The contributions of the multiple-scattering processes in the extended x-ray-absorption fine structure (EXAFS) of tetrahedrally coordinated Cr in ${\mathrm{CrO}}_4$ and ${\mathrm{Cr}}_2$${\mathrm{O}}_7$ configurations have been investigated. The EXAFS measurements were carried out on crystalline and 0.5M aqueous solutions of ${\mathrm{K}}_2$${\mathrm{CrO}}_4$ and ${\mathrm{K}}_2$${\mathrm{Cr}}_2$${\mathrm{O}}_7$ compounds. It is shown that the contributions of the noncollinear multiple-scattering processes occurring in the first coordination shell is significant and these contributions must be included in the EXAFS analysis of the higher shells. The intensity of these contributions strongly depend upon the symmetry of the system. For a distorted tetrahedron, the intensity of the multiple-scattering contributions is less than that found in a regular tetrahedron. The feff code was used to model the contributions of the multiple-scattering processes. The theoretical calculations and the experimental results are in good agreement.

We observed the interference effect of electron-capture x rays emitted by nuclear transformations in radioactive atoms. The interference fringes are generated between the direct monochromatic emissions from the radioactive atoms and the emissions totally reflected by the substrate surface. The site of a radioactive atom can be determined by analyzing the measured interference fringes because the period of these fringes depends on the position of the radioactive atoms relative to the substrate surface. A monolayer of ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ above a Pt substrate was used as a model sample.

The Auger decay process after resonant Mo 2${\mathit{p}}_{3/2}$→4d(5s) excitation in the molybdenum compounds has been studied by photoemission spectroscopy using synchrotron radiation. It was found that the Mo(${\mathit{L}}_3$${\mathit{M}}_{4,5}$${\mathit{M}}_{4,5}$) Auger lines are split into double-peak structures (${\mathrm{Li}}_2$${\mathrm{MoO}}_4$ and ${\mathrm{MoO}}_3$) or broadened (${\mathrm{MoS}}_2$) at the resonant photon energy. These results are attributed to spectator Auger and normal Auger transitions. The spectator Auger lines were found to shift to the higher kinetic energy by 4.5–12 eV. Amount of the energy dispersions and direction of the shifts, almost in proportion to the photon energy, are interpreted in connection with bandlike structure of the unoccupied molecular orbitals in solids compared to isolated atoms or free molecules in a gas phase. The resonantly excited state was also found to decay through the direct recombination between the excited electron and core hole, leading to emission of an electron from one of the outer orbitals. This type of transition, called a participator Auger transition, was especially enhanced in the decay involving the Mo 3${\mathit{d}}_{3/2,5/2}$ orbitals with drastic change in the photoemission branching ratio of 3${\mathit{d}}_{5/2}$ to 3${\mathit{d}}_{3/2}$.

The Ce(${\mathrm{Ni}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$${)}_5$ system has been investigated in the range from x=0 to x∼0.6 including measurements of (a) the lattice parameters at room temperature and down to 4 K on samples quenched from 600 or 800 °C, respectively, (b) the magnetic susceptibility in the temperature range 1.5 <T<800 K and magnetization measurements up to 8 T, (c) the electrical resistivity from 4.2 to 300 K, (d) the specific heat from 1.5 to 60 K and (e) x-ray absorption spectroscopy (XAS) and x-ray absorption near-edge structure (XANES) at 10 and ∼290 K. At 800 °C, a continuous solid solution 0≤x≤0.55 is observed crystallizing with the ${\mathrm{CaCu}}_5$ type. Within this solution range a ${\mathrm{HoNi}}_{2.6}$${\mathrm{Ga}}_{2.4}$-type low-temperature modification develops with a small homogeneity range around ${\mathrm{CeNi}}_3$${\mathrm{Ga}}_2$ and with a maximum congruent transformation point at T≃770 °C. The Ni/Ga substitution leads to a successive occupation of the 3g sites of P6/mmm symmetry by Ga, whereas the 2c sites are Ga free, but ultimately does not reach full atomic order at a hypothetical ‘‘${\mathrm{CeNi}}_2$${\mathrm{Ga}}_3$.’’ Magnetism within the solid solution starts with a nonmagnetic ground state of the cerium atoms in ${\mathrm{CeNi}}_5$ but subsequently changes to an intermediate Ce valence as the Ga content increases.

${\mathrm{CeNi}}_3$${\mathrm{Ga}}_2$ in the low-temperature modification exhibits Curie-Weiss behavior and enhanced values for the electronic contribution to the specific heat as typically observed for heavy-fermion compounds. The Ce valency, directly obtained from XAS data, shows a linear decrease as a function of increasing Ni/Ga substitution, with a strong temperature dependence for the alloy richest in Ga, ${\mathrm{CeNi}}_{2.34}$${\mathrm{Ga}}_{2.66}$. The linear variation of the unit-cell parameters for (Y,La)-substituted alloys ${\mathrm{Ce}}_{1\mathrm{-}\mathit{x}}$(Y,La${)}_{\mathit{x}}$${\mathrm{Ni}}_3$${\mathrm{Ga}}_2$ in both structure modifications and the corresponding magnetic and XAS data revealed practically no influence on the cerium valence compared to the ${\mathrm{CeNi}}_3$${\mathrm{Ga}}_2$ base alloys.

A parameter-free approach is applied to the study of the electronic structure properties and the local chemical order in Fe-Cr and Fe-V alloys. The method is based on a multiple-scattering description of the electronic-structure properties of the random alloys. Configurational order is treated within the generalized perturbation method, and temperature effects are examined with standard statistical methods, namely, the cluster-variation method and Monte Carlo simulations. In reasonable agreement with experiments, FeV exhibits a tendency toward order with a B2 superstructure in contrast to FeCr which shows an overall tendency toward phase separation around equiatomic composition. A more detailed study is performed for Fe-Cr alloys as a function of temperature and concentration, in the light of recent diffuse-scattering experiments. Finally, some conclusions are drawn regarding the structural transformation which occurs in both alloys from the bcc solid solution to a complex Frank-Kasper phase upon cooling.

An ab initio variationally induced breathing (VIB) description of the energetics and dynamics of ionic crystals is developed within the spherical-ion-pair approximation and the Gordon-Kim ansatz. In the VIB method, the total crystal charge density is given by the overlap of Kohn-Sham ionic charge densities. Spherical charge deformation of the ions is accomplished by adding an effective many-body crystal site potential to the atomic potential used in the Kohn-Sham procedure. Parameters defining this effective site potential are treated variationally such that the total crystal electronic energy is a minimum for a given structural configuration. We have explored a number of forms of the effective potential, including Watson-sphere types where both the charge and radius of the sphere are variationally determined. In addition, we have investigated anion-cation charge transfer by incorporating an additional variational parameter. We also present a formulation of the lattice dynamics of ionic crystals based on the VIB prescription in which the electronic variational parameters are treated as dynamical variables within the adiabatic approximation. With the computed phonon density of states, the structural parameters of a crystal can then be determined at any temperature and pressure (or stress condition) by mini- mizing the quasiharmonic Gibbs free energy with respect to the structural parameters along the electronic adiabatic surface. The complete pressure- and temperature-dependent thermal and elastic properties of a crystal can also be determined. We have applied the VIB procedure to calculate the equations of state, elastic properties, phonon dispersion relations, and phase stability of the alkaline earth oxides (MgO, CaO, and SrO). The calculated properties are generally in quite good agreement with experiment.

Spherical charge deformation within the ionic description is responsible for a considerable improvement over rigid-ion elastic constants and bulk moduli, but some of the remaining discrepancies cannot in principle be eliminated within a spherical-ion model. In particular, the effect of spherical breathing on the optical vibrational frequencies is not dramatic and further improvement (e.g., reduction of LO-TO splitting) will require the inclusion of nonspherical charge relaxation (polarizability).

A theory has been developed to examine the depolarization effect on the ferroelectric transition of small ${\mathrm{BaTiO}}_3$ particles. To reduce the depolarization energy, a crystal would break up into domains of different polarization. In this study, we consider cubic particles with alternating domains separated by 180° domain walls. The depolarization energy and the domain-wall energy were incorporated into the Landau-Ginzburg free-energy density. Assuming a hyperbolic tangent polarization profile across the domain wall, the domain-wall energy γ and the domain-wall half thickness ξ can be obtained by minimizing γ with respect to ξ. To account for ${\mathrm{BaTiO}}_3$ not being a perfect insulator, a Schottky space charge layer beneath the particle surface that shields the interior of the crystal from the depolarization field was considered. The equilibrium polarization P and domain width D can be obtained by minimizing the total free-energy density with respect to both P and D. The results of the calculations show that the ferroelectric transition temperature of small particles can be substantially lower than that of the bulk transition temperature as a result of the depolarization effect. Consequently, at a temperature below the bulk transition temperature, the dielectric constant ε can peak at a certain cube size L. These results agree with the existing experimental observations. Finally, the theory can also be applied to other ferroelectric materials such as ${\mathrm{KH}}_2$${\mathrm{PO}}_4$ or ${\mathrm{PbTiO}}_3$.

The nearest-neighbor substitutional nitrogen center [N-N${]}^0$ (A center), is one of the most common defects in natural diamond. [N-N${]}^0$ is diamagnetic and therefore cannot be studied by electron paramagnetic resonance (EPR). However, the [N-N${]}^{+}$ center is paramagnetic, and we report detailed EPR and electron-nuclear double-resonance (ENDOR) studies on this center. The ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ hyperfine coupling matrices show that approximately 100% of the unpaired electron population is in the lowest-energy antibonding orbital formed between the two nitrogen atoms, which are equivalent. Using orthogonality and simple geometric considerations the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ hyperfine interaction is used to make an estimate of the length of the N-N bond in the [N-N${]}^{+}$ center. The result appears consistent with more sophisticated calculations on the [N-N${]}^0$, and single substitutional nitrogen centers [N-C${]}^0$. For several defects incorporating substitutional ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ (including [N-N${]}^{+}$) the quadrupole interaction is proportional to the fraction of unpaired electron population on the nitrogen atom. A simple molecular orbital calculation explains this finding, and determines that the quadrupole interaction for a single unpaired electron in a 2p orbital on ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ is -6.7(3) MHz.

[N-N${]}^{+}$ can be created in some natural diamonds by illumination with photons of energy greater than 3.0 eV. Studies on the number of [N-N${]}^{+}$ centers remaining after the optical excitation is switched off indicate that there is a wide distribution of lifetimes, presumably resulting from a large variation in the separation between a [N-N${]}^{+}$ center and its electron trap and/or donor. Below about 25 K, the decay rate is independent of temperature, indicating tunnelling between the donor and/or trap and the [N-N${]}^{+}$ center; at higher temperatures thermally activated hopping also contributes. In powered diamond [N-N${]}^{+}$ can be observed without illumination whereas in the single crystal it was only observed after illumination, suggesting that a defect created near the surface could be acting as a trap and/or donor. It appears that [N-N${]}^{+}$ can be created via electron capture by [N-N${]}^{2+}$ or by ionization of [N-N${]}^0$, or possibly both, depending on the traps and donors available.

The Fermi surface of the molecular conductor (DMe-DCNQI${)}_2$Cu (DMe-DCNQI=2,5-dimethyl-N,N’-dicyanoquinonediimine) has been investigated by the de Haas–van Alphen method. Seven different oscillations with heavy cyclotron masses are observed at frequencies lower than 3000 T. These effects arise from the three-dimensional (3D) Fermi surface which is dominated mainly by the Cu 3d orbital character. Many oscillations with frequency higher than 3000 T are detected for the magnetic field in the ab plane—an effect which demonstrates the coexistence of the 1D and 3D Fermi surfaces.

Quadrature Fourier transform NMR detection has been employed to study the disorder-order transition in high J=1 concentration solid hydrogen and deuterium. In solid ${\mathit{H}}_2$, where the ortho-para conversion is rapid, quick measurements were made possible by computer batch files containing pulse programs. Newly obtained order parameters were compared with those from the so-called quadrupole glass phase. In addition, peculiar emission of power was detected and regarded as characteristic of the long-range order which distinguishes it from the local order in the quadrupole glass phase.

We present ab initio calculations of the structural, cohesive, and electronic properties of various polymorphic forms of carbon and boron nitride. Our calculations are based on ultrasoft pseudopotentials and a variational approach to the solution of the Kohn-Sham equations. Optimization of the atomic geometries is performed using total energy calculations and by minimizing the energy via a quasi-Newton quench using the Hellmann-Feynman forces. Special attention is devoted to the convergence of the results with respect to the plane-wave basis. The entire set of structural energy differences calculated in our work is in good agreement with the most accurate results obtained using a variety of different techniques—our results represent a consistent set of data based all on the same potential. We show that the use of ultrasoft potentials allows one to achieve accurate results with low cutoff energies (and hence small basis sets).

NMR measurements on single crystals of pure ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ diamond are reported. The line shape is very sensitive to the orientation of the external magnetic field relative to the crystallographic axes, typical of dipolar line broadening. With the magnetic field oriented along the [110] direction, the line is broad and flat, whereas a more narrow, Gaussian shape is seen along [001]. For the [111] direction, a spectacular line splitting of 8.5 kHz is observed. For the sample studied, the spin-lattice relaxation time was about 15 s at room temperature and 140 s at 140 K. The spectra are interpreted by a simple model using dipolar interactions.

We investigate the relaxation of a two-level system (TLS) in the golden-rule approximation by taking into account phonon-mediated interactions between TLS’s.

First-principles electronic-structure and total-energy calculations related to the 1/1 crystal approximant to the Al-Zn-Mg quasicrystal are carried out with different possible atoms at the center of the packing unit. The linear muffin-tin-orbital (LMTO) method with the atomic-sphere approximation and the muffin-tin correction to the Coulomb energy is employed. The density of states shows a very shallow minimum near the Fermi level, supporting the view that the pseudogap exists in the crystal approximants to quasicrystals even in the absence of a d-state contribution to the valence electrons. It is shown that packing units with Al or Zn at the centers are more stable than those with empty centers, supporting the recent positron-annihilation data and pseudopotential calculations, but disagreeing with qualitative conclusions from some LMTO calculations for crystal approximants to other quasicrystals.

Most of the previously used strong-fluctuation theories exclusively deal with electrically isotropic random media. In this paper an extension of the method of changing the field variable is proposed to account for strong fluctuations of a statistically homogeneous random medium which possesses the most general anisotropy of the electrical and statistical properties. For the effective perturbation operator, a full perturbation series solution and a bilocal approximation in the long-wavelength limit are derived referring to a general anisotropic random medium. On this basis, the particular cases of random media characterized by ellipsoidal correlation functions with fixed axes of statistical symmetry as well as with randomly rotating symmetry axes and a random distribution of correlation lengths are considered. For a general model of random media, a coordinate-free solution to the mean-field Green’s dyad problem in the spectral domain is described, and the nonlinear bilocal approximation for the effective perturbation operator is developed.

Energetic growth model of a two-dimensional quasicrystal using Penrose tiles produces phason strain with many topological configurations. These vortexlike structures produce power-law decay of the phason correlation function, with the exponent dependent on the temperature as well as on the interaction energy between the tiles.

${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Cu}$ NMR measurements are reported for powder samples of stable Al-Cu-Fe and Al-Cu-Ru icosahedral quasicrystals and their crystalline approximants, and for an Al-Pd-Mn single-grain quasicrystal. Furthermore, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ NQR spectra at 4.2 K have been observed in the Al-Cu-Fe and Al-Cu-Ru samples. From the quadrupole-perturbed NMR spectra at different magnetic fields, and from the zero-field NQR spectra, a wide distribution of local electric-field gradient (EFG) tensor components and principal-axis-system orientations was found at the Al site. A model EFG calculation based on a 1/1 Al-Cu-Fe approximant was successful in explaining the observed NQR spectra. The average local gradient is largely determined by the p-electron wave function at the Al site, while the width of the distribution is due to the lattice contribution to the EFG. Comparison of ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ NMR with ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ NMR shows the EFG distribution at the two sites is similar, but the electronic contribution to the EFG is considerably smaller at the Cu site, in agreement with a more s-type wave function of the conduction electrons. The overall spread of EFG values is well reproduced by the calculation based on the approximant. However, the experimental spectra indicate a much larger number of nonequivalent sites when compared with the simulated NQR spectra based on the 1/1 approximant. The short-range, local chemical order is well represented by the approximant, but differences in coordination must be included at intermediate range in the quasicrystal. Measurements of ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ Knight shift, magnetic susceptibility, and nuclear spin-lattice relaxation time as a function of temperature yield results which indicate a reduction of the density of states at the Fermi level by a factor of 7 or 8 from the value in Al metal, consistent with the notion of a pseudogap for these quasicrystals. No differences in the measured parameters were detected as a function of composition of the quasicrystalline alloys, arguing against a fine structure in the density of states at the Fermi level.

Mode polarization and energy spectra for the lattice modes of poly(p-phenylene vinylene) are obtained by inelastic-incoherent-neutron-scattering methods. Experiments were performed on stretch-oriented, highly crystalline films with time-of-flight and filter-analyzer spectrometers. By measuring all-hydrogen and vinylene-deuterated samples, we show that almost all of the observed modes can be attributed to phenylene motions. The low-energy features in the vibrational density of states consist of a longitudinal 2.5-meV mode assigned to a damped translational motion along the chain axis, a 7-meV phenyl ring in-phase librational mode (transverse with respect to the chain axis), and strong bands at 15 and 25 meV showing mixed polarization, the latter also displaying negative frequency shift with increasing temperature. Higher-frequency modes are in excellent agreement with published infrared and Raman studies, as well as with the results of our vibrational analysis based on the semiempirical AM1 method.

The macroscopic governing equations controlling the coupled electromagnetics and acoustics of porous media are derived here from first principles. The porous material is assumed to consist of a packing of solid grains that is saturated by an electrolyte. A sedimentary rock is an example of such a material. The approach is to volume average the equations known to apply in the fluid and solid phases while allowing for the boundary conditions that exist on the fluid-solid interface. The coupling is due to a layer of excess charge adsorbed to the sufaces of the solid grains that is balanced by mobile ions in the fluid electrolyte; i.e., the coupling is electrokinetic in nature. The derived equations have the form of Maxwell’s equations coupled to Biot’s equations with coupling occurring in the flux-force (or transport) relations. The frequency-dependent macroscopic-transport coefficients are explicitly obtained and related to each other. Onsager reciprocity is derived and is not simply postulated.

Single-crystal x-ray diffraction and diffuse x-ray-scattering measurements were performed on a crystal of the commensurate intergrowth compound of bis(methylthio)ethylenedithio-tetrathiafulvalene (${\mathrm{C}}_1$TET-TTF) and gold di-iode. The first subsystem comprises of stacks along ${\mathbf{a}}_1$ of planar ${\mathrm{C}}_1$TET-TTF groups on a monoclinic lattice, with lattice parameters ${\mathit{a}}_1$=7.540(2) Å, ${\mathit{b}}_1$=22.450(2) Å, ${\mathit{c}}_1$=11.674(1) Å, ${\mathrm{\beta }}_1$=100.14(1)° and space group P$2_1$/c. The second subsystem comprises of chains of ${\mathrm{AuI}}_2$ parallel to ${\mathbf{a}}_1$, but with a different periodicity ${\mathit{a}}_2$=5/4${\mathit{a}}_1$. Long-range order is only obtained along the chains, as concluded from the observation of diffuse planes of scattered x-ray intensity perpendicular to the stacking axis. Within these planes, there are intensity concentrations which occur as broad spots, the centers of which correspond to a reciprocal lattice ${\mathbf{b}}_2^{\mathrm{*}}$=${\mathbf{b}}_1^{\mathrm{*}}$, ${\mathbf{c}}_2^{\mathrm{*}}$=${\mathbf{c}}_1^{\mathrm{*}}$ and ${\mathbf{a}}_2^{\mathrm{*}}$=4/5${\mathbf{a}}_1^{\mathrm{*}}$+ 2) / 5 ${\mathbf{c}}_1^{\mathrm{*}}$, which makes this a commensurate intergrowth compound. The spacegroup of the second subsystem is again P$2_1$/c.