A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

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Pattern formation outside of equilibrium

Additive manufacturing of metallic components – Process, structure and properties

Thermodynamics and Phase Diagrams Equilibrium Single-Component Systems Binary Solutions Equilibrium in Heterogeneous Systems Binary Phase Diagrams Influence of Interfaces on Equilibrium Ternary Equilibrium Additional Thermodynamic Relationships for Binary Solutions Computation of Phase Diagrams Kinetics of Phase Transformations Exercises References Further Readings Diffusion Atomic Mechanisms of Diffusion Interstitial Diffusion Substitutional Diffusion Atomic Mobility Tracer Diffusion in Binary Alloys Diffusion in Ternary Alloys High-Diffusivity Paths Diffusion in Multiphase Binary Systems Exercises References Further Readings Crystal Interfaces and Microstructure Interfacial Free Energy Solid=Vapor Interfaces Boundaries in Single-Phase Solids Interphase Interfaces in Solids Interface Migration Exercises References Further Readings Solidification Nucleation in Pure Metals Growth of a Pure Solid Alloy Solidification Solidification of Ingots and Castings Solidification of Fusion Welds Solidification during Quenching from the Melt Metallic Glasses Case Studies of Some Practical Castings and Welds Exercises References Further Readings Diffusional Transformations in Solids Homogeneous Nucleation in Solids Heterogeneous Nucleation Precipitate Growth5 Overall Transformation Kinetics-TTT Diagrams Precipitation in Age-Hardening Alloys Precipitation of Ferrite from Austenite Cellular Precipitation Eutectoid Transformations Massive Transformations Ordering Transformations Case Studies Exercises References Further Readings Diffusionless Transformations Characteristics of Diffusionless Transformations Martensite Crystallography Theories of Martensite Nucleation Martensite Growth1 Premartensite Phenomena Tempering of Ferrous Martensites Case Studies Exercises References Further Readings Solutions to Exercises Compiled by John C. Ion

/pdf/phase-transformations-in-metals-and-alloys-3qucrz9924.pdf

Phase transformations in metals and alloys

Additive manufacturing (AM), widely known as 3D printing, is a method of manufacturing that forms parts from powder, wire or sheets in a process that proceeds layer by layer. Many techniques (using many different names) have been developed to accomplish this via melting or solid-state joining. In this review, these techniques for producing metal parts are explored, with a focus on the science of metal AM: processing defects, heat transfer, solidification, solid-state precipitation, mechanical properties and post-processing metallurgy. The various metal AM techniques are compared, with analysis of the strengths and limitations of each. Only a few alloys have been developed for commercial production, but recent efforts are presented as a path for the ongoing development of new materials for AM processes.

The metallurgy and processing science of metal additive manufacturing

Metal-based additive manufacturing, or three-dimensional (3D) printing, is a potentially disruptive technology across multiple industries, including the aerospace, biomedical and automotive industries. Building up metal components layer by layer increases design freedom and manufacturing flexibility, thereby enabling complex geometries, increased product customization and shorter time to market, while eliminating traditional economy-of-scale constraints. However, currently only a few alloys, the most relevant being AlSi10Mg, TiAl6V4, CoCr and Inconel 718, can be reliably printed; the vast majority of the more than 5,500 alloys in use today cannot be additively manufactured because the melting and solidification dynamics during the printing process lead to intolerable microstructures with large columnar grains and periodic cracks. Here we demonstrate that these issues can be resolved by introducing nanoparticles of nucleants that control solidification during additive manufacturing. We selected the nucleants on the basis of crystallographic information and assembled them onto 7075 and 6061 series aluminium alloy powders. After functionalization with the nucleants, we found that these high-strength aluminium alloys, which were previously incompatible with additive manufacturing, could be processed successfully using selective laser melting. Crack-free, equiaxed (that is, with grains roughly equal in length, width and height), fine-grained microstructures were achieved, resulting in material strengths comparable to that of wrought material. Our approach to metal-based additive manufacturing is applicable to a wide range of alloys and can be implemented using a range of additive machines. It thus provides a foundation for broad industrial applicability, including where electron-beam melting or directed-energy-deposition techniques are used instead of selective laser melting, and will enable additive manufacturing of other alloy systems, such as non-weldable nickel superalloys and intermetallics. Furthermore, this technology could be used in conventional processing such as in joining, casting and injection moulding, in which solidification cracking and hot tearing are also common issues.

3D printing of high-strength aluminium alloys

Steady state columnar and equiaxed growth of dendrites and eutectic

Cellular and dendritic growth. I

A numerical model of cellular and dendritic growth has been developed that can predict cellular and dendritic spacings, undercoolings, and the transition between structures. Fully self-consistent solutions are produced for axisymmetric interface shapes. An important feature of the model is that the spacing selection mechanism has been treated. A small, stable range of spacings is predicted for both cells and dendrites, and these agree well with experiment at both low and high velocities. By suitable nondimensionalization, relatively simple analytic expressions can be used to fit the numerical results. These expressions provide an insight into the cellular and dendritic growth processes and are useful for comparing theory with experiment.

J.D. Hunt

Papers

Steady state columnar and equiaxed growth of dendrites and eutectic

Cellular and dendritic growth. I

Numerical modeling of cellular/dendritic array growth: spacing and structure predictions

On the nature of crystal growth from the melt

The measurement of solid-liquid surface energies in the Al-Cu, Al-Si and Pb-Sn systems