Download or read book A Phase Field Model for Rapid Solidification with Non Equilibrium Solute Diffusion written by and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Phase field Investigation on the Non equilibrium Interface Dynamics of Rapid Alloy Solidification written by and published by . This book was released on 2011 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research program reported here is focused on critical issues that represent conspicuous gaps in current understanding of rapid solidification, limiting our ability to predict and control microstructural evolution (id est morphological dynamics and microsegregation) at high undercooling, where conditions depart significantly from local equilibrium. More specifically, through careful application of phase-field modeling, using appropriate thin-interface and anti-trapping corrections and addressing important details such as transient effects and a velocity-dependent (id est adaptive) numerics, the current analysis provides a reasonable simulation-based picture of non-equilibrium solute partitioning and the corresponding oscillatory dynamics associated with single-phase rapid solidification and show that this method is a suitable means for a self-consistent simulation of transient behavior and operating point selection under rapid growth conditions. Moving beyond the limitations of conventional theoretical/analytical treatments of non-equilibrium solute partitioning, these results serve to substantiate recent experimental findings and analytical treatments for single-phase rapid solidification. The departure from the equilibrium solid concentration at the solid-liquid interface was often observed during rapid solidification, and the energetic associated non-equilibrium solute partitioning has been treated in detail, providing possible ranges of interface concentrations for a given growth condition. Use of these treatments for analytical description of specific single-phase dendritic and cellular operating point selection, however, requires a model for solute partitioning under a given set of growth conditions. Therefore, analytical solute trapping models which describe the chemical partitioning as a function of steady state interface velocities have been developed and widely utilized in most of the theoretical investigations of rapid solidification. However, these solute trapping models are not rigorously verified due to the difficulty in experimentally measuring under rapid growth conditions. Moreover, since these solute trapping models include kinetic parameters which are difficult to directly measure from experiments, application of the solute trapping models or the associated analytic rapid solidification model is limited. These theoretical models for steady state rapid solidification which incorporate the solute trapping models do not describe the interdependency of solute diffusion, interface kinetics, and alloy thermodynamics. The phase-field approach allows calculating, spontaneously, the non-equilibrium growth effects of alloys and the associated time-dependent growth dynamics, without making the assumptions that solute partitioning is an explicit function of velocity, as is the current convention. In the research described here, by utilizing the phase-field model in the thin-interface limit, incorporating the anti-trapping current term, more quantitatively valid interface kinetics and solute diffusion across the interface are calculated. In order to sufficiently resolve the physical length scales (id est interface thickness and diffusion boundary length), grid spacings are continually adjusted in calculations. The full trajectories of transient planar growth dynamics under rapid directional solidification conditions with different pulling velocities are described. As a validation of a model, the predicted steady state conditions are consistent with the analytic approach for rapid growth. It was confirmed that rapid interface dynamics exhibits the abrupt acceleration of the planar front when the effect of the non-equilibrium solute partitioning at the interface becomes signi ficant. This is consistent with the previous linear stability analysis for the non-equilibrium interface dynamics. With an appropriate growth condition, the continuous oscillation dynamics was able to be simulated using continually adjusting grid spac...
Download or read book Quantitative Phase Field Modelling of Solidification written by Nikolas Provatas and published by CRC Press. This book was released on 2021-10-12 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a study of phase field modelling of solidification in metal alloy systems. It is divided in two main themes. The first half discusses several classes of quantitative multi-order parameter phase field models for multi-component alloy solidification. These are derived in grand potential ensemble, thus tracking solidification in alloys through the evolution of the chemical potentials of solute species rather than the more commonly used solute concentrations. The use of matched asymptotic analysis for making phase field models quantitative is also discussed at length, and derived in detail in order to make this somewhat abstract topic accessible to students. The second half of the book studies the application of phase field modelling to rapid solidification where solute trapping and interface undercooling follow highly non-equilibrium conditions. In this limit, matched asymptotic analysis is used to map phase field evolution equations onto the continuous growth model, which is generally accepted as a sharp-interface description of solidification at rapid solidification rates. This book will be of interest to graduate students and researchers in materials science and materials engineering. Key Features Presents a clear path to develop quantitative multi-phase and multi-component phase field models for solidification and other phase transformation kinetics Derives and discusses the quantitative nature of the model formulations through matched interface asymptotic analysis Explores a framework for quantitative treatment of rapid solidification to control solute trapping and solute drag dynamics
Download or read book Phase Field Methods in Materials Science and Engineering written by Nikolas Provatas and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and self-contained, one-stop source discusses phase-field methodology in a fundamental way, explaining advanced numerical techniques for solving phase-field and related continuum-field models. It also presents numerical techniques used to simulate various phenomena in a detailed, step-by-step way, such that readers can carry out their own code developments. Features many examples of how the methods explained can be used in materials science and engineering applications.
Download or read book Phase field method and integrated computing materials engineering written by Yu-Hong Zhao and published by Frontiers Media SA. This book was released on 2023-04-19 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Phase Field Crystals written by Peter Galenko and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Phase Field Crystal (PFC) model incorporates microscopic structural details into a mesoscopic continuum theory. Methods for fast propagation of PFC interfaces are discussed in this book. They can handle a wide range of thermal gradients, supersaturations and supercoolings, including applications such as selective laser melting. The reader will find theoretical treatment in the first half, while the latter half discusses numerical models.
Download or read book Principles of Solidification written by Martin Eden Glicksman and published by Springer Science & Business Media. This book was released on 2010-12-17 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Principles of Solidification” offers comprehensive descriptions of liquid-to-solid transitions encountered in shaped casting, welding, and non-biological bulk crystal growth processes. The book logically develops through careful presentation of relevant thermodynamic and kinetic theories and models of solidification occurring in a variety of materials. Major topics encompass the liquid-state, liquid-solid transformations, chemical macro- and microsegregation, purification by fractional crystallization and zone refining, solid-liquid interfaces, polyphase freezing, and rapid solidification processing. Solid-liquid interfaces are discussed quantitatively both as sharp and diffuse entities, with supporting differential geometric descriptions. The book offers: • Detailed mathematical examples throughout to guide readers • Applications of solidification and crystal growth methodologies for preparation and purification of metals, ceramics, polymers and semiconductors • Appendices providing supporting information on special topics covered in the chapters. Readers in materials, metallurgical, chemical, and mechanical engineering will find this to be a useful source on the subjects of solidification and crystal growth. Chemists, physicists, and geologists concerned with melting/freezing phenomena will also find much of value in this book.
Download or read book Metastable Microstructures written by Dipankar Banerjee and published by . This book was released on 1993 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Metastable Solids from Undercooled Melts written by Dieter Herlach and published by Elsevier. This book was released on 2006-12-18 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the physical concepts and tools to characterize and describe the formation of metastable solids from undercooled melts. Its aim is to facilitate understanding of the development of the science and technology of solidification of melts and to introduce new concepts within this exciting research field in order to fulfil the challenges of the future in the field of undercooled melts. A comprehensive description of the science and applications of the undercooling phenomenon is given. It is composed of several main parts: experimental techniques for undercooling; characterization of the undercooled melt as the first step in rapid solidification; introducing the concepts of modern theories of rapid dendrite and eutectic growth and their comparison with experimental results, and a survey of metastable materials formed from the non-equilibrium state of an undercooled melt.* Showing clear links to possible application of results obtained from basic research * The subject matter is multidisciplinary and will be of interest to material scientists, physicists, physical chemists, mechanical and electrical engineers
Download or read book Lattice Boltzmann Modeling written by Michael C. Sukop and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a basic introduction to Lattice Boltzmann models that emphasizes intuition and simplistic conceptualization of processes, while avoiding the complex mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those whose interest is in model application over detailed mathematics will find this a powerful 'quick start' guide. Example simulations, exercises, and computer codes are included.
Download or read book A Grand Potential Based Multi phase Field Model for Alloy Solidification written by Kaushik Shampur and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ability to model phase transitions in complex (i.e. multi-component and multi- phase) alloys, accurately, efficiently, and in an accessible manner, is important in material science. This thesis derives a new model that extends the quantitative model of polycrystalline solidification of Ofori-Opoku et al [3] to the case of multiple components and alloy phases through a grand potential functional description. Here, solidification is described by a set of order parameters describing solid phases and a set chemical potentials describing solute components. Solidification of a solid phase is driven by the grand potential difference between it and the liquid, expanded here to quadratic order in the chemical potential difference (relative to equilibrium) of each solute, i.e., its supersaturation. This allows us to model both near and far- from equilibrium solidification conditions, and to easily make contact with previous quantitative single-crystal phase field theories in the literature. Thermal fluctuations in the theory are treated via stochastic noise, a feature important for modelling multi-phase nucleation self-consistently. Working in the grand canonical ensemble treats the evolution of order parameter and chemical potential as a coupled process, unique compared to the traditional methods. As a result, complete decoupling of all diffusion fields and order parameter fields is achieved at equilibrium, making it possible to easily set solid-liquid or solid- solid interface energy independently of solute distribution across an an interface, an important feature for quantitative meso-scale calculations. Chemical diffusion equations in the model are augmented by a non-variational, so-called anti-trapping flux in each solute species. These fictitious fluxes are used in the literature in some phase field theories to correct for spurious solute trapping effects caused by the use of a diffuse interface, which is done solely for numerical expediency.We demonstrate its workings of our model in the limit of a two-component eutectic alloy system simulated with 2D dynamic adaptive mesh refinement. Benchmark eutectic lamellar simulations and measurements are first performed. Following that, two-phase homogenous nucleation and growth are examined. In the limit of near- equilibrium interfaces (zero interface kinetics), we illustrate two-phase grain growth scaling that is independent of nucleation barrier." --
Download or read book Programming Phase Field Modeling written by S. Bulent Biner and published by Springer. This book was released on 2017-01-25 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a fast-track pathway to numerical implementation of phase-field modeling—a relatively new paradigm that has become the method of choice for modeling and simulation of microstructure evolution in materials. It serves as a cookbook for the phase-field method by presenting a collection of codes that act as foundations and templates for developing other models with more complexity. Programming Phase-Field Modeling uses the Matlab/Octave programming package, simpler and more compact than other high-level programming languages, providing ease of use to the widest audience. Particular attention is devoted to the computational efficiency and clarity during development of the codes, which allows the reader to easily make the connection between the mathematical formulism and the numerical implementation of phase-field models. The background materials provided in each case study also provide a forum for undergraduate level modeling-simulations courses as part of their curriculum.
Download or read book A Phase field Model for Technical Alloy Solidification written by Janin Eiken and published by . This book was released on 2010 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Selected Works of John W Cahn written by W. Craig Carter and published by John Wiley & Sons. This book was released on 2013-10-28 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents a collection of 30 selected papers from the work of John W. Cahn. Dr. Cahn is Senior Fellow at the Materials Science and Engineering Laboratory of the National Institute of Standards and Technology, and is widely recognized as a founder of modern theory and thought in materials science. The range of his research included kinetics and mechanisms of metallurgical phase changes, surfaces, interfaces, defects, quasicrystals, thermodynamics, and other areas impacting the fundamental understanding of materials science. Each paper includes a 2-4 page review of the impact and historical perspective of the work. This is an important collection for students, instructors, and scientists interested in materials science.
Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Download or read book Supercooling written by Peter Wilson and published by BoD – Books on Demand. This book was released on 2012-03-09 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supercooled liquids are found in the atmosphere, in cold hardy organisms, in metallurgy, and in many industrial systems today. Stabilizing the metastable, supercooled state, or encouraging the associated process of nucleation have both been the subject of scientific interest for several hundred years. This book is an invaluable starting point for researchers interested in the supercooling of water and aqueous solutions in biology and industry. The book also deals with modeling and the formation subsequent dendritic growth of supercooled solutions, as well as glass transitions and interface stability.
Download or read book Directions In Condensed Matter Physics Memorial Volume In Honor Of Shang keng Ma written by Geoffrey Grinstein and published by World Scientific. This book was released on 1986-08-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects several in-depth articles giving lucid discussions on new developments in statistical and condensed matter physics. Many, though not all, contributors had been in touch with the late S-K Ma. Written by some of the world's experts and originators of new ideas in the field, this book is a must for all researchers in theoretical physics. Most of the articles should be accessible to diligent graduate students and experienced readers will gain from the wealth of materials contained herein.
