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Gibbs free-energy curves

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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
... of eutectic and binary phase diagrams from Gibbs free-energy curves. binary solution eutectic phase diagram Gibbs free energy Gibbs free-energy curves phase diagram single-component unary system thermodynamics IN RECENT YEARS, the application of phase diagram information obtained from...
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...
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...
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
... free-energy change is zero (Δ G = 0) and it must be negative. Below T m , the free energy does become negative (Δ G < 0) and the metal solidifies. The free-energy change is thus: (Eq 12) Δ G = Δ G S − Δ G L < 0 Fig. 12 Gibbs free-energy curves during solidification...
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...
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...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003085
EISBN: 978-1-62708-199-3
... components, A and B. The result is a series of plots similar to those in Fig. 13 (a) to 13 (e). Fig. 13 Use of Gibbs energy curves to construct a binary phase diagram that shows miscibility in both the liquid and solid states. Source: adapted from Ref 2 At temperature T 1 , the liquid...
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003732
EISBN: 978-1-62708-177-1
... , Metallography and Microstructures , Vol 9 , ASM Handbook , ASM International , 1985 , p 652 – 654 A simple binary phase diagram with a region of spinodal decomposition is shown in Fig. 2(a) with a corresponding free-energy curve ( Fig. 2b ). If a composition X 0 is heated above the critical...
Series: ASM Handbook
Volume: 13C
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v13c.a0004225
EISBN: 978-1-62708-184-9
... change in quantity; an increment; a range Δ E therm thermodynamic driving force Δ G Gibbs free energy Δ G o standard Gibbs free energy Δ H change in enthalpy Δ K stress-intensity factor range Δ S entropy change ε p plastic strain range ε t total...
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
... ). The eutectic temperature and composition for white cast iron are well-defined thermodynamic quantities, just as they are for gray cast iron. Metastable equilibrium at any temperature is given by a common tangent construction to the molar free energy versus composition curves for the liquid, austenite...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005209
EISBN: 978-1-62708-187-0
... distribution coefficient k = 1. In this limiting case, the Gibbs free energies of both phases are equal, but the chemical potentials are not. This can be expressed through the following equations for the interface temperature, T *, and the nonequilibrium liquidus slope, m( V ) ( Ref 18 ): (Eq 22) T...
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
... ) therefore occurs at a higher solute concentration. 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...
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
... phase is the electrolyte containing cations of the metal. The tendency of metals 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...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005511
EISBN: 978-1-62708-197-9
... F.J. , “Computational Thermodynamic Study to Predict Complex Phase Equilibria in the Nickel-Base Superalloy Rene N6,” NASA/TM , 2001 - 210897 26. Wlodek S.T. , The Structure of IN100 , Trans. ASM , Vol 57 , 1964 , p 110 – 119 27. Ross E.W. , Rene 100—A Sigma-Free...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005410
EISBN: 978-1-62708-196-2
... driving force and the interface free energy. A kinetic approach, cluster dynamics, can also be used to describe nucleation. This constitutes the second part of this article. Here, a master equation describes the time evolution of the system, which is modeled as a cluster gas. The key parameters are the...
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
... 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 concentration of...
Book Chapter

Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006229
EISBN: 978-1-62708-163-4
... spinodal decomposition is shown in Fig. 14(a) with a corresponding free-energy curve ( Fig. 14b ). If a composition, X 0 , is heated above the critical temperature, T c , the binary system is in the region of full solid solubility with a single-phase field, α 0 , at temperature T 0 . When the...
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006250
EISBN: 978-1-62708-169-6
... lattice at equilibrium is a consequence of a balance between the energy (Δ H ) required to form the vacancies and the entropy Δ S created by their presence at absolute temperature ( T ). Thus, there is an equilibrium concentration that minimizes the free energy change (Δ G = Δ H − T Δ S ). If a...
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...
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
... adapted. The general aspects of the PF method are only briefly outlined. For a more complete review see ( Ref 21 ). In general, a PF model starts from an appropriate thermodynamic function. For solidification under constant pressure, the Gibbs free energy F is used. It is the integral over the free...