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Lever 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
... 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 as well as in the liquid. Thus, all phases are assumed to be in thermodynamic...
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...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003517
EISBN: 978-1-62708-180-1
... article discusses metallurgical instabilities of steel-based alloys and nickel-base superalloys. It provides information on several life assessment methods, namely, the life fraction rule, parameter-based assessments, the thermal-mechanical fatigue, coating evaluations, hardness testing, microstructural...
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
.... This technique for determining phase fractions has come to be known as the lever rule. Phase diagrams provide useful information for understanding the solidification of alloys. In addition to the liquidus and final freezing temperatures, important quantities for the mathematical treatment of...
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
... 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 rule can be applied to any two-phase...
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
... eutectic phase formation at the late stage 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...
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
...-rich α phase 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...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003085
EISBN: 978-1-62708-199-3
... the line. Tie lines can be used to determine the fractional amounts of the phases in equilibrium by employing the lever rule. The lever rule is a mathematical expression derived by the principle of conservation of matter in which the phase amounts can be calculated from the bulk composition of the...
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
... 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 if the alloy solidifies under...
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
... forms, it can be used to avoid 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...
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: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006226
EISBN: 978-1-62708-163-4
... also 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...
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...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005237
EISBN: 978-1-62708-187-0
... microstructure can be calculated. Equations 1 and 2 are best applied to substitutional alloy elements with attendant low mass diffusivities. Interstitial elements, however, diffuse rapidly, so it is better to assume complete diffusion in the solid during solidification and apply the inverse lever rule for...
Book Chapter

By G.R. Speich
Series: ASM Handbook
Volume: 1
Publisher: ASM International
Published: 01 January 1990
DOI: 10.31399/asm.hb.v01.a0001026
EISBN: 978-1-62708-161-0
... is much higher than that of the original steel C o . Finally, because it is important to maintain the necessary carbon balance, using the lever rule will indicate that the amount of the austenite will vary with the intercritical temperature and the original carbon content of the steel ( Fig. 7...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005215
EISBN: 978-1-62708-187-0
..., negligible macrosegregation; and (5) sufficient mass transport in the forming solid phase(s) to maintain uniform chemical potential. The equilibrium lever rule can be used to compute the progress of solidification: (Eq 1) f S = C L * − C O C L * − C S * ≈ T − T L...
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
... 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 solidification path for casting simulation ( Ref 6 , Ref 7 , Ref 8 ). Obtaining the...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005542
EISBN: 978-1-62708-197-9
... of solid f S = volume fraction of solid k = partition coefficient Lever rule f S = C L * − C O C L ∗ − C S ∗ Assumes complete solute diffusivity through the solid. 2   C L * = composition of liquid   C O = initial...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001753
EISBN: 978-1-62708-178-8
... the second, a quadrupole doublet, associated with a noncubic β phase. The lever rule can be used to determine the location of this composition in the two-phase (α + β) region. Spectrum C is for a TiFeH 1.7 alloy and is in the two-phase region between β and a third noncubic phase γ. A small amount...