We generalize a differential effective-medium approximation previously developed for the effective linear response of a fractal cluster, to treat the effective nonlinear response. We consider a material having a nonlinear J-E characteristic which forms a cluster in another, possibly nonlinear material. A differential equation for the cluster-size-dependent nonlinear susceptibility is derived and a general solution is obtained. Numerical examples are given for two special cases: a cluster of a nonlinear material in a linear host, and a cluster of a linear material in a nonlinear host. An enhancement in the nonlinear response due to clustering is found for the case of clustering of a nonlinear material in a linear host.

We obtain explicit expressions for the correlation functions of transmission and reflection coefficients of coherent electronic waves propagating through a disordered quasi-one-dimensional medium with purely elastic diffusive scattering in the presence of spin-orbit interactions. We find in the metallic regime both large local intensity fluctuations and long-range correlations which ultimately lead to universal conductance fluctuations. We show that the main effect of spin-orbit scattering is to suppress both local and long-range intensity fluctuations by a universal symmetry factor 4. We use a scattering approach based on random transfer matrices.

A renormalization-group treatment is used for investigating the critical properties of d-dimensional systems with anisotropic quenched disorder totally correlated in ${\mathrm{\epsilon }}_{\mathit{d}}$ dimensions and randomly distributed in the remaining d-${\mathrm{\epsilon }}_{\mathit{d}}$ space directions (d=4-ε) with long-range correlation which decays with the distance as a power law involving a characteristic parameter σ. Within a triple (ε,${\mathrm{\epsilon }}_{\mathit{d}}$,σ) expansion it is shown that the recursion relations possess a novel focus-type random fixed point leading to new anisotropic critical properties. Under certain conditions, different critical regimes and crossovers are found to occur, consistent with the modified version of the Harris criterion obtained for the random problem under study.

A sample preparation technique, suitable for x-ray-absorption measurements of liquid and supercooled metals is described. The method is based on an application of the emulsion technique, consisting in a dispersion of micrometric droplets in an inert rigid matrix. It has been applied to Hg and Ga resulting in a very fine average droplet size in the submicrometer range. A theoretical probabilistic model, confirmed by experimental data, suggests a log-normal droplet-size distribution. The supercooling capabilities of the samples are studied by means of x-ray-absorption near-edge structure measurements showing exceptional supercooling rates: 153 K for Hg and no crystallization at all for Ga down to 34 K. The problem of a quantitative study of the x-ray-absorption fine structure is addressed and the nonlinearity in the absorption measurements induced by the nonuniform thickness distribution discussed. A method to calculate the sample metal thickness distribution and to derive the actual absorption coefficient is presented.

In Ti-Mo the low-temeprature instability of the bcc lattice leads to precipitation of metastable ω particles. Their coarsening has been found to be controlled by Mo diffusion, because of the low solubility of Mo in the ω phase. Irrespective of the annealing temeperature, the coarsening of ω particles was found to stop when their average diameter reached ≃160 Å. Such a stagnation of the microstructure can be understood as an effect of elastic inhomogeneity of the two-phase system. The shape of the ω particles was determined as a prolate ellipsoid of revolution. The aspect ratio of these coherent particles was constant at 2:1 not only during their coarsening but also in the state of stable particle size. Upon further annealing, the stablization of the two-phase microstructure was destroyed by the nucleation of platelike α-Ti particles that grew at the expense of ω phase. The rapid growth of α particles during the dissolution of ω particles is explained by a structural transition ω→α. After the dissolution of the ω phase, the following growth of the semicoherent α-Ti particles mainly took place on the incoherent rim of the plates. This led, in contrast to the self-similar coarsening of coherent ω precipitates, to continuously increasing aspect ratios of α-Ti particles. Their shape evolution was found consistent with predictions from literature, based on the elastic anisotropy of the crystal lattice.

We report ab initio calculations of the residual resistivity and the deviations from Matthiessen’s rule for dilute ternary alloys. We consider nonmagnetic (Cu) as well as ferromagnetic host materials (Ni) with an admixture of simple-metal (4sp,5sp) or transition-metal (3d,4d) impurities. The calculations are performed within the frame of density functional theory and the Korringa-Kohn-Rostoker Green’s-function method. The transport is described quasiclassically by means of the Boltzmann equation. In the case of a ferromagnetic host a two-current model is applied. Both impurity atoms are considered as noninteracting and the scattering properties of each impurity atom are calculated self-consistently including in addition to the impurity potential one shell of perturbed host potentials around the impurity. Our results show satisfactory agreement with experiments and confirm the validity of Matthiessen’s rule in nonmagnetic systems. In ferromagnetic systems the two-current model is confirmed.

The source of high-temperature anomalous spin relaxation in a specific metal-hydrogen system has been investigated. Proton spin-lattice relaxation rates ${\mathit{R}}_1$ from 290 to 1025 K were compared for ${\mathrm{Nb}}_{0.5}$${\mathrm{V}}_{0.5}$${\mathrm{H}}_{0.36}$ and its 90% deuterided counterpart, ${\mathrm{Nb}}_{0.5}$${\mathrm{V}}_{0.5}$(${\mathrm{H}}_{0.1}$${\mathrm{D}}_{0.9}$${)}_{0.36}$. A substantial reduction in the anomalous proton relaxation rate ${\mathit{R}}_1$ is observed for the deuterided metal. Thus, the proton relaxation rates ${\mathit{R}}_1$ are determined by proton-proton (or proton-deuteron) dipolar interactions in the anomalous regime, suggesting that ${\mathrm{H}}_2$ (or HD) molecules are the source of the relaxation. Relaxation studies with overpressures of argon and xenon gas indicate that the anomalous relaxation of protons in the metal occurs via fast exchange with rapidly relaxing gas phase ${\mathrm{H}}_2$ molecules. A small fraction of protons in the gas phase, consistent with the ${\mathrm{H}}_2$ vapor pressure of the metal hydride, is adequate to explain our results. A model, based on experiment, is presented along with measurements of the proton ${\mathit{R}}_1$ for pure ${\mathrm{H}}_2$ and HD gas and gaseous mixtures of ${\mathrm{H}}_2$ with Ar and ${\mathrm{H}}_2$ with ${\mathrm{D}}_2$. The model quantitatively accounts for the isotope and rare-gas effects as well as the temperature dependence. Thus, in ${\mathrm{Nb}}_{0.5}$${\mathrm{V}}_{0.5}$${\mathrm{H}}_{0.36}$, the relaxation anomaly is proven not to be an intrinsic effect.

We report the polarized Raman spectra of ${\mathrm{Nd}}_2$${\mathrm{BaZnO}}_5$ and the nonpolarized infrared-absorption spectra of ${\mathrm{Nd}}_2$${\mathrm{BaMO}}_5$ (M=Zn,Cu). Thirteen out of a total of fifteen Raman-allowed modes (3${\mathit{A}}_{1\mathit{g}}$+2${\mathit{B}}_{1\mathit{g}}$+4${\mathit{B}}_{2\mathit{g}}$+6${\mathit{E}}_{\mathit{g}}$) were observed. The optical-phonon assignment was made using molecular-site group analysis, taking account of the fact that the ${\mathrm{ZnO}}_4$ (${\mathrm{CuO}}_4$) groups are relatively isolated. In spite of the different shapes of ${\mathrm{ZnO}}_4$ (tetrahedron) and ${\mathrm{CuO}}_4$ (square) units resulting in different space groups of ${\mathrm{Nd}}_2$${\mathrm{BaZnO}}_5$ (I4/mcm) and ${\mathrm{Nd}}_2$${\mathrm{BaCuO}}_5$ (P4/mbm), a comparison between the modes in the two structures is done. We argue that the high-frequency bands in ir spectra involve mainly vibrations of Nd-plane oxygen atoms.

The dynamical dielectric function of solid electrolytes is derived and analyzed theoretically. The Debye theory of charge screening in liquid electrolytes is modified to account for the effect of the crystalline lattice on the dynamics of ionic transport. The theory is used to process the experimental data on the dispersion of the dynamic conductivity in ${\mathrm{RbAg}}_4$${\mathrm{I}}_5$ and Na β-${\mathrm{Al}}_2$${\mathrm{O}}_3$ and to determine the microscopic characteristics of ionic transport.

We study the nonlinear propagation of thermal waves in rigid heat conductors using a model introduced by Ruggeri et al. We derive the lowest-order nonlinear corrections to the wave speed and show that the quadratic nonlinearity can be small for NaF and Bi. The smallness of the nonlinear steepening parameter complicates the wave dynamics, allowing for both forward and backward steepening waves within the same pulse. We show that this mixed condition places limits on the size of admissible discontinuities; we then argue that this limit on the size of shock waves limits the arrival times of thermal signals. Using this, we propose an experiment to measure arrival times to look for this limiting behavior.

Pure and doped antiferromagnetic ${\mathrm{CsMnCl}}_3$⋅${2\mathrm{H}}_2$O (CMC) crystals have been studied in the temperature range 4.2–300 K. With an increase in temperature the luminescence time and intensity of doped CMC crystals (1% and 0.1% ${\mathrm{Cu}}^{2+}$) decrease. The exciton-emission quenching is associated with exciton migration and trapping. The emission decay kinetics is approximated by the calculated curves obtained using the Kenkre and Onipko, Malysheva, and Zozulenko theories. The exciton hopping (W) and trapping (U) rates have been defined. Exciton trapping by the ${\mathrm{Cu}}^{2+}$ traps in CMC is inefficient. The dependences W(T) and U(T) are given for two dopant concentrations in CMC obtained in the temperature range 77–237 K.

Starting from the path-integral approach to the process of tunneling in the presence of phonons we develop a theoretical procedure for the calculation of the bandwidth of the small-radius polaron in a one-dimensional crystal lattice. A two-site analog of the Holstein molecular crystal model is explored to study the tunneling character in the limit of small phonon frequencies. We do not observe any changeover from the regime of Frank-Condon type of bandwidth renormalization to the so-called adiabatic regime anticipated in the molecular crystal model.

We report an increase in an emission from solid deuterium tritium at 825 nm, while pumping an electron bubble transition centered at ∼350 nm. This experiment implies unbound electrons cause the emission at 825 nm. We find this steady-state emission shifts 8 nm towards longer wavelengths upon increasing the temperature from 4.5 to 10 K. Finally, the same emission in pure solid ${\mathrm{T}}_2$ is shifted 3 nm towards longer wavelengths and contains a triplet structure similar to the triplet structure observed in absorption measurements of the 1S to 1P transition of electron bubbles.

A quantum-mechanical simulation of orientational order in solid molecular hydrogen is presented, based on path-integral Monte Carlo calculations. The effective potential between nearest-neighbor hydrogen molecules is derived from first-principles total energy calculations, taking full account of the symmetries of the Hamiltonian within a hexagonal close-packed arrangement of the molecule centers. A first-order orientational order transition is found by studying short- and long-range angular correlations and the behavior of the corresponding order parameters. A pressure-temperature phase diagram is constructed and compared to relevant experimental and theoretical results.

The two main characteristics of the holmium ions in ${\mathrm{HoF}}_3$ are that their local electronic properties are dominated by two singlet states lying well below the remaining 4f levels, and that the classical dipole coupling is an order of magnitude larger than any other two-ion interactions between the Ho moments. This combination makes the system particularly suitable for testing refinements of the mean-field theory. There are four Ho ions per unit cell and the hyperfine coupled electronic and nuclear moments on the Ho ions order in a ferrimagnetic structure at ${\mathit{T}}_{\mathit{c}}$=0.53 K. The corrections to the mean-field behavior of holmium trifluoride, both in the paramagnetic and ferrimagnetic phase, have been calculated to first order in the high-density 1/z expansion. The effective medium theory, which includes the effects of the single-site fluctuations, leads to a substantially improved description of the magnetic properties of ${\mathrm{HoF}}_3$, in comparison with that based on the mean-field approximation.

The optimum geometries, electronic and magnetic structures, bond dissociation energies (BDE’s), binding energies (${\mathit{D}}_{\mathit{e}}$’s), ionization potentials (IP’s), and electron affinities (EA’s) of small iron clusters are studied by means of a .ul2 linear combination of Gaussian-type orbitals–local and/or nonlocal spin-density method. At the nonlocal level and with respect to nonspherical iron atoms the calculated ${\mathit{D}}_{\mathit{e}}$’s are 1.04, 1.41, 1.87, and 2.20 eV/atom for ${\mathrm{Fe}}_2$, ${\mathrm{Fe}}_3$, ${\mathrm{Fe}}_4$, and ${\mathrm{Fe}}_5$, respectively. The calculated IP’s are 8.16, 7.01, 6.34, 6.20, and 6.52 eV for Fe, ${\mathrm{Fe}}_2$, ${\mathrm{Fe}}_3$, ${\mathrm{Fe}}_4$, and ${\mathrm{Fe}}_5$, respectively, in reasonable agreement with their experimental counterparts of 7.9, 6.3, 6.4–6.5, 6.3–6.5, and 5.9–6.0 eV, and also are close to those obtained by means of ab initio techniques. The lowest-energy states are those with a maximum number of nearest-neighbor (short) bonds, and with high magnetic moments (3, 2.67, and 3 spins per atom for ${\mathrm{Fe}}_2$, ${\mathrm{Fe}}_3$, and ${\mathrm{Fe}}_4$; in ${\mathrm{Fe}}_5$ the magnetization is unevenly distributed and ranges from 2.90 to 3.31 spins per atom) coupled ferromagnetically. The gain in magnetic energy promotes the close-packed structures (for n=3 and 4) or small distortions into somewhat more open geometries (for n=5).

The importance of the s electrons for the bonding properties increases with increasing cluster size; starting from predominantly localized d bonds on earlier clusters, the chemical bond evolves to show a delocalized s pattern at the Fermi level for the larger clusters. The equilibrium bond lengths, for the computed ground states (2.00, 2.10, and 2.22 Å for ${\mathrm{Fe}}_2$, ${\mathrm{Fe}}_3$, and ${\mathrm{Fe}}_4$, respectively; whereas in ${\mathrm{Fe}}_5$ they range from 2.23 to 2.63 Å) are much shorter than the shortest distance in the bulk, 2.48 Å, although for the pentamer some bond lengths approach the bulk value. The fully optimized cations, ${\mathrm{Fe}}_{\mathit{n}}^{+}$, and anions ${\mathrm{Fe}}_{\mathit{n}}^{\mathrm{-}}$, occur in similar structures as those of the ground states; in general, ${\mathrm{Fe}}_{\mathit{n}}^{+}$ show a larger structural relaxation than ${\mathrm{Fe}}_{\mathit{n}}^{\mathrm{-}}$.

A mean-field approach which emphasizes spin-spin pair correlations is used to calculate the freezing temperature ${\mathit{T}}_{\mathit{g}}$ of two-component metallic spin glasses. We calculate the variation in ${\mathit{T}}_{\mathit{g}}$ as a function of the ratio of concentrations of the two magnetic species. Finite-temperature effects and intrinsic sd scattering of electrons play important roles in establishing the trends exhibited by ${\mathit{T}}_{\mathit{g}}$. A clear physical interpretation is given which provides insight into the behavior of ${\mathit{T}}_{\mathit{g}}$ in real, two-component spin glasses. The theory satisfactorily reproduces experimental results without the use of any adjustable parameters. We also predict how ${\mathit{T}}_{\mathit{g}}$ will behave if the concentrations of the two species are varied while the ratio ${\mathit{c}}_2$/${\mathit{c}}_1$ of the concentrations is held fixed.

Spin waves in magnetic-overlayer structures formed by thin overlayers on top of a substrate are considered in this paper. The coupling between spins is the Heisenberg exchange interaction. The magnetic structures of the composite materials are taken to be different from each other. Two systems are considered: (1) ferromagnetic overlayers on an antiferromagnetic substrate; (2) antiferromagnetic overlayers on a ferromagnetic substrate. In obtaining the energy dispersion relations of spin waves, we employed a Green’s-function formalism and introduced transfer functions between successive atomic layers. It is shown that a simple algorithm can be established between the transfer functions, which can greatly simplify the numerical analysis of Green’s functions. The energy of surface states is calculated and the existence of resonant states is discussed.

Small-angle neutron-scattering and some magnetic measurements of ${\mathrm{Cr}}_{0.81}$${\mathrm{Mn}}_{0.19}$Ge gave evidence of a double transition, from a paramagnetic to a helical magnetic state, and to a mixed state of helical and spin-glass-like ordering with decreasing temperature. The helical spin modulation, having a long period (from 360 Å at 5.3 K to 420 Å at 12.5 K), indicates the nature of an itinerant-electron-type magnet, and the reentrant transition is interpreted on the basis of the interacting spin fluctuation.

The magnetization of cubic ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$Se, with x=0.003 and 0.007, was measured at temperatures 2≤T≲50 K in magnetic fields H along the [100] and [111] directions. Data for H≤55 kOe were taken with a superconducting quantum interference device magnetometer. Other data in fields up to 200 kOe were taken with a vibrating sample magnetometer operating in a Bitter magnet. At the lowest temperatures the magnetization M at high magnetic fields is anisotropic: at a given T and for the same magnitude H of the magnetic field, M for H∥[100] is larger than for H∥[111]. The difference between the values of M for these directions reaches a maximum value of 19% at the lowest temperatures and when H≃150 kOe. As the temperature rises, the anisotropy of the high-field magnetization decreases gradually, becoming very small above 40 K. In low fields (H≲10 kOe) the anisotropy is very small at all temperatures. These experimental results are generally in good agreement with theoretical calculations based on crystal field theory and on the assumption that only isolated ${\mathrm{Fe}}^{++}$ ions (singles) contribute to the magnetization. Minor discrepancies between experiment and theory remain, however.