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#### Gibbs phase rule

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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.a0006221

EISBN: 978-1-62708-163-4

.../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...

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.

Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006224

EISBN: 978-1-62708-163-4

... methods to determine a phase diagram with equilibrated alloys: the static method and the dynamic method. The article illustrates the construction of phase boundaries according to the Gibbs' phase rule and describes the calculation methods that allow the prediction of the phases present, the chemical...

Abstract

The term isomorphous refers to metals that are completely miscible in each other in both the liquid and solid states. This article discusses the construction of simple phase diagrams by using the appropriate points obtained from time-temperature cooling curves. It describes the two methods to determine a phase diagram with equilibrated alloys: the static method and the dynamic method. The article illustrates the construction of phase boundaries according to the Gibbs' phase rule and describes the calculation methods that allow the prediction of the phases present, the chemical compositions of the phases present, and the amounts of phases present. Phase diagrams provide useful information for understanding alloy solidification. The article provides two simple models that can describe the limiting cases of solidification behavior.

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005206

EISBN: 978-1-62708-187-0

... the fraction of the other solid phase(s) is zero, that is, the limit where the solvent phase is saturated with the solute constituents, and higher concentrations result in the precipitation of other solid phases. The degrees of freedom, F , of a phase region are governed by the Gibbs phase rule: (Eq 14...

Abstract

This article discusses the application of thermodynamic in the form of phase diagrams for visually representing the state of a material and for understanding the solidification of alloys. It presents the derivation of the relationship between the Gibbs energy functions and phase diagrams, which forms the basis for the calculation of phase diagrams (CALPHAD) method. The article also discusses the calculation of phase diagrams and solidification by using the Scheil-Gulliver equation.

Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006231

EISBN: 978-1-62708-163-4

... application of the Gibbs phase rule, it should be recalled that one degree of freedom has been exercised in the initial construction of the 3-D diagram by electing to draw it at one atmosphere of pressure. Space Model of Ternary Systems To completely represent the phase equilibria at constant pressure...

Abstract

This article describes the liquidus plots, isothermal plots, and isopleth plots used for a hypothetical ternary phase space diagram. It discusses the single-phase boundary (SPB) line and zero-phase fraction (ZPF) line for carbon-chromium-iron isopleth. The article illustrates the Gibbs triangle for plotting ternary composition and discusses the ternary three-phase phase diagrams by using tie triangles. It describes the peritectic system with three-phase equilibrium and ternary four-phase equilibrium. The article presents representative binary iron phase diagrams, showing ferrite stabilization (iron-chromium) and austenite stabilization (iron-nickel).

Series: ASM Desk Editions

Publisher: ASM International

Published: 01 December 1998

DOI: 10.31399/asm.hb.mhde2.a0003085

EISBN: 978-1-62708-199-3

... Sexinary Seven Septenary Eight Octanary Nine Nonary Ten Decinary Phase Rule The phase rule, first announced by J. Willard Gibbs in 1876, relates the physical state of a mixture to the number of constituents in the system and to its conditions. It was also Gibbs that first called...

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.

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.

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

... and pressure. In this case the three phases that can exist correspond to three states of matter: vapor, liquid, and solid. The interpretation of equilibrium diagrams is made easy by the following rule: Only points in the diagram have physical significance. Because the variables are temperature and pressure...

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.

Series: ASM Handbook

Volume: 22B

Publisher: ASM International

Published: 01 November 2010

DOI: 10.31399/asm.hb.v22b.a0005517

EISBN: 978-1-62708-197-9

..., and so on. In multicomponent space, such things are often very difficult to understand, let alone conceptualize. Miscibility gaps can appear in ternary and higher-order systems, even though no miscibility gap exists in the lower-order systems, and the Gibbs phase rule becomes vitally important...

Abstract

This article presents the background to the CALculation of PHAse Diagrams (CALPHAD) method, explaining how it works, and how it can be applied in industrial practice. The extension of CALPHAD methods as a core basis for the modeling of generalized material properties is explored. It informs that one of the aims of CALPHAD methods has been to calculate phase equilibria in the complex, multicomponent alloys that are used regularly by industry. The article discusses the application of CALPHAD calculations to industrial alloys. Modeling of general material properties, such as thermophysical and physical properties, temperature- and strain-rate-dependent mechanical properties, properties for use in the modeling of quench distortion, and properties for use in solidification modeling, is also reviewed. The article also describes the linking of thermodynamic, kinetic, and material property models.

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

.... annealing castings deformation diffusion coefficient grain growth heat treatment heterogeneous nucleation homogeneous nucleation homogenization isothermal transformation nonferrous metals precipitation hardening recrystallization recrystallization temperature solid-state phase transformation...

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.

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

... potentials and temperature (and pressure) are uniform throughout the system. Global equilibrium is invoked at each time instant during cooling for descriptions of solidification that apply the lever rule. At each instant, the system has a uniform temperature and each phase has a uniform composition given...

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 the formation of noncrystalline phases. It considers three factors to understand the fundamentals of these changes: heat flow, thermodynamic constraints/conditions at the liquid-solid interfaces, and diffusional kinetics/microsegregation. These factors are described in detail.

Series: ASM Handbook

Volume: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005406

EISBN: 978-1-62708-196-2

... solidification any material separates into two (or more) different phases: liquid and solid (or different solid phases). The clear reason is the minimization of the total Gibbs energy as the sum of the Gibbs energies of the individual phases weighted by the phase fractions. Neglecting surface energy, the PF...

Abstract

This article focuses on the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of a structure. It presents the cellular automaton (CA) and phase field (PF) methods that represent the state of the art for modeling macrostructure and microstructure. The article describes the principles of the PF method and provides information on the applications of the PF method. The CA model is introduced as a computationally efficient method to predict grain structures in castings using the mesoscopic scale of individual grains. The article discusses the coupling of the CA to macroscopic calculation of heat, flow, and mass transfers in castings and applications to realistic casting conditions.

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

...). The clear reason is the minimization of the total Gibbs energy as the sum of the Gibbs energies of the individual phases weighted by the phase fractions. Neglecting surface energy, the PF and concentration equations described previously will tend to the thermodynamic equilibrium as the minimum of Gibbs...

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 the phase field method and the 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.

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

... 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...

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.

Series: ASM Handbook

Volume: 13A

Publisher: ASM International

Published: 01 January 2003

DOI: 10.31399/asm.hb.v13a.a0003582

EISBN: 978-1-62708-182-5

... be determined. Many natural systems, especially at low temperatures, are not in equilibrium. The calculated values for pe and E H can help ascertain the disequilibrium of a system. All of the previously described calculations in the geochemical model are subject to Gibb's phase rule, better known...

Abstract

Geochemical modeling is being used to understand and predict scaling, susceptibility to corrosion, atmospheric corrosion rates, acid rain, corrosion film solubility, and environmental impacts of aqueous species in runoff. This article discusses the principles, limitations, and applications of the modeling. It explains how to calculate the chemical equilibrium in geochemical modeling and provides information on modeling features.

Series: ASM Handbook

Volume: 4A

Publisher: ASM International

Published: 01 August 2013

DOI: 10.31399/asm.hb.v04a.a0005818

EISBN: 978-1-62708-165-8

... and nitrocarburizing of iron-base materials with gaseous processes. It describes nitriding potentials and the Lehrer diagram, carburizing potentials, controlled nitriding and nitrocarburizing, and the microstructural evolution of the compound layer and the diffusion zone. carburizing iron-nitrogen phase diagram...

Abstract

The nitriding process typically involves the introduction of nitrogen into the surface-adjacent zone of a component, usually at a temperature between 500 and 580 deg C. This article provides an overview of the essential aspects of the thermodynamics and kinetics of nitriding and nitrocarburizing of iron-base materials with gaseous processes. It describes nitriding potentials and the Lehrer diagram, carburizing potentials, controlled nitriding and nitrocarburizing, and the microstructural evolution of the compound layer and the diffusion zone.

Series: ASM Handbook

Volume: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005409

EISBN: 978-1-62708-196-2

... to appropriate boundary and initial conditions. For the case in which the platelet and matrix phases are both terminal solid solutions, the latter relations comprise the classical Gibbs-Thomson equation, the equilibrium equation ( Eq 3 reformatted in terms of the groove slope), and the initial condition...

Abstract

This article focuses on the modeling of microstructure evolution during thermomechanical processing in the two-phase field for alpha/beta and beta titanium alloys. It also discusses the mechanisms of spheroidization, the coarsening, particle growth, and phase decomposition in titanium alloys, with their corresponding equations.

Series: ASM Handbook

Volume: 22B

Publisher: ASM International

Published: 01 November 2010

DOI: 10.31399/asm.hb.v22b.a0005501

EISBN: 978-1-62708-197-9

... used to predict the equilibrium and phase relationships in multicomponent alloys ( Ref 3 , Ref 4 , Ref 5 ). Currently, several packages are able to simulate solidification using the Scheil model and lever rule, such as Thermo-Calc, Pandat, and JMatPro. It is critical to have an accurate...

Abstract

This article reviews the topic of computational thermodynamics and introduces the calculation of solidification paths for casting alloys. It discusses the calculation of thermophysical properties and the fundamentals of the modeling of solidification processes. The article describes several commonly used microstructure simulation methods and presents ductile iron casting as an example to demonstrate the ability of microstructure simulation. The predictions for the major defects of casting, such as porosity, hot tearing, and macrosegregation, are highlighted. Finally, several industry applications are presented.

Series: ASM Handbook

Volume: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005425

EISBN: 978-1-62708-196-2

.... The refinement of models and modeling methods results in greater capability and accuracy of metallurgical predictions, such as phase equilibria, microstructure, and subsequent mechanical properties. The ability to rapidly apply fundamental models to practical component design and manufacturing applications has...

Abstract

This article provides a brief historical perspective, a classification of metallurgical processes, basic model development efforts, and an overview of the potential future directions for the modeling of metals processing. It describes the classification of material behavior models, which can be grouped broadly into three classes: statistical, phenomenological, and mechanistic models. The article also presents an overview of the potential directions for the modeling of metals processing.

Series: ASM Handbook

Volume: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005439

EISBN: 978-1-62708-196-2

... Abstract This article presents various equations that are essential for the modeling of both single-phase and multiphase profiles. It includes the fundamental laws of diffusion, along with its equations and solutions. The article provides information on the series of applications...

Abstract

This article presents various equations that are essential for the modeling of both single-phase and multiphase profiles. It includes the fundamental laws of diffusion, along with its equations and solutions. The article provides information on the series of applications that illustrate how various diffusional processes can be modeled.

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005210

EISBN: 978-1-62708-187-0

... is the diffusion coefficient in the solid, and L is the distance between the cells. The modified equation ensures that the Scheil-Gulliver equation is obtained when D s = 0, and lever rule is obtained when D s = ∞. For single-phase solidification in which the diffusion in the solid is important...

Abstract

Nonplanar microstructures form most frequently during the solidification of alloys, and play a crucial role in governing the properties of the solidified material. This article emphasizes the basic ideas, characteristic lengths, and the processing conditions required to control the columnar and equiaxed microstructures. The formation of cellular and dendritic structures in one- and two-phase structures is presented with emphasis on the effect of processing conditions and composition on the selection of microstructure and microstructure scales.

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