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Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006223

EISBN: 978-1-62708-163-4

... of eutectic and binary phase diagrams from

**Gibbs****free**-**energy****curves**. binary solution eutectic phase diagram**Gibbs****free****energy****Gibbs****free**-**energy****curves**phase diagram single-component unary system thermodynamics IN RECENT YEARS, the application of phase diagram information obtained from...
Abstract

Thermodynamic descriptions have become available for a large number of alloy systems and allow the calculation of the phase diagrams of multicomponent alloys. This article begins with a discussion on three laws of thermodynamics: the Law of Conservation of Energy, the Second Law of Thermodynamics, and the Third Law of Thermodynamics. It informs that for transformations that occur at a constant temperature and pressure, the relative stability of the system is determined by its Gibbs free energy. The article describes the Gibbs free energy of a single-component unary system and the Gibbs free energy of a binary solution. It schematically illustrates the structure of a binary solid solution with interatomic bonds and shows how the equilibrium state of an alloy can be obtained from the free-energy curves at a given temperature. The article concludes with information on the construction of eutectic and binary phase diagrams from Gibbs free-energy curves.

Series: ASM Handbook

Volume: 4E

Publisher: ASM International

Published: 01 June 2016

DOI: 10.31399/asm.hb.v04e.a0006277

EISBN: 978-1-62708-169-6

...

**Gibbs****free****energies**and atomic mobilities are established as functions of temperature, pressure, and composition and serve directly as key inputs of any microstructure modeling. The article presents examples of the integrated computation tool set in simulating microstructural evolution. Burgers...
Abstract

This article describes the integration of thermodynamic modeling, mobility database, and phase-transformation crystallography into phase-field modeling and its combination with transformation texture modeling to predict phase equilibrium, phase transformation, microstructure evolution, and transformation texture development during heat treatment of multicomponent alpha/beta and beta titanium alloys. It includes quantitative description of Burgers orientation relationship and path, discussion of lattice correspondence between the alpha and beta phases, and determination of the total number of Burgers correspondence variants and orientation variants. The article also includes calculation of the transformation strain with contributions from defect structures developed at alpha/beta interfaces as a precipitates grow in size. In the CALculation of PHAse Diagram (CALPHAD) framework, the Gibbs free energies and atomic mobilities are established as functions of temperature, pressure, and composition and serve directly as key inputs of any microstructure modeling. The article presents examples of the integrated computation tool set in simulating microstructural evolution.

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005189

EISBN: 978-1-62708-187-0

... Abstract This article introduces the fundamental concepts of chemical thermodynamics and chemical kinetics in describing presolidification phenomena. For metallurgical systems, the most important thermodynamic variables are enthalpy and

**Gibbs****free****energy**. A qualitative demonstration of the...
Abstract

This article introduces the fundamental concepts of chemical thermodynamics and chemical kinetics in describing presolidification phenomena. For metallurgical systems, the most important thermodynamic variables are enthalpy and Gibbs free energy. A qualitative demonstration of the interrelationship between phase diagrams and thermodynamics is presented. The article discusses processes that generally limit the rates of chemical processes. These include nucleation of the product phase and interphase mass transport. The article provides a discussion on the dissolution of alloy with melting point lower than bath temperature and dissolution of alloy that is solid at bath temperatures.

Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006222

EISBN: 978-1-62708-163-4

...

**free**-**energy**change is zero (Δ G = 0) and it must be negative. Below T m , the**free****energy**does become negative (Δ G < 0) and the metal solidifies. The**free**-**energy**change is thus: (Eq 12) Δ G = Δ G S − Δ G L < 0 Fig. 12**Gibbs****free**-**energy****curves**during solidification...
Abstract

This article begins with the one-component, or unary, diagram for magnesium. The diagram shows what phases are present as a function of the temperature and pressure. When two metals are mixed in the liquid state to produce a solution, the resulting alloy is called a binary alloy. The article describes the various types of solid solutions such as interstitial solid solutions and substitutional solid solutions. Free energy is important because it determines whether or not a phase transformation is thermodynamically possible. The article discusses the thermodynamics of phase transformations and free energy, as well as kinetics of phase transformations. It concludes with a description of solid-state phase transformations that occur when one or more parent phases, usually on cooling, produces a phase or phases.

Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006221

EISBN: 978-1-62708-163-4

..., liquid, and/or solid phases with different crystal structures). When two or more phases are in mutual equilibrium, each phase must be in the lowest

**free**-**energy**state possible under the restrictions imposed by its environment. This equilibrium condition means that each phase is in an internally...
Abstract

The application of phase diagrams is instrumental in solid-state transformations for the processing and heat treatment of alloys. A unary phase diagram plots the phase changes of one element as a function of temperature and pressure. This article discusses the unary system that can exist as a solid, liquid, and/or gas, depending on the specific combination of temperature and pressure. It describes the accomplishment of conversion between weight percentage and atomic percentage in a binary system by the use of formulas. The article analyzes the effects of alloying on melting/solidification and on solid-state transformations. It explains the construction of phase diagrams by the Gibbs phase rule and the Lever rule. The article also reviews the various types of alloy systems that involve solid-state transformations. It concludes with information on the sources of phase diagram.

Series: ASM Handbook

Volume: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005415

EISBN: 978-1-62708-196-2

... dependence on multiple field variables. For instance, a commercial alloy may have more than ten chemical elements, and the corresponding

**Gibbs****free****energy**and mobility matrix are both functions of the concentration of these elements, in addition to temperature and pressure. To present them in tractable forms...
Abstract

This article discusses the fundamental aspects of phase-field microstructure modeling. It describes the evolution of microstructure modeling, including nucleation, growth, and coarsening. The article reviews two approaches used in the modeling nucleation of microstructure: the Langevin force approach and explicit nucleation algorithm. Calculation of activation energy and critical nucleus configuration is discussed. The article presents the deterministic phase-field kinetic equations for modeling growth and coarsening of microstructure. It also describes the material-specific model inputs, chemical free energy and kinetic coefficients, for phase-field microstructure modeling. The article provides four examples that illustrate some aspects of phase-field modeling.

Series: ASM Desk Editions

Publisher: ASM International

Published: 01 December 1998

DOI: 10.31399/asm.hb.mhde2.a0003085

EISBN: 978-1-62708-199-3

... components, A and B. The result is a series of plots similar to those in Fig. 13 (a) to 13 (e). Fig. 13 Use of

**Gibbs****energy****curves**to construct a binary phase diagram that shows miscibility in both the liquid and solid states. Source: adapted from Ref 2 At temperature T 1 , the liquid...
Abstract

Alloy phase diagrams are useful for the development, fabrication, design and control of heat treatment procedures that will produce the required mechanical, physical, and chemical properties of new alloys. They are also useful in solving problems that arise in their performance in commercial applications, thus improving product predictability. This article describes different equilibrium phase diagrams (unary, binary, and ternary) and microstructures, description terms, and general principles of reading alloy phase diagrams. Further, the article discusses plotting schemes; areas in a phase diagram; and the position and shapes of the points, lines, surfaces, and intersections, which are controlled by thermodynamic principles and properties of all phases that comprise the system. It also illustrates the application of the stated principles with suitable phase diagrams.

Series: ASM Handbook

Volume: 9

Publisher: ASM International

Published: 01 December 2004

DOI: 10.31399/asm.hb.v09.a0003732

EISBN: 978-1-62708-177-1

... , Metallography and Microstructures , Vol 9 , ASM Handbook , ASM International , 1985 , p 652 – 654 A simple binary phase diagram with a region of spinodal decomposition is shown in Fig. 2(a) with a corresponding

**free**-**energy****curve**( Fig. 2b ). If a composition X 0 is heated above the critical...Book Chapter

Series: ASM Handbook

Volume: 13C

Publisher: ASM International

Published: 01 January 2006

DOI: 10.31399/asm.hb.v13c.a0004225

EISBN: 978-1-62708-184-9

... change in quantity; an increment; a range Δ E therm thermodynamic driving force Δ G

**Gibbs****free****energy**Δ G o standard**Gibbs****free****energy**Δ H change in enthalpy Δ K stress-intensity factor range Δ S entropy change ε p plastic strain range ε t total...Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005226

EISBN: 978-1-62708-187-0

... ). The eutectic temperature and composition for white cast iron are well-defined thermodynamic quantities, just as they are for gray cast iron. Metastable equilibrium at any temperature is given by a common tangent construction to the molar

**free****energy**versus composition**curves**for the liquid, austenite...
Abstract

Rapid solidification is a tool for modifying the microstructure of alloys that are obtained by ordinary casting. This article describes the fundamentals of the four microstructural changes, namely, microsegregation, identity of the primary phase, identity of the secondary phase, and formation of noncrystalline phases. It considers three factors: heat flow, thermodynamic constraints/conditions at the liquid-solid interfaces, and diffusional kinetics/microsegregation, to understand the fundamentals of these changes. These factors are described in detail.

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005209

EISBN: 978-1-62708-187-0

... distribution coefficient k = 1. In this limiting case, the

**Gibbs****free****energies**of both phases are equal, but the chemical potentials are not. This can be expressed through the following equations for the interface temperature, T *, and the nonequilibrium liquidus slope, m( V ) ( Ref 18 ): (Eq 22) T...
Abstract

One impressive example of plane front solidification (PFS) is the industrial production of large silicon single crystals, used mainly as substrates for integrated circuits. This article explores the PFS of a single phase, without taking convection into account. It discusses the solute build-up at the solid-liquid interface forming transients and steady state, the morphological stability/instability and perturbation theory, and rapid solidification effects, including solute trapping and oscillatory instabilities. The article presents a microstructural selection map that gives an overview of interface stability as a function of composition for a given alloy.

Series: ASM Handbook

Volume: 9

Publisher: ASM International

Published: 01 December 2004

DOI: 10.31399/asm.hb.v09.a0003731

EISBN: 978-1-62708-177-1

... ) therefore occurs at a higher solute concentration. Fig. 5

**Gibbs****free**-**energy**composition diagram (a) and locus of solvus**curves**(b) of metastable and stable equilibrium phases in a precipitation sequence. (a) The points of common tangency show the relationship between compositions of the matrix phase...
Abstract

Precipitation reactions occur in many different alloy systems when one phase transforms into a mixed-phase system as a result of cooling from high temperatures. This article discusses the homogenous and heterogeneous nucleation and growth of coherent and semicoherent precipitates. It describes two precipitation modes, namely, general or continuous precipitation and cellular or discontinuous precipitation. The article also provides information on the precipitation sequences in aluminum alloys.

Series: ASM Handbook

Volume: 13A

Publisher: ASM International

Published: 01 January 2003

DOI: 10.31399/asm.hb.v13a.a0003601

EISBN: 978-1-62708-182-5

... phase is the electrolyte containing cations of the metal. The tendency of metals to oxidize during battery discharge is reflected in the usually substantial negative

**Gibbs****free**-**energy**change for the reactions in Eq 1 or 2 . Metals that oxide more readily have more negative**Gibbs****free**-**energy**changes...
Abstract

This article examines constructive corrosion that occurs in power-generating devices, specifically batteries. It discusses the kinetic aspects of constructive corrosion in batteries and provides examples to illustrate how the kinetics of a corrosion process varies among different battery systems. The article illustrates the constructive roles played by corrosion at anodes in batteries through the use of a zinc anode in a mercury battery and a lithium metal anode in a rechargeable lithium battery. It also outlines the destructive role played by corrosion by illustrating shelf reactions in zinc-carbon batteries and lead grid corrosion in lead-acid batteries.

Series: ASM Handbook

Volume: 22B

Publisher: ASM International

Published: 01 November 2010

DOI: 10.31399/asm.hb.v22b.a0005511

EISBN: 978-1-62708-197-9

... F.J. , “Computational Thermodynamic Study to Predict Complex Phase Equilibria in the Nickel-Base Superalloy Rene N6,” NASA/TM , 2001 - 210897 26. Wlodek S.T. , The Structure of IN100 , Trans. ASM , Vol 57 , 1964 , p 110 – 119 27. Ross E.W. , Rene 100—A Sigma-

**Free**...
Abstract

This article focuses on the industrial applications of phase diagrams. It presents examples to illustrate how a multicomponent phase diagram calculation can be readily useful for industrial applications. The article demonstrates how the integration of a phase diagram calculation with kinetic and microstructural evolution models greatly enhances the power of the CALPHAD approach in materials design and processing development. It also discusses the limitations of the CALPHAD approach.

Series: ASM Handbook

Volume: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005410

EISBN: 978-1-62708-196-2

... driving force and the interface

**free****energy**. A kinetic approach, cluster dynamics, can also be used to describe nucleation. This constitutes the second part of this article. Here, a master equation describes the time evolution of the system, which is modeled as a cluster gas. The key parameters are the...
Abstract

This article describes the results obtained by Volmer, Weber, Farkas, Becker, and Doring, which constitute the classical nucleation theory. These results are the predictions of the precipitate size distribution, steady-state nucleation rate, and incubation time. The article reviews a nucleating system as a homogeneous phase using the classical nucleation theory, along with heterophase fluctuations that led to the formation of precipitates. It discusses the gas cluster dynamics using the kinetic approach to describe nucleation. The article presents key parameters, such as cluster condensation and evaporation rates, to describe the time evolution of the system. The predictions and extensions of the classical nucleation theory are discussed. The article also provides the limitations of classical nucleation theories in cluster dynamics.

Series: ASM Handbook

Volume: 13A

Publisher: ASM International

Published: 01 January 2003

DOI: 10.31399/asm.hb.v13a.a0003580

EISBN: 978-1-62708-182-5

... the most probable electrochemical reactions occurring in a solution containing a specific element. The standard equilibrium potentials are computed from thermodynamic data (standard chemical potentials, or

**Gibbs****free****energies**of formation). The equilibrium relations drawn for a given concentration of...
Abstract

A potential pH diagram is a graphical representation of the relations, derived from the Nernst equation, between the pH and the equilibrium potentials (E) of the most probable electrochemical reactions occurring in a solution containing a specific element. This article describes three types of reactions for calculation and construction of E-pH diagrams: electrochemical reactions of pure charge (electron) transfer; reactions involving both electron and solvated proton transfer; and acid-base reactions of pure solvated proton transfer. It illustrates the practical use of E-pH diagrams for temperature aqueous solutions and adsorbed species and in prediction of corrosion of nickel and copper.

Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006229

EISBN: 978-1-62708-163-4

... spinodal decomposition is shown in Fig. 14(a) with a corresponding

**free**-**energy****curve**( Fig. 14b ). If a composition, X 0 , is heated above the critical temperature, T c , the binary system is in the region of full solid solubility with a single-phase field, α 0 , at temperature T 0 . When the...
Abstract

In some phase diagrams, the appearance of several reactions is the result of the presence of intermediate phases. These are phases whose chemical compositions are intermediate between two pure metals, and whose crystalline structures are different from those of the pure metals. This article describes the order-disorder transformation that typically occurs on cooling from a disordered solid solution to an ordered phase. It provides a table that lists selected superlattice structures and alloy phases that order according to each superlattice. The article informs that spinodal decomposition has been particularly useful in the production of permanent magnet materials, because the morphologies favor high magnetic coercivities. It also describes the theory of spinodal decomposition with a simple binary phase diagram.

Book Chapter

Series: ASM Handbook

Volume: 4E

Publisher: ASM International

Published: 01 June 2016

DOI: 10.31399/asm.hb.v04e.a0006250

EISBN: 978-1-62708-169-6

... lattice at equilibrium is a consequence of a balance between the

**energy**(Δ H ) required to form the vacancies and the entropy Δ S created by their presence at absolute temperature ( T ). Thus, there is an equilibrium concentration that minimizes the**free****energy**change (Δ G = Δ H − T Δ S ). If a...
Abstract

This article introduces the mechanism of diffusion and the common types of heat treatments such as annealing and precipitation hardening, which are applicable to most ferrous and nonferrous systems. Three distinct processes occur during annealing: recovery, recrystallization, and grain growth. The article also describes the various types of solid-state transformations such as isothermal transformation and athermal transformation, resulting from the heat treatment of nonferrous alloys. It provides information on the homogenization of chemical composition within a cast structure.

Series: ASM Handbook

Volume: 22B

Publisher: ASM International

Published: 01 November 2010

DOI: 10.31399/asm.hb.v22b.a0005507

EISBN: 978-1-62708-197-9

... Inclination of grain boundary σ Surface tension D Diameter g

**Gibbs****free****energy**per unit volume H Enthalpy, magnetic field strength k Boltzmann constant, 1.38066 × 10 −23 J/K R Radius of curvature Φ Interatomic potential r ij Atomic distance γ Grain-boundary...
Abstract

Grain boundaries are interfaces between crystallites of the same phase but different crystallographic orientation. They can be characterized as being low angle or high angle. This article discusses the measurements of grain-boundary energy with a brief summary of different schemes for measuring grain-boundary surface tension. The atomistic simulations of grain-boundary energy, measurement of grain-boundary migration and the techniques used to monitor grain-boundary migration are reviewed. Several considerations and effects influencing the computation of grain-boundary mobility are also discussed.

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005236

EISBN: 978-1-62708-187-0

... adapted. The general aspects of the PF method are only briefly outlined. For a more complete review see ( Ref 21 ). In general, a PF model starts from an appropriate thermodynamic function. For solidification under constant pressure, the

**Gibbs****free****energy**F is used. It is the integral over the**free**...
Abstract

Modeling of structure formation in casting of alloys involves several length scales, ranging from the atomic level to macroscopic scale. Intermediate length scales are used to define the microstructure of the growing phases and the grain structure. This article discusses the principles and applications of phase field method and cellular automaton method for modeling the direct evolution of structure at the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure that involves nucleation and growth.