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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

... 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**...
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.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.

Series: ASM Handbook

Volume: 13A

Publisher: ASM International

Published: 01 January 2003

DOI: 10.31399/asm.hb.v13a.a0003588

EISBN: 978-1-62708-182-5

... of gas mixtures and partial pressures of volatile oxidation products. oxygen gaseous corrosion crystal structure molar volume thermal properties pure metals oxides

**free****energy**oxidation process pure divalent metal Richardson-Jeffes diagram**Gibbs****energy**stability range METALS can...
Abstract

Metals can react chemically with oxygen when exposed to air. Essential to an understanding of the gaseous corrosion of a metal are the crystal structure and the molar volume of the metal on which the oxide builds, both of which may affect growth stresses in the oxide. This article presents crystal structures and thermal properties of pure metals and oxides in a tabular form. The free energy of reaction, which describes the oxidation process of a pure divalent metal, is presented. The article illustrates the Richardson-Jeffes diagram, which is used in the determination of the standard Gibbs energy change of formation of oxides and the corresponding dissociation pressures of the oxides as a function of temperature. It demonstrates the Kellogg diagram which shows stability range in more complicated multioxidant systems. The article explains the determination of partial pressures of gas mixtures and partial pressures of volatile oxidation products.

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.

Series: ASM Handbook

Volume: 13C

Publisher: ASM International

Published: 01 January 2006

DOI: 10.31399/asm.hb.v13c.a0004135

EISBN: 978-1-62708-184-9

... →LiMn(IV)O 2 Lithium-carbon monofluoride nLi+(CF) n →nLiF+nC The tendency of metals to oxidize during battery discharge is reflected in their negative

**Gibbs****free****energy**change. Metals that oxidize more readily have more negative**Gibbs****free****energy**change and are considered better anodes for...
Abstract

Batteries and fuel cells are popular forms of portable electrical energy sources. This article discusses the operation and corrosion problems inherent in batteries and fuel cells. Batteries are classified into two groups: primary or nonrechargeable batteries and secondary or rechargeable batteries. Fuel cells are classified into five types: phosphoric acid fuel cell (PAFC), solid polymer electrolyte fuel cell, alkaline electrolyte fuel cell, molten carbonate fuel cell (MCFC), and solid oxide fuel cell. The article presents reactions that occur during charging and discharging of lead-acid batteries, PAFC, and MCFC.

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.

Series: ASM Handbook

Volume: 24

Publisher: ASM International

Published: 15 June 2020

DOI: 10.31399/asm.hb.v24.a0006559

EISBN: 978-1-62708-290-7

... the action of the ultrasonic, the change of

**free****energy**(Δ G ) increases: (Eq 5) Δ G = G S − G L = Δ H S + T Δ S S + Δ V S Δ P The eutectic growth rate ( v ) is expressed as: (Eq 6) v = a S I 0 e x p ( π σ 2 / k B T Δ G...
Abstract

Directed-energy deposition (DED) is a kind of additive manufacturing (AM) technology based on synchronous powder feeding or wire feeding. This article provides a comprehensive coverage of DED for ceramic AM, beginning with an overview of DED equipment setup, followed by a discussion on DED materials and the DED deposition process. The bulk of the article is devoted to the discussion on the microstructure and properties of oxide ceramics, namely alumina and zirconia ceramics.

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

... small in comparison to E ; therefore the enthalpy, H , can be considered as being equal to the internal

**energy**, E ( H ∼ E ). Therefore, this allows the**Gibbs****energy**to be expressed as: (Eq 4) G = E − T S which is the same as the Helmholtz**free****energy**, F : (Eq 5) F = E − T S...
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 Handbook

Volume: 4E

Publisher: ASM International

Published: 01 June 2016

DOI: 10.31399/asm.hb.v04e.a0006257

EISBN: 978-1-62708-169-6

... partly created by the stirring action of the magnetic field of the induction coil, but it is also related to the reduction in

**Gibbs****free****energy**due to the contribution of the large negative entropy term, − T Δ S . Thus, as temperature increases, the entropy term contributes to making the**Gibbs****energy**...
Abstract

Homogenization heat treatment can be useful for improving the performance and life of an alloy while in service or for improving the processability during fabrication and hot working. This article describes the identification of incipient melt point, slowest-diffusing elements, and microstructural scale for homogenization of metal alloys. It also discusses the CALPHAD software to optimize the homogenization heat treatment and the Scheil module of the commercial thermodynamic modeling software.

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

... − , HCO 3 − , CO 3 + , or Cl − . Equilibrium is calculated by determining that state (at fixed temperature and pressure) at which the phases, surfaces, and species within the system have reached the minimum value for the

**Gibb's****free****energy**function. The minimum is determined by...
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: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005434

EISBN: 978-1-62708-196-2

.... , Vol 20 , 1952 , p 359 – 364 48. Dean A.M , J. Phys. Chem. , Vol 89 ( No. 21 ), 1985 , p 4600 – 4608 49. Burgess D.R. , Zachariah M. , Tsang W. , and Westmoreland P.R. , Prog.

**Energy**. Combust. Sci. , Vol 21 , 1996 , p 453 – 529 50...
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.

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

... x d x e x − 1 ] where T is temperature, and E R is the recoil

**energy**of the**free**nucleus: (Eq 3) E R = E γ 2 2 M c 2 where E γ is the**energy**of the γ-ray, M is the mass of the nucleus, and c is the velocity of light. Useful low- and...
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.

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

... − 1 where T is the temperature, and E R is the recoil

**energy**of the**free**nucleus: (Eq 3) E R = E γ 2 2 Mc 2 where E γ is the**energy**of the γ-ray, M is the mass of the nucleus, and c is the velocity of light. Useful low- and high-temperature approximations...
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.a0005208

EISBN: 978-1-62708-187-0

...

**free**surface, but less so for liquids and solids. Equation 7 provides the well-known relation that the surface tension is balanced by a pressure difference across the curved interface. The**energy**balance is one of the most important balances for solidification problems. The most convenient...
Abstract

This article begins with balance equations for mass, momentum, energy, and solute and the necessary boundary conditions for solving problems of interest in casting and solidification. The transport phenomena cover a vast range of length and time scales, from atomic dimensions up to macroscopic casting size and from nanoseconds for interface attachment kinetics to hours for casting solidification. The article describes how to determine which phenomena are most important at the particular length and time scale for the problem. It concludes with several examples of the application of transport phenomena in solidification, focusing in particular on microstructure formation.

Series: ASM Handbook

Volume: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005437

EISBN: 978-1-62708-196-2

... Abstract This article presents the governing equations for moving a solidification front, based on the balance of mass, momentum,

**energy**, and solute. It reviews how material properties and geometry can be analyzed in the context of the governing equations. The article provides several example...
Abstract

This article presents the governing equations for moving a solidification front, based on the balance of mass, momentum, energy, and solute. It reviews how material properties and geometry can be analyzed in the context of the governing equations. The article provides several example problems that illustrate how the hierarchy of time and length scales associated with transport leads to the important features of cast microstructures. It includes equations for estimating microsegregation in cast alloys.

Series: ASM Handbook

Volume: 6A

Publisher: ASM International

Published: 31 October 2011

DOI: 10.31399/asm.hb.v06a.a0005639

EISBN: 978-1-62708-174-0

... than grow because of surface

**energy**, Γ is the**Gibbs**-Thomson coefficient (= σ/Δ s f = surface tension/entropy of fusion per unit volume), and the other terms are as defined previously. While the value for λ i is quite small (∼0.025 μm), it has been calculated that the limit will occur at...
Abstract

Microjoining with high energy density beams is a new subject in the sense that the progress of miniaturization in industry has made the desire to make microjoints rapidly and reliably a current and exciting topic. This article summarizes the current state of microjoining with both electron and laser beams. It considers the elementary physical processes such as heat and fluid flow to introduce the reader to the phenomena that affect melting, coalescence, and solidification needed for a successful microweld. The various forces driving (and resisting) fluid flow are analyzed. The article discusses the equipment suitable for microjoining and the metallurgical consequences and postweld metrology of the process. It also provides examples of developmental welds employing laser and electron beam microwelding techniques.

Series: ASM Handbook

Volume: 17

Publisher: ASM International

Published: 01 August 2018

DOI: 10.31399/asm.hb.v17.a0006456

EISBN: 978-1-62708-190-0

... also provides information on digital radiography, image processing and analysis, dual-

**energy**imaging, and partial angle imaging, of a CT system. computed tomography digital radiography dual-**energy**imaging film radiography partial angle imaging real-time radiography X-ray computed tomography...
Abstract

Computed tomography (CT) is an imaging technique that generates a three-dimensional (3-D) volumetric image of a test piece. This article illustrates the basic principles of CT and provides information on the types, applications, and capabilities of CT systems. A comparison of performance characteristics for film radiography, real-time radiography, and X-ray computed tomography is presented in a table. A functional block diagram of a typical computed tomography system is provided. The article discusses CT scanning geometry that is used to acquire the necessary transmission data. It also provides information on digital radiography, image processing and analysis, dual-energy imaging, and partial angle imaging, of a CT system.

Series: ASM Handbook

Volume: 13A

Publisher: ASM International

Published: 01 January 2003

DOI: 10.31399/asm.hb.v13a.a0003579

EISBN: 978-1-62708-182-5

... driving force for chemical reactions at constant pressure is the

**Gibbs****free****energy**change, which has been expressed in thermodynamic treatments as the balance between the effects of**energy**(enthalpy) change and entropy change. The entropy of a system is related to the number of ways in which microscopic...
Abstract

The electrode potential is one of the most important parameters in the thermodynamics and kinetics of corrosion. This article discusses the fundamentals of electrode potentials and illustrates the thermodynamics of chemical equilibria by using the hydrogen potential scale and the Nernst equation. It describes galvanic cell reactions and corrosion reactions in an aqueous solution in an electrochemical cell. The article explores the most common cathodic reactions encountered in metallic corrosion in aqueous systems. The reactions included are proton reduction, water reduction, reduction of dissolved oxygen, metal ion reduction, and metal deposition. The article also presents the standard equilibrium potentials measured at 25 deg C relative to a standard hydrogen electrode for various metal-ion electrodes in a tabular form.