The structural aspect of the temperature-induced neutral-to-ionic transition in the mixed-stack charge-transfer complex TTF-p-chloranil is directly analyzed using results obtained from neutron-scattering experiments. The symmetry breaking of the structural order parameter is determined together with the complete structural change. It is shown that the ionic phase is characterized by a dimerization along the stacking direction into weakly bond donor-acceptor dimers, which adopt a ferroelectric arrangement. Values of both dipole moment and dipolar energy in the unit cell are evaluated and commented. The evolution of the three-dimensional contacts which interconnect the chains, and in particular of the hydrogen interaction network, is discussed. Moreover, the associated intramolecular deformations are related in a satisfying way with the change of the ionicity and with the loss of centrosymmetry at the transition. Phenomena of metastability are also briefly discussed.

The modified-hypernetted-chain theory is applied to the determination of the phase diagram of the Lennard-Jones (LJ) fluid, and of a model of ${\mathrm{C}}_{60}$ previously investigated [Phys. Rev. Lett. 71, 1200 (1993)] through molecular-dynamics (MD) simulation and a different theoretical approach. In the LJ case the agreement with available MD data is quantitative and superior to other theories. For ${\mathrm{C}}_{60}$, the phase diagram obtained is in quite good agreement with previous MD results: in particular, the theory confirms the existence of a liquid phase between 1600 and 1920 K, the estimated triple point and critical temperature, respectively.

The lattice energy (LE), equilibrium lattice parameter (${\mathit{a}}_0$), elastic constants (${\mathit{C}}_{\mathit{i}\mathit{j}}$), and central-zone phonon frequencies (ν) of LiF, LiCl, NaF, NaCl, KF, and KCI have been evaluated with crystal, a periodic ab initio Hartree-Fock linear combination of atomic orbitals program. The mean error with respect to experiment is 5.7%, 3.4%, 14.6%, and 8.8% for LE, ${\mathit{a}}_0$, B [bulk modulus; B=1/3(${\mathit{C}}_{11}$+2${\mathit{C}}_{12}$)], and ν, respectively. The errors increase systematically with increasing size of the cation or anion. Correlation effects (both intraionic and interionic) are the main reason for the discrepancies with respect to experiment.

The contrast in electron channeling patterns is quantitatively treated using a theory in which electrons in Bloch states excited by the incident electron are scattered through large angles by the fluctuation part of the potential (thermal diffuse scattering). The subsequent multiple elastic and inelastic scattering is described by an inhomogeneous transport equation. Formally this is shown to be identical to the solution of the kinetic equation for the one-particle spectral density matrix. Employing the supermatrix algorithm proposed by Fathers and Rez, we develop a computational technique which makes it possible to perform full-scale multiple scattering simulations of electron backscattering from crystals and to provide a consistent quantitative explanation of a number of experimental observations, including the dependence of the contrast on the detector position and on the energy of the backscattered electrons, the origin of which has not previously been fully accounted for. Our computational results show a substantial increase in the channeling contrast and in the signal-to-noise ratio for the conditions of oblique incidence and low takeoff angle of backscattering, which agrees with recent experimental studies. We show that under the conditions of multiple scattering there exists a perturbation expansion which considerably simplifies the problem of evaluation of the contrast and which can be employed for interpretation of channeling images of defects.

We introduce the augmented-space recursion method coupled with the orbital peeling technique as a powerful tool for the calculation of effective cluster interactions, and useful for the study of alloy phase stability. An application to the well studied Pd-V system has been carried out.

Alloy melts of the intermetallic compounds FeSi and CoSi were deeply undercooled using the melt fluxing technique. Crystal-growth velocities were measured as a function of undercooling by a high-speed photosensing infrared device. The experimental results were analyzed in the framework of dendrite growth theories with special emphasis placed on the kinetic interface undercooling. This analysis gives insight into nonequilibrium effects occurring during rapid solidification of undercooled melts of intermetallic compounds due to short-range diffusion-limited dendritic growth.

A reciprocal-space formulation of the cluster variation is used in order to extract effective pair interactions in alloys from experimental short-range-order diffuse intensities. The method is applied to the analysis of the short-range-order contribution to the neutron diffuse scattering of an Fe–19.5 % Al single crystal. A detailed comparison with real-space methods is carried out for three different levels of approximations. For the highest level of approximation used in this study, effective pair interactions up to fifth neighbors are obtained.

${\mathrm{CaYAlO}}_4$ crystals codoped with ${\mathrm{V}}^{4+}$ and ${\mathrm{Mg}}^{2+}$ ions have been grown in an inert atmosphere. EPR measurements reveal that ${\mathrm{V}}^{4+}$ ions in ${\mathrm{CaYAlO}}_4$ occupy orthorhombic symmetry sites. The optical-absorption spectrum comprises two intense bands with peaks at 330 and 430 nm, together with a weak band around 500 nm. Excitation in the 500-nm band produces a broad luminescence band with a peak at 690 nm. The radiative center associated with these spectra is assigned to ${\mathrm{V}}^{4+}$(3${\mathit{d}}^1$) ions. The peak wavelength of the luminescence band shifts to longer wavelengths with increasing excitation wavelengths in the 500-nm absorption band, an effect associated with the inhomogeneous broadening of the luminescence band caused by random distribution of ${\mathrm{Ca}}^{2+}$ and ${\mathrm{Y}}^{3+}$ ions in the disordered ${\mathrm{CaYAlO}}_4$ lattice.

The spectral momentum density ρ(ε,q) of the valence electrons of a thin polycrystalline silicon carbide (SiC) film has been measured using an (e,2e) spectrometer employing a noncoplanar asymmetric geometry with estimated energy and momentum resolutions of about 2.0 eV and 0.15 a.u., respectively. Well-defined valence-band dispersion has been observed from the measured momentum density which resembles a parabola, but deviates from what is expected for a free electron near the top of the band and at the boundary of the Brillouin zone, where the antisymmetric gap due to the unequal potentials between the Si and C sites in SiC is clearly visible. Based on the assumption that the spectral momentum density of polycrystalline materials is a spherical average of the spectral momentum density of the corresponding single crystalline phase of the materials, ab initio linear muffin-tin orbital calculations have been performed using the zinc-blende structure of β-SiC. The measured dispersion of the energy band is in excellent agreement with theory. Reasonable agreement is also obtained for the energy-integrated momentum density, although the measured momentum density exceeds considerably the calculated one at high momenta. The theoretical implication of using crystal band-structure calculations for studying disordered materials is also discussed.

We have developed a three-body potential based on a two-body model potential and applied it, as an application, to reproduce the experimental phonon frequencies of the fcc Pd–10% Fe alloy. For this purpose two- and three-body interactions have been employed to develop the dynamical matrix of the fcc structure. The parameters defining the two- and three-body potentials for Pd and Fe have been evaluated for the fcc structure at the lattice constant of the alloy. The radial, tangential, and three-body force constants of the alloy have been calculated by the concentration averages of the computed force constants of the component metals. Finally, the phonon frequencies of the alloy along the principal symmetry directions have been computed using the calculated force constants. The theoretical results are in good agreement with the corresponding experimental values.

We report calculations of quantum tunneling in solid deuterium and solid hydrogen using a most-probable-escape-path method for tunneling in quantum crystals. We estimate the rates for tunneling by quantum-mechanical exchange in solid ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ and calculate specifically the tunneling of HD impurities and paradeuterium impurities in solid parahydrogen and solid orthodeuterium. These calculations are compared with the results of recent experiments.

We study the time dependence of the energy redistribution between an initially localized electron and the vibrations of a one-dimensional anharmonic lattice. Numerical solutions show the periodic electron-lattice energy exchange, in contrast to the usual irreversible gradual decrease of the electronic energy. This energy trapping is shown to occur due to the appearance of localized vibrations, induced by strong enough electron-vibrational coupling in the anharmonic lattice. For these strong-coupling situations, we observed both localized (trapped) and conductive electronic charge.

We describe the failure of two-component square- and cubic-lattice random resistor networks. The model behavior is dependent on the ratio of the conductances of the two components g, the ratio of the (brittle) failure thresholds of the two components i, the volume fraction p, and the sample size L. For much of the parameter space, the average strength of the networks shows a rather weak size effect, and a scaling argument suggests that this size effect is logarithmic. As usual, near the percolation points, there can be algebraic scaling provided i and g are very large or small. Near the limits p=0 and p=1, there is a logarithmic (‘‘dilute-limit’’) singularity in average strength. The ability to absorb damage is very strongly dependent on the model parameters. When one phase is more conducting and weaker than the other, and the strong phase is connected, the damage is usually extensive. Basically most of the weak bonds fail prior to the failure of the whole network. In the other regions of parameter space, damage is not extensive, but it does sometimes scale in a nontrivial way with the sample size.

We report the fracton density of states (DOS) and its fluctuation properties on the infinite two-dimensional critical percolation cluster and its backbone. The fracton DOS fluctuations, as expressed by the number variance 〈[δN(E)${]}^2$〉 in an energy width E, follow the quadratic law 〈[δN(E)${]}^2$〉∝〈N(E)${\mathrm{〉}}^2$, instead of the usual linear Poissonic behavior normally expected for localized states. We also find that the average DOS for the percolation backbone obeys the one-parameter fracton scaling theory with a spectral dimension ${\mathit{d}}_{\mathit{s}}^{\mathrm{BB}}$=1.23±0.02. This kind of violent DOS fluctuation cannot be understood in the context of random matrix theories and is discussed in connection to intermittency and multifractal localization.

The lowering of the total energy due to the electron-vibration interaction is calculated for ${\mathit{C}}_{60}^{\mathit{n}\mathrm{-}}$ molecules and the electron-vibration contribution to the on-site interaction is obtained. It is found that ${\mathit{C}}_{60}^{\mathit{n}\mathrm{-}}$ is in the intermediate- to strong-coupling limit, and that the vibration contribution to the on-site interaction if of the order -0.1 to -0.2 eV for n=1 and 3 and of the order +0.3 eV for n=2 and 4.

We predict that the response of a weakly damped one-dimensional lattice to a localized ac driving force demonstrates a strong resonance when the driving frequency is close to the upper edge of the lattice phonon band. The response is considered in terms of the energy absorption rate vs the driving frequency, which is an experimentally observable characteristic. We consider the effect semianalytically for the linear lattice, and then display results of systematic direct numerical simulations of both linear and nonlinear cases, which clearly demonstrate the resonance predicted. In comparison with the known resonance for the case when the driving frequency is close to the lower edge of the phonon band, the new resonance is stronger, and also more robust when competing with dissipation and nonlinearity. Both resonances are closely related to the singularities of the lattice’s density of states at the edges of the phonon band.

We report the results of measurements of the proton ${(}^1$H) spin-lattice relaxation rate ${\mathit{R}}_1$ at high temperatures (to ∼1400 K) in the hcp (α) solid-solution phases of the Sc-H, Y-H, and Lu-H systems, and of ${\mathit{R}}_1$${(}^{45}$Sc) in Sc-H and Sc-D solid solutions. The latter measurements show unambiguous evidence of an anomalous increase at ∼1000 K, whereas ${\mathit{R}}_1$${(}^1$H) shows no such increase at any temperature. This behavior of ${\mathit{R}}_1$${(}^1$H) contrasts with that in the bcc V-H, etc., solid solutions where anomalous relaxation occurs below ∼1000 K, and in all investigated metal dihydride phases, M${\mathrm{H}}_{2\mathrm{-}\mathit{x}}$. The anomalous ${\mathit{R}}_1$${(}^1$H) behavior in α-${\mathrm{VH}}_{\mathit{x}}$, α-${\mathrm{NbH}}_{\mathit{x}}$, etc., may be understood in terms of fast spin relaxation in the ${\mathrm{H}}_2$ gas in equilibrium with the solid, mediated by fast gas-solid exchange of hydrogen. However, in the present systems, α-${\mathrm{ScH}}_{\mathit{x}}$, α-${\mathrm{YH}}_{\mathit{x}}$, etc., the ${\mathrm{H}}_2$ gas pressure in equilibrium with the hcp systems is extremely low, resulting in negligible ${\mathrm{H}}_2$ concentration in the gas phase, and consequently a negligible contribution to ${\mathit{R}}_1$${(}^1$H). In contrast, some of the present measurements indicate that the ${\mathit{R}}_1$${(}^{45}$Sc) anomaly does result from the hydrogen content of the metal, but the mechanism remains unexplained.

A translation-invariant adiabatic theory is constructed for the bipolaron. It is shown that motions in the bipolaron are divided: the relative electron coordinates describe fast electron oscillations in the induced polarization well and the center of mass coordinates represent slow electron movement followed by polarization. Nonlinear differential bipolaron equations are derived which are asymptotically exact in the adiabatic limit. Particlelike solutions of these equations correspond to the bipolaron bound state. The exact solution yields the value of the ion critical parameter η=0.31 for which the bipolaron state is stable, where η=${\mathrm{\epsilon }}_{\mathrm{\infty }}$/${\mathrm{\epsilon }}_0$ and ${\mathrm{\epsilon }}_{\mathrm{\infty }}$,${\mathrm{\epsilon }}_0$ are high-frequency and static dielectric permittivities. The energy, the total energy, the effective mass, the radius, and the critical values of the electron-phonon coupling constants are calculated for the bipolaron. The results obtained are generalized to the case of two-dimensional bipolarons.

Following general ideas proposed by C. Feldman et al. and extended by D. C. Wallace in his book on the thermodynamic properties of crystals, we have derived detailed expressions for both external and internal strain derivatives of the Helmholtz free energy of a perfect crystal. The thermodynamic functions are calculated in the quasiharmonic approximation though the present theory can be straightforwardly extended for an arbitrary order of anharmonicity. The formalism developed in this paper is similar, but not equal, to those proposed by previous authors. We have made several important generalizations of the existing theory and, besides, have obtained equations which are much simpler. It makes it possible to consider an arbitrary shell-model crystal with nonprimitive lattice (including piezoelectric crystals) and to pay special attention to the numerical implementation of the formulas obtained. Moreover, by careful consideration, we have corrected a physically doubtful conclusion existing in a particular piece of the literature, namely that microscopic and macroscopic expressions for the crystal energy may not coincide. We prove rigorously that a proper microscopic consideration does lead to the same macroscopic expression. In the second part of this work the theory developed here will be applied to KCl and NaCl crystals.

In Part I, the theory for external and internal strain derivatives of the Helmholtz free energy of a perfect crystal was developed in the quasiharmonic approximation. The theory allows us to consider arbitrary piezoelectric shell-model-like crystals at any temperature and under general external stress conditions. In the present part of this work we show how these derivatives can be utilized in the simplest way in order to calculate a wide range of macroscopic thermoelastic properties of the crystals. The method was realized in a computer code written without additional artificial constraints concerning crystal symmetry and structure. Special attention is paid to the numerical implementation of the formulas obtained. Using different types of pair potentials including ab initio ones, various elastic, dielectric, and general thermodynamic properties of KCl and NaCl crystals are calculated here for a wide range of temperatures and pressures (only for NaCl). Our calculations in the vicinity of the melting point demonstrate that the free energy has a minimum which disappears at some critical temperature, and the transition is controlled only by the isothermal elastic constant ${\mathit{C}}_{11}^{\mathit{T}}$. It decreases so catastrophically rapidly with increase of temperature that it leads to an immediate violation of the stability condition ${\mathit{C}}_{11}^{\mathit{T}}$>${\mathit{C}}_{12}^{\mathit{T}}$ before the isothermal bulk modulus reaches zero. The calculations also clearly show that the empirical pair potentials of Catlow et al. are in reasonably good agreement with most of the experimental data. In addition, we show, in accord with other authors, that the quasiharmonic approximation can be successfully used almost up to half of the crystal melting temperature, although physically correct qualitative results could be expected even near the melting point.