We study Haldane’s and Jain’s proposals for the quasiparticle wave function on a sphere. The expectation values of the energy and the pair angular momenta distribution are calculated at filling factor 1/3 and compared with the data of an exact numerical diagonalization for up to 10 electrons with Coulomb and truncated quasipotential interaction.

The optical-absorption transitions originating from the lowest 4f5d excited state of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Y}}_3$${\mathrm{Al}}_5$${\mathrm{O}}_{12}$ have been studied. The experimental arrangement uses a 7-ns 266-nm light pulse to populate the lowest 4f5d state, and a spatially overlapped, time-sequenced pulse from a frequency-tunable dye laser to induce transitions from that excited state. The excited-state-absorption (ESA) spectrum covering the 900–300-nm probe wavelength range is characterized by two broad peaks centered at 700 and 350 nm on a slowly rising background. The peak ESA cross section at 355 nm is (1±0.1)×${10}^{\mathrm{-}17}$ ${\mathrm{cm}}^2$. The position, shape, and strength of the spectrum suggest that the terminal states of the ESA transitions are the second 4f5d state of ${\mathrm{Pr}}^{3+}$ and the conduction band of the host lattice. The ESA measurements have been extended to transitions from the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ excited states of the 4${\mathit{f}}^2$ configuration of ${\mathrm{Pr}}^{3+}$ as well. The ESA cross sections at a probe wavelength of 532 nm are (8±1)×${10}^{\mathrm{-}19}$ ${\mathrm{cm}}^2$ and (5.7±0.6)×${10}^{\mathrm{-}19}$ ${\mathrm{cm}}^2$ for transitions from the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ excited states, respectively. The terminal state of ESA transitions from these two levels is the lowest 4f5d state. The strong ESA completely inhibits the potential laser action based on emission from these states in this crystal.

The synchrotron-radiation-induced Auger and photoelectron spectra of the xenonlike ions ${\mathrm{I}}^{\mathrm{-}}$ (in CsI), ${\mathrm{Cs}}^{+}$ (in CsI), ${\mathrm{Ba}}^{2+}$ (in ${\mathrm{BaF}}_2$), and ${\mathrm{La}}^{3+}$ (in ${\mathrm{LaF}}_3$) have been measured in the vicinity of the ${\mathit{M}}_{4,5}$ absorption edges of these ions. It is shown that the spectra of La and Ba measured at 3${\mathit{d}}^{10}$→3${\mathit{d}}^9$4f resonances exhibit a very intense 4f-spectator structure which changes its energy and intensity with the energy of the exciting photons. Calculation of the Auger decay of the 3${\mathit{d}}^{\mathrm{-}1}$4f configuration shows that this structure is due to transitions to the 4${\mathit{d}}^{\mathrm{-}2}$4f+4${\mathit{p}}^{\mathrm{-}1}$ final ionic configuration, the high-energy part of which overlaps the 4${\mathit{d}}^{\mathrm{-}2}$ continuum. In the case of Ba this structure coexists with the normal Auger structure which appears as a result of the ${\mathit{M}}_4$${\mathit{M}}_5$${\mathit{N}}_{6,7}$ Coster-Kronig transitions. The spectra of ${\mathrm{I}}^{\mathrm{-}}$ contain only the normal ${\mathit{M}}_{4,5}$${\mathit{N}}_{4,5}$${\mathit{N}}_{4,5}$ Auger structure related to the 3${\mathit{d}}^{\mathrm{-}1}$→4${\mathit{d}}^{\mathrm{-}2}$ transitions. The spectra of ${\mathrm{Cs}}^{+}$ are similar to those of ${\mathrm{I}}^{\mathrm{-}}$ with a small admixture of the 4f-spectator-like structure.

A configurational model for silicon oxide damaged after a high-dose ion implantation of a nonreactive species is presented. Based on statistics of silicon-centered tetrahedra, the model takes into account not only the closest environment of a given silicon atom, but also the second neighborhood, so it is specified whether the oxygen attached to one given silicon is bridging two tetrahedra or not. The frequencies and intensities of infrared vibrational bands have been calculated by averaging over the distributions and these results are in agreement with the ones obtained from infrared experimental spectra. Likewise, the chemical shifts obtained from x-ray photoelectron spectroscopy (XPS) analysis are similar to the reported values for the charge-transfer model of ${\mathrm{SiO}}_{\mathit{x}}$ compounds.

Diffraction of synchrotron radiation in crystals of potassium chromate and germanium reveals a tetrahedral anisotropy of anomalous (resonant) scattering with respect to polarization and wave vectors that introduces a third-rank tensor into the intensity equations. This tensor arises from a mixed dipole-quadrupole term that vanishes for forward scattering and for centrosymmetric atoms. At resonances 13 eV below the Cr K edge and 7 eV above the Ge K edge large changes of intensities with rotation of azimuth are observed for weak and forbidden Bragg reflections in agreement with the optical model.

The semiempirical intermediate neglect of differential overlap method was used for calculating optical properties of ${\mathit{F}}^{+}$ and F centers (oxygen vacancy trapped one and two electrons, respectively) embedded into large quantum clusters, ${\mathrm{Al}}_{26}$${\mathrm{O}}_{39}$. The geometry was optimized for both the ground and excited states of defects. Calculated absorption and luminescence energies obtained for ${\mathit{F}}^{+}$ and F centers are in good agreement with experimental data. Their energy levels lie in the gap between the upper valence band and conduction band, like for similar centers in MgO and alkali halides. It is shown that the oxygen vacancy in corundum crystals is able also to trap a third electron; experimental evidence for this is discussed.

We have carried out a series of molecular-dynamics simulations on a model three-dimensional molecular solid to study the dynamics of shock-induced collapse of void defects. Molecular-dynamics methods were used for a model system of identical particles arranged as diatomic molecules aligned with the center of mass of each molecule at fcc lattice sites, using a {111} layering for the two-dimensional boundary conditions. The diatoms were internally coupled via a harmonic potential; all other interactions were modeled with Morse potentials between all particles other than the immediate diatomic partner. Using this model, we have investigated the effect of a cylindrical void at right angles to the direction of layering (and impact). Depending on the strength of the incident shock wave, the void is found to collapse either smoothly and symmetrically (like a balloon gradually losing air), or asymmetrically and turbulently. In the latter case, we note the transient formation (for periods of several hundreds of femtoseconds) of ‘‘hot spots’’ at the void location both in terms of the local effective temperature and the vibrational energies of the diatoms.

The growth of ${\mathrm{PbTiO}}_3$ films by a metalorganic chemical-vapor-deposition technique has resulted in three-dimensionally epitaxial heterostructures on various single-crystal substrates. These heterostructures consist of ${\mathrm{PbTiO}}_3$ films on the (001) surface of the single crystals: potassium tantalate (${\mathrm{KTaO}}_3$), strontium titanate (${\mathrm{SrTiO}}_3$), and magnesium oxide (MgO). It was found that the presence of a structural (ferroelectric) phase transition in ${\mathrm{PbTiO}}_3$ leads to a ‘‘strain-accommodating’’ mechanism in which a domain pattern forms as the system cools through the Curie temperature and limits the extension of interfacial strain in the heterostructure—thus minimizing the total energy of the heterostructure. For ${\mathrm{PbTiO}}_3$/${\mathrm{KTaO}}_3$(001), the interfacial strain is accommodated by the formation of a periodic domain pattern in the overlayer. In ${\mathrm{PbTiO}}_3$/${\mathrm{SrTiO}}_3$(001), which exhibits an excellent lattice match between respective a lattice parameters, the film exists as a single c domain. The ${\mathrm{PbTiO}}_3$/MgO(001) system, having a poor lattice match for both the a and c axes, appears to find the energy minimum by locking into domains of two-dimensional superlattices with the greatest atomic coincidences. It is found that the nature of the domain pattern depends very strongly on both the film thickness and measuring temperature. A theoretical model of the domain-pattern formation has been developed by using linear-elasticity theory and a Landau-Ginzburg-Devonshire-type phenomenological theory for the substrate and the overlayer, respectively. The theoretical predictions and the experimental measurements were in good agreement in both the thickness and temperature dependence of the relative domain population and the spontaneous strains.

In this paper we present spectroscopic and scintillation studies of mixed cerium lanthanum trifluoride crystals ${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{La}}_{1\mathrm{-}\mathit{x}}$${\mathrm{F}}_3$. A scintillation mechanism is proposed in which the light output of the ${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{La}}_{1\mathrm{-}\mathit{x}}$${\mathrm{F}}_3$ scintillator is determined by three processes: a direct excitation of ${\mathrm{Ce}}^{3+}$ ions by secondary electrons and x rays, an ionization of ${\mathrm{Ce}}^{3+}$ ions followed by the capture of electrons and formation of Ce bound excitons and, eventually, a transfer of the energy from the electronic-lattice excitations to ${\mathrm{Ce}}^{3+}$ ions. These three processes occur in various degrees in all inorganic Ce scintillators, and the mixed (Ce,La) trifluorides provide, therefore, an excellent example of their relative importance. The peculiarity of fluorides is that ${\mathrm{Ce}}^{3+}$ ions occur in regular and ‘‘perturbed’’ sites. The lack of a fast energy migration between the Ce ions and, at the same time, an efficient energy transfer to ‘‘perturbed’’ Ce ions lead to nonexponential decays of the Ce emission. Thermal quenching is moderate and radiation trapping can be minimized, and there is no evidence of luminescence concentration quenching. The light output under γ excitation has a maximum value of about 4500 photons per MeV, which is significantly lower than the estimated conversion-limited value of about 25 000 photons per MeV. It is suggested that the stable ${\mathrm{Ce}}^{2+}$ provides electron traps, competing for electrons with holes localized on ${\mathrm{F}}_2^{\mathrm{-}}$ and ${\mathrm{Ce}}^{4+}$ ions. Therefore, mostly one process, namely the direct excitation of ${\mathrm{Ce}}^{3+}$ ions by secondary electrons and photons, contributes to the light output of ${\mathrm{CeF}}_3$. The deomonstrated feasibility of reducing perturbed Ce makes it a strong contender in those applications where high speed, not high light output, is of prime concern.

An infinite set of coupled equations for envelopes of harmonics is obtained, and the successive approximations procedure for it is demonstrated. For the stationary wave, the amplitude of the third harmonic having a maximum at a certain depth and the correction for the first harmonic due to back action of the third harmonic are found. It is ascertained that the fundamental harmonic approximation is legitimate under the monochromatic excitation.

We develop a recursion-relation approach for the failure probability of heterogeneous networks with continuously distributed bond strengths and with local stress enhancements after bond failure. Current computational methods to solve these models scale as $2^{\mathit{n}}$ where n is sample size, while our method provides a rapidly converging sequence of approximations which scale algebraically with the sample size. The method is applied to systems with uniform and Weibull distributions of local bond-failure thresholds. We find that the characteristic feature which occurs when there is a continuous distribution of local breaking strengths is that, as a function of sample size, the failure probability ${\mathit{F}}_{\mathit{n}}$(σ) shows a minimum at ${\mathit{n}}_{\mathit{c}}$, which deepens and moves to higher n as the external stress σ is reduced. At large n, there is a stable ‘‘weak-link’’ scaling form for the failure probability, in agreement with work by Harlow and Phoenix. For sufficiently large n≫${\mathit{n}}_{\mathit{c}}$, the failure probability is of double-exponential form, and the size effect is logarithmic. For small n<${\mathit{n}}_{\mathit{c}}$, however, the low-stress tail of the failure probability appears to be of Weibull form with n-dependent parameters, and the size effect can be algebraic.

Temperature dependences of ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ nuclear-quadrupole resonance frequencies have been measured in tetragonal paraelectric phases of ${\mathrm{KH}}_2$${\mathrm{PO}}_4$, ${\mathrm{KH}}_2$${\mathrm{AsO}}_4$, ${\mathrm{RbH}}_2$${\mathrm{PO}}_4$, and ${\mathrm{RbH}}_2$${\mathrm{AsO}}_4$. The measured quadrupole coupling constants are compared to the quadrupole coupling constants calculated in a point-charge model in which a cation bears a positive charge e whereas the negative charge -e of a ${\mathrm{PO}}_4^{\mathrm{-}}$ or ${\mathrm{AsO}}_4^{\mathrm{-}}$ ion is, in a time average, equally shared by the four oxygen atoms. The influence of the anisotropic thermal expansion of the crystal lattices on the temperature dependence of the quadrupole coupling constants is calculated in the same model. Both the calculated and measured quadrupole coupling constants as well as the calculated and measured temperature coefficients of the quadrupole coupling constants agree within the experimental error. Thus the ‘‘antiferroelectric’’ Slater configurations of the ${\mathrm{H}}_2$${\mathrm{PO}}_4$ and of the ${\mathrm{H}}_2$${\mathrm{AsO}}_4$ groups which seem to have a strong influence on the ${}_{}{}^{75}{}_{}{}^{}\mathrm{As}$ NQR frequencies in the tetragonal paraelectric phase are of a local nature and they have nearly no influence on the potassium and rubidium NQR frequencies.

Tight-binding models with on-site energies forming (i) a Cantor sequence and (ii) a quasiperiodic sequence are considered. For a certain ordering of the eigenvalues, the localized wave functions are seen to be strongly correlated with the corresponding energies, provided the binding-to-hopping ratio is large enough. As a consequence we show that, under periodic kicking with large enough strength, initially localized wave packets diffuse through the lattice. The contrast with random lattices is pointed out.

The free energy of defects in solids is computed with Monte Carlo simulation techniques and by various approximate techniques. The results are compared in order to determine the accuracy and range of applicability of the various approximate methods. The systems studied are a bulk crystal, a vacancy, a (100) free surface, and a Σ5(310)/[001] symmetric tilt boundary in Cu described by embedded-atom method potentials. The Monte Carlo simulations employ both the Frenkel-Ladd method and thermodynamic integration. The approximate techniques include quasiharmonic calculations and the recently proposed local harmonic method. The results indicate that the harmonic methods significantly underestimate the temperature variation of the defect-free energies for this potential. The discrepancies become large for temperatures above about half of the melting point.

The electric-field gradient (EFG) at the probe-atom site in binary oxides has been theoretically estimated, assuming it is composed of two terms. The first term is local, due to deformation of the valence orbitals of the probe atom, and was calculated by methods of quantum chemistry. The second term is due to the rest of the lattice ions, and these were taken as point charges. In this work we found, for the well-known ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$ probe, a correlation between the local and ionic contributions to the EFG for the 29 oxides studied, which is very similar to the one deduced empirically from time-differential perturbed-angular-correlation experiments. Therefore, the hypothesis used to perform that empirical correlation is confirmed, i.e., both terms have different sign and the absolute value of the local contribution is larger than the ionic one in most cases.

The mechanical properties of ${\mathrm{C}}_{60}$ crystals were investigated using the Vickers microhardness indentation technique. Firstly, the temperature dependence of the hardness was measured at temperatures from about 240 to 470 K. A discontinuous change in the hardness was observed at around 260 K. Such a marked change in hardness is due to the phase transition of the ${\mathrm{C}}_{60}$ crystal. At temperatures higher than 300 K, the hardness showed an anomalous behavior: the hardness increased with increasing temperature and reached a maximum at around 370 K.

A method for estimating the concentration of quasielastic-light-scattering (QELS) centers is developed and a decrease of the concentration of scattering centers in stabilized ${\mathrm{ZrO}}_2$ is observed at high temperatures. The hopping mechanism of the ${\mathrm{O}}^{\mathrm{-}2}$ ion in the yttrium-stabilized ${\mathrm{ZrO}}_2$ is investigated in detail by measuring the integrated intensity and the fixed frequency intensity of the QELS. The observed polarization character and temperature dependence of QELS are interpreted by three kinds of clusters as QELS. From the polarization characters and association energy of the clusters, the QELS centers for depolarized light are found to be the clusters which contain one ${\mathrm{O}}^{2\mathrm{-}}$ vacancy and two next- and/or third-nearest-neighbor ${\mathrm{Y}}^{3+}$ ions and the QELS centers for polarized light to be the clusters above and the cluster which contains one ${\mathrm{O}}^{2\mathrm{-}}$ vacancy and two nearest-neighbor ${\mathrm{Y}}^{3+}$ ions.

The late-time growth law of the vapor-liquid phase separation in two- and three-dimensional one-component fluids has been investigated by molecular dynamics simulations in which instantaneous quenching of fluid composed of 50 000 (2D) or 78 732 (3D) Lennard-Jones particles into the corresponding two phase (spinodal) region has been performed. The power law growth of the characteristic length scale, i.e., l(t)∼${\mathit{t}}^{\mathit{a}}$ is observed in both the 2D and 3D systems in the late stage. All molecular dynamics simulations which we have carried out, except for the cases in which the scaling regime has not been reached in simulation time, confirm that the asymptotic growth exponent is 1/2 in common with two and three dimensions. It is also found that thermal noises have no effect on the growth exponent but give rise to a substantial delay of the transition time to the asymptotic regime. This work provides temporal domain patterns associated with the phase separation processes suggesting that the domain structures are sensitive to the temperature of the system.

We have measured low-frequency Raman scattering (RS) spectra of the glass formers ${\mathrm{B}}_2$${\mathrm{O}}_3$, glycerol, m-tricresyl phosphate (m-TCP), and ${\mathrm{K}}_3$${\mathrm{Ca}}_2$(${\mathrm{NO}}_3$${)}_7$ in a broad temperature range above the glass transition temperature. The basic difference between the spectra is the ratio of relaxational to vibrational contributions: the more fragile the glass, the smaller is the vibrational contribution. Features of the relaxational contributions are quite similar. Testing predictions of mode-coupling theory (MCT) for m-TCP, we find that the dynamics is well described, and as the critical temperature we find ${\mathit{T}}_{\mathit{c}}$∼260 K. In the case of glycerol, due to the strong vibrational contribution to the RS spectrum, a consistent interpolation of the rescaled data is only possible if other exponents than those predicted by MCT are applied; however, the MCT exponents are obtained in a narrow frequency range, provided the contribution of the α process is subtracted first. Thus, MCT describes the dynamics for ν<300 GHz even in the nonfragile glass former glycerol. We extract ${\mathit{T}}_{\mathit{c}}$∼310 K. Combining the RS results with those of NMR in the case of m-TCP, we further find (i) a change of stretching parameter close to ${\mathit{T}}_{\mathit{c}}$ and (ii) a change of the temperature dependence of the Debye-Waller factor at T∼280 K which is close to ${\mathit{T}}_{\mathit{c}}$ for this system.

We have reported a comparative study of the Landauer resistance of Thue-Morse (TM) and Fibonacci lattices. Our main objective is to examine the degree of aperiodicity of TM lattices vis-à-vis that of (quasiperiodic) Fibonacci lattices, with the use of relevant Landauer resistances. Our study reveals that TM lattices are more periodic than Fibonacci lattices.