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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...
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
... the fraction of the other solid phase(s) is zero, that is, the limit where the solvent phase is saturated with the solute constituents, and higher concentrations result in the precipitation of other solid phases. The degrees of freedom, F , of a phase region are governed by the Gibbs phase rule: (Eq 14...
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. Space Model of Ternary Systems To completely represent the phase equilibria at constant pressure...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003085
EISBN: 978-1-62708-199-3
... Sexinary Seven Septenary Eight Octanary Nine Nonary Ten Decinary Phase Rule The phase rule, first announced by J. Willard Gibbs in 1876, relates the physical state of a mixture to the number of constituents in the system and to its conditions. It was also Gibbs that first called...
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: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006222
EISBN: 978-1-62708-163-4
... and pressure. In this case the 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...
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
..., and so on. In multicomponent space, such things are often very difficult to understand, let alone conceptualize. Miscibility gaps can appear in ternary and higher-order systems, even though no miscibility gap exists in the lower-order systems, and the Gibbs phase rule becomes vitally important...
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
.... annealing castings deformation diffusion coefficient grain growth heat treatment heterogeneous nucleation homogeneous nucleation homogenization isothermal transformation nonferrous metals precipitation hardening recrystallization recrystallization temperature solid-state phase transformation...
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
... potentials and temperature (and pressure) are uniform throughout the system. Global equilibrium is invoked 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...
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
... solidification any material separates into two (or more) different phases: liquid and solid (or different solid phases). The clear reason is the minimization of the total Gibbs energy as the sum of the Gibbs energies of the individual phases weighted by the phase fractions. Neglecting surface energy, the PF...
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
...). The clear reason is the minimization of the total Gibbs energy as the sum of the Gibbs energies of the individual phases weighted by the phase fractions. Neglecting surface energy, the PF and concentration equations described previously will tend to the thermodynamic equilibrium as the minimum of 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 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...
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
... be determined. Many natural systems, especially at low temperatures, are not in equilibrium. The calculated values for pe and E H can help ascertain the disequilibrium of a system. All of the previously described calculations in the geochemical model are subject to Gibb's phase rule, better known...
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005818
EISBN: 978-1-62708-165-8
... and nitrocarburizing of iron-base materials with gaseous processes. It describes nitriding potentials and the Lehrer diagram, carburizing potentials, controlled nitriding and nitrocarburizing, and the microstructural evolution of the compound layer and the diffusion zone. carburizing iron-nitrogen phase diagram...
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
... to appropriate boundary and initial conditions. For the case in which the platelet and matrix 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...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005501
EISBN: 978-1-62708-197-9
... used to predict the equilibrium and phase relationships in multicomponent alloys ( Ref 3 , Ref 4 , Ref 5 ). Currently, several packages are able to simulate solidification using the Scheil model and lever rule, such as Thermo-Calc, Pandat, and JMatPro. It is critical to have an accurate...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005425
EISBN: 978-1-62708-196-2
.... The refinement of models and modeling methods results in greater capability and accuracy of metallurgical predictions, such as phase equilibria, microstructure, and subsequent mechanical properties. The ability to rapidly apply fundamental models to practical component design and manufacturing applications has...
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
... Abstract This article presents various equations that are essential for the modeling of both single-phase and multiphase profiles. It includes the fundamental laws of diffusion, along with its equations and solutions. The article provides information on the series of applications...
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
... 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 single-phase solidification in which the diffusion in the solid is important...