The [100], [110], and [111] directional Compton profiles from Ag single crystals measured using ${}_{}{}^{198}{}_{}{}^{}\mathrm{Au}$ (412 keV) and ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$ (662 keV) sources, together with the corresponding theoretical profiles obtained within the charge self-consistent relativistic Korringa-Kohn-Rostoker band-structure methodology are presented. The overall amplitude and shape of the measured directional anisotropies are found to be in good accord with theoretical predictions based on the local-density approximation. In considering absolute Compton profiles, a substantial discrepancy between theory and experiment is found; however, this discrepancy is essentially removed by invoking an energy-independent correction to the data consistent with the presence of a significant bremsstrahlung background. The experimental and theoretical results are compared and contrasted with other relevant available data in the literature.

The crystal-field energy-level structures of three different ${\mathrm{Er}}^{3+}$-doped garnet systems are analyzed and compared in this study. The garnet hosts are ${\mathrm{Y}}_3$${\mathrm{Al}}_5$${\mathrm{O}}_{12}$ (YAG), ${\mathrm{Y}}_3$${\mathrm{Sc}}_2$${\mathrm{Al}}_3$${\mathrm{O}}_{12}$ (YSAG) doped with ${\mathrm{Tm}}^{3+}$ as a sensitizer ion, and ${\mathrm{Y}}_3$${\mathrm{Sc}}_2$${\mathrm{Ga}}_3$${\mathrm{O}}_{12}$ (YSGG) doped with ${\mathrm{Cr}}^{3+}$ as a sensitizer ion. The focus is on energy levels assigned to ${\mathrm{Er}}^{3+}$ ions substituted for ${\mathrm{Y}}^{3+}$ at dodecahedral (${\mathit{D}}_2$ symmetry) sites in the cubic garnet lattices. Analyses are carried out on experimental energy-level data that span up to 29 different ${}_{}{}^{2\mathit{S}+1\mathrm{}}{}_{}{}^{}$${\mathit{L}}_{\mathit{J}}$ multiplet manifolds (between 0 and 44 000 ${\mathrm{cm}}^{\mathrm{-}1}$) of the ${\mathrm{Er}}^{3+}$ 4${\mathit{f}}^{11}$ electronic configuration. These data include the locations of 117 crystal-field levels of ${\mathrm{Er}}^{3+}$ in YAG, 109 levels of ${\mathrm{Er}}^{3+}$ in YSAG, and 92 levels of ${\mathrm{Er}}^{3+}$ in YSGG.

The energy-level analyses are based on the use of a parametrized model Hamiltonian for the 4${\mathit{f}}^{11}$ electronic configuration of ${\mathrm{Er}}^{3+}$ in a crystal field of ${\mathit{D}}_2$ symmetry. The model Hamiltonian includes both atomic (‘‘free-ion’’) and crystal-field interactions, parametrized to fit calculated eigenvalues to experimentally observed energies. The crystal-field part of the Hamiltonian is defined to include the standard one-electron interaction operators, as well as additional operators that provide a partial, phenomenological consideration of electron-correlation effects in the 4f-electron–crystal-field interactions. The latter, correlation crystal-field (CCF) interactions, are introduced to address crystal-field splittings within several J-multiplet manifolds that are poorly represented by one-electron crystal-field interaction models. Inclusion of CCF terms in the model Hamiltonian leads to dramatic improvement in the fits between calculated and observed crystal-field splittings within the problematic multiplet manifolds. All of the energy-level analyses reported in this study were carried out within commensurate parametrization schemes, and the Hamiltonian parameters derived from these analyses provide a suitable basis for comparing the 4f-electron–crystal-field interaction properties of ${\mathrm{Er}}^{3+}$ in YAG, YSAG, and YSGG. These analyses are based entirely on experimental data that specify the locations of energy levels, but do not provide any explicit information about the angular momentum (${\mathit{JM}}_{\mathit{J}}$) compositions of the crystal-field wave functions.

Crystallographic phase transitions between close-packed structures in Y have been studied theoretically, using a full-potential, linear muffin-tin orbitals method. At the equilibrium volume the hcp structure is correctly found to have the lowest energy, and at a calculated pressure of 60 kbar the fcc phase becomes stable. It is found that the so-called ω phase is only marginally lower than the hcp and the fcc structures over a large volume range. At even higher pressures another crystal phase in yttrium is found, namely the bcc phase, which is predicted to become stable at a pressure of 2.8 Mbar.

A band-structure method has been developed for modeling the near-edge structure in fluorine K-edge x-ray absorption in ${\mathrm{CaF}}_2$ and ${\mathrm{BaF}}_2$. The core-hole potential is included with a supercell technique. The model describes the main features of the experimental absorption spectra up to about 15 eV above the absorption threshold. The excitonic peak at the absorption threshold is followed by a series of peaks whose spacing changes in going from ${\mathrm{CaF}}_2$ to ${\mathrm{BaF}}_2$ by an amount consistent with electron diffraction from crystal-lattice planes. The interpretation of the higher-energy part of the absorption spectrum is complicated by possible multielectron excitations.

Electron-spin-resonance (ESR) and vacuum-ultraviolet (vuv) absorption measurements were performed on a series of high-purity silica glasses exposed to 6.4-eV photons, 7.9-eV photons from excimer lasers, and to γ rays. The concentration of defect centers varies from ${10}^{14}$ to ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{-}3}$ depending on the method of material fabrication and photon energy of the irradiating lasers. Variation of the defect species with both the incident-photon energy and manufacturing condition is observed by ESR measurements. E’ centers (°Si⋅) are observed in all types of silicas. Nonbridging-oxygen hole centers (NBOHC’s °Si-O⋅) in high-OH silica ([OH]≊1000 ppm) and peroxy radicals (PR’s, °Si-O-O⋅) in oxygen-surplus silica ([OH]<1 ppm) are observed, only when the samples are exposed to 7.9 eV photons. The defect centers observed in γ-irradiated silica are qualitatively in agreement with those in 7.9 eV laser-irradiated silica. The variation of defect species with manufacturing methods indicates that the observed paramagnetic centers are created from preexisting defects. Concentration of the defects induced by either 6.4 or 7.9 eV laser photons is proportional to the square of the pulse energy, indicating that two-photon absorption process dominates in the defect formation. The defect formation process can be understood in terms of the creation of an electron-hole (e-h) pair by two-photon excitation and the subsequent hole trapping or decay of an e-h pair at the site of preexisting defects. Dependence of the induced-defect species on incident-photon energy can be explained by the variation in the energy level of preexisting defects or in the defect formation energy. Results of vuv-absorption measurements reveal the conversion of diamagnetic precursor defects (e.g., °Si-Si°, °Si-O-O-Si°, and °Si-OH) introduced during the manufacturing process, into paramagnetic defect centers, the E’ centers, NBOHC’s, and PR’s.

The recent discovery, by high-resolution x-ray-diffraction measurements, of two length scales in ${\mathrm{SrTiO}}_3$ motivated a reinvestigation by neutron scattering of the soft phonon and associated central peak above the zone-boundary structural-phase-transition temperature (${\mathit{T}}_{\mathit{c}}$=99.5 K). The central peak has an anisotropic q width which is determined by the anisotropy of the slopes of the dispersion curves. The correlation length derived from the energy-integrated intensities of the phonon and the central peak agree well with the short length scale measured in the x-ray studies. The sharp component, corresponding to the long length scale observed in the x-ray experiment just above ${\mathit{T}}_{\mathit{c}}$, is absent in the neutron-scattering measurement. Since the neutron experiment probes the total sample volume, the absence of the narrow component supports the view that it originates in the near-surface region of the crystal.

Auger rates are computed and analyzed for a ${\mathrm{He}}^{+}$ ion in a wide range of ion–metal-surface separations. For neutralization-relevant distances close to the surface, the rate scales approximately quadratically with the density from the electron tails. (W∝${\mathit{n}}^{1.80}$ for ${\mathit{r}}_{\mathit{s}}$=2.07${\mathit{a}}_0$ and W∝${\mathit{n}}^{1.93}$ for ${\mathit{r}}_{\mathit{s}}$=3.99${\mathit{a}}_0$). Further away from the surface there is a gradual transition to a more linear scaling of the rate with the electron density (W∝${\mathit{n}}^{1.16}$). Computed Auger spectra are analyzed as well. For all ion-surface distances there is excellent agreement between the spectra and a convolution of the two hole energy distributions, left behind by the metal electrons neutralizing the ion and exciting to the Auger level, respectively. Closer to the surface the two hole spectra are almost identical. This is argued to indicate the localness of the Auger transition around the ion. For larger distances the hole spectra start to differ, indicating that the neutralization becomes increasingly nonlocal. The changeover in the scaling of the rate for larger ion-surface separations is consistent with the spectra analysis. The self-convolutions of the local density of states at the position of the ion do not agree quantitatively with the spectra. Therefore, despite the local character of the Auger process, the variations of the metal orbitals over the region of the ion cannot be neglected.

An interferometric method is applied to determine the refractive indices of litihum niobate single crystals over a wide wavelength and composition range. In combination with a careful review of the literature data, a temperature-dependent generalized Sellmeier equation is derived which takes into account the defect structure of Li-deficient ${\mathrm{LiNbO}}_3$. On the basis of this generalized Sellmeier equation, all refractive-index-dependent effects in lithium niobate can be calculated in the wavelength range 400–1200 nm, the composition range 47–50 mol % ${\mathrm{Li}}_2$O, and the temperature range 50–600 K. The parameters of several optical-characterization methods are computed to state calibration curves in the respective composition range. The calculations of the phase matching conditions for nonlinear effects, such as second-harmonic generation and optical parametric oscillation, show excellent agreement with the respective experimental values.

The activation energy for dc electrical conduction due to alkali ions of binary alkali silicate glasses and due to protons of binary alkaline-earth phosphate glasses decreases linearly with the logarithm of their concentrations (in mol/l). The activation energy is discussed in relation to the ionic radius and concentration. Hydrogen-bonded protons are much more mobile than sodium ions in the case of calcium phosphate glasses. The conduction mechanism due to protons is suggested to be different from that due to alkali ions.

A systematic Raman-scattering investigation has been carried out on sol-gel alumina prepared by the hot-water hydrolysis and condensation of Al(${\mathrm{OC}}_4$${\mathrm{H}}_9$${)}_3$, the Yoldas process, as a function of process variables such as the time spent in the sol phase. Nanocrystalline boehmite, γ-AlO(OH), is the principal component of these materials. We have found small but systematic changes, as a function of sol aging time, in the line shape and position of the dominant boehmite Raman band observed in the alumina hydrogels. These spectral changes are interpreted in terms of nanocrystallinity-induced finite-size effects associated with the slow growth of AlO(OH) nanocrystals in the sol. X-ray-diffraction experiments were used to determine nanocrystal sizes (as small as 3 nm for gels prepared from fresh sols) and to estimate growth kinetics from the Raman-line-shape results. The Raman peak-position shift is proportional to ${\mathit{L}}^{\mathrm{-}\mathrm{\alpha }}$, where L is the average nanocrystal size and α is a Raman-versus-size scaling exponent. For AlO(OH) we find α to be 1.0, close to the scaling-exponent values reported for graphite and boron nitride (BN) and different from the values (about 1.5) that describe the reported behavior of Si and GaAs.

A Gaussian size distribution of independently relaxing domains is used to model the response of various glass-forming liquids. With a single temperature-dependent parameter, the model accurately characterizes the observed dielectric susceptibility of salol and glycerol [P. K. Dixon et al., Phys. Rev. Lett. 65, 1108 (1990); N. Menon et al., J. Non-Cryst. Solids 141, 61 (1992)] over more than 13 orders of magnitude in frequency. The quality and range of these data allow quantitative confirmation of all assumptions of the model. As a function of temperature, the model gives excellent agreement with observed asymptotic relaxation rates (${\mathit{w}}_{\mathrm{\infty }}$) via [ln(l/${\mathit{w}}_{\mathrm{\infty }}$)-ln(1/${\mathit{w}}_0$)]∝s¯, where s¯ is a temperature-dependent average domain size, and ${\mathit{w}}_0$ a constant intrinsic relaxation rate. Thus, the model provides a physical explanation for non-Arrhenius primary response, without resorting to the three adjustable parameters of the Vogel-Tammann-Fulcher law.

We have investigated the properties of low-amplitude vibrations in dry unconsolidated granular materials. The velocity of sound can vary by a factor of 5 depending upon whether one measures either the arrival time of the rising edge of the pulse or the quantity analogous to the group velocity. If we increase the amplitude of the vibrations, we observe nonlinearity near the point at which we first see hysteretic behavior. This is interpreted as due to the presence of force chains. We also find frequency shifts in all of the features that characterize the transmission spectrum.

Quasielastic light scattering (QELS) due to hopping of ${\mathrm{Ag}}^{+}$ ions was studied on superionic glasses (AgI${)}_{\mathit{x}}$(${\mathrm{Ag}}_2$${\mathrm{OMoO}}_3$${)}_{1\mathrm{-}\mathit{x}}$ (x=0.60,0.70,0.75). The temperature dependence of the QELS intensity at a fixed frequency as well as the integrated QELS intensity were measured. The activation energy for ionic hopping did not depend on glass composition, and the value (≊0.1 eV) was close to that determined in α-AgI. From these results, it was concluded that the local hopping of ${\mathrm{Ag}}^{+}$ ions in the region like α-AgI contributes to QELS. It was found from the temperature dependence of the QELS intensity that the concentration of hopping ions increased with increasing temperature above 220 K. The increase in hopping-ion concentration may be related to a dc conduction process.

The microscopic model for two-dimensional distribution function P(σ,η) for quadrupolar glass freezing of axial (σ) and eccentric (η) order parameters in solid hydrogen is considered within the Sherrington-Kirkpatrick mean-field approach. Assuming the exchange interactions between axial and eccentric quadrupoles to be independent Gaussian random variables with variance ${\mathit{J}}^2$/N and ${\mathit{K}}^2$/N, respectively (with N being the number of lattice sites), we derived a set of self-consistent equations for quadrupolar order parameters and the corresponding local susceptibilities. While for J≠K the axial quadrupolar order parameter is nonvanishing in the high-temperature phase due to broken local symmetry and the corresponding quadrupolar susceptibility exhibits smeared-out behavior, the eccentric order parameter becomes zero at well-defined critical temperature depending on the ratio K/J. Furthermore, the properties of the P(σ,η) distribution function are investigated by introducing a single effective order parameter ${\mathrm{\sigma }}_{\mathit{e}\mathit{f}\mathit{f}}$ (1<${\mathrm{\sigma }}_{\mathit{e}\mathit{f}\mathit{f}}$<0) directly related to the second frequency moment of the nuclear magnetic resonance line shapes. Comparison of the present microscopic theory with earlier phenomenological approaches to the problem is also made.

The specific heat of glassy Zr-Rh-Pd alloys at low temperatures is investigated. The results are interpreted within the framework of the model of soft atomic potentials (Karpov et al., Solid State Comun. 44, 333 (1982); Zh. Eksp. Teor. Fiz. 84, 760 (1983) [Sov. Phys. JETP 57, 439 (1983)]). Using the experimental data for the normal and superconducting states, low-energy vibrational excitation parameters are obtained.

We review the experimental evidence and qualitative arguments for the existence of small highly regular rings of bonds in amorphous (a-)${\mathrm{SiO}}_2$ and selected other ${\mathit{AX}}_2$ tetrahedral glasses. The structure and vibrations of planar 3-rings and regular puckered 4-rings in a-${\mathrm{SiO}}_2$ are then modeled using Born central and noncentral forces. The vibrational coupling of these rings to the more disordered glass network is modeled by attaching a Bethe lattice at each connection. The calculated vibrational properties of the breathing modes of the rings are found to be quite consistent with the observed frequencies, linewidths, and isotope shifts of the sharp lines ${\mathit{D}}_1$ and ${\mathit{D}}_2$ seen in the Raman spectra of a-${\mathrm{SiO}}_2$. The results support the previous assignment of ${\mathit{D}}_2$ (606 ${\mathrm{cm}}^{\mathrm{-}1}$) to a planar 3-ring and ${\mathit{D}}_1$ (495 ${\mathrm{cm}}^{\mathrm{-}1}$) to a regular ring. Similar calculations for a-${\mathrm{GeO}}_2$ are consistent with the suggestion that this material contains a substantial concentration of nearly planar 3-rings. Our methods can be generalized to treat similar forms of intermediate range order in glasses having other network connectivities.

We have performed polarized absorption and resonance Raman experiments on a permanganate ion doped in a potassium perchlorate single crystal at temperature T=15 K. At this low temperature the m(${\mathit{C}}_{\mathit{s}}$) site splitting of the excited degenerate ${}_{}{}^1{}_{}{}^{}$${\mathit{T}}_2$ electronic level of the permanganate ion is well resolved and the amount of splitting is about 40 ${\mathrm{cm}}^{\mathrm{-}1}$. Due to the electronic configuration, one would expect that non-Condon terms have to be considered in the description of the absorption spectrum. For the theoretical simulation of our experimental results we have used expressions derived from the time-correlator formulation for the optical absorption. These are much easier to handle and they cause significant shorter calculation times than the usual sum-over-states expressions. In order to determine the symmetries and the wave-number positions of the site-split permanganate vibrations, we have performed resonance Raman experiments. The results obtained from these experiments form the basis for the interpretation of the absorption spectrum. The applied model includes the linear and quadratic electron-phonon and linear non-Condon coupling. Within this model we describe the multimode system and we show how a normal vibration, which apparently has no significant effects in the absorption spectrum, influences the discussion of the model system. For the fully symmetric breathing mode of the permanganate ion, we have calculated the change of the Mn-O equilibrium bond length in the electronic excited state from the corresponding linear electron-phonon coupling constant to be 4.6±0.4 pm.

Polarized infrared reflectivity spectra of 6H-SiC single crystals under different angles of incidence are reported. A new sharp line in the reststrahl band was observed in the extraordinary ray, whose line shape is dependent on the angle of incidence. It was possible to show that crystal anisotropy of 6H-SiC is the reason for the new line in the reflectivity spectrum. A numerical calculation using a Lorentz oscillator model confirmed this result. Two weak one-phonon absorption lines in the reststrahl-band region for E∥c were observed. Furthermore, we found a line at 859 ${\mathrm{cm}}^{\mathrm{-}1}$ in the extraordinary ray and an unusual structure near ${\mathrm{\omega }}_{\mathrm{TO}}$ in the reststrahl band of parallel c-cut 6H-SiC samples, which could not be explained in terms of the classical Lorentz oscillator model.

Neutron-scattering techniques have been used to study the premartensitic state of a family of Cu-Al-Be alloys, which transform from the bcc phase to an 18R martensitic structure. We find that the phonon modes of the ${\mathrm{TA}}_2$[110] branch have very low energies with anomalous temperature dependence. A slight anomaly at q=2/3 was observed; this anomaly, however, does not change significantly with temperature. No elastic peaks, related to the martensite structure, were found in the premartensitic state of these alloys. The results are compared with measurements, performed under the same instrumental conditions, on two Cu-Al-Ni and a Cu-Zn-Al martensitic alloy.

The static and dynamic properties of β-Sn, SnO, and ${\mathrm{SnO}}_2$ are studied using the full-potential linear-muffin-tin-orbital method within the local-density approximation (LDA). Equilibrium lattice parameters and bulk moduli (including pressure variations) are in excellent agreement with experimental values. The cohesive energies are calculated too large, in accordance with the usual overbinding found in the LDA. Optical Γ-point phonon frequencies are obtained using the frozen phonon approach. For those phonon modes which have been measured, experimental identifications are confirmed, with the single exception of the ${\mathit{B}}_{1\mathit{g}}$ mode of SnO, for which we find a frequency that is three times larger than the measured value. It is argued that the assignment of the observed mode is wrong.