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lever rule

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Image
Published: 27 April 2016
Fig. 10 Visual representation of lever rule. Source: Ref 11 More
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...
Image
Published: 01 November 2010
Fig. 1 Solidification paths of a 2219 aluminum alloy, temperature versus solid fraction, from two models and the lever rule. L, liquid; fcc, face-centered cubic More
Image
Published: 01 December 2008
Fig. 2 Temperature versus fraction solid curves of three iron-carbon alloys: Fe-0.8wt%C, Fe-3wt%C, and Fe-4wt%C. These curves are obtained using a lever rule. More
Image
Published: 01 December 1998
Fig. 15 Portion of a binary phase diagram containing a two-phase liquid-plus-solid field illustrating (a) application of the lever rule to (b) equilibrium freezing, (c) nonequilibrium freezing, and (d) heating of a homogenized sample. Source: Ref 1 More
Image
Published: 01 December 2004
of alloy A-B completely solidify after slow (equilibrium) cooling. (c) The lever rule can be used to determine phase compositions and volume fractions at intermediate points along the solidus and liquidus lines when alloy A-B freezes under equilibrium conditions. See text in the section “Isomorphous Alloy More
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
... for determining phase fractions has come to be known as the lever rule. Metastable Phase Diagrams Metastable equilibria occur when a phase is missing, for example, if the phase fails to nucleate. The failure of an equilibrium phase to form may result in the formation of a metastable phase. In the Gibbs...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005217
EISBN: 978-1-62708-187-0
... phase diagram, the liquidus temperature for this alloy is 1268 °C (2314 °F). At this temperature, dendritic crystals of austenite are formed. Because carbon has a very high diffusivity in austenite, the lever rule can be used to determine the fraction of solid as a function of temperature. The lever...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005222
EISBN: 978-1-62708-187-0
... of solidification. Fig. 2 Temperature versus fraction solid curves of three iron-carbon alloys: Fe-0.8wt%C, Fe-3wt%C, and Fe-4wt%C. These curves are obtained using a lever rule. For the Fe-3wt%C alloy, 58% of the solid forms as primary austenite dendrites in the temperature range between 1150 and 1300...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003085
EISBN: 978-1-62708-199-3
... B 3 for the low-temperature form and βA 2 B 3 for the high-temperature form). Lever Rule As explained in the section on “Thermodynamics and Phase Diagrams,” a tie line is an imaginary horizontal line drawn in a two-phase field connecting two points that represent two coexisting phases...
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
... can be obtained from phase diagrams for the mathematical treatment of solidification processes. Two simple models can describe the limiting cases of solidification behavior. For solidification obeying the lever rule at each temperature during cooling, complete diffusion is assumed in the solid...
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
... a phase, for example an embrittling phase, or to promote a phase, for example a precipitation-hardening phase. By drawing these lines, the reader can focus on one phase at a time and ignore the lines that concern other phases. Although it is true that the lever rule cannot be used here, it can...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001752
EISBN: 978-1-62708-178-8
... intensity of the two signals can be used to provide quantitative information on the positions of the phase boundaries. The second method will be discussed. Use of a technique such as NMR, which depends on sensing atomic nuclei, can provide an advantage over the usual lever rule of metallurgy...
Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006227
EISBN: 978-1-62708-163-4
... forms first. The liquid composition shifts toward the monotectic composition of 36 wt% Pb. Then, the liquid transforms to more solid α and a second liquid containing 87 wt% Pb. The lever rule provides that only a very small amount of the second liquid is present. On further cooling, the second liquid...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005214
EISBN: 978-1-62708-187-0
... solidify to α-crystals and then transform to stable β-crystals. Alloys between I and II also solidify to α-crystals, but they are partially transformed to β-crystals later. Fig. 2 Phase diagram with a peritectic reaction The volume fraction of each phase will be given by the lever rule...
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: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006226
EISBN: 978-1-62708-163-4
... solidify to α crystals, but they are partially transformed to β crystals later. The volume fraction of each phase is determined with the lever rule if the alloy solidifies under equilibrium conditions. In practice, the lever rule usually will not give the volume fraction of the different phases from...
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: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006223
EISBN: 978-1-62708-163-4
... when phase mixtures are present. Suppose an alloy consists of two phases, α and β, each of which has a molar free energy given by G α and G β , 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...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002437
EISBN: 978-1-62708-194-8
...-probability situations. Inductive logic Can go from specific cases to general rules or laws. No good at inductive logic. Distraction Easily distracted by competing stimuli. Cannot be distracted by competing stimuli. Source: Ref 4 Further Design Guidelines The designer certainly must...