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Image

**Published:**01 January 2003

Fig. 3 Richardson-Jeffes diagram showing standard Gibbs free energy of formation as a function of temperature for metal oxide systems. Source: Ref 7
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Image

**Published:**01 December 2004

Fig. 5 Gibbs free-energy composition diagram (a) and locus of solvus curves (b) of metastable and stable equilibrium phases in a precipitation sequence. (a) The points of common tangency show the relationship between compositions of the matrix phase (C″, C′, and C eq ) and the various forms
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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

... 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...

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 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...

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: 4E

Publisher: ASM International

Published: 01 June 2016

DOI: 10.31399/asm.hb.v04e.a0006277

EISBN: 978-1-62708-169-6

...) 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...

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.

Image

**Published:**01 December 2004

Fig. 5 Limit of massive growth of ferrite in the iron-nickel system according to experimental data (triangles and dashed line), compared with calculated phase boundaries and the T 0 line, which is the locus of points where the Gibbs free energy of α equals γ. Source: Ref 5
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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

... quantitative data concerning known equilibria that later can be used to predict other equilibria. The 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...

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.

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: 13A

Publisher: ASM International

Published: 01 January 2003

DOI: 10.31399/asm.hb.v13a.a0003580

EISBN: 978-1-62708-182-5

... ( E ) of the most probable electrochemical reactions occurring in a solution containing a specific element. The standard equilibrium potentials are computed from thermodynamic data (standard chemical potentials, or Gibbs free energies of formation). The equilibrium relations drawn for a given...

Abstract

A potential pH diagram is a graphical representation of the relations, derived from the Nernst equation, between the pH and the equilibrium potentials (E) of the most probable electrochemical reactions occurring in a solution containing a specific element. This article describes three types of reactions for calculation and construction of E-pH diagrams: electrochemical reactions of pure charge (electron) transfer; reactions involving both electron and solvated proton transfer; and acid-base reactions of pure solvated proton transfer. It illustrates the practical use of E-pH diagrams for temperature aqueous solutions and adsorbed species and in prediction of corrosion of nickel and copper.

Series: ASM Handbook

Volume: 13B

Publisher: ASM International

Published: 01 January 2005

DOI: 10.31399/asm.hb.v13b.9781627081832

EISBN: 978-1-62708-183-2

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

... 1) E = F + T S where E is the internal energy, F is the Helmholtz free energy, T is the absolute temperature in degrees Kelvin (K), and S is entropy, a measure of the thermal energy unavailable for useful work. The Gibbs energy is defined as: (Eq 2) G = H − 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: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005191

EISBN: 978-1-62708-187-0

... are determined from experimental data on the ternary system i-j-s . Values of γ o and ε for aluminum-base and copper-base alloys are given in Table 20 , 21 , 22 , 23 , 24 . Standard Gibbs free energies for solution of elements in liquid aluminum Table 20 Standard Gibbs free energies for solution...

Abstract

This article provides accessible information on the thermodynamic properties of liquid aluminum-base and copper-base alloys with the help of phase diagrams. It contains tables that compile the thermodynamic data in the form of activities, activity coefficients, partial molar thermal properties, and integral molar properties for selected aluminum-based and copper-based alloys.

Series: ASM Handbook

Volume: 13C

Publisher: ASM International

Published: 01 January 2006

DOI: 10.31399/asm.hb.v13c.9781627081849

EISBN: 978-1-62708-184-9

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

...+SO 2 Lithium-manganese dioxide Li+Mn(IV)O 2 →LiMn(IV)O 2 Lithium-carbon monofluoride nLi+(CF) n →nLiF+nC Corrosion of Batteries The tendency of metals to oxidize during battery discharge is reflected in their negative Gibbs free energy change. Metals that oxidize more readily...

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, PAFCs, and MCFCs.

Series: ASM Handbook

Volume: 13A

Publisher: ASM International

Published: 01 January 2003

DOI: 10.31399/asm.hb.v13a.a0003601

EISBN: 978-1-62708-182-5

... to oxidize during battery discharge is reflected in the usually substantial negative Gibbs free-energy change for the reactions in Eq 1 or 2 . Metals that oxide more readily have more negative Gibbs free-energy changes, and one might conclude that these metals should make better anodes for batteries...

Abstract

This article examines constructive corrosion that occurs in power-generating devices, specifically batteries. It discusses the kinetic aspects of constructive corrosion in batteries and provides examples to illustrate how the kinetics of a corrosion process varies among different battery systems. The article illustrates the constructive roles played by corrosion at anodes in batteries through the use of a zinc anode in a mercury battery and a lithium metal anode in a rechargeable lithium battery. It also outlines the destructive role played by corrosion by illustrating shelf reactions in zinc-carbon batteries and lead grid corrosion in lead-acid batteries.

Series: ASM Handbook

Volume: 9

Publisher: ASM International

Published: 01 December 2004

DOI: 10.31399/asm.hb.v09.a0003731

EISBN: 978-1-62708-177-1

... and can be seen on a free-energy diagram ( Fig. 5a ). Smaller particles have a higher free energy due to increased pressure because of high surface curvature. The point of common tangent ( Fig. 5a ) therefore occurs at a higher solute concentration. Fig. 5 Gibbs free-energy composition diagram...

Abstract

Precipitation reactions occur in many different alloy systems when one phase transforms into a mixed-phase system as a result of cooling from high temperatures. This article discusses the homogenous and heterogeneous nucleation and growth of coherent and semicoherent precipitates. It describes two precipitation modes, namely, general or continuous precipitation and cellular or discontinuous precipitation. The article also provides information on the precipitation sequences in aluminum alloys.

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

... is the Gibbs free energy. The steepest descending direction of the total energy is given by derivatives of E with respect to each field variable and constitutes the thermodynamic driving force for the change of that variable at each location. When an unconstrained system is in a thermodynamic equilibrium...

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 Desk Editions

Publisher: ASM International

Published: 01 December 1998

DOI: 10.31399/asm.hb.mhde2.a0003085

EISBN: 978-1-62708-199-3

... materials can be taken as zero at absolute zero temperature” (0 K). This principle allows calculation of the absolute values of entropy of pure substances solely from heat capacity. Gibbs Energy Because both S and V are difficult to control experimentally, an additional term, Gibbs energy, G...

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.

Series: ASM Handbook

Volume: 13A

Publisher: ASM International

Published: 01 January 2003

DOI: 10.31399/asm.hb.v13a.a0003587

EISBN: 978-1-62708-182-5

... according to the reaction: (Eq 11) 4 UF 3 ( d ) ↔ 3 UF 4 ( d ) + U ( d ) Standard Gibbs free energies (Δ<italic>G</italic><sup>f</sup>) of formation for species in molten 2LiF-BeF<sub>2</sub>. Table 2 Standard Gibbs free energies (Δ G f ) of formation for species...

Abstract

Molten salts, or fused salts, can cause corrosion by the solution of constituents of the container material, selective attack, pitting, electrochemical reactions, mass transport due to thermal gradients, and reaction of constituents and impurities of the molten salt with the container material. This article describes a test method performed using thermal convection loop for corrosion studies of molten salts. It discusses the purification of salts that are used in the Oak Ridge molten salt reactor experiment. The article also reviews the corrosion characteristics of nitrates/nitrites and fluoride salts with the aid of illustrations and equations.

Series: ASM Handbook

Volume: 9

Publisher: ASM International

Published: 01 December 2004

DOI: 10.31399/asm.hb.v09.a0003735

EISBN: 978-1-62708-177-1

... data (triangles and dashed line), compared with calculated phase boundaries and the T 0 line, which is the locus of points where the Gibbs free energy of α equals γ. Source: Ref 5 It is generally accepted that the nucleation process controls the rate of the massive transformation ( Ref 6...

Abstract

Massive transformations are thermally activated phenomena and exhibit nucleation and growth characteristics primarily controlled by the interface between parent and product phases that is generally considered incoherent. This article focuses on the nucleation and growth kinetics involved in massive transformations and illustrates the resulting phases and structures in ferrous and nonferrous metals and alloys.