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Gibbs phase rule

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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...
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
... 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...
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...
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
... application of the Gibbs phase rule, it should be recalled that one degree of freedom has been exercised in the initial construction of the 3-D diagram by electing to draw it at one atmosphere of pressure. References 1. Askeland D.R. , The Science and...
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
... phase diagram is usually determined from direct measurement of concentrations and temperature, it is important to understand the underlying thermodynamic basis for these diagrams, since it creates rules that experimentally determined phase diagrams must obey. Fig. 1 Relation between the Gibbs...
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
... of Variant Selection Rules for Grain Boundary α in Titanium Alloys , Acta Mater ., Vol 102 , 2016 , p 197 – 211 10.1016/j.actamat.2015.09.021 138. Gey N. , Humbert M. , Philippe M.J. , and Combres Y. , Investigation of the Alpha- and Beta-Texture Evolution of Hot...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003085
EISBN: 978-1-62708-199-3
... would require construction of a three-dimensional graph. Most metallurgical problems, however, are concerned only with a fixed pressure of one atmosphere, and the graph reduces to a two-dimensional plot of temperature and composition ( TX ) diagram. The Gibbs phase rule applies to all states of...
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
... three phases that can exist correspond to three states of matter: vapor, liquid, and solid. The interpretation of equilibrium diagrams is made easy by the following rule: Only points in the diagram have physical significance. Because the variables are temperature and pressure, evidently a point is...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003698
EISBN: 978-1-62708-182-5
... concluded that VCIs of the amine type are capable of forming the protective layers for up to 3 months and exhibit a posttreatment effect on the metal surfaces due to irreversible adsorption. The tendency of irreversible adsorption of a VCI depends on its chemical structure. As a rule, low-molecular- weight...
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
... drastically change the composition of the gas phase. As a rule of thumb, the higher the pressure and temperature, the higher the importance of homogeneous reactions. To perform reliable simulations of CVD processes, a chemical scheme must be included in the coupled transfer model, which at least captures the...
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...
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...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005517
EISBN: 978-1-62708-197-9
... alloy must be represented. A Gibbs energy minimization must be performed so that the phase equilibria between the requisite phases can be calculated. While thermodynamic modeling provides useful information on specific aspects of materials processing, modern-day simulation...
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
..., solute composition of the liquid, and volume fraction of solid. This can be carried out by applying a simple microsegregation model, such as the lever-rule approximation deduced from the phase diagram data, at the microscopic scale of the dendrite arm spacing. In such a purely macroscopic calculation...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005409
EISBN: 978-1-62708-196-2
... phases are both terminal solid solutions, the latter relations comprise the classical Gibbs-Thomson equation, the equilibrium equation ( Eq 3 reformatted in terms of the groove slope), and the initial condition (an initially flat interface). Hence, the complete set of equations is as follows: (Eq 4a...
Series: ASM Handbook
Volume: 4B
Publisher: ASM International
Published: 30 September 2014
DOI: 10.31399/asm.hb.v04b.a0005936
EISBN: 978-1-62708-166-5
... tempering of steel components in order to optimize tribological properties. It focuses on the heat treatment of tempering and bearing steels and on volume changes that take place due to phase transformations. Plastic deformations that occur due to shrinking and phase transformation are also discussed. The...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005406
EISBN: 978-1-62708-196-2
... enthalpy and solute composition are converted into evolutions of temperature, solute composition of the liquid, and volume fraction of solid. This can be carried out by applying a simple microsegregation model, such as the lever-rule approximation deduced from the phase diagram data, at the microscopic...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005439
EISBN: 978-1-62708-196-2
... detected for ternary systems by plotting composition data as diffusion paths on phase diagrams. If the program assumes local equilibrium, then rules must be followed for how the diffusion path can appear (see the section “Zero-Flux Planes” in this article as well as Ref 15 , 31 , and 32 ). Special...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005210
EISBN: 978-1-62708-187-0
... − exp ( − 1 / α ) ] − 0.5   exp ( − 1 2 α ) D s is the diffusion coefficient in the solid, and L is the distance between the cells. The modified equation ensures that the Scheil-Gulliver equation is obtained when D s = 0, and lever rule is obtained when D s = ∞. For...
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
... dislocation content is given by Frank's rule ( Ref 5 ): (Eq 1) B = Σ c i ( Y ) b i = 2 sin ⁡ ω 2 ( Y × a ) where Y is an arbitrary vector in the grain boundary; B is the closure failure, that is, the sum of the Burgers vectors, b i , of the...