We apply the kinetic Bragg-Williams model, introduced recently, to coherent precipitation of ordered phases. We show that the relaxation rate of the long-range order parameter (nonconserved) and of the concentration (conserved order parameter) are coupled not only by the free energy as usually assumed, but also by nondiagonal terms in the linear operator that connects the relaxation rate of both order parameters to the driving forces, i.e., the partial derivatives of the free-energy functional with respect to the order parameters. Moreover, we show that the relaxation of the nonconserved order parameter may occur by two routes, a homogeneous one (on site relaxation) and a heterogeneous one (migration of domain boundary). All such effects are ignored by existing theories.

The infrared-to-blue upconversion in ${\mathrm{Pr}}^{3+}$-doped yttrium aluminum garnet and yttrium lithium fluoride crystals has been studied at temperatures between 4.4 and 300 K for different activator concentrations. The excitation spectra and decay-time measurements indicated the sequential absorption of two photons between levels of the 4${\mathit{f}}^2$ electronic configuration. The first photon is absorbed nonresonantly by a weak phonon band associated with the ${}_{}{}^3{}_{}{}^{}$${\mathit{H}}_4$${\to }^1$${\mathit{G}}_4$ transition; the second resonant absorption step is from the ${}_{}{}^1{}_{}{}^{}$${\mathit{G}}_4$(1) to one of the ${}_{}{}^1{}_{}{}^{}$${\mathit{I}}_6$ levels that relax to the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ state. Transitions from the excited ${}_{}{}^1{}_{}{}^{}$${\mathit{G}}_4$ state obeyed the spin and point symmetry selection rules for electric-dipole transitions. Excited-state-absorption spectra revealed structure not observed in one photon absorption and excitation spectra.

From the phenomenological theory, the size effects on dielectric properties of ferroelectric thin films were calculated. When the spontaneous polarization is reduced in the surface layer, the mean susceptibility of the film increases with the decrease in film thickness and a size-driven phase transition will take place at a critical thickness. If the temperature-driven phase transition of the bulk is a second-order one, the size-driven transition will be accompanied by a dielectric divergence; if it is a first-order transition, a finite dielectric peak will appear. When the spontaneous polarization is enhanced in the surface layer, the mean susceptibility of the film decreases with the decrease in film thickness. No size-driven phase transition and hence no dielectric anomaly will occur in this case.

The effect of pressure on structural properties of potassium and rubidium is studied with diamond-anvil cells by energy-dispersive x-ray diffraction with synchrotron radiation at room temperature up to 50 GPa. The K III structure of potassium at pressures above 23 GPa is indexed by the use of a tetragonal-body-centered lattice (tI16) with 16 atoms in the unit cell. A new phase is found for rubidium above 46 GPa. Equation of state data for these heavy alkali metals are presented and compared with earlier data for cesium.

An EXAFS (extended x-ray-absorption fine structure) study of nanocrystalline iron prepared by high-energy ball milling is presented. Accurate data analysis has been performed using a recently developed ab initio multiple-scattering method (GNXAS). The crystalline iron EXAFS spectrum, taken as reference, has been analyzed taking proper account of the important multiple-scattering signal. Results of the data analysis are shown to be in good agreement with known structural values. The dramatic decrease of the first-neighbor coordination number found in nanocrystalline iron, as a function of the milling time, is shown to be related to the presence of a large defect density. The corresponding decrease of the coordination numbers of the second and further neighbors, as well as the significant decrease of the multiplicities of the three-atom configurations, confirms this interpretation. A simple model which takes into account the presence of atomic defects is shown to lead to marked reduction of coordination numbers and three-atom multiplicities in agreement with the experimental data. Selected models without lattice defects are shown to be unable to give a quantitative explanation of the intensity reduction of the EXAFS signal found in milled nanocrystalline iron. An in situ annealing of the sample (up to about 1100 °C) milled for the longer time (32 h) is shown to reduce considerably the density of the defects, as expected, although no complete recovering of the crystalline order is found. The transition from α iron to γ iron has been directly observed for such nanocrystalline material.

The distortions induced by dislocation loops are studied in finite systems. The influence of finite size, D, of the system, surface tension, and surface-bending elastic constant on the nematic-smectic (NA) phase transition is discussed. In thin freely suspended smectic liquid-crystal films the nematic-smectic transition temperature, ${\mathit{T}}_{\mathrm{NA}}$(D), is proportional to 1/ √D , providing the transition is initiated by the unbinding of the dislocation loops. The smectic phase is stabilized in films, i.e., ${\mathit{T}}_{\mathrm{NA}}$(D)>${\mathit{T}}_{\mathrm{NA}}$(∞). The loop-unbinding mechanism for the NA transition is completely suppressed in films sandwiched between solid boundaries, because the distortion energy in this case is proportional to the area of the loop, while the loop configurational entropy is proportional to its length. For temperatures T≥${\mathit{T}}_{\mathrm{NA}}$(∞) the equilibrium size of the loop, ${\mathit{R}}_{\mathrm{eq}}$, is proportional to the distance between solid boundaries, D. It could grow to infinity only for D→∞ and T≥${\mathit{T}}_{\mathrm{NA}}$(∞).

The local atomic structure of Co, Fe, and Ce in aluminum-rich amorphous alloys of ${\mathrm{Al}}_{100\mathrm{-}2\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$ (x=8, 9, and 10) and Ce in ${\mathrm{Al}}_{80}$${\mathrm{Fe}}_{10}$${\mathrm{Ce}}_{10}$ has been investigated by x-ray-absorption fine structure (XAFS) spectroscopy. The materials, 1- and 3-μm-thick films, were prepared by vapor quenching using the dc magnetron sputtering method. We show that the composition of the glass-forming region of these magnetron-sputtered alloys strictly follows the theoretical limit calculated on the basis of the atomic size criterion. From analyses of the XAFS data at the K edges of Co and Fe and the ${\mathit{L}}_3$ edge of Ce, the following conclusions with regard to local structure are made. The first coordination sphere of Co in ${\mathrm{Al}}_{100\mathrm{-}2\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$ (x=8, 9, and 10) consists of 5.8 to 6.4 Al atoms at a distance of 2.44 Å. The local coordination sphere for Fe in ${\mathrm{Al}}_{80}$${\mathrm{Fe}}_{10}$${\mathrm{Ce}}_{10}$ consists of 6.4 Al atoms at a distance of 2.47 Å. Ce in both systems appears to be coordinated with roughly 5 and 9 Al atoms at distances of 2.95 and 3.15 Å, respectively. These results are discussed in light of the dense random packing (DRP) of hard spheres model. Both Co-Al and Fe-Al bond lengths are anomalously short (9 and 8 % contraction, respectively) with also anomalously low coordination numbers (45% reduction) from values based on the DRP model using the metallic state radii.

These anomalous changes indicate a strong interaction between Co or Fe atoms and the Al atoms which perhaps may be a result of a covalently bonded environment. The Ce-Al distance in both the Al-Co-Ce and Al-Fe-Ce systems, on the other hand, is smaller by only 0.17 Å (a contraction of only 5%) and the coordination number is reduced by only 13% from expected values based on the DRP model. The contraction in the distance and reduction in the coordination number for Ce are much smaller than those values of the Co or Fe and, hence, the local bonding for Ce is likely to be metallic in character.

The composition ranges of Al-Ni-Co decagonal quasicrystals in superlattice-ordered and disordered states have been investigated. The single-decagonal-phase region is limited to a very small area around ${\mathrm{Al}}_{71}$${\mathrm{Ni}}_{16}$${\mathrm{Co}}_{13}$ at 650 °C, which expands along an almost Al-constant line at 850 °C. The single-decagonal-phase area at 650 °C entirely yields the completely ordered state, while that at 850 °C yields either a partially ordered state or the completely disordered state. The real-space structural change between the ordered and disordered states has been investigated by high-resolution transmission electron microscopy (HRTEM). The HRTEM images for both states comprise the arrangements of ringlike contrasts, forming tiling patterns with the edge length of about 20 Å. These tiling patterns have been analyzed on the basis of a high-dimensional description of the quasicrystalline structure. The analysis has revealed that the two tiling structures have characteristic features of the ordered and disordered quasicrystalline lattices, respectively. This leads to the conclusion that the rearrangement of the atomic clusters giving the ring contrasts in the HRTEM image is responsible for the present order-disorder structural transformation, which is a new type of order-disorder transformation characteristic of quasicrystals.

The phase diagram of the deuteron glass ${\mathrm{Rb}}_{1\mathrm{-}\mathit{x}}$(${\mathrm{ND}}_4$${)}_{\mathit{x}}$${\mathrm{D}}_2$${\mathrm{PO}}_4$ has been determined experimentally in the entire range of concentration x. A recently introduced temperature-frequency plot has been used to analyze the shape of the dielectric relaxation spectrum, indicating that in the glassy regime the longest relaxation time diverges according to the Vogel-Fulcher law. The corresponding Vogel-Fulcher temperature has been identified as the static limit of the freezing temperature ${\mathit{T}}_{\mathit{f}}$. The phase boundaries of the ferroelectric and antiferroelectric phases have been obtained in a standard manner by observing the peaks and breaks, respectively, in the temperature dependence of the quasistatic dielectric constant. It is shown that in a broad concentration range the observed phase diagram can be quantitatively described by a mean-field theory based on the static random-bond random-field model of dipolar glasses. The absence of macroscopic polarization in the ferroelectric region close to the glassy phase is probably due to the formation of microdomains in the presence of local random fields, however, recent NMR data suggest that a phase segregation between ferroelectric and glassy regions may occur.

Amorphous carbon (a-C) structures over a wide range of densities are generated using tight-binding molecular-dynamics simulations. The a-C networks obtained by quenching low-density liquids consist of mostly threefold coordinated atoms. These a-C structures correspond to those obtained experimentally by evaporation of sputtering of graphite. However, the a-C networks generated by quenching high-density liquids are found to be dominated by tetrahedral bonding sites, which resemble the diamondlike a-C films produced by the mass-selected ion beam deposition technique. Our study shows that the shape and position of the first peak of the radial distribution function in a-C are very sensitive to the relative concentration of sp, ${\mathit{sp}}^2$, and ${\mathit{sp}}^3$ bondings. The peak position shifts towards larger distance as the percentage of the fourfold sites increases, which gives a good indication of the relative population of threefold to fourfold sites in the system.

With the help of thermodynamic perturbation theory the quantum effects on the quadrupolar glass order parameter of solid hydrogen are studied. It is shown that due to the quantum nature of the system, in the zero temperature limit the quadrupolar glass order parameter is reduced 50% in comparison with the case when quantum effects are not taken into account implicitly.

The Landau theory used by Choi and Mele (CM) to treat their rotor model on a triangular lattice for the orientational ordering of polyacetylene chains in alkali-metal-doped polyacetylene is studied. A reanalysis of the higher-order terms in the Landau expansion indicates that cosine ordering can support a nonzero cubic term in the Landau expansion whereas the sine-ordered phase has no such term. To construct a phase diagram requires a numerical solution of the self-consistent equations of mean-field theory. Although this analysis does not convincingly treat the incommensurate phases found by CM, it does identify an unusually rich variety of thermodynamically stable phases and leads to significant modifications of the previous phase diagram. However, we do confirm the principle result of CM, that alkali-metal doping tends to destabilize the herringbone phase that exists in the undoped system. We also identify a number of interesting multicritical points. At one of these, the quadratic terms in the Landau expansion are totally independent of wave vector. This situation is similar to that for the kagome$iaa— antiferromagnet.

A general theory on the transfer of perfect matching rules for a quasiperiodic tiling to perfect matching rules for an atomic decoration of the tiling is presented. General conditions on the possibility of such a transfer are discussed, and an upper bound on the range of the matching rules for the atomic structure is derived. This range is identical to the range of interactions needed to stabilize such a quasiperiodic ground state. The main tool in this analysis is the concept of mutual local derivability. The general principles are then applied to two examples of binary tiling quasicrystals. The first one, based on the Tübingen triangle tiling, needs matching rules of a rather long range, whereas the second example, which is a decoration of the Penrose rhombus tiling, has matching rules of reasonable range. Finally, the concepts put forward in this paper are set into a broader context, and we compare them with other theories for the propagation of quasiperiodic order.

We introduce a dynamic fuse model for the damage done to a current-carrying polycrystalline metal thin film by electromigration. We determine the exact scaling behavior of the crack tip velocity for a single crack oriented perpendicularly to the direction of the ambient current. A Lifshitz-type theory works well only when the initial density of defects (p) is small. For all p, the mean failure time is to an excellent approximation proportional to the average length of the shortest path across the film in a certain metric. This conclusion is supported by our simulations and by analytical work based on a variational formulation of our problem. Using the shortest-path approximation, we show that the mean failure time tends to zero as (${\mathit{p}}_{\mathit{c}}$-p${)}^{4/3}$ as the percolation threshold p=${\mathit{p}}_{\mathit{c}}$ is approached. We also use the shortest-path approximation to account for experimental results on the lifetime of long polycrystalline metal wires of varying lengths and widths.

The polarization conductivity σ’(ω) of ${\mathrm{Na}}_2$O-${3\mathrm{S}\mathrm{i}\mathrm{O}}_2$ glass has been studied by impedance spectroscopy (100 Hz–5 MHz). The results are explained on the basis of a free-volume model applied to ionically conducting glasses. The experimental relationship σ’(ω)=A${\mathrm{\omega }}^{\mathit{S}}$ was found and the parameter s calculated according to the model. The distribution of relaxation times included in the expression of σ’(ω) was evaluated by thermally stimulated polarization-depolarization current peaks attributed to the bulk polarization. The experimental results related to σ’(ω) and parameter s were compared with the calculations performed by means of a distribution function, determined by the thermally stimulated current technique. There is good agreement between the results showing that the two approaches are complementary.

We present a comparative vibrational study of leucoemeraldine, emeraldine, and pernigraniline bases: fully reduced, half oxidized, and fully oxidized forms of polyaniline, respectively. By performing a general vibrational calculation based on the symmetrized dynamical matrix, we determine the force constants, the potential-energy distribution, and the Cartesian displacements for the three forms of polyaniline and associated model compounds. We discuss the assignment of the fundamental Raman and ir vibrational modes of the polymers. The modifications of the frequencies and consequently of the main force constants observed from one compound to the other are analyzed by considering the quinoid and aromatic characters along the chain. In this way, we determine a force field with physical significance which may be used to interpret the electronic modification between neutral and protonated as well as photoexcited emeraldine forms. This comparative analysis demonstrates the important changes of the electronic distribution around the nitrogen atom, which plays a major role in the conduction mechanism in this class of conducting polymers.

Heat transport is studied in a simple model system of Anderson localized optical (carrier) phonons which perform thermally activated hopping due to anharmonic interaction with delocalized acoustic phonons. The corresponding kinetic equations (rate equations) are derived by using the density-matrix formalism. The calculated hopping contribution to the heat conductivity exhibits a linear increase with temperature at lower temperatures and (depending on the choice of parameters) eventually reaches a ‘‘saturated’’ value at higher temperatures. Thus, unlike other authors, we do not need a special mechanism, such as lifetime broadening of the optical phonon states, to explain the transition to the saturation region. Furthermore, we show that particle (carrier) number nonconservation leads to a quenching of the hopping mechanism.

We calculate the resistance of one-, two-, and three-dimensional localized systems in the hopping regime, simulated by random-resistor networks within the r-resistor model. The analysis of the logarithm of the resistance as a function of the degree of spatial disorder reveals that in one- and two-dimensional samples the resistance increases with disorder, while in three-dimensional samples the resistance decreases. We also study the fluctuations of the conductance from sample to sample.

The one-dimensional (1D) large bipolaron is investigated in the limit of strong electron-phonon coupling. The nonlinear integro-differential equation for the bipolaron wave function is solved numerically, from which we obtained estimates for the main characteristics. An enlargement of the stability region for the bipolaron ground state is found in 1D as compared to the stability regions in 2D and 3D. The energy of the first relaxed excited state (RES) equals the energy of two single polarons and the ground state in the potential generated by the first RES has a slightly lower energy than this RES and is therefore stable. The nonlinearity causes the feature that the combination of the ground state and an excited state of one-particle wave functions could lead to a higher bipolaron energy than the combination of two excited states.

Applicability of linear theory to magnetic anisotropy of 3d-4f intermetallics is investigated with particular reference to ${\mathrm{Sm}}_2$${\mathrm{Fe}}_{17}$${\mathrm{N}}_3$. A general quantitative criterion for the breakdown of the linear theory is established, according to which the theory falls beyond a 20% accuracy limit for most permanent magnet materials. By rigorous numerical treatment of published experimental data on high-field magnetization of ${\mathrm{Sm}}_2$${\mathrm{Fe}}_{17}$${\mathrm{N}}_3$, the crystal-field parameters are determined to be ${\mathit{A}}_2^0$ =-333${\mathit{Ka}}_0^{\mathrm{-}2}$,${\mathit{A}}_4^0$=0.84${\mathit{Ka}}_0^{\mathrm{-}4}$. The linear theory fails for ${\mathrm{Sm}}_2$${\mathrm{Fe}}_{17}$${\mathrm{N}}_3$ due to its disregard for both J-mixing, predominant at all temperatures, and the intramultiplet nonlinear effects, important at low temperatures. Nevertheless these effects can be largely compensated for by rescaling the crystal-field parameters within the framework of the linear theory, which then provides an accurate analytical description of anisotropic magnetic properties of ${\mathrm{Sm}}_2$${\mathrm{Fe}}_{17}$${\mathrm{N}}_3$ in the practically important range of temperatures, T≳300 K.