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Phase Diagrams and Phase Transformations
Published in Bankim Chandra Ray, Rajesh Kumar Prusty, Deepak Nayak, Phase Transformations and Heat Treatments of Steels, 2020
Bankim Chandra Ray, Rajesh Kumar Prusty, Deepak Nayak
For a system comprising two phases, the Lever rule is very often used to determine the weight fraction of each phase at a given combination of temperature and alloy composition. Let us take 1 g of an alloy with composition wB, which consists of two phases α and β at a given temperature T. Thus, TotalweightofBinthealloy=wB
Microstructure and phase transformations in alloys
Published in Ash Ahmed, John Sturges, Materials Science in Construction: An Introduction, 2014
The lever rule is a way in which to calculate the proportions of each phase present on a phase diagram in a two-phase field at a given temperature and composition. This rule is applied as follows: Construct the tie line.Obtain ratios of line segments lengths.Calculate the fraction of one phase by taking the length of the tie line from the overall alloy composition to the phase boundary for the other phase; then divide by the total tie line length. Note: the fractions are inversely proportional to the length to the boundary for the particular phase. If the point in the diagram is close to the phase line, the fraction of that phase is large.Express the values as a fraction or percentage.
Phase Equilibria
Published in George A. Lane, Solar Heat Storage: Latent Heat Materials, 1983
Figure 29 illustrates the addition of tie lines to Figure 27. These are used in isothermal sections of ternary phase diagrams to show the composition of the phases in two-phase fields. The tie lines join the boundary lines separating a two-phase field from its constituent one-phase fields. The tie lines are generally fan-shaped, and cannot cross one another. As an example, in Figure 29, a system with overall composition n1, brought to equilibrium at temperature T6, will consist of liquid phase of composition nℓ and solid solution S of composition ns. The lever rule can be used to calculate the relative amounts of the two phases.
Thermal anisotropy in binary alloy solidification: An equivalent isotropic model
Published in Numerical Heat Transfer, Part B: Fundamentals, 2020
Amman Jakhar, Prasenjit Rath, Prodyut Ranjan Chakraborty, Swarup Kumar Mahapatra
As solidification progresses, solute gets redistributed in a nonhomogeneous manner within solid, mushy, and liquid phases of the alloy. Figure 7 shows the liquid fraction and solute concentration distribution for AR = 2 at three different time levels: t* = 0.0125, 0.0375 and 0.075 for first test case where front evolution is almost planar. Lever rule is used for computation of solute mixture concentration in the mushy region. The flow of molten alloy is driven mainly due to thermal and solutal buoyancy. The thermal buoyant forces are mainly dominant at initial stage due higher temperature gradients present during initial stage of solidification.