Motion Of Junctions Research Articles

Dynamics of phase separation of metastable crystal surfaces by surface diffusion: A phase-field study.

A new phase-field approach is designed to model surface diffusion of crystals with strongly anisotropic surface energy. The model can be shown to asymptotically converge toward the sharp-interface equationfor surface diffusion in the limit of vanishing interface width. It is employed to investigate the dynamical evolution of a thermodynamically metastable crystal surface. We find that nucleation and growth by surface diffusion of the newly formed surface induce the formation of additional stable surfaces at its wake. This induced nucleation mechanism is found to produce domains composed of several stable surfaces of prescribed width. The domains propagate on the crystal surface and then coalesce to form a hill-and-valley structure. The resulting morphology is more regular than the typical hill-and-valley surface produced by random thermal nucleation, i.e., when motion-by-curvature controls the phase separation dynamics. Moreover, the induced nucleation mechanism is found to be peculiar to surface diffusion and to dominate the phase separation at high degree of metastability. Once the hill-and-valley structure is formed, coarsening operates by motion and elimination of facet junctions, points where two facets merge to form one and we find the following scaling law L∼t^{1/6}, for the growth in time t of the characteristic length scale L during this coarsening stage. The density of junctions is found to exhibit a t^{-2/3} regime. Our results elucidate the role of the induced nucleation mechanism on the dynamics of interfacial phase separation and corroborate surface faceting experiments on ceramics.

Quantum dynamics of the internal motion of biphenyl-based molecular junctions.

Single molecule junctions based on selected 4,4'-biphenyldithiol and 4,4'-dicyanobiphenyl derivatives bonded to gold electrodes are analyzed from a dynamical point of view. A fully quantum mechanical description of the internal rotation of the biphenyl moiety is carried out in terms of the nuclear wavepacket dynamics obtained by the solution of the time-dependent Schrödinger equation expressed in terms of the torsion angle between the phenyl rings. The required potential energy surfaces are computed using abinitio electronic structure methods. The nature and positions of the substituents on the phenyl rings determine the features of the potential energy surfaces. The effect of the initial conditions on the time propagation of the nuclear wavepackets and, as a consequence, on the evolution of the conformational distribution is also analyzed. In addition, the conductances at zero bias for the nanojunctions were computed for different conformations of the biphenyl fragments. Weighted by the wavepacket amplitudes, non-stationary conductance expectation values, and time-averaged torsion angles and conductances for the entire simulation are obtained. The consequences of using the time-averaged values to perform a linear regression between the conductance and the square of the cosine of the dihedral angle between the phenyl rings are analyzed and compared to the usual static approach based only on the information for equilibrium geometries. The study of the time dependent conformational variations of the biphenyl moieties in the nanojunctions allows for a better understanding of the quantum chemical phenomena that affect their transport properties.

Dislocation content of grain boundary phase junctions and its relation to grain boundary excess properties

We analyze the dislocation content of grain boundary (GB) phase junctions, i.e., line defects separating two different GB phases coexisting on the same GB plane. While regular GB disconnections have been characterized for a variety of interfaces, GB phase junctions formed by GBs with different structures and different numbers of excess atoms have not been previously studied. We apply a general Burgers circuit analysis to calculate the Burgers vectors b of junctions in two {\Sigma}5 Cu boundaries previously simulated with molecular dynamics. The Burgers vectors of these junctions cannot be described by the displacement shift complete (DSC) lattice alone. We show that, in general, the normal component of b is not equal to the difference in the GB excess volumes, but contains another contribution from the numbers of GB atoms per unit area {\Delta}N required to transform one GB phase into another. In the boundaries studied, the latter component dominates and even changes the sign of b. We derive expressions for the normal and tangential components of b in terms of the DSC lattice vectors and the non-DSC part due to {\Delta}N and additional GB excess properties, including excess volume and shears. These expressions provide a connection between GB phase transformations driven by the GB free energy difference and the motion of GB junctions under applied normal and shear stresses. The proposed analysis quantifies b and therefore makes it possible to calculate the elastic part of the energy of these defects, evaluate their contribution to the nucleation barrier during GB phase transformations, and treat elastic interactions with other defects.

Early dynamic changes within the spine following posterior fusion using hybrid instrumentation in adolescents with idiopathic scoliosis: a gait analysis study.

In adolescent idiopathic scoliosis (AIS) patients, mechanical consequences of posterior spinal fusion within the spine remain unclear. Through dynamic assessment, gait analysis could help elucidating this particular point. The aim of this study was to describe early changes within the spine following fusion with hybrid instrumentation in adolescents with idiopathic scoliosis, using gait analysis MATERIALS AND METHODS: We conducted a single-centre prospective study including AIS patients scheduled for posterior spinal fusion (PSF) using hybrid instrumentation with sublaminar bands. Patients underwent radiographic and gait analyses preoperatively and during early postoperative period. Among gait parameters, motion of cervicothoracic, thoracolumbar and lumbosacral junctions was measured in the three planes. We included 55 patients (mean age 15 years, 84% girls). Fusion was performed on 12 levels and mean follow-up was 8 months. There was a moderately strong correlation between thoracolumbar sagittal motion and lumbosacral junction pre- and postoperatively (R = - 0.6413 and R = - 0.7040, respectively, all p < 0.001), meaning that the more thoracolumbar junction was in extension, the more lumbosacral extension movements decreased. There was a trend to significance between postoperative SVA change and thoracolumbar sagittal motion change (R = - 0.2550, p = 0.059). This is the first series reporting dynamic changes within the spine following PSF using hybrid instrumentation in AIS patients. PSF led to symmetrization of gait pattern. In the sagittal plane, we found that thoracolumbar extension within the fused area led to decreased extension at cervicothoracic and lumbosacral junctions. Even though consequences of such phenomenon are unclear, attention must be paid not to give a too posterior alignment when performing PSF for AIS patients.

Disconnection description of triple-junction motion

Grain boundary (GB) migration in polycrystalline materials necessarily implies the concurrent motion of triple junctions (TJs), the lines along which three GBs meet. Today, we understand that GB migration occurs through the motion of disconnections in the GB plane (line defects with both step and dislocation character). We present evidence from molecular dynamics grain growth simulations and idealized microstructures that demonstrates that TJ motion and GB migration are coupled through disconnection dynamics. Based on these results, we develop a theory of coupled GB/TJ migration and use it to develop a physically based, disconnection mechanism-specific continuum model of microstructure evolution. The continuum approach provides a means of reducing the complexity of the discrete disconnection picture to extract the features of disconnection dynamics that are important for microstructure evolution. We implement this model in a numerical, continuum simulation and demonstrate that it is capable of reproducing the molecular dynamics (MD) simulation results.

Anomalous Diffusion of Endoplasmic Reticulum Constituents

Diffusion of macromolecules and higher-order structures in the crowded interior of cells frequently shows an anomalous behavior with the mean-square displacement (MSD) increasing nonlinearly in time, MSD∝tα. Here we have probed to which extent also larger organelle structures show such an anomalous diffusion and how non-equilibrium contributions affect their diffusional motion [Phys. Rev. E 98, 012406 (2018), in press: Biophys. J. 115 (2018)]. In particular, we have employed single-particle tracking to monitor the motion of tubular junctions in the endoplasmic reticulum (ER) network and of long-lived membrane domains on the ER, called ER exit sites (ERES). Our results show that both, ER junctions and ERES show a distinct anomalous diffusion with a significant anti-correlation of successive step increments that is reminiscent of fractional Brownian motion. Disrupting the microtubule cytoskeleton significantly altered the subdiffusive characteristics of both entities, highlighting that even anomalous diffusion is an actively driven process in living cells. While the diffusion behavior of ER junctions was seen to be directly dependent on the presence and activity of microtubules, ERES were only indirectly affected. ERES therefore can be seen as mobile membrane domains that perform a quasi-one-dimensional random walk on the shivering ER backbone.

Relation between Cross-Link Fluctuations and Elasticity in Entangled Polymer Networks

Computer simulation data on junction fluctuations in end-linked model networks are analyzed using the framework of the constraint junction model and the slip tube model for entangled networks. It is argued that cross-linking freezes in conformational fluctuations of chains and cross-links, which creates a small preload of entangled strands. This can be modeled using a “confinement degree of polymerization” Nc(N) with a weak dependence on the degree of polymerization N. The confined motion of network junctions with f active connections to the network is well described by using the exact solution of the constrained junction model with a constraining term that is given by the superposition of f/2 entanglement tubes with confinement Nc(N). It is shown that the modulus of end-linked model networks is the sum of a phantom and an entanglement contribution, whereby the entanglement contribution shows the same correction Nc(N) as both the cross-link fluctuations and the time average bond orientations. The results ...

Stability and motion of arbitrary grain boundary junctions

The Herring condition is known as the stability condition for a junction line, but the stability conditions for junction points are not readily available. This paper derives stability conditions for arbitrary junction points and allows for anisotropic surface energies and line energies. A junction is considered to be stable when the force on a small neighborhood around the junction vanishes. When the force does not vanish, the junction is expected to move. Equations of motion are derived for the nodes belonging to polygonal curves or triangulated surfaces, and allow for junction lines and junction points to contribute to the drag on a node. The accuracy of the equations of motion is evaluated by the relative error in the rate of volume change of an adjoining grain. They are found to be second-order accurate for nodes on a boundary and first-order accurate for nodes at a junction. A simulation of boundary motion in two dimensions suggests that the equations of motion are of comparable accuracy to alternatives in the literature, and have the advantage of less computational complexity.

Effect of texture on grain growth in an interstitial-free steel sheet

Abstract The effect of crystallographic texture on grain growth was studied in two samples from an interstitial-free steel sheet with two different primary recrystallization textures, one with a pronounced {111} fiber texture and the other with an almost random texture. Upon grain growth annealing, the sample with the random texture showed slow continuous grain growth. In the strongly textured material discontinuous grain growth prevailed at a higher growth rate. The effect of texture on the rate of grain growth is discussed in terms of the motion of the grain boundary triple junctions in the two samples with different distributions of grain-to-grain misorientations. Numerical simulations with a 2D vertex model confirmed the influence of the triple junctions on the development of microstructure and texture observed during grain growth in the two differently textured steel samples.

Growth History of Individual Grains in Polycrystals: Theoretical Model and Simulation Studies

A 3D grain growth model is developed based on a generalised mean-field approach. It allows the prediction of the growth history of individual grains of a polycrystal during normal grain growth, which has been compared with results from Monte Carlo Potts simulations showing a good agreement. Based on a stochastic grain growth model the diffusivity of the Brownian-like motion of individual quadruple points and triple junctions in 2D sections can be related to the average growth rate providing a possibility for the determination of the average growth law of the grain ensemble solely from the stochastic growth behaviour of single grains.

Subglass Cooperative Mechanical Relaxations and Activation Entropy in Heterocyclic Polymer Networks

Measurements of differential scanning calorimetry, dynamic mechanical analysis, and dilatometry have been performed in heterocyclic polymer networks (HPNs), whose effective network density has been gradually varied keeping the overall chemical structure essentially unchanged. Evidence of a growing intermolecular cooperativity for a local relaxation motion is offered by the investigation of the subglass mechanical β-relaxation, whose frequency factor and apparent activation energy strongly increase with increasing cross-linking density from about 1015 s−1 and 44.2 kJ/mol to about 1019 s−1 and 69.8 kJ/mol. The analysis of the characteristics of the mechanical β-relaxation suggests the existence of cooperative transitions of consecutive relaxing units, mainly driven by the crank-shaft motion of the network junctions between the isocyanurate heterocycles building up the structure. Comparison with previous results concerning the dielectric β-relaxation evidence a less cooperative character and a different microscopic origin for the conformational transitions driving the dielectric process. Moreover, a decrease in the thermodynamic fragility with increasing network density has been revealed, which contrasts with the increasing dynamic fragility, as measured by dielectric and mechanical probes.

Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions

We consider a system of three surfaces, graphs over a bounded domain in ℝ2, intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to 2π/3.) For the corresponding two-dimensional parabolic free boundary problem we prove short-time existence of classical solutions (in parabolic Hölder spaces), for sufficiently regular initial data satisfying a compatibility condition.

Structure and motion of junctions between coherent and incoherent twin boundaries in copper

The atomic mechanisms of twin boundary migration in copper under externally applied mechanical loads and during thermal annealing are investigated utilizing molecular dynamics computer simulations. The migration dynamics of the incoherent Σ = 3 [ 1 1 0 ] ( 1 1 2 ) twin boundary (ITB), pinned between two Σ = 3 [ 1 1 0 ] ( 1 1 1 ) twin boundaries, is determined. A three-dimensional structural model is described for the junction between intersecting coherent and incoherent twin boundaries, and migration velocities are calculated under thermal annealing conditions. It is shown that the coherent twin boundary (CTB)/ITB junction results in breaking the crystal symmetry by creation of either an edge dislocation or a mixed (edge/screw) at the intersection. These two types of defects can lead to pronounced differences in the observed migration (and hence annealing) rates of ICT/CTB junctions. The annealing rate resulting from the migration of ITBs with a mixed dislocation is found to be more than twice that of the edge dislocation. The mechanism of ITB motion is shown to be governed by successive kink-like motion of neighboring atomic columns, each of which is shifted by 1/4[1 1 0], followed by structural relaxation to accommodate boundary motion.

Time dependence in 3‐D mantle convection models featuring evolving plates: Effect of lower mantle viscosity

Evolving plate configurations and dynamically determined plate velocities are featured in Cartesian geometry mantle convection simulations. The numerical model enables the evolution of plate shape and size by migrating idealized plate triple junctions. The motion of the model triple junctions responds to the time‐dependent velocities of the adjacent plates. Each calculation includes four high‐viscosity plates in a 3 × 3 × 1 solution domain. We analyze the effect of plate evolution on the time dependence of plate velocity and heat flux in three different models characterized by lower mantle to upper mantle viscosity ratios of 30, 90, and 300. We examine the difference in behavior between calculations featuring fixed and mobile plate boundaries for each viscosity model. When plates are permitted to evolve in response to the convective vigor of the system, plate positions and shapes can change considerably while features in the high‐viscosity lower mantle may change very little. In addition, plate velocities and surface heat flux can be highly time dependent. We find that when the contrast between lower mantle and upper mantle viscosity magnitude is a factor of 30, surface velocities may fluctuate by 75% of the mean value and heat flux by 60%. We also find that plate velocity evolution is characterized by periods of reorganization, punctuating more stable periods. When the lower mantle viscosity is increased to 90 times the upper mantle value, plate reorganization events also occur, but only when plate boundary motion is enabled. When the lower mantle to upper mantle viscosity contrast is increased to a factor of 300, we find that the mean surface velocity and heat flux become very steady in cases both with and without plate boundary evolution, despite the substantial migration of convergent plate boundaries in the former case.

Features of migration of triple junctions of different configuration

The stationary motion of individual triple junctions of different crystal geometry has been experimentally investigated. It is shown that triple junctions are characterized by intrinsic finite mobilities and drag parameters. The difference in the temperature dependences of the drag parameters of triple junctions may lead to the formation of an inhomogeneous polycrystalline microstructure during isothermal annealings.

Theory of relaxation spectra and dielectric relaxation of rigid rodlike particles incorporated in a polymer network

The theory of molecular mobility and relaxation spectra is developed for rodlike particles embedded in a polymer network with allowance for the involvement of the particles in collective network dynamics through topological entanglements with network fragments. A regular cubic coarse-grained network model is used, where the motion of junctions describes the mobility of large fragments (domains) of the initial network with a size equal to the distance between adjacent rodlike particles. The involvement of the rods in collective network dynamics is taken into account by introducing an effective quasi-elastic potential acting between the rods and junctions of the coarse-grained network and preventing long-distance diffusion of the embedded particles. The viscoelastic parameters of the coarse-grained (“renormalized”) network are functions of the viscoelastic characteristics of the initial network. The relaxation time spectra are calculated as well as the frequency dependences of the dielectric loss factor of the embedded particles that possess a permanent dipole moment directed along the major axis of each rod. Depending on the ratio between the viscoelastic characteristics of the rods and the network, the frequency dependence of the dielectric loss factor may have two maxima. The high-frequency maximum corresponds to local orientational movements of particles at fixed junctions of the coarse-grained network, which correspond to the position of the domain centers in the initial network. The low-frequency maximum corresponds to movements of particles involved in large-scale dynamics of network fragments. The dependence of the dielectric loss factor on the ratio between the viscoelastic parameters of the rods and the network is studied.

Grain microstructure evolution and grain boundary junction engineering

The grain microstructure evolution in the course of two dimensional (2D) grain growth is considered in greater detail, taking into account the influence of grain boundary triple junctions. It is shown that there are two limiting regimes of grain growth in polycrystals: the first one is associated with the situation when the kinetics of grain growth are controlled by the motion of grain boundaries, while the second one is defined by the motion of grain boundary triple junctions, i.e. when the mobility of triple junctions determines the kinetics of grain growth. A generalised theory of 2D grain growth including a limited triple junction mobility is presented. The theoretical predictions are compared with results of computer simulations by a virtual vertex model. We introduce a new branch of grain boundary engineering, namely, grain boundary junction engineering that utilises junction properties for microstructure control.

Athermal Motion of Grain Boundaries, Twins and Triple Junctions in Zn

When a bicrystal or polycrystal are subjected to a change in temperature, the individual responses of the two adjoining crystals may differ in a manner, which tends to produce a dilatational mismatch along grain boundaries. If compatibility is to be retained along the interface, an additional set of stresses must then be generated in order to conserve this compatibility. ‘Compatibility stresses’ will also be generated whenever a polycrystal is heated or cooled and the thermal expansion coefficients of the individual grains are different due to thermal expansion anisotropy. In such cases adjacent grains will attempt to change dimensions and develop mismatches by amounts controlled by the parameter Δa*ΔΤ, where Δa is the difference between the thermal expansion coefficients in the appropriate directions, and ΔΤ is the temperature change. These ‘compatibility stresses’ may be relieves if grain boundary motion, triple junction migration and grain growth are possible. These ‘compatibility stresses’ may play important role in the kinetic behavior of the microstructure ranging from influencing the behavior of lattice dislocations near the grain boundaries to promoting grain boundary and triple junction dragging or moving. The motion of the ‘special’ grain boundaries, triple junctions with ‘special’ grain boundaries and twins under the influence of internal mechanical stresses is the main subject of this paper.

Thermal and dielectric properties and curing kinetics of nanomaterials formed from poss-epoxy and meta-phenylenediamine

A nanoporous polyhedral oligomeric silisesquioxane (POSS) containing eight epoxy functional groups [octakis(dimethylsiloxypropylglycidyl ether)silsesquioxane, OG] reacts with meta-phenylenediamine (mPDA) to form epoxy resin network with nanostructures. The glass transition temperature ( T g) of the cured OG/mPDA product is significantly higher than that of the diglycidyl ether of bisphenol A (DGEBA) cured with mPDA (DGEBA/mPDA) material due to the presence of the POSS cages that is able to effectively hinder the motion of the network junctions. The cured OG/mPDA product inherently possesses higher thermal stability than the cured DGEBA/mPDA product based on higher maximum decomposition rate temperature, and higher char yield of the former. However, the existence of large fraction of the unreacted amine groups causes lower initial decomposition temperature of the OG/mPDA because it tends to decompose or volatilize on heating at relatively low temperature. The dielectric constant of the OG/mPDA material (2.31) is substantially lower than that of the DGEBA/mPDA (3.51) as a consequence the presence of nanoporous POSS cubes in the epoxy matrix.

Study of the motion of individual triple junctions in aluminum

The mobility of individual triple junctions in aluminum is studied. Triple junctions with 〈111〉, 〈100〉, and 〈110〉 tilt boundaries are studied. The data obtained show that, at low temperatures, the mobility of the system of grain boundaries with a triple junction is controlled by the mobility of the triple junction (the junction kinetics). At high temperatures, the system mobility is determined by the mobility of the grain boundaries (the boundary kinetics). There is a temperature at which the transition from the junction kinetics to the boundary kinetics occurs; this temperature is determined by the crystallographic parameters of the sample.