We derive an ab initio ${\mathrm{Nb}}^{5+}$–${\mathrm{O}}^{2\mathrm{-}}$ short-range pair potential appropriate to ${\mathrm{KNbO}}_3$, which is based on suitable cluster Hartree-Fock calculations. The cluster to be chosen must necessarily represent a larger portion of ${\mathrm{KNbO}}_3$ crystals than a lone ${\mathrm{Nb}}^{5+}$${\mathrm{O}}^{2\mathrm{-}}$ pair embedded in the appropriate Madelung potential. Our final Hartree-Fock pair potential derived from (embedded) (${\mathrm{NbO}}_6$${)}^{7\mathrm{-}}$ cluster calculations is in good agreement with a corresponding empirical potential obtained from fitting procedures to macroscopic properties of ${\mathrm{KNb}}_3$${\mathrm{O}}_8$. Both potentials generate the cubic phase of ${\mathrm{KNbO}}_3$. Finally, the implications of these two ${\mathrm{Nb}}^{5+}$–${\mathrm{O}}^{2\mathrm{-}}$ pair potentials are discussed by means of shell-model defect simulations in ${\mathrm{KNbO}}_3$ and ${\mathrm{KTaO}}_3$.

The polarized optical absorption spectra of ${\mathrm{Cr}}^{3+}$ ions have been systematically investigated in two acentric crystals with Ca-gallogermanate structure: ${\mathrm{La}}_3$${\mathrm{Ga}}_{5.5}$${\mathrm{Nb}}_{0.5}$${\mathrm{O}}_{14}$ and ${\mathrm{La}}_3$${\mathrm{Ga}}_{5.5}$${\mathrm{Ta}}_{0.5}$${\mathrm{O}}_{14}$. Crystal-field parameters have been determined for both ${\mathrm{Cr}}^{3+}$-doped crystals. Features observed in the long-wavelength ${}_{}{}^4{}_{}{}^{}$${\mathit{A}}_2$${\to }^4$${\mathit{T}}_2$ absorption band of ${\mathrm{Cr}}^{3+}$ have been associated with Fano antiresonances, due to interaction between the ${}_{}{}^2{}_{}{}^{}$E and ${}_{}{}^2{}_{}{}^{}$${\mathit{T}}_1$ sharp levels and the vibrationally broadened ${}_{}{}^4{}_{}{}^{}$${\mathit{T}}_2$ quasicontinuum. The line shapes have been analyzed in terms of the four-parameter theory of Fano, so that the interaction has been evaluated for both crystals and compared with other ${\mathit{d}}^3$ ion-doped systems.

The quenching of the radiative ${\mathit{e}}^{\mathrm{-}\mathrm{-}}$${\mathit{h}}^{+}$ recombination in barium aluminoborate glass, x irradiated at 77 K, was investigated by EPR and thermoluminescence (TL) techniques as a function of an iron impurity concentration ranging from ${10}^{\mathrm{-}3}$ to 0.1 at. %. The analysis of the EPR line shape of ${\mathrm{Fe}}^{3+}$, observed in these glasses, suggested that a large fraction of Fe impurity occupies substitutional sites of the glass-forming network, locally charge compensated by a pair of ${\mathrm{Ba}}^{2+}$ interstitial cations. The electron untrapping activation energy from the boron electron centers [D. L. Griscom, J. Chem. Phys. 55, 1113 (1971)], obtained from the TL initial slope, is equal to 0.21 eV. The correlation between the TL intensity and the Fe concentration was found to be exponential, and is discussed on the basis of some recent theories for the nonradiative ${\mathit{e}}^{\mathrm{-}\mathrm{-}}$${\mathit{h}}^{+}$ recombination mechanism.

The slowing-down process of Ti atoms in crystalline Ti and Si atoms in crystalline Si is studied using the molecular-dynamics method. Based on an experimental technique available for studies of the slowing-down process of atoms at ultralow velocities in bulk matter, the initial recoil energy was 261 eV for Ti and 677 eV for Si atoms. The values correspond to the energies imparted after the thermal neutron capture by primary γ rays. The effect of the crystalline structure on the slowing-down process is studied by calculating the energy distribution of the Doppler-shifted secondary γ rays emitted by the recoiling nuclei. The dependence of the distribution on the interatomic potential used in the simulations is also investigated.

We study a one-dimensional model of ferroelectrics with proton tunneling on the hydrogen bonds. The influence of tunneling on the thermodynamics of the model is considered in the approximation of Nagle [exp(-w/T)=0] and for energies of the forbidden configurations w much larger than the tunneling constant Γ. The rearrangement of the energy levels due to the inclusion of proton tunneling is investigated by secular perturbation theory, using Γ/w as a small parameter. Exactly solvable six-vertex one-dimensional models with tunneling are obtained as the first nonvanishing orders of this theory. The phase transition from the disordered to the polar phase is found to be first order as in the case of Γ=0, but the transition temperature ${\mathit{T}}_{\mathit{c}}$ and the entropy jump ΔS decrease with the increase of the parameter δ=${\mathrm{\Gamma }}^2$/ɛw, where ɛ is the energy of the excited configurations obeying the ice rule. When γ=(1-δ)→0, ${\mathit{T}}_{\mathit{c}}$, ΔS, and the energy gap, separating the ground ferroelectric state from the excited states, tend to zero as 2ɛ/ln(1/γ), (γ/2)ln(1/γ), and ɛγ, respectively. The results are compared with the experimental data on the ferroelectric, K(${\mathrm{H}}_{\mathit{x}}$${\mathrm{D}}_{1\mathrm{-}\mathit{x}}$)${\mathrm{PO}}_4$.

The optical properties of trivalent chromium ions in ${\mathrm{La}}_3$${\mathrm{Ga}}_5$${\mathrm{SiO}}_{14}$ crystals have been investigated by means of absorption, emission, excitation, and lifetime measurements. The particular intermediate value of the octahedral crystal field Dq/B∼2.5 causes the overlapping of the ${}_{}{}^4{}_{}{}^{}$${\mathit{T}}_2$ with the ${}_{}{}^2{}_{}{}^{}$E and ${}_{}{}^2{}_{}{}^{}$${\mathit{T}}_1$ levels. This overlap is the origin of Fano resonances in the absorption spectrum and of the simultaneous presence of broadband and narrow-line emissions. Polarized measurements have allowed the determinations of second-order effects such as the tetragonal or orthorhomic distortion of the octahedron of oxygen ions around the chromium ion. Moreover the temperature shift of the peak and the nonexponential decay of the broad emission band are indications of the disorder present in the crystal lattice. All these results produce a fairly complete picture of the energy levels of ${\mathrm{Cr}}^{3+}$ ions in a typical crystal of the Ca-gallogermanate family.

The thermodynamics and kinetics of order-disorder processes derived from the cluster-activation method (CAM) and microscopic diffusion theory (MDT) are examined. In the single-site approximation, the homogeneous long-range-order kinetic equations for the direct exchange mechanism (Kawasaki dynamics) in the CAM are derived by employing a kinetic theory of a Markovian nature whereas the kinetic equations in MDT are derived from the Onsager-type diffusion equations based on a microscopic mean-field free-energy functional. While the single-site approximation in MDT results in equilibrium states corresponding to the Bragg-Williams approximation, the same approximation in the CAM produces equilibrium states close to the Bethe (nearest-neighbor-pair) approximation. The physical origin underlying the partial inclusion of nearest-neighbor-pair correlation information in the single-site approximation of the CAM is discussed. It is shown that if the values of (ordering energy)/${\mathit{k}}_{\mathit{B}}$T and the time-dependent long-range parameter η are small (≪1), the kinetic equations in the CAM reduce to those in MDT. It is demonstrated that the disordering kinetics obtained from the linearized equations for both models agree, at least qualitatively, with those from nonlinear equations but not the ordering kinetics.

An extension of the well-known coherent-potential approximation is developed for the study of various properties of random arrangements of spherical dielectric scatterers. Some of the short-range order is taken into account by considering a coated sphere as the basic scattering unit. A generalization of the energy-transport velocity is obtained. The validity of our approach is checked by comparison with experimental results, as well as with numerical calculations. Results for the long-wavelength effective dielectric constant, phase velocity, energy-transport velocity, mean free path, and diffusion coefficient are presented and compared with experiments on scattering from dielectric spheres. In addition, our findings suggest that the positions of the band gaps in periodic dielectric structures are closely related with the range of localized states in random dielectric media.

The three partial structure factors of liquid hydrogen bromide along the coexistence curve have been measured by neutron diffraction using the isotopic substitution technique. The structure factors and corresponding pair correlation functions obtained suggest that it is an excellent approximation to regard the bromine atom as the center of mass of the hydrogen bromide molecule. The anisotropic terms in the intermolecular potential manifest themselves primarily by causing a significant degree of correlation between the orientations of neighboring molecules. In order to gauge the size of these orientational correlations an image reconstruction technique is employed. This analysis shows that there is a pronounced correlation between the relative orientations of neighboring molecules, but that there is not a strong directionality in the local coordination of any particular molecule. The results are discussed in relation to a previous experiment on hydrogen bromide which proposed the formation of hydrogen bonds in this liquid.

The multiphonon relaxation (MR) rates for a large number of 3- to 5-phonon transitions of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{LiYF}}_4$ and ${\mathrm{LaF}}_3$ crystals were measured at 77 K. The MR rates of ${\mathrm{Nd}}^{3+}$ and ${\mathrm{Er}}^{3+}$ ions in these crystals have been analyzed with a point-charge (or ionic) nonlinear relaxation mechanism and a covalent nonlinear relaxation mechanism, rather than the traditional linear relaxation mechanism. The functional dependencies of the experimental MR rates on the number of phonons n participating in the radiationless transitions were explained in terms of the two nonlinear coupling mechanisms. The mean values of the parameter of the theory η=${\mathit{u}}^2$/${\mathit{R}}_0^2$, where ${\mathit{R}}_0$ is the equilibrium minimal distance between the rare-earth ion and the ligands and u is the amplitude of the vibrations of the ligands, have been evaluated in these crystals for n=3–4 where the contribution of the exchange interaction is small. On the basis of these calculations it was established that the strength of dynamic electron-phonon coupling is larger in ${\mathrm{LaF}}_3$ than in ${\mathrm{LiYF}}_4$. Also, the influence on the MR rates of the exchange interaction between the 4f electron and the ligands has been analyzed. Its inclusion gives higher theoretical MR probabilities and better agreement with the experimental relaxation rates.

The basis of dry friction is discussed using an independent oscillator model with longitudinal motion. This sample system is treated both numerically and with analytical methods. At vanishing velocity a sliding dry friction force is calculated which is smaller than the pinning force. At finite but not too large velocities the system displays bifurcation, chaotic motion, resonances at fractional and multiple frequencies of the oscillator, and hysteresis. Dry friction results from these complicated features. This force varies rapidly with velocity within this range, however, with a roughly constant mean value.

Numerical investigations of the trapping of Frenkel excitons in one-dimensional lattices with interstitial traps randomly placed in pairs are presented. The probabilities of finding the exciton both in the q=0 mode P(t) and in any mode Q(t) have been obtained following the numerical approach recently developed by Huber and Ching [Phys. Rev. B 42, 7718 (1990)] for unpaired traps. We have found that the pairing of traps enhances both probabilities at all times, in comparison with lattices containing the same fraction of unpaired traps. We suggest that this behavior is related to the occurrence of larger segments of the lattice that are free of traps, where there exists a major contribution of the slowly decaying modes.

The differences in the observed properties of solid ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ are reviewed, and in particular those encountered in NMR experiments. The failure to detect a sharp NMR (I=1) impurity ‘‘isolated pair’’ spectrum in p-${\mathrm{D}}_2$ is discussed in terms of a larger crystalline field than in ${\mathrm{H}}_2$, where an intense and sharp pair spectrum has been observed. Furthermore, we discuss the dramatic (I=1) solid echo signal loss with decreasing temperature which is observed in solid ${\mathrm{D}}_2$, but not for solid ${\mathrm{H}}_2$. A theory of the solid echo damping through orientational fluctuations is developed. This theory accounts for the observed solid echo decay in ${\mathrm{D}}_2$ as a function of the pulse spacing time τ and leads to an estimation of the order parameter fluctuation amplitude and the correlation time ${\mathrm{\tau }}_{\mathit{c}}$. However, the theory cannot account for the loss of spin (as determined from Curie’s law), which must occur for very small values of τ that are not covered by the theory.

NMR frequency shifts between the (I=1) and (I=2) spin systems for hcp p-${\mathrm{D}}_2$ and o-${\mathrm{D}}_2$ are reported with a p-${\mathrm{D}}_2$ concentration X=0.32. The solid-echo method was used, and the temperature range was from 0.09 to 1.0 K, where the respective echo signals can be well resolved. The echo amplitude ratio S(I=1)/S(I=2) reveals singularities in the off-resonance experiments. The magnitudes and shapes of these singularities were interpreted as a temperature-dependent frequency shift and the fitted curves with the frequency shift as free parameter agreed well with the experiments. The shift is ν(I=1)-ν(I=2)=30±5 Hz below 0.2 K and decreases to zero as the temperature increases to 1 K. The results are discussed in terms of recent predictions.

The structural transition from cubic to orthorhombic has been found in ${\mathrm{LaFe}}_7$${\mathrm{Al}}_6$. Measurements of the magnetization reveal that the ${\mathrm{LaFe}}_7$${\mathrm{Al}}_6$ with cubic ${\mathrm{NaZn}}_{13}$-type structure has a paramagnetic-mictomagnetic (spin-glass) transition, while the orthorhombic ${\mathrm{LaFe}}_7$${\mathrm{Al}}_6$ exhibits paramagnetic-ferromagnetic-mictomagnetic transitions. These magnetic transition behaviors can be statisfactorily explained by a solvable model of a spin glass.

We present a computer-simulation study of the effect of the distribution of energy barriers in an anisotropic magnetic system on the relaxation behavior of the magnetization. While the relaxation law for the magnetization can be approximated in all cases by a time logarithmic decay, the law for the dependence of the magnetic viscosity with temperature is found to be quite sensitive to the shape of the distribution of barriers. The low-temperature region for the magnetic viscosity never extrapolates to a positive no-null value. Moreover our computer simulation results agree reasonably well with some recent relaxation experiments on highly anisotropic single-domain particles.

We present an analysis of the nature of antiferromagnetic coupling at the rare-earth-metal surface in the framework of a simple s-f model with rigid, highly localized f moments. We demonstrate that antiferromagnetic coupling takes place at the rare-earth-metal surface, if the effect of density of states distortion via surface perturbation prevails over the effect of spin-subband splitting with the same energy. The results of calculations for the hcp (0001) surface deformed along the normal axis have shown that there is an optimal degree of deformation that corresponds to the most probable observation of antiferromagnetic coupling. The coexistence of antiferromagnetic coupling and surface-enhanced magnetic order observed in experiments with Gd(0001) is explained.

We discuss the spin excitations of a simple model of an ultrathin ferromagnetic film, in which the magnetic moment bearing electrons are itinerant in character. The one-band Hubbard model, treated in mean-field theory, forms the basis of the discussion. The spin excitations are treated by means of the random-phase approximation. We find spin-wave modes of standing wave character, and a spectrum of Stoner excitations influenced strongly by size effects. While the dispersion relations of the standing spin-wave modes appear as expected from a localized-spin model, there are substantive differences between the itinerant- and localized-spin cases. An example is the number of spin-wave modes evident in the appropriate spectral density functions, for each wave vector. We use a previously developed formalism of spin-polarized electron-energy-loss scattering (SPEELS) to compute SPEELS spectra for our model film. In addition to a broad feature with origin in Stoner excitations, we find clear and relatively intense spin-wave loss peaks.

Measurements of the superconducting critical temperature ${\mathit{T}}_{\mathit{c}}$(n,P) as a function of Ce concentration n and pressure P≤20 kbar are reported for the superconducting Kondo systems (${\mathrm{La}}_{1\mathrm{-}\mathit{n}}$${\mathrm{Ce}}_{\mathit{n}}$)${\mathrm{Al}}_2$ and (${\mathrm{La}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Th}}_{\mathit{x}}$${)}_{1\mathrm{-}\mathit{n}}$${\mathrm{Ce}}_{\mathit{n}}$ (0≤x≤0.25). Data for the (${\mathrm{La}}_{1\mathrm{-}\mathit{n}}$${\mathrm{Ce}}_{\mathit{n}}$)${\mathrm{Al}}_2$ system are partially consistent with the theory of Müller-Hartmann and Zittartz (MHZ), assuming an increase of ${\mathit{T}}_{\mathit{K}}$/${\mathit{T}}_{\mathit{c}0}$ with P, where ${\mathit{T}}_{\mathit{K}}$ is the Kondo temperature and ${\mathit{T}}_{\mathit{c}0}$ is the critical temperature of the pure host superconductor. However, the pressure evolution of the reentrant superconducting-normal phase boundaries for the (${\mathrm{La}}_{0.8}$${\mathrm{Th}}_{0.2}$${)}_{1\mathrm{-}\mathit{n}}$${\mathrm{Ce}}_{\mathit{n}}$ system is unexpected, and inconsistent with the MHZ theory. We find no evidence for the existence of a third transition (predicted by MHZ) back to the superconducting state for either the (${\mathrm{La}}_{0.8}$${\mathrm{Th}}_{0.2}$${)}_{1\mathrm{-}\mathit{n}}$${\mathrm{Ce}}_{\mathit{n}}$ or (${\mathrm{La}}_{1\mathrm{-}\mathit{n}}$${\mathrm{Ce}}_{\mathit{n}}$)${\mathrm{Al}}_2$ systems. Recent Monte Carlo calculations by Jarrell may explain our data for both alloy systems, provided strong electron-phonon coupling effects are taken into account, although the effects of interimpurity interactions on the data remain uncertain.

We describe a method for the computation of resistivity in a periodic or nonperiodic multilayer of magnetic materials. We show that the approach that leads to the well-known constant-relaxation-time solution to the Boltzmann equation in systems with spherical symmetry [J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, Cambridge, England, 1964)] can be generalized to cylindrical symmetry. The effects of interface scattering are included. For a layered system with a step-function potential, we have calculated scattering matrix elements from the exact quantum-mechanical wave functions. In the special case of two layers these are the well-known Kronig-Penney wave functions, but we have developed a transfer-matrix method for obtaining them in general, so our code will work for an arbitrary number of layers. We find that in realistic models there are often states trapped between high-potential layers, for which numerical divergences occur; we show how to handle these cases by a recursive procedure. The advantages of the quantum method over semiclassical ones are that (a) it includes interference effects exactly, and (b) it involves fewer free parameters. We give results for the ‘‘giant magnetoresistance’’ of a model of an FeCr sandwich structure for various numbers of layers. The approach to the result for an infinite periodic system is highly singular.