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heterogeneous equilibrium

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Published: 01 December 2008
Fig. 4.1 Conditional equations of heterogeneous equilibrium in a unitary (a) and a binary (b) system. (a) Intersection of free-energy curves is the equilibrium temperature in a unitary system. (b) Points of contact ① and ② on the common tangent indicate each More
Image
Published: 01 December 2008
Fig. 4.3 Heterogeneous equilibrium in A-B-C ternary system (the common tangent law). The upper diagrams show free energy. The lower diagrams give a view of isothermal sections. (a) Two-phase equilibrium of α/β. (b) Three-phase equilibrium of α/β/γ More
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.tb.tm.t52320091
EISBN: 978-1-62708-357-7
... Abstract This chapter explains the significance of the phase diagram and its use in the development of new materials. The chapter describes the basic rules of heterogeneous equilibrium, presents a comparison between liquidus line and solidus line, and provides information on the solubility...
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Published: 01 December 2016
Fig. 1.14 Heterogeneous nucleus-surface energy equilibrium at the contact point of three phases (L, liquid alloy; C, crystal; S, substrate): λ LS = λ CS + λ LC cosθ. Source: Ref 27 , 28 More
Series: ASM Technical Books
Publisher: ASM International
Published: 01 June 2008
DOI: 10.31399/asm.tb.emea.t52240053
EISBN: 978-1-62708-251-8
... possible. Essentially, the change in free energy, either Δ F or Δ G , must be negative for a reaction to occur; that is, the reaction must result in an overall reduction of the free energy of the system. If the free-energy change is zero, the system is in a state of equilibrium, and no reaction will occur...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420339
EISBN: 978-1-62708-310-2
... that of the initial single-phase (parent) phase and the resultant product matrix. The matrix retains the same crystal structure as the initial one-phase parent but with a different equilibrium composition (α, β, or I) and usually a different lattice parameter than the parent phase. This general type of phase change...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420015
EISBN: 978-1-62708-310-2
... approaching the melting point. Instead of transforming directly to the equilibrium phase, metastable transition phases can form prior to forming the final equilibrium phase. Like solidification, nucleation in solid-state reactions is almost always heterogeneous. Heterogeneous nucleation occurs at structural...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420041
EISBN: 978-1-62708-310-2
... career at Yale. Between 1876 and 1878, Gibbs wrote a series of papers on the graphical analysis of multiphase chemical systems. These were eventually published together in a monograph titled On the Equilibrium of Heterogeneous Substances , his most renowned work. It is now deemed one of the greatest...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.tb.msisep.t59220193
EISBN: 978-1-62708-259-4
... equilibrium. In a classical work, Turnbull ( Ref 5 ) was able, through the almost complete elimination of heterogeneities that could act as nuclei for iron solidification, to undercool liquid iron 295 °C (565 °F) below its melting point. More recently, Ref 6 showed that it is possible to control...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2016
DOI: 10.31399/asm.tb.ascaam.t59190001
EISBN: 978-1-62708-296-9
.... 1.14 Heterogeneous nucleus-surface energy equilibrium at the contact point of three phases (L, liquid alloy; C, crystal; S, substrate): λ LS = λ CS + λ LC cosθ. Source: Ref 27 , 28 Fig. 1.15 Geometry at αAl-substrate interface. (a) TiB 2 boride; (b) AlB 2 boride; (c) TiC carbide; (d...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420117
EISBN: 978-1-62708-310-2
... postulates heterogeneous nucleation of β at the α-liquid interface at the peritectic equilibrium temperature, T p . Undercoolings of up to 4% of T p are required for the systems investigated. If nucleation is limited to a few locations and lateral growth of the β nuclei does not readily occur...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420001
EISBN: 978-1-62708-310-2
... observations of temperature would coincide at the equilibrium transformation temperature. The equilibrium states that are represented on phase diagrams are known as heterogeneous equilibria, because they refer to the coexistence of different states of matter. However, for two or more phases to attain...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.tb.msisep.t59220101
EISBN: 978-1-62708-259-4
... Abstract This chapter describes the phases and constituents present in iron-carbon steels in near-equilibrium conditions. It explains how to use phase diagrams to predict and manage the development of ferrite, austenite, cementite, and pearlite through controlled cooling. It discusses...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 January 2015
DOI: 10.31399/asm.tb.tpmpa.t54480031
EISBN: 978-1-62708-318-8
..., or clusters of atoms, form. These small units or nuclei, consisting of several to thousands of atoms, are not stable above the melting point. However, as the temperature of the liquid is lowered below the equilibrium freezing temperature, the probability increases that atoms (and molecules) will form clusters...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2016
DOI: 10.31399/asm.tb.ascaam.t59190vii
EISBN: 978-1-62708-296-9
... 319 Different thin-wall cast parts, medium and high loaded AlSi9Cu AC46400 332 Pressure-cast parts (a) Source: Ref 3 . (b) Source: Ref 4 Equilibrium phase composition of alloys, identified according to the equilibrium solidification path ( Table 2 and Fig. 1 ), is very...
Series: ASM Technical Books
Publisher: ASM International
Published: 31 December 2020
DOI: 10.31399/asm.tb.phtbp.t59310001
EISBN: 978-1-62708-326-3
... solution. It also explains the aspects of a phase diagram that shows what phase or phases are present in the alloy under conditions of thermal equilibrium. Finally, a discussion on the applications of equilibrium phase diagrams is presented. atomic bonding body-centered cubic equilibrium phase...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.tb.tm.t52320225
EISBN: 978-1-62708-357-7
..., the radius of a critical nucleus is usually r c ≈ 1 nm. [2] Equilibrium Distribution Density of Critical Nuclei Consider how much density the above critical nuclei exist with in the following exercise. [Exercise 8.3] Show that the number of critical nuclei existent in 1 mole...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.tb.tm.t52320123
EISBN: 978-1-62708-357-7
... A + ( μ X g b − μ X α ) d m X = 0 Here μ A and μ X are the chemical potentials of A and X (see Section 4.1 “Basic Rules of Heterogeneous Equilibrium” ). Because we can choose dm A and dm X arbitrarily in a usual two-phase equilibrium, the solutions...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.tb.msisep.t59220001
EISBN: 978-1-62708-259-4
... with a world production on the order of 1000 Mt/yr (1649 Mt in 2013) results in heterogeneities in chemical composition and properties in larger dimensions, at a scale conventionally called macrostructural (mm scale). Figure 1.1 schematically depicts steel structural features in the ranges discussed...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.tb.ems.t53730011
EISBN: 978-1-62708-283-9
... theoretical chemist and physicist. He spent his entire professional career at Yale University, which awarded him the first American PhD in engineering in 1863. His paper, On the Equilibrium of Heterogeneous Substances, published in 1876, formed the basis for the development of phase diagrams. As one...