A unified model of ionic motion in glasses is presented which relates consistently the different quantities observed in nuclear-spin relaxation and electrical-conductivity relaxation due to thermally activated ionic diffusion. Corresponding experimental data obtained in a low-ionic-conductivity fluorozirconate glass are shown to be in reasonable agreement with the present approach. Limitations of the model are pointed out and are discussed in view of observed deviations between the different experimental results.

Internal and external factors that influence the morphology of crystals are studied based on an inhomogeneous cell model. After discussing the reason of the failure of two basic assumptions, the equivalent wetting condition and the proportionality condition, the influence of the ambient phase is explicitly taken into account in terms of the surface characteristic scaling factor ${\mathit{C}}_{\mathit{l}}^{\mathrm{*}}$. In connection with the solid-fluid interfacial structure, which is commonly determined by the crystal and the ambient phase, ${\mathit{C}}_{\mathit{l}}^{\mathrm{*}}$ will provide the essential information concerning how the morphology of the crystals is affected. Within the framework of our formalism, internal and external factors controlling both equilibrium forms and growth forms of crystals are described separately. This offers a guideline for the modification of the habit of crystals. To describe the morphology of crystals, the periodic bond chain analysis can be used to determine the internal controlling factors, and the interfacial structure analysis, which is developed in this paper, can be used to determine the external controlling factors. These analyses are applied to predict the growth forms of n-paraffin crystals.

Using high-resolution x-ray diffraction on single crystals we specify the phase diagram of barium sodium niobate between 20 and 300 °C. Its main characteristics are the coexistence of two incommensurate phases in the vicinity of the normal-incommensurate transition, a 2q tetragonal phase and a 1q orthorhombic phase, and a progressive 2q/1q transformation in the temperature range where a large thermal hysteresis of the misfit parameter is observed. A complex memory effect is evidenced when the sample is annealed inside the incommensurate phases or the quasicommensurate phase: a pinning of the modulation on a very large plateau of temperature and a delay or an anticipation of the 2q/1q transformation and of the lock-in transition is evidenced. We discuss our results on the basis of the 2q/1q phase coexistence and the existence of mobile effects in the structure of barium sodium niobate (sodium vacancies) interacting with the modulations.

As a model for atom ejection from fast-ion tracks, molecular-dynamics simulations of a cylindrical track of energized particles are performed. An idealized situation is studied where every atom in a cylindrical track of radius ${\mathit{R}}_0$ is energized with energy ${\mathit{E}}_0$. The emission yield Y(${\mathit{E}}_0$,${\mathit{R}}_0$) shows the existence of two ejection regimes. If the particle energy ${\mathit{E}}_0$ is below the sublimation energy U of the material, a threshold regime is seen in which Y rises roughly like the third power of ${\mathit{E}}_0$; for high-energy densities ${\mathit{E}}_0$≳U, the yield rises much more slowly, roughly linearly. In both cases, ejected particles mostly originate from the track, rather than from its surroundings, and from the first or the first few monolayers. The behavior found is interpreted here in terms of emission due to a pressure-driven jet (linear regime) or due to a pressure pulse (threshold regime). These both behave differently from the often-used thermal-spike sputtering model.

We have used Raman scattering to investigate the effects of intense laser pulses on the structure of resolidified graphite. Graphite was irradiated with 0.325–3.25-J/${\mathrm{cm}}^2$, 620-nm, 90-fs single-laser pulses causing it to melt and rapidly resolidify. Raman studies of the resolidified carbon in the crater show that the rapid annealing process (by pulses with energy fluences ≥0.82 J/${\mathrm{cm}}^2$) causes a breakdown in the ordered layers of hexagonal carbon rings and disorder in the intraplanar spacing upon resolidification into a nanocrystalline material. The thickness of the nanocrystalline-graphite near-surface layer increases with increasing fluence. Residual planar structure of the resulting material is observed for the various pulse-energy values by comparing the narrow graphitic 1581-${\mathrm{cm}}^{\mathrm{-}1}$ and the broad 1360-${\mathrm{cm}}^{\mathrm{-}1}$ and 1600-${\mathrm{cm}}^{\mathrm{-}1}$ vibrational bands. The interplanar structure of our nanocrystalline graphite is also studied quantitatively via the low-frequency shear mode at 42 ${\mathrm{cm}}^{\mathrm{-}1}$. The Raman spectrum of our glassy carbon is found to be well described by planar ordering approximately 2 to 3 layers in extent using a simple correlation function approach. Our results indicate a layered morphology is present in our nanocrystalline graphite, confirming a strong ${\mathit{sp}}^2$ bonding character.

Ground-state symmetry can be broken by an external field. The threshold value of the symmetry-breaking field may be roughly estimated by comparing experimentally the behavior of two identical physical quantities, as functions of the field, for the set of field directions equivalent, with respect to the action, to a group generator. The kinetic coefficients as the functions of magnetic induction B are used as an illustration.

It is shown how a rather strong soliton regime as that detected experimentally in the incommensurate phase of thiourea can be described by a thermodynamic potential expanded in terms of a one-dimensional order parameter. The modulation of the order parameter admits a parametrization similar to that commonly used for incommensurate phases with Lifshitz invariants (usually termed as type I). It is demonstrated that, if this parametrization is used, the sine-Gordon equation, which is usually considered only adequate for type-I incommensurate phases, is also approximately valid for those of type II, such as thiourea. In this way, the evolution of the order-parameter modulation towards a two-stepped function can be easily modeled. By extending the thermodynamic potential to include acoustic degrees of freedom, the coexistence (experimentally detected in thiourea) of solitonic and sinusoidal structural modulations is also explained. According to the present work, the differences between some of the so-called incommensurate phases of types I and II can be essentially reduced to the fact that, while in the former ones the eigenvector of the order parameter mode can be considered constant, in the latter, the variation of the soft-mode eigenvector with the modulation wave vector cannot be neglected.

Phase transitions of the rare-earth metal ytterbium were studied under pressure up to 70 GPa at room temperature with an energy-dispersive x-ray-diffraction technique using synchrotron radiation. A new phase transition hcp→fcc(II) was observed at 57 GPa. The phase sequence with pressure up to 70 GPa is fcc(I)→bcc→hcp→fcc(II). The hcp and fcc(II) phases show some similarity in their compression behavior to the lower pressure phases of praseodymium which is considered as first evidence for a strong hybridization between f electrons and conduction electrons.

We calculated the 2s and 2p x-ray photoelectron spectroscopy (XPS) core-hole spectra of ${\mathrm{TiCl}}_4$ molecule by an ab initio two-hole–one-particle (2h1p) configuration-interaction (CI) method, using an extended basis set. The present calculation gives a good overall description of the spectra, except for the main (second) satellite whose energy separation is overestimated by about 4 eV. The first satellite line is due to the ligand [Cl(3p)] to metal [Ti(3d)] charge-transfer (CT) shakeup excitation, while the second one is the ligand [Cl(3p)] to metal [Ti(4s)] CT shakeup excitation rather than the excitonic intraligand excitation. The core relaxation is very modest, despite significant CT in the core ionized state. So the main-line state is the Koopmans state. A comparison with the results obtained by previous molecular orbital approaches and the Anderson impurity-Hamiltonian-model approach is made.

Many lithium transition-metal oxides (LiM${\mathrm{O}}_2$, M=Ti, V, Cr, Mn, Fe, Co, Ni) have structures made up of oxygen atoms occupying a cubic close-packed fcc or distorted fcc lattice, with cations occupying all octahedral interstices. The cation lattice is therefore also fcc and the arrangements of the cations on that lattice can be studied with a lattice-gas model. The ${\mathrm{LiNiO}}_2$, layered ${\mathrm{LiCoO}}_2$, spinel ${\mathrm{LiCoO}}_2$, ${\mathrm{Li}}_2$${\mathrm{Ti}}_2$${\mathrm{O}}_4$, and γ-${\mathrm{LiFeO}}_2$ structures are predicted for appropriate values of first- (${\mathit{J}}_1$) and second- (${\mathit{J}}_2$) neighbor interactions within such a model by analogy with binary-alloy materials having similar structures. We are able to assign allowable ranges for the interactions for each of the oxides above based on their position in the ${\mathit{J}}_{1\mathrm{-}}$${\mathit{J}}_{2\mathrm{-}}$T phase diagram. A surprising result is that the layered and spinel ${\mathrm{LiCoO}}_2$ structures are equally stable over the same wide range of ${\mathit{J}}_1$ and ${\mathit{J}}_2$, as predicted by mean-field and Monte Carlo results. Although ${\mathrm{LiMnO}}_2$ is structurally related to the above materials, the ${\mathrm{LiMnO}}_2$ structure is not stable for any choice of ${\mathit{J}}_1$, ${\mathit{J}}_2$, or T. Further neighbor interactions or anisotropies in the near-neighbor interactions are needed to stabilize the ${\mathrm{LiMnO}}_2$ structure.

A random network is defined as a random array of waveguide segments with variable lengths. Each waveguide segment provides a continuous one-dimensional propagation channel. Wave scattering occurs only at the nodes of the network. The network model is shown to be equivalent to a zero-energy state of an equivalent tight-binding Hamiltonian. There can be two kinds of randomness in a network. The coordination number at each node and the length of each waveguide segment can be varied independently. A network becomes ordered only when each node has the same coordination number and all the segments are either equal in length or differ by some integral multiple of the wavelength. A uniformly extended state is found for any random network provided all the segments are of some integral multiple of the wavelength, modulo 2π. Both analytical and numerical approaches are used to investigate the critical localization behavior in the vicinity of either the uniform state or the ordered network. Our results show that the network model belongs to the same universality class as the disordered tight-binding Anderson model, but with special tunable characteristics. It is thus suggested that a random network of optical fibers can be an effective system for the observation of light localization.

Calorimetric and x-ray-diffraction studies of the commensurate (C)-incommensurate (IC) and incommensurate (IC)-normal (N) phase transitions in [P(${\mathrm{CH}}_3$${)}_4$${]}_2$${\mathrm{CuCl}}_4$ are reported. The C-IC transition at T=346.20±0.25 K is shown to be first order with a value of ${\mathrm{\Delta }}_{\mathit{t}\mathit{r}}$S=3.70±0.09 J ${\mathrm{K}}^{\mathrm{-}1}$ ${\mathrm{mol}}^{\mathrm{-}1}$. The IC-N transition at T=381.23±0.25 K appears to be second order with ${\mathrm{\Delta }}_{\mathit{t}\mathit{r}}$S=5.40±0.10 J ${\mathrm{K}}^{\mathrm{-}1}$ ${\mathrm{mol}}^{\mathrm{-}1}$. The orders of the transitions are based on the calorimetric data and the lattice parameters; the latter show a discontinuity at the C-IC transition but only show a discontinuity in slope at the IC-N transition. An additional anomaly, of unknown origin, is observed in the heat-capacity data following particular thermal histories, but it is not observed by diffraction studies. Critical-point analysis of the intensity of the satellite diffraction peaks within about 6 K of the IC-N transition leads to the estimate that 2β=0.54. Similar analysis of the thermal data within 1 K of the transition shows that α’ depends on the temperature range of the fit and α’<0.04. The temperature dependence of the effective values of the critical exponents, especially α’, and the discrepancies between observed α’ and β values with predictions for a three-dimensional XY model show that data closer to ${\mathit{T}}_{\mathit{c}}$ are required to carry out more complete critical-behavior analysis in this system.

It is shown that the icosahedral phase of ${\mathrm{FeTi}}_2$ can be obtained as the result of a reconstructive transformation of the displacive type from its crystalline fcc phase. The transformation mechanism is an inhomogeneous deformation of the fcc structure which can be associated with four systems of incommen- surate density waves.

In the present paper, a theory based on Zener’s model is developed to study the self-diffusion in solids as a function of pressure. The calculated values of self-diffusion in sodium are found to be in good agreement with the experimental data. The activation volume, ${\mathit{v}}^{\mathrm{act}}$, along with the activation energy ${\mathit{g}}^{\mathrm{act}}$, and isothermal compressibility, ${\mathit{k}}_{\mathit{T}}^{\mathrm{act}}$, are also calculated for sodium as a function of pressure. Further, a linear relation between lnD(P,T) and ${\mathit{v}}^{\mathrm{act}}$(P,T) is observed in the case of sodium. Hence, it may be concluded that the curvature between lnD(P,T) and P can be attributed to the variation of the activation volume associated with the formation and migration of a single entity.

Absorption bands A, B, and D in KBr:${\mathrm{Ag}}^{+}$ have been investigated under hydrostatic pressure at low temperature. The pressure shifts of these bands at 85 K are A: 5.093+0.14p-0.012${\mathit{p}}^2$ eV, B: 5.343+0.05p+0.006${\mathit{p}}^2$ eV, and D: 5.882+0.13p-0.016${\mathit{p}}^2$ eV, where pressure p is given in GPa units. The absorption intensity decreases and the half width becomes narrower under higher pressure. The pressure dependence of the peak position is analyzed by taking into consideration the ligand field interaction in addition to Drickamer’s framework. The rather large blue shift is attributed to the enhancement of the ligand field under pressure, and the different shift rate (0.08∼0.09 eV/GPa) between the A(D) and B bands results from the ligand field splitting of the d electron. It is suggested that the adiabatic potential in the excited states is deformed in Q(${\mathit{T}}_{1\mathit{u}}$) space. The changes of adiabatic potential in both the configuration coordinates of Q(${\mathit{A}}_{1\mathit{g}}$) and Q(${\mathit{T}}_{1\mathit{u}}$) are discussed.

The (1+1)-dimensional sine-Gordon model is studied in the framework of the variational Gaussian wave functionals. The renormalized mass depends on two dimensionless parameters. In the phase diagram a first-order phase transition will replace the second-order phase transition for large bare mass. The spectrum of the two-particle states consists of a continuum of scattering states and the isolated values connected to the excitonlike bound states. The energy of the bound states and the phase shifts of the scattering states are explicitly calculated.

Many properties of crystalline solids are controlled by the presence of point defects. Traditionally the concentrations of these defects are calculated using mass action laws that describe the reactions among the defects and with the environment. This formulation, however, is not applicable in the high-defect-concentration regime because it is based on assumptions that are valid only at the limit of dilute defect concentration. In the present work a statistical thermodynamic approach is used to develop a defect chemistry formulation that has general applicability at all levels of defect concentrations. This is accomplished by deriving an expression for the virtual chemical potential of point defects from the Gibbs free energy that includes contributions from short-range and long-range Coulombic interactions, and from a configurational entropy that incorporates generalized exclusion effects. By balancing the chemical potentials of different species and the environment as required under thermodynamic equilibrium conditions, one can derive equations that govern the concentrations of defects. At the limit of low defect concentration, the current approach is shown to be equivalent to that of the traditional theory. This formulation is demonstrated by working out an example in detail using undoped ${\mathrm{CeO}}_{2\mathrm{-}\mathrm{\delta }}$ as a model system. The concentrations of different species are calculated as functions of T and ${\mathit{P}}_{\mathrm{O}2\mathrm{}}$ using a numerical routine based on the conjugate gradient algorithm. The oxygen deficiency δ is obtained as the net concentrations of all oxygen vacancy containing species, and is found to be in good agreement with literature data. The effects of defect interactions and exclusions are discussed, and the thermodynamic activities of different species are calculated as functions of environmental parameters.

A study of the ${\mathrm{Ho}}^{3+}$ 2-μm laser emission in ${\mathrm{Gd}}_3$${\mathrm{Ga}}_5$${\mathrm{O}}_{12}$ using ${\mathrm{Yb}}^{3+}$ and ${\mathrm{Tm}}^{3+}$ ions as sensitizers is presented. We show by quantum-yield measurements that up-conversion energy losses are weak in the triply doped crystal. Models that describe the excited-state dynamics for both up- and down-conversion processes are given.

Temperature-dependent extended x-ray-absorption fine-structure (EXAFS) measurements at the oxygen and fluorine K edges of CuO, ${\mathrm{Cu}}_2$O, ZnO, ${\mathrm{CaF}}_2$, and LiF have been performed. We present an EXAFS analysis of bulk samples in the soft-x-ray region of hν≤1500 eV determining the moments of the radial pair distribution function (RDF) of the oxygen and fluorine nearest-neighbor bonds by use of the conventional cumulant expansion method, i.e., coordination numbers, bond lengths, atomic mean-square, and mean-cubic relative displacements of the RDF. It is shown that high-quality Kα-fluorescence-yield measurements, analyzed in combination with theoretical standards, allow a determination of nearest-neighbor distances within 0.015 Å and of coordination numbers with 10–20 % accuracy. Using quantum-mechanical models for the description of the atomic motions, the EXAFS Debye and Einstein temperatures, as well as the local thermal expansion of the bond under consideration, are obtained. In particular, these quantities for ${\mathrm{CaF}}_2$ are found to be in good agreement with those measured by other techniques. In contrast to the fluorides, no thermal expansion could be observed up to room temperature for the transition-metal oxides, which confirms a recent finding of enhanced anharmonicity in the low-Z adsorbate-surface interaction. A detailed compilation is given of the majority of EXAFS studies from the literature where moments of the RDF higher than the second one are reported. For these compounds the local thermal expansion is quantum mechanically calculated in contrast to previous calculations that were performed in the classical limit. Debye temperatures and the local thermal expansion measured by EXAFS and other techniques agree well for fcc metals. For binary compounds like alkali halides or superionic conductors a deviation up to 100% can be found.

Two kinds of multiple-light-scattering measurements were performed for porous glass plates of several pore radii from 0.15 to 0.50 μm. One is the measurement of the angular dependence of the backscattered light intensity, and the other is the measurement of the temporal profile of light pulses transmitted through the sample. The measured curves were in very good agreement with the theoretical ones based on the diffusion model in uniform scattering media, and no features specific to the local geometry of porous glass were found. The pore radius dependence of the transport mean free path ${\mathit{l}}^{\mathrm{*}}$ could be explained well by a Mie scattering calculation based on the independent scattering approximation. The transport velocity of light in the porous glasses in the measured range of the pore size calculated from the obtained values of ${\mathit{l}}^{\mathrm{*}}$ and the diffusion constants was around 60% of the phase velocity in the bulk glass.