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Molecular dynamics simulation is employed to study the tension and compression deformation behaviors of magnesium single crystals with different orientations. The angle between the loading axis and the basal direction ranges from 0° to 90°. The simulation results show that the initial defects usually nucleate at free surfaces, but the initial plastic deformation and the subsequent microstructural evolutions are various due to different loading directions. The tension simulations exhibit the deformation mechanisms of twinning, slip, crystallographic reorientation and basal/prismatic transformation. The twinning, crystallographic reorientation and basal/prismatic transformation can only appear in the crystal model loaded along or near the a-axis or c-axis. For the compression simulations, the basal, prismatic and pyramidal slips are responsible for the initial plasticity, and no twinning is observed. Moreover, the plastic deformation models affect the yield strengths for the samples with different orientations. The maximum yield stresses for the samples loaded along the c-axis or a-axis are much higher than those loaded in other directions.

The Peierls structural transition in quasi-one-dimensional organic crystals of TTF-TCNQ is investigated in the frame of a more complete physical model. The two most important electron-phonon interaction mechanisms are taken into account simultaneously. One is similar of that of deformation potential and the other is of polaron type. For simplicity, the 2D crystal model is considered. The renormalized phonon spectrum and the phonon polarization operator are calculated in the random phase approximation for different temperatures. The effects of interchain interaction on renormalized acoustic phonons and on the Peierls critical temperature are analyzed.

The conservative Swift&ndash, Hohenberg equation was introduced to reformulate the phase-field crystal model. A challenge in solving the conservative Swift&ndash, Hohenberg equation numerically is how to treat the nonlinear term to preserve mass conservation without compromising efficiency and accuracy. To resolve this problem, we present a linear, high-order, and mass conservative method by placing the linear and nonlinear terms in the implicit and explicit parts, respectively, and employing the implicit-explicit Runge&ndash, Kutta method. We show analytically that the method inherits the mass conservation. Numerical experiments are presented demonstrating the efficiency and accuracy of the proposed method. In particular, long time simulation for pattern formation in 2D is carried out, where the phase diagram can be observed clearly. The MATLAB code for numerical implementation of the proposed method is provided in Appendix.

The current study is based on employing the torsional test parameters to observe the texture evolution of Al–Mg alloy with the face-centered cubic structure. We considered the Mg content in the alloy, which is an alloying composition, as our prime test parameter and examined how its variations are related to the test variables, such as temperature and strain rate. To confirm the torsion texture evolution of Al–Mg alloy, it was tested using the electron backscattered diffraction method and represented using a pole figure and an orientation distribution function. In the Al–Mg alloy, the change of Mg content causes a transformation of the physical properties, such as the stacking fault energy. Therefore, the difference in the shear texture evolution is observed to be remarkable. Further, the test results were compared to examine the validity of the rate sensitive crystal model. As the Mg content and strain rate increase, a specific face-centered cubic texture has been pronounced. Furthermore, as the temperature rises, the intensity of A fiber weakens, and the overall orientation distribution becomes random. From the results, this shear texture is discovered to be well suited for the rate sensitive crystal model, which demonstrates that the orientation persistence increases with increasing Mg content, higher strain rate, and lower temperatures.

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.

We propose a new chirality-imbalance phenomenon arising in baryonic/high dense matters under a magnetic field. A locally chiral-imbalanced (parity-odd) domain can be created due to the electromagnetically induced $U(1)_A$ anomaly in high-dense matters. The proposed local-chiral imbalance generically possesses a close relationship to a spacial distribution of an inhomogeneous chiral (pion)-vector current coupled to the magnetic field. To demonstrate such a nontrivial correlation, we take the skyrmion crystal approach to model baryonic/high dense matters. Remarkably enough, we find the chirality-imbalance distribution takes a wave form in a high density region (dobbed ``chiral-imbalance density wave''), when the inhomogeneous chiral condensate develops to form a chiral density wave. This implies the emergence of a nontrivial density wave for the explicitly broken $U(1)_A$ current simultaneously with the chiral density wave for the spontaneously broken chiral-flavor current. We further find that the topological phase transition in the skyrmion crystal model (between skyrmion and half-skyrmion phases) undergoes the deformation of the chiral-imbalance density wave in shape and periodicity. The emergence of this chiral-imbalance density wave could give a crucial contribution to studies on the chiral phase transition, as well as the nuclear matter structure, in compact stars under a magnetic field., 11 pages, 16 figures

The orientation relationships and interfaces between α′-Al13Cr4Si4 and the matrix in Al-Si-Cr-Mg alloy are characterized by HAADF-STEM electron microscopy. Multiple orientation relationships are found between α′-Al13Cr4Si4 and Al matrix in Al-Si-Cr-Mg and four of them are rarely common. By unraveling the atomic structure of dispersoids, the crystal model of α′-Al13Cr4Si4 is approved by the atomic-resolution for the first time. The interface we investigated proves that orientation relationships always rely on specific planes of Al matrix.

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.

Phase-field crystal model with one mode is introduced to describe morphological transition. The relationship between growth morphology and smooth density distribution was investigated. The results indicate that the pattern selection of dendrite growth is caused by the competition between interface energy anisotropy and interface kinetic anisotropy based on the 2D phase diagram. When the calculation time increases, the crystal grows to secondary dendrite at the dimensionless undercooling equal to − 0.4. Moreover, when noise is introduced in the growth progress, the symmetry is broken in the growth mode, and there becomes irregular fractal-like growth morphology. Furthermore, the single crystal shape develops into polycrystalline when the noise amplitude is large enough. When the dimensionless undercooling is less than − 0.3, the noise has a significant effect on the growth shape. In addition, the growth velocity of crystal near to liquid phase line is slow, while the shape far away from the liquid adapts to fast growth. Based on the simulation results, the method was proved to be effective, and it can easily obtain different crystal shapes by choosing the different points in 2D phase diagram.

We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element method calculations. This approach allows for the description of microscopic features, such as dislocations, while simultaneously being able to describe length scales that are orders of magnitude larger than the lattice spacing. Moreover, it allows for the direct description of extended defects by means of a scalar order parameter. The versatility of this framework is shown by considering both fcc and bcc lattice symmetries and different rotation axes. First, the specific case of planar, twist grain boundaries is illustrated. The details of the method are reported and the consistency of the results with literature is discussed. Then, the dislocation networks forming at the interface between a spherical, rotated crystal embedded in an unrotated crystalline structure, are shown. Although explicitly accounting for dislocations which lead to an anisotropic shrinkage of the rotated grain, the extension of the spherical grain boundary is found to decrease linearly over time in agreement with the classical theory of grain growth and recent atomistic investigations. It is shown that the results obtained for a system with bcc symmetry agree very well with existing results, validating the methodology. Furthermore, fully original results are shown for fcc lattice symmetry, revealing the generality of the reported observations., 11 pages, 9 figures

The conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory for self-propelled particles, Menzel and Lowen [Phys. Rev. Lett. 110, 055702 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.055702] obtained a model for crystallization (swarm formation) in active systems. Here, we study the occurrence of resting and traveling localized states, i.e., crystalline clusters, within the resulting active PFC model. Based on linear stability analyses and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of periodic and localized, resting and traveling states in a one-dimensional active PFC model. This allows us, for instance, to explore how the slanted homoclinic snaking of steady localized states found for the passive PFC model is amended by activity. A particular focus lies on the onset of motion, where we show that it occurs either through a drift-pitchfork or a drift-transcritical bifurcation. A corresponding general analytical criterion is derived.

We explore magnetic field effects on the nuclear matter based on the skrymion crystal approach for the first time. It is found that the magnetic effect plays the role of a catalyzer for the topological phase transition (topological deformation for the skyrmion crystal configuration from the skrymion phase to half-skyrmion phase). Furthermore, we observe that in the presence of the magnetic field, the inhomogeneous chiral condensate persists both in the skyrmion and half-skyrmion phases. Explicitly, as the strength of magnetic field gets larger, the inhomogeneous chiral condensate in the skyrmion phase tends to be drastically localized, while in the half-skyrmion phase the inhomogeneity configuration is hardly affected. It also turns out that a large magnetic effect in a low density region distorts the baryon shape to an elliptic form but the crystal structure is intact. However, in a high density region, the crystal structure is strongly effected by the strong magnetic field. A possible correlation between the chiral inhomogeneity and the deformation of the skrymion configuration is also addressed. The results obtained in this paper might be realized in the deep interior of compact stars., Comment: 13 pages, 31 figures, minor corrections made, some revision made, references added

The chiral soliton lattice (CSL) has been studied in condensed-matter system such as chiral magnets, which arises as a parity-violating topological soliton. In hadron physics, various attempts have also been made to apply the idea of CSL to baryonic matter. In this work, we explore the CSL effects on the baryonic matter based on the skrymion crystal approach. It is found that the CSL causes an inverse catalysis for the topology change in the dense baryonic matter. Furthermore, we observe that the CSL makes the single-baryon shape deformed to be highly oscillating as the frequency of the CSL gets larger, which leads to the enhancement of a baryon energy. Of interest is that in a high density region, the CSL goes away due to the topology change in the baryonic matter. What we find here might deepen our understanding of dense matter systems as well as compact stars., Comment: 12 pages, 29 figures

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.

Dynamics of a one-dimensional Holstein molecular crystal model is investigated by making use of the hierarchical equations of motion (HEOM) introduced by Tanimura and Kubo [J. Phys. Soc. Jpn. 1989, 104, 101]. Our extended, numerically exact HEOM approach is capable of treating exciton-phonon coupling in a nonperturbative manner and is applicable to any temperature. It is revealed that strong exciton phonon coupling leads to excitonic localization, while a large exciton transfer integral facilitates exciton transport. Temperature effects on excitonic scattering have also been examined. A proof of concept, our work also serves as a benchmark for future comparisons with other numerical approaches to Holstein polaron dynamics.

The properties of a two dimensional crystalline phase invading a metastable or unstable liquid state are examined using the amplitude expansion formulation of the hyperbolic and parabolic phase-field crystal model. When the amplitudes are real and equal to each other, analytic expressions are derived for the profile of a steady state liquid–solid front traveling at constant velocity. Numerical simulations of the full amplitude formulation are conducted and compared with the analytic results. Close to the melting transition the analytic results for the liquid–solid profile, velocity and width are in quantitative agreement with the numerical results and disagree far from the transition.

Crystallization of supersaturated liquids usually starts by epitaxial growth or by heterogeneous nucleation on foreign surfaces. Herein, we review recent advances made in modeling heteroepitaxy and heterogeneous nucleation on flat/modulated surfaces and nanoparticles within the framework of a simple dynamical density functional theory, known as the phase-field crystal model. It will be shown that the contact angle and the nucleation barrier are nonmonotonous functions of the lattice mismatch between the substrate and the crystalline phase. In continuous cooling studies for substrates with lattice mismatch, we recover qualitatively the Matthews–Blakeslee mechanism of stress release via the misfit dislocations. The simulations performed for particle-induced freezing will be confronted with recent analytical results, exploring thus the validity range of the latter. It will be demonstrated that time-dependent studies are essential, as investigations based on equilibrium properties often cannot identify the preferred nucleation pathways. Modeling of these phenomena is essential for designing materials on the basis of controlled nucleation and/or nano-patterning.

A self-consistent theoretical framework is developed to model the thermo-mechanical behaviors of irradiated face-centered cubic (FCC) polycrystalline metals at low to intermediate homologous temperatures. In this model, both irradiation and temperature effects are considered at the grain level with the assist of a tensorial plasticity crystal model, and the elastic-visocoplastic self-consistent method is applied for the scale transition from individual grains to macroscopic polycrystals. The proposed theory is applied to analyze the mechanical behaviors of irradiated FCC copper. It is found that: (1) the numerical results match well with experimental data, which includes the comparison of results for single crystals under the load in different directions, and for polycrystals with the influences of irradiation and temperature. Therefore, the feasibility and accuracy of the present model are well demonstrated. (2) The main irradiation effects including irradiation hardening, post-yield softening, strain-hardening coefficient (SHC) dropping and the non-zero stress offset are all captured by the proposed model. (3) The increase of temperature results in the decrease of yield strength and SHC. The former is attributed to the weakened dislocation–defect interaction, while the latter is due to the temperature-strengthened dynamic recovery of dislocations through the thermally activated mechanism. The present model may provide a theoretical guide to predict the thermo-mechanical behaviors of irradiated FCC metals for the selection of structural materials in nuclear equipment.

A large data set of volume element models of aggregate snowflakes was created, building the snowflakes from various models of ice crystals found in the atmosphere: dendrites, needles, plates, and bullet rosettes, as well as spheroidal crystals for comparison. Several different sizes for the constituent crystals were also used. The radar backscattering cross sections of the snowflakes were computed from the models using the discrete dipole approximation (DDA) at 13.6 GHz (Ku band), 35.6 GHz (Ka band) and 94.0 GHz (W band), and the effects of the choice of crystal model and size on the Ku/Ka band and Ka/W band dual-wavelength ratios (DWR) was investigated. It was found that the aggregate DWRs were very similar for all naturally occurring ice crystal types investigated in this study. This implies that the choice of crystal type is at most of secondary importance in the forward model of scattering used for snowfall retrievals but also, conversely, that the identification of the crystal type from triple-frequency observations is likely to be difficult. In contrast, the size of the constituent ice crystals does have a nonnegligible impact on the triple-frequency signatures. Additionally, it was found that the triple-frequency signatures found in some experimental data, resembling those resulting from spheroidal model snowflakes, cannot be reproduced using the aggregates with any of the crystal types that were investigated. This suggests that besides aggregation, other mechanisms of snowflake formation from ice crystals must be considered in snowfall retrieval algorithms.

To investigate the deformation twinning and the plastic anisotropy of the hexagonal-close-packed (HCP) single crystal, the crystal plastic constitutive model including slip and twinning deformation was established with finite element method based on crystal plasticity theory. The model was verified by test data. Newton–Raphson iteration method was developed with the stress components directly as the basic variables of iteration. The plastic deformation behavior of single crystal AZ31 alloy was analyzed numerically under monotonic tension and compression, respectively, in four different strain paths (i.e. along 〈 2 1 ¯ 1 ¯ 0 〉 , 〈 01 1 ¯ 0 〉 , 〈0001〉 and 〈 01 1 ¯ 1 〉 ) with this model. The stress–strain curves were obtained in the above paths. The numerical calculation results show that this crystal model is feasible to predict the activity of slip/twinning system and to describe the number of active twin variants, the types of dominant twin variants and twin intersection. Due to the polar nature of mechanical twinning in inelastic deformation of the material, the plastic behavior of the single crystal material is demonstrated to be notably anisotropic and high asymmetry.

Binary phase field crystal (PFC) models have been successful in describing a broad selection of phenomena in binary alloy materials: eutectic and dendritic solidification, the Kirkendall effect, clustering, solid state precipitation, and many more. In this paper, authors present improvements to the binary structural PFC model and show that these improvements allow us to model new material phase diagrams. They apply their improved model to study the kinetics of precipitation from a liquid solution where they observe a two-step nucleation pathway. This agrees with recent experimental observations in which spinodal decomposition precedes nucleation in solute-rich domains. They also find a phenomenon not previously described in the literature in which precipitate growth is accelerated in the presence of uncrystallized, solute-rich liquid domains.

A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy and show that it obeys the stress strain relation of linear elasticity. Dislocations in a two dimensional hexagonal lattice are shown to be composite topological defects in the amplitude expansion of the phase field, with topological charges given by the Burgers vector. This allows us to introduce a formal relation between dislocation velocity and the evolution of the coarse grained envelopes of the phase field. Standard dissipative dynamics of the phase field crystal model is shown to determine the velocity of the dislocations. When the amplitude equation is valid, we derive the Peach-Koehler force on a dislocation, and compute the associated defect mobility. A numerical integration of the phase field crystal equations in two dimensions is used to compute the motion of a dislocation dipole, and good agreement is found with the theoretical predictions., 11 pages, 3 figures

Materials Theory 1(2), [1]-20 (2017). doi:10.1186/s41313-017-0004-2, Published by Springer International Publishers, [Cham]

The phase-field crystal, PFC, method introduced by Elder and coworkers [1–3], can be viewed as multiscale simulation algorithm that bridges the classical molecular dynamics, MD, simulations and the phase-field methods covered in the previous chapters. PFC method introduces an order parameter defined as the local-time-averaged atomic number density which is able to produce periodicity of crystal lattices. In the model, any perturbation or lattice defects result in an increase in the free energy, thus enabling to obtain the information which has been only possible by the atomistic simulations previously. In addition, PFC method produces various atomistic events in much larger spatial and temporal dimensions that are not easily accessible with current MD simulation techniques. Therefore, PFC method has emerged as an attractive simulation approach.

We introduce a phase-field crystal model that creates an array of complex three- and two-dimensional crystal structures via a numerically tractable three-point correlation function. The three-point correlation function is designed in order to energetically favor the principal interplanar angles of a target crystal structure. This is achieved via an analysis performed by examining the crystal's structure factor. This approach successfully yields energetically stable simple cubic, diamond cubic, simple hexagonal, graphene layers, and CaF$_2$ crystals. To illustrate the ability of the method to yield a particularly complex and technologically important crystal structure, we show how this three-point correlation function method can be used to generate perovskite crystals.

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.

The segregation-induced grain boundary (GB) premelting is studied by phase-field crystal model. We investigate the microstructure evolution of GBs with different misorientation angles and the variation of concentration distribution during premelting process. The liquid film thickness is calculated by an excessive mass technique. The results show that for low-angle GBs, the liquid phase first appears at individual dislocations region where the solute atoms segregate, and there exist two structural transitions during premelting process, which behave as two inflection points in the curve of w versus Δ B 0 . For high-angle GBs, the liquid film is rather uniform and its thickness diverges logarithmically when the melting point is approached. Moreover, the higher misorientation angle and segregation the GB has, the lower temperature the liquid film occurs. The concentration variation law indicates that GB segregation and GB premelting promote each other when the liquid phase appears. The critical wetting angle is almost equal to 12.5° and this value is much closer to the reality.

Experimental accessibility of crystal shape is still limited today. We present a new method for extracting three-dimensional (3D) crystal shape from measurement data. The algorithm is demonstrated on data obtained by microcomputed tomography (μCT) for potash alum, although the approach is applicable to any 3D imaging technique and any faceted crystal. First, the crystal face normals are identified using a 3D Hough transform. In a second step, the relationship between the identified and all potentially arising crystal face normals is matched to obtain the relative orientation between the measurement data and the crystal model. The final shape parameters guarantee maintainance of the symmetry of the geometric crystal model and, hence, are compatible with common approaches to model the growth of multifaceted crystals. The procedure can be automated, which opens the possibility of evaluating full particle size-and-shape distributions, within the discussed limitations concerning crystal quality and sample size.

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.

The paper considers a one-dimensional crystal model consisting of pairwise interacting particles. The critical points of potential energy for the crystal system under tension are studied on the assumption that the pair interaction potential has a single minimum. It is shown that new critical points of potential energy appear in a bifurcational manner.

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.

Models of plastic-bonded explosives were created with the aim of studying the mechanical properties and sensitivity because the latter is one of the most important problems in relation to energetic materials. Previous models proposed in the literature used short plastic chains, which are appropriate for interaction modeling. In the present work, a model with a single, long chain was built, which is more appropriate for modeling mechanical properties. The representative hydroxyl-terminated polybutadiene (HTPB)/dioctyladipate (DOA)/cyclotrimethylenetrinitramine (RDX) system was used (81.4 w/w% of RDX and 18.6 w/w% of the amorphous HTPB/DOA phase, with a 60/40 ratio between the polymer and plasticizer). The HTPB chain was composed of 48 trans groups, 16 cis groups, and 16 vinyl groups. Due to the length of the chain, superposing the crystalline RDX cell [cleaved at the crystalline (2 0 0), (0 2 0), and (2 1 0) planes] to the amorphous HTPB/DOA cell introduced considerable void, and therefore resulted in low density—much more so than when using models with shorter chains. A compression/minimization iterative procedure was used to converge to the optimal density. Pair distributions were calculated to verify that the procedure did not lead to abnormal changes in the RDX crystal model. Comparable energies were obtained for models built with each cleavage plane, contrary to previous work with small molecules. Long chains have lower entropy and are less able to change conformations and maximize interactions with the crystal surface. Models with densities higher than the minimum value were shown to have energy stored in two main components; i.e., the internal energy was stored mainly in the bond and torsion contributions, whereas the external energy storage was performed by van der Waals interactions. These preliminary models show the potential for studying the sensitivity of explosives through molecular modeling.

To describe the homogeneous nucleation process, an interfacial free energy adjustable phase-field crystal model (IPFC) was proposed by reconstructing the energy functional of the original phase field crystal (PFC) methodology. Compared with the original PFC model, the additional interface term in the IPFC model effectively can adjust the magnitude of the interfacial free energy, but does not affect the equilibrium phase diagram and the interfacial energy anisotropy. The IPFC model overcame the limitation that the interfacial free energy of the original PFC model is much less than the theoretical results. Using the IPFC model, we investigated some basic issues in homogeneous nucleation. From the viewpoint of simulation, we proceeded with an in situ observation of the process of cluster fluctuation and obtained quite similar snapshots to colloidal crystallization experiments. We also counted the size distribution of crystal-like clusters and the nucleation rate. Our simulations show that the size distribution is independent of the evolution time, and the nucleation rate remains constant after a period of relaxation, which are consistent with experimental observations. The linear relation between logarithmic nucleation rate and reciprocal driving force also conforms to the steady state nucleation theory.

Using the phase-field crystal model, we investigate the orientation selection of the cubic dendrite growth at the atomic scale. Our simulation results reproduce how a face-centered cubic (fcc) octahedral nucleus and a body-centered cubic (bcc) truncated-rhombic dodecahedral nucleus choose the preferred growth direction and then evolve into the dendrite pattern. The interface energy anisotropy inherent in the fcc crystal structure leads to the fastest growth velocity in the directions. New {111} atomic layers prefer to nucleate at positions near the tips of the fcc octahedron, which leads to the directed growth of the fcc dendrite tips in the directions. A similar orientation selection process is also found during the early stage of bcc dendrite growth. The orientation selection regime obtained by phase-field crystal simulation is helpful for understanding the orientation selection processes of real dendrite growth. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The possibility of propagation of second sound waves in diamond single crystals depending on their dimensions, concentrations of isotopes and temperature is studied. At this correct account of phonon scattering on boundaries is important. The calculation of phonon collision frequencies is carried out in the reduced isotropic crystal model using second and third modules of elasticity and in Callaway model on the basis of experimental data on diamond thermal conductivity. Both models give us the consistent values of parameters under which the propagation of SSW is possible. It is discovered in concentrations of isotopes 13 C − 6 , temperatures T

The characteristic crystal model is applied to the study of phase stability and thermodynamics in substitutional bcc-based Nb-Mo alloys. The basic principle and method of alloy thermodynamics which is described by the characteristic crystal model is introduced in detail. The thermodynamic properties of the Nb-Mo system are evaluated to describe the Gibbs energies of various phases including both disordered and ordered phases. The phase diagram of Nb-Mo is assessed and predicted. The results are in good agreement with experiments. An unambiguous tendency toward order with a B2 superstructure in a broad range of alloy composition is predicted.

In the present work, the interaction between electrons and long-wavelength transverse optical (TO) vibrations in a polar insulator is considered. The crystal model employed for the theoretical analysis includes classical potentials and electronic polarizabilities. A significant enhancement of the strength of the electron–TO-phonon interaction in ferroelectrics has been found. A microscopic justification of this effect is given. A bridge that relates the interaction of electrons with the polar long-wavelength TO modes of lattice vibrations to the long-range dipole–dipole interaction is established. As an application of our analysis, a novel method for quantitative predictions of the electron–TO–phonon interaction constants in polar crystals via the data of experimental studies is suggested.

We study a nematic crystal model appearing in [Liu et al.,2007] modeling stretching effects depending on the different shape of microscopic molecules of the material, under periodic boundary conditions. The aim of the present article is twofold: to extend the results given in [Sun & Liu, 2009], to a model with more complete stretching terms and to obtain some stability and asymptotic stability properties for this model. Ministerio de Educación y Ciencia Junta de Andalucía

This paper re-examines our previous molecular dynamics (MD) study on cellulose IIII crystal models with finite dimensions solvated in explicit water molecules. Eight crystal models, differing in a constituent lattice plane and dimensions, were studied. One calculation allowed for O–H and C–H bond stretching, and had a small time step of 0.5 fs. The other calculation adopted non-scaling factors of the 1–4 non-bonded interactions. As in our previous study, in the former MD calculations, six of the eight crystal models exhibited structure conversion with cooperative chain slippages generated by a progressive fiber bend. This converted the initial non-staggered chain packing of cellulose IIII into a near one-quarter staggering and gave the crystal model a triclinic-like configuration. In contrast, in the non-1–4 scaling MD calculations, all of the eight crystal models retained the initial cellulose IIII crystal structure. Another series of non-1–4 scaling MD calculations were performed for the four crystal models containing chains with a degree of polymerization (DP) of 40 at 370 K, which simulated hot water treatment to convert cellulose IIII to Iβ. Some of the hydroxymethyl groups irreversibly rotated from gt into tg conformation. This accompanied exchange of the intrasheet hydrogen bonding scheme along the (1 −1 0) lattice plane from O2–O6 to O3–O6. The original corrugated (1 −1 0) chain sheet was partly converted into a cellulose I-like flat chain sheet.

In this paper, numerical and implementation aspects of the phase-field crystal model with elastic interactions are addressed. This model leads to a time-dependent, sixth-order system of differential equations which yields a continuous density field, from which individual atom positions can be extracted and tracked in time. We solve the system using high-order finite elements, and reconstruct the elastic properties of the crystal from the atomic displacements with a meshless interpolation scheme. Numerical simulations are performed of benchmark experiments, which include deformation and dislocation dynamics.

We applied the mosaic crystal model to calculate the dynamical x-ray rocking curves for a coherently-strained GaAs/In0.3Ga0.7As/GaAs single quantum well grown epitaxially on a GaAs (001) substrate for a number of reflection profiles, including 004, 113, 224, 044 and 444 reflections. We show that it is possible to estimate the threading dislocation density in the quantum well, and therefore detect the pseudomorphic-metamorphic transition, using the widths or normalized intensities of the primary quantum well Bragg peak, or using the widths of the Pendellösung fringes associated with the quantum well structure.

The phase-field crystal approach describes the dynamics of the local atomic probability density on atomic length and diffusive time scales. However, the small grid spacing required to resolve the atomic length scale restricts the applicability to relatively small systems. We present a new amplitude-equation formulation that can be applied to model the evolution of a two-phase system by building upon the multiple-scale approach developed for the phase-field crystal model that explicitly incorporates a miscibility gap in the atomic density field. The new set of equations are less stiff by two orders in the spatial derivative and are found to retain acceptable accuracy even with a significantly larger grid size. Furthermore, the proposed model provides insight into the link between the phase-field-crystal model and a phase-field model in which conserved and nonconserved dynamics are coupled to describe a solid–liquid system. Models and simulation results are presented for two-dimensional hexagonal and three-...

The transition from band to hopping conductivity of small polaron is examined within Holsteins molecular crystal model. The conditions under which each of these mechanisms prevail are formulated in terms of the values of the coupling constant S and adiabatic parameter B. Particular attention was paid to the possible influence of the polaron induced modification of phonon spectrum. (C) 2008 Elsevier B.V. All rights reserved.

Weakly nonlinear spatially periodic patterns coupled to a Goldstone (zero) mode of the phase-field crystal model are investigated. Rotationally invariant equations for the dynamics of the amplitudes of a hexagonal pattern are derived first, which then allows us to determine stability regions for stripes and hexagons. There are parameter regimes in which all periodic patterns become unstable as a result of long-wavelength instabilities generated by the zero mode.