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**Published:**27 April 2016

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.

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**Published:**01 November 2010

Fig. 1 Solidification paths of a 2219 aluminum alloy, temperature versus solid fraction, from two models and the lever rule. L, liquid; fcc, face-centered cubic
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**Published:**01 December 2008

Fig. 2 Temperature versus fraction solid curves of three iron-carbon alloys: Fe-0.8wt%C, Fe-3wt%C, and Fe-4wt%C. These curves are obtained using a lever rule.
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**Published:**01 December 1998

Fig. 15 Portion of a binary phase diagram containing a two-phase liquid-plus-solid field illustrating (a) application of the lever rule to (b) equilibrium freezing, (c) nonequilibrium freezing, and (d) heating of a homogenized sample. Source: Ref 1
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in Physical Metallurgy Concepts in Interpretation of Microstructures
> Metallography and Microstructures

**Published:**01 December 2004

of alloy A-B completely solidify after slow (equilibrium) cooling. (c) The lever rule can be used to determine phase compositions and volume fractions at intermediate points along the solidus and liquidus lines when alloy A-B freezes under equilibrium conditions. See text in the section “Isomorphous Alloy
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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

... for determining phase fractions has come to be known as the lever rule. Metastable Phase Diagrams Metastable equilibria occur when a phase is missing, for example, if the phase fails to nucleate. The failure of an equilibrium phase to form may result in the formation of a metastable phase. In 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.

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005217

EISBN: 978-1-62708-187-0

... phase diagram, the liquidus temperature for this alloy is 1268 °C (2314 °F). At this temperature, dendritic crystals of austenite are formed. Because carbon has a very high diffusivity in austenite, the lever rule can be used to determine the fraction of solid as a function of temperature. The lever...

Abstract

Thermal analysis is a classical method of determining phase diagrams and can be used to analyze the deviation from solidification under equilibrium conditions. This article discusses the use of thermal analysis in industrial processes and in research. It describes the theoretical basis of simplified and differential thermal analysis. Techniques for determining liquidus and solidus temperatures using cooling curves are also discussed.

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005222

EISBN: 978-1-62708-187-0

... of solidification. Fig. 2 Temperature versus fraction solid curves of three iron-carbon alloys: Fe-0.8wt%C, Fe-3wt%C, and Fe-4wt%C. These curves are obtained using a lever rule. For the Fe-3wt%C alloy, 58% of the solid forms as primary austenite dendrites in the temperature range between 1150 and 1300...

Abstract

This article provides a detailed discussion on the causes of formation of shrinkage porosity and gas porosity along with the methods involved in eliminating them. It discusses the process of porosity formation and the factors affecting porosity formation, including alloy composition, external pressure, and cooling conditions.

Series: ASM Desk Editions

Publisher: ASM International

Published: 01 December 1998

DOI: 10.31399/asm.hb.mhde2.a0003085

EISBN: 978-1-62708-199-3

... B 3 for the low-temperature form and βA 2 B 3 for the high-temperature form). Lever Rule As explained in the section on “Thermodynamics and Phase Diagrams,” a tie line is an imaginary horizontal line drawn in a two-phase field connecting two points that represent two coexisting phases...

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.a0006224

EISBN: 978-1-62708-163-4

... can be obtained from phase diagrams for the mathematical treatment of solidification processes. Two simple models can describe the limiting cases of solidification behavior. For solidification obeying the lever rule at each temperature during cooling, complete diffusion is assumed in the solid...

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.a0006231

EISBN: 978-1-62708-163-4

... a phase, for example an embrittling phase, or to promote a phase, for example a precipitation-hardening phase. By drawing these lines, the reader can focus on one phase at a time and ignore the lines that concern other phases. Although it is true that the lever rule cannot be used here, it can...

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 Handbook Archive

Volume: 10

Publisher: ASM International

Published: 01 January 1986

DOI: 10.31399/asm.hb.v10.a0001752

EISBN: 978-1-62708-178-8

... intensity of the two signals can be used to provide quantitative information on the positions of the phase boundaries. The second method will be discussed. Use of a technique such as NMR, which depends on sensing atomic nuclei, can provide an advantage over the usual lever rule of metallurgy...

Abstract

Nuclear magnetic resonance (NMR) is a form of radio frequency spectroscopy based on interactions between nuclear magnetic dipole or electric quadrupole moments and an applied magnetic field or electric-field gradient. This article provides an overview of the fundamental principles of nuclear magnetic resonance with emphasis on nuclei properties, the basic equation of nuclear magnetic resonance, the classical theory of nuclear magnetization, line broadening, and measurement sensitivity. It describes the pulse-echo method for observing NMR. The article provides useful information on ferromagnetic nuclear resonance and nuclear quadrupole resonance, and illustrates the experimental arrangement of NMR with a block diagram. It also presents several application examples.

Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006227

EISBN: 978-1-62708-163-4

... forms first. The liquid composition shifts toward the monotectic composition of 36 wt% Pb. Then, the liquid transforms to more solid α and a second liquid containing 87 wt% Pb. The lever rule provides that only a very small amount of the second liquid is present. On further cooling, the second liquid...

Abstract

Monotectic alloys can be classified based on the difference between the critical temperature and the monotectic temperature. This article begins with a schematic illustration of monotectic reaction in copper-lead system. It discusses the solidification structures of monotectics and illustrates the monotectic solidification for low-dome alloys. The forming mechanism of the banded structure of copper-lead alloy in upward directional solidification is also described.

Book Chapter

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005214

EISBN: 978-1-62708-187-0

... solidify to α-crystals and then transform to stable β-crystals. Alloys between I and II also solidify to α-crystals, but they are partially transformed to β-crystals later. Fig. 2 Phase diagram with a peritectic reaction The volume fraction of each phase will be given by the lever rule...

Abstract

This article describes the three solidification mechanisms of peritectic structures, namely, peritectic reaction, peritectic transformation, and direct precipitation. It discusses the theoretical analysis, which shows that the rate of the peritectic transformation is influenced by the diffusion rate and the extension of the beta-phase region in the phase diagram. The article also provides information on the peritectic transformations in multicomponent systems.

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.

Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006226

EISBN: 978-1-62708-163-4

... solidify to α crystals, but they are partially transformed to β crystals later. The volume fraction of each phase is determined with the lever rule if the alloy solidifies under equilibrium conditions. In practice, the lever rule usually will not give the volume fraction of the different phases from...

Abstract

Similar to the eutectic group of invariant transformations is a group of peritectic reactions, in which a liquid and solid phase decomposes into a solid phase on cooling through the peritectic isotherm. This article describes the equilibrium freezing and nonequilibrium freezing of peritectic alloys. It informs that peritectic reactions or transformations are very common in the solidification of metals. The article discusses the formation of peritectic structures that can occur by three mechanisms: peritectic reaction, peritectic transformation, and direct precipitation of beta from the melt. It provides a discussion on the peritectic structures in iron-base alloys and concludes with information on multicomponent systems.

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.

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

... when phase mixtures are present. Suppose an alloy consists of two phases, α and β, each of which has a molar free energy given by G α and G β , 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...

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: 20

Publisher: ASM International

Published: 01 January 1997

DOI: 10.31399/asm.hb.v20.a0002437

EISBN: 978-1-62708-194-8

...-probability situations. Inductive logic Can go from specific cases to general rules or laws. No good at inductive logic. Distraction Easily distracted by competing stimuli. Cannot be distracted by competing stimuli. Source: Ref 4 Further Design Guidelines The designer certainly must...

Abstract

The central approach of human factors engineering is the systemic application of relevant information about human characteristics and behavior to the design of human-made objects, facilities, and environments that people use. This article focuses on the elements that are considered for an acceptable level of human performance. These include the state or condition of the human being; the activity, including equipment and required tools; and the context in which the activity is performed.

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