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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

... 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 as well as in the liquid. Thus, all phases are assumed to be in thermodynamic...
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

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.

Series: ASM Handbook Archive

Volume: 11

Publisher: ASM International

Published: 01 January 2002

DOI: 10.31399/asm.hb.v11.a0003517

EISBN: 978-1-62708-180-1

... article discusses metallurgical instabilities of steel-based alloys and nickel-base superalloys. It provides information on several life assessment methods, namely, the life fraction

**rule**, parameter-based assessments, the thermal-mechanical fatigue, coating evaluations, hardness testing, microstructural...
Abstract

This article focuses on the life assessment methods for elevated-temperature failure mechanisms and metallurgical instabilities that reduce life or cause loss of function or operating time of high-temperature components, namely, gas turbine blade, and power plant piping and tubing. The article discusses metallurgical instabilities of steel-based alloys and nickel-base superalloys. It provides information on several life assessment methods, namely, the life fraction rule, parameter-based assessments, the thermal-mechanical fatigue, coating evaluations, hardness testing, microstructural evaluations, the creep cavitation damage assessment, the oxide-scale-based life prediction, and high-temperature crack growth methods.

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

.... This technique for determining phase fractions has come to be known as the

**lever****rule**. Phase diagrams provide useful information for understanding the solidification of alloys. In addition to the liquidus and final freezing temperatures, important quantities for the mathematical treatment of...
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

... 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****rule**can be applied to any two-phase...
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. The article explains how to determine the liquidus and solidus temperatures by using cooling curves.

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

... eutectic phase formation at the late stage 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...
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.

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

...-rich α phase 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...
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.

Series: ASM Desk Editions

Publisher: ASM International

Published: 01 December 1998

DOI: 10.31399/asm.hb.mhde2.a0003085

EISBN: 978-1-62708-199-3

... the line. Tie lines can be used to determine the fractional amounts of the phases in equilibrium by employing the

**lever****rule**. The**lever****rule**is a mathematical expression derived by the principle of conservation of matter in which the phase amounts can be calculated from the bulk composition of the...
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: 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

... 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**if the alloy solidifies under...
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 provides information on peritectic transformations in multicomponent systems.

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

... forms, it can be used to avoid 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**...
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.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.

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

... also 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...
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.

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: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005237

EISBN: 978-1-62708-187-0

... microstructure can be calculated. Equations 1 and 2 are best applied to substitutional alloy elements with attendant low mass diffusivities. Interstitial elements, however, diffuse rapidly, so it is better to assume complete diffusion in the solid during solidification and apply the inverse

**lever****rule**for...
Abstract

In order to model macrosegregation, one must consider convection and the partitioning of the segregating elements at the dendritic length scale. This article describes microsegregation with diffusion in the solid. It presents a continuum model of macrosegregation and illustrates the simulation of macrosegregation and microsegregation.

Series: ASM Handbook

Volume: 1

Publisher: ASM International

Published: 01 January 1990

DOI: 10.31399/asm.hb.v01.a0001026

EISBN: 978-1-62708-161-0

... is much higher than that of the original steel C o . Finally, because it is important to maintain the necessary carbon balance, using the

**lever****rule**will indicate that the amount of the austenite will vary with the intercritical temperature and the original carbon content of the steel ( Fig. 7...
Abstract

Dual-phase steels are a new class of high-strength low alloy (HSLA) steels characterized by a microstructure consisting of about 20% hard martensite particles dispersed in a soft ductile ferrite matrix. In addition to high tensile strength, in the range of 550 MPa (80 ksi), dual-phase steels exhibit continuous yielding behavior, a low 0.2% offset yield strength, and a higher total elongation than other HSLA steels of similar strength. The article discusses some of the more pertinent aspects of dual-phase steels, such as heat treatment, microstructure, mechanical properties, chemical composition, and manufacturability. In general, these steels have a carbon content of less than 0.1%, which ensures that they can be spot welded. However, newer high-carbon dual-phase steels in development are generating interest due to their unique combination of total elongation and tensile strength.

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005215

EISBN: 978-1-62708-187-0

..., negligible macrosegregation; and (5) sufficient mass transport in the forming solid phase(s) to maintain uniform chemical potential. The equilibrium

**lever****rule**can be used to compute the progress of solidification: (Eq 1) f S = C L * − C O C L * − C S * ≈ T − T L...
Abstract

This article discusses the two extremes of solute redistribution that results in microsegregation. The solute redistribution includes equilibrium solidification, nonequilibrium Gulliver-Scheil solidification, and nonequilibrium solidification with back diffusion. The measurement and kinetics of microsegregation are discussed for the binary isomorphous systems: titanium-molybdenum; binary eutectic systems: aluminum-copper and aluminum-silicon; binary peritectic systems: copper-zinc; multicomponent eutectic systems: Al-Si-Cu-Mg; and for systems with both eutectic and peritectic reactions: Fe-C-Cr and nickel-base superalloy.

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

... 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 solidification path for casting simulation ( Ref 6 , Ref 7 , Ref 8 ). Obtaining the...
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

Series: ASM Handbook

Volume: 22B

Publisher: ASM International

Published: 01 November 2010

DOI: 10.31399/asm.hb.v22b.a0005542

EISBN: 978-1-62708-197-9

... of solid f S = volume fraction of solid k = partition coefficient

**Lever****rule**f S = C L * − C O C L ∗ − C S ∗ Assumes complete solute diffusivity through the solid. 2 C L * = composition of liquid C O = initial...
Abstract

This article is a comprehensive collection of tables containing formulas for metals processing, namely, casting and solidification, flat (sheet) rolling, conical-die extrusion, wire drawing, bending, and deep drawing. Formulas for compression, tension, and torsion testing of isotropic materials are included. The article also lists the formulas for effective stress, strain, and strain rate (isotropic material) in arbitrary and principal coordinates; dimensionless groups in fluid mechanics; and anisotropic sheet materials at various loading conditions.

Series: ASM Handbook Archive

Volume: 10

Publisher: ASM International

Published: 01 January 1986

DOI: 10.31399/asm.hb.v10.a0001753

EISBN: 978-1-62708-178-8

... the second, a quadrupole doublet, associated with a noncubic β phase. The

**lever****rule**can be used to determine the location of this composition in the two-phase (α + β) region. Spectrum C is for a TiFeH 1.7 alloy and is in the two-phase region between β and a third noncubic phase γ. A small amount...
Abstract

The Mossbauer effect (ME) is a spectroscopic method for observing nuclear gamma-ray fluorescence based on recoil-free transitions in a nucleus embedded in a solid lattice. This article provides an overview of the fundamental principles of ME and related concepts such as recoil-free fraction, absorption cross section, gamma-ray polarization, isomer shift, and quadrupole and magnetic interactions. It illustrates the experimental arrangement for obtaining ME spectra and presents several application examples.