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Since the edge-to-edge matching relationship of close-packed planes on an incoherent interphase boundary was found, the one-dimensional ledge migration mechanism has been put forward. However, owing to the lack of direct experimental evidence, the existence of the one-dimensional ledge is still questioned and it is thus usually treated as just an assumption. In this study, focusing on the existence of one-dimensional ledges and the migration mechanism of incoherent interphase boundaries, an atomic scale investigation on the migration of incoherent interphase boundaries in a body- to face-centered cubic transformation has been carried out using the phase-field crystal model. Simulation results demonstrated the presence of one-dimensional ledges on incoherent interphase boundaries, but only on those boundaries with high atomic densities. The simulation results further showed that the interphase boundaries with one-dimensional ledges migrate as a result of the nucleation and extension of the one-dimensional ledge, similar to the mechanism for two-dimensional ledges; meanwhile the interphase boundaries without one-dimensional ledges migrate according to a continuous mechanism by random atomic jumping. Because it is difficult for one-dimensional ledges to nucleate under low driving forces, interphase boundary migration based on the one-dimensional ledge mechanism is slower than that based on the continuous mechanism. This study reveals the structures and mechanisms of complex transitions of incoherent interphase boundaries and can aid a deeper understanding of solid phase transformations.

Formation of quasicrystal structures has always been mysterious since the discovery of these magic structures. In this work, the nucleation of decagonal, dodecagonal, heptagonal, and octagonal quasicrystal structures controlled by the coupling among multiple length scales is investigated using a dynamic phase-field crystal model. We observe that the nucleation of quasicrystals proceeds through local rearrangement of length scales, i.e., the generation, merging and stacking of 3-atom building blocks constructed by the length scales, and accordingly, propose a geometric model to describe the cooperation of length scales during structural transformation in quasicrystal nucleation. Essentially, such cooperation is crucial to quasicrystal formation, and controlled by the match and balance between length scales. These findings clarify the scenario and microscopic mechanism of the structural evolution during quasicrystal nucleation, and help us to understand the common rule for the formation of periodic crystal and quasicrystal structures with various symmetries.

Roles of non-/symmetric triple and quadruple junctions on plasticity of ploycrystals are examined using phase-filed crystal model combined with an isovolumetric deformation technique. We designed four polycrystalline samples containing the four types of junctions respectively to simulate the deformation process under a strain rate comparable to practical situations. Our results uncover relationships between the ability of resistances to external deformations and the deformation mechanisms. For the ploycrystals containing quadruple junctions, the symmetric junction is beneficial to maintain the stability of the junctions during deformations, while asymmetric ones would be disjointed and result in formation and growth of sub-grains. For the polycrystals containing triple junctions, the stability of the junction is strongly related to the misorientation angles of the associated grains. The triple junction composed with high-angle GBs exhibits excellent stability under successive deformations and the deformation is dominated by GB migrations. Low-angle GBs migrate more easily than the high-angle ones.

Time crystal is defined as a phase of matter spontaneously exhibiting a periodicity in time. Previous studies focused on discrete quantum time crystals under periodic drive. Here, we propose a time crystal model based on a levitated charged nanoparticle in a static magnetic field without drive. Both the classical time crystal in thermal equilibrium and the quantum time crystal in the ground state can emerge in the spin rotational mode, under the strong magnetic field or the large charge-to-mass ratio limit. Besides, for the first time, the \emph{time polycrystal} is defined and naturally appears in this model. Our model paves a way for realizing time crystals in thermal equilibrium., Comment: 10 pages, 7 figures

Elucidating the interplay of defect and stress at the microscopic level is a fundamental physical problem that has strong connection with materials science. Here, based on the two-dimensional crystal model, we show that the instability mode of vacancies with varying size and morphology conforms to a common scenario. A vacancy under compression is fissioned into a pair of dislocations that glide and vanish at the boundary. This neat process is triggered by the local shear stress around the vacancy. The remarkable fractionalization of vacancies creates rich modes of interaction between vacancies and other topological defects, and provides a new dimension for mechanical engineering of defects in extensive crystalline structures., Comment: 7 pages, 6 figures

A phase-field crystal model that spontaneously undergoes displacive phase transitions is introduced by explicitly studying a two-component two-dimensional square crystal reminiscent of a perovskite. When the intercomponent free energy is a simple polynomial, the crystal undergoes displacive transitions in the $\ensuremath{\langle}10\ensuremath{\rangle}$ and $\ensuremath{\langle}11\ensuremath{\rangle}$ directions. When the interaction is a correlation function, displacements in any direction can occur. This displacive phase-field crystal (DPFC) model maps to Landau-Ginzburg-Devonshire (LGD) theories for ferroelectrics, and the DPFC and LGD models are compared in terms of phase transitions and domain walls. Dynamical simulations of quadrijunctions were also performed and found stable spiraling quadrijunctions and unstable nonspiraling quadrijunctions. Last, domain coarsening across a small-angle grain boundary demonstrates multiple forms of non-mean-curvature-driven growth.

An electronic phase-field crystal model is proposed where the thermodynamics of electrons are considered in a free-energy-functional formulation. The free-electron-gas system is considered initially as the noninteracting limit of the model. The excess free-energy contribution to the functional is incorporated by including Coulombic repulsions among electrons and exchange-correlation interactions. The evolution of an electron mean field is considered in the low-temperature limit using diffusive dynamics. Three-dimensional Wigner crystallization can be achieved from the model when the density of the system is lowered sufficiently. Through this approach, we are able to provide insight into topological defect formation and evolution during Wigner crystallization.

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.

Investigation of the heteroepitaxial film growth for anisotropic systems has been carried out by means of the anisotropic phase-field crystal model. Numerical simulations have been performed by varying the anisotropic parameters, orientations, and lattice misfit between isotropic substrate and anisotropic film layers. The simulation results demonstrate the formation of dislocations during the growth of layers with non-cubic anisotropic lattice in the presence of the elastic strain caused by the lattice misfits. It is shown that for any particular choice of misfit, both the lattice anisotropy of the film and the orientation of the substrate influence the parameters of dislocation formation such as the number of dislocations, the characteristic distance at which dislocations begin to nucleate, and the excess elastic energy.

Multipolaron solutions were studied in the framework of the Holstein one-dimensional molecular crystal model. The study was performed in the continuous limit where the crystal model maps into the nonlinear Schr\"odinger equation for which a new periodic dnoidal solution was found for the multipolaron system. In addition, the stability of the multi-polaron solutions was examined, and it was found that cnoidal and dnoidal solutions stabilize in different ranges of the parameter space. Moreover, the model was studied under the influence of nonlocal effects and the polaronic dynamics was described in terms of internal solitonic modes., Comment: 5 pages, 2 figures and Supplementary information

With the help of the McMillan formula and virtual crystal model, we predict $T_c$ may exceed 34 K in a beryllium-based alloy with a specific composition, reminiscent of $T_c$ = 35 K in the first cuprate superconductor. This may similarly inspire research efforts to seek high temperature superconductors in ambient., Comment: Accepted by Solid State Communications on 23/10/19

The degree of agglomeration and the aggregate shape influence the quality of crystalline products and the ease of downstream processing. Studying the shape of primary particles in an aggregate can lead to a better understanding of the underlying aggregation mechanism. We present an automatic image processing procedure for identifying the shape, size, and position of each primary particle in microcomputed tomography (μCT) images of potash alum aggregates. Splitting an aggregate into primary particles is based on recombining watershed-transform regions, where concavity points are considered as indicators of correct segmentation. The shape identification algorithm uses the Hough transform to identify visible face normals and matches them to the set of face normals defined by a crystal model. In principle, the algorithm is applicable to other crystalline compounds provided that sufficient symmetry is present to determine the shape of a primary particle from its visible part.

International audience; Understanding the driving forces observed during the first steps of beta-hematin crystal formation is vital in view of developing new therapeutic treatments against malaria. In this context a new additive Amber force field specific to the cyclic dimer of ferriprotoporphyrin IX coordinated via Fe-O propionate bonds (FPD) was developed and validated in the context of a crystal model. The structure and dynamics of small clusters or oligomers of the FPD entity were studied by molecular dynamics in condensed phase. New hydrogen bond patterns were identified in the dynamical process of the simulations: the characteristic pair of coplanar hydrogen bonds reported in crystallographic structures between FPD sheets (Pagola et al. Nature 2000, 404, 307) is found to be in a subtle equilibrium with new hydrogen bonds between FPD located within the same sheet. Hydrophobic interactions appeared to play a key role in oligomer cohesion: clusters with intersheet hydrogen bonds are found unstable compared to clusters with embedded-type molecular systems. We propose that oligomers enclosing this kind of embedded structure could serve as elementary building motifs for crystal growth in the digestive vacuole of Plasmodium, and could represent an attractive target for impairing hemozoin formation in a therapeutic approach.

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 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.

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

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 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.

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.

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

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] .

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.

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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