Skip Nav Destination
Filter
Filter
Filter
Filter
Filter

Search Results for
Gibbs phase rule

Update search

Filter

- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References

- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References

- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References

- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References

- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References

- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References

### NARROW

Format

#### Topics

Book Series

Date

Availability

1-20 of 56 Search Results for

#### Gibbs phase rule

**Follow your search**

Access your saved searches in your account

Would you like to receive an alert when new items match your search?

*Close Modal*

Sort by

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 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

... , respectively ( Fig. 20 ). If the overall composition of the

**phase**mixture is X B 0 , the lever**rule**gives the relative number of moles of α and β that must be present, and the molar free energy of the**phase**mixture, G , is given by the point on the straight line between α and β, as shown in the figure...
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.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. References 1. Askeland D.R. , The Science and...
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).

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

...

**phase**diagram is usually determined from direct measurement of concentrations and temperature, it is important to understand the underlying thermodynamic basis for these diagrams, since it creates**rules**that experimentally determined**phase**diagrams must obey. Fig. 1 Relation between the**Gibbs**...
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.

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 Variant Selection

**Rules**for Grain Boundary α in Titanium Alloys , Acta Mater ., Vol 102 , 2016 , p 197 – 211 10.1016/j.actamat.2015.09.021 138. Gey N. , Humbert M. , Philippe M.J. , and Combres Y. , Investigation of the Alpha- and Beta-Texture Evolution of Hot...
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 Desk Editions

Publisher: ASM International

Published: 01 December 1998

DOI: 10.31399/asm.hb.mhde2.a0003085

EISBN: 978-1-62708-199-3

... would require construction of a three-dimensional graph. Most metallurgical problems, however, are concerned only with a fixed pressure of one atmosphere, and the graph reduces to a two-dimensional plot of temperature and composition ( TX ) diagram. The

**Gibbs****phase****rule**applies to all states of...
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.a0006222

EISBN: 978-1-62708-163-4

... 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, evidently a point is...
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: 13A

Publisher: ASM International

Published: 01 January 2003

DOI: 10.31399/asm.hb.v13a.a0003698

EISBN: 978-1-62708-182-5

... concluded that VCIs of the amine type are capable of forming the protective layers for up to 3 months and exhibit a posttreatment effect on the metal surfaces due to irreversible adsorption. The tendency of irreversible adsorption of a VCI depends on its chemical structure. As a

**rule**, low-molecular- weight...
Abstract

This article discusses the definitions, classifications, structural features, vapor pressure values, corrosion inhibition mechanisms, and methods of evaluation of vapor-phase-corrosion inhibitors or volatile corrosion inhibitors (VCIs). Practical methods of using VCIs for corrosion protection of aluminum, ferrous, and nonferrous alloys are discussed with specific examples. The article contains tables that summarize the applications of different VCIs used for protecting ferrous metals, copper and its alloys, and silver.

Series: ASM Handbook

Volume: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005434

EISBN: 978-1-62708-196-2

... drastically change the composition of the gas

**phase**. As a**rule**of thumb, the higher the pressure and temperature, the higher the importance of homogeneous reactions. To perform reliable simulations of CVD processes, a chemical scheme must be included in the coupled transfer model, which at least captures the...
Abstract

This article focuses on transport phenomena and modeling approaches that are specific to vapor-phase processes (VPP). It discusses the VPP for the synthesis of materials. The article reviews the basic notions of molecular collisions and gas flows, and presents transport equations. It describes the modeling of vapor-surface interactions and kinetics of hetereogeneous processes as well as the modeling and kinetics of homogenous reactions in chemical vapor deposition (CVD). The article provides information on the various stages of developing models for numerical simulation of the transport phenomena in continuous media and transition regime flows of VPP. It explains the methods used for molecular modeling in computational materials science. The article also presents examples that illustrate multiscale simulations of CVD or PVD processes and examples that focus on sputtering deposition and reactive or ion beam etching.

Book Chapter

Series: ASM Handbook

Volume: 10

Publisher: ASM International

Published: 15 December 2019

DOI: 10.31399/asm.hb.v10.a0006646

EISBN: 978-1-62708-213-6

... TiFe. This cubic

**phase**, based on TiFe, is termed α. The spectrum for a composition of TiFeH 0.9 , spectrum B, can be resolved into two lines: one identified with α and the second, a quadrupole doublet, associated with a noncubic β-**phase**. The lever**rule**can be used to determine the location of this...
Abstract

The Mossbauer effect (ME) is a spectroscopic method for observing nuclear gamma-ray fluorescence using the recoil-free transitions of a nucleus embedded in a solid lattice. This article provides an overview of the fundamental principles of ME, covering recoil-free fraction, absorption, selection rules, gamma-ray polarization, isomer shift, quadrupole interaction, and magnetic interaction. Experimental arrangement for obtaining ME spectra is described and several examples of the applications of ME are presented. The article contains tables listing some properties of Mossbauer transitions and principal methods used for producing ME sources.

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

... 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 by the**phase**diagram. As time progresses, the temperature drops, the compositions of the**phases**change...
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.

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

... alloy must be represented. A

**Gibbs**energy minimization must be performed so that the**phase**equilibria between the requisite**phases**can be calculated. While thermodynamic modeling provides useful information on specific aspects of materials processing, modern-day simulation...
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: 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

..., solute composition of the liquid, and volume fraction of solid. This can be carried out by applying a simple microsegregation model, such as the lever-

**rule**approximation deduced from the**phase**diagram data, at the microscopic scale of the dendrite arm spacing. In such a purely macroscopic calculation...
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.

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

...

**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 (an initially flat interface). Hence, the complete set of equations is as follows: (Eq 4a...
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: 4B

Publisher: ASM International

Published: 30 September 2014

DOI: 10.31399/asm.hb.v04b.a0005936

EISBN: 978-1-62708-166-5

... tempering of steel components in order to optimize tribological properties. It focuses on the heat treatment of tempering and bearing steels and on volume changes that take place due to

**phase**transformations. Plastic deformations that occur due to shrinking and**phase**transformation are also discussed. The...
Abstract

In the case of steels, heat treatment plays a fundamental role because no other process step can manipulate the microstructure in order to fulfill such a wide variety of possible in-service conditions. This article addresses heat treatment with regard to hardening and subsequent tempering of steel components in order to optimize tribological properties. It focuses on the heat treatment of tempering and bearing steels and on volume changes that take place due to phase transformations. Plastic deformations that occur due to shrinking and phase transformation are also discussed. The article also describes the generation of thermal, transformation, and hardening residual stresses.

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

... enthalpy and solute composition are converted into evolutions of temperature, solute composition of the liquid, and volume fraction of solid. This can be carried out by applying a simple microsegregation model, such as the lever-

**rule**approximation deduced from the**phase**diagram data, at the microscopic...
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.

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

... detected for ternary systems by plotting composition data as diffusion paths on

**phase**diagrams. If the program assumes local equilibrium, then**rules**must be followed for how the diffusion path can appear (see the section “Zero-Flux Planes” in this article as well as Ref 15 , 31 , and 32 ). Special...
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

... − exp ( − 1 / α ) ] − 0.5 exp ( − 1 2 α ) D s 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...
Abstract

Nonplanar microstructures form most frequently during the solidification of alloys, and they 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.

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

... dislocation content is given by Frank's

**rule**( Ref 5 ): (Eq 1) B = Σ c i ( Y ) b i = 2 sin ω 2 ( Y × a ) where Y is an arbitrary vector in the grain boundary; B is the closure failure, that is, the sum of the Burgers vectors, b i , of the...
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.