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The limitation in sample size and the choice in parameters for the application of the micro-crystal (MC) model have been tested and discussed. The testing was performed through the fitting of calculated Raman spectra by using the MC model with the observe

A crystal plasticity model for near-alpha hcp titanium alloys embodying a quasi-cleavage failure mechanism is presented and employed to investigate the conditions necessary in order for facet nucleation to occur in cold-dwell fatigue. A model polycrystal is used to investigate the effects of combinations of crystallographic orientations (and in particular, a rogue grain combination), the essential role of (cold) creep during hold periods in the loading cycle and the more damaging effect of a load hold rather than a strain hold in facet nucleation. Direct comparisons of model predictions are made with dwell fatigue test results. More generally, the crystal model for faceting is found to be consistent with a range of experimental observations.

The new technique of nuclear resonance vibrational spectroscopy (NRVS) has increased the range and quality of dynamical data from Fe-containing molecules that when combined with Raman and infrared spectroscopies impose stricter constraints on normal mode simulations, especially at lower frequencies. Going beyond the usual single molecule approximation, a classical normal-mode analysis that includes intermolecular coupling and the full crystalline symmetry is found to produce a better fit with fewer free parameters for the heme compound iron octaethylporphyrin (FeOEP), using NRVS data from polycrystalline material. Off-diagonal force constants were completely unnecessary, indicating that their role in previous single molecule fits was just to emulate intermolecular coupling. Sound velocities deduced from the calculated phonon dispersion curves are compared to NRVS measurements to further constrain the intermolecular force constants. The NRVS data by themselves are insufficient to rigorously determine all unknown force constants for molecules of this size, but the improved crystal model fit indicates the necessity of including intermolecular interactions for normal-mode analyses.

The results are presented of a feasibility study for the application of absorption corrections to macromolecular crystallographic X-ray diffraction data using a three-dimensional crystal model generated photographically. The model allows path lengths through the crystal, the solvent and the crystal mount system to be determined. The approach has been tested on the macromolecular crystallography beamline ID23-1 at the ESRF in Grenoble using a model insulin system with the standard mini diffractometer facilities, which incorporate high-quality camera systems for sample alignment. Data from the insulin crystal at low incident beam energy (6.0 keV or 2.1 Å) were recorded and processed using this approach. The resulting data are compared against those treated using an empirical method and show significant improvement. The methods described here are of general interest, particularly for long-wavelength X-ray work, and may also be applied to account for absorption effects in neutron crystallography.

The undercooled melt growth behaviors of benzophenone crystals were in situ observed to measure the growth rates of two selected crystal faces and aspect ratio of grown crystal. The results showed that the relations between growth rate, as well as aspect ratio, and the undercooling presented exponential profile. The expression of the aspect ratio with the undercooling was also deduced by using a two-dimensional crystal model. The agreement between theoretical prediction and experimental results implies that the undercooled melt growth kinetics of benzophenone crystals satisfied the two-dimensional nucleation mechanism.

Crystals of aluminum-and indium-doped Ge1−x Si x (0

Long-range NMR restraints, such as diamagnetic residual dipolar couplings and paramagnetic data, can be used to determine 3D structures of macromolecules. They are also used to monitor, and potentially to improve, the accuracy of a macromolecular structure in solution by validating or "correcting" a crystal model. Since crystal structures suffer from crystal packing forces they may not be accurate models for the macromolecular structures in solution. However, the presence of real differences should be tested for by simultaneous refinement of the structure using both crystal and solution NMR data. To achieve this, the program REFMAC5 from CCP4 was modified to allow the simultaneous use of X-ray crystallographic and paramagnetic NMR data and/or diamagnetic residual dipolar couplings. Inconsistencies between crystal structures and solution NMR data, if any, may be due either to structural rearrangements occurring on passing from the solution to solid state, or to a greater degree of conformational heterogeneity in solution with respect to the crystal. In the case of multidomain proteins, paramagnetic restraints can provide the correct mutual orientations and positions of domains in solution, as well as information on the conformational variability experienced by the macromolecule.

PbTe1-x Se x alloys are of special interest to thermoelectric applications. Inelastic x-ray scattering determination of phonon dispersion and lifetimes along the high symmetry directions for PbTe1-x Se x alloys are presented. By comparing with calculated results based on the virtual crystal model calculations combined with ab initio density functional theory, the validity of virtual crystal model is evaluated. The results indicate that the virtual crystal model is overall a good assumption for phonon frequencies and group velocities despite the softening of transverse acoustic phonon modes along [1 1 1] direction, while the treatment of lifetimes warrants caution. In addition, phonons remain a good description of vibrational modes in PbTe1-x Se x alloys.

We present a structural phase-field crystal model [M. Greenwood et al., Phys. Rev. Lett. 105, 045702 (2010)] that yields a stable $dc$ structure. The stabilization of a $dc$ structure is accomplished by constructing a two-body direct correlation function (DCF) approximated by a combination of two Gaussian functions in Fourier space. A phase diagram containing a $dc$-liquid phase coexistence region is calculated for this model. We examine the energies of solid-liquid interfaces with normals along the [100], [110], and [111] directions. The dependence of the interfacial energy on a temperature parameter, which controls the heights of the peaks in the two-body DCF, is described by a Gaussian function. Furthermore, the dependence of the interfacial energy on the peak widths of the two-body DCF, which controls the excess energy associated with interfaces, defects, and strain, is described by an inverse power law. These relationships can be used to parametrize the phase-field crystal model for the $dc$ structure to match solid-liquid interfacial energies to those measured experimentally or calculated from atomistic simulations.

The various crystal models of cellulose Ibeta, each differing in crystal size, have been studied by computer simulation using the amber molecular-dynamics package and the GLYCAM parameters. The four types of crystal model were constructed by a combination of two base-plane sizes, consisting of either 24 or 48 chains and two chain lengths having either 10 or 20 residues. The base planes of the crystal models were composed by the edges of the [1,1,0], [1,-1,0], and [1,0,0] crystal planes, where the [1,1,0] plane was assigned to the longest edge. The crystal models were soaked in water boxes to investigate their swelling behavior. Unexpectedly, the crystal models twisted quickly to form a slightly right-handed shape during the initial approximately 50 ps and that, in a steady, swollen state, the twisted forms remained for the rest of the simulation time. In spite of such overall deformation, the inner part of the swollen model fairly reproduced the important structural features of the original crystal structure, such as the rotational positions of the substituent groups and the hydrogen-bonding scheme. On heating the crystal model up to 550 K, the twisted shape was conserved in most of the temperature range, while the initial conformations of the substituent groups deviated above approximately 430 K, followed by appreciable disordering in chain sheets at higher temperatures. It is suggested that some internal tensions are involved within a chain sheet of the initial structure. In the course of swelling, some of these tensions were released to introduce a twisted shape in the crystal models.

The elastic modulus of natural cellulose crystal was estimated by the molecular simulation technique. Values between 124 and 155 GPa were derived for the reasonable cellulose Iβ crystal model that were nearly equal to the observed value of 138 GPa. While the second-generation force fields were found to be superior to the first-generation ones for the optimization of cellulose structure, neither of these was good enough to achieve the structural optimization. They were, however, adequate for estimating the mechanical properties of cellulose, especially the second-generation force fields. The lateral (that is, intermolecular) interactions between cellulose chains were found to play an important role in the expression of the mechanical properties of cellulose crystal.

The molecular-dynamics method was used to examine the effect of cross-sectional sample size on detonation processes in molecular crystals. It was shown that, in the molecular crystal model considered, an increase in cross-sectional size has no noticeable effect on the propagation velocity of detonation waves, on the delay time of the chemical reaction, and on the energy macrocharacteristics of the disturbed region. Also, the results of the present molecular-dynamic modeling were compared with the predictions of the continuum theory of detonation. Good agreement between the detonation velocities and between the values of thermodynamic parameters at the Chapman–Jouguet point was obtained.

We propose a charge crystal model that captures all the essential physics of the high temperature superconductivity (HTS) in the long wavelength limit. Based on the recent transport and the far-infrared (far-IR) experiments, we argue that the three-dimensional (3D) ordering of the pinned two-dimensional (2D) square electronic lattice (EL) in each CuO 2 plane is the building block of HTS. Incorporating the physical picture derived from the neutron scattering experiments, we demonstrate that our model presents a coherent picture of the HTS. We suggest that the charge crystal model serves as a model for the microscopic theory and, hence, offers the key to the mechanism for the HTS.

This study looks at the crack propagation characteristics based on the cohesive zone model (CZM), which is implemented as a user defined element within FE system ABAQUS. A planar crystal model is applied to the polycrystalline material at elevated temperature in which grain boundary regions are included. From the point of energy, interactions between the cohesive fracture process zones and matrix material are studied. It’s shown that the material parameter such as strain rate sensitivity of grain interior and grain boundary strongly influences the plastic and cohesive energy dissipation mechanisms. The higher the strain rate sensitivity is, the larger amount of the external work will be transformed into plastic dissipation energy than into cohesive energy which could delay the rupturing of cohesive zone. By comparisons, when strain rate sensitivity decreases, plastic dissipation energy is reduced and the cohesive dissipation energy increases. In this case, the cohesive zones fracture more quickly. In addition to the matrix material parameter, influence of cohesive strength and critical displacement in CZM on stress triaxiality at grain interior and grain boundary regions are also investigated. It’s shown that enhancing cohesive zones ductility could improve matrix materials resistance to void damage.

The exact analytical solution for the plane S-wave, propagating along the axis of spirality in the simple 1-D anisotropic “simplified twisted crystal” model, is compared with four different approximate ray-theory solutions. The four different ray methods are (a) the coupling ray theory, (b) the coupling ray theory with the quasi-isotropic perturbation of travel times, (c) the anisotropic ray theory, (d) the isotropic ray theory. The comparison is carried out numerically, by evaluating both the exact analytical solution and the analytical solutions of the equations of the four ray methods. The comparison simultaneously demonstrates the limits of applicability of the isotropic and anisotropic ray theories, and the superior accuracy of the coupling ray theory over a broad frequency range. The comparison also shows the possible inaccuracy due to the quasi-isotropic perturbation of travel times in the equations of the coupling ray theory. The coupling ray theory thus should definitely be preferred to the isotropic and anisotropic ray theories, but the quasi-isotropic perturbation of travel times should be avoided. Although the simplified twisted crystal model is designed for testing purposes and has no direct relation to geological structures, the wave-propagation phenomena important in the comparison are similar to those in the models of the geological structures.

The coupling ray theory bridges the gap between the isotropic and anisotropic ray theories, and is considerably more accurate than the anisotropic ray theory. The coupling ray theory is often approximated by various quasi-isotropic approximations.

Analytical expressions for the exact 2 × 2 one-way propagator matrix of a plane S wave, propagating along the axis of spirality in the simple 1-D anisotropic “simplified twisted crystal” model, are presented. The analytical equations are useful in testing the applicability and accuracy of various approximate wavefield modelling methods, especially of the coupling ray theory and of its various quasi-isotropic approximations and various numerical implementations. In addition to the exact analytical solution of the elastodynamic equation in the “simplified twisted crystal” model, the analytical solutions of the equations of the four ray methods are given. The ray methods are (a) the coupling ray theory, (b) the coupling ray theory with the quasi-isotropic perturbation of travel times, (c) the anisotropic ray theory, (d) the isotropic ray theory. These four approximate solutions of the elastodynamic equation are roughly compared with the exact solution. Both the exact analytical solution and the analytical ray-theory solutions in the “simplified twisted crystal” model are also helpful in debugging computer codes for various approximate wavefield modelling methods, especially for the coupling ray theory.

A new ansatz is presented for analytic study of the properties of the Holstein model. New analytic results for the polaronic band structure, ground state energy, phonon distribution, hopping probability of electron, and effective masses, of the Holstein molecular crystal model, are given in one dimension. All the analytic results obtained are in accord with the numerical results completed recently and valid both in the adiabatic and nonadiabatic regimes, and accurate enough in the region of validity.

A mathematical model is given to study how the twin width of the needle-like laminate is related to the twin length and the surface energy density in austenite–martensite phase transition. A numerical method based on the mesh transformation method is given, and numerical experiments are made to establish such a relationship for an elastic crystal model.

A mathematical model is given to study the branched laminated microstructure in austenite-martensite phase transition. A numerical method based on a mesh transformation method is applied to a two dimensional elastic crystal model, and the numerical results show that, for sufficiently small surface energy density and sufficiently long laminates, the branched laminates are energetically favorable; the numerical results also show that there is certain finite order asymptotically self-similar structure in the branched laminates.

The classical Kossel–Stranski crystal model is adapted to a critical re-examination of surface nucleation in polyethylene. Several aspects of the diverse morphologies displayed by this polymer are well accounted for. The suggestion is made that curved {200} faces in lenticular crystals arise as a consequence of normal growth rather than nucleated growth on these faces. Processes generally involved in surface nucleation and subsequent layer spreading are discussed with emphasis upon entropic considerations. This leads to the view that, although nucleation kinetics are followed, molecular conformations can become more tightly clumped than is commonly thought to follow inevitably from layer spreading.

A method is described for analysing strain in a plate–shaped crystal divided into growth sectors differing in lattice parameter and joined together at coherent dislocation–free sector boundaries running between the surfaces of the plate. The specimen studied was a large synthetic diamond, grown by the high–pressure hightemperature method, from which a near–central slice had been cut and polished parallel to (110). It contained dilatation–producing atomically dispersed substitutional nitrogen impurity, with adjacent growth sectors alternating in nitrogen concentration. In order that stress functions could be used to approximate the exact solution of the three–dimensional problem, the configuration of crystal growth sectors was modelled by an assembly of elongated rectangular parallelepipeds of alternating lattice parameter. Such a model is considered to be a good representation of the sector configuration of special interest in the real crystal. Using this model, the strains induced by lattice–parameter mismatch were calculated by adapting the classical theory of initial stresses due to Timoshenko and Goodier. In the present application, this involved four stages of imaginary operations: disassembly of the crystal model into stress–free sectors, deforming them by uniform lattice–matching strains, in planes parallel to the sector boundaries, ‘welding’ them together, and restoration of the initial conditions by application of ‘annulling’ stresses to cancel those applied in the deformations. Because uniform strains were applied in the matching procedure, only forces on the free surfaces of the crystal were required in this final stage, and it is argued that these should be applied in plane strain in planes orthogonal both to the sector boundaries and to the crystal–plate surface. Stress functions for orthorhombic symmetry are derived from first principles and applied to the geometry of the present problem, namely that of a cubic crystal under plane strain in which the cubic axes are rotated by 45 ° about the axis determined by the sector–boundary normal, [001]. Displacements and strains have been calculated at all points within the sector cross–section of interest, and extended to include wide variations in ratios between sector widths, and between sector width and plate thickness; the physical reasons for the resultant changes in strain distributions are discussed. Convergence of the Fourier–series solution under this variation of parameters is examined in detail. Representative deformation profiles of (110) planes in the real crystal are exhibited. The calculation has enabled a close limit to be placed on systematic error due to coherency strains in the findings of earlier X–ray–diffractometric experiments on the specimen discussed in the present study. Those experiments compared the symmetrical 440 surface Bragg reflection from a large (11 bar 1) growth sector fairly rich in substitutional nitrogen impurity with that from an adjacent, smaller, (11 bar 0) sector, virtually nitrogen free. The measurements aimed to establish the proportionality factor between substitutional nitrogen concentration and dilatation. The present analysis supports the earlier X–ray diffractometry: it changes the finding for Δa 0 /ā 0 quite insignificantly from (1.18 ±) × 10 −5 to (1.20 ± 0.07) × 10 −5 . On the other hand, revision of the nitrogen–concentration difference between the two growth sectors concerned, resulting from a more recent conversion factor between infrared absorption and nitrogen content (independent of the present study), raises that difference from ca .88 to ca .100 ppm atomic. Combining this large change with the small change in Δa 0 /ā 0 reduces the earlier finding for the ratio of the effective volume of a single substitutional nitrogen atom to the volume of the carbon atom it replaces from 1.41 ± 0.06 to 1.36 ± 0.1.

Modern concepts in the safe and economical design of components and structures need modern material models, which describe the material behavior more correctly. In high temperature design, the study of creep damage accumulation and its influence on the deformation behavior is very important. For ductile materials large deformation takes place at the level of damage appearance. Damage is anisotropic in nature. In this paper an anisotropic damage mechanics model based on a continuum damage mechanics (CDM) has been developed to model creep behavior of single crystal superalloys. Using the theory of CDM, the slip system model coupling with anisotropic damage model is developed. The model is formulated in the context of irreversible thermodynamics and the internal state variable theory. The distinguishing characteristic of the proposed constitutive model is that, by construction, the corresponding incremental stress–strain relations including damage evolution equation derive from a thermodynamical framework. The finite element program ABAQUS has been used and the slip system model is written using a user material subroutine. The numerical simulations show that the developed damage crystal model can reflect the microstructure such as the lattice orientation, self- and latent-hardening and rate sensitivity has great influence on the creep and damage development.

Low-frequency Raman spectra of even and odd n-alcohols have been recorded. The longitudinal acoustic modes (LAM) are described, and the effects of hydrogen-bonding, chain length, and temperature on the frequencies of these vibrations are discussed. The frequencies of the LAMs are interpreted in terms of the one-dimensional crystal model of Minoni and Zerbi and also ab initio calculations on isolated single chains. The low-frequency LAM-1 mode of the hydrogen-bonded dimer exhibited an odd−even effect, and to gain insight into this, the crystal structures of the C17 and C20 alcohols were determined by single-crystal X-ray diffractometry. C17H35OH packs in the β form, with half the oxygen atoms trans and half gauche, with respect to the alkyl chains. C20H41OH adopts an all trans conformation and the packing is in the γ form. The hydrogen-bonding interactions differ in the two structures. We therefore ascribe the odd−even effect in the LAM-1 frequencies to an odd−even effect in crystal structure.

In this paper we apply a mosaic crystal model for dynamical x-ray diffraction to step-graded metamorphic semiconductor device structures containing dislocations. This model represents an extension of the previously-reported phase-invariant model, which is broadly applicable and serves as the basis for the x-ray characterization of metamorphic structures, allowing determination of the depth profiles of strain, composition, and dislocation density. The new model has more general applicability and is more appropriate for step-graded metamorphic device structures, which are of particular interest for high electron mobility transistors and light emitting diodes. Here we present the computational details of the mosaic crystal model and demonstrate its application to step-graded InxGa1-xAs/GaAs (001) and InxAl1-xAs/GaAs (001) metamorphic buffers and device structures.

The authors present a detailed x-ray dynamical diffraction analysis of metamorphic InxGa1-xAs/InyGa1-yAs superlattices grown epitaxially on GaAs (001) substrates. The x-ray rocking curve analysis was conducted for a number of hkl reflection profiles, including 004, 115, 026, and 117, assuming Cu kα1 radiation, by using the mosaic crystal model for dynamical diffraction. The authors show that the threading dislocation density in the superlattice can be estimated from nondestructive x-ray rocking curve measurements, by observing the superlattice peak widths.

This work develops a method for calibrating a crystal plasticity model to the results of discrete dislocation (DD) simulations. The crystal model explicitly represents junction formation and annihilation mechanisms and applies these mechanisms to describe hardening in hexagonal close packed metals. The model treats these dislocation mechanisms separately from elastic interactions among populations of dislocations, which the model represents through a conventional strength-interaction matrix. This split between elastic interactions and junction formation mechanisms more accurately reproduces the DD data and results in a multi-scale model that better represents the lower scale physics. The fitting procedure employs concepts of machine learning—feature selection by regularized regression and cross-validation—to develop a robust, physically accurate crystal model. The work also presents a method for ensuring the final, calibrated crystal model respects the physical symmetries of the crystal system. Calibrating the crystal model requires fitting two linear operators: one describing elastic dislocation interactions and another describing junction formation and annihilation dislocation reactions. The structure of these operators in the final, calibrated model reflect the crystal symmetry and slip system geometry of the DD simulations.

We examine high quality, single crystal CdTe epilayer grown by molecular beam epitaxy (MBE) on (2 1 1)B GaAs substrate using both positions and full width at half maximums (FWHMs) of reciprocal lattice points (RLPs). Our results demonstrate that reciprocal space mapping (RSM) is an effective way to study the structural characteristics of the high-index oriented epitaxial thin films having a large lattice mismatch with the substrate. The measurement method is defined first, and then the influence of shear strain ( xz) on the position of the (5 1 1) node of epilayer is clarified. It is concluded that the lattice tilting is likely to be related with the lattice mismatch. Nondestructive measurement of the dislocation density is achieved by applying the mosaic crystal model. The screw dislocation density, estimated to be 7.56×107 cm2, was calculated utilizing the broadened peakwidths of the asymmetric RLP of the epilayer lattice.

Plastic deformation mediated by collective dislocation dynamics is investigated in the two-dimensional phase-field crystal model of sheared single crystals. We find that intermittent fluctuations in the dislocation population number accompany bursts in the plastic strain-rate fluctuations. Dislocation number fluctuations exhibit a power-law spectral density $1/{f}^{2}$ at high frequencies $f$. The probability distribution of number fluctuations becomes bimodal at low driving rates corresponding to a scenario where low density of defects alternates at irregular times with high populations of defects. We propose a simple stochastic model of dislocation reaction kinetics that is able to capture these statistical properties of the dislocation density fluctuations as a function of shear rate.

This work describes a 3-D Finite-Difference Time-Domain (FDTD) computational approach for the optical characterization of an opal photonic crystal. To fully validate the approach we compare the computed transmittance of a crystal model with the transmittance of an actual crystal sample, as measured over the 400 divided by 750 nm wavelength range. The opal photonic crystal considered has a face-centered cubic (FCC) lattice structure of spherical particles made of polystyrene (a non-absorptive material with constant relative dielectric permittivity). Light-matter interaction is described by numerically solving Maxwell's equations via a parallelized FDTD code. Periodic boundary conditions (PBCs) at the outer edges of the crystal are used to effectively enforce an infinite lateral extension of the sample. A method to study the propagating Bloch modes inside the crystal bulk is also proposed, which allows the reconstruction of the omega-k dispersion curve for k sweeping discretely the Brillouin zone of the crystal. (C) 2014 Optical Society of America

Molecular dynamics simulation starting from a lamellar crystal model of a single polyethylene chain is performed to investigate the lamellar reorganization during heating at the molecular level. It is shown that three stages are involved in the process of the reorganization: at temperatures 300 K 500 K the lamella starts to melt and becomes a random coil in the end. Particularly, the thickening process is investigated in our simulations. It is found that the lamellar thickening occurs in discrete steps and is driven mainly by the van der Waal attraction between the chain segments. There are two mechanisms for the lamellar thickening. At lower temperature the thickening occurs by the sliding diffusion of adjacent chain segments, while at higher temperature the recrystallization after the partial melting of thinner stems leads to the thickening.

We report some numerical results on the computation of needle-like microstructures at mesoscopic scale obtained by applying the mesh transformation method, which basically includes a mesh optimization into the finite element approximations, on a nonquasiconvex elastic crystal model. Numerical experiments show that the branched needle-like microstructures can be well resolved near the interfaces between twinned layers of martensite and a single variant of martensite, which are in good qualitative agreement with the physical experiments.

We introduce an effective one-mode phase-field crystal model for studying the commensurate-incommensurate transition and domain wall dynamics of the phase found in systems such as Xe/Pt(111), or Xe and Kr on graphite. The model allows us to study large systems where the domain walls can be separated over large macroscopic distances and at the same time incorporate the microscopic details of the domain wall structures. The resulting phase diagram shows that an intermediate stripe incommensurate phase always separates the commensurate phase from the honeycomb incommensurate phases. The energy of the domain wall crossing is investigated. We also find that near a step edge, the domain walls tend to align perpendicularly to the step edge, in agreement with recent experimental observations.

A one-dimensional crystal model is constructed with a complex periodic potential. A wave function solution for the crystal model is derived without relying on Bloch functions. The new wave function solution of this model is shown to correspond to the solution for the probability amplitude of a two-level system. The energy discriminant is evaluated using an analytic formula derived from the probability amplitude solution, and based on an expansion parameter related to the energy and potential amplitude. From the wave function energy discriminant the crystal band structure is derived and related to standard energy bands and gaps. It is also shown that several of the properties of the two-level system apply to the one-dimensional crystal model. The two-level system solution which evolves in time is shown to manifest as a spatial configuration of the one-dimensional crystal model. The sensitivity of the wave function probability density is interpreted in the context of the new solution. The spatial configurat...

A quenched disordered phase of solid nitrogen has been studied in the temperature region where a dynamical crossover is observed between nearly free rotations and activated tumbling motion. The orientational dynamics of the molecules is fast enough to be simulated using the Monte Carlo Metropolis algorithm and Molecular Dynamics. However, these methods become non-ergodic at very low temperature where formation of a glassy state could be observed. The crystal structure below the crossover temperature remains hcp with the molecular orientations frustrated due to the incompatibility of the strong quadrupolar interactions with the hexagonal lattice. For this reason, quenched nitrogen at low temperature seems to be a good candidate for a glassy crystal model.

It is well known that the mechanical material properties of a material sample after solidification are strongly tied to its microstructure structure. Nevertheless, the precise laws governing the initial stage of this structuring process, i.e. nucleation and the scenario of the successive transiental microstructure evolution, are still far from being fully understood. Here we will show that the phase-field method, which originally established itself to tackle the free boundary problem given by microstructure evolution, can also be employed to investigate the energetics of heterogeneous nucleation in a solidifying sample. Moreover it is demonstrated at the example of a generalized phase-field crystal model recently derived by the authors [R. Prieler, B. Verleye, R. Haberkern, D. Li, H. Emmerich, J. Phys. Condens. Matter, accepted for publication], how the phase-field crystal method can shade more light in open questions regarding a quantitative formulation of nucleation statistics to thereby simulate the phase transition phenomena in solidification from nucleation to crystallization in larger domains thoroughly. The aim of this contribution is to give an overview how both methods allow to study jointly nucleation from the atomic to the microscale.

This paper addresses the issue of integrable structure in a modified melting crystal model of topological string theory on the resolved conifold. The partition function can be expressed as the vacuum expectation value of an operator on the Fock space of 2D complex free fermion fields. The quantum torus algebra of fermion bilinears behind this expression is shown to have an extended set of "shift symmetries". They are used to prove that the partition function (deformed by external potentials) is essentially a tau function of the 2D Toda hierarchy. This special solution of the 2D Toda hierarchy can be characterized by a factorization problem of $\ZZ\times\ZZ$ matrices as well. The associated Lax operators turn out to be quotients of first order difference operators. This implies that the solution of the 2D Toda hierarchy in question is actually a solution of the Ablowitz-Ladik (equivalently, relativistic Toda) hierarchy. As a byproduct, the shift symmetries are shown to be related to matrix-valued quantum dilogarithmic functions., latex2e, 33 pages, no figure; (v2) accepted for publication

A recently introduced active phase field crystal model describes the formation of ordered resting and traveling crystals in systems of self-propelled particles. Increasing the active drive, a resting crystal can be forced to perform collectively ordered migration as a single traveling object. We demonstrate here that these ordered migrating structures are linearly stable. In other words, during migration, the single crystalline texture together with the globally ordered collective motion is preserved even on large length scales. Furthermore, we consider self-propelled particles on a substrate that are surrounded by a thin fluid film. We find that in this case the resulting hydrodynamic interactions can destabilize the order., Comment: 15 pages, 8 figures

Recently it was emphasized once again that the use of the free gas model instead of the harmonic crystal model at the experimental analysis stage could introduce non-negligible errors in the deduced neutron resonance parameters. In the present paper we will show how the use of the harmonic crystal model can affect the resonance parameters of 237 Np bound in NpO 2 when analysing the recent experimental data obtained at the GELINA (Geel Electron LINear Accelerator) facility, Belgium. Further using the harmonic crystal model at the experimental analysis stage we will deduce a new set of improved resonance parameters of 237 Np.

The polaron features of the one-dimensional Holstein Molecular Crystal Model are investigated by improving a variational method introduced recently and based on a linear superposition of Bloch states that describe large and small polaron wave functions. The mean number of phonons, the polaron kinetic energy, the electron-phonon local correlation function, and the ground state spectral weight are calculated and discussed. A crossover regime between large and small polaron for any value of the adiabatic parameter $\omega_0/t$ is found and a polaron phase diagram is proposed., Comment: 12 pages, 2 figures

Ground and temperature quantum Gibbs states are constructed for a ferroelectric anharmonic quantum oscillator model with small masses. It is shown that they possess mixing properties. The construction relies on the Feynman–Kac–Nelson representation of the conditional reduced density matrices and on the cluster expansions for the corresponding Gibbs field of trajectories.

The statistical theory of X-ray diffraction and a mosaic crystal model are used to calculate the reflection and transmission factors for a row of pyrolytic graphite plates (echelon-monochromator). Experimental angular dependencies of reflection and transmission factors are compared with theoretical results. The data of reflection and transmission factors for both CuK α - and CuK β -lines depending on thickness of plates are given. The thickness of graphite plates for which the efficiency of the echelon-monochromator is optimal is determined.

The one-dimensional molecular-crystal model of polaron motion, described in the preceding paper, is here analyzed for the case in which the electronic-overlap term of the total Hamiltonian is a small perturbation. In zeroth order—i.e., in the absence of this term—the electron is localized at a given site, p. The vibrational state of the system is specified by a set of quantum-numbers, Nk, giving the degree of excitation of each vibration-mode; the latter differ from the conventional modes in that in each of them, the equilibrium displacement, about which the system oscillates, depends upon the location of the electron. The presence of a nonvanishing electronic-overlap term gives rise to transitions in which the electron jumps to a neighboring site (p→p±1), and in which either all of the Nk remain unaltered (“diagonal” transitions) or in which some of them change by ±1 (“nondiagonal” transitions). The two types of transitions play fundamentally different roles. At sufficiently low temperatures, the diagonal transitions are dominant. They give rise to the formation of Bloch-type bands whose widths (see Eq. 37) are each given by the product of the electronic-overlap integral, and a vibrational overlap-integral, the latter being an exponentially falling function of the Nk (and, hence, of temperature). In this low-temperature domain, the role of the non- diagonal transitions is essentially one of scattering. In the absence of other scattering mechanisms, such as impurity scattering, they determine the lifetimes of the polaron-band states and, hence, the mean free path for typical transport quantities, such as electron diffusivity. With rising temperature, the probability of the off-diagonal transitions goes up exponentially. This feature, together with the above-mentioned drop in bandwidth, results, e.g., in an exponentially diminishing diffusivity. Eventually, a temperature, Tt∼ 1 2 the Debye Θ, is reached at which the energy uncertainty, ℏ/τ, associated with the finite lifetime of the states, is equal to the bandwidth. At this point, the Bloch states lose their individual characteristics (in particular, those which depend upon electronic wave number); the bands may then be considered as “washed out.” For temperatures >Tt, electron motion is predominantly a diffusion process. The elementary steps of this process consist of the random-jumps between neighboring sites associated with the nondiagonal transitions. In conformance with this picture, the electron diffusivity is, apart from a numerical factor, the product of the square of the lattice distance and the total non-diagonal transition probability, and is therefore an exponentially rising function of temperature. The limit, Jmax, of the magnitude of the electronic overlap term, beyond which the perturbation treatment of the present paper becomes inapplicable, is investigated. For representative values of the parameters entering into the theory, Jmax∼0.12 ev and 0.035 ev for the extreme cases of (a) width of the ground-state polaron-band and (b) high-temperature site-jump probabilities (these numbers correspond to electronic bandwidths of 0.24 ev and 0.07 ev, respectively). For electronic bandwidths in excess of these limits, a treatment based on the adiabatic approach is required; preliminary results of such a treatment are given for the above two cases.

The ground-state binding energies of deep impurities (Cu, Ag, Au, Zn, Cd, Hg, Ni, Fe, S, Se, Te) in Ge 1− x Si x (0≤ x ≤0.35) have been experimentally determined on the basis of Hall measurements. It is shown that the average activation energies (Δ E ) of different charge states of the impurities in Ge 1− x Si x increase approximately linearly with silicon concentration in agreement with the concept of virtual crystal model for alloys. Random-alloy splitting of the deep impurity levels due to different local surroundings of the defect core in the crystals is discussed. Obtained results allow binding energies and possible charge states of the investigated deep impurities in all Ge 1− x Si x system to be determined.

Experimental results are presented of the oscillatory convection of mercury melts coupled with crucible rotation under an imposed cusp shaped magnetic field in a Czochralski crystal growing configuration. It is shown that irregular thermal waves induced by the crucible rotation can be transformed into regular waves by the action of cusp magnetic field. Consequently, temperature fluctuations underneath a fixed nonrotating disk as a crystal model are significantly suppressed. The suppression effect due to the cusp magnetic field is more efficient for lower depth-to-radius aspect ratios of melts in which the more regular wave occurs.

Structural antiferrodistortive phase transitions have been studied in mixed disordered perovskites Rb 1− x K x CaF 3 crystals over a wide concentration range (0 x < 1) by Raman spectroscopy and a full group theory analysis has been carried out. Raman spectra have been indexed in all phases and a “one mode” behavior is evidenced. The influence of the cationic substitution on the mechanism driving the transitions is characterized by: i) the disappearance of the strong first-order character of the low temperature transition in RbCaF 3 ; ii) the continuous evolution of the Raman spectra as a function of temperature, with no sharp indication of a transition except for the classical soft mode behavior; iii) the persistence of hard Raman modes even in the ideal cubic phase; iiii) the appearance of a broad central component associated with relaxation processes. Finally, the results of lattice dynamics calculations, when compared to inelastic neutron scattering measurements, show that the classical virtual crystal model fails. These results are examined in terms of a simple displacive transition for these fluoro-perovskites in which the interactions between F 6 octahedra are anisotropic and the importance of the substitutional disorder is highlighted.

A mechanism of the phase transition between two modulated structures with different wave vectors was proposed and investigated numerically. The phase transition occurs through the mechanism of nucleation and growth of the new phase. The role of the nucleus is played by an unstable domain wall and the domain of a new low energy phase grows due to the motion of autowaves.

The behavior of rare earth dopants in GaN was investigated by means of theoretical techniques. The Density Functional based Tight-Binding method (DFTB) has been extended to include orbital dependent potentials (LDA+U and SIC-like) in attempt to model. the 4f states of lanthanide impurities within a realistic crystal model. We present results of an investigation into the structural and and energetic Properties of rare earth (Eu, Er and Tm) point defects in GaN. Lanthanide ions (either isolated or complexed with GaN native defects) prefer the Ga-site. Among the investigated defects the REGa V-N pairs are the most promising candidates as luminescent centers, while, interstitial lauthanides are found not to be compatible with the observed luminescence. Differences in the behavior of the single lanthanide ions are explained in term of different 4f-shell occupation and ion size.

A transmission electron microscopy study reveals that the so-called twelvefold quasicrystal Ta 62 Te 38 is a crystal subjected to structure modulation. It is composed of two incommensurate layers rotated by 30° to each other about their normal. High-resolution electron microscope images show the formation of commensurate domains and their discommensuration. The observed electron diffraction patterns may be explained by a kinematical calculation for the commensurate cell, designated as a 7 × 7 cell. The modulation is considered to be due to the rearrangement of atomic vacancies in response to the occurrence of charge-density waves.

An improved solution for soliton excitations of a one-dimensional molecular-crystal model with the dispersion term is found. Under the approximation of neglecting the dispersion term, the improved solution tends to the usual polaron solution. We calculate the lattice, displacement of the self-trapped state, the self-trapped well of the electron, the density of current carried by soliton excitations and the width, the peak the effective mass and the binding energy of the soliton excitation in the model. The differences between the soliton excitation in the model and the usual polaron are pointed out.