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Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

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https://www.readbyqxmd.com/read/29311216/a-complete-analytical-solution-of-the-fokker-planck-and-balance-equations-for-nucleation-and-growth-of-crystals
#1
Eugenya V Makoveeva, Dmitri V Alexandrov
This article is concerned with a new analytical description of nucleation and growth of crystals in a metastable mushy layer (supercooled liquid or supersaturated solution) at the intermediate stage of phase transition. The model under consideration consisting of the non-stationary integro-differential system of governing equations for the distribution function and metastability level is analytically solved by means of the saddle-point technique for the Laplace-type integral in the case of arbitrary nucleation kinetics and time-dependent heat or mass sources in the balance equation...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311215/the-boundary-integral-theory-for-slow-and-rapid-curved-solid-liquid-interfaces-propagating-into-binary-systems
#2
REVIEW
Peter K Galenko, Dmitri V Alexandrov, Ekaterina A Titova
The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived. This equation contains the steady-state conditions of solidification as a special case. The boundary integral analysis demonstrates how to derive the quasi-stationary Ivantsov and Horvay-Cahn solutions that, respectively, define the paraboloidal and elliptical crystal shapes...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311214/analytical-solutions-of-mushy-layer-equations-describing-directional-solidification-in-the-presence-of-nucleation
#3
Dmitri V Alexandrov, Alexander A Ivanov, Irina V Alexandrova
The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber-Volmer-Frenkel-Zel'dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: [Formula: see text], where Z1(t)=βt7/2 and Z1(t)=βt2 in cases of kinetic and diffusionally controlled scenarios...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311213/nonlinear-dynamics-of-mushy-layers-induced-by-external-stochastic-fluctuations
#4
Dmitri V Alexandrov, Irina A Bashkirtseva, Lev B Ryashko
The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the 'solid phase-mushy layer' and 'mushy layer-liquid phase' phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311212/thermo-solutal-and-kinetic-modes-of-stable-dendritic-growth-with-different-symmetries-of-crystalline-anisotropy-in-the-presence-of-convection
#5
REVIEW
Dmitri V Alexandrov, Peter K Galenko, Lyubov V Toropova
Motivated by important applications in materials science and geophysics, we consider the steady-state growth of anisotropic needle-like dendrites in undercooled binary mixtures with a forced convective flow. We analyse the stable mode of dendritic evolution in the case of small anisotropies of growth kinetics and surface energy for arbitrary Péclet numbers and n-fold symmetry of dendritic crystals. On the basis of solvability and stability theories, we formulate a selection criterion giving a stable combination between dendrite tip diameter and tip velocity...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311211/dendrite-fragmentation-an-experiment-driven-simulation
#6
T Cool, P W Voorhees
The processes leading to the fragmentation of secondary dendrite arms are studied using a three-dimensional Sn dendritic structure that was measured experimentally as an initial condition in a phase-field simulation. The phase-field model replicates the kinetics of the coarsening process seen experimentally. Consistent with the experiment, the simulations of the Sn-rich dendrite show that secondary dendrite arm coalescence is prevalent and that fragmentation is not. The lack of fragmentation is due to the non-axisymmetric morphology and comparatively small spacing of the dendrite arms...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311210/a-phase-field-crystal-alloy-model-for-late-stage-solidification-studies-involving-the-interaction-of-solid-liquid-and-gas-phases
#7
Nan Wang, Gabriel Kocher, Nikolas Provatas
We present a multiphase binary alloy phase-field-crystal model. By introducing density difference between solid and liquid into a previous alloy model, this new fusion leads to a practical tool that can be used to investigate formation of defects in late-stage alloy solidification. It is shown that this model can qualitatively capture the liquid pressure drop due to solidification shrinkage in confined geometry. With an inherited gas phase from a previous multiphase model, cavitation of liquid from shrinkage-induced pressure is also included in this framework...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311209/two-component-structural-phase-field-crystal-models-for-graphene-symmetries
#8
K L M Elder, M Seymour, M Lee, M Hilke, N Provatas
We extend the three-point XPFC model of Seymour & Provatas (Seymour & Provatas 2016 Phys. Rev. B93, 035447 (doi:10.1103/PhysRevB.93.035447)) to two components to capture chemical vapour deposition-grown graphene, and adapt a previous two-point XPFC model of Greenwood et al. (Greenwood et al. 2011 Phys. Rev. B84, 064104 (doi:10.1103/PhysRevB.84.064104)) into a simple model of two-component graphene. The equilibrium properties of these models are examined and the two models are compared and contrasted. The first model is used to study the possible roles of hydrogen in graphene grain boundaries...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311208/from-atomistic-interfaces-to-dendritic-patterns
#9
P K Galenko, D V Alexandrov
Transport processes around phase interfaces, together with thermodynamic properties and kinetic phenomena, control the formation of dendritic patterns. Using the thermodynamic and kinetic data of phase interfaces obtained on the atomic scale, one can analyse the formation of a single dendrite and the growth of a dendritic ensemble. This is the result of recent progress in theoretical methods and computational algorithms calculated using powerful computer clusters. Great benefits can be attained from the development of micro-, meso- and macro-levels of analysis when investigating the dynamics of interfaces, interpreting experimental data and designing the macrostructure of samples...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311207/a-model-for-free-growth-of-a-lamellar-eutectic-dendrite-with-an-incident-flow
#10
Jianrong Gao
A model for free growth of a lamellar eutectic dendrite with an incident flow was proposed for the breakdown of a planar solid/liquid interface into a dendritic contour due to a negative thermal gradient in an undercooled liquid. The model was used to predict the growth kinetics of an α-Ni/Ni3Sn eutectic dendrite with and without an incident flow in the growth direction. The modelling showed that free eutectic growth is not sensitive to the tip selection parameter of the eutectic dendrite, but is sensitive to incident flow of magnitude larger than eutectic growth velocities...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311206/kinetic-transition-in-the-order-disorder-transformation-at-a-solid-liquid-interface
#11
P K Galenko, I G Nizovtseva, K Reuther, M Rettenmayr
Phase-field analysis for the kinetic transition in an ordered crystal structure growing from an undercooled liquid is carried out. The results are interpreted on the basis of analytical and numerical solutions of equations describing the dynamics of the phase field, the long-range order parameter as well as the atomic diffusion within the crystal/liquid interface and in the bulk crystal. As an example, the growth of a binary A50B50 crystal is described, and critical undercoolings at characteristic changes of growth velocity and the long-range order parameter are defined...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311205/thermoelectric-magnetohydrodynamic-effects-on-the-crystal-growth-rate-of-undercooled-ni-dendrites
#12
A Kao, J Gao, K Pericleous
In the undercooled solidification of pure metals, the dendrite tip velocity has been shown experimentally to have a strong dependence on the intensity of an external magnetic field, exhibiting several maxima and minima. In the experiments conducted in China, the undercooled solidification dynamics of pure Ni was studied using the glass fluxing method. Visual recordings of the progress of solidification are compared at different static fields up to 6 T. The introduction of microscopic convective transport through thermoelectric magnetohydrodynamics is a promising explanation for the observed changes of tip velocities...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311204/crystal-growth-kinetics-in-undercooled-melts-of-pure-ge-si-and-ge-si-alloys
#13
REVIEW
Dieter M Herlach, Daniel Simons, Pierre-Yves Pichon
We report on measurements of crystal growth dynamics in semiconducting pure Ge and pure Si melts and in Ge100-x Si x (x = 25, 50, 75) alloy melts as a function of undercooling. Electromagnetic levitation techniques are applied to undercool the samples in a containerless way. The growth velocity is measured by the utilization of a high-speed camera technique over an extended range of undercooling. Solidified samples are examined with respect to their microstructure by scanning electron microscopic investigations...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311203/domain-shape-instabilities-and-dendrite-domain-growth-in-uniaxial-ferroelectrics
#14
Vladimir Ya Shur, Andrey R Akhmatkhanov
The effects of domain wall shape instabilities and the formation of nanodomains in front of moving walls obtained in various uniaxial ferroelectrics are discussed. Special attention is paid to the formation of self-assembled nanoscale and dendrite domain structures under highly non-equilibrium switching conditions. All obtained results are considered in the framework of the unified kinetic approach to domain structure evolution based on the analogy with first-order phase transformation.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311202/coarse-graining-for-fast-dynamics-of-order-parameters-in-the-phase-field-model
#15
D Jou, P K Galenko
In standard descriptions, the master equation can be obtained by coarse-graining with the application of the hypothesis of full local thermalization that is equivalent to the local thermodynamic equilibrium. By contrast, fast transformations proceed in the absence of local equilibrium and the master equation must be obtained with the absence of thermalization. In the present work, a non-Markovian master equation leading, in specific cases of relaxation to local thermodynamic equilibrium, to hyperbolic evolution equations for a binary alloy, is derived for a system with two order parameters...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29311201/travelling-wave-amplitudes-as-solutions-of-the-phase-field-crystal-equation
#16
I G Nizovtseva, P K Galenko
The dynamics of the diffuse interface between liquid and solid states is analysed. The diffuse interface is considered as an envelope of atomic density amplitudes as predicted by the phase-field crystal model (Elder et al. 2004 Phys. Rev. E70, 051605 (doi:10.1103/PhysRevE.70.051605); Elder et al. 2007 Phys. Rev. B75, 064107 (doi:10.1103/PhysRevB.75.064107)). The propagation of crystalline amplitudes into metastable liquid is described by the hyperbolic equation of an extended Allen-Cahn type (Galenko & Jou 2005 Phys...
February 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29277748/new-horizons-for-cellulose-nanotechnology
#17
S J Eichhorn, S S Rahatekar, S Vignolini, A H Windle
No abstract text is available yet for this article.
February 13, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29277747/transparent-wood-for-functional-and-structural-applications
#18
REVIEW
Yuanyuan Li, Qiliang Fu, Xuan Yang, Lars Berglund
Optically transparent wood combines mechanical performance with optical functionalities is an emerging candidate for applications in smart buildings and structural optics and photonics. The present review summarizes transparent wood preparation methods, optical and mechanical performance, and functionalization routes, and discusses potential applications. The various challenges are discussed for the purpose of improved performance, scaled-up production and realization of advanced applications.This article is part of a discussion meeting issue 'New horizons for cellulose nanotechnology'...
February 13, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29277746/bioinspired-bouligand-cellulose-nanocrystal-composites-a-review-of-mechanical-properties
#19
REVIEW
Bharath Natarajan, Jeffrey W Gilman
The twisted plywood, or Bouligand, structure is the most commonly observed microstructural motif in natural materials that possess high mechanical strength and toughness, such as that found in bone and the mantis shrimp dactyl club. These materials are isotropically toughened by a low volume fraction of soft, energy-dissipating polymer and by the Bouligand structure itself, through shear wave filtering and crack twisting, deflection and arrest. Cellulose nanocrystals (CNCs) are excellent candidates for the bottom-up fabrication of these structures, as they naturally self-assemble into 'chiral nematic' films when cast from solutions and possess outstanding mechanical properties...
February 13, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29277745/cellulose-synthase-complex-organization-and-cellulose-microfibril-structure
#20
REVIEW
Simon Turner, Manoj Kumar
Cellulose consists of linear chains of β-1,4-linked glucose units, which are synthesized by the cellulose synthase complex (CSC). In plants, these chains associate in an ordered manner to form the cellulose microfibrils. Both the CSC and the local environment in which the individual chains coalesce to form the cellulose microfibril determine the structure and the unique physical properties of the microfibril. There are several recent reviews that cover many aspects of cellulose biosynthesis, which include trafficking of the complex to the plasma membrane and the relationship between the movement of the CSC and the underlying cortical microtubules (Bringmann et al...
February 13, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
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