-one-dimensional models we solve can be written in terms of a transition matrix introduced by Harlow. For large sample sizes, the largest eigenvalue of this transition matrix approaches one, and our solution rests on a perturbative expansion of the largest eigenvalue about one. The small and intermediate lattice behavior of the model is analyzed by using sparse matrix methods to find the largest eigenvalue of the transition matrix, and the trace of powers of the transition matrix.

The magnetic susceptibilities, resistivities, and Hall coefficients of amorphous ${\mathrm{Ni}}_{0.80\mathrm{-}\mathit{x}}$${\mathrm{Cr}}_{\mathit{x}}$${\mathrm{P}}_{0.20}$ (0.00≤x≤0.40) alloys are reported. A sign change with temperature of the Hall coefficient for a single paramagnetic amorphous alloy that correlates with the temperature-dependent valence susceptibility has been observed (x=0.20), indicating that an extraordinary contribution to ${\mathit{R}}_{\mathit{H}}$ is responsible for the positive Hall effect in these paramagnetic alloys. Also, an unexplained relatively large contribution to ${\mathit{R}}_{\mathit{H}}$ that is linear in T has been observed in some of these alloys. A gradual change in magnetic properties with composition from large cluster-dominant phase to Kondo-impurity phase has been observed.

We consider semi-infinite two-dimensional layered Ising models in the extreme anisotropic limit with an aperiodic modulation of the couplings. Using substitution rules to generate the aperiodic sequences, we derive functional equations for the surface magnetization. These equations are solved by iteration and the critical exponent ${\mathrm{\beta }}_{\mathit{s}}$ can be determined exactly. The method is applied to three specific aperiodic sequences, which represent different types of perturbation, according to a relevance-irrelevance criterion. On the Thue-Morse lattice, for which the modulation is an irrelevant perturbation, the surface magnetization vanishes with a square-root singularity, like in the homogeneous lattice. For the period-doubling sequence, the perturbation is marginal and ${\mathrm{\beta }}_{\mathit{s}}$ is a continuous function of the modulation amplitude. Finally, the Rudin-Shapiro sequence, which corresponds to the relevant case, displays an anomalous surface critical behavior which is analyzed via scaling considerations. Depending on the value of the modulation, the surface magnetization either vanishes with an essential singularity or remains finite at the bulk critical point, i.e., the surface phase transition is of first order.

Starting from a microscopic Hamiltonian for interacting quadrupoles (QP’s) randomly placed in a solid, we obtain a model for the two-level tunneling states and the constant density of states in quadrupolar glasses from fundamentals. We use perturbation theory to show that in a quenched system of strongly interacting QP’s, 180° reorientational flips of single QP’s give low-energy excitations. These low-energy excitations arise from our starting Hamiltonian and are described in the form of an effective two-level state (TLS) Hamiltonian. For intermediate concentrations of ${\mathrm{CN}}^{\mathrm{-}}$ ions dissolved in KBr, we propose that it is the center of mass displacement of the ${\mathrm{CN}}^{\mathrm{-}}$ ion that leads to a constant density of states rather than the electric dipole interaction between the cyanides, as was proposed earlier by Sethna et al. The physical mechanism for the glasslike low-energy excitations proposed here thus involves 180° tunneling flips with a translation of the center of mass of the tunneling unit. We then show that it is the elastic random fields experienced by the QP’s that give a constant density of states and specific heat linear in temperature and logarithmic in time and that this result is not sensitive to the exact form of the QP-QP interaction or the presence of a weak electric dipole interaction. We suggest that the concepts developed for KCN-KBr mixed crystals may also help to explain the quasiuniversal low-temperature thermal properties of canonical and other quadrupolar glasses.

In order to clarify the transport mechanism in fully protanated highly conductive polyaniline the origin and size of the electronic localization centers and barriers have to be determined. Dispersions of polyaniline in an insulating polymer have been studied by temperature-dependent broadband dielectric spectroscopy (5 Hz to 2 GHz, 100–320 K). The electronic transport in the blends and in pure polyaniline is shown to be governed by three-dimensional (3D) hopping between mesoscopic crystalline regions surrounded by amorphous polyaniline and not by intermolecular hopping or molecular scale disorder. Two independent approaches yield an average size of 8 nm for the metallic regions in polyaniline with 3D extended electron wave functions. The barrier width is estimated to be 1.6 nm. The crystalline metallic regions with an amorphous shell correspond to the primary particles which were found in morphological studies.

Asymptotic analysis and finite-element simulations are used to explore the nonlinear dynamics present in cellular interface patterns that arise in thin-film directional solidification, as caused by the presence of a codimension-two bifurcation at a specific value of the spatial wavelength for the cells. For certain parameter sets, the quadratic nonlinearities that dominate the dynamics because of 2:1 spatial resonance give rise to secondary steady-state bifurcation and to time-periodic states with periods that scale as ${\mathrm{\delta }}^{\mathrm{-}3/2}$, where δ measures the distance from the parameter values for the codimension-two state. The structure of this dynamics is explored in closed form for a modified Swift-Hohenberg equation and for the two-sided, solutal model for directional solidification. The asymptotic results for directional solidification are verified by finite-element numerical simulations for small amplitude cells.

A description of vibrational excitations in one-dimensional monoatomic Bravais lattices is presented in terms of an algebraic model of coupled anharmonic oscillators. The energy corresponding to one-phonon excitations is obtained analytically. We discuss the connection between the normal-mode picture and the local mode in our approach. We also present numerical results for two-phonon excitations and apply the model to study the behavior of the density of states for the normal to local transition.