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Migration mechanisms of interphase boundaries (IPBs) are essential for understanding solid phase transformations. Most studies of the migration mechanisms of IPBs are focused on transformations under rational or near-rational orientation relationships. However, for cases of irrational orientation relationships that widely exist in massive transformations and grain boundary (GB) precipitations, knowledge remains extremely lacking. In this study, taking a triangular-square massive transformation as an example, we explored the migration mechanisms of IPBs with irrational orientation relationships at atomic scales by using the phase-field crystal method. Crystallography analysis based on near-coincidence site calculations also were conducted to verify simulated IPBs structures. Both massive transformations and precipitation transformations were reproduced using the phase-field crystal model. The simulation results show that, similar to the case of rational orientation relationships, the IPBs with irrational orientation relationships migrate by a ledge mechanism due to the satisfying of the edge-to-edge matching relationship. Further simulations on the interactions between IPBs and GBs indicate that GBs can make the newly generated massive phase change its orientation during the process of massive phase transfer across some low-angle GBs.

We have extended the multiconfigurational Ehrenfest (MCE) approach to investigate the dynamics of a one-dimensional Holstein molecular crystal model. It has been shown that the extended MCE approach yields results in perfect agreement with benchmark calculations by the hierarchy equations of motion method. The accuracies of the MCE approach in describing the dynamical properties of the Holstein polaron over a wide range of exciton transfer integrals and exciton-phonon couplings are carefully examined by a detailed comparison with the fully variational multiple Davydov D2 ansatz. It is found that while the MCE approach and the multi-D2 ansatz produce almost exactly the same results for a small transfer integral, the results obtained by the multi-D2 ansatz start to deviate from those by the MCE approach at longer times for a large transfer integral. A large number of coherent state basis functions are required to characterize the delocalized features of the phonon wavefunction in the case of large transfer integral, which becomes computationally too demanding for the multi-D2 ansatz. The MCE approach, on the other hand, uses hundreds to thousands of trajectory guided basis functions and converges very well, thus providing an effective tool for accurate and efficient simulations of polaron dynamics.

Coarsening is a common physical process that occurs in polydisperse two-phase mixture systems, which had been widely studied for decades. However, accurate prediction of the volume fraction dependence of the diffusion-controlled coarsening kinetic process is still very difficult. In this work, by using the atomic-scale phase-field crystal model, we investigated the coarsening kinetics of crystalline nanoparticles in the semi-solid region. The results showed that the details of the atomic-scale nature of particles do not affect the kinetics of coarsening for low solid volume fractions and the coarsening process of the nanoparticles is in agreement with the classical coarsening theory. While, for high solid volume fractions, our simulation results show that the coarsening rates of crystalline particles decrease with the solid volume fraction, which runs counter to the theoretical models based on mean-field theories. By checking the competitive growth process of all the particles, we found the appearance of grain rotation and volume diffusion mechanisms leads to the failure of the classical coarsening models.

Branching is a fundamental mechanism for lamellar spacing adjustment during eutectic solidification. However, the kinetic mechanism of branching is still unclear due to the lack of in-situ observations. In this work, utilizing the binary phase-field crystal model, we investigated the lamellar branching process during eutectic directional growth on an atomic scale. By visualizing the new lamella creation process, we found that new α lamellae form from heterogeneous nucleation at the front of the β/liquid interface. After further simulating eutectic solidification with different temperatures and lattice-mismatches, we found that the conditions that promote the heterogeneous nucleation could also stimulate lamellar branching. Conversely, if we suppress the heterogeneous nucleation process, lamellar branching will be hard to emerge, and the eutectic morphology will be a 2λ oscillating pattern.

A self-contained theoretical analysis of the bandgap opening and merging behavior for the designed phononic crystal model which is composed of three-component coated ball and four short connecting plates is reported in this study by finite element numerical simulations. The results show that there are multiple bandgaps of the designed model in the middle and low frequency range simultaneously. The structure symmetry is reduced to open a new bandgap via the separation of resonance modes, and an ultra-wide bandgap obtained. Especially, the equivalent spring mass model is constructed and the corresponding calculation formula of torsional resonance frequency is presented. In addition, the influence of the structural parameters on the band structure is investigated.

This work deals with the quantification and application of the modified two-mode phase-field crystal model (M2PFC; Asadi and Asle Zaeem, 2015) for face-centered cubic (FCC) metals at their melting point. The connection of M2PFC model to the classical density functional theory is explained in this article. M2PFC model in its dimensionless form contains three parameters (two independent and one dependent) which are determined using an iterative procedure based on the molecular dynamics and experimental data. The quantification process and computer simulations are performed for Ni and Al as two case studies. The quantitative M2PFC models are used in series of numerical simulations to determine the two-phase FCC-liquid coexisting and the bulk properties at the melting points of Ni and Al. The calculated and predicted properties are the expansion in melting, elastic constants, solid-liquid interface free energy, and surface anisotropy, which are also compared with their available experimental or computational counterparts in the literature.

The structure of an M-type lead hexaferrite (magnetoplumbite) crystal is studied via the diffraction of synchrotron radiation. The crystal model contains two iron ions positions with dynamic disorder. The dynamics of the crystal lattice in the temperature range of 80 to 775 K is studied by Raman scattering. Particular attention is given to the discussing the nature of the local disorder of iron ions in the trigonal bipyramidal environment of oxygen ions.

Directing individual motions of many constituents to coherent dynamical state is a fundamental challenge in multiple fields. Here, based on the spherical crystal model, we show that topological defects in particle arrays can be a crucial element in regulating collective dynamics. Specifically, we highlight the defect-driven synchronized breathing modes around disclinations and collective oscillations with strong connection to disruption of crystalline order. This work opens the promising possibility of an organizational principle based on topological defects, and may inspire new strategies for harnessing intriguing collective dynamics in extensive nonequilibrium systems., 5 pages, 4 figures

The phase-field crystal (PFC) equation is derived by the gradient flow for the Swift–Hohenberg free energy functional; thus, the numerical method requires the energy of the functional to decrease. Convex Splitting Runge–Kutta (CSRK) methods can be suitably applied to achieve high-order temporal accuracy as well as unconditional energy stability and unique solvability. For the PFC equation, we prove the unconditional energy stability and unique solvability of the CSRK methods and provide one family of parameters of the second-order CSRK methods and possible examples of third-order CSRK methods. We present numerical experiments to demonstrate the accuracy and energy stability of the methods. Specifically, based on the high-order accuracy and energy stability of the CSRK method, we propose an indicator function capable of characterizing the pattern formation of the phase-field crystal model for long-time simulation.

Wax precipitation is a major flow assurance issue for petroleum production, oil blending, downstream processing, and oil products usage. While numerous thermodynamic models have been proposed to calculate wax appearance temperature (WAT) and precipitation profile at temperatures below WAT, the existing models are correlative in nature and fail to comply with phase behavior experimentally observed for wax precipitation. This work presents a predictive thermodynamic model for wax precipitation based on an explicit co-crystal formation assumption for precipitated wax, a treatment consistent with experimental findings. With a simple Flory-Huggins expression accounting for the liquid phase nonideality and the treatment of lamella structure for wax precipitation below WAT, the model satisfactorily predicts WAT at low pressures for multicomponent paraffin mixtures and wax precipitation amounts and contents as the temperature drops below WAT.

In this paper, we consider numerical approximations for solving a modified phase-field crystal model with a strong nonlinear vacancy potential. We develop an efficient time marching numerical scheme which combines the newly developed SAV approach with the traditional stabilization technique, where a new auxiliary variable is introduced to reformulate the model and a crucial linear stabilization term is added to stabilize the scheme and keep the required accuracy while using large time steps. We prove the unconditional energy stability of the developed scheme rigorously and perform numerous benchmark numerical examples in 2D and 3D. Through the comparisons with the non-stabilized SAV scheme, the stability and accuracy of the proposed scheme are demonstrated numerically.

Using a reduced isotropic crystal model the relationship between the fourth-order elastic moduli of an isotropic medium and the independent components of the fourth-order elastic moduli tensor of real crystals of various crystal systems is found. To calculate the coefficients of these relations, computer algebra systems Redberry and Mathematica for working with high order tensors in the symbolic and explicit form were used, in light of the overly complex computation. In an isotropic medium, there are four independent fourth order elastic moduli. This is due to the presence of four invariants for an eighth-rank tensor in the three-dimensional space, that has symmetries over the pairs of indices. As an example, the moduli of elasticity of an isotropic medium corresponding to certain crystals of cubic system are given (LiF, NaCl, MgO, CaF2). From the obtained results it can be seen that the reduced isotropic crystal model can be most effectively applied to high-symmetry crystal systems.

Treated traditionally by the Ehrenfest approximation, dynamics of a one-dimensional molecular crystal model with off-diagonal exciton-phonon coupling is investigated in this work using the Dirac-Frenkel time-dependent variational principle with the multi-D$_2$ {\it Ansatz}. It is shown that the Ehrenfest method is equivalent to our variational method with the single D$_2$ {\it Ansatz}, and with the multi-D$_2$ {\it Ansatz}, the accuracy of our simulated dynamics is significantly enhanced in comparison with the semi-classical Ehrenfest dynamics. The multi-D$_2$ {\it Ansatz} is able to capture numerically accurate exciton momentum probability and help clarify the relation between the exciton momentum redistribution and the exciton energy relaxation. The results demonstrate that the exciton momentum distributions in the steady state are determined by a combination of the transfer integral and the off-diagonal coupling strength, independent of the excitonic initial conditions. We also probe the effect of the transfer integral and the off-diagonal coupling on exciton transport in both real and reciprocal space representations. Finally, the variational method with importance sampling is employed to investigate temperature effects on exciton transport using the multi-$\rm D_2$ {\it Ansatz}, and it is demonstrated that the variational approach is valid in both low and high temperature regimes.

In this paper we present the application of an anisotropic phase-field crystal model to the process of the heteroepitaxial growth in anisotropic systems. During the growth of the thin films with sheared non-cubic lattice the elastic strain gives rise to dislocations and grain boundaries due to the difference between the film and the substrate lattice in terms of lattice constant (misfit) and lattice shearing (anisotropy difference). The numerical simulations for various misfits and anisotropy difference demonstrate that the anisotropic evolution equation for the phase-field variables allows to simulate the growth of the layers in anisotropic systems. We investigate this phenomenon and derive the relationships for the phenomenological dependencies such as the dependence of the characteristic layer thickness and the number of defects on the misfit for various anisotropy difference based on our recently developed anisotropic phase-field crystal model [28] .

Finding the possible stopping sites for muons inside a crystalline sample is a key problem of muon spectroscopy. In a previous study, we suggested a computational approach to this problem when dealing with muonium, the pseudoatom formed by a positive muon that has captured an electron, using density functional theory software in combination with a random structure searching approach that relies on a Poisson sphere distribution. In this work, we test this methodology further by applying it to muonium in three organic molecular crystal model systems: durene, bithiophene, and tetracyanoquinodimethane. Using the same sets of random structures, we compare the performance of density functional theory software CASTEP and the much faster lower level approximation of Density Functional Tight Binding provided by DFTB+ combined with the use of the 3ob-3-1 parameter set. We show the benefits and limitations of such an approach, and we propose the use of DFTB+ as a viable alternative to more cumbersome simulations for routine site-finding in organic materials. Finally, we introduce the Muon Spectroscopy Computational Project software suite, a library of Python tools meant to make these methods standardized and easy to use.

A lot of the physical and the numerical modeling of Czochralski crystal growth is done on the generic Rayleigh-B´enard system. To better approximate the conditions in a Czochralski puller, the influences of a rounded crucible bottom, deviations of the thermal boundary conditions from the generic case, crucible and/or crystal rotation, and the influence of magnetic fields are often studied separately. The present contribution reviews some of these topics while concentrating on studies of the flow and related temperature fluctuations in systems where a rotating magnetic field (RMF) was applied. The three-dimensional convective patterns and the resulting temperature fluctuations will be discussed both for the mere buoyant case and for the application of an RMF. It is shown that a system between a Rayleigh-Benard and a more realistic configuration, which is still cylindrical but whose surface is partially covered by a crystal model, behaves much the same as a Rayleigh-Benard system. An RMF can be used to damp the temperature fluctuations. Secondly, a more Czochralski-like system is examined. It turns out that the RMF does not provide the desired damping of the temperature fluctutions in the parameter range considered.

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.

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.

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.

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 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.

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.

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.

As part of a series of studies on energy transfer processes between optical centers in condensed matter, an analysis is made of the problem of a crystalline system made up by a majority of regular optical centers and small amounts of defective optical centers. Within the conceptual framework of the crystal model, analytic equations are derived that allow a direct connection between the microscopic study of the interaction and kinetic type equations to describe the relaxation dynamics from excited states. As an example, Ln3+ ions in elpasolite type lattices are used, showing the biexponential character of the decay curves. These results can be used in the study of relaxation from excited states in crystals with heterogeneities due to crystallographic defects, trace impurities, or slightly distorted optical centers.

The study of energy transfer processes between optical centers in crystalline cubic materials is reexamined within the conceptual framework of the crystal model. The initial assumption of modest transfer rates is relaxed, thereby correcting the master equation of the crystal model and making it possible to explain the nonexponential behavior of the radiation decay curves from excited states. This study shows that such experimental trends are the result of a purely statistical effect related to the fluctuation in the population of optically active ions in a crystal lattice. The corrected crystal model does not need to invoke migration of excitation processes to explain the fast exponential decay observed in crystals with a high concentration of optical centers.

A simple one-dimensional crystal model was proposed in order to study the incommensurate phase formation and its properties were numerically analyzed. In this model each particle (molecule) of the crystal has two degrees of freedom so that a longitudinal sound wave propagation is possible. In the case of small displacements and incompressible molecules the model has the Hamiltonian identical to that for a linear chain with a local fourth order anharmonic potential and the harmonic nearest- and next-nearest-neighbor interactions. Particular emphasis has been placed on the analysis of the incommensurate phases caused by the soft modes with short wavelength which has not been studied in most of the previous investigations.

A general study of energy transfer processes in organized condensed matter is presented. Considering the nature of these media, i.e., the periodic properties of the lattice, a theoretical microscopic model is worked out for the general case. It takes full advantage of the translational periodicities in the crystalline phase, using the real discrete distribution of ions in the lattice. A general master equation is obtained and, for the sake of completeness, a particular case is analyzed for the dipole–dipole nonradiative mechanism for energy transfer processes in the elpasolite lattices where the Ln3+ impurities are in cubic sites.

A gradient-enhanced crystal plasticity model is presented that explicitly accounts for the evolution of the densities of geometrically necessary dislocations (GNDs) on individual slip systems of deforming crystals. The GND densities are fully coupled with the crystal slip rule. Application of the model to two distinct and technologically important crystal types, namely hcp Ti and ccp Ni, is given. For the hcp crystals, slip is permitted with a -type slip directions on basal, prismatic and pyramidal planes and c + a -type slip directions on pyramidal planes. First, a single crystal under four-point bending is simulated as the uniform strain gradient expected in the central span provides a good validation of the code. Then, uniaxial deformation of a model near- α Ti polycrystal has been analysed. The resulting distributions of GND densities that develop on the various slip system types have been compared with independent experimental observations. The model predicts that GND density on the c + a systems is approximately an order of magnitude lower than that for a -type systems in agreement with experiment. For the ccp case, slip is considered to take place on the {111} slip systems. Thermal loading of a single-crystal nickel alloy sample containing carbide particles of size approximately 30 μm has been analysed. Detailed comparisons are presented between model predictions and results of high-resolution electron backscatter diffraction (EBSD) measurements of the micro-deformations, lattice rotations, curvatures and GND densities local to the nickel–carbide interface. Qualitatively, good agreement is achieved between the coupled and decoupled model elastic strains with the EBSD measurements, but lattice rotations and GND densities are quantitatively well predicted by the coupled crystal model but are less well captured by the decoupled model. The GND coupling is found to lead to reduced lattice rotations and plastic strains in the region of highest heterogeneity close to the Ni matrix/particle interface, which is in agreement with the experimental measurements. The results presented provide objective evidence of the effectiveness of gradient-enhanced crystal plasticity finite element analysis and demonstrate that GND coupling is required in order to capture strains and lattice rotations in regions of high heterogeneity.

Significant advances in fragment-based electronic structure methods have created a real alternative to force-field and density functional techniques in condensed-phase problems such as molecular crystals. This perspective article highlights some of the important challenges in modeling molecular crystals and discusses techniques for addressing them. First, we survey recent developments in fragment-based methods for molecular crystals. Second, we use examples from our own recent research on a fragment-based QM/MM method, the hybrid many-body interaction (HMBI) model, to analyze the physical requirements for a practical and effective molecular crystal model chemistry. We demonstrate that it is possible to predict molecular crystal lattice energies to within a couple kJ mol(-1) and lattice parameters to within a few percent in small-molecule crystals. Fragment methods provide a systematically improvable approach to making predictions in the condensed phase, which is critical to making robust predictions regarding the subtle energy differences found in molecular crystals.

We apply the Unsymmetrized Self-Consistent-Field-Method (USCFM) to a linear infinite chain of identical atoms with a quartic pair interaction potential. We show that an exact solution of the USCFM can be found in terms of a single auxiliary function ℒ1 which is studied here in details. We use it to calculate the partition function, the energy and the free energy, the moments of the position, the corrections due to quantum effects and higher terms of the potential, the specific heat and the thermal expansion. An anharmonic approximative approach, based on the self-consistent potential of the used method, is developed also. We apply these two approaches to the study of the thermoelastic properties of a one dimensional system (krypton). It is demonstrated that the approximate approach is very effective when dealing with pairwise potentials of positive second derivative. The Lennard-Jones potential is used in our calculations.

We study a two-level system coupled to the set of harmonic oscillators by application of a simple variational approach whose equations can in principle be solved in the whole range of system parameters. The conditions for localization are studied for the molecular crystal model and the acoustic deformation potential model.

Bulk-immiscible binary systems often form stress-induced miscible alloy phases when deposited on a substrate. Both alloying and surface dislocation formation lead to the decrease of the elastic strain energy, and the competition between these two strain-relaxation mechanisms gives rise to the emergence of pseudomorphic compositional nanoscale domains, often coexisting with a partially coherent single phase. In this work, we develop a phase-field crystal model for compositional patterning in monolayer aggregates of binary metallic systems. We first demonstrate that the model naturally incorporates the competition between alloying and misfit dislocations, and quantify the effects of misfit and line tension on equilibrium domain size. Then, we quantitatively relate the parameters of the phase-field crystal model to a specific system, CoAg/Ru(0001), and demonstrate that the simulations capture experimentally observed morphologies.

Vibronic spectra of the Holstein model for molecular crystals are investigated using the dynamical mean field theory with the additional aid of the multi-mode Brownian oscillator model. The effects of temperature, intermolecular transfer integral, damping constant and quadratic coupling on the vibronic spectra are examined, and spectra in the presence of two phonon modes are studied in detail. Results from the dynamical mean field theory are corroborated by those from the multi-mode Brownian oscillator model. Strength and weakness of the two approaches are discussed to point out the corresponding regimes of application for each. Published version

Stationary and spatially periodic localized modes are found in 1-D for an anharmonic molecular crystal model within the rotating wave approximation. One class of odd modes solves the recurrence relations for the shape function asymptotically exactly in the limit of large anharmonicity. Other classes of odd and even modes which solve the recurrence relations exactly are also found.

An algorithm is proposed for the finite element implementation of a rate-dependent crystal plasticity model. A ‘planar double slip’ two-dimensional crystal model is used. The constitutive equations are derived in detail, and it is shown that they reduce to a set of three ordinary differential equations: two for the resolved shear stresses on the slip planes, and one for the angle that defines the slip systems’ orientation. The proposed algorithm, which is suitable for implementation in an explicit finite element code such as PRONTO2D, is based on a weighted residual method for the approximate solution of these equations. It turns out that the performance of the algorithm does not restrict the selection of the global time increment. The efficiency and performance of the algorithm is demonstrated through a comparison with the so-called rate-tangent method. Also, numerical examples are given to demonstrate the model's capability to capture shear localization phenomena at high strain rates, using the PRONTO2D explicit finite element code.

A new concise approach is presented for analytic study of the properties of the Holstein model. New analytic results for the polaronic band structure and phonon distribution, of the Holstein molecular crystal model, are given in one dimension. And all analytic results given are in accordance with the known numerical research results.

A two-dimensional finite cluster model is proposed to describe the coupling of low energy charge transfer and Frenkel states of an anthracene-like molecular crystal. The results confirm most of the qualitative conclusions of the extensively used linear crystal model, but suggest the necessity to review some of its quantitative results. Potential usefulness of the cluster model for the description of doped crystals is pointed out.

The band structure of low energy CT excitons in tetracene is calculated within the linear crystal model. The results show that, due to the inequivalence of two sublattices, the eigenstates are generally non-degenerate and have a substantial permanent dipole moment. This suggests that the mechanism of electro-absorption may be different in centrosymmetric and non-centrosymmetric polyacene crystals.

Orbifold generalizations of the ordinary and modified melting crystal models are introduced. They are labelled by a pair $a,b$ of positive integers, and geometrically related to $\mathbf{Z}_a\times\mathbf{Z}_b$ orbifolds of local $\mathbf{CP}^1$ geometry of the $\mathcal{O}(0)\oplus\mathcal{O}(-2)$ and $\mathcal{O}(-1)\oplus\mathcal{O}(-1)$ types. The partition functions have a fermionic expression in terms of charged free fermions. With the aid of shift symmetries in a fermionic realization of the quantum torus algebra, one can convert these partition functions to tau functions of the 2D Toda hierarchy. The powers $L^a,\bar{L}^{-b}$ of the associated Lax operators turn out to take a special factorized form that defines a reduction of the 2D Toda hierarchy. The reduced integrable hierarchy for the orbifold version of the ordinary melting crystal model is the bi-graded Toda hierarchy of bi-degree $(a,b)$. That of the orbifold version of the modified melting crystal model is the rational reduction of bi-degree $(a,b)$. This result seems to be in accord with recent work of Brini et al. on a mirror description of the genus-zero Gromov-Witten theory on a $\mathbf{Z}_a\times\mathbf{Z}_b$ orbifold of the resolved conifold., Comment: 41 pages, no figure; (v2) minor change, typos corrected, accepted for publication

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and used to analyse colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth., Comment: 4 pages, 10 figures

The strict virtual crystal model has been shown to describe accurately the mixing enthalpy of III-V ternary alloys. We allocate the different components of this model to both subreactions, i.e., the reactions forming III-V-I and III-V-II, present in the molecular-beam epitaxial growth of III-(VVII)-V-I compound alloys, and derive thereof a model that describes accurately the composition obtained. A good correspondence with experimental growth data is obtained. We apply this model to both relaxed and strained layer growth and the evolution in the composition is given when a relaxed layer is grown on a substrate with a different lattice constant. (C) 2000 American Institute of Physics. [S0021- 8979(00)01901-0]. ispartof: Journal of Applied Physics vol:87 issue:1 pages:564-571 status: published

In the present analysis, the interaction system of an fee d-band metal is considered to be composed of two-body and three-body parts. We use a new three-body potential developed by Akgiin and Ugur to deduce the contribution of many-body forces to the dynamical matrix of the fee structure. Two- and three-body potentials are first used, as an application to investigate the dynamical behaviors of fee rf-band metals, Ni, Pd, Cu and Ag. The parameters defining the two- and three-body potentials for the metals are evaluated from knowledge of the equilibrium pair energies, bulk modulus and total cohesive energies of the metals, following a procedure given by Akgün and Ugur. In this scheme the input data is independent of phonon frequencies and elastic constants of the metals. Finally, the phonon frequencies of the metals along the principal symmetry directions are computed using the calculated radial, tangential and three-body force constants. The theoretical results are compared to experimental phonon dispersions. The agreement shows that the proposed potentials and crystal model provide a reasonable description of the lattice dynamics of fee d-band metals.

We modify the anisotropic phase-field crystal model (APFC), and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model. The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite-difference scheme, thereby, allowing us to work on a large system and for a long time. The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed. In particular, we investigate the morphological evolution in heteroepitaxial growth of our model. A new formation mechanism of misfit dislocations caused by vacancy trapping is found. The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions, and it could significantly change the growth orientation of epitaxial layers.

The ability of the classical nucleation theory (CNT) and atomistic nucleation theory (ANT) to predict the stationary nucleation rate J of single-component crystals and crystalline monolayers is verified with the aid of numerical and computer simulation data obtained in the scope of the Kossel crystal model. It is found that in both cases CNT significantly overestimates J because it does not account for the work needed to attach an atom to the periphery of the two-dimensional nucleus or to form such a nucleus on the surface of the three-dimensional one. In contrast, ANT is successful in providing a good quantitative description of J, especially for high enough effective binding energy between nearest-neighbor atoms in the crystal and in capturing the existence of extended, nearly linear portions in the dependence of ln J on the supersaturation s when the values of both s and the binding energy are sufficiently great. However, the ANT prediction about broken linear ln J versus s dependence is not confirmed by the numerical and simulation results presented. General formulas for the nucleation work, the nucleus size, and the nucleation rate are proposed which are applicable to nucleation of single-component crystals and crystalline monolayers in vapors, solutions, or melts and which correct the respective CNT formulas. The proposed J(s) formula provides a good description of the numerical and simulation data and can justifiably be used up to the supersaturation at which the nucleus becomes monomer. When experimental data for the J(s) dependence are available and the nucleus specific edge and surface energies are unknown parameters, the proposed J(s) formula can be employed for estimation of these energies even if the nucleus is constituted of a few atoms only.

The author is concerned with the polaronic states of a tightly bound particle interacting with the elastic displacements of a linear host crystal. A new variational approach to Holstein's molecular-crystal model is introduced, which includes the 'adiabatic' and the 'dynamic' approximate solutions treated so far separately in the literature. It turns out that the transition from one type of solution to the other does not coincide with the transition from small to large polarons. Instead, there is a continuous transition from adiabatic to dynamic solutions in the small-polaron region while there is a discontinuous crossover in the region polarons, and six different types of polarons have to be distinguished with respect to their size and degree of adiabaticity.

The low-lying energy levels of electrons moving in a potential of the form V(x)=(1- gamma 2)/(1-2 gamma cos x+ gamma 2) have been calculated. In the limits gamma to 0 and gamma =1, well known results are recovered. The bandgaps are studied as a function of gamma .

We present the outcome of a simple variational calculation for the ground-state wavefunction of the molecular crystal model (MCM) on a lattice. We discuss the two-site MCM and the MCM in one, two and three dimensions. For all cases we find a transition to a self-trapped state. The results seem to support our recent Monte Carlo investigations. Our variational results for the two-site MCM, including the presence of the phase transition, are in exact agreement with the rigorous solution for this model.

The peierls stress of a screw dislocation in a simplified crystal model is given exactly. The stress oscillates strongly as the dislocation width increases.

This paper is a sequel to an earlier work (Holstein 1978) in which small-polaron hopping between two sites was treated from the standpoint of a heuristic Eyringtype reaction-rate approach. In the present paper, the relationship of this approach to basic quantum perturbation theory is investigated, and conditions for its validity are established. An essential physical feature has to do with the relaxation of localized vibrational excitation (the ‘activated’ configuration). The relevant time constant associated with this relaxation is determined within the framework of the molecular crystal model (of previous small-polaron studies) by a method which focuses attention on the dynamics of an appropriately denned local ‘reaction’ coordinate, and its coupling to the vibrational degrees of freedom of the host crystal ('reservoir’ system). Agreement with previous calculations based upon an explicitly multiphonon approach is obtained. In particular, the reciprocal of the effective lime-duration of a single...